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"▁pitch": 15905, + "дол": 15906, + "outube": 15907, + "▁Santi": 15908, + "OnClickListener": 15909, + "▁Magyar": 15910, + "▁vue": 15911, + "ião": 15912, + "▁`#": 15913, + "collect": 15914, + "▁Rou": 15915, + "analysis": 15916, + "istrzost": 15917, + "▁Digital": 15918, + "▁crist": 15919, + "riere": 15920, + "▁campo": 15921, + "Us": 15922, + "▁circa": 15923, + "▁Component": 15924, + "▁NSString": 15925, + "pd": 15926, + "▁prince": 15927, + "▁invoke": 15928, + "▁Marine": 15929, + "Allow": 15930, + "estic": 15931, + "ристи": 15932, + "bone": 15933, + "туры": 15934, + "▁passion": 15935, + "áció": 15936, + "▁orn": 15937, + "вед": 15938, + "▁invari": 15939, + "▁ні": 15940, + "Remove": 15941, + "encies": 15942, + "ilib": 15943, + "▁Director": 15944, + "\"\"": 15945, + "▁Conse": 15946, + "googleapis": 15947, + "ók": 15948, + "▁Укра": 15949, + "▁Having": 15950, + "Domain": 15951, + "ierz": 15952, + "нологи": 15953, + "Cho": 15954, + "undefined": 15955, + "alloc": 15956, + "▁pied": 15957, + "▁fraction": 15958, + "bia": 15959, + "▁поло": 15960, + "ugno": 15961, + "minister": 15962, + "▁principale": 15963, + "▁refused": 15964, + "browser": 15965, + "*,": 15966, + "▁Hospital": 15967, + "▁universal": 15968, + "▁Ernst": 15969, + "who": 15970, + "▁Gard": 15971, + "'_": 15972, + "conde": 15973, + "▁[{": 15974, + "sob": 15975, + "▁Crit": 15976, + "▁декабря": 15977, + "▁punto": 15978, + "▁eingesetzt": 15979, + "▁tör": 15980, + "▁Ni": 15981, + "▁worry": 15982, + "▁legend": 15983, + "▁були": 15984, + "▁komm": 15985, + "rijk": 15986, + "effect": 15987, + "Ori": 15988, + "RES": 15989, + "▁Peters": 15990, + "▁Baron": 15991, + "▁Got": 15992, + "▁honest": 15993, + "äre": 15994, + "ász": 15995, + "▁noble": 15996, + "▁conclusion": 15997, + "▁formatting": 15998, + "▁otto": 15999, + "▁deleg": 16000, + "мб": 16001, + "ptop": 16002, + "▁sends": 16003, + "urname": 16004, + "▁festival": 16005, + ",‎": 16006, + "рус": 16007, + "▁doch": 16008, + "subject": 16009, + "▁careful": 16010, + "quent": 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"catal": 16431, + "detail": 16432, + "ependant": 16433, + "fg": 16434, + "▁bew": 16435, + "▁fis": 16436, + "▁BO": 16437, + "▁wsp": 16438, + "▁pipeline": 16439, + "hd": 16440, + "▁Session": 16441, + "länd": 16442, + "iveau": 16443, + "estr": 16444, + "▁particle": 16445, + "▁laravel": 16446, + "pic": 16447, + "▁nau": 16448, + "▁fins": 16449, + "▁Vil": 16450, + "▁fus": 16451, + "▁quasi": 16452, + "operation": 16453, + "▁aller": 16454, + "▁analy": 16455, + "▁Он": 16456, + "▁Mes": 16457, + "▁опера": 16458, + "▁handled": 16459, + "▁deprec": 16460, + "tto": 16461, + "▁Ek": 16462, + "▁stran": 16463, + "▁anglais": 16464, + "jure": 16465, + "▁Silver": 16466, + "▁closely": 16467, + "enkins": 16468, + "anos": 16469, + "sted": 16470, + "▁сентября": 16471, + "brand": 16472, + "ньо": 16473, + "▁présent": 16474, + "rok": 16475, + "mount": 16476, + "▁Anthony": 16477, + "▁Furthermore": 16478, + "inha": 16479, + "▁архи": 16480, + "▁разли": 16481, + "▁октября": 16482, + "▁pint": 16483, + "ný": 16484, + "pts": 16485, + "▁italien": 16486, + "▁реги": 16487, + "лез": 16488, + "дина": 16489, + "atherine": 16490, + "Internal": 16491, + "Question": 16492, + "▁settlement": 16493, + "▁Все": 16494, + "▁folders": 16495, + "дри": 16496, + "▁valor": 16497, + "▁Miller": 16498, + "▁Assert": 16499, + "▁patient": 16500, + "▁Nieder": 16501, + "▁EP": 16502, + "▁Agr": 16503, + "▁onde": 16504, + "▁scop": 16505, + "sequence": 16506, + "▁PL": 16507, + "▁seek": 16508, + "javase": 16509, + "▁Vector": 16510, + "▁ná": 16511, + "▁categoría": 16512, + "clone": 16513, + "NR": 16514, + "available": 16515, + "▁Besch": 16516, + "▁eclipse": 16517, + "wicklung": 16518, + "deploy": 16519, + "enie": 16520, + "▁\")": 16521, + "äst": 16522, + "▁sync": 16523, + "CODE": 16524, + "▁Че": 16525, + "▁floating": 16526, + "/`": 16527, + "▁retired": 16528, + "deb": 16529, + "▁particul": 16530, + "▁collected": 16531, + "▁downloaded": 16532, + "nice": 16533, + "▁Buffer": 16534, + "▁Account": 16535, + "▁maggio": 16536, + "▁реда": 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"addEventListener": 16592, + "sync": 16593, + "azzo": 16594, + "abstract": 16595, + "assets": 16596, + "▁Dru": 16597, + "зд": 16598, + "ordnet": 16599, + "▁bigger": 16600, + "▁initialized": 16601, + "каз": 16602, + "ogene": 16603, + "viously": 16604, + "▁guid": 16605, + "scheidung": 16606, + "▁Zent": 16607, + "▁frames": 16608, + "rieben": 16609, + "▁issued": 16610, + "▁dow": 16611, + "▁describes": 16612, + "ilst": 16613, + "▁criteria": 16614, + "▁gentleman": 16615, + "Basic": 16616, + "nez": 16617, + "Dev": 16618, + "Move": 16619, + "▁estaba": 16620, + "▁settembre": 16621, + "circle": 16622, + "▁fais": 16623, + "▁myst": 16624, + "▁archiv": 16625, + "dynamic": 16626, + "jà": 16627, + "itas": 16628, + "▁який": 16629, + "▁dor": 16630, + "▁Amazon": 16631, + "▁neces": 16632, + "▁Marcel": 16633, + "▁ella": 16634, + "рок": 16635, + "▁Pennsylvania": 16636, + "cular": 16637, + "Pack": 16638, + "itage": 16639, + "▁Burn": 16640, + "▁RO": 16641, + "▁они": 16642, + "~$": 16643, + "TeX": 16644, + "assign": 16645, + "▁beat": 16646, + "idense": 16647, + "acent": 16648, + "Alert": 16649, + "▁strateg": 16650, + "▁månaden": 16651, + "LOC": 16652, + "▁catalog": 16653, + "printStackTrace": 16654, + "()).": 16655, + "usted": 16656, + "▁Framework": 16657, + "ECK": 16658, + "▁até": 16659, + "Framework": 16660, + "▁attacks": 16661, + "▁Bert": 16662, + "▁тран": 16663, + ":%": 16664, + "arsi": 16665, + "notation": 16666, + "▁logical": 16667, + "weet": 16668, + "▁visited": 16669, + "bru": 16670, + "▁surprise": 16671, + "^^": 16672, + "inale": 16673, + "remote": 16674, + "'},": 16675, + "Syntax": 16676, + "iane": 16677, + "onnen": 16678, + "▁breaking": 16679, + "parser": 16680, + "apk": 16681, + "▁Miguel": 16682, + "▁§": 16683, + "▁acting": 16684, + "▁gebru": 16685, + "AtIndex": 16686, + "ються": 16687, + "▁offers": 16688, + "▁prac": 16689, + "▁grant": 16690, + "ternoon": 16691, + "▁acquired": 16692, + "▁Ny": 16693, + "▁comma": 16694, + "ník": 16695, + "▁Step": 16696, + "inners": 16697, + "▁SA": 16698, + "▁wat": 16699, + "days": 16700, + "▁rectangle": 16701, + "dar": 16702, + "▁trac": 16703, + "▁Indones": 16704, + "▁feedback": 16705, + "▁breaks": 16706, + "partition": 16707, + "icans": 16708, + "▁Notices": 16709, + "▁improved": 16710, + "phan": 16711, + "▁differential": 16712, + "scripts": 16713, + "▁XIII": 16714, + "▁Labor": 16715, + "▁precision": 16716, + "▁seed": 16717, + "bundle": 16718, + "idents": 16719, + "hre": 16720, + "▁Douglas": 16721, + "uld": 16722, + "▁secondary": 16723, + "▁brig": 16724, + "▁confirmed": 16725, + "▁claims": 16726, + "Role": 16727, + "▁Jewish": 16728, + "▁před": 16729, + "▁hotel": 16730, + "▁compte": 16731, + "▁recursive": 16732, + "](#)": 16733, + "▁rotate": 16734, + "▁chrome": 16735, + "inea": 16736, + "%;\r": 16737, + "▁Environment": 16738, + "platz": 16739, + "▁Single": 16740, + "▁sevent": 16741, + "▁posting": 16742, + "▁dealing": 16743, + "parameters": 16744, + "граф": 16745, + "Authentication": 16746, + "touch": 16747, + "Az": 16748, + "▁gray": 16749, + "encing": 16750, + "boldmath": 16751, + "▁сайте": 16752, + "▁Za": 16753, + "anje": 16754, + "▁polar": 16755, + "▁ули": 16756, + "kil": 16757, + "▁hover": 16758, + "▁REST": 16759, + "▁Come": 16760, + "jb": 16761, + "▁Georgia": 16762, + "▁Estado": 16763, + "OutputStream": 16764, + "ћи": 16765, + "▁dump": 16766, + "▁Age": 16767, + "▁swo": 16768, + "mobile": 16769, + "occup": 16770, + "шего": 16771, + "▁constitution": 16772, + "good": 16773, + "aku": 16774, + "▁анг": 16775, + "ieck": 16776, + "▁Psych": 16777, + "▁roots": 16778, + "▁vest": 16779, + "▁годах": 16780, + "▁República": 16781, + "▁pian": 16782, + "igration": 16783, + "▁préc": 16784, + "▁generates": 16785, + "LY": 16786, + "(`": 16787, + "▁=~": 16788, + "шения": 16789, + "▁Rah": 16790, + "▁connecting": 16791, + "ží": 16792, + "▁fő": 16793, + "▁appel": 16794, + "▁Railway": 16795, + "гли": 16796, + "▁développ": 16797, + "▁apo": 16798, + "fran": 16799, + "▁immediate": 16800, + "вого": 16801, + "Runner": 16802, + "äg": 16803, + "Something": 16804, + "▁généra": 16805, + "EventArgs": 16806, + "inction": 16807, + "gly": 16808, + "▁Due": 16809, + "▁prost": 16810, + "▁referring": 16811, + "▁jog": 16812, + "▁executable": 16813, + "▁Dream": 16814, + "acs": 16815, + "▁Cole": 16816, + "ampf": 16817, + "▁Bis": 16818, + "▁июня": 16819, + "lieder": 16820, + "тек": 16821, + "▁vb": 16822, + "▁mom": 16823, + "▁:(": 16824, + "▁dernier": 16825, + "'=>": 16826, + "▁этого": 16827, + "▁neue": 16828, + "▁Ча": 16829, + "▁weitere": 16830, + "▁alleg": 16831, + "▁reality": 16832, + "▁judge": 16833, + "▁Balt": 16834, + "▁thin": 16835, + "▁Ged": 16836, + "ieval": 16837, + "mx": 16838, + "ціональ": 16839, + "▁выпу": 16840, + "▁IX": 16841, + "▁blind": 16842, + "▁Motor": 16843, + "▁ша": 16844, + "▁approximation": 16845, + "dam": 16846, + "▁fog": 16847, + "кор": 16848, + "▁Writ": 16849, + "▁ling": 16850, + "▁писа": 16851, + "▁Mars": 16852, + "otti": 16853, + "Enum": 16854, + "▁Trib": 16855, + "▁merc": 16856, + "zung": 16857, + "vanced": 16858, + "cfg": 16859, + "нах": 16860, + "schen": 16861, + "\"].": 16862, + "bek": 16863, + "▁ster": 16864, + "jp": 16865, + "▁Rap": 16866, + "▁recording": 16867, + "▁peint": 16868, + "▁lets": 16869, + "änge": 16870, + ">\";": 16871, + "▁місце": 16872, + "▁caval": 16873, + "▁CSV": 16874, + "▁entstand": 16875, + "▁helper": 16876, + "endet": 16877, + "▁Gram": 16878, + "▁Diego": 16879, + "▁Bishop": 16880, + "TAG": 16881, + "▁ecc": 16882, + "▁Een": 16883, + "▁AV": 16884, + "City": 16885, + "▁Guide": 16886, + "hind": 16887, + "rical": 16888, + "▁Основ": 16889, + "Bus": 16890, + "▁zunächst": 16891, + "▁tick": 16892, + "▁Colonel": 16893, + "Thanks": 16894, + "▁ferm": 16895, + "▁granted": 16896, + "▁threshold": 16897, + "omorphic": 16898, + "▁Hun": 16899, + "enis": 16900, + "▁прав": 16901, + "▁які": 16902, + "PG": 16903, + "▁ws": 16904, + "▁technical": 16905, + "estro": 16906, + "klär": 16907, + "vars": 16908, + "ocrat": 16909, + "▁општи": 16910, + "onso": 16911, + "iba": 16912, + "▁Save": 16913, + "▁programa": 16914, + "▁въ": 16915, + "▁invån": 16916, + ">()": 16917, + "▁mejor": 16918, + "▁слова": 16919, + "▁replacement": 16920, + "▁impr": 16921, + "▁Francesco": 16922, + "▁Hotel": 16923, + "▁UPDATE": 16924, + "▁музы": 16925, + "ugs": 16926, + "vard": 16927, + "▁faz": 16928, + "inton": 16929, + "▁arts": 16930, + "▁Ky": 16931, + "▁Ils": 16932, + "▁sera": 16933, + "▁Volume": 16934, + "▁giugno": 16935, + "▁asym": 16936, + "▁Pir": 16937, + "▁NAS": 16938, + "▁Tam": 16939, + "ěl": 16940, + "Sequ": 16941, + "kmal": 16942, + "▁Eins": 16943, + "▁компа": 16944, + "obe": 16945, + "oor": 16946, + "▁heap": 16947, + "ctl": 16948, + "▁separately": 16949, + "reader": 16950, + "▁significantly": 16951, + "▁Lag": 16952, + "notes": 16953, + "▁sele": 16954, + "▁dedicated": 16955, + "▁Host": 16956, + "choice": 16957, + "wing": 16958, + "▁Titel": 16959, + "▁befindet": 16960, + "large": 16961, + "▁conten": 16962, + "JavaScript": 16963, + "▁deser": 16964, + "▁Gordon": 16965, + "спе": 16966, + "▁patri": 16967, + "▁Random": 16968, + "▁Returns": 16969, + "ым": 16970, + "рома": 16971, + "▁Studies": 16972, + "Sl": 16973, + "▁frü": 16974, + "TEXT": 16975, + "inate": 16976, + "▁Tol": 16977, + "▁everywhere": 16978, + "arta": 16979, + "▁orbit": 16980, + "▁Aires": 16981, + "▁Iss": 16982, + "▁też": 16983, + "▁diverse": 16984, + "▁numeric": 16985, + "maz": 16986, + "▁mise": 16987, + "▁battery": 16988, + "▁Akadem": 16989, + "нение": 16990, + "▁simultane": 16991, + "▁Dead": 16992, + "▁clust": 16993, + "▁otro": 16994, + "▁cerca": 16995, + "()`,": 16996, + "roz": 16997, + "ăt": 16998, + "▁MO": 16999, + "riften": 17000, + "important": 17001, + "▁jeho": 17002, + "▁findViewById": 17003, + "▁consequence": 17004, + "▁measured": 17005, + "ishes": 17006, + "▁sze": 17007, + "iendo": 17008, + "▁Wahl": 17009, + "strip": 17010, + "ARD": 17011, + "▁opacity": 17012, + "WORD": 17013, + "▁Ві": 17014, + "▁Location": 17015, + "rai": 17016, + "пен": 17017, + "▁rif": 17018, + "aussian": 17019, + "FileName": 17020, + "▁disco": 17021, + "ilen": 17022, + "▁vagy": 17023, + "licity": 17024, + "Border": 17025, + "▁Track": 17026, + "бом": 17027, + "fact": 17028, + "oka": 17029, + "▁gior": 17030, + "▁XVII": 17031, + "▁där": 17032, + "Site": 17033, + "ało": 17034, + "ská": 17035, + "▁pixels": 17036, + "vity": 17037, + "jQuery": 17038, + "▁sculpt": 17039, + "▁cargo": 17040, + "▁directive": 17041, + "▁wal": 17042, + "▁conna": 17043, + "▁Through": 17044, + "▁этом": 17045, + "Static": 17046, + "omsnitt": 17047, + "▁rund": 17048, + "▁claimed": 17049, + "зня": 17050, + "sha": 17051, + "▁rag": 17052, + "crement": 17053, + "▁fünf": 17054, + "▁rival": 17055, + "rin": 17056, + "slash": 17057, + "▁thirty": 17058, + "sleep": 17059, + "ологи": 17060, + "SM": 17061, + "gate": 17062, + "izations": 17063, + "vik": 17064, + "▁bless": 17065, + "▁Illinois": 17066, + "▁TE": 17067, + "uting": 17068, + "▁solving": 17069, + "GER": 17070, + "▁XIV": 17071, + "▁Indians": 17072, + "express": 17073, + "▁Heil": 17074, + "▁mujer": 17075, + "▁invånare": 17076, + "']);": 17077, + "▁aur": 17078, + "boost": 17079, + "GO": 17080, + "▁nin": 17081, + "tok": 17082, + "god": 17083, + "oter": 17084, + ")$$": 17085, + "▁descend": 17086, + "рю": 17087, + "▁Language": 17088, + "▁diver": 17089, + "▁Assuming": 17090, + "▁frequent": 17091, + "чні": 17092, + "▁Biography": 17093, + ",[": 17094, + "urm": 17095, + "▁walked": 17096, + "▁federal": 17097, + "▁Michigan": 17098, + "▁facts": 17099, + "▁Integr": 17100, + "LES": 17101, + "▁Alan": 17102, + "▁coup": 17103, + "Ber": 17104, + "▁particles": 17105, + "ће": 17106, + "Inflater": 17107, + "+(": 17108, + "Bound": 17109, + "▁Sü": 17110, + "Audio": 17111, + "citet": 17112, + "yect": 17113, + "▁nr": 17114, + "xe": 17115, + "▁Brun": 17116, + "▁_,": 17117, + "avor": 17118, + "▁discipl": 17119, + "alm": 17120, + "▁ноября": 17121, + "▁SSL": 17122, + "▁Kaiser": 17123, + "▁recher": 17124, + "ygon": 17125, + "▁regardless": 17126, + "▁configur": 17127, + "▁unnecess": 17128, + "▁Clark": 17129, + "PHP": 17130, + "▁FALSE": 17131, + "▁pad": 17132, + "$}": 17133, + "▁valu": 17134, + "▁disease": 17135, + "▁maior": 17136, + "▁hommes": 17137, + "▁Edition": 17138, + "slant": 17139, + "▁ending": 17140, + "▁settled": 17141, + "urus": 17142, + "hed": 17143, + "Pattern": 17144, + "▁година": 17145, + "▁Philadel": 17146, + "tikzpicture": 17147, + "▁coal": 17148, + "▁sede": 17149, + "▁satisfies": 17150, + "▁trim": 17151, + "▁bat": 17152, + "▁américain": 17153, + "▁luglio": 17154, + "▁поча": 17155, + "ffff": 17156, + "▁Target": 17157, + "generate": 17158, + "▁Zie": 17159, + "ția": 17160, + "▁gard": 17161, + "▁workers": 17162, + "▁Job": 17163, + "▁urban": 17164, + "ahlen": 17165, + "▁Building": 17166, + "▁neu": 17167, + "▁chron": 17168, + "▁Earl": 17169, + "gro": 17170, + "USE": 17171, + "▁XII": 17172, + "▁wealth": 17173, + "inae": 17174, + "▁Бра": 17175, + "▁libert": 17176, + "iros": 17177, + ":$": 17178, + "lee": 17179, + "ieves": 17180, + "▁Justice": 17181, + "▁oil": 17182, + "▁Athlet": 17183, + "▁clo": 17184, + "Scale": 17185, + "▁lips": 17186, + "▁april": 17187, + "▁impression": 17188, + "▁perce": 17189, + "▁участи": 17190, + "vil": 17191, + "éch": 17192, + "▁equality": 17193, + "▁мет": 17194, + "▁annotation": 17195, + "ernal": 17196, + "▁Mach": 17197, + "▁intitul": 17198, + "problem": 17199, + "ющих": 17200, + "oplus": 17201, + "▁thousands": 17202, + "▁calculations": 17203, + "umps": 17204, + "▁triangle": 17205, + "phal": 17206, + "▁Dorf": 17207, + "▁dollars": 17208, + "▁denen": 17209, + "lès": 17210, + "olid": 17211, + "▁Results": 17212, + "▁Stadium": 17213, + "▁Desp": 17214, + "▁Eisen": 17215, + "imir": 17216, + "▁sotto": 17217, + "▁či": 17218, + "atable": 17219, + "orum": 17220, + "▁convergence": 17221, + "▁jeune": 17222, + "oking": 17223, + "▁живо": 17224, + "aining": 17225, + "pointer": 17226, + "culo": 17227, + "▁jsou": 17228, + "▁grab": 17229, + "akte": 17230, + "▁hoping": 17231, + "▁Mak": 17232, + "▁sag": 17233, + "origine": 17234, + "▁послед": 17235, + "▁Veg": 17236, + "▁theoret": 17237, + "▁Tru": 17238, + "nement": 17239, + "▁faces": 17240, + "Hor": 17241, + "Join": 17242, + "arel": 17243, + "▁около": 17244, + "However": 17245, + "▁catal": 17246, + "bourg": 17247, + "▁mysqli": 17248, + "acions": 17249, + "▁Initial": 17250, + "▁rain": 17251, + "iture": 17252, + "▁Sciences": 17253, + "▁Kreis": 17254, + ".__": 17255, + "▁cinq": 17256, + "▁Auß": 17257, + "ithmet": 17258, + "itors": 17259, + "amazon": 17260, + "▁gap": 17261, + "▁ignored": 17262, + "adv": 17263, + "кої": 17264, + "▁часть": 17265, + "▁corpor": 17266, + "цер": 17267, + "▁crime": 17268, + "uous": 17269, + "▁налази": 17270, + "DataFrame": 17271, + "води": 17272, + "Ign": 17273, + "▁Lincoln": 17274, + "▁menos": 17275, + "▁Luft": 17276, + "▁Lind": 17277, + "▁Cook": 17278, + "▁materials": 17279, + "apped": 17280, + "ignore": 17281, + "▁откры": 17282, + "fried": 17283, + "▁gouvernement": 17284, + "▁fired": 17285, + "▁screenshot": 17286, + "сен": 17287, + "▁[(": 17288, + "▁организа": 17289, + "Graphics": 17290, + "▁проти": 17291, + "▁phen": 17292, + "craft": 17293, + "▁brain": 17294, + "▁Como": 17295, + "▁Everything": 17296, + "anes": 17297, + "IGN": 17298, + "▁nederbörd": 17299, + "▁Forest": 17300, + "zahl": 17301, + "▁Among": 17302, + "Qt": 17303, + "▁togg": 17304, + "▁variant": 17305, + "▁hill": 17306, + "писи": 17307, + "colon": 17308, + "▁dicembre": 17309, + "гор": 17310, + "▁Wind": 17311, + "ünstler": 17312, + "▁=\\": 17313, + "saved": 17314, + "▁nej": 17315, + "unte": 17316, + "utto": 17317, + "▁recens": 17318, + "▁sick": 17319, + "▁desen": 17320, + "UST": 17321, + "▁worst": 17322, + "▁Angel": 17323, + "odox": 17324, + "▁Province": 17325, + "▁Maz": 17326, + "▁agreement": 17327, + "▁Bass": 17328, + "▁segunda": 17329, + "onces": 17330, + "▁Linki": 17331, + "▁CL": 17332, + "▁já": 17333, + "itement": 17334, + "▁área": 17335, + "▁scalar": 17336, + "▁Рес": 17337, + "awt": 17338, + "sieme": 17339, + "▁juni": 17340, + "▁худож": 17341, + "ikus": 17342, + "▁lid": 17343, + "ppel": 17344, + "avi": 17345, + "▁balance": 17346, + "ipping": 17347, + "cussion": 17348, + "ческих": 17349, + "(\".": 17350, + "Also": 17351, + "▁whis": 17352, + "HOME": 17353, + "▁brown": 17354, + "▁día": 17355, + "▁può": 17356, + "plotlib": 17357, + "▁Jahrhunderts": 17358, + "DK": 17359, + "▁anchor": 17360, + "...]": 17361, + "▁Austria": 17362, + "▁marca": 17363, + "▁gez": 17364, + "iously": 17365, + "▁lazy": 17366, + "xa": 17367, + "▁Channel": 17368, + "▁neuen": 17369, + "das": 17370, + "▁searched": 17371, + "▁staat": 17372, + "▁Так": 17373, + "▁Josef": 17374, + "▁Sher": 17375, + "pois": 17376, + "▁enem": 17377, + "▁accessing": 17378, + "▁неко": 17379, + "▁furono": 17380, + "▁pseudo": 17381, + "?>": 17382, + "▁estadoun": 17383, + "▁Види": 17384, + "▁motiv": 17385, + "▁recall": 17386, + "isson": 17387, + "ób": 17388, + ")--": 17389, + "▁Erz": 17390, + "▁савез": 17391, + "Direct": 17392, + "соб": 17393, + "▁sho": 17394, + "völker": 17395, + "Ap": 17396, + "gens": 17397, + "ништво": 17398, + "▁Amsterdam": 17399, + "usk": 17400, + "пло": 17401, + "▁simulation": 17402, + "▁BC": 17403, + "▁Woj": 17404, + "autom": 17405, + "Alex": 17406, + "▁economic": 17407, + "гом": 17408, + "ikai": 17409, + "▁altre": 17410, + "▁'-": 17411, + "▁Weg": 17412, + "NotFound": 17413, + "йской": 17414, + "▁converting": 17415, + "phabet": 17416, + "atrice": 17417, + "bourne": 17418, + "alom": 17419, + "▁comparing": 17420, + "▁Zo": 17421, + "▁fla": 17422, + "вая": 17423, + "▁entra": 17424, + "▁charset": 17425, + "developers": 17426, + "ística": 17427, + "}>": 17428, + "▁Jazz": 17429, + "▁Howard": 17430, + "шта": 17431, + "▁clone": 17432, + "door": 17433, + "▁Pin": 17434, + "***": 17435, + "▁silent": 17436, + "ecycle": 17437, + "isce": 17438, + "▁mud": 17439, + "▁Display": 17440, + "▁lip": 17441, + "▁использова": 17442, + "▁characteristic": 17443, + "▁sb": 17444, + "firebase": 17445, + "▁Bew": 17446, + "Calendar": 17447, + "▁uso": 17448, + "èse": 17449, + "▁Rat": 17450, + "▁esper": 17451, + "▁throwing": 17452, + "▁rodz": 17453, + "▁yards": 17454, + "▁grass": 17455, + "▁marker": 17456, + "▁Kos": 17457, + "Theta": 17458, + "▁organis": 17459, + "kernel": 17460, + "▁personas": 17461, + "keep": 17462, + "▁exclaimed": 17463, + "oslav": 17464, + "▁Entertain": 17465, + "нер": 17466, + "▁inwon": 17467, + "▁Rand": 17468, + "reduce": 17469, + "fac": 17470, + "expression": 17471, + "yj": 17472, + "▁differenti": 17473, + "aglia": 17474, + "▁templates": 17475, + "▁mű": 17476, + "▁prv": 17477, + "▁mois": 17478, + "▁gewann": 17479, + "▁була": 17480, + "bibli": 17481, + "demo": 17482, + "▁Anderson": 17483, + "▁ред": 17484, + "▁porque": 17485, + "▁Pologne": 17486, + "▁trip": 17487, + "▁exemple": 17488, + "▁Internacional": 17489, + "▁као": 17490, + "Insert": 17491, + "general": 17492, + "SESSION": 17493, + "berga": 17494, + "hält": 17495, + "unas": 17496, + "мира": 17497, + "▁yields": 17498, + "mapsto": 17499, + "spot": 17500, + "▁+\\": 17501, + "лла": 17502, + "▁precisely": 17503, + "▁член": 17504, + "shadow": 17505, + "Are": 17506, + "unal": 17507, + "▁dispar": 17508, + "▁título": 17509, + "nest": 17510, + "▁Low": 17511, + "▁prot": 17512, + "▁Costa": 17513, + "named": 17514, + "▁gained": 17515, + "lesia": 17516, + "▁administration": 17517, + "Import": 17518, + "branch": 17519, + "▁sympath": 17520, + "voj": 17521, + "▁EC": 17522, + "▁municipio": 17523, + "▁animated": 17524, + "▁directories": 17525, + "▁roof": 17526, + "ząd": 17527, + "imet": 17528, + "proto": 17529, + "bla": 17530, + ":]": 17531, + "have": 17532, + "atem": 17533, + "▁ns": 17534, + "▁sector": 17535, + "three": 17536, + "owane": 17537, + "wers": 17538, + "ових": 17539, + "rence": 17540, + "▁extr": 17541, + "igten": 17542, + "▁occident": 17543, + "ță": 17544, + "▁eat": 17545, + "▁hydro": 17546, + "ubernetes": 17547, + "[@": 17548, + "▁Moon": 17549, + "▁Sho": 17550, + "▁elsewhere": 17551, + "üller": 17552, + "Upload": 17553, + "ланд": 17554, + "▁För": 17555, + "wissenschaft": 17556, + "KS": 17557, + "▁physics": 17558, + "tz": 17559, + "▁серед": 17560, + "▁Arbeit": 17561, + "▁мест": 17562, + "▁Gebiet": 17563, + "▁insect": 17564, + "Ah": 17565, + "izado": 17566, + "▁temple": 17567, + "▁annual": 17568, + "stad": 17569, + "▁habitat": 17570, + "▁AB": 17571, + "wort": 17572, + "▁repos": 17573, + "▁Neu": 17574, + "▁$(\".": 17575, + "Vorlage": 17576, + "▁reprezent": 17577, + "estanden": 17578, + "Intern": 17579, + ".`": 17580, + "▁failing": 17581, + "▁Material": 17582, + "▁effectively": 17583, + "телем": 17584, + "▁гла": 17585, + "▁nahm": 17586, + "▁differently": 17587, + "extension": 17588, + "▁Verm": 17589, + "enabled": 17590, + "configure": 17591, + "nio": 17592, + "ciones": 17593, + "▁Beach": 17594, + "сона": 17595, + "▁copying": 17596, + "▁україн": 17597, + "▁призна": 17598, + "zh": 17599, + "Desktop": 17600, + "▁sost": 17601, + "▁subsequently": 17602, + "▁Lehr": 17603, + "▁ó": 17604, + "lär": 17605, + "odor": 17606, + "phon": 17607, + "nc": 17608, + "iterator": 17609, + "▁эти": 17610, + "▁europé": 17611, + "▁Toronto": 17612, + "ódigo": 17613, + "▁posto": 17614, + "ffe": 17615, + "▁crew": 17616, + "▁Schwar": 17617, + "Sa": 17618, + "square": 17619, + "▁beside": 17620, + "▁Мі": 17621, + "▁ath": 17622, + "▁advent": 17623, + "cji": 17624, + "written": 17625, + "▁russ": 17626, + "rost": 17627, + "HI": 17628, + "▁dice": 17629, + "cca": 17630, + "▁dép": 17631, + "ply": 17632, + "bigg": 17633, + "ział": 17634, + "ütt": 17635, + "▁одно": 17636, + "JECT": 17637, + "ському": 17638, + "nos": 17639, + "mock": 17640, + "Launch": 17641, + "same": 17642, + "▁jobs": 17643, + "▁widely": 17644, + "▁defines": 17645, + "▁Pse": 17646, + "▁neighbour": 17647, + "ющие": 17648, + "▁closer": 17649, + "▁располо": 17650, + "▁clubs": 17651, + "fly": 17652, + "шим": 17653, + "▁suffered": 17654, + "▁nar": 17655, + "▁lavor": 17656, + "Extension": 17657, + "itionally": 17658, + "▁grace": 17659, + "▁Campeonato": 17660, + "▁Christmas": 17661, + "middle": 17662, + "othek": 17663, + "elements": 17664, + "▁sondern": 17665, + "▁tarde": 17666, + "▁permanent": 17667, + "▁conclude": 17668, + "Seg": 17669, + "▁акаде": 17670, + "}\",": 17671, + "▁февраля": 17672, + "řed": 17673, + "▁IL": 17674, + "jud": 17675, + "▁USS": 17676, + "▁Nature": 17677, + "ifference": 17678, + "Serializer": 17679, + "▁twelve": 17680, + "tid": 17681, + "мия": 17682, + "ческого": 17683, + "▁calendar": 17684, + "concat": 17685, + "▁intersection": 17686, + "▁PA": 17687, + "azure": 17688, + "▁située": 17689, + "▁kinds": 17690, + "▁ausge": 17691, + "▁rural": 17692, + "Theme": 17693, + "▁tale": 17694, + "noindent": 17695, + "going": 17696, + "rx": 17697, + "agi": 17698, + "wrapper": 17699, + "▁Coast": 17700, + "mbH": 17701, + "▁перед": 17702, + "spre": 17703, + "▁}\\": 17704, + "▁LI": 17705, + "znam": 17706, + "itled": 17707, + "Sample": 17708, + "uliar": 17709, + "*\\": 17710, + "▁resistance": 17711, + "stock": 17712, + "ked": 17713, + "▁HE": 17714, + "▁possession": 17715, + "▁Ring": 17716, + "▁magyar": 17717, + "outs": 17718, + "▁Secretary": 17719, + "nde": 17720, + "▁Wald": 17721, + "-(": 17722, + "▁ISO": 17723, + "▁afternoon": 17724, + "ionen": 17725, + "▁stops": 17726, + "▁constants": 17727, + "guard": 17728, + "bow": 17729, + "▁ers": 17730, + "▁Firebase": 17731, + "▁Clear": 17732, + "▁Holy": 17733, + "Win": 17734, + "▁titles": 17735, + "▁трав": 17736, + "▁contrib": 17737, + "häng": 17738, + "▁photograph": 17739, + "▁Distribution": 17740, + "ifts": 17741, + "▁aunque": 17742, + "comb": 17743, + "ADD": 17744, + "▁publication": 17745, + "▁служ": 17746, + "▁кня": 17747, + "▁ayant": 17748, + "▁restore": 17749, + "▁belief": 17750, + "▁vég": 17751, + "▁extensions": 17752, + "▁decom": 17753, + "вший": 17754, + "WT": 17755, + "▁parti": 17756, + "▁gioc": 17757, + "▁мира": 17758, + "▁issu": 17759, + "pipe": 17760, + "▁props": 17761, + "▁willing": 17762, + "▁nest": 17763, + "aso": 17764, + "pot": 17765, + "▁handles": 17766, + "▁фо": 17767, + "▁moder": 17768, + "▁ebenfalls": 17769, + "▁fighting": 17770, + "umbn": 17771, + "▁transparent": 17772, + "▁Krist": 17773, + "▁homes": 17774, + "▁voyage": 17775, + "Failed": 17776, + "▁Bird": 17777, + "▁Heart": 17778, + "Counter": 17779, + "▁Scottish": 17780, + "ática": 17781, + "▁arbeit": 17782, + "^{-\\": 17783, + "▁Sor": 17784, + "▁engaged": 17785, + "▁aside": 17786, + "▁Fou": 17787, + "▁wiel": 17788, + "▁reconst": 17789, + "ousin": 17790, + "▁hosted": 17791, + "▁classe": 17792, + "▁contest": 17793, + "...\"": 17794, + "мом": 17795, + "▁bean": 17796, + "gem": 17797, + "▁consultato": 17798, + "▁bio": 17799, + "▁subjects": 17800, + "boBox": 17801, + "▁Schrift": 17802, + "▁dinner": 17803, + "ăr": 17804, + "▁równ": 17805, + "▁%%": 17806, + "bage": 17807, + "▁veröff": 17808, + "▁detected": 17809, + "ienn": 17810, + "rose": 17811, + "▁Ton": 17812, + "Complete": 17813, + "▁proto": 17814, + "ichts": 17815, + "STAT": 17816, + "Checked": 17817, + "▁inten": 17818, + "▁smile": 17819, + "▁strip": 17820, + "neut": 17821, + "');\r": 17822, + "four": 17823, + "▁todas": 17824, + "Controls": 17825, + "▁thorough": 17826, + "rup": 17827, + "▁држави": 17828, + "ită": 17829, + "Protocol": 17830, + "Ка": 17831, + "▁expanded": 17832, + "extra": 17833, + "oport": 17834, + "▁Станов": 17835, + "leases": 17836, + "▁notion": 17837, + "▁guest": 17838, + "▁Islands": 17839, + "icked": 17840, + "▁Dave": 17841, + "▁reflection": 17842, + "liv": 17843, + "ální": 17844, + "▁revealed": 17845, + "▁sog": 17846, + "▁Tax": 17847, + "▁periodo": 17848, + "▁Weltkrie": 17849, + "catalina": 17850, + "qué": 17851, + "▁Father": 17852, + "▁Bir": 17853, + "expect": 17854, + "▁regression": 17855, + "iné": 17856, + "▁dabei": 17857, + "perm": 17858, + "мене": 17859, + "▁Abd": 17860, + "▁CF": 17861, + "arks": 17862, + "resolve": 17863, + "wedge": 17864, + "▁initialization": 17865, + "▁Véase": 17866, + "▁приня": 17867, + "stmt": 17868, + "▁income": 17869, + "MY": 17870, + "▁odkazy": 17871, + "▁Siehe": 17872, + "▁bodies": 17873, + "▁soc": 17874, + "Random": 17875, + "▁senza": 17876, + "ablo": 17877, + "▁regarded": 17878, + "onCreate": 17879, + "▁Magazine": 17880, + "▁Raf": 17881, + "▁Buenos": 17882, + "ил": 17883, + ")));": 17884, + "capt": 17885, + "redirect": 17886, + "▁petit": 17887, + "▁farm": 17888, + "▁rôle": 17889, + "▁статьи": 17890, + "    ": 17891, + "subfigure": 17892, + "èces": 17893, + "ziel": 17894, + "▁окон": 17895, + "EE": 17896, + "mee": 17897, + "▁perten": 17898, + "▁représent": 17899, + "▁LA": 17900, + "?'": 17901, + "▁тру": 17902, + "▁rational": 17903, + "osof": 17904, + "▁kne": 17905, + "▁artists": 17906, + "Flow": 17907, + "▁Аль": 17908, + "izard": 17909, + "▁numero": 17910, + "actic": 17911, + "▁destruct": 17912, + "▁Пра": 17913, + "onsieur": 17914, + "qt": 17915, + "abestanden": 17916, + "ność": 17917, + "Connect": 17918, + "▁oracle": 17919, + "▁Stockholm": 17920, + "sizeof": 17921, + "▁gemäß": 17922, + "ACT": 17923, + "▁expert": 17924, + "utions": 17925, + "▁hacia": 17926, + "▁logger": 17927, + "▁fool": 17928, + "rypto": 17929, + "ær": 17930, + "▁cidade": 17931, + "▁составе": 17932, + "oker": 17933, + "▁Transfer": 17934, + "▁denied": 17935, + "Track": 17936, + "▁radi": 17937, + "zec": 17938, + "▁Historic": 17939, + "▁Einwohner": 17940, + "кою": 17941, + "▁хра": 17942, + "▁Category": 17943, + "▁Disney": 17944, + "▁swap": 17945, + "Begin": 17946, + "▁mientras": 17947, + "▁dance": 17948, + "▁tête": 17949, + "▁droit": 17950, + "erta": 17951, + "▁birds": 17952, + "▁convin": 17953, + "parator": 17954, + "дра": 17955, + "▁ES": 17956, + "▁Ressources": 17957, + "EGIN": 17958, + "ücke": 17959, + "▁Cruz": 17960, + "abling": 17961, + "▁\"@": 17962, + "▁metres": 17963, + "▁Beg": 17964, + "▁Gründ": 17965, + "▁Boh": 17966, + "▁mile": 17967, + "▁Technology": 17968, + "\"+": 17969, + "acco": 17970, + "▁ss": 17971, + "▁Fed": 17972, + "▁Hend": 17973, + "usch": 17974, + "itä": 17975, + "folk": 17976, + "▁absor": 17977, + "antal": 17978, + "odge": 17979, + "▁WHEN": 17980, + "▁Externí": 17981, + "▁Regiment": 17982, + "▁evaluation": 17983, + "▁Tai": 17984, + "▁vocals": 17985, + "▁experimental": 17986, + "embed": 17987, + "▁Minn": 17988, + "▁вме": 17989, + "prec": 17990, + "every": 17991, + "▁hoof": 17992, + "▁Fernando": 17993, + "▁Bibliographie": 17994, + "▁nag": 17995, + "amerikanischer": 17996, + "▁marks": 17997, + "▁UTC": 17998, + "▁uncertain": 17999, + "дия": 18000, + "olia": 18001, + "▁cup": 18002, + "▁fille": 18003, + "▁dok": 18004, + "useppe": 18005, + "esterd": 18006, + "▁Brand": 18007, + "▁Third": 18008, + "PP": 18009, + "nodes": 18010, + "▁Pad": 18011, + "▁loved": 18012, + "swing": 18013, + "▁surprised": 18014, + "ardi": 18015, + "▁GR": 18016, + "]\"": 18017, + "▁equally": 18018, + "ihe": 18019, + "care": 18020, + "писок": 18021, + "lijk": 18022, + "rinn": 18023, + "▁\\[\\": 18024, + "▁sons": 18025, + "▁tät": 18026, + "icamente": 18027, + "▁listing": 18028, + "iellement": 18029, + "▁nyelven": 18030, + "▁ds": 18031, + "▁agricult": 18032, + "▁Hermann": 18033, + "▁besides": 18034, + "progress": 18035, + "▁peculiar": 18036, + "focus": 18037, + "cn": 18038, + "-$": 18039, + "ственный": 18040, + "ourg": 18041, + "▁wyn": 18042, + "▁conducted": 18043, + "▁Становништво": 18044, + "connected": 18045, + "▁bott": 18046, + "▁смер": 18047, + "▁Poz": 18048, + "unct": 18049, + "conda": 18050, + "▁савезној": 18051, + "▁havet": 18052, + "ligt": 18053, + "orted": 18054, + "▁entering": 18055, + "multip": 18056, + "▁Temple": 18057, + "▁Plant": 18058, + "typeof": 18059, + "▁Vlad": 18060, + "▁qued": 18061, + "▁reste": 18062, + "▁май": 18063, + "▁Very": 18064, + "ambiguation": 18065, + "▁challeng": 18066, + "▁respective": 18067, + "▁тор": 18068, + "Ctrl": 18069, + "▁absence": 18070, + "aru": 18071, + "вое": 18072, + "▁först": 18073, + "▁sq": 18074, + "▁Emperor": 18075, + "▁Ign": 18076, + "▁това": 18077, + ":`": 18078, + "adoop": 18079, + "▁Madame": 18080, + "▁gruppo": 18081, + "stud": 18082, + "▁externas": 18083, + "▁Александр": 18084, + "▁dign": 18085, + "▁живе": 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"▁counts": 18139, + "rinningsområ": 18140, + "щё": 18141, + "▁spé": 18142, + "▁pierws": 18143, + "▁Sver": 18144, + "▁acknow": 18145, + "Boolean": 18146, + "▁фамили": 18147, + "▁Senate": 18148, + "шов": 18149, + "agers": 18150, + "▁Nueva": 18151, + "bil": 18152, + "kiem": 18153, + "▁Mey": 18154, + "wij": 18155, + "▁GmbH": 18156, + "validation": 18157, + "▁ensuite": 18158, + "inking": 18159, + "▁campion": 18160, + "▁financial": 18161, + "izon": 18162, + "Headers": 18163, + "▁deprecated": 18164, + "▁fonction": 18165, + "REG": 18166, + "▁volumes": 18167, + "▁Chi": 18168, + "▁encountered": 18169, + "lak": 18170, + "рая": 18171, + "▁continues": 18172, + "▁~[": 18173, + "uerte": 18174, + "▁\\;": 18175, + "▁Dok": 18176, + "▁weights": 18177, + "▁rh": 18178, + "▁Napole": 18179, + "▁naturally": 18180, + "sku": 18181, + "pas": 18182, + "▁gegründ": 18183, + "etr": 18184, + "▁Ku": 18185, + "icted": 18186, + "▁fabric": 18187, + "▁ASC": 18188, + "▁Entertainment": 18189, + "▁energ": 18190, + "клад": 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"▁projection": 18246, + "▁También": 18247, + "verb": 18248, + "▁terre": 18249, + "rugu": 18250, + "▁september": 18251, + "▁=": 18572, + "▁Beat": 18573, + "▁Sax": 18574, + "vertical": 18575, + "кто": 18576, + "▁plants": 18577, + "▁Références": 18578, + "▁ogni": 18579, + "▁curs": 18580, + "▁SK": 18581, + "они": 18582, + "▁destac": 18583, + "\");\r": 18584, + "▁Sure": 18585, + "▁partido": 18586, + "▁Folge": 18587, + "▁Moore": 18588, + "▁wz": 18589, + "скус": 18590, + "ltre": 18591, + "ondo": 18592, + "▁pose": 18593, + "imos": 18594, + "бой": 18595, + "ципа": 18596, + "jus": 18597, + ".....": 18598, + "▁época": 18599, + "▁quanto": 18600, + "▁Support": 18601, + "geschichte": 18602, + "SERVER": 18603, + "▁Georges": 18604, + "enum": 18605, + "▁herm": 18606, + "▁nebo": 18607, + "▁Chr": 18608, + "character": 18609, + "▁***": 18610, + "▁Forsch": 18611, + "iami": 18612, + "▁¿": 18613, + "cych": 18614, + "▁fifth": 18615, + "sent": 18616, + "▁anderem": 18617, + "▁proportion": 18618, + "▁prest": 18619, + "▁Girl": 18620, + "▁drama": 18621, + "wand": 18622, + "▁Mail": 18623, + "▁Lux": 18624, + "▁který": 18625, + "▁Gesellschaft": 18626, + "▁Hinweis": 18627, + "nisse": 18628, + "▁mondo": 18629, + "Eq": 18630, + "▁perí": 18631, + "▁eastern": 18632, + "▁UEFA": 18633, + "uale": 18634, + "▁convex": 18635, + "▁поль": 18636, + "▁Hey": 18637, + "zenie": 18638, + "initely": 18639, + "▁Zusammen": 18640, + "SSL": 18641, + "ocal": 18642, + "▁canal": 18643, + "voy": 18644, + "▁Кри": 18645, + "▁között": 18646, + "▁cars": 18647, + "▁versión": 18648, + "Environment": 18649, + "Her": 18650, + "▁señ": 18651, + "▁spatial": 18652, + "ymi": 18653, + "Fire": 18654, + "▁veget": 18655, + "▁Wie": 18656, + "▁znaj": 18657, + "▁damage": 18658, + "▁endl": 18659, + "gif": 18660, + "▁quali": 18661, + "▁которых": 18662, + "ellan": 18663, + "▁mens": 18664, + "▁plug": 18665, + "▁abund": 18666, + "FIG": 18667, + "▁sf": 18668, + "▁confl": 18669, + "▁населения": 18670, + "▁principles": 18671, + "▁Gabriel": 18672, + "ibe": 18673, + "▁{%": 18674, + "▁població": 18675, + "ніципа": 18676, + "▁extreme": 18677, + "▁asse": 18678, + "▁vu": 18679, + "Mock": 18680, + "▁spielte": 18681, + "▁Aer": 18682, + "▁datos": 18683, + "endes": 18684, + "▁Gel": 18685, + "▁Gor": 18686, + "Christ": 18687, + "chos": 18688, + "Processor": 18689, + "▁instruct": 18690, + "▁picked": 18691, + "nahme": 18692, + "fahr": 18693, + "▁indicated": 18694, + "▁%.": 18695, + "▁ts": 18696, + "▁notable": 18697, + "▁qualified": 18698, + "▁Ал": 18699, + "Black": 18700, + "▁council": 18701, + "▁overhead": 18702, + "aci": 18703, + "année": 18704, + "▁initWith": 18705, + "bió": 18706, + "▁introduction": 18707, + "▁companion": 18708, + "▁expon": 18709, + "▁kör": 18710, + "oby": 18711, + "burn": 18712, + "gnu": 18713, + "virtual": 18714, + "▁intellect": 18715, + "▁держа": 18716, + "'+": 18717, + "бле": 18718, + "▁strictly": 18719, + "▁recognize": 18720, + "hour": 18721, + "▁Wrest": 18722, + "ennen": 18723, + "$).": 18724, + "fff": 18725, + 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"▁сторо": 18779, + "▁NaN": 18780, + "▁priest": 18781, + "▁exha": 18782, + "UND": 18783, + "pair": 18784, + "alone": 18785, + "▁moon": 18786, + "▁#!/": 18787, + "▁guns": 18788, + "rola": 18789, + "чита": 18790, + "▁Encyclopedia": 18791, + "atis": 18792, + "▁'\"": 18793, + "zych": 18794, + "▁superfic": 18795, + "▁эк": 18796, + "едера": 18797, + "feed": 18798, + "LAY": 18799, + "Fi": 18800, + "unks": 18801, + "isecond": 18802, + "▁'@": 18803, + "▁Adding": 18804, + "рое": 18805, + "▁tang": 18806, + "цо": 18807, + "hung": 18808, + "bis": 18809, + "ského": 18810, + "▁advert": 18811, + "▁занима": 18812, + "uzz": 18813, + "ágina": 18814, + "▁Tel": 18815, + "sig": 18816, + "▁Ez": 18817, + "▁guarantee": 18818, + "▁teaching": 18819, + "oty": 18820, + "termin": 18821, + "▁distributions": 18822, + "FLA": 18823, + "▁Giuseppe": 18824, + "querySelector": 18825, + "▁/\\": 18826, + "▁Squad": 18827, + "gz": 18828, + "delay": 18829, + "▁surrounding": 18830, + "▁manus": 18831, + "▁Hou": 18832, + "²,": 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"▁enorm": 18886, + ",’": 18887, + "▁Christopher": 18888, + "jev": 18889, + "▁quad": 18890, + "▁AJAX": 18891, + "▁relief": 18892, + "▁modes": 18893, + "sklär": 18894, + "▁Vid": 18895, + "▁Serial": 18896, + "▁tokens": 18897, + "▁Poland": 18898, + "\\]": 18899, + "▁vide": 18900, + "rooms": 18901, + "omas": 18902, + "▁Bureau": 18903, + "cx": 18904, + "ностью": 18905, + "▁signs": 18906, + "шение": 18907, + "lossen": 18908, + "▁Queens": 18909, + "▁membre": 18910, + "▁mez": 18911, + "▁Bool": 18912, + "▁Naj": 18913, + "▁Memory": 18914, + "▁Khan": 18915, + "▁là": 18916, + "▁Hud": 18917, + "▁dismiss": 18918, + "ighth": 18919, + "▁fs": 18920, + "prevent": 18921, + "▁меда": 18922, + "▁Police": 18923, + "▁ско": 18924, + "finite": 18925, + "▁ami": 18926, + "▁Much": 18927, + "owania": 18928, + "ORY": 18929, + "iors": 18930, + "▁Premio": 18931, + "▁textbox": 18932, + "dm": 18933, + "▁afin": 18934, + "▁Donald": 18935, + "▁Priv": 18936, + "▁decid": 18937, + "▁Maurice": 18938, + "agan": 18939, + "▁Britannica": 18940, + "▁oft": 18941, + "▁consecutive": 18942, + "\"?>": 18943, + "овий": 18944, + "student": 18945, + "▁peque": 18946, + "▁dieses": 18947, + "▁retour": 18948, + "étr": 18949, + "▁сез": 18950, + "▁kre": 18951, + "▁votes": 18952, + "ruption": 18953, + "izada": 18954, + "▁Wiel": 18955, + "▁Gray": 18956, + "▁Leop": 18957, + "teilung": 18958, + "(['": 18959, + "▁whites": 18960, + "frica": 18961, + "animation": 18962, + "curl": 18963, + "lings": 18964, + "=\"$": 18965, + "loyd": 18966, + "textsc": 18967, + "ору": 18968, + "▁села": 18969, + "esian": 18970, + "▁Mission": 18971, + "▁неза": 18972, + "▁ultimately": 18973, + "бов": 18974, + "olen": 18975, + "скому": 18976, + "nete": 18977, + "▁Dit": 18978, + "▁costru": 18979, + "dependent": 18980, + "▁Resource": 18981, + "▁hosts": 18982, + "▁rear": 18983, + "Duration": 18984, + "ників": 18985, + "Ма": 18986, + "▁planning": 18987, + "▁prediction": 18988, + "▁Lyn": 18989, + "▁kir": 18990, + "▁Legisl": 18991, + "мат": 18992, + "▁Soccer": 18993, + "▁survey": 18994, + "▁estadounidense": 18995, + "orgen": 18996, + "jourd": 18997, + "▁aprile": 18998, + "▁ids": 18999, + "ське": 19000, + "▁employee": 19001, + "▁Schauspieler": 19002, + "ръ": 19003, + "▁multimedia": 19004, + "▁свою": 19005, + "▁wine": 19006, + "▁EU": 19007, + "ică": 19008, + "▁Rhein": 19009, + "▁Palmar": 19010, + "oteca": 19011, + "▁prepare": 19012, + "▁Tot": 19013, + "▁Null": 19014, + "▁kin": 19015, + "inals": 19016, + "▁Newton": 19017, + "▁tbl": 19018, + "▁Sold": 19019, + "▁verf": 19020, + "aturing": 19021, + "▁laptop": 19022, + "▁Совет": 19023, + "secret": 19024, + "▁Olympic": 19025, + "▁footballer": 19026, + "▁Rudolf": 19027, + "▁conhe": 19028, + "zysk": 19029, + "▁evaluated": 19030, + "»)": 19031, + "shop": 19032, + "repository": 19033, + "▁zach": 19034, + "▁losing": 19035, + "etter": 19036, + "▁Wirtschaft": 19037, + "так": 19038, + "▁unnecessary": 19039, + "▁Phot": 19040, + "anska": 19041, + "▁Native": 19042, + "CCE": 19043, + "▁fifty": 19044, 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"▁organized": 19098, + "ční": 19099, + "▁ox": 19100, + "lingen": 19101, + "▁luego": 19102, + "cció": 19103, + "▁rely": 19104, + "▁tussen": 19105, + "erten": 19106, + "▁honour": 19107, + "▁Claude": 19108, + "▁Korea": 19109, + "▁Metropol": 19110, + "Super": 19111, + "rien": 19112, + "érature": 19113, + "attro": 19114, + "▁біль": 19115, + "▁Herbert": 19116, + "▁auteurs": 19117, + "▁darauf": 19118, + "▁mental": 19119, + "▁rang": 19120, + "▁són": 19121, + "▁Soph": 19122, + ")\",": 19123, + "Descriptor": 19124, + "prepare": 19125, + "▁Landkreis": 19126, + "HC": 19127, + "cross": 19128, + "лиза": 19129, + "▁Login": 19130, + "onen": 19131, + "Feature": 19132, + "▁museum": 19133, + "vek": 19134, + "▁Nelson": 19135, + "▁rejo": 19136, + "▁команди": 19137, + "▁summar": 19138, + "▁следу": 19139, + "ämp": 19140, + "▁Gas": 19141, + "вом": 19142, + "VALUE": 19143, + "inge": 19144, + "period": 19145, + "lassen": 19146, + "ával": 19147, + "▁altogether": 19148, + "umph": 19149, + "istro": 19150, + "ąż": 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"BeanFactory": 24793, + "▁помощ": 24794, + "▁pressing": 24795, + "▁equivalence": 24796, + "▁catt": 24797, + "icity": 24798, + "▁accomplished": 24799, + "▁yo": 24800, + "▁sic": 24801, + "▁imports": 24802, + "▁accommod": 24803, + "▁Porto": 24804, + "▁яка": 24805, + "▁loan": 24806, + "тики": 24807, + "▁checkout": 24808, + "▁assess": 24809, + "▁Population": 24810, + "urent": 24811, + "clojure": 24812, + "▁Santos": 24813, + "▁információ": 24814, + "POS": 24815, + "▁gare": 24816, + "▁kick": 24817, + "▁radical": 24818, + "▁Peace": 24819, + "▁streaming": 24820, + "camp": 24821, + "ząt": 24822, + "говор": 24823, + "▁Regierung": 24824, + "▁proceeded": 24825, + "fm": 24826, + "лены": 24827, + "▁earnest": 24828, + "▁Parad": 24829, + "requests": 24830, + "▁Raum": 24831, + "šč": 24832, + "▁policies": 24833, + "▁Tig": 24834, + "▁sitt": 24835, + "▁Energy": 24836, + "▁purely": 24837, + "▁Haut": 24838, + "▁Speed": 24839, + "bio": 24840, + "▁orange": 24841, + "▁biggest": 24842, + "▁britannique": 24843, + 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26048, + "▁Affairs": 26049, + "ske": 26050, + "▁notify": 26051, + "imoine": 26052, + "▁Arena": 26053, + "▁liberal": 26054, + "▁obec": 26055, + "ifa": 26056, + "guez": 26057, + "iono": 26058, + "ператор": 26059, + "▁retained": 26060, + "failed": 26061, + "bine": 26062, + "тных": 26063, + "▁CGRect": 26064, + "camera": 26065, + "idenote": 26066, + "KB": 26067, + "▁lights": 26068, + "▁Pictures": 26069, + "▁Squadron": 26070, + "▁Volk": 26071, + "▁burg": 26072, + ",]": 26073, + "Gi": 26074, + "êque": 26075, + "makeText": 26076, + "▁everybody": 26077, + "▁Hyper": 26078, + "▁Deux": 26079, + "▁glory": 26080, + "presentation": 26081, + "onica": 26082, + "▁frère": 26083, + "aget": 26084, + "▁hints": 26085, + "▁tunnel": 26086, + "▁Ej": 26087, + "ális": 26088, + "▁Viv": 26089, + "ственных": 26090, + "▁caps": 26091, + "PART": 26092, + "oci": 26093, + "▁prices": 26094, + "currency": 26095, + "▁achter": 26096, + "romagnet": 26097, + "gender": 26098, + "▁suis": 26099, + "versions": 26100, + "▁Training": 26101, + "inside": 26102, + "ege": 26103, + "▁totale": 26104, + "▁Daar": 26105, + "▁grudnia": 26106, + "▁Ier": 26107, + "▁occasions": 26108, + "▁kde": 26109, + "▁tensorflow": 26110, + "▁ór": 26111, + "Methods": 26112, + "▁looping": 26113, + "▁directeur": 26114, + "kę": 26115, + "▁isomorphism": 26116, + "▁João": 26117, + "▁aligned": 26118, + "онов": 26119, + "urger": 26120, + "▁nova": 26121, + "morrow": 26122, + "altern": 26123, + "HD": 26124, + "▁marqu": 26125, + "ativas": 26126, + "ggreg": 26127, + "▁ancien": 26128, + "nit": 26129, + "▁secured": 26130, + "mier": 26131, + "▁Ole": 26132, + "▁инте": 26133, + "▁minus": 26134, + "▁clearer": 26135, + "▁nello": 26136, + "▁információk": 26137, + "▁propre": 26138, + "{.": 26139, + "ilog": 26140, + "▁Quick": 26141, + "▁accus": 26142, + "employee": 26143, + "▁зу": 26144, + "цький": 26145, + "фіцій": 26146, + "▁публи": 26147, + "▁bent": 26148, + "▁позво": 26149, + "▁Пор": 26150, + "ází": 26151, + "ánico": 26152, + "emptyset": 26153, + "▁surtout": 26154, + "reno": 26155, + "unya": 26156, + "▁уез": 26157, + "▁Millionen": 26158, + "▁listopada": 26159, + "▁Maine": 26160, + "▁grupos": 26161, + "▁Storage": 26162, + "▁apple": 26163, + "▁Lö": 26164, + "oused": 26165, + "дро": 26166, + "sci": 26167, + "▁hibernate": 26168, + "dog": 26169, + "▁восто": 26170, + "▁intensity": 26171, + "legend": 26172, + "▁Wille": 26173, + "▁szerint": 26174, + "gesellschaft": 26175, + "▁Living": 26176, + "allo": 26177, + "▁Split": 26178, + "dru": 26179, + "need": 26180, + "▁Джон": 26181, + "▁Swiss": 26182, + "▁spraw": 26183, + "▁beho": 26184, + "▁fotograf": 26185, + "▁rencontre": 26186, + "▁kis": 26187, + "▁signing": 26188, + "akult": 26189, + "▁indexing": 26190, + "apor": 26191, + "▁conception": 26192, + "aggreg": 26193, + "▁Савез": 26194, + "▁affair": 26195, + "ění": 26196, + "August": 26197, + "▁секре": 26198, + "▁mieszkań": 26199, + "UIImage": 26200, + "▁bishop": 26201, + "▁servants": 26202, + "▁trail": 26203, + "digit": 26204, + "▁joins": 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"vic": 26311, + "baut": 26312, + "▁дов": 26313, + "▁interven": 26314, + "▁Gü": 26315, + "ónica": 26316, + "▁Pon": 26317, + "▁disponible": 26318, + "▁Feb": 26319, + "▁worship": 26320, + "▁Specifically": 26321, + "Hy": 26322, + "iju": 26323, + "▁cb": 26324, + "▁spac": 26325, + "leveland": 26326, + "▁localidad": 26327, + "▁preceding": 26328, + "▁Hessen": 26329, + "xp": 26330, + "▁Wein": 26331, + "▁Româ": 26332, + "▁giorno": 26333, + "▁квітня": 26334, + "llaços": 26335, + "▁Academia": 26336, + "▁kül": 26337, + "▁Års": 26338, + "▁нај": 26339, + "uclide": 26340, + "Internet": 26341, + "orton": 26342, + "▁corn": 26343, + "ями": 26344, + "▁\"*": 26345, + "▁Felix": 26346, + "apat": 26347, + "▁свои": 26348, + "MIT": 26349, + "made": 26350, + "▁locomot": 26351, + "хода": 26352, + "FP": 26353, + "▁pm": 26354, + ".*;": 26355, + "▁Hamm": 26356, + "`}": 26357, + "LayoutInflater": 26358, + "==\"": 26359, + "▁Eur": 26360, + "▁dogs": 26361, + "жении": 26362, + "▁azon": 26363, + "▁emulator": 26364, + "▁ricon": 26365, + "beeld": 26366, + "▁ну": 26367, + "▁approximate": 26368, + "LM": 26369, + "▁Bond": 26370, + "▁enh": 26371, + "ędz": 26372, + "▁solit": 26373, + "RelativeLayout": 26374, + "eteor": 26375, + "amentos": 26376, + "▁indirect": 26377, + "iből": 26378, + "▁gros": 26379, + "▁Originals": 26380, + "commands": 26381, + "Export": 26382, + "▁Avec": 26383, + "▁solemn": 26384, + "▁correction": 26385, + "▁проводи": 26386, + "▁Mosk": 26387, + "▁подо": 26388, + "▁gebied": 26389, + "▁następ": 26390, + "▁Driver": 26391, + "▁Ook": 26392, + "▁Vec": 26393, + "▁lungo": 26394, + "ficos": 26395, + "▁svol": 26396, + "▁kid": 26397, + "nja": 26398, + "▁Hr": 26399, + "▁поддер": 26400, + "▁visibility": 26401, + "▁Méd": 26402, + "▁cpu": 26403, + "discussion": 26404, + "Asset": 26405, + "▁defense": 26406, + "▁Anyone": 26407, + "▁Justin": 26408, + "iszt": 26409, + "▁Collins": 26410, + "▁Valent": 26411, + "▁Pale": 26412, + "▁fuel": 26413, + "▁nose": 26414, + "ríguez": 26415, + "▁Schles": 26416, + "▁Malays": 26417, + "▁commut": 26418, + "dro": 26419, + "uing": 26420, + "▁Rico": 26421, + "▁Emma": 26422, + "orp": 26423, + "▁Kirk": 26424, + "▁Quando": 26425, + "▁Neue": 26426, + "▁demande": 26427, + "▁Cover": 26428, + "▁rescue": 26429, + "▁gewählt": 26430, + "▁Calendar": 26431, + "▁Madonna": 26432, + "WP": 26433, + "oshi": 26434, + "▁Maven": 26435, + "▁belle": 26436, + "▁wx": 26437, + "▁sugar": 26438, + "▁Betrieb": 26439, + "▁equilibrium": 26440, + "EAR": 26441, + "▁texts": 26442, + "слов": 26443, + "▁czerwca": 26444, + "▁Düsseld": 26445, + "▁ELSE": 26446, + "▁amery": 26447, + "▁ani": 26448, + "▁obey": 26449, + "▁Nell": 26450, + "▁inne": 26451, + "▁тро": 26452, + "FD": 26453, + "cco": 26454, + "▁Zob": 26455, + "alette": 26456, + "▁május": 26457, + "ected": 26458, + "▁Turkey": 26459, + "▁Whether": 26460, + "qi": 26461, + "▁што": 26462, + "▁headquarters": 26463, + "endi": 26464, + "arus": 26465, + "opus": 26466, + "▁золо": 26467, + "▁destru": 26468, + "▁Lok": 26469, + "▁satisfaction": 26470, + "()\r": 26471, + "▁Тер": 26472, + "Jose": 26473, + "▁conquer": 26474, + "▁Effect": 26475, + "LayoutParams": 26476, + "iez": 26477, + "▁externs": 26478, + "▁gegenüber": 26479, + "▁ESP": 26480, + "olta": 26481, + "processor": 26482, + "▁Kult": 26483, + "▁Atlanta": 26484, + "▁tier": 26485, + "Operator": 26486, + "▁диа": 26487, + "▁пись": 26488, + "▁groß": 26489, + "▁hearts": 26490, + "▁millimeter": 26491, + "although": 26492, + "alles": 26493, + "▁Magic": 26494, + "training": 26495, + "oline": 26496, + "▁органі": 26497, + ">\\<^": 26498, + "ціаль": 26499, + "exports": 26500, + "Workbook": 26501, + "▁вересня": 26502, + "▁teles": 26503, + "▁economy": 26504, + "▁trap": 26505, + "▁refuse": 26506, + "▁stranger": 26507, + "▁instinct": 26508, + "пода": 26509, + "olan": 26510, + "▁ning": 26511, + "inflate": 26512, + "itatea": 26513, + "acks": 26514, + "▁Joy": 26515, + "FLAG": 26516, + "ailand": 26517, + "▁sorti": 26518, + "▁впер": 26519, + "▁pén": 26520, + "Nothing": 26521, + "▁száz": 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"cija": 26575, + "▁poem": 26576, + "▁negro": 26577, + "хар": 26578, + "▁Ask": 26579, + "▁avo": 26580, + "▁Meyer": 26581, + "▁Westen": 26582, + "▁oko": 26583, + "agin": 26584, + "▁Süden": 26585, + "entries": 26586, + "▁Republik": 26587, + "CollectionView": 26588, + "-------": 26589, + "▁firefox": 26590, + "▁alcune": 26591, + "▁фото": 26592, + "▁отрима": 26593, + "~~~~~~~~": 26594, + "▁Раз": 26595, + "▁Complex": 26596, + "▁pia": 26597, + "▁publicada": 26598, + "wei": 26599, + "cedure": 26600, + "occupation": 26601, + "▁medicine": 26602, + "▁drove": 26603, + "Problem": 26604, + "▁beginner": 26605, + "▁thoroughly": 26606, + "uria": 26607, + "avant": 26608, + "ucha": 26609, + "▁lever": 26610, + "▁teatro": 26611, + "AVA": 26612, + "squ": 26613, + "trat": 26614, + "ivatal": 26615, + "▁dirty": 26616, + "▁seconde": 26617, + "▁gravit": 26618, + "▁proposition": 26619, + "hbar": 26620, + "omini": 26621, + "▁”": 26622, + "▁Camil": 26623, + "▁queen": 26624, + "modifier": 26625, + "Jan": 26626, + 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26784, + "RESS": 26785, + "▁chemin": 26786, + "▁główn": 26787, + "GG": 26788, + "▁Germania": 26789, + "▁Alexandre": 26790, + "hens": 26791, + "swift": 26792, + "oop": 26793, + "Subview": 26794, + "▁requiring": 26795, + "ędzy": 26796, + "▁fict": 26797, + "▁Констан": 26798, + "▁déput": 26799, + "▁surprising": 26800, + "▁deix": 26801, + "▁unterschied": 26802, + "inson": 26803, + "▁Character": 26804, + "▁gestion": 26805, + "chus": 26806, + "comes": 26807, + "▁neur": 26808, + "▁yeux": 26809, + "ollar": 26810, + "▁parad": 26811, + "▁maggiore": 26812, + "TRAN": 26813, + "▁votre": 26814, + "▁descent": 26815, + "▁Icon": 26816, + "▁Judge": 26817, + "▁occupation": 26818, + "eping": 26819, + "▁tongue": 26820, + "▁Enllaços": 26821, + "ruf": 26822, + "▁protein": 26823, + "▁visitors": 26824, + "axy": 26825, + "esten": 26826, + "blica": 26827, + "hw": 26828, + "▁spirits": 26829, + "▁reduces": 26830, + "▁мен": 26831, + "▁Lamb": 26832, + "▁Mine": 26833, + "▁verified": 26834, + "▁Baby": 26835, + 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"fluss": 26944, + "Drawable": 26945, + "▁surve": 26946, + "Setup": 26947, + "▁należ": 26948, + "▁conjunto": 26949, + "▁Его": 26950, + "▁oldal": 26951, + "▁verbose": 26952, + "▁Electric": 26953, + "▁Harrison": 26954, + "engen": 26955, + "paragraph": 26956, + "▁nouvelles": 26957, + "▁време": 26958, + "▁memor": 26959, + "▁mayoría": 26960, + "сад": 26961, + "▁bataille": 26962, + "▁thermal": 26963, + "▁Хронологи": 26964, + "▁Better": 26965, + "bye": 26966, + "▁театра": 26967, + "roe": 26968, + "▁segle": 26969, + "rott": 26970, + "▁opinions": 26971, + ")})": 26972, + "ühle": 26973, + "▁Gün": 26974, + "▁Щ": 26975, + "ból": 26976, + "▁Larry": 26977, + "▁solic": 26978, + "▁zwar": 26979, + "▁Caroline": 26980, + "▁Reichs": 26981, + "Extensions": 26982, + "migr": 26983, + ":@": 26984, + "▁enumerate": 26985, + "▁eigenen": 26986, + "▁explore": 26987, + "ému": 26988, + "▁gat": 26989, + "▁imperial": 26990, + "▁Usually": 26991, + "▁tud": 26992, + "▁укра": 26993, + "him": 26994, + "▁corners": 26995, + 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27048, + "kv": 27049, + "▁häufig": 27050, + "▁Agricult": 27051, + "▁huit": 27052, + "▁inoltre": 27053, + "▁Lloyd": 27054, + "▁француз": 27055, + "▁выпол": 27056, + "▁faithful": 27057, + "▁Вар": 27058, + "▁verl": 27059, + "▁juego": 27060, + "▁Резултати": 27061, + ",...,": 27062, + "▁implicitly": 27063, + "irks": 27064, + "Calcul": 27065, + "▁meses": 27066, + "omed": 27067, + "▁pak": 27068, + "herit": 27069, + "▁optical": 27070, + "▁Історія": 27071, + "veis": 27072, + "▁capitale": 27073, + "placeholder": 27074, + "intrag": 27075, + "▁Atlas": 27076, + ")];": 27077, + "icons": 27078, + "▁Bent": 27079, + "▁Widget": 27080, + "▁volunt": 27081, + "avo": 27082, + "égr": 27083, + "lige": 27084, + "▁NAME": 27085, + "▁abstra": 27086, + "▁fís": 27087, + "▁Browser": 27088, + "▁bush": 27089, + "hall": 27090, + "▁clouds": 27091, + "▁SUB": 27092, + "▁tandis": 27093, + "▁Commonwealth": 27094, + "тая": 27095, + "▁exhaust": 27096, + "________________": 27097, + "▁Statistics": 27098, + "▁Religion": 27099, 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"май": 27152, + "enant": 27153, + "-}": 27154, + "лад": 27155, + "▁Москва": 27156, + "gom": 27157, + "▁Fernández": 27158, + "fund": 27159, + "interno": 27160, + "▁Mari": 27161, + "▁rius": 27162, + "▁Prozent": 27163, + "стрі": 27164, + "▁внут": 27165, + "anterie": 27166, + "▁прис": 27167, + "▁обы": 27168, + "▁Marina": 27169, + "▁occurrence": 27170, + "rikt": 27171, + "▁физи": 27172, + "▁schwer": 27173, + "▁Гре": 27174, + "Reset": 27175, + "▁mucho": 27176, + "andr": 27177, + "▁Wies": 27178, + "▁Keith": 27179, + "▁Julian": 27180, + "▁cole": 27181, + "ciendo": 27182, + "▁Contempor": 27183, + "etry": 27184, + "elian": 27185, + "гии": 27186, + "▁голо": 27187, + "▁dél": 27188, + "▁decent": 27189, + "РСР": 27190, + "▁szeptember": 27191, + "мест": 27192, + "castle": 27193, + "▁держав": 27194, + "}\")": 27195, + "▁ASCII": 27196, + "▁Glen": 27197, + "itzerland": 27198, + "Toggle": 27199, + "▁tradicional": 27200, + "▁Plat": 27201, + "vee": 27202, + "abgerufen": 27203, + "(|": 27204, + "CLI": 27205, + "}}$,": 27206, + "▁Bowl": 27207, + "▁Male": 27208, + "▁Bres": 27209, + "▁пси": 27210, + "▁Challenge": 27211, + "zó": 27212, + "▁projekt": 27213, + "▁negoti": 27214, + "above": 27215, + "▁перио": 27216, + "▁longest": 27217, + "authentic": 27218, + "▁tradu": 27219, + "▁mujeres": 27220, + "▁Andre": 27221, + "▁hadn": 27222, + "▁Schule": 27223, + "odel": 27224, + "bled": 27225, + "▁Trade": 27226, + "▁mobil": 27227, + "▁algunas": 27228, + "▁Lak": 27229, + "▁Connecticut": 27230, + "▁alco": 27231, + "▁Selbst": 27232, + "ił": 27233, + "▁alb": 27234, + "ouverneur": 27235, + "▁sr": 27236, + "▁vba": 27237, + "loped": 27238, + "▁Partei": 27239, + "uate": 27240, + "▁Authentication": 27241, + "bei": 27242, + "}}.": 27243, + "▁konnten": 27244, + "▁допо": 27245, + "▁hyd": 27246, + "Office": 27247, + "données": 27248, + "▁Cleveland": 27249, + "rita": 27250, + "íos": 27251, + "▁выше": 27252, + "▁Roberts": 27253, + "▁élections": 27254, + "▁'')": 27255, + "▁publishing": 27256, + "▁bapt": 27257, + "<>();": 27258, + "missing": 27259, + "ровано": 27260, + "▁housing": 27261, + "▁inference": 27262, + "▁Renaissance": 27263, + "▁règ": 27264, + "▁Steph": 27265, + "CES": 27266, + "ERE": 27267, + "кет": 27268, + "OU": 27269, + "▁grouping": 27270, + "verkehr": 27271, + "jih": 27272, + "agli": 27273, + "▁milk": 27274, + "lait": 27275, + "Stage": 27276, + "▁byly": 27277, + "▁wooden": 27278, + "keley": 27279, + "etra": 27280, + "▁Peg": 27281, + "▁donné": 27282, + "adal": 27283, + "sequently": 27284, + "▁insbesondere": 27285, + "ELD": 27286, + "▁Mam": 27287, + "▁volte": 27288, + "▁prospect": 27289, + "нове": 27290, + "▁denoted": 27291, + "▁overlay": 27292, + "Permission": 27293, + "een": 27294, + "▁EM": 27295, + "▁uz": 27296, + "Mc": 27297, + "olit": 27298, + "▁servi": 27299, + "▁Heidel": 27300, + "▁Wiener": 27301, + "▁illegal": 27302, + "▁predictions": 27303, + "▁goog": 27304, + "hon": 27305, + "▁Cinema": 27306, + "▁револю": 27307, + "▁Rule": 27308, + "wod": 27309, + "▁radiation": 27310, + "oł": 27311, + "ової": 27312, + "▁Perform": 27313, + "▁prisoner": 27314, + "▁amet": 27315, + "▁figura": 27316, + "▁Commander": 27317, + "▁официаль": 27318, + "▁trov": 27319, + "▁acted": 27320, + "▁workflow": 27321, + "▁Республики": 27322, + "▁guidance": 27323, + "▁мене": 27324, + "National": 27325, + "▁Kel": 27326, + "webpack": 27327, + "простра": 27328, + "▁llamado": 27329, + "alog": 27330, + "terra": 27331, + "ixen": 27332, + "legraph": 27333, + "äischen": 27334, + "▁teachers": 27335, + "uden": 27336, + "▁også": 27337, + "possible": 27338, + "▁Soul": 27339, + "▁Geography": 27340, + "▁зада": 27341, + "hit": 27342, + "▁anger": 27343, + "▁remporte": 27344, + "Pod": 27345, + "чке": 27346, + "▁aria": 27347, + "▁Astronom": 27348, + "chapter": 27349, + "▁fork": 27350, + "▁Cuando": 27351, + "mense": 27352, + "▁Christians": 27353, + "gc": 27354, + "▁#(": 27355, + "Organ": 27356, + "▁steady": 27357, + "pse": 27358, + "жить": 27359, + "ignes": 27360, + "aterra": 27361, + "movie": 27362, + 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28253, + "▁Maler": 28254, + "▁proyecto": 28255, + "▁Bath": 28256, + "ellers": 28257, + "▁GP": 28258, + "oning": 28259, + "cloudflare": 28260, + "▁při": 28261, + "▁ded": 28262, + "▁Odkazy": 28263, + "▁Msg": 28264, + "▁Being": 28265, + "▁Depuis": 28266, + "▁Primary": 28267, + "▁Appro": 28268, + "▁formally": 28269, + "ступил": 28270, + "▁fuera": 28271, + "▁Root": 28272, + "▁autonom": 28273, + "▁secretary": 28274, + "▁osób": 28275, + "▁cuales": 28276, + "▁Depending": 28277, + "▁asi": 28278, + "vera": 28279, + "▁russe": 28280, + "▁proves": 28281, + "▁presiden": 28282, + "RU": 28283, + "▁Watson": 28284, + "▁webpack": 28285, + "elligence": 28286, + "кам": 28287, + "▁Officer": 28288, + "▁delivery": 28289, + "ждён": 28290, + "▁импе": 28291, + "▁wil": 28292, + "▁vesc": 28293, + "usztus": 28294, + "▁Geoff": 28295, + "()}": 28296, + "▁Fore": 28297, + "▁wenig": 28298, + "▁Airl": 28299, + "▁Efter": 28300, + "▁Break": 28301, + "▁Städ": 28302, + "ismiss": 28303, + "íp": 28304, + "▁avoided": 28305, + "▁assertion": 28306, + "DN": 28307, + "▁teat": 28308, + "ína": 28309, + "▁mechanical": 28310, + "isu": 28311, + "@{": 28312, + "▁nou": 28313, + "Italie": 28314, + "sourceforge": 28315, + "▁svo": 28316, + "▁király": 28317, + "▁References": 28318, + "six": 28319, + "▁Archives": 28320, + "▁finishing": 28321, + "acje": 28322, + "état": 28323, + "iffs": 28324, + "▁stead": 28325, + "▁feas": 28326, + "aware": 28327, + "lande": 28328, + "Inject": 28329, + "▁Agent": 28330, + "▁Normdatei": 28331, + "▁amen": 28332, + "▁Architecture": 28333, + "aze": 28334, + "ște": 28335, + "▁usar": 28336, + "▁cores": 28337, + "лін": 28338, + "▁Castro": 28339, + "▁væ": 28340, + ">\",": 28341, + "omena": 28342, + "▁gesam": 28343, + "▁Martín": 28344, + "egung": 28345, + "▁společ": 28346, + "▁amplitude": 28347, + "▁importing": 28348, + "▁listview": 28349, + "THE": 28350, + "ziale": 28351, + "cedes": 28352, + "▁particulier": 28353, + "▁Расподела": 28354, + "▁край": 28355, + "▁divent": 28356, + "▁ké": 28357, + "quit": 28358, + "тором": 28359, + "CheckBox": 28360, + "▁Zobacz": 28361, + "phe": 28362, + "pta": 28363, + "▁sjö": 28364, + "▁розташ": 28365, + "▁tedesco": 28366, + "▁stal": 28367, + "▁Beruf": 28368, + "овая": 28369, + "▁svě": 28370, + "▁flush": 28371, + "▁відбу": 28372, + "▁radial": 28373, + "▁différentes": 28374, + "анта": 28375, + "▁Perry": 28376, + "Coll": 28377, + "liqu": 28378, + "▁Optional": 28379, + "▁Санкт": 28380, + "▁LINQ": 28381, + "▁Franc": 28382, + "cije": 28383, + "▁Guillaume": 28384, + "know": 28385, + "▁Units": 28386, + "olk": 28387, + "▁Système": 28388, + "▁Sales": 28389, + "▁ehemaligen": 28390, + "мирова": 28391, + "xhtml": 28392, + "setopt": 28393, + "▁mellan": 28394, + "▁zie": 28395, + "▁giant": 28396, + "Board": 28397, + "▁Caval": 28398, + "▁defence": 28399, + "----------": 28400, + "pshire": 28401, + "mart": 28402, + "▁Dioc": 28403, + "iskt": 28404, + "▁inse": 28405, + "▁épisode": 28406, + "чик": 28407, + "bars": 28408, + "Sito": 28409, + "▁integrity": 28410, + "auff": 28411, + "▁vär": 28412, + "Azure": 28413, + "▁starb": 28414, + "▁контра": 28415, + "▁Мексичка": 28416, + "▁запа": 28417, + "▁Mountains": 28418, + "}}=": 28419, + "▁pulling": 28420, + "▁satellite": 28421, + "▁atoms": 28422, + "▁profesor": 28423, + "▁repeatedly": 28424, + "▁invasion": 28425, + "programming": 28426, + "├──": 28427, + "▁Lip": 28428, + "вшие": 28429, + "▁keen": 28430, + "▁critics": 28431, + "▁Nicola": 28432, + "▁Cand": 28433, + "▁distint": 28434, + "▁heading": 28435, + "pragma": 28436, + "{|": 28437, + "ymen": 28438, + "▁terrain": 28439, + "iedenis": 28440, + "▁besonders": 28441, + "▁nominated": 28442, + "BOOL": 28443, + "▁Kay": 28444, + "cian": 28445, + "stelle": 28446, + "▁dispute": 28447, + "▁щ": 28448, + "DataSet": 28449, + "nothing": 28450, + "Autom": 28451, + "hören": 28452, + "▁shed": 28453, + "▁paused": 28454, + "san": 28455, + "▁nunca": 28456, + "!(\"": 28457, + "▁położ": 28458, + "Secret": 28459, + "▁Domain": 28460, + "▁возмож": 28461, + "XV": 28462, + "lv": 28463, + "ikh": 28464, + "▁Sony": 28465, + "mq": 28466, + "otrop": 28467, + "▁Logger": 28468, + "▁threat": 28469, + "asted": 28470, + "зько": 28471, + "▁freely": 28472, + "▁improvements": 28473, + "istema": 28474, + "▁illustrate": 28475, + "▁tact": 28476, + "▁figur": 28477, + "ués": 28478, + "riminal": 28479, + "odon": 28480, + "intendo": 28481, + "▁influenced": 28482, + "FFER": 28483, + "▁Ghost": 28484, + "▁совер": 28485, + "nad": 28486, + "ioned": 28487, + "▁Events": 28488, + "▁wrapping": 28489, + "---------+": 28490, + "fif": 28491, + "▁(**": 28492, + "={{": 28493, + "маль": 28494, + "▁losses": 28495, + "▁Galerie": 28496, + "tel": 28497, + "▁лютого": 28498, + "▁Kru": 28499, + "▁Polen": 28500, + "нім": 28501, + "near": 28502, + "▁shame": 28503, + "▁moyenne": 28504, + "▁CP": 28505, + "preis": 28506, + "▁passenger": 28507, + "lek": 28508, + "ionales": 28509, + "kafka": 28510, + "▁participe": 28511, + "▁membership": 28512, + "[_": 28513, + "lando": 28514, + "stelling": 28515, + "Sem": 28516, + "gon": 28517, + "▁Correct": 28518, + "▁valle": 28519, + "▁readily": 28520, + "▁Dokument": 28521, + "honneur": 28522, + "▁testim": 28523, + "ulative": 28524, + "doFilter": 28525, + "▁dominant": 28526, + "ammer": 28527, + "▁која": 28528, + "▁Monsieur": 28529, + "zeg": 28530, + "▁війни": 28531, + "▁Fo": 28532, + "▁Amy": 28533, + "▁¡": 28534, + "▁február": 28535, + "▁downloading": 28536, + "▁leng": 28537, + "\\}$,": 28538, + "▁neat": 28539, + "▁Cache": 28540, + "ICATION": 28541, + "▁deve": 28542, + "▁sorrow": 28543, + "slow": 28544, + "▁hinaus": 28545, + "▁reconoc": 28546, + "▁Linked": 28547, + "▁Shaw": 28548, + "market": 28549, + "▁Dic": 28550, + "▁Ski": 28551, + "▁delimiter": 28552, + "▁MainActivity": 28553, + "▁Musical": 28554, + "▁Reyn": 28555, + "ScrollView": 28556, + "▁conventional": 28557, + "ença": 28558, + "▁refactor": 28559, + "'-": 28560, + "▁Hed": 28561, + "sprech": 28562, + "▁athlet": 28563, + "▁especies": 28564, + "▁Schön": 28565, + "▁kleinen": 28566, + "шко": 28567, + "▁Йо": 28568, + "▁Happy": 28569, + "multirow": 28570, + "▁augusti": 28571, + "▁Gand": 28572, + "▁appointment": 28573, + "▁Mediabestanden": 28574, + "Three": 28575, + "▁Kenneth": 28576, + "NEW": 28577, + "▁Notification": 28578, + "▁Marx": 28579, + "▁insc": 28580, + "Mor": 28581, + "вый": 28582, + "väst": 28583, + "vidia": 28584, + "▁demonstrated": 28585, + "fonts": 28586, + "▁kamen": 28587, + "▁Ster": 28588, + "▁mieszkańców": 28589, + "▁Koh": 28590, + "~$\\": 28591, + "»).": 28592, + "rene": 28593, + "insic": 28594, + "ická": 28595, + "xygen": 28596, + "▁mn": 28597, + "▁sched": 28598, + "ASC": 28599, + "Ig": 28600, + "▁Constant": 28601, + "▁opportun": 28602, + "▁MyClass": 28603, + "sef": 28604, + "oped": 28605, + "▁injured": 28606, + "VIS": 28607, + "▁Pero": 28608, + "▁Until": 28609, + "▁flesh": 28610, + "orphism": 28611, + "▁Portal": 28612, + "▁gminy": 28613, + "▁власти": 28614, + "▁Nä": 28615, + "ктиче": 28616, + "▁hrab": 28617, + "▁Cub": 28618, + "avoir": 28619, + "▁Lars": 28620, + "▁Бело": 28621, + "▁seizoen": 28622, + "▁Genomsnitt": 28623, + "▁Lil": 28624, + "▁Pool": 28625, + "▁Dios": 28626, + "TX": 28627, + "aes": 28628, + "autore": 28629, + "Alpha": 28630, + "states": 28631, + "Lab": 28632, + "nederbörd": 28633, + "erton": 28634, + "▁brid": 28635, + "▁richt": 28636, + "▁Ela": 28637, + "▁сла": 28638, + "▁weapon": 28639, + "▁combatt": 28640, + "agar": 28641, + "▁regnig": 28642, + "▁utilisé": 28643, + "▁servir": 28644, + "▁brick": 28645, + "▁gateway": 28646, + "▁torraste": 28647, + "▁procedures": 28648, + "▁årsnederbörd": 28649, + "▁Genomsnittlig": 28650, + "чёт": 28651, + "▁områ": 28652, + "▁regnigaste": 28653, + "▁честь": 28654, + "▁amid": 28655, + "▁grateful": 28656, + "▁DIS": 28657, + "DAY": 28658, + "▁ору": 28659, + "▁rivière": 28660, + "heure": 28661, + "▁Richmond": 28662, + "▁Compar": 28663, + "▁Нор": 28664, + "DOC": 28665, + "esia": 28666, + "calc": 28667, + "▁IU": 28668, + "▁vorg": 28669, + "▁habían": 28670, + "çoit": 28671, + "▁arist": 28672, + "▁кли": 28673, + "▁Sue": 28674, + "▁Touch": 28675, + "▁Writing": 28676, + "ifiable": 28677, + "▁wc": 28678, + "▁withdraw": 28679, + "зар": 28680, + "▁presently": 28681, + "▁FK": 28682, + "▁prakt": 28683, + "▁colored": 28684, + "usb": 28685, + "▁Perú": 28686, + "▁plata": 28687, + "▁wishes": 28688, + "▁кам": 28689, + "azar": 28690, + "ável": 28691, + "▁lamp": 28692, + "bishop": 28693, + "▁inclusion": 28694, + "jq": 28695, + "arth": 28696, + "▁Flag": 28697, + "▁нор": 28698, + "ædia": 28699, + "UNCTION": 28700, + "▁Bahnhof": 28701, + "▁approaching": 28702, + "▁Gött": 28703, + "▁cube": 28704, + "▁argued": 28705, + "▁Things": 28706, + "Gui": 28707, + "дови": 28708, + "▁recre": 28709, + "▁réseau": 28710, + "▁significa": 28711, + "Git": 28712, + "gebracht": 28713, + "▁liga": 28714, + "▁assured": 28715, + "alus": 28716, + "рит": 28717, + "▁энциклопеди": 28718, + "▁%).": 28719, + "▁Première": 28720, + "▁declarations": 28721, + "▁tricky": 28722, + "▁profiles": 28723, + "▁Fon": 28724, + "▁Jas": 28725, + "âr": 28726, + "babel": 28727, + "▁Friday": 28728, + "▁június": 28729, + "▁cols": 28730, + "▁EXISTS": 28731, + "▁Italiana": 28732, + "▁authorization": 28733, + "▁sulle": 28734, + "▁Emb": 28735, + "▁Variable": 28736, + "trees": 28737, + "▁Fly": 28738, + "riors": 28739, + "▁damals": 28740, + "▁findet": 28741, + "▁Sept": 28742, + "▁mundial": 28743, + "▁removal": 28744, + "▁longitude": 28745, + "clic": 28746, + "▁fade": 28747, + "▁gradle": 28748, + "▁zák": 28749, + "▁timing": 28750, + "trightarrow": 28751, + "atia": 28752, + "-.": 28753, + "uche": 28754, + "▁serialize": 28755, + "▁Hmm": 28756, + "▁Representatives": 28757, + "bah": 28758, + "rend": 28759, + "assador": 28760, + "▁shield": 28761, + "ucion": 28762, + "▁américaine": 28763, + "zę": 28764, + "villa": 28765, + "▁hombre": 28766, + "áss": 28767, + "▁SF": 28768, + "▁repeating": 28769, + "▁criter": 28770, + "▁Struct": 28771, + "???": 28772, + "▁cheap": 28773, + "▁rings": 28774, + "abhäng": 28775, + "▁corte": 28776, + "▁administ": 28777, + "ixon": 28778, + "gypt": 28779, + "▁puntos": 28780, + "▁mezi": 28781, + "▁pochod": 28782, + "isko": 28783, + "nię": 28784, + "▁осу": 28785, + "▁ár": 28786, + "тельной": 28787, + "▁Metropolitan": 28788, + "jin": 28789, + "zess": 28790, + "▁віці": 28791, + "▁conflicts": 28792, + "ijst": 28793, + "▁Market": 28794, + "стров": 28795, + "▁\",\"": 28796, + "▁Scroll": 28797, + "gun": 28798, + "тара": 28799, + "▁amateur": 28800, + "▁róż": 28801, + "poss": 28802, + "▁generalized": 28803, + "▁Harm": 28804, + "cita": 28805, + "▁Switzerland": 28806, + "icola": 28807, + "▁muit": 28808, + "located": 28809, + "▁có": 28810, + "▁arose": 28811, + "▁communauté": 28812, + "})^": 28813, + "visibility": 28814, + "ída": 28815, + "▁FB": 28816, + "▁Freund": 28817, + "gat": 28818, + "\":{\"": 28819, + "intellij": 28820, + "ifie": 28821, + "hmen": 28822, + "▁édition": 28823, + "▁које": 28824, + "▁інших": 28825, + "oming": 28826, + "▁arquitect": 28827, + "▁Presidente": 28828, + "▁Під": 28829, + "▁cabin": 28830, + "Theorem": 28831, + "▁Gay": 28832, + "ifice": 28833, + "▁hect": 28834, + "lą": 28835, + "irmingham": 28836, + "▁semantic": 28837, + "▁Louisiana": 28838, + "▁sacrifice": 28839, + "▁Christoph": 28840, + "▁Executive": 28841, + "_+": 28842, + "ják": 28843, + "▁seria": 28844, + "▁Overflow": 28845, + "▁Lucy": 28846, + "▁melhor": 28847, + "▁voices": 28848, + "cza": 28849, + "▁капи": 28850, + "▁университета": 28851, + "INCT": 28852, + "▁coloc": 28853, + "▁prue": 28854, + "▁geomet": 28855, + "▁diretto": 28856, + "reso": 28857, + "▁Akt": 28858, + "▁unh": 28859, + "▁сери": 28860, + "▁Alert": 28861, + "Wel": 28862, + "audi": 28863, + "äler": 28864, + "▁guests": 28865, + "▁иде": 28866, + "Studio": 28867, + "▁кате": 28868, + "▁exponent": 28869, + "rze": 28870, + "pmod": 28871, + "rolle": 28872, + "▁Limited": 28873, + "Allemagne": 28874, + "▁pity": 28875, + "▁lä": 28876, + "▁runner": 28877, + "kende": 28878, + "EQ": 28879, + "▁MM": 28880, + "szág": 28881, + "поді": 28882, + "▁regret": 28883, 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30604, + "プ": 30605, + "平": 30606, + "式": 30607, + "ῖ": 30608, + "қ": 30609, + "व": 30610, + "غ": 30611, + "Ò": 30612, + "家": 30613, + "ʒ": 30614, + "サ": 30615, + "≡": 30616, + "ダ": 30617, + "ต": 30618, + "∃": 30619, + "₹": 30620, + "प": 30621, + "第": 30622, + "ര": 30623, + "ض": 30624, + "▄": 30625, + "城": 30626, + "ミ": 30627, + "ɐ": 30628, + "¦": 30629, + "美": 30630, + "件": 30631, + "ნ": 30632, + "Ð": 30633, + "ַ": 30634, + "ニ": 30635, + "部": 30636, + "ņ": 30637, + "ǐ": 30638, + "ט": 30639, + "य": 30640, + "あ": 30641, + "¾": 30642, + "ả": 30643, + "ち": 30644, + "ュ": 30645, + "÷": 30646, + "女": 30647, + "神": 30648, + "♦": 30649, + "¢": 30650, + "以": 30651, + "้": 30652, + "র": 30653, + "太": 30654, + "্": 30655, + "チ": 30656, + "յ": 30657, + "前": 30658, + "金": 30659, + "ւ": 30660, + "野": 30661, + "北": 30662, + "ห": 30663, + "‰": 30664, + "っ": 30665, + "加": 30666, + "原": 30667, + "ʲ": 30668, + "置": 30669, + "安": 30670, + "ガ": 30671, + "我": 30672, + "Ḥ": 30673, + "യ": 30674, + "京": 30675, + "▀": 30676, + "მ": 30677, + "ვ": 30678, + "ʾ": 30679, + "∨": 30680, + "ִ": 30681, + "可": 30682, + "取": 30683, + "县": 30684, + "二": 30685, + "▒": 30686, + "理": 30687, + "自": 30688, + "信": 30689, + "代": 30690, + "ี": 30691, + "צ": 30692, + "်": 30693, + "द": 30694, + "⁸": 30695, + "̯": 30696, + "お": 30697, + "要": 30698, + "ῦ": 30699, + "க": 30700, + "ễ": 30701, + "ु": 30702, + "ƒ": 30703, + "ʰ": 30704, + "化": 30705, + "✓": 30706, + "പ": 30707, + "의": 30708, + "다": 30709, + "木": 30710, + "ُ": 30711, + "̀": 30712, + "ˌ": 30713, + "ह": 30714, + "パ": 30715, + "水": 30716, + "ế": 30717, + "ด": 30718, + "ズ": 30719, + "⁹": 30720, + "島": 30721, + "‍": 30722, + "も": 30723, + "正": 30724, + "■": 30725, + "آ": 30726, + "พ": 30727, + "内": 30728, + "Ì": 30729, + "ǔ": 30730, + "┬": 30731, + "作": 30732, + "合": 30733, + "ὸ": 30734, + "み": 30735, + "▼": 30736, + "ῶ": 30737, + "⊙": 30738, + "~": 30739, + "ị": 30740, + "ْ": 30741, + "回": 30742, + "了": 30743, + "所": 30744, + "事": 30745, + "表": 30746, + "ำ": 30747, + "分": 30748, + "⁷": 30749, + "ү": 30750, + "€": 30751, + "入": 30752, + "全": 30753, + "إ": 30754, + "里": 30755, + "Χ": 30756, + "ं": 30757, + "ハ": 30758, + "ค": 30759, + "⁻": 30760, + "モ": 30761, + "郎": 30762, + "据": 30763, + "●": 30764, + "州": 30765, + "∩": 30766, + "者": 30767, + "通": 30768, + "都": 30769, + "ℤ": 30770, + "♭": 30771, + "╌": 30772, + "つ": 30773, + "ḍ": 30774, + "江": 30775, + "ז": 30776, + "Ý": 30777, + "ө": 30778, + "์": 30779, + "到": 30780, + "ி": 30781, + "ʂ": 30782, + "对": 30783, + "스": 30784, + "使": 30785, + "ি": 30786, + "よ": 30787, + "Ἀ": 30788, + "Ï": 30789, + "∘": 30790, + "사": 30791, + "ন": 30792, + "世": 30793, + "ɕ": 30794, + "կ": 30795, + "უ": 30796, + "ട": 30797, + "ბ": 30798, + "ो": 30799, + "വ": 30800, + "果": 30801, + "十": 30802, + "ุ": 30803, + "藤": 30804, + "来": 30805, + "面": 30806, + "け": 30807, + "ĕ": 30808, + "ビ": 30809, + "这": 30810, + "지": 30811, + "ം": 30812, + "街": 30813, + "石": 30814, + "能": 30815, + "空": 30816, + "տ": 30817, + "ئ": 30818, + "武": 30819, + "ʹ": 30820, + "ϕ": 30821, + "后": 30822, + "ะ": 30823, + "元": 30824, + "ʔ": 30825, + "리": 30826, + "기": 30827, + "河": 30828, + "町": 30829, + "花": 30830, + "ὐ": 30831, + "类": 30832, + "░": 30833, + "物": 30834, + "Η": 30835, + "¸": 30836, + "ு": 30837, + "თ": 30838, + "ث": 30839, + "െ": 30840, + "╠": 30841, + "⊆": 30842, + "》": 30843, + "ツ": 30844, + "版": 30845, + "动": 30846, + "如": 30847, + "真": 30848, + "ɲ": 30849, + "号": 30850, + "ذ": 30851, + "정": 30852, + "林": 30853, + "書": 30854, + "民": 30855, + "口": 30856, + "ّ": 30857, + "示": 30858, + "മ": 30859, + "아": 30860, + "图": 30861, + "∪": 30862, + "戦": 30863, + "李": 30864, + "ല": 30865, + "《": 30866, + "光": 30867, + "白": 30868, + "心": 30869, + "த": 30870, + "ज": 30871, + "设": 30872, + "ί": 30873, + "路": 30874, + "ग": 30875, + "∥": 30876, + "한": 30877, + "最": 30878, + "Ћ": 30879, + "手": 30880, + "ս": 30881, + "?": 30882, + "型": 30883, + "ầ": 30884, + "セ": 30885, + "建": 30886, + "ェ": 30887, + "主": 30888, + "시": 30889, + "대": 30890, + "ῆ": 30891, + "‡": 30892, + "集": 30893, + "დ": 30894, + "目": 30895, + "Ρ": 30896, + "ァ": 30897, + "度": 30898, + "長": 30899, + "星": 30900, + "ノ": 30901, + "ộ": 30902, + "가": 30903, + "五": 30904, + "چ": 30905, + "로": 30906, + "ョ": 30907, + "重": 30908, + "于": 30909, + "发": 30910, + "史": 30911, + "ظ": 30912, + "ช": 30913, + "え": 30914, + "國": 30915, + "ĭ": 30916, + "ப": 30917, + "인": 30918, + "你": 30919, + "駅": 30920, + "‒": 30921, + "♥": 30922, + "多": 30923, + "ħ": 30924, + "Қ": 30925, + "ồ": 30926, + "士": 30927, + "四": 30928, + "┴": 30929, + "ம": 30930, + "司": 30931, + "ে": 30932, + "ὰ": 30933, + "∂": 30934, + "╬": 30935, + "次": 30936, + "Ľ": 30937, + "⟶": 30938, + "立": 30939, + "点": 30940, + "音": 30941, + "⠀": 30942, + "器": 30943, + "하": 30944, + "井": 30945, + "存": 30946, + "ֹ": 30947, + "当": 30948, + "Ë": 30949, + "★": 30950, + "寺": 30951, + "性": 30952, + "也": 30953, + "め": 30954, + "だ": 30955, + "位": 30956, + "ങ": 30957, + "ہ": 30958, + "值": 30959, + "古": 30960, + "გ": 30961, + "ব": 30962, + "院": 30963, + "േ": 30964, + "▶": 30965, + "ர": 30966, + "界": 30967, + "語": 30968, + "സ": 30969, + "수": 30970, + "ǒ": 30971, + "愛": 30972, + "✔": 30973, + "時": 30974, + "ọ": 30975, + "റ": 30976, + "մ": 30977, + "ケ": 30978, + "东": 30979, + "同": 30980, + "주": 30981, + "保": 30982, + "Õ": 30983, + "ố": 30984, + "ἰ": 30985, + "青": 30986, + "ゴ": 30987, + "体": 30988, + "清": 30989, + "相": 30990, + "จ": 30991, + "ء": 30992, + "情": 30993, + "𝕜": 30994, + "ক": 30995, + "ḫ": 30996, + "ờ": 30997, + "将": 30998, + "族": 30999, + "동": 31000, + "Υ": 31001, + "┌": 31002, + "ボ": 31003, + "宮": 31004, + "』": 31005, + "ম": 31006, + "『": 31007, + "ļ": 31008, + "श": 31009, + "ป": 31010, + "Ա": 31011, + "ब": 31012, + "자": 31013, + "政": 31014, + "ா": 31015, + "间": 31016, + "fi": 31017, + "松": 31018, + "ṃ": 31019, + "始": 31020, + "息": 31021, + "少": 31022, + "教": 31023, + "获": 31024, + "列": 31025, + "开": 31026, + "ტ": 31027, + "ワ": 31028, + "კ": 31029, + "科": 31030, + "春": 31031, + "治": 31032, + "吉": 31033, + "ས": 31034, + "ศ": 31035, + "ɒ": 31036, + "台": 31037, + "ネ": 31038, + "း": 31039, + "ĩ": 31040, + "工": 31041, + "ά": 31042, + "知": 31043, + "八": 31044, + "場": 31045, + "画": 31046, + "百": 31047, + "☆": 31048, + "記": 31049, + "得": 31050, + "ソ": 31051, + "氏": 31052, + "ာ": 31053, + "에": 31054, + "ল": 31055, + "ṛ": 31056, + "关": 31057, + "ġ": 31058, + "έ": 31059, + "∑": 31060, + "ベ": 31061, + "标": 31062, + "니": 31063, + "ὴ": 31064, + "ֵ": 31065, + "外": 31066, + "♠": 31067, + "わ": 31068, + "間": 31069, + "ภ": 31070, + "校": 31071, + "制": 31072, + "แ": 31073, + "力": 31074, + "門": 31075, + "好": 31076, + "ғ": 31077, + "Ù": 31078, + "ℓ": 31079, + "ֶ": 31080, + "는": 31081, + "┐": 31082, + "∗": 31083, + "指": 31084, + "色": 31085, + "返": 31086, + "馬": 31087, + "请": 31088, + "≫": 31089, + "風": 31090, + "ό": 31091, + "接": 31092, + "서": 31093, + "↳": 31094, + "せ": 31095, + "志": 31096, + "̲": 31097, + "魔": 31098, + "ң": 31099, + "更": 31100, + "程": 31101, + "김": 31102, + "郡": 31103, + "ོ": 31104, + "ũ": 31105, + "ച": 31106, + "利": 31107, + "県": 31108, + "周": 31109, + "そ": 31110, + "や": 31111, + "谷": 31112, + "香": 31113, + "♯": 31114, + "じ": 31115, + "،": 31116, + "期": 31117, + "∅": 31118, + "┘": 31119, + "初": 31120, + "福": 31121, + "片": 31122, + "ザ": 31123, + "動": 31124, + "参": 31125, + "성": 31126, + "Ə": 31127, + "╦": 31128, + "어": 31129, + "ხ": 31130, + "義": 31131, + "च": 31132, + "象": 31133, + "功": 31134, + "♂": 31135, + "도": 31136, + "고": 31137, + "过": 31138, + "վ": 31139, + "皇": 31140, + "特": 31141, + "ậ": 31142, + "长": 31143, + "英": 31144, + "ấ": 31145, + "ണ": 31146, + "Ъ": 31147, + "স": 31148, + "其": 31149, + "ত": 31150, + "流": 31151, + "除": 31152, + "일": 31153, + "ু": 31154, + "្": 31155, + "永": 31156, + "直": 31157, + "상": 31158, + "千": 31159, + "ắ": 31160, + "館": 31161, + "Ť": 31162, + "朝": 31163, + "ட": 31164, + "ɣ": 31165, + "单": 31166, + "ʀ": 31167, + "格": 31168, + "德": 31169, + "전": 31170, + "☺": 31171, + "ピ": 31172, + "歌": 31173, + "进": 31174, + "限": 31175, + "夫": 31176, + "트": 31177, + "⊢": 31178, + "園": 31179, + "量": 31180, + "土": 31181, + "放": 31182, + "码": 31183, + "等": 31184, + "系": 31185, + "∼": 31186, + "華": 31187, + "↵": 31188, + "소": 31189, + "常": 31190, + "否": 31191, + "見": 31192, + "源": 31193, + "ׁ": 31194, + "实": 31195, + "博": 31196, + "라": 31197, + "원": 31198, + "보": 31199, + "⊕": 31200, + "解": 31201, + "〜": 31202, + "男": 31203, + "দ": 31204, + "ポ": 31205, + "ろ": 31206, + "나": 31207, + "ག": 31208, + "無": 31209, + "Û": 31210, + "̥": 31211, + "ұ": 31212, + "查": 31213, + "̣": 31214, + "╗": 31215, + "╩": 31216, + "条": 31217, + "য": 31218, + "ὁ": 31219, + "後": 31220, + "他": 31221, + "网": 31222, + "ல": 31223, + "≃": 31224, + "화": 31225, + "ە": 31226, + "阿": 31227, + "ေ": 31228, + "户": 31229, + "∫": 31230, + "구": 31231, + "ར": 31232, + "မ": 31233, + "▸": 31234, + "լ": 31235, + "○": 31236, + "命": 31237, + "就": 31238, + "龍": 31239, + "君": 31240, + "夏": 31241, + "": 31242, + "言": 31243, + "先": 31244, + "➜": 31245, + "შ": 31246, + "ძ": 31247, + "ਾ": 31248, + "வ": 31249, + "ど": 31250, + "ヒ": 31251, + "ไ": 31252, + "ன": 31253, + "ば": 31254, + "ギ": 31255, + "գ": 31256, + "ἄ": 31257, + "ヤ": 31258, + "典": 31259, + "府": 31260, + "̄": 31261, + "신": 31262, + "组": 31263, + "改": 31264, + "ὲ": 31265, + "华": 31266, + "与": 31267, + "调": 31268, + "╝": 31269, + "ヴ": 31270, + "ქ": 31271, + "由": 31272, + "修": 31273, + "學": 31274, + "♣": 31275, + "消": 31276, + "符": 31277, + "ʌ": 31278, + "부": 31279, + "ớ": 31280, + "‾": 31281, + "▲": 31282, + "录": 31283, + "ള": 31284, + "연": 31285, + "을": 31286, + "ひ": 31287, + "영": 31288, + "┤": 31289, + "已": 31290, + "陽": 31291, + "င": 31292, + "국": 31293, + "容": 31294, + "未": 31295, + "宗": 31296, + "ᴇ": 31297, + "び": 31298, + "장": 31299, + "龙": 31300, + "්": 31301, + "提": 31302, + "ĝ": 31303, + "六": 31304, + "形": 31305, + "제": 31306, + "Հ": 31307, + "伊": 31308, + "ϵ": 31309, + "ข": 31310, + "Ű": 31311, + "ゃ": 31312, + "火": 31313, + "Ṣ": 31314, + "佐": 31315, + "⊥": 31316, + "̪": 31317, + "ứ": 31318, + "□": 31319, + "结": 31320, + "九": 31321, + "雄": 31322, + "թ": 31323, + "ា": 31324, + "而": 31325, + "བ": 31326, + "우": 31327, + "张": 31328, + "ट": 31329, + "ष": 31330, + "向": 31331, + "ῥ": 31332, + "选": 31333, + "공": 31334, + "ゲ": 31335, + "ʐ": 31336, + "仁": 31337, + "堂": 31338, + "ך": 31339, + "ု": 31340, + "ἔ": 31341, + "അ": 31342, + "ề": 31343, + "ད": 31344, + "선": 31345, + "오": 31346, + "久": 31347, + "œ": 31348, + "义": 31349, + "अ": 31350, + "╔": 31351, + "无": 31352, + "
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"poque": 15635, + "▁Ло": 15636, + "Temp": 15637, + "loaded": 15638, + "▁!==": 15639, + "▁singer": 15640, + "far": 15641, + "▁Comple": 15642, + "▁Österreich": 15643, + "Policy": 15644, + "▁worker": 15645, + "Wrapper": 15646, + "obi": 15647, + "▁discussed": 15648, + "▁buy": 15649, + "▁января": 15650, + "▁Din": 15651, + "▁ged": 15652, + "ској": 15653, + "Europe": 15654, + "▁tall": 15655, + "hos": 15656, + "лаго": 15657, + "▁Block": 15658, + "▁identified": 15659, + "ListView": 15660, + "▁attempting": 15661, + "▁typical": 15662, + "psum": 15663, + "oster": 15664, + "▁журна": 15665, + "Pe": 15666, + "merce": 15667, + "▁unexpected": 15668, + "hui": 15669, + "letter": 15670, + "▁nuevo": 15671, + "▁або": 15672, + "▁VALUES": 15673, + "▁Iz": 15674, + "Flags": 15675, + "▁TRUE": 15676, + "ización": 15677, + "▁growing": 15678, + "estre": 15679, + "▁poly": 15680, + "▁Stone": 15681, + "▁VIII": 15682, + "▁localhost": 15683, + "ählt": 15684, + "▁embedded": 15685, + "jdbc": 15686, + "▁convention": 15687, 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+ "▁Label": 15796, + "Sk": 15797, + "▁кре": 15798, + "▁Литература": 15799, + "▁см": 15800, + "Attributes": 15801, + "aye": 15802, + "ськ": 15803, + "▁высо": 15804, + "-)": 15805, + "oses": 15806, + "calcul": 15807, + "▁Cannot": 15808, + "Generic": 15809, + "emo": 15810, + "▁Autor": 15811, + "лён": 15812, + "лага": 15813, + "vote": 15814, + "licates": 15815, + "rus": 15816, + "éli": 15817, + "opf": 15818, + "atique": 15819, + "scala": 15820, + "▁Ohio": 15821, + "▁Britann": 15822, + "▁bef": 15823, + "▁Евро": 15824, + "▁Career": 15825, + "isée": 15826, + "ót": 15827, + "bose": 15828, + "▁Бер": 15829, + "▁Controller": 15830, + "pole": 15831, + "▁allen": 15832, + "▁hack": 15833, + "▁extent": 15834, + "▁calci": 15835, + "Mer": 15836, + "▁summary": 15837, + "Mart": 15838, + "▁historical": 15839, + "imat": 15840, + "bud": 15841, + "▁FOR": 15842, + "export": 15843, + "edi": 15844, + "Mapping": 15845, + "▁Ay": 15846, + "▁Ruby": 15847, + "▁definitions": 15848, + "▁{$": 15849, + "▁yours": 15850, + 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"pts": 16485, + "▁italien": 16486, + "▁реги": 16487, + "лез": 16488, + "дина": 16489, + "atherine": 16490, + "Internal": 16491, + "Question": 16492, + "▁settlement": 16493, + "▁Все": 16494, + "▁folders": 16495, + "дри": 16496, + "▁valor": 16497, + "▁Miller": 16498, + "▁Assert": 16499, + "▁patient": 16500, + "▁Nieder": 16501, + "▁EP": 16502, + "▁Agr": 16503, + "▁onde": 16504, + "▁scop": 16505, + "sequence": 16506, + "▁PL": 16507, + "▁seek": 16508, + "javase": 16509, + "▁Vector": 16510, + "▁ná": 16511, + "▁categoría": 16512, + "clone": 16513, + "NR": 16514, + "available": 16515, + "▁Besch": 16516, + "▁eclipse": 16517, + "wicklung": 16518, + "deploy": 16519, + "enie": 16520, + "▁\")": 16521, + "äst": 16522, + "▁sync": 16523, + "CODE": 16524, + "▁Че": 16525, + "▁floating": 16526, + "/`": 16527, + "▁retired": 16528, + "deb": 16529, + "▁particul": 16530, + "▁collected": 16531, + "▁downloaded": 16532, + "nice": 16533, + "▁Buffer": 16534, + "▁Account": 16535, + "▁maggio": 16536, + "▁реда": 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16966, + "▁patri": 16967, + "▁Random": 16968, + "▁Returns": 16969, + "ым": 16970, + "рома": 16971, + "▁Studies": 16972, + "Sl": 16973, + "▁frü": 16974, + "TEXT": 16975, + "inate": 16976, + "▁Tol": 16977, + "▁everywhere": 16978, + "arta": 16979, + "▁orbit": 16980, + "▁Aires": 16981, + "▁Iss": 16982, + "▁też": 16983, + "▁diverse": 16984, + "▁numeric": 16985, + "maz": 16986, + "▁mise": 16987, + "▁battery": 16988, + "▁Akadem": 16989, + "нение": 16990, + "▁simultane": 16991, + "▁Dead": 16992, + "▁clust": 16993, + "▁otro": 16994, + "▁cerca": 16995, + "()`,": 16996, + "roz": 16997, + "ăt": 16998, + "▁MO": 16999, + "riften": 17000, + "important": 17001, + "▁jeho": 17002, + "▁findViewById": 17003, + "▁consequence": 17004, + "▁measured": 17005, + "ishes": 17006, + "▁sze": 17007, + "iendo": 17008, + "▁Wahl": 17009, + "strip": 17010, + "ARD": 17011, + "▁opacity": 17012, + "WORD": 17013, + "▁Ві": 17014, + "▁Location": 17015, + "rai": 17016, + "пен": 17017, + "▁rif": 17018, + "aussian": 17019, + "FileName": 17020, + "▁disco": 17021, + "ilen": 17022, + "▁vagy": 17023, + "licity": 17024, + "Border": 17025, + "▁Track": 17026, + "бом": 17027, + "fact": 17028, + "oka": 17029, + "▁gior": 17030, + "▁XVII": 17031, + "▁där": 17032, + "Site": 17033, + "ało": 17034, + "ská": 17035, + "▁pixels": 17036, + "vity": 17037, + "jQuery": 17038, + "▁sculpt": 17039, + "▁cargo": 17040, + "▁directive": 17041, + "▁wal": 17042, + "▁conna": 17043, + "▁Through": 17044, + "▁этом": 17045, + "Static": 17046, + "omsnitt": 17047, + "▁rund": 17048, + "▁claimed": 17049, + "зня": 17050, + "sha": 17051, + "▁rag": 17052, + "crement": 17053, + "▁fünf": 17054, + "▁rival": 17055, + "rin": 17056, + "slash": 17057, + "▁thirty": 17058, + "sleep": 17059, + "ологи": 17060, + "SM": 17061, + "gate": 17062, + "izations": 17063, + "vik": 17064, + "▁bless": 17065, + "▁Illinois": 17066, + "▁TE": 17067, + "uting": 17068, + "▁solving": 17069, + "GER": 17070, + "▁XIV": 17071, + "▁Indians": 17072, + "express": 17073, + "▁Heil": 17074, + "▁mujer": 17075, + "▁invånare": 17076, + "']);": 17077, + "▁aur": 17078, + "boost": 17079, + "GO": 17080, + "▁nin": 17081, + "tok": 17082, + "god": 17083, + "oter": 17084, + ")$$": 17085, + "▁descend": 17086, + "рю": 17087, + "▁Language": 17088, + "▁diver": 17089, + "▁Assuming": 17090, + "▁frequent": 17091, + "чні": 17092, + "▁Biography": 17093, + ",[": 17094, + "urm": 17095, + "▁walked": 17096, + "▁federal": 17097, + "▁Michigan": 17098, + "▁facts": 17099, + "▁Integr": 17100, + "LES": 17101, + "▁Alan": 17102, + "▁coup": 17103, + "Ber": 17104, + "▁particles": 17105, + "ће": 17106, + "Inflater": 17107, + "+(": 17108, + "Bound": 17109, + "▁Sü": 17110, + "Audio": 17111, + "citet": 17112, + "yect": 17113, + "▁nr": 17114, + "xe": 17115, + "▁Brun": 17116, + "▁_,": 17117, + "avor": 17118, + "▁discipl": 17119, + "alm": 17120, + "▁ноября": 17121, + "▁SSL": 17122, + "▁Kaiser": 17123, + "▁recher": 17124, + "ygon": 17125, + "▁regardless": 17126, + "▁configur": 17127, + "▁unnecess": 17128, + "▁Clark": 17129, + "PHP": 17130, + "▁FALSE": 17131, + "▁pad": 17132, + "$}": 17133, + "▁valu": 17134, + "▁disease": 17135, + "▁maior": 17136, + "▁hommes": 17137, + "▁Edition": 17138, + "slant": 17139, + "▁ending": 17140, + "▁settled": 17141, + "urus": 17142, + "hed": 17143, + "Pattern": 17144, + "▁година": 17145, + "▁Philadel": 17146, + "tikzpicture": 17147, + "▁coal": 17148, + "▁sede": 17149, + "▁satisfies": 17150, + "▁trim": 17151, + "▁bat": 17152, + "▁américain": 17153, + "▁luglio": 17154, + "▁поча": 17155, + "ffff": 17156, + "▁Target": 17157, + "generate": 17158, + "▁Zie": 17159, + "ția": 17160, + "▁gard": 17161, + "▁workers": 17162, + "▁Job": 17163, + "▁urban": 17164, + "ahlen": 17165, + "▁Building": 17166, + "▁neu": 17167, + "▁chron": 17168, + "▁Earl": 17169, + "gro": 17170, + "USE": 17171, + "▁XII": 17172, + "▁wealth": 17173, + "inae": 17174, + "▁Бра": 17175, + "▁libert": 17176, + "iros": 17177, + ":$": 17178, + "lee": 17179, + "ieves": 17180, + "▁Justice": 17181, + "▁oil": 17182, + "▁Athlet": 17183, + "▁clo": 17184, + "Scale": 17185, + "▁lips": 17186, + "▁april": 17187, + "▁impression": 17188, + "▁perce": 17189, + "▁участи": 17190, + "vil": 17191, + "éch": 17192, + "▁equality": 17193, + "▁мет": 17194, + "▁annotation": 17195, + "ernal": 17196, + "▁Mach": 17197, + "▁intitul": 17198, + "problem": 17199, + "ющих": 17200, + "oplus": 17201, + "▁thousands": 17202, + "▁calculations": 17203, + "umps": 17204, + "▁triangle": 17205, + "phal": 17206, + "▁Dorf": 17207, + "▁dollars": 17208, + "▁denen": 17209, + "lès": 17210, + "olid": 17211, + "▁Results": 17212, + "▁Stadium": 17213, + "▁Desp": 17214, + "▁Eisen": 17215, + "imir": 17216, + "▁sotto": 17217, + "▁či": 17218, + "atable": 17219, + "orum": 17220, + "▁convergence": 17221, + "▁jeune": 17222, + "oking": 17223, + "▁живо": 17224, + "aining": 17225, + "pointer": 17226, + "culo": 17227, + "▁jsou": 17228, + "▁grab": 17229, + "akte": 17230, + "▁hoping": 17231, + "▁Mak": 17232, + "▁sag": 17233, + "origine": 17234, + "▁послед": 17235, + "▁Veg": 17236, + "▁theoret": 17237, + "▁Tru": 17238, + "nement": 17239, + "▁faces": 17240, + "Hor": 17241, + "Join": 17242, + "arel": 17243, + "▁около": 17244, + "However": 17245, + "▁catal": 17246, + "bourg": 17247, + "▁mysqli": 17248, + "acions": 17249, + "▁Initial": 17250, + "▁rain": 17251, + "iture": 17252, + "▁Sciences": 17253, + "▁Kreis": 17254, + ".__": 17255, + "▁cinq": 17256, + "▁Auß": 17257, + "ithmet": 17258, + "itors": 17259, + "amazon": 17260, + "▁gap": 17261, + "▁ignored": 17262, + "adv": 17263, + "кої": 17264, + "▁часть": 17265, + "▁corpor": 17266, + "цер": 17267, + "▁crime": 17268, + "uous": 17269, + "▁налази": 17270, + "DataFrame": 17271, + "води": 17272, + "Ign": 17273, + "▁Lincoln": 17274, + "▁menos": 17275, + "▁Luft": 17276, + "▁Lind": 17277, + "▁Cook": 17278, + "▁materials": 17279, + "apped": 17280, + "ignore": 17281, + "▁откры": 17282, + "fried": 17283, + "▁gouvernement": 17284, + "▁fired": 17285, + "▁screenshot": 17286, + "сен": 17287, + "▁[(": 17288, + "▁организа": 17289, + "Graphics": 17290, + "▁проти": 17291, + "▁phen": 17292, + "craft": 17293, + "▁brain": 17294, + "▁Como": 17295, + "▁Everything": 17296, + "anes": 17297, + "IGN": 17298, + "▁nederbörd": 17299, + "▁Forest": 17300, + "zahl": 17301, + "▁Among": 17302, + "Qt": 17303, + "▁togg": 17304, + "▁variant": 17305, + "▁hill": 17306, + "писи": 17307, + "colon": 17308, + "▁dicembre": 17309, + "гор": 17310, + "▁Wind": 17311, + "ünstler": 17312, + "▁=\\": 17313, + "saved": 17314, + "▁nej": 17315, + "unte": 17316, + "utto": 17317, + "▁recens": 17318, + "▁sick": 17319, + "▁desen": 17320, + "UST": 17321, + "▁worst": 17322, + "▁Angel": 17323, + "odox": 17324, + "▁Province": 17325, + "▁Maz": 17326, + "▁agreement": 17327, + "▁Bass": 17328, + "▁segunda": 17329, + "onces": 17330, + "▁Linki": 17331, + "▁CL": 17332, + "▁já": 17333, + "itement": 17334, + "▁área": 17335, + "▁scalar": 17336, + "▁Рес": 17337, + "awt": 17338, + "sieme": 17339, + "▁juni": 17340, + "▁худож": 17341, + "ikus": 17342, + "▁lid": 17343, + "ppel": 17344, + "avi": 17345, + "▁balance": 17346, + "ipping": 17347, + "cussion": 17348, + "ческих": 17349, + "(\".": 17350, + "Also": 17351, + "▁whis": 17352, + "HOME": 17353, + "▁brown": 17354, + "▁día": 17355, + "▁può": 17356, + "plotlib": 17357, + "▁Jahrhunderts": 17358, + "DK": 17359, + "▁anchor": 17360, + "...]": 17361, + "▁Austria": 17362, + "▁marca": 17363, + "▁gez": 17364, + "iously": 17365, + "▁lazy": 17366, + "xa": 17367, + "▁Channel": 17368, + "▁neuen": 17369, + "das": 17370, + "▁searched": 17371, + "▁staat": 17372, + "▁Так": 17373, + "▁Josef": 17374, + "▁Sher": 17375, + "pois": 17376, + "▁enem": 17377, + "▁accessing": 17378, + "▁неко": 17379, + "▁furono": 17380, + "▁pseudo": 17381, + "?>": 17382, + "▁estadoun": 17383, + "▁Види": 17384, + "▁motiv": 17385, + "▁recall": 17386, + "isson": 17387, + "ób": 17388, + ")--": 17389, + "▁Erz": 17390, + "▁савез": 17391, + "Direct": 17392, + "соб": 17393, + "▁sho": 17394, + "völker": 17395, + "Ap": 17396, + "gens": 17397, + "ништво": 17398, + "▁Amsterdam": 17399, + "usk": 17400, + "пло": 17401, + "▁simulation": 17402, + "▁BC": 17403, + "▁Woj": 17404, + "autom": 17405, + "Alex": 17406, + "▁economic": 17407, + "гом": 17408, + "ikai": 17409, + "▁altre": 17410, + "▁'-": 17411, + "▁Weg": 17412, + "NotFound": 17413, + "йской": 17414, + "▁converting": 17415, + "phabet": 17416, + "atrice": 17417, + "bourne": 17418, + "alom": 17419, + "▁comparing": 17420, + "▁Zo": 17421, + "▁fla": 17422, + "вая": 17423, + "▁entra": 17424, + "▁charset": 17425, + "developers": 17426, + "ística": 17427, + "}>": 17428, + "▁Jazz": 17429, + "▁Howard": 17430, + "шта": 17431, + "▁clone": 17432, + "door": 17433, + "▁Pin": 17434, + "***": 17435, + "▁silent": 17436, + "ecycle": 17437, + "isce": 17438, + "▁mud": 17439, + "▁Display": 17440, + "▁lip": 17441, + "▁использова": 17442, + "▁characteristic": 17443, + "▁sb": 17444, + "firebase": 17445, + "▁Bew": 17446, + "Calendar": 17447, + "▁uso": 17448, + "èse": 17449, + "▁Rat": 17450, + "▁esper": 17451, + "▁throwing": 17452, + "▁rodz": 17453, + "▁yards": 17454, + "▁grass": 17455, + "▁marker": 17456, + "▁Kos": 17457, + "Theta": 17458, + "▁organis": 17459, + "kernel": 17460, + "▁personas": 17461, + "keep": 17462, + "▁exclaimed": 17463, + "oslav": 17464, + "▁Entertain": 17465, + "нер": 17466, + "▁inwon": 17467, + "▁Rand": 17468, + "reduce": 17469, + "fac": 17470, + "expression": 17471, + "yj": 17472, + "▁differenti": 17473, + "aglia": 17474, + "▁templates": 17475, + "▁mű": 17476, + "▁prv": 17477, + "▁mois": 17478, + "▁gewann": 17479, + "▁була": 17480, + "bibli": 17481, + "demo": 17482, + "▁Anderson": 17483, + "▁ред": 17484, + "▁porque": 17485, + "▁Pologne": 17486, + "▁trip": 17487, + "▁exemple": 17488, + "▁Internacional": 17489, + "▁као": 17490, + "Insert": 17491, + "general": 17492, + "SESSION": 17493, + "berga": 17494, + "hält": 17495, + "unas": 17496, + "мира": 17497, + "▁yields": 17498, + "mapsto": 17499, + "spot": 17500, + "▁+\\": 17501, + "лла": 17502, + "▁precisely": 17503, + "▁член": 17504, + "shadow": 17505, + "Are": 17506, + "unal": 17507, + "▁dispar": 17508, + "▁título": 17509, + "nest": 17510, + "▁Low": 17511, + "▁prot": 17512, + "▁Costa": 17513, + "named": 17514, + "▁gained": 17515, + "lesia": 17516, + "▁administration": 17517, + "Import": 17518, + "branch": 17519, + "▁sympath": 17520, + "voj": 17521, + "▁EC": 17522, + "▁municipio": 17523, + "▁animated": 17524, + "▁directories": 17525, + "▁roof": 17526, + "ząd": 17527, + "imet": 17528, + "proto": 17529, + "bla": 17530, + ":]": 17531, + "have": 17532, + "atem": 17533, + "▁ns": 17534, + "▁sector": 17535, + "three": 17536, + "owane": 17537, + "wers": 17538, + "ових": 17539, + "rence": 17540, + "▁extr": 17541, + "igten": 17542, + "▁occident": 17543, + "ță": 17544, + "▁eat": 17545, + "▁hydro": 17546, + "ubernetes": 17547, + "[@": 17548, + "▁Moon": 17549, + "▁Sho": 17550, + "▁elsewhere": 17551, + "üller": 17552, + "Upload": 17553, + "ланд": 17554, + "▁För": 17555, + "wissenschaft": 17556, + "KS": 17557, + "▁physics": 17558, + "tz": 17559, + "▁серед": 17560, + "▁Arbeit": 17561, + "▁мест": 17562, + "▁Gebiet": 17563, + "▁insect": 17564, + "Ah": 17565, + "izado": 17566, + "▁temple": 17567, + "▁annual": 17568, + "stad": 17569, + "▁habitat": 17570, + "▁AB": 17571, + "wort": 17572, + "▁repos": 17573, + "▁Neu": 17574, + "▁$(\".": 17575, + "Vorlage": 17576, + "▁reprezent": 17577, + "estanden": 17578, + "Intern": 17579, + ".`": 17580, + "▁failing": 17581, + "▁Material": 17582, + "▁effectively": 17583, + "телем": 17584, + "▁гла": 17585, + "▁nahm": 17586, + "▁differently": 17587, + "extension": 17588, + "▁Verm": 17589, + "enabled": 17590, + "configure": 17591, + "nio": 17592, + "ciones": 17593, + "▁Beach": 17594, + "сона": 17595, + "▁copying": 17596, + "▁україн": 17597, + "▁призна": 17598, + "zh": 17599, + "Desktop": 17600, + "▁sost": 17601, + "▁subsequently": 17602, + "▁Lehr": 17603, + "▁ó": 17604, + "lär": 17605, + "odor": 17606, + "phon": 17607, + "nc": 17608, + "iterator": 17609, + "▁эти": 17610, + "▁europé": 17611, + "▁Toronto": 17612, + "ódigo": 17613, + "▁posto": 17614, + "ffe": 17615, + "▁crew": 17616, + "▁Schwar": 17617, + "Sa": 17618, + "square": 17619, + "▁beside": 17620, + "▁Мі": 17621, + "▁ath": 17622, + "▁advent": 17623, + "cji": 17624, + "written": 17625, + "▁russ": 17626, + "rost": 17627, + "HI": 17628, + "▁dice": 17629, + "cca": 17630, + "▁dép": 17631, + "ply": 17632, + "bigg": 17633, + "ział": 17634, + "ütt": 17635, + "▁одно": 17636, + "JECT": 17637, + "ському": 17638, + "nos": 17639, + "mock": 17640, + "Launch": 17641, + "same": 17642, + "▁jobs": 17643, + "▁widely": 17644, + "▁defines": 17645, + "▁Pse": 17646, + "▁neighbour": 17647, + "ющие": 17648, + "▁closer": 17649, + "▁располо": 17650, + "▁clubs": 17651, + "fly": 17652, + "шим": 17653, + "▁suffered": 17654, + "▁nar": 17655, + "▁lavor": 17656, + "Extension": 17657, + "itionally": 17658, + "▁grace": 17659, + "▁Campeonato": 17660, + "▁Christmas": 17661, + "middle": 17662, + "othek": 17663, + "elements": 17664, + "▁sondern": 17665, + "▁tarde": 17666, + "▁permanent": 17667, + "▁conclude": 17668, + "Seg": 17669, + "▁акаде": 17670, + "}\",": 17671, + "▁февраля": 17672, + "řed": 17673, + "▁IL": 17674, + "jud": 17675, + "▁USS": 17676, + "▁Nature": 17677, + "ifference": 17678, + "Serializer": 17679, + "▁twelve": 17680, + "tid": 17681, + "мия": 17682, + "ческого": 17683, + "▁calendar": 17684, + "concat": 17685, + "▁intersection": 17686, + "▁PA": 17687, + "azure": 17688, + "▁située": 17689, + "▁kinds": 17690, + "▁ausge": 17691, + "▁rural": 17692, + "Theme": 17693, + "▁tale": 17694, + "noindent": 17695, + "going": 17696, + "rx": 17697, + "agi": 17698, + "wrapper": 17699, + "▁Coast": 17700, + "mbH": 17701, + "▁перед": 17702, + "spre": 17703, + "▁}\\": 17704, + "▁LI": 17705, + "znam": 17706, + "itled": 17707, + "Sample": 17708, + "uliar": 17709, + "*\\": 17710, + "▁resistance": 17711, + "stock": 17712, + "ked": 17713, + "▁HE": 17714, + "▁possession": 17715, + "▁Ring": 17716, + "▁magyar": 17717, + "outs": 17718, + "▁Secretary": 17719, + "nde": 17720, + "▁Wald": 17721, + "-(": 17722, + "▁ISO": 17723, + "▁afternoon": 17724, + "ionen": 17725, + "▁stops": 17726, + "▁constants": 17727, + "guard": 17728, + "bow": 17729, + "▁ers": 17730, + "▁Firebase": 17731, + "▁Clear": 17732, + "▁Holy": 17733, + "Win": 17734, + "▁titles": 17735, + "▁трав": 17736, + "▁contrib": 17737, + "häng": 17738, + "▁photograph": 17739, + "▁Distribution": 17740, + "ifts": 17741, + "▁aunque": 17742, + "comb": 17743, + "ADD": 17744, + "▁publication": 17745, + "▁служ": 17746, + "▁кня": 17747, + "▁ayant": 17748, + "▁restore": 17749, + "▁belief": 17750, + "▁vég": 17751, + "▁extensions": 17752, + "▁decom": 17753, + "вший": 17754, + "WT": 17755, + "▁parti": 17756, + "▁gioc": 17757, + "▁мира": 17758, + "▁issu": 17759, + "pipe": 17760, + "▁props": 17761, + "▁willing": 17762, + "▁nest": 17763, + "aso": 17764, + "pot": 17765, + "▁handles": 17766, + "▁фо": 17767, + "▁moder": 17768, + "▁ebenfalls": 17769, + "▁fighting": 17770, + "umbn": 17771, + "▁transparent": 17772, + "▁Krist": 17773, + "▁homes": 17774, + "▁voyage": 17775, + "Failed": 17776, + "▁Bird": 17777, + "▁Heart": 17778, + "Counter": 17779, + "▁Scottish": 17780, + "ática": 17781, + "▁arbeit": 17782, + "^{-\\": 17783, + "▁Sor": 17784, + "▁engaged": 17785, + "▁aside": 17786, + "▁Fou": 17787, + "▁wiel": 17788, + "▁reconst": 17789, + "ousin": 17790, + "▁hosted": 17791, + "▁classe": 17792, + "▁contest": 17793, + "...\"": 17794, + "мом": 17795, + "▁bean": 17796, + "gem": 17797, + "▁consultato": 17798, + "▁bio": 17799, + "▁subjects": 17800, + "boBox": 17801, + "▁Schrift": 17802, + "▁dinner": 17803, + "ăr": 17804, + "▁równ": 17805, + "▁%%": 17806, + "bage": 17807, + "▁veröff": 17808, + "▁detected": 17809, + "ienn": 17810, + "rose": 17811, + "▁Ton": 17812, + "Complete": 17813, + "▁proto": 17814, + "ichts": 17815, + "STAT": 17816, + "Checked": 17817, + "▁inten": 17818, + "▁smile": 17819, + "▁strip": 17820, + "neut": 17821, + "');\r": 17822, + "four": 17823, + "▁todas": 17824, + "Controls": 17825, + "▁thorough": 17826, + "rup": 17827, + "▁држави": 17828, + "ită": 17829, + "Protocol": 17830, + "Ка": 17831, + "▁expanded": 17832, + "extra": 17833, + "oport": 17834, + "▁Станов": 17835, + "leases": 17836, + "▁notion": 17837, + "▁guest": 17838, + "▁Islands": 17839, + "icked": 17840, + "▁Dave": 17841, + "▁reflection": 17842, + "liv": 17843, + "ální": 17844, + "▁revealed": 17845, + "▁sog": 17846, + "▁Tax": 17847, + "▁periodo": 17848, + "▁Weltkrie": 17849, + "catalina": 17850, + "qué": 17851, + "▁Father": 17852, + "▁Bir": 17853, + "expect": 17854, + "▁regression": 17855, + "iné": 17856, + "▁dabei": 17857, + "perm": 17858, + "мене": 17859, + "▁Abd": 17860, + "▁CF": 17861, + "arks": 17862, + "resolve": 17863, + "wedge": 17864, + "▁initialization": 17865, + "▁Véase": 17866, + "▁приня": 17867, + "stmt": 17868, + "▁income": 17869, + "MY": 17870, + "▁odkazy": 17871, + "▁Siehe": 17872, + "▁bodies": 17873, + "▁soc": 17874, + "Random": 17875, + "▁senza": 17876, + "ablo": 17877, + "▁regarded": 17878, + "onCreate": 17879, + "▁Magazine": 17880, + "▁Raf": 17881, + "▁Buenos": 17882, + "ил": 17883, + ")));": 17884, + "capt": 17885, + "redirect": 17886, + "▁petit": 17887, + "▁farm": 17888, + "▁rôle": 17889, + "▁статьи": 17890, + "    ": 17891, + "subfigure": 17892, + "èces": 17893, + "ziel": 17894, + "▁окон": 17895, + "EE": 17896, + "mee": 17897, + "▁perten": 17898, + "▁représent": 17899, + "▁LA": 17900, + "?'": 17901, + "▁тру": 17902, + "▁rational": 17903, + "osof": 17904, + "▁kne": 17905, + "▁artists": 17906, + "Flow": 17907, + "▁Аль": 17908, + "izard": 17909, + "▁numero": 17910, + "actic": 17911, + "▁destruct": 17912, + "▁Пра": 17913, + "onsieur": 17914, + "qt": 17915, + "abestanden": 17916, + "ność": 17917, + "Connect": 17918, + "▁oracle": 17919, + "▁Stockholm": 17920, + "sizeof": 17921, + "▁gemäß": 17922, + "ACT": 17923, + "▁expert": 17924, + "utions": 17925, + "▁hacia": 17926, + "▁logger": 17927, + "▁fool": 17928, + "rypto": 17929, + "ær": 17930, + "▁cidade": 17931, + "▁составе": 17932, + "oker": 17933, + "▁Transfer": 17934, + "▁denied": 17935, + "Track": 17936, + "▁radi": 17937, + "zec": 17938, + "▁Historic": 17939, + "▁Einwohner": 17940, + "кою": 17941, + "▁хра": 17942, + "▁Category": 17943, + "▁Disney": 17944, + "▁swap": 17945, + "Begin": 17946, + "▁mientras": 17947, + "▁dance": 17948, + "▁tête": 17949, + "▁droit": 17950, + "erta": 17951, + "▁birds": 17952, + "▁convin": 17953, + "parator": 17954, + "дра": 17955, + "▁ES": 17956, + "▁Ressources": 17957, + "EGIN": 17958, + "ücke": 17959, + "▁Cruz": 17960, + "abling": 17961, + "▁\"@": 17962, + "▁metres": 17963, + "▁Beg": 17964, + "▁Gründ": 17965, + "▁Boh": 17966, + "▁mile": 17967, + "▁Technology": 17968, + "\"+": 17969, + "acco": 17970, + "▁ss": 17971, + "▁Fed": 17972, + "▁Hend": 17973, + "usch": 17974, + "itä": 17975, + "folk": 17976, + "▁absor": 17977, + "antal": 17978, + "odge": 17979, + "▁WHEN": 17980, + "▁Externí": 17981, + "▁Regiment": 17982, + "▁evaluation": 17983, + "▁Tai": 17984, + "▁vocals": 17985, + "▁experimental": 17986, + "embed": 17987, + "▁Minn": 17988, + "▁вме": 17989, + "prec": 17990, + "every": 17991, + "▁hoof": 17992, + "▁Fernando": 17993, + "▁Bibliographie": 17994, + "▁nag": 17995, + "amerikanischer": 17996, + "▁marks": 17997, + "▁UTC": 17998, + "▁uncertain": 17999, + "дия": 18000, + "olia": 18001, + "▁cup": 18002, + "▁fille": 18003, + "▁dok": 18004, + "useppe": 18005, + "esterd": 18006, + "▁Brand": 18007, + "▁Third": 18008, + "PP": 18009, + "nodes": 18010, + "▁Pad": 18011, + "▁loved": 18012, + "swing": 18013, + "▁surprised": 18014, + "ardi": 18015, + "▁GR": 18016, + "]\"": 18017, + "▁equally": 18018, + "ihe": 18019, + "care": 18020, + "писок": 18021, + "lijk": 18022, + "rinn": 18023, + "▁\\[\\": 18024, + "▁sons": 18025, + "▁tät": 18026, + "icamente": 18027, + "▁listing": 18028, + "iellement": 18029, + "▁nyelven": 18030, + "▁ds": 18031, + "▁agricult": 18032, + "▁Hermann": 18033, + "▁besides": 18034, + "progress": 18035, + "▁peculiar": 18036, + "focus": 18037, + "cn": 18038, + "-$": 18039, + "ственный": 18040, + "ourg": 18041, + "▁wyn": 18042, + "▁conducted": 18043, + "▁Становништво": 18044, + "connected": 18045, + "▁bott": 18046, + "▁смер": 18047, + "▁Poz": 18048, + "unct": 18049, + "conda": 18050, + "▁савезној": 18051, + "▁havet": 18052, + "ligt": 18053, + "orted": 18054, + "▁entering": 18055, + "multip": 18056, + "▁Temple": 18057, + "▁Plant": 18058, + "typeof": 18059, + "▁Vlad": 18060, + "▁qued": 18061, + "▁reste": 18062, + "▁май": 18063, + "▁Very": 18064, + "ambiguation": 18065, + "▁challeng": 18066, + "▁respective": 18067, + "▁тор": 18068, + "Ctrl": 18069, + "▁absence": 18070, + "aru": 18071, + "вое": 18072, + "▁först": 18073, + "▁sq": 18074, + "▁Emperor": 18075, + "▁Ign": 18076, + "▁това": 18077, + ":`": 18078, + "adoop": 18079, + "▁Madame": 18080, + "▁gruppo": 18081, + "stud": 18082, + "▁externas": 18083, + "▁Александр": 18084, + "▁dign": 18085, + "▁живе": 18086, + "Amount": 18087, + "▁correlate": 18088, + "▁Fant": 18089, + "▁rails": 18090, + "fp": 18091, + "министратив": 18092, + "▁bought": 18093, + "▁filters": 18094, + "▁ancora": 18095, + "▁partner": 18096, + "▁quand": 18097, + "symbol": 18098, + "ulating": 18099, + "▁zd": 18100, + "awn": 18101, + "▁Grant": 18102, + "because": 18103, + "rable": 18104, + "\\}": 18105, + "ísticas": 18106, + "▁уче": 18107, + "▁période": 18108, + "▁ske": 18109, + "▁Anyway": 18110, + "▁indexes": 18111, + "▁directions": 18112, + "▁RAM": 18113, + "chrome": 18114, + "▁apost": 18115, + "▁warnings": 18116, + "▁Airport": 18117, + "VI": 18118, + "abile": 18119, + "▁lord": 18120, + "provider": 18121, + "▁Ji": 18122, + "ostream": 18123, + "▁gemeente": 18124, + "tableView": 18125, + "Extra": 18126, + "cursor": 18127, + "eground": 18128, + "▁Moz": 18129, + "▁rib": 18130, + "▁morph": 18131, + "loads": 18132, + "elsk": 18133, + "▁MAX": 18134, + "▁Santiago": 18135, + "▁Him": 18136, + "codes": 18137, + "▁lanz": 18138, + "▁counts": 18139, + "rinningsområ": 18140, + "щё": 18141, + "▁spé": 18142, + "▁pierws": 18143, + "▁Sver": 18144, + "▁acknow": 18145, + "Boolean": 18146, + "▁фамили": 18147, + "▁Senate": 18148, + "шов": 18149, + "agers": 18150, + "▁Nueva": 18151, + "bil": 18152, + "kiem": 18153, + "▁Mey": 18154, + "wij": 18155, + "▁GmbH": 18156, + "validation": 18157, + "▁ensuite": 18158, + "inking": 18159, + "▁campion": 18160, + "▁financial": 18161, + "izon": 18162, + "Headers": 18163, + "▁deprecated": 18164, + "▁fonction": 18165, + "REG": 18166, + "▁volumes": 18167, + "▁Chi": 18168, + "▁encountered": 18169, + "lak": 18170, + "рая": 18171, + "▁continues": 18172, + "▁~[": 18173, + "uerte": 18174, + "▁\\;": 18175, + "▁Dok": 18176, + "▁weights": 18177, + "▁rh": 18178, + "▁Napole": 18179, + "▁naturally": 18180, + "sku": 18181, + "pas": 18182, + "▁gegründ": 18183, + "etr": 18184, + "▁Ku": 18185, + "icted": 18186, + "▁fabric": 18187, + "▁ASC": 18188, + "▁Entertainment": 18189, + "▁energ": 18190, + "клад": 18191, + "omon": 18192, + "theme": 18193, + "▁харак": 18194, + "▁draft": 18195, + "▁channels": 18196, + "▁desert": 18197, + "▁través": 18198, + "▁Lock": 18199, + "▁siendo": 18200, + "фек": 18201, + "même": 18202, + "▁packet": 18203, + "▁Mountain": 18204, + "▁Fahr": 18205, + "braio": 18206, + "пере": 18207, + "▁genannt": 18208, + "▁deployment": 18209, + "Pal": 18210, + "ног": 18211, + "стру": 18212, + "Prim": 18213, + "für": 18214, + "▁dangerous": 18215, + "▁szám": 18216, + "reck": 18217, + "▁popup": 18218, + "icky": 18219, + "inar": 18220, + "cowo": 18221, + "нцикло": 18222, + "ítás": 18223, + "▁plugins": 18224, + "▁driven": 18225, + "лев": 18226, + "▁\"(": 18227, + "tta": 18228, + "▁Ú": 18229, + "▁eb": 18230, + "▁'';": 18231, + "▁knock": 18232, + "▁основа": 18233, + "▁maison": 18234, + "гля": 18235, + "▁Honor": 18236, + "tail": 18237, + "ritz": 18238, + "▁guys": 18239, + "▁combinations": 18240, + "ondere": 18241, + "▁Ald": 18242, + "▁fiddle": 18243, + "дав": 18244, + "urd": 18245, + "▁projection": 18246, + "▁También": 18247, + "verb": 18248, + "▁terre": 18249, + "rugu": 18250, + "▁september": 18251, + "▁=": 18572, + "▁Beat": 18573, + "▁Sax": 18574, + "vertical": 18575, + "кто": 18576, + "▁plants": 18577, + "▁Références": 18578, + "▁ogni": 18579, + "▁curs": 18580, + "▁SK": 18581, + "они": 18582, + "▁destac": 18583, + "\");\r": 18584, + "▁Sure": 18585, + "▁partido": 18586, + "▁Folge": 18587, + "▁Moore": 18588, + "▁wz": 18589, + "скус": 18590, + "ltre": 18591, + "ondo": 18592, + "▁pose": 18593, + "imos": 18594, + "бой": 18595, + "ципа": 18596, + "jus": 18597, + ".....": 18598, + "▁época": 18599, + "▁quanto": 18600, + "▁Support": 18601, + "geschichte": 18602, + "SERVER": 18603, + "▁Georges": 18604, + "enum": 18605, + "▁herm": 18606, + "▁nebo": 18607, + "▁Chr": 18608, + "character": 18609, + "▁***": 18610, + "▁Forsch": 18611, + "iami": 18612, + "▁¿": 18613, + "cych": 18614, + "▁fifth": 18615, + "sent": 18616, + "▁anderem": 18617, + "▁proportion": 18618, + "▁prest": 18619, + "▁Girl": 18620, + "▁drama": 18621, + "wand": 18622, + "▁Mail": 18623, + "▁Lux": 18624, + "▁který": 18625, + "▁Gesellschaft": 18626, + "▁Hinweis": 18627, + "nisse": 18628, + "▁mondo": 18629, + "Eq": 18630, + "▁perí": 18631, + "▁eastern": 18632, + "▁UEFA": 18633, + "uale": 18634, + "▁convex": 18635, + "▁поль": 18636, + "▁Hey": 18637, + "zenie": 18638, + "initely": 18639, + "▁Zusammen": 18640, + "SSL": 18641, + "ocal": 18642, + "▁canal": 18643, + "voy": 18644, + "▁Кри": 18645, + "▁között": 18646, + "▁cars": 18647, + "▁versión": 18648, + "Environment": 18649, + "Her": 18650, + "▁señ": 18651, + "▁spatial": 18652, + "ymi": 18653, + "Fire": 18654, + "▁veget": 18655, + "▁Wie": 18656, + "▁znaj": 18657, + "▁damage": 18658, + "▁endl": 18659, + "gif": 18660, + "▁quali": 18661, + "▁которых": 18662, + "ellan": 18663, + "▁mens": 18664, + "▁plug": 18665, + "▁abund": 18666, + "FIG": 18667, + "▁sf": 18668, + "▁confl": 18669, + "▁населения": 18670, + "▁principles": 18671, + "▁Gabriel": 18672, + "ibe": 18673, + "▁{%": 18674, + "▁població": 18675, + "ніципа": 18676, + "▁extreme": 18677, + "▁asse": 18678, + "▁vu": 18679, + "Mock": 18680, + "▁spielte": 18681, + "▁Aer": 18682, + "▁datos": 18683, + "endes": 18684, + "▁Gel": 18685, + "▁Gor": 18686, + "Christ": 18687, + "chos": 18688, + "Processor": 18689, + "▁instruct": 18690, + "▁picked": 18691, + "nahme": 18692, + "fahr": 18693, + "▁indicated": 18694, + "▁%.": 18695, + "▁ts": 18696, + "▁notable": 18697, + "▁qualified": 18698, + "▁Ал": 18699, + "Black": 18700, + "▁council": 18701, + "▁overhead": 18702, + "aci": 18703, + "année": 18704, + "▁initWith": 18705, + "bió": 18706, + "▁introduction": 18707, + "▁companion": 18708, + "▁expon": 18709, + "▁kör": 18710, + "oby": 18711, + "burn": 18712, + "gnu": 18713, + "virtual": 18714, + "▁intellect": 18715, + "▁держа": 18716, + "'+": 18717, + "бле": 18718, + "▁strictly": 18719, + "▁recognize": 18720, + "hour": 18721, + "▁Wrest": 18722, + "ennen": 18723, + "$).": 18724, + "fff": 18725, + "▁Centro": 18726, + "▁Pitt": 18727, + "▁dział": 18728, + "▁cela": 18729, + "▁francese": 18730, + "рами": 18731, + "special": 18732, + "▁Dup": 18733, + "toire": 18734, + "каль": 18735, + "COUNT": 18736, + "▁Brook": 18737, + "▁руково": 18738, + "publique": 18739, + "▁seconda": 18740, + "▁compt": 18741, + "▁bland": 18742, + "Before": 18743, + "▁Pack": 18744, + "alty": 18745, + "öder": 18746, + "▁intervals": 18747, + "▁Datenbank": 18748, + "Movie": 18749, + "▁transm": 18750, + "▁tap": 18751, + "▁поч": 18752, + "fon": 18753, + "iai": 18754, + "▁fib": 18755, + "▁wyd": 18756, + "▁hung": 18757, + "▁alive": 18758, + "Clear": 18759, + "▁pushed": 18760, + "▁tuple": 18761, + "achen": 18762, + "гово": 18763, + "▁revers": 18764, + "▁augment": 18765, + "▁challenge": 18766, + "lost": 18767, + "▁deuxième": 18768, + "structor": 18769, + "▁mehrerer": 18770, + "atural": 18771, + "Split": 18772, + "стем": 18773, + "шла": 18774, + ")\\\\": 18775, + "▁Dog": 18776, + "▁developers": 18777, + "▁nod": 18778, + "▁сторо": 18779, + "▁NaN": 18780, + "▁priest": 18781, + "▁exha": 18782, + "UND": 18783, + "pair": 18784, + "alone": 18785, + "▁moon": 18786, + "▁#!/": 18787, + "▁guns": 18788, + "rola": 18789, + "чита": 18790, + "▁Encyclopedia": 18791, + "atis": 18792, + "▁'\"": 18793, + "zych": 18794, + "▁superfic": 18795, + "▁эк": 18796, + "едера": 18797, + "feed": 18798, + "LAY": 18799, + "Fi": 18800, + "unks": 18801, + "isecond": 18802, + "▁'@": 18803, + "▁Adding": 18804, + "рое": 18805, + "▁tang": 18806, + "цо": 18807, + "hung": 18808, + "bis": 18809, + "ského": 18810, + "▁advert": 18811, + "▁занима": 18812, + "uzz": 18813, + "ágina": 18814, + "▁Tel": 18815, + "sig": 18816, + "▁Ez": 18817, + "▁guarantee": 18818, + "▁teaching": 18819, + "oty": 18820, + "termin": 18821, + "▁distributions": 18822, + "FLA": 18823, + "▁Giuseppe": 18824, + "querySelector": 18825, + "▁/\\": 18826, + "▁Squad": 18827, + "gz": 18828, + "delay": 18829, + "▁surrounding": 18830, + "▁manus": 18831, + "▁Hou": 18832, + "²,": 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"▁enorm": 18886, + ",’": 18887, + "▁Christopher": 18888, + "jev": 18889, + "▁quad": 18890, + "▁AJAX": 18891, + "▁relief": 18892, + "▁modes": 18893, + "sklär": 18894, + "▁Vid": 18895, + "▁Serial": 18896, + "▁tokens": 18897, + "▁Poland": 18898, + "\\]": 18899, + "▁vide": 18900, + "rooms": 18901, + "omas": 18902, + "▁Bureau": 18903, + "cx": 18904, + "ностью": 18905, + "▁signs": 18906, + "шение": 18907, + "lossen": 18908, + "▁Queens": 18909, + "▁membre": 18910, + "▁mez": 18911, + "▁Bool": 18912, + "▁Naj": 18913, + "▁Memory": 18914, + "▁Khan": 18915, + "▁là": 18916, + "▁Hud": 18917, + "▁dismiss": 18918, + "ighth": 18919, + "▁fs": 18920, + "prevent": 18921, + "▁меда": 18922, + "▁Police": 18923, + "▁ско": 18924, + "finite": 18925, + "▁ami": 18926, + "▁Much": 18927, + "owania": 18928, + "ORY": 18929, + "iors": 18930, + "▁Premio": 18931, + "▁textbox": 18932, + "dm": 18933, + "▁afin": 18934, + "▁Donald": 18935, + "▁Priv": 18936, + "▁decid": 18937, + "▁Maurice": 18938, + "agan": 18939, + 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"▁Pho": 21884, + "kem": 21885, + "▁Customer": 21886, + "▁складі": 21887, + "▁courses": 21888, + "Platform": 21889, + "navbar": 21890, + "learning": 21891, + "▁Swedish": 21892, + "▁zast": 21893, + "▁Lig": 21894, + "management": 21895, + "▁lod": 21896, + "uffle": 21897, + "Texture": 21898, + "arga": 21899, + "átum": 21900, + "▁DDR": 21901, + "нії": 21902, + "▁Société": 21903, + "▁domains": 21904, + "▁permitted": 21905, + "▁externe": 21906, + "▁quelque": 21907, + "vt": 21908, + "yman": 21909, + "▁Ward": 21910, + "▁agli": 21911, + "▁andra": 21912, + "Snapshot": 21913, + "▁må": 21914, + "▁yeah": 21915, + "дена": 21916, + "ępu": 21917, + "askell": 21918, + "▁République": 21919, + "inject": 21920, + "▁';": 21921, + "änn": 21922, + "▁zelf": 21923, + "▁Entwicklung": 21924, + "ária": 21925, + "onomy": 21926, + "▁svil": 21927, + "iese": 21928, + "▁conser": 21929, + "▁nim": 21930, + "▁rész": 21931, + "▁Итали": 21932, + "▁partici": 21933, + "▁Lion": 21934, + "sr": 21935, + "always": 21936, + 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"▁femin": 21991, + "▁specification": 21992, + "soap": 21993, + "▁operate": 21994, + "▁principalmente": 21995, + "▁aust": 21996, + "ibile": 21997, + "itime": 21998, + "лежа": 21999, + "iframe": 22000, + "▁concepts": 22001, + "▁tack": 22002, + "▁viss": 22003, + "▁carbon": 22004, + "tery": 22005, + "▁naming": 22006, + "▁Orts": 22007, + "idente": 22008, + "▁Capit": 22009, + "▁expr": 22010, + "▁насељу": 22011, + "▁Selected": 22012, + "▁hinter": 22013, + "▁iframe": 22014, + "▁zb": 22015, + "indexPath": 22016, + "coll": 22017, + "▁wrześ": 22018, + "▁acht": 22019, + "▁gradually": 22020, + "▁чу": 22021, + "зей": 22022, + "haft": 22023, + "▁tran": 22024, + "▁laquelle": 22025, + "ytics": 22026, + "IDE": 22027, + "▁pygame": 22028, + "▁Package": 22029, + "▁className": 22030, + "Bal": 22031, + "perl": 22032, + "тина": 22033, + "Occ": 22034, + "▁infrastr": 22035, + "▁Champions": 22036, + "▁classic": 22037, + "▁Raw": 22038, + "▁partially": 22039, + "▁Ted": 22040, + "▁stolet": 22041, + "rained": 22042, 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"Longrightarrow": 22893, + "▁ря": 22894, + "▁Isra": 22895, + "[^": 22896, + "nou": 22897, + "▁synd": 22898, + "working": 22899, + "▁Nation": 22900, + "▁Pent": 22901, + "▁klass": 22902, + "▁applicable": 22903, + "▁Diam": 22904, + "▁brasile": 22905, + "▁pac": 22906, + "▁Height": 22907, + "Put": 22908, + "▁intro": 22909, + "▁unusual": 22910, + "nas": 22911, + "▁Gebäude": 22912, + "▁beam": 22913, + "▁Rect": 22914, + "▁Primera": 22915, + "▁haut": 22916, + "▁trait": 22917, + "prüft": 22918, + "inación": 22919, + "▁configurations": 22920, + "▁gilt": 22921, + "▁territoire": 22922, + "hez": 22923, + "▁alte": 22924, + "relative": 22925, + "Excel": 22926, + "▁Wright": 22927, + "GV": 22928, + "поли": 22929, + "Quant": 22930, + "▁gauge": 22931, + "▁multiply": 22932, + "ASS": 22933, + "ственно": 22934, + "ану": 22935, + "▁jeden": 22936, + "▁literary": 22937, + "▁Dro": 22938, + "▁advise": 22939, + "itzen": 22940, + "▁disag": 22941, + "website": 22942, + "▁дія": 22943, + "▁observer": 22944, + 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22999, + "ptic": 23000, + "▁Navigation": 23001, + "Russ": 23002, + "галь": 23003, + "▁Ful": 23004, + "▁має": 23005, + "чная": 23006, + "wner": 23007, + "contra": 23008, + "▁joueur": 23009, + "▁Jess": 23010, + "▁renew": 23011, + "▁lap": 23012, + "▁casting": 23013, + "gal": 23014, + "▁tématu": 23015, + "▁называ": 23016, + "зах": 23017, + "чне": 23018, + ")-\\": 23019, + "▁часто": 23020, + "}$-": 23021, + "▁licz": 23022, + "▁emot": 23023, + "harm": 23024, + "▁occasionally": 23025, + "▁horror": 23026, + "east": 23027, + "▁printer": 23028, + "aran": 23029, + "▁Mississ": 23030, + "follow": 23031, + "▁Barry": 23032, + "▁investigate": 23033, + "gow": 23034, + "▁Americans": 23035, + "Since": 23036, + "▁відо": 23037, + "▁reun": 23038, + "osci": 23039, + "▁Chapter": 23040, + "▁bay": 23041, + "роме": 23042, + "ethe": 23043, + "édie": 23044, + "comot": 23045, + "▁miejscowo": 23046, + "▁studierte": 23047, + "ouvert": 23048, + "▁кур": 23049, + "▁DESC": 23050, + "▁touched": 23051, + "▁Jerry": 23052, + 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25055, + "▁Bonn": 25056, + "▁unlikely": 25057, + "RAM": 25058, + "enst": 25059, + "Stats": 25060, + "▁политиче": 25061, + ")--(": 25062, + "▁trom": 25063, + "!...": 25064, + "▁Meanwhile": 25065, + "стана": 25066, + "▁Reino": 25067, + "▁Arist": 25068, + "$}}%": 25069, + "▁solem": 25070, + "closure": 25071, + "ignation": 25072, + "łod": 25073, + "▁divor": 25074, + "▁международ": 25075, + "=\"": 25230, + "Orientation": 25231, + "cid": 25232, + "Cart": 25233, + "▁murm": 25234, + "▁assez": 25235, + "▁linking": 25236, + "building": 25237, + "▁reconna": 25238, + "▁shook": 25239, + "managed": 25240, + "landa": 25241, + "▁León": 25242, + "▁création": 25243, + "дой": 25244, + "ocity": 25245, + "▁wij": 25246, + "▁wieś": 25247, + "xtart": 25248, + "▁Move": 25249, + "lungen": 25250, + "ствует": 25251, + "orney": 25252, + "optional": 25253, + "macro": 25254, + "Condition": 25255, + "▁squares": 25256, + "▁mistaken": 25257, + "ánt": 25258, + "▁Ris": 25259, + "▁sentences": 25260, + "erea": 25261, + "▁mij": 25262, + "Und": 25263, + "▁nombr": 25264, + "zA": 25265, + "▁Independent": 25266, + "▁preview": 25267, + "imas": 25268, + "▁males": 25269, + "inental": 25270, + "Thank": 25271, + "▁popol": 25272, + "▁pover": 25273, + "▁grasp": 25274, + "▁imped": 25275, + "▁campionato": 25276, + "▁Wei": 25277, + "▁titled": 25278, + "▁Además": 25279, + "▁Password": 25280, + "▁Pam": 25281, + "UILD": 25282, + "▁липня": 25283, + "werb": 25284, + "................": 25285, + "▁Río": 25286, + "▁teeth": 25287, + "bp": 25288, + "▁SW": 25289, + "ulaire": 25290, + "▁seized": 25291, + "▁Stef": 25292, + "úl": 25293, + "▁viz": 25294, + "iony": 25295, + "▁junt": 25296, + "▁která": 25297, + "▁września": 25298, + "<>": 25299, + "▁surg": 25300, + "▁tutte": 25301, + "▁Hob": 25302, + "повід": 25303, + "▁wohl": 25304, + "▁trag": 25305, + "▁Crown": 25306, + "▁trova": 25307, + "стову": 25308, + "▁Vienna": 25309, + "esehen": 25310, + "▁metropol": 25311, + "▁reflected": 25312, + "тета": 25313, + "▁traduc": 25314, + "▁Bast": 25315, + "▁erschien": 25316, + "woord": 25317, + "()\"": 25318, + "talet": 25319, + "▁roads": 25320, + "ведения": 25321, + "ührung": 25322, + "▁cogn": 25323, + "▁Valle": 25324, + "▁landing": 25325, + "▁Regex": 25326, + "▁Iowa": 25327, + "dział": 25328, + "▁erreichte": 25329, + "aum": 25330, + "▁founder": 25331, + "apolis": 25332, + "Compiler": 25333, + "▁kop": 25334, + "▁marc": 25335, + "▁територ": 25336, + "))`": 25337, + "▁lei": 25338, + "geon": 25339, + "▁weapons": 25340, + "▁horn": 25341, + "▁elif": 25342, + "▁Capital": 25343, + "će": 25344, + "▁forall": 25345, + "▁эта": 25346, + "preview": 25347, + "▁DNA": 25348, + "▁sid": 25349, + "orch": 25350, + "▁Ras": 25351, + "▁arab": 25352, + "Best": 25353, + "▁счита": 25354, + "▁López": 25355, + "ança": 25356, + "▁funkc": 25357, + "▁tienen": 25358, + ";&": 25359, + "museum": 25360, + "▁Err": 25361, + "▁resort": 25362, + "Nov": 25363, + "▁kal": 25364, + "MW": 25365, + "шь": 25366, + "anchor": 25367, + "▁роман": 25368, + "leading": 25369, + "▁manten": 25370, + "▁Silva": 25371, + "dade": 25372, + "▁designated": 25373, + "▁revista": 25374, + "Oct": 25375, + "percent": 25376, + "▁уні": 25377, + "identifier": 25378, + "mass": 25379, + "@@": 25380, + "ulsion": 25381, + "germeister": 25382, + "▁predicted": 25383, + "▁сви": 25384, + "жной": 25385, + "▁Ergeb": 25386, + "▁cust": 25387, + "▁removes": 25388, + "charg": 25389, + "пример": 25390, + "▁forming": 25391, + "asma": 25392, + "stdout": 25393, + "Fun": 25394, + "yme": 25395, + "tered": 25396, + "ursive": 25397, + "ighed": 25398, + "▁след": 25399, + "verband": 25400, + "▁LOG": 25401, + "rams": 25402, + "éon": 25403, + "endra": 25404, + "▁Bereich": 25405, + "▁temporal": 25406, + "▁langue": 25407, + "▁Inn": 25408, + "▁moreover": 25409, + "▁tutorials": 25410, + "Middle": 25411, + "▁советский": 25412, + "▁maintenance": 25413, + "asures": 25414, + "▁válto": 25415, + "BASE": 25416, + "▁disappear": 25417, + "ския": 25418, + "▁conocido": 25419, + "▁Нау": 25420, + "▁Libert": 25421, + "▁Harold": 25422, + "▁lifetime": 25423, + "▁Tür": 25424, + "▁zawod": 25425, + "omic": 25426, + "▁Retrieved": 25427, + "architecture": 25428, + "čka": 25429, + "iformes": 25430, + "development": 25431, + "ordnung": 25432, + "Inf": 25433, + "leben": 25434, + "▁Stars": 25435, + "signal": 25436, + "▁grammar": 25437, + "▁corso": 25438, + "▁Wagner": 25439, + "▁geht": 25440, + "▁royale": 25441, + "warn": 25442, + "umbled": 25443, + "▁instit": 25444, + "▁Ши": 25445, + "hh": 25446, + "▁refuge": 25447, + "▁favorite": 25448, + "ierto": 25449, + "▁condado": 25450, + "▁Ther": 25451, + "▁человека": 25452, + "▁Food": 25453, + "▁seizo": 25454, + "▁Initialize": 25455, + "▁connu": 25456, + "▁overlap": 25457, + "▁Emil": 25458, + "▁Martí": 25459, + "▁жовтня": 25460, + "erva": 25461, + "▁boats": 25462, + "ações": 25463, + "▁derrot": 25464, + "▁malloc": 25465, + "▁conject": 25466, + "jk": 25467, + "▁sare": 25468, + "лемен": 25469, + "▁sums": 25470, + "Authorization": 25471, + "▁Kun": 25472, + 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"cija": 26575, + "▁poem": 26576, + "▁negro": 26577, + "хар": 26578, + "▁Ask": 26579, + "▁avo": 26580, + "▁Meyer": 26581, + "▁Westen": 26582, + "▁oko": 26583, + "agin": 26584, + "▁Süden": 26585, + "entries": 26586, + "▁Republik": 26587, + "CollectionView": 26588, + "-------": 26589, + "▁firefox": 26590, + "▁alcune": 26591, + "▁фото": 26592, + "▁отрима": 26593, + "~~~~~~~~": 26594, + "▁Раз": 26595, + "▁Complex": 26596, + "▁pia": 26597, + "▁publicada": 26598, + "wei": 26599, + "cedure": 26600, + "occupation": 26601, + "▁medicine": 26602, + "▁drove": 26603, + "Problem": 26604, + "▁beginner": 26605, + "▁thoroughly": 26606, + "uria": 26607, + "avant": 26608, + "ucha": 26609, + "▁lever": 26610, + "▁teatro": 26611, + "AVA": 26612, + "squ": 26613, + "trat": 26614, + "ivatal": 26615, + "▁dirty": 26616, + "▁seconde": 26617, + "▁gravit": 26618, + "▁proposition": 26619, + "hbar": 26620, + "omini": 26621, + "▁”": 26622, + "▁Camil": 26623, + "▁queen": 26624, + "modifier": 26625, + "Jan": 26626, + 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"fluss": 26944, + "Drawable": 26945, + "▁surve": 26946, + "Setup": 26947, + "▁należ": 26948, + "▁conjunto": 26949, + "▁Его": 26950, + "▁oldal": 26951, + "▁verbose": 26952, + "▁Electric": 26953, + "▁Harrison": 26954, + "engen": 26955, + "paragraph": 26956, + "▁nouvelles": 26957, + "▁време": 26958, + "▁memor": 26959, + "▁mayoría": 26960, + "сад": 26961, + "▁bataille": 26962, + "▁thermal": 26963, + "▁Хронологи": 26964, + "▁Better": 26965, + "bye": 26966, + "▁театра": 26967, + "roe": 26968, + "▁segle": 26969, + "rott": 26970, + "▁opinions": 26971, + ")})": 26972, + "ühle": 26973, + "▁Gün": 26974, + "▁Щ": 26975, + "ból": 26976, + "▁Larry": 26977, + "▁solic": 26978, + "▁zwar": 26979, + "▁Caroline": 26980, + "▁Reichs": 26981, + "Extensions": 26982, + "migr": 26983, + ":@": 26984, + "▁enumerate": 26985, + "▁eigenen": 26986, + "▁explore": 26987, + "ému": 26988, + "▁gat": 26989, + "▁imperial": 26990, + "▁Usually": 26991, + "▁tud": 26992, + "▁укра": 26993, + "him": 26994, + "▁corners": 26995, + 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"▁assertion": 28306, + "DN": 28307, + "▁teat": 28308, + "ína": 28309, + "▁mechanical": 28310, + "isu": 28311, + "@{": 28312, + "▁nou": 28313, + "Italie": 28314, + "sourceforge": 28315, + "▁svo": 28316, + "▁király": 28317, + "▁References": 28318, + "six": 28319, + "▁Archives": 28320, + "▁finishing": 28321, + "acje": 28322, + "état": 28323, + "iffs": 28324, + "▁stead": 28325, + "▁feas": 28326, + "aware": 28327, + "lande": 28328, + "Inject": 28329, + "▁Agent": 28330, + "▁Normdatei": 28331, + "▁amen": 28332, + "▁Architecture": 28333, + "aze": 28334, + "ște": 28335, + "▁usar": 28336, + "▁cores": 28337, + "лін": 28338, + "▁Castro": 28339, + "▁væ": 28340, + ">\",": 28341, + "omena": 28342, + "▁gesam": 28343, + "▁Martín": 28344, + "egung": 28345, + "▁společ": 28346, + "▁amplitude": 28347, + "▁importing": 28348, + "▁listview": 28349, + "THE": 28350, + "ziale": 28351, + "cedes": 28352, + "▁particulier": 28353, + "▁Расподела": 28354, + "▁край": 28355, + "▁divent": 28356, + "▁ké": 28357, + "quit": 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"âr": 28726, + "babel": 28727, + "▁Friday": 28728, + "▁június": 28729, + "▁cols": 28730, + "▁EXISTS": 28731, + "▁Italiana": 28732, + "▁authorization": 28733, + "▁sulle": 28734, + "▁Emb": 28735, + "▁Variable": 28736, + "trees": 28737, + "▁Fly": 28738, + "riors": 28739, + "▁damals": 28740, + "▁findet": 28741, + "▁Sept": 28742, + "▁mundial": 28743, + "▁removal": 28744, + "▁longitude": 28745, + "clic": 28746, + "▁fade": 28747, + "▁gradle": 28748, + "▁zák": 28749, + "▁timing": 28750, + "trightarrow": 28751, + "atia": 28752, + "-.": 28753, + "uche": 28754, + "▁serialize": 28755, + "▁Hmm": 28756, + "▁Representatives": 28757, + "bah": 28758, + "rend": 28759, + "assador": 28760, + "▁shield": 28761, + "ucion": 28762, + "▁américaine": 28763, + "zę": 28764, + "villa": 28765, + "▁hombre": 28766, + "áss": 28767, + "▁SF": 28768, + "▁repeating": 28769, + "▁criter": 28770, + "▁Struct": 28771, + "???": 28772, + "▁cheap": 28773, + "▁rings": 28774, + "abhäng": 28775, + "▁corte": 28776, + "▁administ": 28777, + "ixon": 28778, + "gypt": 28779, + "▁puntos": 28780, + "▁mezi": 28781, + "▁pochod": 28782, + "isko": 28783, + "nię": 28784, + "▁осу": 28785, + "▁ár": 28786, + "тельной": 28787, + "▁Metropolitan": 28788, + "jin": 28789, + "zess": 28790, + "▁віці": 28791, + "▁conflicts": 28792, + "ijst": 28793, + "▁Market": 28794, + "стров": 28795, + "▁\",\"": 28796, + "▁Scroll": 28797, + "gun": 28798, + "тара": 28799, + "▁amateur": 28800, + "▁róż": 28801, + "poss": 28802, + "▁generalized": 28803, + "▁Harm": 28804, + "cita": 28805, + "▁Switzerland": 28806, + "icola": 28807, + "▁muit": 28808, + "located": 28809, + "▁có": 28810, + "▁arose": 28811, + "▁communauté": 28812, + "})^": 28813, + "visibility": 28814, + "ída": 28815, + "▁FB": 28816, + "▁Freund": 28817, + "gat": 28818, + "\":{\"": 28819, + "intellij": 28820, + "ifie": 28821, + "hmen": 28822, + "▁édition": 28823, + "▁које": 28824, + "▁інших": 28825, + "oming": 28826, + "▁arquitect": 28827, + "▁Presidente": 28828, + "▁Під": 28829, + "▁cabin": 28830, + "Theorem": 28831, + "▁Gay": 28832, + "ifice": 28833, + "▁hect": 28834, + "lą": 28835, + "irmingham": 28836, + "▁semantic": 28837, + "▁Louisiana": 28838, + "▁sacrifice": 28839, + "▁Christoph": 28840, + "▁Executive": 28841, + "_+": 28842, + "ják": 28843, + "▁seria": 28844, + "▁Overflow": 28845, + "▁Lucy": 28846, + "▁melhor": 28847, + "▁voices": 28848, + "cza": 28849, + "▁капи": 28850, + "▁университета": 28851, + "INCT": 28852, + "▁coloc": 28853, + "▁prue": 28854, + "▁geomet": 28855, + "▁diretto": 28856, + "reso": 28857, + "▁Akt": 28858, + "▁unh": 28859, + "▁сери": 28860, + "▁Alert": 28861, + "Wel": 28862, + "audi": 28863, + "äler": 28864, + "▁guests": 28865, + "▁иде": 28866, + "Studio": 28867, + "▁кате": 28868, + "▁exponent": 28869, + "rze": 28870, + "pmod": 28871, + "rolle": 28872, + "▁Limited": 28873, + "Allemagne": 28874, + "▁pity": 28875, + "▁lä": 28876, + "▁runner": 28877, + "kende": 28878, + "EQ": 28879, + "▁MM": 28880, + "szág": 28881, + "поді": 28882, + "▁regret": 28883, + "▁publié": 28884, + "▁departamento": 28885, + "▁accused": 28886, + "hp": 28887, + "▁Pfl": 28888, + "▁Sint": 28889, + "▁ekonom": 28890, + "ractor": 28891, + "▁Пів": 28892, + "▁awful": 28893, + "ować": 28894, + "]->": 28895, + "▁Fine": 28896, + "Са": 28897, + "tis": 28898, + "éta": 28899, + "▁Роди": 28900, + "▁Düsseldorf": 28901, + "LOB": 28902, + "osas": 28903, + "werke": 28904, + "▁lance": 28905, + "▁листопада": 28906, + "▁incomplete": 28907, + "▁Picture": 28908, + "('\\": 28909, + "esters": 28910, + "▁belonged": 28911, + "▁Sank": 28912, + "ammed": 28913, + "▁repositories": 28914, + "▁addr": 28915, + "Collect": 28916, + "Hot": 28917, + "▁tyl": 28918, + "▁instanceof": 28919, + "▁bonus": 28920, + "ový": 28921, + "▁моря": 28922, + "▁interactive": 28923, + "▁Mys": 28924, + "▁Edmund": 28925, + "fileName": 28926, + "emor": 28927, + "▁Три": 28928, + "▁Rosen": 28929, + "▁Prima": 28930, + "▁voting": 28931, + "▁XP": 28932, + "▁Zero": 28933, + "▁Led": 28934, + "amsung": 28935, + "▁enables": 28936, + "▁redirects": 28937, + "AST": 28938, + "Paint": 28939, + "acker": 28940, + "lecht": 28941, + "▁chairman": 28942, + "▁Aven": 28943, + "▁Sach": 28944, + "(\"<": 28945, + "кер": 28946, + "▁mistakes": 28947, + "▁Weit": 28948, + "▁prowad": 28949, + "▁didnt": 28950, + "énario": 28951, + "unless": 28952, + "▁backwards": 28953, + "boa": 28954, + "duino": 28955, + "```": 28956, + "stor": 28957, + "Completion": 28958, + "puesta": 28959, + "▁dinast": 28960, + "últ": 28961, + "▁SY": 28962, + "ifolia": 28963, + "œuvres": 28964, + "▁racing": 28965, + "▁cabinet": 28966, + "▁cutting": 28967, + "▁thumb": 28968, + "▁Кара": 28969, + "highlight": 28970, + "куп": 28971, + "▁sd": 28972, + "▁національ": 28973, + "▁campagne": 28974, + "▁registers": 28975, + "▁educational": 28976, + "▁pesar": 28977, + "üge": 28978, + "▁oro": 28979, + "burgo": 28980, + "▁Athletics": 28981, + "▁MTV": 28982, + "getMessage": 28983, + "▁Hyp": 28984, + "▁victim": 28985, + "))\\": 28986, + "▁drums": 28987, + "hostname": 28988, + "tał": 28989, + "making": 28990, + "▁powiat": 28991, + "őd": 28992, + "threads": 28993, + "▁absolv": 28994, + "▁люди": 28995, + "▁stepped": 28996, + "exist": 28997, + "▁NK": 28998, + "▁ves": 28999, + "istiche": 29000, + "%'": 29001, + "ativos": 29002, + "▁такой": 29003, + "▁MongoDB": 29004, + "▁Ung": 29005, + "▁Рус": 29006, + "▁elim": 29007, + "▁Fif": 29008, + "icación": 29009, + "▁Tennis": 29010, + "▁Jefferson": 29011, + "ján": 29012, + "fog": 29013, + "anha": 29014, + "zor": 29015, + "▁університе": 29016, + "ahu": 29017, + "iada": 29018, + "Sdk": 29019, + "Setting": 29020, + "▁Kill": 29021, + "▁Wend": 29022, + "▁bald": 29023, + "▁Kub": 29024, + "▁visto": 29025, + "▁jeunes": 29026, + "collections": 29027, + "ací": 29028, + "вропей": 29029, + "▁arise": 29030, + "оні": 29031, + "MAIN": 29032, + "доступ": 29033, + "▁berg": 29034, + "▁criticism": 29035, + "▁Torre": 29036, + "▁descript": 29037, + "ières": 29038, + "▁estudio": 29039, + "▁ili": 29040, + "▁militare": 29041, + "▁Clara": 29042, + "▁Ellen": 29043, + "limited": 29044, + "лм": 29045, + "▁Españ": 29046, + "▁infinitely": 29047, + "America": 29048, + "ouc": 29049, + "glass": 29050, + "▁rud": 29051, + "▁zat": 29052, + "▁rin": 29053, + "▁Bibliografía": 29054, + "▁merchant": 29055, + "tensorflow": 29056, + "▁dér": 29057, + "▁ActiveRecord": 29058, + "IES": 29059, + "▁linker": 29060, + "▁estudios": 29061, + "cdnjs": 29062, + "▁Государ": 29063, + "ánchez": 29064, + "appe": 29065, + "club": 29066, + "▁další": 29067, + "▁Algorithm": 29068, + "dfs": 29069, + "▁Bac": 29070, + "▁кафе": 29071, + "▁&=\\": 29072, + "▁ат": 29073, + "▁Глав": 29074, + "▁Mou": 29075, + "Machine": 29076, + "(...)": 29077, + "▁compart": 29078, + "▁augusztus": 29079, + "avan": 29080, + "▁rolled": 29081, + "▁еди": 29082, + "Scan": 29083, + "▁регі": 29084, + "▁świata": 29085, + "▁mines": 29086, + "},{": 29087, + "▁Tier": 29088, + "Cannot": 29089, + "мін": 29090, + "▁NEW": 29091, + "▁Вол": 29092, + "▁Manh": 29093, + "▁Gregory": 29094, + "▁principe": 29095, + "ISO": 29096, + "prog": 29097, + "▁Fail": 29098, + "▁aa": 29099, + "▁fecha": 29100, + "▁WCF": 29101, + "▁magistr": 29102, + "▁Zach": 29103, + "▁unicode": 29104, + "▁converter": 29105, + "▁dispers": 29106, + "ksam": 29107, + "▁Uncle": 29108, + "PropertyChanged": 29109, + "▁lider": 29110, + "▁opts": 29111, + "▁там": 29112, + "locked": 29113, + "zak": 29114, + "▁counted": 29115, + "▁persone": 29116, + "▁hurried": 29117, + "ätter": 29118, + "▁outras": 29119, + "▁genu": 29120, + "BD": 29121, + "veg": 29122, + "due": 29123, + "▁Pract": 29124, + "▁posible": 29125, + "▁contribute": 29126, + "UMN": 29127, + "▁Bürger": 29128, + "▁wars": 29129, + "▁exhibition": 29130, + "hill": 29131, + "▁astr": 29132, + "▁музе": 29133, + "▁CASE": 29134, + "manifest": 29135, + "yellow": 29136, + "Fn": 29137, + "▁RC": 29138, + "▁sott": 29139, + "▁sujet": 29140, + "▁Socket": 29141, + "▁Chine": 29142, + "▁frameworks": 29143, + "Hold": 29144, + "êts": 29145, + "▁філь": 29146, + "Loaded": 29147, + "ophe": 29148, + "texte": 29149, + "▁expres": 29150, + "▁consume": 29151, + "▁Richtung": 29152, + "ografi": 29153, + "▁magnific": 29154, + "àt": 29155, + "▁indul": 29156, + "ryty": 29157, + "▁offici": 29158, + "▁assault": 29159, + "rund": 29160, + "▁variants": 29161, + "▁сельсов": 29162, + "▁excitement": 29163, + "Times": 29164, + "kotlin": 29165, + "▁gering": 29166, + "▁Engel": 29167, + "▁Timer": 29168, + "²).": 29169, + "▁Ng": 29170, + "ässt": 29171, + "schau": 29172, + "SError": 29173, + "▁Edwards": 29174, + "▁Terminal": 29175, + "lict": 29176, + "Under": 29177, + "▁spawn": 29178, + "ürgen": 29179, + "▁Außerdem": 29180, + "▁kitchen": 29181, + "fahrt": 29182, + "▁Colors": 29183, + "▁система": 29184, + "▁terminated": 29185, + "▁LaTeX": 29186, + "igkeiten": 29187, + "▁mesure": 29188, + "▁Amts": 29189, + "▁empir": 29190, + "▁striking": 29191, + "▁exclusive": 29192, + "тех": 29193, + "▁rez": 29194, + "▁quan": 29195, + "▁Glasgow": 29196, + "▁lecture": 29197, + "▁Testament": 29198, + "▁funds": 29199, + "▁stessa": 29200, + "▁tribes": 29201, + "▁parfois": 29202, + "▁treball": 29203, + "nitz": 29204, + "bove": 29205, + "▁заслу": 29206, + "▁absent": 29207, + "▁Lauf": 29208, + "Smith": 29209, + "▁Николай": 29210, + "▁européenne": 29211, + "lr": 29212, + "▁programma": 29213, + "▁midst": 29214, + "▁daughters": 29215, + "Syn": 29216, + "oben": 29217, + "ână": 29218, + "idan": 29219, + "▁ther": 29220, + "odore": 29221, + "sdl": 29222, + "▁Quint": 29223, + "▁casos": 29224, + "▁Zam": 29225, + "▁страны": 29226, + "▁sprite": 29227, + "кал": 29228, + "▁nasc": 29229, + "▁сотруд": 29230, + "▁trava": 29231, + "▁хозяй": 29232, + "▁Uruguay": 29233, + "▁sparse": 29234, + "▁поле": 29235, + "▁mystery": 29236, + "▁Mang": 29237, + "registr": 29238, + "▁CGFloat": 29239, + "▁submission": 29240, + "вана": 29241, + "▁\":": 29242, + "▁Traceback": 29243, + "▁Pit": 29244, + "▁Ehr": 29245, + "▁сра": 29246, + "▁Graphics": 29247, + "Updated": 29248, + "▁svensk": 29249, + "▁spacing": 29250, + "tritt": 29251, + "▁Guinea": 29252, + "▁França": 29253, + "Associ": 29254, + "▁Tová": 29255, + "stab": 29256, + "▁Learning": 29257, + "▁Bright": 29258, + "śc": 29259, + "▁idő": 29260, + "}}_{\\": 29261, + "▁droite": 29262, + "▁raising": 29263, + "getting": 29264, + "ythm": 29265, + "onyme": 29266, + "żs": 29267, + "▁blah": 29268, + "TagName": 29269, + "Vertical": 29270, + "▁aper": 29271, + "postgresql": 29272, + "▁Handle": 29273, + "zew": 29274, + "▁skulle": 29275, + "▁opere": 29276, + "layers": 29277, + "▁possono": 29278, + "▁relate": 29279, + "ąc": 29280, + "▁Mih": 29281, + "âge": 29282, + "▁Świ": 29283, + "isses": 29284, + "▁servlet": 29285, + "Los": 29286, + "▁Advanced": 29287, + "atica": 29288, + "▁ced": 29289, + "▁elementos": 29290, + "рона": 29291, + "iks": 29292, + "arf": 29293, + "ariat": 29294, + "Mobile": 29295, + "agua": 29296, + "▁timp": 29297, + "▁Comité": 29298, + "▁combining": 29299, + "wohl": 29300, + "▁Study": 29301, + "coordinate": 29302, + "▁recommendation": 29303, 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31247, + "ਾ": 31248, + "வ": 31249, + "ど": 31250, + "ヒ": 31251, + "ไ": 31252, + "ன": 31253, + "ば": 31254, + "ギ": 31255, + "գ": 31256, + "ἄ": 31257, + "ヤ": 31258, + "典": 31259, + "府": 31260, + "̄": 31261, + "신": 31262, + "组": 31263, + "改": 31264, + "ὲ": 31265, + "华": 31266, + "与": 31267, + "调": 31268, + "╝": 31269, + "ヴ": 31270, + "ქ": 31271, + "由": 31272, + "修": 31273, + "學": 31274, + "♣": 31275, + "消": 31276, + "符": 31277, + "ʌ": 31278, + "부": 31279, + "ớ": 31280, + "‾": 31281, + "▲": 31282, + "录": 31283, + "ള": 31284, + "연": 31285, + "을": 31286, + "ひ": 31287, + "영": 31288, + "┤": 31289, + "已": 31290, + "陽": 31291, + "င": 31292, + "국": 31293, + "容": 31294, + "未": 31295, + "宗": 31296, + "ᴇ": 31297, + "び": 31298, + "장": 31299, + "龙": 31300, + "්": 31301, + "提": 31302, + "ĝ": 31303, + "六": 31304, + "形": 31305, + "제": 31306, + "Հ": 31307, + "伊": 31308, + "ϵ": 31309, + "ข": 31310, + "Ű": 31311, + "ゃ": 31312, + "火": 31313, + "Ṣ": 31314, + "佐": 31315, + "⊥": 31316, + "̪": 31317, + "ứ": 31318, 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": 31353, + "은": 31354, + "ʷ": 31355, + "那": 31356, + "線": 31357, + "务": 31358, + "基": 31359, + "属": 31360, + "配": 31361, + "미": 31362, + "軍": 31363, + "โ": 31364, + "津": 31365, + "完": 31366, + "研": 31367, + "注": 31368, + "失": 31369, + "应": 31370, + "က": 31371, + "╚": 31372, + "友": 31373, + "章": 31374, + "Ψ": 31375, + "求": 31376, + "ण": 31377, + "경": 31378, + "‬": 31379, + "भ": 31380, + "们": 31381, + "模": 31382, + "需": 31383, + "ச": 31384, + "電": 31385, + "প": 31386, + "դ": 31387, + "へ": 31388, + "此": 31389, + "夜": 31390, + "或": 31391, + "橋": 31392, + "根": 31393, + "Ī": 31394, + "玉": 31395, + "ู": 31396, + "ṅ": 31397, + "交": 31398, + "品": 31399, + "良": 31400, + "ང": 31401, + "ォ": 31402, + "则": 31403, + "開": 31404, + "Ζ": 31405, + "문": 31406, + "被": 31407, + "조": 31408, + "株": 31409, + "记": 31410, + "會": 31411, + "经": 31412, + "ू": 31413, + "ょ": 31414, + "转": 31415, + "崎": 31416, + "마": 31417, + "⌘": 31418, + "比": 31419, + "造": 31420, + "ܐ": 31421, + "ื": 31422, + "没": 31423, + "现": 31424, + "七": 31425, + "Ά": 31426, + "商": 31427, + "ை": 31428, + "机": 31429, + "阳": 31430, + "ĉ": 31431, + "角": 31432, + "站": 31433, + "բ": 31434, + "해": 31435, + "及": 31436, + "ध": 31437, + "術": 31438, + "认": 31439, + "‘": 31440, + "创": 31441, + "編": 31442, + "ղ": 31443, + "ḩ": 31444, + "伝": 31445, + "岡": 31446, + "ड": 31447, + "ホ": 31448, + "港": 31449, + "任": 31450, + "登": 31451, + "ི": 31452, + "็": 31453, + "布": 31454, + "究": 31455, + "帝": 31456, + "여": 31457, + "산": 31458, + "န": 31459, + "◦": 31460, + "密": 31461, + "变": 31462, + "序": 31463, + "♀": 31464, + "∣": 31465, + "计": 31466, + "曲": 31467, + "Ă": 31468, + "ύ": 31469, + "ʋ": 31470, + "传": 31471, + "】": 31472, + "包": 31473, + "意": 31474, + "去": 31475, + "沙": 31476, + "⸮": 31477, + "【": 31478, + "写": 31479, + "超": 31480, + "ய": 31481, + "今": 31482, + "┈": 31483, + "森": 31484, + "ි": 31485, + "⊗": 31486, + "비": 31487, + "հ": 31488, + "Ḩ": 31489, + "ǫ": 31490, + "黄": 31491, + "∙": 31492, + "드": 31493, + "🌍": 31494, + "景": 31495, 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31567, + "视": 31568, + "秋": 31569, + "因": 31570, + "년": 31571, + "ے": 31572, + "输": 31573, + "̱": 31574, + "Մ": 31575, + "∆": 31576, + "康": 31577, + "세": 31578, + "思": 31579, + "死": 31580, + "聖": 31581, + "민": 31582, + "-": 31583, + "头": 31584, + "ർ": 31585, + "∉": 31586, + "車": 31587, + "┃": 31588, + "▇": 31589, + "按": 31590, + "⍵": 31591, + "夢": 31592, + "汉": 31593, + "从": 31594, + "ী": 31595, + "题": 31596, + "ˆ": 31597, + "ἡ": 31598, + "展": 31599, + "省": 31600, + "ུ": 31601, + "葉": 31602, + "호": 31603, + "ਰ": 31604, + "素": 31605, + "関": 31606, + "그": 31607, + ";": 31608, + "න": 31609, + "页": 31610, + "共": 31611, + "宿": 31612, + "态": 31613, + "ན": 31614, + "技": 31615, + "乐": 31616, + "控": 31617, + "移": 31618, + "影": 31619, + "ụ": 31620, + "ゆ": 31621, + "ご": 31622, + "್": 31623, + "管": 31624, + "ൾ": 31625, + "╣": 31626, + "戸": 31627, + "⇔": 31628, + "函": 31629, + "ẓ": 31630, + "尾": 31631, + "场": 31632, + "介": 31633, + "": 31634, + "育": 31635, + "ර": 31636, + "泉": 31637, + "ൽ": 31638, 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31710, + "結": 31711, + "ා": 31712, + "昌": 31713, + "樹": 31714, + "ள": 31715, + "무": 31716, + "হ": 31717, + "ゼ": 31718, + "̈": 31719, + "շ": 31720, + "勝": 31721, + "足": 31722, + "ရ": 31723, + "위": 31724, + "į": 31725, + "Ἰ": 31726, + "航": 31727, + "陳": 31728, + "业": 31729, + "富": 31730, + "雪": 31731, + "आ": 31732, + "再": 31733, + "안": 31734, + "默": 31735, + "박": 31736, + "용": 31737, + "✿": 31738, + "楽": 31739, + "沢": 31740, + "羅": 31741, + "Ė": 31742, + "ʎ": 31743, + "忠": 31744, + "错": 31745, + "단": 31746, + "면": 31747, + "ķ": 31748, + "桥": 31749, + "雲": 31750, + "该": 31751, + "ṯ": 31752, + "岩": 31753, + "남": 31754, + "ỹ": 31755, + "专": 31756, + "切": 31757, + "店": 31758, + "朱": 31759, + "ף": 31760, + "ず": 31761, + "幸": 31762, + "母": 31763, + "ɫ": 31764, + "々": 31765, + "∷": 31766, + "串": 31767, + "击": 31768, + "Ἐ": 31769, + "設": 31770, + "⊤": 31771, + "ₗ": 31772, + "經": 31773, + "강": 31774, + "ပ": 31775, + "।": 31776, + "ѐ": 31777, + "ᾶ": 31778, + "➖": 31779, + "座": 31780, + "씨": 31781, 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+ "▁▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁", + "▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁" + ], + [ + "▁", + "▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁", + "▁▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁", + "▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁▁▁▁", + "▁" + ], + [ + "▁▁▁", + "▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁", + "▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁", + "▁▁▁▁▁▁▁▁" + ], + [ + "▁▁▁▁▁▁▁▁▁▁▁", + "▁▁▁▁" + ], + [ + "▁", + "▁▁▁▁▁▁▁▁▁▁▁▁▁▁" + ], + [ + "▁<", + "SU" + ], + [ + "▁" + ], + [ + "▁" + ], + [ + "▁" + ], + [ + "▁" + ] + ] + } +} \ No newline at end of file diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/_virtualenv.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/_virtualenv.py new file mode 100644 index 0000000000000000000000000000000000000000..da98b827a2461bd42b9517239dacad80fb0b46e2 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/_virtualenv.py @@ -0,0 +1,130 @@ +"""Patches that are applied at runtime to the virtual environment""" +# -*- coding: utf-8 -*- + +import os +import sys + +VIRTUALENV_PATCH_FILE = os.path.join(__file__) + + +def patch_dist(dist): + """ + Distutils allows user to configure some arguments via a configuration file: + https://docs.python.org/3/install/index.html#distutils-configuration-files + + Some of this arguments though don't make sense in context of the virtual environment files, let's fix them up. + """ + # we cannot allow some install config as that would get packages installed outside of the virtual environment + old_parse_config_files = dist.Distribution.parse_config_files + + def parse_config_files(self, *args, **kwargs): + result = old_parse_config_files(self, *args, **kwargs) + install = self.get_option_dict("install") + + if "prefix" in install: # the prefix governs where to install the libraries + install["prefix"] = VIRTUALENV_PATCH_FILE, os.path.abspath(sys.prefix) + for base in ("purelib", "platlib", "headers", "scripts", "data"): + key = "install_{}".format(base) + if key in install: # do not allow global configs to hijack venv paths + install.pop(key, None) + return result + + dist.Distribution.parse_config_files = parse_config_files + + +# Import hook that patches some modules to ignore configuration values that break package installation in case +# of virtual environments. +_DISTUTILS_PATCH = "distutils.dist", "setuptools.dist" +if sys.version_info > (3, 4): + # https://docs.python.org/3/library/importlib.html#setting-up-an-importer + from functools import partial + from importlib.abc import MetaPathFinder + from importlib.util import find_spec + + class _Finder(MetaPathFinder): + """A meta path finder that allows patching the imported distutils modules""" + + fullname = None + + # lock[0] is threading.Lock(), but initialized lazily to avoid importing threading very early at startup, + # because there are gevent-based applications that need to be first to import threading by themselves. + # See https://github.com/pypa/virtualenv/issues/1895 for details. + lock = [] + + def find_spec(self, fullname, path, target=None): + if fullname in _DISTUTILS_PATCH and self.fullname is None: + # initialize lock[0] lazily + if len(self.lock) == 0: + import threading + + lock = threading.Lock() + # there is possibility that two threads T1 and T2 are simultaneously running into find_spec, + # observing .lock as empty, and further going into hereby initialization. However due to the GIL, + # list.append() operation is atomic and this way only one of the threads will "win" to put the lock + # - that every thread will use - into .lock[0]. + # https://docs.python.org/3/faq/library.html#what-kinds-of-global-value-mutation-are-thread-safe + self.lock.append(lock) + + with self.lock[0]: + self.fullname = fullname + try: + spec = find_spec(fullname, path) + if spec is not None: + # https://www.python.org/dev/peps/pep-0451/#how-loading-will-work + is_new_api = hasattr(spec.loader, "exec_module") + func_name = "exec_module" if is_new_api else "load_module" + old = getattr(spec.loader, func_name) + func = self.exec_module if is_new_api else self.load_module + if old is not func: + try: + setattr(spec.loader, func_name, partial(func, old)) + except AttributeError: + pass # C-Extension loaders are r/o such as zipimporter with for details and usage. +""" +# Dev Notes: +# - MSDN on where to store app data files: +# http://support.microsoft.com/default.aspx?scid=kb;en-us;310294#XSLTH3194121123120121120120 +# - Mac OS X: http://developer.apple.com/documentation/MacOSX/Conceptual/BPFileSystem/index.html +# - XDG spec for Un*x: http://standards.freedesktop.org/basedir-spec/basedir-spec-latest.html + +__version__ = "1.4.4" +__version_info__ = tuple(int(segment) for segment in __version__.split(".")) + + +import sys +import os + +PY3 = sys.version_info[0] == 3 + +if PY3: + unicode = str + +if sys.platform.startswith('java'): + import platform + os_name = platform.java_ver()[3][0] + if os_name.startswith('Windows'): # "Windows XP", "Windows 7", etc. + system = 'win32' + elif os_name.startswith('Mac'): # "Mac OS X", etc. + system = 'darwin' + else: # "Linux", "SunOS", "FreeBSD", etc. + # Setting this to "linux2" is not ideal, but only Windows or Mac + # are actually checked for and the rest of the module expects + # *sys.platform* style strings. + system = 'linux2' +else: + system = sys.platform + + + +def user_data_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user data directories are: + Mac OS X: ~/Library/Application Support/ + Unix: ~/.local/share/ # or in $XDG_DATA_HOME, if defined + Win XP (not roaming): C:\Documents and Settings\\Application Data\\ + Win XP (roaming): C:\Documents and Settings\\Local Settings\Application Data\\ + Win 7 (not roaming): C:\Users\\AppData\Local\\ + Win 7 (roaming): C:\Users\\AppData\Roaming\\ + + For Unix, we follow the XDG spec and support $XDG_DATA_HOME. + That means, by default "~/.local/share/". + """ + if system == "win32": + if appauthor is None: + appauthor = appname + const = roaming and "CSIDL_APPDATA" or "CSIDL_LOCAL_APPDATA" + path = os.path.normpath(_get_win_folder(const)) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + elif system == 'darwin': + path = os.path.expanduser('~/Library/Application Support/') + if appname: + path = os.path.join(path, appname) + else: + path = os.getenv('XDG_DATA_HOME', os.path.expanduser("~/.local/share")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def site_data_dir(appname=None, appauthor=None, version=None, multipath=False): + r"""Return full path to the user-shared data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "multipath" is an optional parameter only applicable to *nix + which indicates that the entire list of data dirs should be + returned. By default, the first item from XDG_DATA_DIRS is + returned, or '/usr/local/share/', + if XDG_DATA_DIRS is not set + + Typical site data directories are: + Mac OS X: /Library/Application Support/ + Unix: /usr/local/share/ or /usr/share/ + Win XP: C:\Documents and Settings\All Users\Application Data\\ + Vista: (Fail! "C:\ProgramData" is a hidden *system* directory on Vista.) + Win 7: C:\ProgramData\\ # Hidden, but writeable on Win 7. + + For Unix, this is using the $XDG_DATA_DIRS[0] default. + + WARNING: Do not use this on Windows. See the Vista-Fail note above for why. + """ + if system == "win32": + if appauthor is None: + appauthor = appname + path = os.path.normpath(_get_win_folder("CSIDL_COMMON_APPDATA")) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + elif system == 'darwin': + path = os.path.expanduser('/Library/Application Support') + if appname: + path = os.path.join(path, appname) + else: + # XDG default for $XDG_DATA_DIRS + # only first, if multipath is False + path = os.getenv('XDG_DATA_DIRS', + os.pathsep.join(['/usr/local/share', '/usr/share'])) + pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)] + if appname: + if version: + appname = os.path.join(appname, version) + pathlist = [os.sep.join([x, appname]) for x in pathlist] + + if multipath: + path = os.pathsep.join(pathlist) + else: + path = pathlist[0] + return path + + if appname and version: + path = os.path.join(path, version) + return path + + +def user_config_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific config dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user config directories are: + Mac OS X: same as user_data_dir + Unix: ~/.config/ # or in $XDG_CONFIG_HOME, if defined + Win *: same as user_data_dir + + For Unix, we follow the XDG spec and support $XDG_CONFIG_HOME. + That means, by default "~/.config/". + """ + if system in ["win32", "darwin"]: + path = user_data_dir(appname, appauthor, None, roaming) + else: + path = os.getenv('XDG_CONFIG_HOME', os.path.expanduser("~/.config")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def site_config_dir(appname=None, appauthor=None, version=None, multipath=False): + r"""Return full path to the user-shared data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "multipath" is an optional parameter only applicable to *nix + which indicates that the entire list of config dirs should be + returned. By default, the first item from XDG_CONFIG_DIRS is + returned, or '/etc/xdg/', if XDG_CONFIG_DIRS is not set + + Typical site config directories are: + Mac OS X: same as site_data_dir + Unix: /etc/xdg/ or $XDG_CONFIG_DIRS[i]/ for each value in + $XDG_CONFIG_DIRS + Win *: same as site_data_dir + Vista: (Fail! "C:\ProgramData" is a hidden *system* directory on Vista.) + + For Unix, this is using the $XDG_CONFIG_DIRS[0] default, if multipath=False + + WARNING: Do not use this on Windows. See the Vista-Fail note above for why. + """ + if system in ["win32", "darwin"]: + path = site_data_dir(appname, appauthor) + if appname and version: + path = os.path.join(path, version) + else: + # XDG default for $XDG_CONFIG_DIRS + # only first, if multipath is False + path = os.getenv('XDG_CONFIG_DIRS', '/etc/xdg') + pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)] + if appname: + if version: + appname = os.path.join(appname, version) + pathlist = [os.sep.join([x, appname]) for x in pathlist] + + if multipath: + path = os.pathsep.join(pathlist) + else: + path = pathlist[0] + return path + + +def user_cache_dir(appname=None, appauthor=None, version=None, opinion=True): + r"""Return full path to the user-specific cache dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "opinion" (boolean) can be False to disable the appending of + "Cache" to the base app data dir for Windows. See + discussion below. + + Typical user cache directories are: + Mac OS X: ~/Library/Caches/ + Unix: ~/.cache/ (XDG default) + Win XP: C:\Documents and Settings\\Local Settings\Application Data\\\Cache + Vista: C:\Users\\AppData\Local\\\Cache + + On Windows the only suggestion in the MSDN docs is that local settings go in + the `CSIDL_LOCAL_APPDATA` directory. This is identical to the non-roaming + app data dir (the default returned by `user_data_dir` above). Apps typically + put cache data somewhere *under* the given dir here. Some examples: + ...\Mozilla\Firefox\Profiles\\Cache + ...\Acme\SuperApp\Cache\1.0 + OPINION: This function appends "Cache" to the `CSIDL_LOCAL_APPDATA` value. + This can be disabled with the `opinion=False` option. + """ + if system == "win32": + if appauthor is None: + appauthor = appname + path = os.path.normpath(_get_win_folder("CSIDL_LOCAL_APPDATA")) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + if opinion: + path = os.path.join(path, "Cache") + elif system == 'darwin': + path = os.path.expanduser('~/Library/Caches') + if appname: + path = os.path.join(path, appname) + else: + path = os.getenv('XDG_CACHE_HOME', os.path.expanduser('~/.cache')) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def user_state_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific state dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user state directories are: + Mac OS X: same as user_data_dir + Unix: ~/.local/state/ # or in $XDG_STATE_HOME, if defined + Win *: same as user_data_dir + + For Unix, we follow this Debian proposal + to extend the XDG spec and support $XDG_STATE_HOME. + + That means, by default "~/.local/state/". + """ + if system in ["win32", "darwin"]: + path = user_data_dir(appname, appauthor, None, roaming) + else: + path = os.getenv('XDG_STATE_HOME', os.path.expanduser("~/.local/state")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def user_log_dir(appname=None, appauthor=None, version=None, opinion=True): + r"""Return full path to the user-specific log dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "opinion" (boolean) can be False to disable the appending of + "Logs" to the base app data dir for Windows, and "log" to the + base cache dir for Unix. See discussion below. + + Typical user log directories are: + Mac OS X: ~/Library/Logs/ + Unix: ~/.cache//log # or under $XDG_CACHE_HOME if defined + Win XP: C:\Documents and Settings\\Local Settings\Application Data\\\Logs + Vista: C:\Users\\AppData\Local\\\Logs + + On Windows the only suggestion in the MSDN docs is that local settings + go in the `CSIDL_LOCAL_APPDATA` directory. (Note: I'm interested in + examples of what some windows apps use for a logs dir.) + + OPINION: This function appends "Logs" to the `CSIDL_LOCAL_APPDATA` + value for Windows and appends "log" to the user cache dir for Unix. + This can be disabled with the `opinion=False` option. + """ + if system == "darwin": + path = os.path.join( + os.path.expanduser('~/Library/Logs'), + appname) + elif system == "win32": + path = user_data_dir(appname, appauthor, version) + version = False + if opinion: + path = os.path.join(path, "Logs") + else: + path = user_cache_dir(appname, appauthor, version) + version = False + if opinion: + path = os.path.join(path, "log") + if appname and version: + path = os.path.join(path, version) + return path + + +class AppDirs(object): + """Convenience wrapper for getting application dirs.""" + def __init__(self, appname=None, appauthor=None, version=None, + roaming=False, multipath=False): + self.appname = appname + self.appauthor = appauthor + self.version = version + self.roaming = roaming + self.multipath = multipath + + @property + def user_data_dir(self): + return user_data_dir(self.appname, self.appauthor, + version=self.version, roaming=self.roaming) + + @property + def site_data_dir(self): + return site_data_dir(self.appname, self.appauthor, + version=self.version, multipath=self.multipath) + + @property + def user_config_dir(self): + return user_config_dir(self.appname, self.appauthor, + version=self.version, roaming=self.roaming) + + @property + def site_config_dir(self): + return site_config_dir(self.appname, self.appauthor, + version=self.version, multipath=self.multipath) + + @property + def user_cache_dir(self): + return user_cache_dir(self.appname, self.appauthor, + version=self.version) + + @property + def user_state_dir(self): + return user_state_dir(self.appname, self.appauthor, + version=self.version) + + @property + def user_log_dir(self): + return user_log_dir(self.appname, self.appauthor, + version=self.version) + + +#---- internal support stuff + +def _get_win_folder_from_registry(csidl_name): + """This is a fallback technique at best. I'm not sure if using the + registry for this guarantees us the correct answer for all CSIDL_* + names. + """ + if PY3: + import winreg as _winreg + else: + import _winreg + + shell_folder_name = { + "CSIDL_APPDATA": "AppData", + "CSIDL_COMMON_APPDATA": "Common AppData", + "CSIDL_LOCAL_APPDATA": "Local AppData", + }[csidl_name] + + key = _winreg.OpenKey( + _winreg.HKEY_CURRENT_USER, + r"Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders" + ) + dir, type = _winreg.QueryValueEx(key, shell_folder_name) + return dir + + +def _get_win_folder_with_pywin32(csidl_name): + from win32com.shell import shellcon, shell + dir = shell.SHGetFolderPath(0, getattr(shellcon, csidl_name), 0, 0) + # Try to make this a unicode path because SHGetFolderPath does + # not return unicode strings when there is unicode data in the + # path. + try: + dir = unicode(dir) + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in dir: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + try: + import win32api + dir = win32api.GetShortPathName(dir) + except ImportError: + pass + except UnicodeError: + pass + return dir + + +def _get_win_folder_with_ctypes(csidl_name): + import ctypes + + csidl_const = { + "CSIDL_APPDATA": 26, + "CSIDL_COMMON_APPDATA": 35, + "CSIDL_LOCAL_APPDATA": 28, + }[csidl_name] + + buf = ctypes.create_unicode_buffer(1024) + ctypes.windll.shell32.SHGetFolderPathW(None, csidl_const, None, 0, buf) + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in buf: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + buf2 = ctypes.create_unicode_buffer(1024) + if ctypes.windll.kernel32.GetShortPathNameW(buf.value, buf2, 1024): + buf = buf2 + + return buf.value + +def _get_win_folder_with_jna(csidl_name): + import array + from com.sun import jna + from com.sun.jna.platform import win32 + + buf_size = win32.WinDef.MAX_PATH * 2 + buf = array.zeros('c', buf_size) + shell = win32.Shell32.INSTANCE + shell.SHGetFolderPath(None, getattr(win32.ShlObj, csidl_name), None, win32.ShlObj.SHGFP_TYPE_CURRENT, buf) + dir = jna.Native.toString(buf.tostring()).rstrip("\0") + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in dir: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + buf = array.zeros('c', buf_size) + kernel = win32.Kernel32.INSTANCE + if kernel.GetShortPathName(dir, buf, buf_size): + dir = jna.Native.toString(buf.tostring()).rstrip("\0") + + return dir + +if system == "win32": + try: + import win32com.shell + _get_win_folder = _get_win_folder_with_pywin32 + except ImportError: + try: + from ctypes import windll + _get_win_folder = _get_win_folder_with_ctypes + except ImportError: + try: + import com.sun.jna + _get_win_folder = _get_win_folder_with_jna + except ImportError: + _get_win_folder = _get_win_folder_from_registry + + +#---- self test code + +if __name__ == "__main__": + appname = "MyApp" + appauthor = "MyCompany" + + props = ("user_data_dir", + "user_config_dir", + "user_cache_dir", + "user_state_dir", + "user_log_dir", + "site_data_dir", + "site_config_dir") + + print("-- app dirs %s --" % __version__) + + print("-- app dirs (with optional 'version')") + dirs = AppDirs(appname, appauthor, version="1.0") + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (without optional 'version')") + dirs = AppDirs(appname, appauthor) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (without optional 'appauthor')") + dirs = AppDirs(appname) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (with disabled 'appauthor')") + dirs = AppDirs(appname, appauthor=False) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/decorator.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/decorator.py new file mode 100644 index 0000000000000000000000000000000000000000..40a39f2f1b6d07036d98260318108fdaf173de44 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/decorator.py @@ -0,0 +1,459 @@ +# ######################### LICENSE ############################ # + +# Copyright (c) 2005-2025, Michele Simionato +# All rights reserved. + +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions are +# met: + +# Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# Redistributions in bytecode form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. + +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +# HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS +# OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND +# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR +# TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE +# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH +# DAMAGE. + +""" +Decorator module, see +https://github.com/micheles/decorator/blob/master/docs/documentation.md +for the documentation. +""" +import re +import sys +import inspect +import operator +import itertools +import functools +from contextlib import _GeneratorContextManager +from inspect import getfullargspec, iscoroutinefunction, isgeneratorfunction + +__version__ = '5.2.1' + +DEF = re.compile(r'\s*def\s*([_\w][_\w\d]*)\s*\(') +POS = inspect.Parameter.POSITIONAL_OR_KEYWORD +EMPTY = inspect.Parameter.empty + + +# this is not used anymore in the core, but kept for backward compatibility +class FunctionMaker(object): + """ + An object with the ability to create functions with a given signature. + It has attributes name, doc, module, signature, defaults, dict and + methods update and make. + """ + + # Atomic get-and-increment provided by the GIL + _compile_count = itertools.count() + + # make pylint happy + args = varargs = varkw = defaults = kwonlyargs = kwonlydefaults = () + + def __init__(self, func=None, name=None, signature=None, + defaults=None, doc=None, module=None, funcdict=None): + self.shortsignature = signature + if func: + # func can be a class or a callable, but not an instance method + self.name = func.__name__ + if self.name == '': # small hack for lambda functions + self.name = '_lambda_' + self.doc = func.__doc__ + self.module = func.__module__ + if inspect.isroutine(func) or isinstance(func, functools.partial): + argspec = getfullargspec(func) + self.annotations = getattr(func, '__annotations__', {}) + for a in ('args', 'varargs', 'varkw', 'defaults', 'kwonlyargs', + 'kwonlydefaults'): + setattr(self, a, getattr(argspec, a)) + for i, arg in enumerate(self.args): + setattr(self, 'arg%d' % i, arg) + allargs = list(self.args) + allshortargs = list(self.args) + if self.varargs: + allargs.append('*' + self.varargs) + allshortargs.append('*' + self.varargs) + elif self.kwonlyargs: + allargs.append('*') # single star syntax + for a in self.kwonlyargs: + allargs.append('%s=None' % a) + allshortargs.append('%s=%s' % (a, a)) + if self.varkw: + allargs.append('**' + self.varkw) + allshortargs.append('**' + self.varkw) + self.signature = ', '.join(allargs) + self.shortsignature = ', '.join(allshortargs) + self.dict = func.__dict__.copy() + # func=None happens when decorating a caller + if name: + self.name = name + if signature is not None: + self.signature = signature + if defaults: + self.defaults = defaults + if doc: + self.doc = doc + if module: + self.module = module + if funcdict: + self.dict = funcdict + # check existence required attributes + assert hasattr(self, 'name') + if not hasattr(self, 'signature'): + raise TypeError('You are decorating a non function: %s' % func) + + def update(self, func, **kw): + """ + Update the signature of func with the data in self + """ + func.__name__ = self.name + func.__doc__ = getattr(self, 'doc', None) + func.__dict__ = getattr(self, 'dict', {}) + func.__defaults__ = self.defaults + func.__kwdefaults__ = self.kwonlydefaults or None + func.__annotations__ = getattr(self, 'annotations', None) + try: + frame = sys._getframe(3) + except AttributeError: # for IronPython and similar implementations + callermodule = '?' + else: + callermodule = frame.f_globals.get('__name__', '?') + func.__module__ = getattr(self, 'module', callermodule) + func.__dict__.update(kw) + + def make(self, src_templ, evaldict=None, addsource=False, **attrs): + """ + Make a new function from a given template and update the signature + """ + src = src_templ % vars(self) # expand name and signature + evaldict = evaldict or {} + mo = DEF.search(src) + if mo is None: + raise SyntaxError('not a valid function template\n%s' % src) + name = mo.group(1) # extract the function name + names = set([name] + [arg.strip(' *') for arg in + self.shortsignature.split(',')]) + for n in names: + if n in ('_func_', '_call_'): + raise NameError('%s is overridden in\n%s' % (n, src)) + + if not src.endswith('\n'): # add a newline for old Pythons + src += '\n' + + # Ensure each generated function has a unique filename for profilers + # (such as cProfile) that depend on the tuple of (, + # , ) being unique. + filename = '' % next(self._compile_count) + try: + code = compile(src, filename, 'single') + exec(code, evaldict) + except Exception: + print('Error in generated code:', file=sys.stderr) + print(src, file=sys.stderr) + raise + func = evaldict[name] + if addsource: + attrs['__source__'] = src + self.update(func, **attrs) + return func + + @classmethod + def create(cls, obj, body, evaldict, defaults=None, + doc=None, module=None, addsource=True, **attrs): + """ + Create a function from the strings name, signature and body. + evaldict is the evaluation dictionary. If addsource is true an + attribute __source__ is added to the result. The attributes attrs + are added, if any. + """ + if isinstance(obj, str): # "name(signature)" + name, rest = obj.strip().split('(', 1) + signature = rest[:-1] # strip a right parens + func = None + else: # a function + name = None + signature = None + func = obj + self = cls(func, name, signature, defaults, doc, module) + ibody = '\n'.join(' ' + line for line in body.splitlines()) + caller = evaldict.get('_call_') # when called from `decorate` + if caller and iscoroutinefunction(caller): + body = ('async def %(name)s(%(signature)s):\n' + ibody).replace( + 'return', 'return await') + else: + body = 'def %(name)s(%(signature)s):\n' + ibody + return self.make(body, evaldict, addsource, **attrs) + + +def fix(args, kwargs, sig): + """ + Fix args and kwargs to be consistent with the signature + """ + ba = sig.bind(*args, **kwargs) + ba.apply_defaults() # needed for test_dan_schult + return ba.args, ba.kwargs + + +def decorate(func, caller, extras=(), kwsyntax=False): + """ + Decorates a function/generator/coroutine using a caller. + If kwsyntax is True calling the decorated functions with keyword + syntax will pass the named arguments inside the ``kw`` dictionary, + even if such argument are positional, similarly to what functools.wraps + does. By default kwsyntax is False and the the arguments are untouched. + """ + sig = inspect.signature(func) + if isinstance(func, functools.partial): + func = functools.update_wrapper(func, func.func) + if iscoroutinefunction(caller): + async def fun(*args, **kw): + if not kwsyntax: + args, kw = fix(args, kw, sig) + return await caller(func, *(extras + args), **kw) + elif isgeneratorfunction(caller): + def fun(*args, **kw): + if not kwsyntax: + args, kw = fix(args, kw, sig) + for res in caller(func, *(extras + args), **kw): + yield res + else: + def fun(*args, **kw): + if not kwsyntax: + args, kw = fix(args, kw, sig) + return caller(func, *(extras + args), **kw) + + fun.__name__ = func.__name__ + fun.__doc__ = func.__doc__ + fun.__wrapped__ = func + fun.__signature__ = sig + fun.__qualname__ = func.__qualname__ + # builtin functions like defaultdict.__setitem__ lack many attributes + try: + fun.__defaults__ = func.__defaults__ + except AttributeError: + pass + try: + fun.__kwdefaults__ = func.__kwdefaults__ + except AttributeError: + pass + try: + fun.__annotations__ = func.__annotations__ + except AttributeError: + pass + try: + fun.__module__ = func.__module__ + except AttributeError: + pass + try: + fun.__name__ = func.__name__ + except AttributeError: # happens with old versions of numpy.vectorize + func.__name__ == 'noname' + try: + fun.__dict__.update(func.__dict__) + except AttributeError: + pass + return fun + + +def decoratorx(caller): + """ + A version of "decorator" implemented via "exec" and not via the + Signature object. Use this if you are want to preserve the `.__code__` + object properties (https://github.com/micheles/decorator/issues/129). + """ + def dec(func): + return FunctionMaker.create( + func, + "return _call_(_func_, %(shortsignature)s)", + dict(_call_=caller, _func_=func), + __wrapped__=func, __qualname__=func.__qualname__) + return dec + + +def decorator(caller, _func=None, kwsyntax=False): + """ + decorator(caller) converts a caller function into a decorator + """ + if _func is not None: # return a decorated function + # this is obsolete behavior; you should use decorate instead + return decorate(_func, caller, (), kwsyntax) + # else return a decorator function + sig = inspect.signature(caller) + dec_params = [p for p in sig.parameters.values() if p.kind is POS] + + def dec(func=None, *args, **kw): + na = len(args) + 1 + extras = args + tuple(kw.get(p.name, p.default) + for p in dec_params[na:] + if p.default is not EMPTY) + if func is None: + return lambda func: decorate(func, caller, extras, kwsyntax) + else: + return decorate(func, caller, extras, kwsyntax) + dec.__signature__ = sig.replace(parameters=dec_params) + dec.__name__ = caller.__name__ + dec.__doc__ = caller.__doc__ + dec.__wrapped__ = caller + dec.__qualname__ = caller.__qualname__ + dec.__kwdefaults__ = getattr(caller, '__kwdefaults__', None) + dec.__dict__.update(caller.__dict__) + return dec + + +# ####################### contextmanager ####################### # + + +class ContextManager(_GeneratorContextManager): + def __init__(self, g, *a, **k): + _GeneratorContextManager.__init__(self, g, a, k) + + def __call__(self, func): + def caller(f, *a, **k): + with self.__class__(self.func, *self.args, **self.kwds): + return f(*a, **k) + return decorate(func, caller) + + +_contextmanager = decorator(ContextManager) + + +def contextmanager(func): + # Enable Pylint config: contextmanager-decorators=decorator.contextmanager + return _contextmanager(func) + + +# ############################ dispatch_on ############################ # + +def append(a, vancestors): + """ + Append ``a`` to the list of the virtual ancestors, unless it is already + included. + """ + add = True + for j, va in enumerate(vancestors): + if issubclass(va, a): + add = False + break + if issubclass(a, va): + vancestors[j] = a + add = False + if add: + vancestors.append(a) + + +# inspired from simplegeneric by P.J. Eby and functools.singledispatch +def dispatch_on(*dispatch_args): + """ + Factory of decorators turning a function into a generic function + dispatching on the given arguments. + """ + assert dispatch_args, 'No dispatch args passed' + dispatch_str = '(%s,)' % ', '.join(dispatch_args) + + def check(arguments, wrong=operator.ne, msg=''): + """Make sure one passes the expected number of arguments""" + if wrong(len(arguments), len(dispatch_args)): + raise TypeError('Expected %d arguments, got %d%s' % + (len(dispatch_args), len(arguments), msg)) + + def gen_func_dec(func): + """Decorator turning a function into a generic function""" + + # first check the dispatch arguments + argset = set(getfullargspec(func).args) + if not set(dispatch_args) <= argset: + raise NameError('Unknown dispatch arguments %s' % dispatch_str) + + typemap = {} + + def vancestors(*types): + """ + Get a list of sets of virtual ancestors for the given types + """ + check(types) + ras = [[] for _ in range(len(dispatch_args))] + for types_ in typemap: + for t, type_, ra in zip(types, types_, ras): + if issubclass(t, type_) and type_ not in t.mro(): + append(type_, ra) + return [set(ra) for ra in ras] + + def ancestors(*types): + """ + Get a list of virtual MROs, one for each type + """ + check(types) + lists = [] + for t, vas in zip(types, vancestors(*types)): + n_vas = len(vas) + if n_vas > 1: + raise RuntimeError( + 'Ambiguous dispatch for %s: %s' % (t, vas)) + elif n_vas == 1: + va, = vas + mro = type('t', (t, va), {}).mro()[1:] + else: + mro = t.mro() + lists.append(mro[:-1]) # discard t and object + return lists + + def register(*types): + """ + Decorator to register an implementation for the given types + """ + check(types) + + def dec(f): + check(getfullargspec(f).args, operator.lt, ' in ' + f.__name__) + typemap[types] = f + return f + return dec + + def dispatch_info(*types): + """ + An utility to introspect the dispatch algorithm + """ + check(types) + lst = [] + for ancs in itertools.product(*ancestors(*types)): + lst.append(tuple(a.__name__ for a in ancs)) + return lst + + def _dispatch(dispatch_args, *args, **kw): + types = tuple(type(arg) for arg in dispatch_args) + try: # fast path + f = typemap[types] + except KeyError: + pass + else: + return f(*args, **kw) + combinations = itertools.product(*ancestors(*types)) + next(combinations) # the first one has been already tried + for types_ in combinations: + f = typemap.get(types_) + if f is not None: + return f(*args, **kw) + + # else call the default implementation + return func(*args, **kw) + + return FunctionMaker.create( + func, 'return _f_(%s, %%(shortsignature)s)' % dispatch_str, + dict(_f_=_dispatch), register=register, default=func, + typemap=typemap, vancestors=vancestors, ancestors=ancestors, + dispatch_info=dispatch_info, __wrapped__=func) + + gen_func_dec.__name__ = 'dispatch_on' + dispatch_str + return gen_func_dec diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/distutils-precedence.pth b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/distutils-precedence.pth new file mode 100644 index 0000000000000000000000000000000000000000..6de4198fcc39b317cc664bf389f2fc5646e167eb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/distutils-precedence.pth @@ -0,0 +1 @@ +import os; var = 'SETUPTOOLS_USE_DISTUTILS'; enabled = os.environ.get(var, 'stdlib') == 'local'; enabled and __import__('_distutils_hack').add_shim(); diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/ipykernel_launcher.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/ipykernel_launcher.py new file mode 100644 index 0000000000000000000000000000000000000000..0739d4b1ae506c88ca00fd5986071fc703cba446 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/ipykernel_launcher.py @@ -0,0 +1,18 @@ +"""Entry point for launching an IPython kernel. + +This is separate from the ipykernel package so we can avoid doing imports until +after removing the cwd from sys.path. +""" + +import sys +from pathlib import Path + +if __name__ == "__main__": + # Remove the CWD from sys.path while we load stuff. + # This is added back by InteractiveShellApp.init_path() + if sys.path[0] == "" or Path(sys.path[0]) == Path.cwd(): + del sys.path[0] + + from ipykernel import kernelapp as app + + app.launch_new_instance() diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/isympy.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/isympy.py new file mode 100644 index 0000000000000000000000000000000000000000..50e9bc78d08904b8c177105ee90d984ea4b01d20 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/isympy.py @@ -0,0 +1,342 @@ +""" +Python shell for SymPy. + +This is just a normal Python shell (IPython shell if you have the +IPython package installed), that executes the following commands for +the user: + + >>> from __future__ import division + >>> from sympy import * + >>> x, y, z, t = symbols('x y z t') + >>> k, m, n = symbols('k m n', integer=True) + >>> f, g, h = symbols('f g h', cls=Function) + >>> init_printing() + +So starting 'isympy' is equivalent to starting Python (or IPython) and +executing the above commands by hand. It is intended for easy and quick +experimentation with SymPy. isympy is a good way to use SymPy as an +interactive calculator. If you have IPython and Matplotlib installed, then +interactive plotting is enabled by default. + +COMMAND LINE OPTIONS +-------------------- + +-c CONSOLE, --console=CONSOLE + + Use the specified shell (Python or IPython) shell as the console + backend instead of the default one (IPython if present, Python + otherwise), e.g.: + + $isympy -c python + + CONSOLE must be one of 'ipython' or 'python' + +-p PRETTY, --pretty PRETTY + + Setup pretty-printing in SymPy. When pretty-printing is enabled, + expressions can be printed with Unicode or ASCII. The default is + to use pretty-printing (with Unicode if the terminal supports it). + When this option is 'no', expressions will not be pretty-printed + and ASCII will be used: + + $isympy -p no + + PRETTY must be one of 'unicode', 'ascii', or 'no' + +-t TYPES, --types=TYPES + + Setup the ground types for the polys. By default, gmpy ground types + are used if gmpy2 or gmpy is installed, otherwise it falls back to python + ground types, which are a little bit slower. You can manually + choose python ground types even if gmpy is installed (e.g., for + testing purposes): + + $isympy -t python + + TYPES must be one of 'gmpy', 'gmpy1' or 'python' + + Note that the ground type gmpy1 is primarily intended for testing; it + forces the use of gmpy version 1 even if gmpy2 is available. + + This is the same as setting the environment variable + SYMPY_GROUND_TYPES to the given ground type (e.g., + SYMPY_GROUND_TYPES='gmpy') + + The ground types can be determined interactively from the variable + sympy.polys.domains.GROUND_TYPES. + +-o ORDER, --order ORDER + + Setup the ordering of terms for printing. The default is lex, which + orders terms lexicographically (e.g., x**2 + x + 1). You can choose + other orderings, such as rev-lex, which will use reverse + lexicographic ordering (e.g., 1 + x + x**2): + + $isympy -o rev-lex + + ORDER must be one of 'lex', 'rev-lex', 'grlex', 'rev-grlex', + 'grevlex', 'rev-grevlex', 'old', or 'none'. + + Note that for very large expressions, ORDER='none' may speed up + printing considerably but the terms will have no canonical order. + +-q, --quiet + + Print only Python's and SymPy's versions to stdout at startup. + +-d, --doctest + + Use the same format that should be used for doctests. This is + equivalent to -c python -p no. + +-C, --no-cache + + Disable the caching mechanism. Disabling the cache may slow certain + operations down considerably. This is useful for testing the cache, + or for benchmarking, as the cache can result in deceptive timings. + + This is equivalent to setting the environment variable + SYMPY_USE_CACHE to 'no'. + +-a, --auto-symbols (requires at least IPython 0.11) + + Automatically create missing symbols. Normally, typing a name of a + Symbol that has not been instantiated first would raise NameError, + but with this option enabled, any undefined name will be + automatically created as a Symbol. + + Note that this is intended only for interactive, calculator style + usage. In a script that uses SymPy, Symbols should be instantiated + at the top, so that it's clear what they are. + + This will not override any names that are already defined, which + includes the single character letters represented by the mnemonic + QCOSINE (see the "Gotchas and Pitfalls" document in the + documentation). You can delete existing names by executing "del + name". If a name is defined, typing "'name' in dir()" will return True. + + The Symbols that are created using this have default assumptions. + If you want to place assumptions on symbols, you should create them + using symbols() or var(). + + Finally, this only works in the top level namespace. So, for + example, if you define a function in isympy with an undefined + Symbol, it will not work. + + See also the -i and -I options. + +-i, --int-to-Integer (requires at least IPython 0.11) + + Automatically wrap int literals with Integer. This makes it so that + things like 1/2 will come out as Rational(1, 2), rather than 0.5. This + works by preprocessing the source and wrapping all int literals with + Integer. Note that this will not change the behavior of int literals + assigned to variables, and it also won't change the behavior of functions + that return int literals. + + If you want an int, you can wrap the literal in int(), e.g. int(3)/int(2) + gives 1.5 (with division imported from __future__). + +-I, --interactive (requires at least IPython 0.11) + + This is equivalent to --auto-symbols --int-to-Integer. Future options + designed for ease of interactive use may be added to this. + +-D, --debug + + Enable debugging output. This is the same as setting the + environment variable SYMPY_DEBUG to 'True'. The debug status is set + in the variable SYMPY_DEBUG within isympy. + +-- IPython options + + Additionally you can pass command line options directly to the IPython + interpreter (the standard Python shell is not supported). However you + need to add the '--' separator between two types of options, e.g the + startup banner option and the colors option. You need to enter the + options as required by the version of IPython that you are using, too: + + in IPython 0.11, + + $isympy -q -- --colors=NoColor + + or older versions of IPython, + + $isympy -q -- -colors NoColor + +See also isympy --help. +""" + +import os +import sys + +# DO NOT IMPORT SYMPY HERE! Or the setting of the sympy environment variables +# by the command line will break. + +def main() -> None: + from argparse import ArgumentParser, RawDescriptionHelpFormatter + + VERSION = None + if '--version' in sys.argv: + # We cannot import sympy before this is run, because flags like -C and + # -t set environment variables that must be set before SymPy is + # imported. The only thing we need to import it for is to get the + # version, which only matters with the --version flag. + import sympy + VERSION = sympy.__version__ + + usage = 'isympy [options] -- [ipython options]' + parser = ArgumentParser( + usage=usage, + description=__doc__, + formatter_class=RawDescriptionHelpFormatter, + ) + + parser.add_argument('--version', action='version', version=VERSION) + + parser.add_argument( + '-c', '--console', + dest='console', + action='store', + default=None, + choices=['ipython', 'python'], + metavar='CONSOLE', + help='select type of interactive session: ipython | python; defaults ' + 'to ipython if IPython is installed, otherwise python') + + parser.add_argument( + '-p', '--pretty', + dest='pretty', + action='store', + default=None, + metavar='PRETTY', + choices=['unicode', 'ascii', 'no'], + help='setup pretty printing: unicode | ascii | no; defaults to ' + 'unicode printing if the terminal supports it, otherwise ascii') + + parser.add_argument( + '-t', '--types', + dest='types', + action='store', + default=None, + metavar='TYPES', + choices=['gmpy', 'gmpy1', 'python'], + help='setup ground types: gmpy | gmpy1 | python; defaults to gmpy if gmpy2 ' + 'or gmpy is installed, otherwise python') + + parser.add_argument( + '-o', '--order', + dest='order', + action='store', + default=None, + metavar='ORDER', + choices=['lex', 'grlex', 'grevlex', 'rev-lex', 'rev-grlex', 'rev-grevlex', 'old', 'none'], + help='setup ordering of terms: [rev-]lex | [rev-]grlex | [rev-]grevlex | old | none; defaults to lex') + + parser.add_argument( + '-q', '--quiet', + dest='quiet', + action='store_true', + default=False, + help='print only version information at startup') + + parser.add_argument( + '-d', '--doctest', + dest='doctest', + action='store_true', + default=False, + help='use the doctest format for output (you can just copy and paste it)') + + parser.add_argument( + '-C', '--no-cache', + dest='cache', + action='store_false', + default=True, + help='disable caching mechanism') + + parser.add_argument( + '-a', '--auto-symbols', + dest='auto_symbols', + action='store_true', + default=False, + help='automatically construct missing symbols') + + parser.add_argument( + '-i', '--int-to-Integer', + dest='auto_int_to_Integer', + action='store_true', + default=False, + help="automatically wrap int literals with Integer") + + parser.add_argument( + '-I', '--interactive', + dest='interactive', + action='store_true', + default=False, + help="equivalent to -a -i") + + parser.add_argument( + '-D', '--debug', + dest='debug', + action='store_true', + default=False, + help='enable debugging output') + + (options, ipy_args) = parser.parse_known_args() + if '--' in ipy_args: + ipy_args.remove('--') + + if not options.cache: + os.environ['SYMPY_USE_CACHE'] = 'no' + + if options.types: + os.environ['SYMPY_GROUND_TYPES'] = options.types + + if options.debug: + os.environ['SYMPY_DEBUG'] = str(options.debug) + + if options.doctest: + options.pretty = 'no' + options.console = 'python' + + session = options.console + + if session is not None: + ipython = session == 'ipython' + else: + try: + import IPython + ipython = True + except ImportError: + if not options.quiet: + from sympy.interactive.session import no_ipython + print(no_ipython) + ipython = False + + args = { + 'pretty_print': True, + 'use_unicode': None, + 'use_latex': None, + 'order': None, + 'argv': ipy_args, + } + + if options.pretty == 'unicode': + args['use_unicode'] = True + elif options.pretty == 'ascii': + args['use_unicode'] = False + elif options.pretty == 'no': + args['pretty_print'] = False + + if options.order is not None: + args['order'] = options.order + + args['quiet'] = options.quiet + args['auto_symbols'] = options.auto_symbols or options.interactive + args['auto_int_to_Integer'] = options.auto_int_to_Integer or options.interactive + + from sympy.interactive import init_session + init_session(ipython, **args) + +if __name__ == "__main__": + main() diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jsonpointer.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jsonpointer.py new file mode 100644 index 0000000000000000000000000000000000000000..3e97adda448bc6d24ffda7b15cd827cfde6d0926 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jsonpointer.py @@ -0,0 +1,348 @@ +# -*- coding: utf-8 -*- +# +# python-json-pointer - An implementation of the JSON Pointer syntax +# https://github.com/stefankoegl/python-json-pointer +# +# Copyright (c) 2011 Stefan Kögl +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in the +# documentation and/or other materials provided with the distribution. +# 3. The name of the author may not be used to endorse or promote products +# derived from this software without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR +# IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES +# OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. +# IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT +# NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF +# THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +# + +""" Identify specific nodes in a JSON document (RFC 6901) """ + +# Will be parsed by setup.py to determine package metadata +__author__ = 'Stefan Kögl ' +__version__ = '3.0.0' +__website__ = 'https://github.com/stefankoegl/python-json-pointer' +__license__ = 'Modified BSD License' + +import copy +import re +from collections.abc import Mapping, Sequence +from itertools import tee, chain + +_nothing = object() + + +def set_pointer(doc, pointer, value, inplace=True): + """Resolves a pointer against doc and sets the value of the target within doc. + + With inplace set to true, doc is modified as long as pointer is not the + root. + + >>> obj = {'foo': {'anArray': [ {'prop': 44}], 'another prop': {'baz': 'A string' }}} + + >>> set_pointer(obj, '/foo/anArray/0/prop', 55) == \ + {'foo': {'another prop': {'baz': 'A string'}, 'anArray': [{'prop': 55}]}} + True + + >>> set_pointer(obj, '/foo/yet another prop', 'added prop') == \ + {'foo': {'another prop': {'baz': 'A string'}, 'yet another prop': 'added prop', 'anArray': [{'prop': 55}]}} + True + + >>> obj = {'foo': {}} + >>> set_pointer(obj, '/foo/a%20b', 'x') == \ + {'foo': {'a%20b': 'x' }} + True + """ + + pointer = JsonPointer(pointer) + return pointer.set(doc, value, inplace) + + +def resolve_pointer(doc, pointer, default=_nothing): + """ Resolves pointer against doc and returns the referenced object + + >>> obj = {'foo': {'anArray': [ {'prop': 44}], 'another prop': {'baz': 'A string' }}, 'a%20b': 1, 'c d': 2} + + >>> resolve_pointer(obj, '') == obj + True + + >>> resolve_pointer(obj, '/foo') == obj['foo'] + True + + >>> resolve_pointer(obj, '/foo/another prop') == obj['foo']['another prop'] + True + + >>> resolve_pointer(obj, '/foo/another prop/baz') == obj['foo']['another prop']['baz'] + True + + >>> resolve_pointer(obj, '/foo/anArray/0') == obj['foo']['anArray'][0] + True + + >>> resolve_pointer(obj, '/some/path', None) == None + True + + >>> resolve_pointer(obj, '/a b', None) == None + True + + >>> resolve_pointer(obj, '/a%20b') == 1 + True + + >>> resolve_pointer(obj, '/c d') == 2 + True + + >>> resolve_pointer(obj, '/c%20d', None) == None + True + """ + + pointer = JsonPointer(pointer) + return pointer.resolve(doc, default) + + +def pairwise(iterable): + """ Transforms a list to a list of tuples of adjacent items + + s -> (s0,s1), (s1,s2), (s2, s3), ... + + >>> list(pairwise([])) + [] + + >>> list(pairwise([1])) + [] + + >>> list(pairwise([1, 2, 3, 4])) + [(1, 2), (2, 3), (3, 4)] + """ + a, b = tee(iterable) + for _ in b: + break + return zip(a, b) + + +class JsonPointerException(Exception): + pass + + +class EndOfList(object): + """Result of accessing element "-" of a list""" + + def __init__(self, list_): + self.list_ = list_ + + def __repr__(self): + return '{cls}({lst})'.format(cls=self.__class__.__name__, + lst=repr(self.list_)) + + +class JsonPointer(object): + """A JSON Pointer that can reference parts of a JSON document""" + + # Array indices must not contain: + # leading zeros, signs, spaces, decimals, etc + _RE_ARRAY_INDEX = re.compile('0|[1-9][0-9]*$') + _RE_INVALID_ESCAPE = re.compile('(~[^01]|~$)') + + def __init__(self, pointer): + + # validate escapes + invalid_escape = self._RE_INVALID_ESCAPE.search(pointer) + if invalid_escape: + raise JsonPointerException('Found invalid escape {}'.format( + invalid_escape.group())) + + parts = pointer.split('/') + if parts.pop(0) != '': + raise JsonPointerException('Location must start with /') + + parts = [unescape(part) for part in parts] + self.parts = parts + + def to_last(self, doc): + """Resolves ptr until the last step, returns (sub-doc, last-step)""" + + if not self.parts: + return doc, None + + for part in self.parts[:-1]: + doc = self.walk(doc, part) + + return doc, JsonPointer.get_part(doc, self.parts[-1]) + + def resolve(self, doc, default=_nothing): + """Resolves the pointer against doc and returns the referenced object""" + + for part in self.parts: + + try: + doc = self.walk(doc, part) + except JsonPointerException: + if default is _nothing: + raise + else: + return default + + return doc + + get = resolve + + def set(self, doc, value, inplace=True): + """Resolve the pointer against the doc and replace the target with value.""" + + if len(self.parts) == 0: + if inplace: + raise JsonPointerException('Cannot set root in place') + return value + + if not inplace: + doc = copy.deepcopy(doc) + + (parent, part) = self.to_last(doc) + + if isinstance(parent, Sequence) and part == '-': + parent.append(value) + else: + parent[part] = value + + return doc + + @classmethod + def get_part(cls, doc, part): + """Returns the next step in the correct type""" + + if isinstance(doc, Mapping): + return part + + elif isinstance(doc, Sequence): + + if part == '-': + return part + + if not JsonPointer._RE_ARRAY_INDEX.match(str(part)): + raise JsonPointerException("'%s' is not a valid sequence index" % part) + + return int(part) + + elif hasattr(doc, '__getitem__'): + # Allow indexing via ducktyping + # if the target has defined __getitem__ + return part + + else: + raise JsonPointerException("Document '%s' does not support indexing, " + "must be mapping/sequence or support __getitem__" % type(doc)) + + def get_parts(self): + """Returns the list of the parts. For example, JsonPointer('/a/b').get_parts() == ['a', 'b']""" + + return self.parts + + def walk(self, doc, part): + """ Walks one step in doc and returns the referenced part """ + + part = JsonPointer.get_part(doc, part) + + assert hasattr(doc, '__getitem__'), "invalid document type %s" % (type(doc),) + + if isinstance(doc, Sequence): + if part == '-': + return EndOfList(doc) + + try: + return doc[part] + + except IndexError: + raise JsonPointerException("index '%s' is out of bounds" % (part,)) + + # Else the object is a mapping or supports __getitem__(so assume custom indexing) + try: + return doc[part] + + except KeyError: + raise JsonPointerException("member '%s' not found in %s" % (part, doc)) + + def contains(self, ptr): + """ Returns True if self contains the given ptr """ + return self.parts[:len(ptr.parts)] == ptr.parts + + def __contains__(self, item): + """ Returns True if self contains the given ptr """ + return self.contains(item) + + def join(self, suffix): + """ Returns a new JsonPointer with the given suffix append to this ptr """ + if isinstance(suffix, JsonPointer): + suffix_parts = suffix.parts + elif isinstance(suffix, str): + suffix_parts = JsonPointer(suffix).parts + else: + suffix_parts = suffix + try: + return JsonPointer.from_parts(chain(self.parts, suffix_parts)) + except: # noqa E722 + raise JsonPointerException("Invalid suffix") + + def __truediv__(self, suffix): # Python 3 + return self.join(suffix) + + @property + def path(self): + """Returns the string representation of the pointer + + >>> ptr = JsonPointer('/~0/0/~1').path == '/~0/0/~1' + """ + parts = [escape(part) for part in self.parts] + return ''.join('/' + part for part in parts) + + def __eq__(self, other): + """Compares a pointer to another object + + Pointers can be compared by comparing their strings (or splitted + strings), because no two different parts can point to the same + structure in an object (eg no different number representations) + """ + + if not isinstance(other, JsonPointer): + return False + + return self.parts == other.parts + + def __hash__(self): + return hash(tuple(self.parts)) + + def __str__(self): + return self.path + + def __repr__(self): + return type(self).__name__ + "(" + repr(self.path) + ")" + + @classmethod + def from_parts(cls, parts): + """Constructs a JsonPointer from a list of (unescaped) paths + + >>> JsonPointer.from_parts(['a', '~', '/', 0]).path == '/a/~0/~1/0' + True + """ + parts = [escape(str(part)) for part in parts] + ptr = cls(''.join('/' + part for part in parts)) + return ptr + + +def escape(s): + return s.replace('~', '~0').replace('/', '~1') + + +def unescape(s): + return s.replace('~1', '/').replace('~0', '~') diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jupyter.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jupyter.py new file mode 100644 index 0000000000000000000000000000000000000000..852ee3118bee3af01263765837785d0a454919ae --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/jupyter.py @@ -0,0 +1,7 @@ +"""Launch the root jupyter command""" +from __future__ import annotations + +if __name__ == "__main__": + from jupyter_core.command import main + + main() diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/nest_asyncio.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/nest_asyncio.py new file mode 100644 index 0000000000000000000000000000000000000000..1cb5c253fa0658a0adea3516f6463904396cf573 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/nest_asyncio.py @@ -0,0 +1,219 @@ +"""Patch asyncio to allow nested event loops.""" + +import asyncio +import asyncio.events as events +import os +import sys +import threading +from contextlib import contextmanager, suppress +from heapq import heappop + + +def apply(loop=None): + """Patch asyncio to make its event loop reentrant.""" + _patch_asyncio() + _patch_policy() + _patch_tornado() + + loop = loop or asyncio.get_event_loop() + _patch_loop(loop) + + +def _patch_asyncio(): + """Patch asyncio module to use pure Python tasks and futures.""" + + def run(main, *, debug=False): + loop = asyncio.get_event_loop() + loop.set_debug(debug) + task = asyncio.ensure_future(main) + try: + return loop.run_until_complete(task) + finally: + if not task.done(): + task.cancel() + with suppress(asyncio.CancelledError): + loop.run_until_complete(task) + + def _get_event_loop(stacklevel=3): + loop = events._get_running_loop() + if loop is None: + loop = events.get_event_loop_policy().get_event_loop() + return loop + + # Use module level _current_tasks, all_tasks and patch run method. + if hasattr(asyncio, '_nest_patched'): + return + if sys.version_info >= (3, 6, 0): + asyncio.Task = asyncio.tasks._CTask = asyncio.tasks.Task = \ + asyncio.tasks._PyTask + asyncio.Future = asyncio.futures._CFuture = asyncio.futures.Future = \ + asyncio.futures._PyFuture + if sys.version_info < (3, 7, 0): + asyncio.tasks._current_tasks = asyncio.tasks.Task._current_tasks + asyncio.all_tasks = asyncio.tasks.Task.all_tasks + if sys.version_info >= (3, 9, 0): + events._get_event_loop = events.get_event_loop = \ + asyncio.get_event_loop = _get_event_loop + asyncio.run = run + asyncio._nest_patched = True + + +def _patch_policy(): + """Patch the policy to always return a patched loop.""" + + def get_event_loop(self): + if self._local._loop is None: + loop = self.new_event_loop() + _patch_loop(loop) + self.set_event_loop(loop) + return self._local._loop + + policy = events.get_event_loop_policy() + policy.__class__.get_event_loop = get_event_loop + + +def _patch_loop(loop): + """Patch loop to make it reentrant.""" + + def run_forever(self): + with manage_run(self), manage_asyncgens(self): + while True: + self._run_once() + if self._stopping: + break + self._stopping = False + + def run_until_complete(self, future): + with manage_run(self): + f = asyncio.ensure_future(future, loop=self) + if f is not future: + f._log_destroy_pending = False + while not f.done(): + self._run_once() + if self._stopping: + break + if not f.done(): + raise RuntimeError( + 'Event loop stopped before Future completed.') + return f.result() + + def _run_once(self): + """ + Simplified re-implementation of asyncio's _run_once that + runs handles as they become ready. + """ + ready = self._ready + scheduled = self._scheduled + while scheduled and scheduled[0]._cancelled: + heappop(scheduled) + + timeout = ( + 0 if ready or self._stopping + else min(max( + scheduled[0]._when - self.time(), 0), 86400) if scheduled + else None) + event_list = self._selector.select(timeout) + self._process_events(event_list) + + end_time = self.time() + self._clock_resolution + while scheduled and scheduled[0]._when < end_time: + handle = heappop(scheduled) + ready.append(handle) + + for _ in range(len(ready)): + if not ready: + break + handle = ready.popleft() + if not handle._cancelled: + # preempt the current task so that that checks in + # Task.__step do not raise + curr_task = curr_tasks.pop(self, None) + + try: + handle._run() + finally: + # restore the current task + if curr_task is not None: + curr_tasks[self] = curr_task + + handle = None + + @contextmanager + def manage_run(self): + """Set up the loop for running.""" + self._check_closed() + old_thread_id = self._thread_id + old_running_loop = events._get_running_loop() + try: + self._thread_id = threading.get_ident() + events._set_running_loop(self) + self._num_runs_pending += 1 + if self._is_proactorloop: + if self._self_reading_future is None: + self.call_soon(self._loop_self_reading) + yield + finally: + self._thread_id = old_thread_id + events._set_running_loop(old_running_loop) + self._num_runs_pending -= 1 + if self._is_proactorloop: + if (self._num_runs_pending == 0 + and self._self_reading_future is not None): + ov = self._self_reading_future._ov + self._self_reading_future.cancel() + if ov is not None: + self._proactor._unregister(ov) + self._self_reading_future = None + + @contextmanager + def manage_asyncgens(self): + if not hasattr(sys, 'get_asyncgen_hooks'): + # Python version is too old. + return + old_agen_hooks = sys.get_asyncgen_hooks() + try: + self._set_coroutine_origin_tracking(self._debug) + if self._asyncgens is not None: + sys.set_asyncgen_hooks( + firstiter=self._asyncgen_firstiter_hook, + finalizer=self._asyncgen_finalizer_hook) + yield + finally: + self._set_coroutine_origin_tracking(False) + if self._asyncgens is not None: + sys.set_asyncgen_hooks(*old_agen_hooks) + + def _check_running(self): + """Do not throw exception if loop is already running.""" + pass + + if hasattr(loop, '_nest_patched'): + return + if not isinstance(loop, asyncio.BaseEventLoop): + raise ValueError('Can\'t patch loop of type %s' % type(loop)) + cls = loop.__class__ + cls.run_forever = run_forever + cls.run_until_complete = run_until_complete + cls._run_once = _run_once + cls._check_running = _check_running + cls._check_runnung = _check_running # typo in Python 3.7 source + cls._num_runs_pending = 1 if loop.is_running() else 0 + cls._is_proactorloop = ( + os.name == 'nt' and issubclass(cls, asyncio.ProactorEventLoop)) + if sys.version_info < (3, 7, 0): + cls._set_coroutine_origin_tracking = cls._set_coroutine_wrapper + curr_tasks = asyncio.tasks._current_tasks \ + if sys.version_info >= (3, 7, 0) else asyncio.Task._current_tasks + cls._nest_patched = True + + +def _patch_tornado(): + """ + If tornado is imported before nest_asyncio, make tornado aware of + the pure-Python asyncio Future. + """ + if 'tornado' in sys.modules: + import tornado.concurrent as tc # type: ignore + tc.Future = asyncio.Future + if asyncio.Future not in tc.FUTURES: + tc.FUTURES += (asyncio.Future,) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/pandocfilters.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/pandocfilters.py new file mode 100644 index 0000000000000000000000000000000000000000..68569d9543f21da356e37631ab891f6355b25cef --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/pandocfilters.py @@ -0,0 +1,304 @@ +# Author: John MacFarlane +# Copyright: (C) 2013 John MacFarlane +# License: BSD3 + +""" +Functions to aid writing python scripts that process the pandoc +AST serialized as JSON. +""" + +import codecs +import hashlib +import io +import json +import os +import sys +import atexit +import shutil +import tempfile + + +# some utility-functions: make it easier to create your own filters + + +def get_filename4code(module, content, ext=None): + """Generate filename based on content + + The function ensures that the (temporary) directory exists, so that the + file can be written. + + By default, the directory won't be cleaned up, + so a filter can use the directory as a cache and + decide not to regenerate if there's no change. + + In case the user preferres the files to be temporary files, + an environment variable `PANDOCFILTER_CLEANUP` can be set to + any non-empty value such as `1` to + make sure the directory is created in a temporary location and removed + after finishing the filter. In this case there's no caching and files + will be regenerated each time the filter is run. + + Example: + filename = get_filename4code("myfilter", code) + """ + if os.getenv('PANDOCFILTER_CLEANUP'): + imagedir = tempfile.mkdtemp(prefix=module) + atexit.register(lambda: shutil.rmtree(imagedir)) + else: + imagedir = module + "-images" + fn = hashlib.sha1(content.encode(sys.getfilesystemencoding())).hexdigest() + try: + os.makedirs(imagedir, exist_ok=True) + sys.stderr.write('Created directory ' + imagedir + '\n') + except OSError: + sys.stderr.write('Could not create directory "' + imagedir + '"\n') + if ext: + fn += "." + ext + return os.path.join(imagedir, fn) + +def get_value(kv, key, value = None): + """get value from the keyvalues (options)""" + res = [] + for k, v in kv: + if k == key: + value = v + else: + res.append([k, v]) + return value, res + +def get_caption(kv): + """get caption from the keyvalues (options) + + Example: + if key == 'CodeBlock': + [[ident, classes, keyvals], code] = value + caption, typef, keyvals = get_caption(keyvals) + ... + return Para([Image([ident, [], keyvals], caption, [filename, typef])]) + """ + caption = [] + typef = "" + value, res = get_value(kv, u"caption") + if value is not None: + caption = [Str(value)] + typef = "fig:" + + return caption, typef, res + + +def get_extension(format, default, **alternates): + """get the extension for the result, needs a default and some specialisations + + Example: + filetype = get_extension(format, "png", html="svg", latex="eps") + """ + try: + return alternates[format] + except KeyError: + return default + +# end of utilities + + +def walk(x, action, format, meta): + """Walk a tree, applying an action to every object. + Returns a modified tree. An action is a function of the form + `action(key, value, format, meta)`, where: + + * `key` is the type of the pandoc object (e.g. 'Str', 'Para') `value` is + * the contents of the object (e.g. a string for 'Str', a list of + inline elements for 'Para') + * `format` is the target output format (as supplied by the + `format` argument of `walk`) + * `meta` is the document's metadata + + The return of an action is either: + + * `None`: this means that the object should remain unchanged + * a pandoc object: this will replace the original object + * a list of pandoc objects: these will replace the original object; the + list is merged with the neighbors of the orignal objects (spliced into + the list the original object belongs to); returning an empty list deletes + the object + """ + if isinstance(x, list): + array = [] + for item in x: + if isinstance(item, dict) and 't' in item: + res = action(item['t'], + item['c'] if 'c' in item else None, format, meta) + if res is None: + array.append(walk(item, action, format, meta)) + elif isinstance(res, list): + for z in res: + array.append(walk(z, action, format, meta)) + else: + array.append(walk(res, action, format, meta)) + else: + array.append(walk(item, action, format, meta)) + return array + elif isinstance(x, dict): + return {k: walk(v, action, format, meta) for k, v in x.items()} + else: + return x + +def toJSONFilter(action): + """Like `toJSONFilters`, but takes a single action as argument. + """ + toJSONFilters([action]) + + +def toJSONFilters(actions): + """Generate a JSON-to-JSON filter from stdin to stdout + + The filter: + + * reads a JSON-formatted pandoc document from stdin + * transforms it by walking the tree and performing the actions + * returns a new JSON-formatted pandoc document to stdout + + The argument `actions` is a list of functions of the form + `action(key, value, format, meta)`, as described in more + detail under `walk`. + + This function calls `applyJSONFilters`, with the `format` + argument provided by the first command-line argument, + if present. (Pandoc sets this by default when calling + filters.) + """ + try: + input_stream = io.TextIOWrapper(sys.stdin.buffer, encoding='utf-8') + except AttributeError: + # Python 2 does not have sys.stdin.buffer. + # REF: https://stackoverflow.com/questions/2467928/python-unicodeencode + input_stream = codecs.getreader("utf-8")(sys.stdin) + + source = input_stream.read() + if len(sys.argv) > 1: + format = sys.argv[1] + else: + format = "" + + sys.stdout.write(applyJSONFilters(actions, source, format)) + +def applyJSONFilters(actions, source, format=""): + """Walk through JSON structure and apply filters + + This: + + * reads a JSON-formatted pandoc document from a source string + * transforms it by walking the tree and performing the actions + * returns a new JSON-formatted pandoc document as a string + + The `actions` argument is a list of functions (see `walk` + for a full description). + + The argument `source` is a string encoded JSON object. + + The argument `format` is a string describing the output format. + + Returns a the new JSON-formatted pandoc document. + """ + + doc = json.loads(source) + + if 'meta' in doc: + meta = doc['meta'] + elif doc[0]: # old API + meta = doc[0]['unMeta'] + else: + meta = {} + altered = doc + for action in actions: + altered = walk(altered, action, format, meta) + + return json.dumps(altered) + + +def stringify(x): + """Walks the tree x and returns concatenated string content, + leaving out all formatting. + """ + result = [] + + def go(key, val, format, meta): + if key in ['Str', 'MetaString']: + result.append(val) + elif key == 'Code': + result.append(val[1]) + elif key == 'Math': + result.append(val[1]) + elif key == 'LineBreak': + result.append(" ") + elif key == 'SoftBreak': + result.append(" ") + elif key == 'Space': + result.append(" ") + + walk(x, go, "", {}) + return ''.join(result) + + +def attributes(attrs): + """Returns an attribute list, constructed from the + dictionary attrs. + """ + attrs = attrs or {} + ident = attrs.get("id", "") + classes = attrs.get("classes", []) + keyvals = [[x, attrs[x]] for x in attrs if (x != "classes" and x != "id")] + return [ident, classes, keyvals] + + +def elt(eltType, numargs): + def fun(*args): + lenargs = len(args) + if lenargs != numargs: + raise ValueError(eltType + ' expects ' + str(numargs) + + ' arguments, but given ' + str(lenargs)) + if numargs == 0: + xs = [] + elif len(args) == 1: + xs = args[0] + else: + xs = list(args) + return {'t': eltType, 'c': xs} + return fun + +# Constructors for block elements + +Plain = elt('Plain', 1) +Para = elt('Para', 1) +CodeBlock = elt('CodeBlock', 2) +RawBlock = elt('RawBlock', 2) +BlockQuote = elt('BlockQuote', 1) +OrderedList = elt('OrderedList', 2) +BulletList = elt('BulletList', 1) +DefinitionList = elt('DefinitionList', 1) +Header = elt('Header', 3) +HorizontalRule = elt('HorizontalRule', 0) +Table = elt('Table', 5) +Div = elt('Div', 2) +Null = elt('Null', 0) + +# Constructors for inline elements + +Str = elt('Str', 1) +Emph = elt('Emph', 1) +Strong = elt('Strong', 1) +Strikeout = elt('Strikeout', 1) +Superscript = elt('Superscript', 1) +Subscript = elt('Subscript', 1) +SmallCaps = elt('SmallCaps', 1) +Quoted = elt('Quoted', 2) +Cite = elt('Cite', 2) +Code = elt('Code', 2) +Space = elt('Space', 0) +LineBreak = elt('LineBreak', 0) +Math = elt('Math', 2) +RawInline = elt('RawInline', 2) +Link = elt('Link', 3) +Image = elt('Image', 3) +Note = elt('Note', 1) +SoftBreak = elt('SoftBreak', 0) +Span = elt('Span', 2) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/pip-22.0.2.virtualenv b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/pip-22.0.2.virtualenv new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/protobuf-3.20.3-py3.10-nspkg.pth b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/protobuf-3.20.3-py3.10-nspkg.pth new file mode 100644 index 0000000000000000000000000000000000000000..baef7a0f418633ed421ab4c995e4a4a233d9c368 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/protobuf-3.20.3-py3.10-nspkg.pth @@ -0,0 +1 @@ +import sys, types, os;has_mfs = sys.version_info > (3, 5);p = os.path.join(sys._getframe(1).f_locals['sitedir'], *('google',));importlib = has_mfs and __import__('importlib.util');has_mfs and __import__('importlib.machinery');m = has_mfs and sys.modules.setdefault('google', importlib.util.module_from_spec(importlib.machinery.PathFinder.find_spec('google', [os.path.dirname(p)])));m = m or sys.modules.setdefault('google', types.ModuleType('google'));mp = (m or []) and m.__dict__.setdefault('__path__',[]);(p not in mp) and mp.append(p) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__config__.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__config__.py new file mode 100644 index 0000000000000000000000000000000000000000..faf528c80a751867267f1885e6f3a5d93d61b475 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__config__.py @@ -0,0 +1,161 @@ +# This file is generated by SciPy's build process +# It contains system_info results at the time of building this package. +from enum import Enum + +__all__ = ["show"] +_built_with_meson = True + + +class DisplayModes(Enum): + stdout = "stdout" + dicts = "dicts" + + +def _cleanup(d): + """ + Removes empty values in a `dict` recursively + This ensures we remove values that Meson could not provide to CONFIG + """ + if isinstance(d, dict): + return { k: _cleanup(v) for k, v in d.items() if v != '' and _cleanup(v) != '' } + else: + return d + + +CONFIG = _cleanup( + { + "Compilers": { + "c": { + "name": "gcc", + "linker": r"ld.bfd", + "version": "10.2.1", + "commands": r"cc", + "args": r"", + "linker args": r"", + }, + "cython": { + "name": r"cython", + "linker": r"cython", + "version": r"3.0.11", + "commands": r"cython", + "args": r"", + "linker args": r"", + }, + "c++": { + "name": "gcc", + "linker": r"ld.bfd", + "version": "10.2.1", + "commands": r"c++", + "args": r"", + "linker args": r"", + }, + "fortran": { + "name": "gcc", + "linker": r"ld.bfd", + "version": "10.2.1", + "commands": r"gfortran", + "args": r"", + "linker args": r"", + }, + "pythran": { + "version": r"0.16.1", + "include directory": r"../../tmp/pip-build-env-h_xz8lfs/overlay/lib/python3.10/site-packages/pythran" + }, + }, + "Machine Information": { + "host": { + "cpu": r"x86_64", + "family": r"x86_64", + "endian": r"little", + "system": r"linux", + }, + "build": { + "cpu": r"x86_64", + "family": r"x86_64", + "endian": r"little", + "system": r"linux", + }, + "cross-compiled": bool("False".lower().replace('false', '')), + }, + "Build Dependencies": { + "blas": { + "name": "scipy-openblas", + "found": bool("True".lower().replace('false', '')), + "version": "0.3.27.dev", + "detection method": "pkgconfig", + "include directory": r"/opt/_internal/cpython-3.10.14/lib/python3.10/site-packages/scipy_openblas32/include", + "lib directory": r"/opt/_internal/cpython-3.10.14/lib/python3.10/site-packages/scipy_openblas32/lib", + "openblas configuration": r"OpenBLAS 0.3.27.dev DYNAMIC_ARCH NO_AFFINITY Zen MAX_THREADS=64", + "pc file directory": r"/project", + }, + "lapack": { + "name": "scipy-openblas", + "found": bool("True".lower().replace('false', '')), + "version": "0.3.27.dev", + "detection method": "pkgconfig", + "include directory": r"/opt/_internal/cpython-3.10.14/lib/python3.10/site-packages/scipy_openblas32/include", + "lib directory": r"/opt/_internal/cpython-3.10.14/lib/python3.10/site-packages/scipy_openblas32/lib", + "openblas configuration": r"OpenBLAS 0.3.27.dev DYNAMIC_ARCH NO_AFFINITY Zen MAX_THREADS=64", + "pc file directory": r"/project", + }, + "pybind11": { + "name": "pybind11", + "version": "2.12.0", + "detection method": "config-tool", + "include directory": r"unknown", + }, + }, + "Python Information": { + "path": r"/opt/python/cp310-cp310/bin/python", + "version": "3.10", + }, + } +) + + +def _check_pyyaml(): + import yaml + + return yaml + + +def show(mode=DisplayModes.stdout.value): + """ + Show libraries and system information on which SciPy was built + and is being used + + Parameters + ---------- + mode : {`'stdout'`, `'dicts'`}, optional. + Indicates how to display the config information. + `'stdout'` prints to console, `'dicts'` returns a dictionary + of the configuration. + + Returns + ------- + out : {`dict`, `None`} + If mode is `'dicts'`, a dict is returned, else None + + Notes + ----- + 1. The `'stdout'` mode will give more readable + output if ``pyyaml`` is installed + + """ + if mode == DisplayModes.stdout.value: + try: # Non-standard library, check import + yaml = _check_pyyaml() + + print(yaml.dump(CONFIG)) + except ModuleNotFoundError: + import warnings + import json + + warnings.warn("Install `pyyaml` for better output", stacklevel=1) + print(json.dumps(CONFIG, indent=2)) + elif mode == DisplayModes.dicts.value: + return CONFIG + else: + raise AttributeError( + f"Invalid `mode`, use one of: {', '.join([e.value for e in DisplayModes])}" + ) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__init__.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..cc2ccee425ff92117c00aeacccdb38b92261a0ca --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/__init__.py @@ -0,0 +1,141 @@ +""" +SciPy: A scientific computing package for Python +================================================ + +Documentation is available in the docstrings and +online at https://docs.scipy.org. + +Subpackages +----------- +Using any of these subpackages requires an explicit import. For example, +``import scipy.cluster``. + +:: + + cluster --- Vector Quantization / Kmeans + constants --- Physical and mathematical constants and units + datasets --- Dataset methods + fft --- Discrete Fourier transforms + fftpack --- Legacy discrete Fourier transforms + integrate --- Integration routines + interpolate --- Interpolation Tools + io --- Data input and output + linalg --- Linear algebra routines + misc --- Utilities that don't have another home. + ndimage --- N-D image package + odr --- Orthogonal Distance Regression + optimize --- Optimization Tools + signal --- Signal Processing Tools + sparse --- Sparse Matrices + spatial --- Spatial data structures and algorithms + special --- Special functions + stats --- Statistical Functions + +Public API in the main SciPy namespace +-------------------------------------- +:: + + __version__ --- SciPy version string + LowLevelCallable --- Low-level callback function + show_config --- Show scipy build configuration + test --- Run scipy unittests + +""" + +import importlib as _importlib + +from numpy import __version__ as __numpy_version__ + + +try: + from scipy.__config__ import show as show_config +except ImportError as e: + msg = """Error importing SciPy: you cannot import SciPy while + being in scipy source directory; please exit the SciPy source + tree first and relaunch your Python interpreter.""" + raise ImportError(msg) from e + + +from scipy.version import version as __version__ + + +# Allow distributors to run custom init code +from . import _distributor_init +del _distributor_init + + +from scipy._lib import _pep440 +# In maintenance branch, change to np_maxversion N+3 if numpy is at N +np_minversion = '1.23.5' +np_maxversion = '2.3.0' +if (_pep440.parse(__numpy_version__) < _pep440.Version(np_minversion) or + _pep440.parse(__numpy_version__) >= _pep440.Version(np_maxversion)): + import warnings + warnings.warn(f"A NumPy version >={np_minversion} and <{np_maxversion}" + f" is required for this version of SciPy (detected " + f"version {__numpy_version__})", + UserWarning, stacklevel=2) +del _pep440 + + +# This is the first import of an extension module within SciPy. If there's +# a general issue with the install, such that extension modules are missing +# or cannot be imported, this is where we'll get a failure - so give an +# informative error message. +try: + from scipy._lib._ccallback import LowLevelCallable +except ImportError as e: + msg = "The `scipy` install you are using seems to be broken, " + \ + "(extension modules cannot be imported), " + \ + "please try reinstalling." + raise ImportError(msg) from e + + +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester + + +submodules = [ + 'cluster', + 'constants', + 'datasets', + 'fft', + 'fftpack', + 'integrate', + 'interpolate', + 'io', + 'linalg', + 'misc', + 'ndimage', + 'odr', + 'optimize', + 'signal', + 'sparse', + 'spatial', + 'special', + 'stats' +] + +__all__ = submodules + [ + 'LowLevelCallable', + 'test', + 'show_config', + '__version__', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + if name in submodules: + return _importlib.import_module(f'scipy.{name}') + else: + try: + return globals()[name] + except KeyError: + raise AttributeError( + f"Module 'scipy' has no attribute '{name}'" + ) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/_distributor_init.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/_distributor_init.py new file mode 100644 index 0000000000000000000000000000000000000000..5df134975aa27d31beaff74c3cbfd2d3fb0a55dd --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/_distributor_init.py @@ -0,0 +1,18 @@ +""" Distributor init file + +Distributors: you can replace the contents of this file with your own custom +code to support particular distributions of SciPy. + +For example, this is a good place to put any checks for hardware requirements +or BLAS/LAPACK library initialization. + +The SciPy standard source distribution will not put code in this file beyond +the try-except import of `_distributor_init_local` (which is not part of a +standard source distribution), so you can safely replace this file with your +own version. +""" + +try: + from . import _distributor_init_local # noqa: F401 +except ImportError: + pass diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/conftest.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/conftest.py new file mode 100644 index 0000000000000000000000000000000000000000..084c29a8ef24374d9e93898bbf47ba82fcc3541d --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/conftest.py @@ -0,0 +1,413 @@ +# Pytest customization +import json +import os +import warnings +import tempfile +from contextlib import contextmanager + +import numpy as np +import numpy.testing as npt +import pytest +import hypothesis + +from scipy._lib._fpumode import get_fpu_mode +from scipy._lib._testutils import FPUModeChangeWarning +from scipy._lib._array_api import SCIPY_ARRAY_API, SCIPY_DEVICE +from scipy._lib import _pep440 + +try: + from scipy_doctest.conftest import dt_config + HAVE_SCPDT = True +except ModuleNotFoundError: + HAVE_SCPDT = False + + +def pytest_configure(config): + config.addinivalue_line("markers", + "slow: Tests that are very slow.") + config.addinivalue_line("markers", + "xslow: mark test as extremely slow (not run unless explicitly requested)") + config.addinivalue_line("markers", + "xfail_on_32bit: mark test as failing on 32-bit platforms") + try: + import pytest_timeout # noqa:F401 + except Exception: + config.addinivalue_line( + "markers", 'timeout: mark a test for a non-default timeout') + try: + # This is a more reliable test of whether pytest_fail_slow is installed + # When I uninstalled it, `import pytest_fail_slow` didn't fail! + from pytest_fail_slow import parse_duration # type: ignore[import-not-found] # noqa:F401,E501 + except Exception: + config.addinivalue_line( + "markers", 'fail_slow: mark a test for a non-default timeout failure') + config.addinivalue_line("markers", + "skip_xp_backends(*backends, reasons=None, np_only=False, cpu_only=False): " + "mark the desired skip configuration for the `skip_xp_backends` fixture.") + + +def pytest_runtest_setup(item): + mark = item.get_closest_marker("xslow") + if mark is not None: + try: + v = int(os.environ.get('SCIPY_XSLOW', '0')) + except ValueError: + v = False + if not v: + pytest.skip("very slow test; " + "set environment variable SCIPY_XSLOW=1 to run it") + mark = item.get_closest_marker("xfail_on_32bit") + if mark is not None and np.intp(0).itemsize < 8: + pytest.xfail(f'Fails on our 32-bit test platform(s): {mark.args[0]}') + + # Older versions of threadpoolctl have an issue that may lead to this + # warning being emitted, see gh-14441 + with npt.suppress_warnings() as sup: + sup.filter(pytest.PytestUnraisableExceptionWarning) + + try: + from threadpoolctl import threadpool_limits + + HAS_THREADPOOLCTL = True + except Exception: # observed in gh-14441: (ImportError, AttributeError) + # Optional dependency only. All exceptions are caught, for robustness + HAS_THREADPOOLCTL = False + + if HAS_THREADPOOLCTL: + # Set the number of openmp threads based on the number of workers + # xdist is using to prevent oversubscription. Simplified version of what + # sklearn does (it can rely on threadpoolctl and its builtin OpenMP helper + # functions) + try: + xdist_worker_count = int(os.environ['PYTEST_XDIST_WORKER_COUNT']) + except KeyError: + # raises when pytest-xdist is not installed + return + + if not os.getenv('OMP_NUM_THREADS'): + max_openmp_threads = os.cpu_count() // 2 # use nr of physical cores + threads_per_worker = max(max_openmp_threads // xdist_worker_count, 1) + try: + threadpool_limits(threads_per_worker, user_api='blas') + except Exception: + # May raise AttributeError for older versions of OpenBLAS. + # Catch any error for robustness. + return + + +@pytest.fixture(scope="function", autouse=True) +def check_fpu_mode(request): + """ + Check FPU mode was not changed during the test. + """ + old_mode = get_fpu_mode() + yield + new_mode = get_fpu_mode() + + if old_mode != new_mode: + warnings.warn(f"FPU mode changed from {old_mode:#x} to {new_mode:#x} during " + "the test", + category=FPUModeChangeWarning, stacklevel=0) + + +# Array API backend handling +xp_available_backends = {'numpy': np} + +if SCIPY_ARRAY_API and isinstance(SCIPY_ARRAY_API, str): + # fill the dict of backends with available libraries + try: + import array_api_strict + xp_available_backends.update({'array_api_strict': array_api_strict}) + if _pep440.parse(array_api_strict.__version__) < _pep440.Version('2.0'): + raise ImportError("array-api-strict must be >= version 2.0") + array_api_strict.set_array_api_strict_flags( + api_version='2023.12' + ) + except ImportError: + pass + + try: + import torch # type: ignore[import-not-found] + xp_available_backends.update({'pytorch': torch}) + # can use `mps` or `cpu` + torch.set_default_device(SCIPY_DEVICE) + except ImportError: + pass + + try: + import cupy # type: ignore[import-not-found] + xp_available_backends.update({'cupy': cupy}) + except ImportError: + pass + + try: + import jax.numpy # type: ignore[import-not-found] + xp_available_backends.update({'jax.numpy': jax.numpy}) + jax.config.update("jax_enable_x64", True) + jax.config.update("jax_default_device", jax.devices(SCIPY_DEVICE)[0]) + except ImportError: + pass + + # by default, use all available backends + if SCIPY_ARRAY_API.lower() not in ("1", "true"): + SCIPY_ARRAY_API_ = json.loads(SCIPY_ARRAY_API) + + if 'all' in SCIPY_ARRAY_API_: + pass # same as True + else: + # only select a subset of backend by filtering out the dict + try: + xp_available_backends = { + backend: xp_available_backends[backend] + for backend in SCIPY_ARRAY_API_ + } + except KeyError: + msg = f"'--array-api-backend' must be in {xp_available_backends.keys()}" + raise ValueError(msg) + +if 'cupy' in xp_available_backends: + SCIPY_DEVICE = 'cuda' + +array_api_compatible = pytest.mark.parametrize("xp", xp_available_backends.values()) + +skip_xp_invalid_arg = pytest.mark.skipif(SCIPY_ARRAY_API, + reason = ('Test involves masked arrays, object arrays, or other types ' + 'that are not valid input when `SCIPY_ARRAY_API` is used.')) + + +@pytest.fixture +def skip_xp_backends(xp, request): + """ + Skip based on the ``skip_xp_backends`` marker. + + Parameters + ---------- + *backends : tuple + Backends to skip, e.g. ``("array_api_strict", "torch")``. + These are overriden when ``np_only`` is ``True``, and are not + necessary to provide for non-CPU backends when ``cpu_only`` is ``True``. + reasons : list, optional + A list of reasons for each skip. When ``np_only`` is ``True``, + this should be a singleton list. Otherwise, this should be a list + of reasons, one for each corresponding backend in ``backends``. + If unprovided, default reasons are used. Note that it is not possible + to specify a custom reason with ``cpu_only``. Default: ``None``. + np_only : bool, optional + When ``True``, the test is skipped for all backends other + than the default NumPy backend. There is no need to provide + any ``backends`` in this case. To specify a reason, pass a + singleton list to ``reasons``. Default: ``False``. + cpu_only : bool, optional + When ``True``, the test is skipped on non-CPU devices. + There is no need to provide any ``backends`` in this case, + but any ``backends`` will also be skipped on the CPU. + Default: ``False``. + """ + if "skip_xp_backends" not in request.keywords: + return + backends = request.keywords["skip_xp_backends"].args + kwargs = request.keywords["skip_xp_backends"].kwargs + np_only = kwargs.get("np_only", False) + cpu_only = kwargs.get("cpu_only", False) + if np_only: + reasons = kwargs.get("reasons", ["do not run with non-NumPy backends."]) + reason = reasons[0] + if xp.__name__ != 'numpy': + pytest.skip(reason=reason) + return + if cpu_only: + reason = "do not run with `SCIPY_ARRAY_API` set and not on CPU" + if SCIPY_ARRAY_API and SCIPY_DEVICE != 'cpu': + if xp.__name__ == 'cupy': + pytest.skip(reason=reason) + elif xp.__name__ == 'torch': + if 'cpu' not in xp.empty(0).device.type: + pytest.skip(reason=reason) + elif xp.__name__ == 'jax.numpy': + for d in xp.empty(0).devices(): + if 'cpu' not in d.device_kind: + pytest.skip(reason=reason) + + if backends is not None: + reasons = kwargs.get("reasons", False) + for i, backend in enumerate(backends): + if xp.__name__ == backend: + if not reasons: + reason = f"do not run with array API backend: {backend}" + else: + reason = reasons[i] + pytest.skip(reason=reason) + + +# Following the approach of NumPy's conftest.py... +# Use a known and persistent tmpdir for hypothesis' caches, which +# can be automatically cleared by the OS or user. +hypothesis.configuration.set_hypothesis_home_dir( + os.path.join(tempfile.gettempdir(), ".hypothesis") +) + +# We register two custom profiles for SciPy - for details see +# https://hypothesis.readthedocs.io/en/latest/settings.html +# The first is designed for our own CI runs; the latter also +# forces determinism and is designed for use via scipy.test() +hypothesis.settings.register_profile( + name="nondeterministic", deadline=None, print_blob=True, +) +hypothesis.settings.register_profile( + name="deterministic", + deadline=None, print_blob=True, database=None, derandomize=True, + suppress_health_check=list(hypothesis.HealthCheck), +) + +# Profile is currently set by environment variable `SCIPY_HYPOTHESIS_PROFILE` +# In the future, it would be good to work the choice into dev.py. +SCIPY_HYPOTHESIS_PROFILE = os.environ.get("SCIPY_HYPOTHESIS_PROFILE", + "deterministic") +hypothesis.settings.load_profile(SCIPY_HYPOTHESIS_PROFILE) + + +############################################################################ +# doctesting stuff + +if HAVE_SCPDT: + + # FIXME: populate the dict once + @contextmanager + def warnings_errors_and_rng(test=None): + """Temporarily turn (almost) all warnings to errors. + + Filter out known warnings which we allow. + """ + known_warnings = dict() + + # these functions are known to emit "divide by zero" RuntimeWarnings + divide_by_zero = [ + 'scipy.linalg.norm', 'scipy.ndimage.center_of_mass', + ] + for name in divide_by_zero: + known_warnings[name] = dict(category=RuntimeWarning, + message='divide by zero') + + # Deprecated stuff in scipy.signal and elsewhere + deprecated = [ + 'scipy.signal.cwt', 'scipy.signal.morlet', 'scipy.signal.morlet2', + 'scipy.signal.ricker', + 'scipy.integrate.simpson', + 'scipy.interpolate.interp2d', + ] + for name in deprecated: + known_warnings[name] = dict(category=DeprecationWarning) + + from scipy import integrate + # the funcions are known to emit IntergrationWarnings + integration_w = ['scipy.special.ellip_normal', + 'scipy.special.ellip_harm_2', + ] + for name in integration_w: + known_warnings[name] = dict(category=integrate.IntegrationWarning, + message='The occurrence of roundoff') + + # scipy.stats deliberately emits UserWarnings sometimes + user_w = ['scipy.stats.anderson_ksamp', 'scipy.stats.kurtosistest', + 'scipy.stats.normaltest', 'scipy.sparse.linalg.norm'] + for name in user_w: + known_warnings[name] = dict(category=UserWarning) + + # additional one-off warnings to filter + dct = { + 'scipy.sparse.linalg.norm': + dict(category=UserWarning, message="Exited at iteration"), + # tutorials + 'linalg.rst': + dict(message='the matrix subclass is not', + category=PendingDeprecationWarning), + 'stats.rst': + dict(message='The maximum number of subdivisions', + category=integrate.IntegrationWarning), + } + known_warnings.update(dct) + + # these legitimately emit warnings in examples + legit = set('scipy.signal.normalize') + + # Now, the meat of the matter: filter warnings, + # also control the random seed for each doctest. + + # XXX: this matches the refguide-check behavior, but is a tad strange: + # makes sure that the seed the old-fashioned np.random* methods is + # *NOT* reproducible but the new-style `default_rng()` *IS* repoducible. + # Should these two be either both repro or both not repro? + + from scipy._lib._util import _fixed_default_rng + import numpy as np + with _fixed_default_rng(): + np.random.seed(None) + with warnings.catch_warnings(): + if test and test.name in known_warnings: + warnings.filterwarnings('ignore', + **known_warnings[test.name]) + yield + elif test and test.name in legit: + yield + else: + warnings.simplefilter('error', Warning) + yield + + + dt_config.user_context_mgr = warnings_errors_and_rng + dt_config.skiplist = set([ + 'scipy.linalg.LinAlgError', # comes from numpy + 'scipy.fftpack.fftshift', # fftpack stuff is also from numpy + 'scipy.fftpack.ifftshift', + 'scipy.fftpack.fftfreq', + 'scipy.special.sinc', # sinc is from numpy + 'scipy.optimize.show_options', # does not have much to doctest + 'scipy.signal.normalize', # manipulates warnings (XXX temp skip) + 'scipy.sparse.linalg.norm', # XXX temp skip + ]) + + # these are affected by NumPy 2.0 scalar repr: rely on string comparison + if np.__version__ < "2": + dt_config.skiplist.update(set([ + 'scipy.io.hb_read', + 'scipy.io.hb_write', + 'scipy.sparse.csgraph.connected_components', + 'scipy.sparse.csgraph.depth_first_order', + 'scipy.sparse.csgraph.shortest_path', + 'scipy.sparse.csgraph.floyd_warshall', + 'scipy.sparse.csgraph.dijkstra', + 'scipy.sparse.csgraph.bellman_ford', + 'scipy.sparse.csgraph.johnson', + 'scipy.sparse.csgraph.yen', + 'scipy.sparse.csgraph.breadth_first_order', + 'scipy.sparse.csgraph.reverse_cuthill_mckee', + 'scipy.sparse.csgraph.structural_rank', + 'scipy.sparse.csgraph.construct_dist_matrix', + 'scipy.sparse.csgraph.reconstruct_path', + 'scipy.ndimage.value_indices', + 'scipy.stats.mstats.describe', + ])) + + # help pytest collection a bit: these names are either private + # (distributions), or just do not need doctesting. + dt_config.pytest_extra_ignore = [ + "scipy.stats.distributions", + "scipy.optimize.cython_optimize", + "scipy.test", + "scipy.show_config", + ] + + dt_config.pytest_extra_xfail = { + # name: reason + "io.rst": "", + "ND_regular_grid.rst": "ReST parser limitation", + "extrapolation_examples.rst": "ReST parser limitation", + "sampling_pinv.rst": "__cinit__ unexpected argument", + "sampling_srou.rst": "nan in scalar_power", + "probability_distributions.rst": "integration warning", + } + + # tutorials + dt_config.pseudocode = set(['integrate.nquad(func,']) + dt_config.local_resources = {'io.rst': ["octave_a.mat"]} +############################################################################ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/linalg.pxd b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/linalg.pxd new file mode 100644 index 0000000000000000000000000000000000000000..c7c49f9ad8f4c90ee93725fdcdbe73c2e7f5aacd --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/linalg.pxd @@ -0,0 +1 @@ +from scipy.linalg cimport cython_blas, cython_lapack diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize.pxd b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize.pxd new file mode 100644 index 0000000000000000000000000000000000000000..2402eeb020d34ad8b82e287e32545423911ff66c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize.pxd @@ -0,0 +1 @@ +from .optimize cimport cython_optimize diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/README b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/README new file mode 100644 index 0000000000000000000000000000000000000000..a355e0c447f2d36275877225fcbddd42f14636dd --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/README @@ -0,0 +1,76 @@ +From the website for the L-BFGS-B code (from at +http://www.ece.northwestern.edu/~nocedal/lbfgsb.html): + +""" +L-BFGS-B is a limited-memory quasi-Newton code for bound-constrained +optimization, i.e. for problems where the only constraints are of the +form l<= x <= u. +""" + +This is a Python wrapper (using F2PY) written by David M. Cooke + and released as version 0.9 on April 9, 2004. +The wrapper was slightly modified by Joonas Paalasmaa for the 3.0 version +in March 2012. + +License of L-BFGS-B (Fortran code) +================================== + +The version included here (in lbfgsb.f) is 3.0 (released April 25, 2011). It was +written by Ciyou Zhu, Richard Byrd, and Jorge Nocedal . It +carries the following condition for use: + + """ + This software is freely available, but we expect that all publications + describing work using this software, or all commercial products using it, + quote at least one of the references given below. This software is released + under the BSD License. + + References + * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound + Constrained Optimization, (1995), SIAM Journal on Scientific and + Statistical Computing, 16, 5, pp. 1190-1208. + * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, + FORTRAN routines for large scale bound constrained optimization (1997), + ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560. + * J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, + FORTRAN routines for large scale bound constrained optimization (2011), + ACM Transactions on Mathematical Software, 38, 1. + """ + +The Python wrapper +================== + +This code uses F2PY (http://cens.ioc.ee/projects/f2py2e/) to generate +the wrapper around the Fortran code. + +The Python code and wrapper are copyrighted 2004 by David M. Cooke +. + +Example usage +============= + +An example of the usage is given at the bottom of the lbfgsb.py file. +Run it with 'python lbfgsb.py'. + +License for the Python wrapper +============================== + +Copyright (c) 2004 David M. Cooke + +Permission is hereby granted, free of charge, to any person obtaining a copy of +this software and associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies +of the Software, and to permit persons to whom the Software is furnished to do +so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/__init__.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..d41cb5033af15131fa7d5a8ab490648553dc544b --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/__init__.py @@ -0,0 +1,452 @@ +""" +===================================================== +Optimization and root finding (:mod:`scipy.optimize`) +===================================================== + +.. currentmodule:: scipy.optimize + +.. toctree:: + :hidden: + + optimize.cython_optimize + +SciPy ``optimize`` provides functions for minimizing (or maximizing) +objective functions, possibly subject to constraints. It includes +solvers for nonlinear problems (with support for both local and global +optimization algorithms), linear programming, constrained +and nonlinear least-squares, root finding, and curve fitting. + +Common functions and objects, shared across different solvers, are: + +.. autosummary:: + :toctree: generated/ + + show_options - Show specific options optimization solvers. + OptimizeResult - The optimization result returned by some optimizers. + OptimizeWarning - The optimization encountered problems. + + +Optimization +============ + +Scalar functions optimization +----------------------------- + +.. autosummary:: + :toctree: generated/ + + minimize_scalar - Interface for minimizers of univariate functions + +The `minimize_scalar` function supports the following methods: + +.. toctree:: + + optimize.minimize_scalar-brent + optimize.minimize_scalar-bounded + optimize.minimize_scalar-golden + +Local (multivariate) optimization +--------------------------------- + +.. autosummary:: + :toctree: generated/ + + minimize - Interface for minimizers of multivariate functions. + +The `minimize` function supports the following methods: + +.. toctree:: + + optimize.minimize-neldermead + optimize.minimize-powell + optimize.minimize-cg + optimize.minimize-bfgs + optimize.minimize-newtoncg + optimize.minimize-lbfgsb + optimize.minimize-tnc + optimize.minimize-cobyla + optimize.minimize-cobyqa + optimize.minimize-slsqp + optimize.minimize-trustconstr + optimize.minimize-dogleg + optimize.minimize-trustncg + optimize.minimize-trustkrylov + optimize.minimize-trustexact + +Constraints are passed to `minimize` function as a single object or +as a list of objects from the following classes: + +.. autosummary:: + :toctree: generated/ + + NonlinearConstraint - Class defining general nonlinear constraints. + LinearConstraint - Class defining general linear constraints. + +Simple bound constraints are handled separately and there is a special class +for them: + +.. autosummary:: + :toctree: generated/ + + Bounds - Bound constraints. + +Quasi-Newton strategies implementing `HessianUpdateStrategy` +interface can be used to approximate the Hessian in `minimize` +function (available only for the 'trust-constr' method). Available +quasi-Newton methods implementing this interface are: + +.. autosummary:: + :toctree: generated/ + + BFGS - Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy. + SR1 - Symmetric-rank-1 Hessian update strategy. + +.. _global_optimization: + +Global optimization +------------------- + +.. autosummary:: + :toctree: generated/ + + basinhopping - Basinhopping stochastic optimizer. + brute - Brute force searching optimizer. + differential_evolution - Stochastic optimizer using differential evolution. + + shgo - Simplicial homology global optimizer. + dual_annealing - Dual annealing stochastic optimizer. + direct - DIRECT (Dividing Rectangles) optimizer. + +Least-squares and curve fitting +=============================== + +Nonlinear least-squares +----------------------- + +.. autosummary:: + :toctree: generated/ + + least_squares - Solve a nonlinear least-squares problem with bounds on the variables. + +Linear least-squares +-------------------- + +.. autosummary:: + :toctree: generated/ + + nnls - Linear least-squares problem with non-negativity constraint. + lsq_linear - Linear least-squares problem with bound constraints. + isotonic_regression - Least squares problem of isotonic regression via PAVA. + +Curve fitting +------------- + +.. autosummary:: + :toctree: generated/ + + curve_fit -- Fit curve to a set of points. + +Root finding +============ + +Scalar functions +---------------- +.. autosummary:: + :toctree: generated/ + + root_scalar - Unified interface for nonlinear solvers of scalar functions. + brentq - quadratic interpolation Brent method. + brenth - Brent method, modified by Harris with hyperbolic extrapolation. + ridder - Ridder's method. + bisect - Bisection method. + newton - Newton's method (also Secant and Halley's methods). + toms748 - Alefeld, Potra & Shi Algorithm 748. + RootResults - The root finding result returned by some root finders. + +The `root_scalar` function supports the following methods: + +.. toctree:: + + optimize.root_scalar-brentq + optimize.root_scalar-brenth + optimize.root_scalar-bisect + optimize.root_scalar-ridder + optimize.root_scalar-newton + optimize.root_scalar-toms748 + optimize.root_scalar-secant + optimize.root_scalar-halley + + + +The table below lists situations and appropriate methods, along with +*asymptotic* convergence rates per iteration (and per function evaluation) +for successful convergence to a simple root(*). +Bisection is the slowest of them all, adding one bit of accuracy for each +function evaluation, but is guaranteed to converge. +The other bracketing methods all (eventually) increase the number of accurate +bits by about 50% for every function evaluation. +The derivative-based methods, all built on `newton`, can converge quite quickly +if the initial value is close to the root. They can also be applied to +functions defined on (a subset of) the complex plane. + ++-------------+----------+----------+-----------+-------------+-------------+----------------+ +| Domain of f | Bracket? | Derivatives? | Solvers | Convergence | ++ + +----------+-----------+ +-------------+----------------+ +| | | `fprime` | `fprime2` | | Guaranteed? | Rate(s)(*) | ++=============+==========+==========+===========+=============+=============+================+ +| `R` | Yes | N/A | N/A | - bisection | - Yes | - 1 "Linear" | +| | | | | - brentq | - Yes | - >=1, <= 1.62 | +| | | | | - brenth | - Yes | - >=1, <= 1.62 | +| | | | | - ridder | - Yes | - 2.0 (1.41) | +| | | | | - toms748 | - Yes | - 2.7 (1.65) | ++-------------+----------+----------+-----------+-------------+-------------+----------------+ +| `R` or `C` | No | No | No | secant | No | 1.62 (1.62) | ++-------------+----------+----------+-----------+-------------+-------------+----------------+ +| `R` or `C` | No | Yes | No | newton | No | 2.00 (1.41) | ++-------------+----------+----------+-----------+-------------+-------------+----------------+ +| `R` or `C` | No | Yes | Yes | halley | No | 3.00 (1.44) | ++-------------+----------+----------+-----------+-------------+-------------+----------------+ + +.. seealso:: + + `scipy.optimize.cython_optimize` -- Typed Cython versions of root finding functions + +Fixed point finding: + +.. autosummary:: + :toctree: generated/ + + fixed_point - Single-variable fixed-point solver. + +Multidimensional +---------------- + +.. autosummary:: + :toctree: generated/ + + root - Unified interface for nonlinear solvers of multivariate functions. + +The `root` function supports the following methods: + +.. toctree:: + + optimize.root-hybr + optimize.root-lm + optimize.root-broyden1 + optimize.root-broyden2 + optimize.root-anderson + optimize.root-linearmixing + optimize.root-diagbroyden + optimize.root-excitingmixing + optimize.root-krylov + optimize.root-dfsane + +Linear programming / MILP +========================= + +.. autosummary:: + :toctree: generated/ + + milp -- Mixed integer linear programming. + linprog -- Unified interface for minimizers of linear programming problems. + +The `linprog` function supports the following methods: + +.. toctree:: + + optimize.linprog-simplex + optimize.linprog-interior-point + optimize.linprog-revised_simplex + optimize.linprog-highs-ipm + optimize.linprog-highs-ds + optimize.linprog-highs + +The simplex, interior-point, and revised simplex methods support callback +functions, such as: + +.. autosummary:: + :toctree: generated/ + + linprog_verbose_callback -- Sample callback function for linprog (simplex). + +Assignment problems +=================== + +.. autosummary:: + :toctree: generated/ + + linear_sum_assignment -- Solves the linear-sum assignment problem. + quadratic_assignment -- Solves the quadratic assignment problem. + +The `quadratic_assignment` function supports the following methods: + +.. toctree:: + + optimize.qap-faq + optimize.qap-2opt + +Utilities +========= + +Finite-difference approximation +------------------------------- + +.. autosummary:: + :toctree: generated/ + + approx_fprime - Approximate the gradient of a scalar function. + check_grad - Check the supplied derivative using finite differences. + + +Line search +----------- + +.. autosummary:: + :toctree: generated/ + + bracket - Bracket a minimum, given two starting points. + line_search - Return a step that satisfies the strong Wolfe conditions. + +Hessian approximation +--------------------- + +.. autosummary:: + :toctree: generated/ + + LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian. + HessianUpdateStrategy - Interface for implementing Hessian update strategies + +Benchmark problems +------------------ + +.. autosummary:: + :toctree: generated/ + + rosen - The Rosenbrock function. + rosen_der - The derivative of the Rosenbrock function. + rosen_hess - The Hessian matrix of the Rosenbrock function. + rosen_hess_prod - Product of the Rosenbrock Hessian with a vector. + +Legacy functions +================ + +The functions below are not recommended for use in new scripts; +all of these methods are accessible via a newer, more consistent +interfaces, provided by the interfaces above. + +Optimization +------------ + +General-purpose multivariate methods: + +.. autosummary:: + :toctree: generated/ + + fmin - Nelder-Mead Simplex algorithm. + fmin_powell - Powell's (modified) conjugate direction method. + fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm. + fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno). + fmin_ncg - Line-search Newton Conjugate Gradient. + +Constrained multivariate methods: + +.. autosummary:: + :toctree: generated/ + + fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer. + fmin_tnc - Truncated Newton code. + fmin_cobyla - Constrained optimization by linear approximation. + fmin_slsqp - Minimization using sequential least-squares programming. + +Univariate (scalar) minimization methods: + +.. autosummary:: + :toctree: generated/ + + fminbound - Bounded minimization of a scalar function. + brent - 1-D function minimization using Brent method. + golden - 1-D function minimization using Golden Section method. + +Least-squares +------------- + +.. autosummary:: + :toctree: generated/ + + leastsq - Minimize the sum of squares of M equations in N unknowns. + +Root finding +------------ + +General nonlinear solvers: + +.. autosummary:: + :toctree: generated/ + + fsolve - Non-linear multivariable equation solver. + broyden1 - Broyden's first method. + broyden2 - Broyden's second method. + NoConvergence - Exception raised when nonlinear solver does not converge. + +Large-scale nonlinear solvers: + +.. autosummary:: + :toctree: generated/ + + newton_krylov + anderson + + BroydenFirst + InverseJacobian + KrylovJacobian + +Simple iteration solvers: + +.. autosummary:: + :toctree: generated/ + + excitingmixing + linearmixing + diagbroyden + +""" # noqa: E501 + +from ._optimize import * +from ._minimize import * +from ._root import * +from ._root_scalar import * +from ._minpack_py import * +from ._zeros_py import * +from ._lbfgsb_py import fmin_l_bfgs_b, LbfgsInvHessProduct +from ._tnc import fmin_tnc +from ._cobyla_py import fmin_cobyla +from ._nonlin import * +from ._slsqp_py import fmin_slsqp +from ._nnls import nnls +from ._basinhopping import basinhopping +from ._linprog import linprog, linprog_verbose_callback +from ._lsap import linear_sum_assignment +from ._differentialevolution import differential_evolution +from ._lsq import least_squares, lsq_linear +from ._isotonic import isotonic_regression +from ._constraints import (NonlinearConstraint, + LinearConstraint, + Bounds) +from ._hessian_update_strategy import HessianUpdateStrategy, BFGS, SR1 +from ._shgo import shgo +from ._dual_annealing import dual_annealing +from ._qap import quadratic_assignment +from ._direct_py import direct +from ._milp import milp + +# Deprecated namespaces, to be removed in v2.0.0 +from . import ( + cobyla, lbfgsb, linesearch, minpack, minpack2, moduleTNC, nonlin, optimize, + slsqp, tnc, zeros +) + +__all__ = [s for s in dir() if not s.startswith('_')] + +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_basinhopping.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_basinhopping.py new file mode 100644 index 0000000000000000000000000000000000000000..333a7af410de7ed84ecd46b1cbc8d2b0c4362f4b --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_basinhopping.py @@ -0,0 +1,753 @@ +""" +basinhopping: The basinhopping global optimization algorithm +""" +import numpy as np +import math +import inspect +import scipy.optimize +from scipy._lib._util import check_random_state + +__all__ = ['basinhopping'] + + +_params = (inspect.Parameter('res_new', kind=inspect.Parameter.KEYWORD_ONLY), + inspect.Parameter('res_old', kind=inspect.Parameter.KEYWORD_ONLY)) +_new_accept_test_signature = inspect.Signature(parameters=_params) + + +class Storage: + """ + Class used to store the lowest energy structure + """ + def __init__(self, minres): + self._add(minres) + + def _add(self, minres): + self.minres = minres + self.minres.x = np.copy(minres.x) + + def update(self, minres): + if minres.success and (minres.fun < self.minres.fun + or not self.minres.success): + self._add(minres) + return True + else: + return False + + def get_lowest(self): + return self.minres + + +class BasinHoppingRunner: + """This class implements the core of the basinhopping algorithm. + + x0 : ndarray + The starting coordinates. + minimizer : callable + The local minimizer, with signature ``result = minimizer(x)``. + The return value is an `optimize.OptimizeResult` object. + step_taking : callable + This function displaces the coordinates randomly. Signature should + be ``x_new = step_taking(x)``. Note that `x` may be modified in-place. + accept_tests : list of callables + Each test is passed the kwargs `f_new`, `x_new`, `f_old` and + `x_old`. These tests will be used to judge whether or not to accept + the step. The acceptable return values are True, False, or ``"force + accept"``. If any of the tests return False then the step is rejected. + If ``"force accept"``, then this will override any other tests in + order to accept the step. This can be used, for example, to forcefully + escape from a local minimum that ``basinhopping`` is trapped in. + disp : bool, optional + Display status messages. + + """ + def __init__(self, x0, minimizer, step_taking, accept_tests, disp=False): + self.x = np.copy(x0) + self.minimizer = minimizer + self.step_taking = step_taking + self.accept_tests = accept_tests + self.disp = disp + + self.nstep = 0 + + # initialize return object + self.res = scipy.optimize.OptimizeResult() + self.res.minimization_failures = 0 + + # do initial minimization + minres = minimizer(self.x) + if not minres.success: + self.res.minimization_failures += 1 + if self.disp: + print("warning: basinhopping: local minimization failure") + self.x = np.copy(minres.x) + self.energy = minres.fun + self.incumbent_minres = minres # best minimize result found so far + if self.disp: + print("basinhopping step %d: f %g" % (self.nstep, self.energy)) + + # initialize storage class + self.storage = Storage(minres) + + if hasattr(minres, "nfev"): + self.res.nfev = minres.nfev + if hasattr(minres, "njev"): + self.res.njev = minres.njev + if hasattr(minres, "nhev"): + self.res.nhev = minres.nhev + + def _monte_carlo_step(self): + """Do one Monte Carlo iteration + + Randomly displace the coordinates, minimize, and decide whether + or not to accept the new coordinates. + """ + # Take a random step. Make a copy of x because the step_taking + # algorithm might change x in place + x_after_step = np.copy(self.x) + x_after_step = self.step_taking(x_after_step) + + # do a local minimization + minres = self.minimizer(x_after_step) + x_after_quench = minres.x + energy_after_quench = minres.fun + if not minres.success: + self.res.minimization_failures += 1 + if self.disp: + print("warning: basinhopping: local minimization failure") + if hasattr(minres, "nfev"): + self.res.nfev += minres.nfev + if hasattr(minres, "njev"): + self.res.njev += minres.njev + if hasattr(minres, "nhev"): + self.res.nhev += minres.nhev + + # accept the move based on self.accept_tests. If any test is False, + # then reject the step. If any test returns the special string + # 'force accept', then accept the step regardless. This can be used + # to forcefully escape from a local minimum if normal basin hopping + # steps are not sufficient. + accept = True + for test in self.accept_tests: + if inspect.signature(test) == _new_accept_test_signature: + testres = test(res_new=minres, res_old=self.incumbent_minres) + else: + testres = test(f_new=energy_after_quench, x_new=x_after_quench, + f_old=self.energy, x_old=self.x) + + if testres == 'force accept': + accept = True + break + elif testres is None: + raise ValueError("accept_tests must return True, False, or " + "'force accept'") + elif not testres: + accept = False + + # Report the result of the acceptance test to the take step class. + # This is for adaptive step taking + if hasattr(self.step_taking, "report"): + self.step_taking.report(accept, f_new=energy_after_quench, + x_new=x_after_quench, f_old=self.energy, + x_old=self.x) + + return accept, minres + + def one_cycle(self): + """Do one cycle of the basinhopping algorithm + """ + self.nstep += 1 + new_global_min = False + + accept, minres = self._monte_carlo_step() + + if accept: + self.energy = minres.fun + self.x = np.copy(minres.x) + self.incumbent_minres = minres # best minimize result found so far + new_global_min = self.storage.update(minres) + + # print some information + if self.disp: + self.print_report(minres.fun, accept) + if new_global_min: + print("found new global minimum on step %d with function" + " value %g" % (self.nstep, self.energy)) + + # save some variables as BasinHoppingRunner attributes + self.xtrial = minres.x + self.energy_trial = minres.fun + self.accept = accept + + return new_global_min + + def print_report(self, energy_trial, accept): + """print a status update""" + minres = self.storage.get_lowest() + print("basinhopping step %d: f %g trial_f %g accepted %d " + " lowest_f %g" % (self.nstep, self.energy, energy_trial, + accept, minres.fun)) + + +class AdaptiveStepsize: + """ + Class to implement adaptive stepsize. + + This class wraps the step taking class and modifies the stepsize to + ensure the true acceptance rate is as close as possible to the target. + + Parameters + ---------- + takestep : callable + The step taking routine. Must contain modifiable attribute + takestep.stepsize + accept_rate : float, optional + The target step acceptance rate + interval : int, optional + Interval for how often to update the stepsize + factor : float, optional + The step size is multiplied or divided by this factor upon each + update. + verbose : bool, optional + Print information about each update + + """ + def __init__(self, takestep, accept_rate=0.5, interval=50, factor=0.9, + verbose=True): + self.takestep = takestep + self.target_accept_rate = accept_rate + self.interval = interval + self.factor = factor + self.verbose = verbose + + self.nstep = 0 + self.nstep_tot = 0 + self.naccept = 0 + + def __call__(self, x): + return self.take_step(x) + + def _adjust_step_size(self): + old_stepsize = self.takestep.stepsize + accept_rate = float(self.naccept) / self.nstep + if accept_rate > self.target_accept_rate: + # We're accepting too many steps. This generally means we're + # trapped in a basin. Take bigger steps. + self.takestep.stepsize /= self.factor + else: + # We're not accepting enough steps. Take smaller steps. + self.takestep.stepsize *= self.factor + if self.verbose: + print(f"adaptive stepsize: acceptance rate {accept_rate:f} target " + f"{self.target_accept_rate:f} new stepsize " + f"{self.takestep.stepsize:g} old stepsize {old_stepsize:g}") + + def take_step(self, x): + self.nstep += 1 + self.nstep_tot += 1 + if self.nstep % self.interval == 0: + self._adjust_step_size() + return self.takestep(x) + + def report(self, accept, **kwargs): + "called by basinhopping to report the result of the step" + if accept: + self.naccept += 1 + + +class RandomDisplacement: + """Add a random displacement of maximum size `stepsize` to each coordinate. + + Calling this updates `x` in-place. + + Parameters + ---------- + stepsize : float, optional + Maximum stepsize in any dimension + random_gen : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + + """ + + def __init__(self, stepsize=0.5, random_gen=None): + self.stepsize = stepsize + self.random_gen = check_random_state(random_gen) + + def __call__(self, x): + x += self.random_gen.uniform(-self.stepsize, self.stepsize, + np.shape(x)) + return x + + +class MinimizerWrapper: + """ + wrap a minimizer function as a minimizer class + """ + def __init__(self, minimizer, func=None, **kwargs): + self.minimizer = minimizer + self.func = func + self.kwargs = kwargs + + def __call__(self, x0): + if self.func is None: + return self.minimizer(x0, **self.kwargs) + else: + return self.minimizer(self.func, x0, **self.kwargs) + + +class Metropolis: + """Metropolis acceptance criterion. + + Parameters + ---------- + T : float + The "temperature" parameter for the accept or reject criterion. + random_gen : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Random number generator used for acceptance test. + + """ + + def __init__(self, T, random_gen=None): + # Avoid ZeroDivisionError since "MBH can be regarded as a special case + # of the BH framework with the Metropolis criterion, where temperature + # T = 0." (Reject all steps that increase energy.) + self.beta = 1.0 / T if T != 0 else float('inf') + self.random_gen = check_random_state(random_gen) + + def accept_reject(self, res_new, res_old): + """ + Assuming the local search underlying res_new was successful: + If new energy is lower than old, it will always be accepted. + If new is higher than old, there is a chance it will be accepted, + less likely for larger differences. + """ + with np.errstate(invalid='ignore'): + # The energy values being fed to Metropolis are 1-length arrays, and if + # they are equal, their difference is 0, which gets multiplied by beta, + # which is inf, and array([0]) * float('inf') causes + # + # RuntimeWarning: invalid value encountered in multiply + # + # Ignore this warning so when the algorithm is on a flat plane, it always + # accepts the step, to try to move off the plane. + prod = -(res_new.fun - res_old.fun) * self.beta + w = math.exp(min(0, prod)) + + rand = self.random_gen.uniform() + return w >= rand and (res_new.success or not res_old.success) + + def __call__(self, *, res_new, res_old): + """ + f_new and f_old are mandatory in kwargs + """ + return bool(self.accept_reject(res_new, res_old)) + + +def basinhopping(func, x0, niter=100, T=1.0, stepsize=0.5, + minimizer_kwargs=None, take_step=None, accept_test=None, + callback=None, interval=50, disp=False, niter_success=None, + seed=None, *, target_accept_rate=0.5, stepwise_factor=0.9): + """Find the global minimum of a function using the basin-hopping algorithm. + + Basin-hopping is a two-phase method that combines a global stepping + algorithm with local minimization at each step. Designed to mimic + the natural process of energy minimization of clusters of atoms, it works + well for similar problems with "funnel-like, but rugged" energy landscapes + [5]_. + + As the step-taking, step acceptance, and minimization methods are all + customizable, this function can also be used to implement other two-phase + methods. + + Parameters + ---------- + func : callable ``f(x, *args)`` + Function to be optimized. ``args`` can be passed as an optional item + in the dict `minimizer_kwargs` + x0 : array_like + Initial guess. + niter : integer, optional + The number of basin-hopping iterations. There will be a total of + ``niter + 1`` runs of the local minimizer. + T : float, optional + The "temperature" parameter for the acceptance or rejection criterion. + Higher "temperatures" mean that larger jumps in function value will be + accepted. For best results `T` should be comparable to the + separation (in function value) between local minima. + stepsize : float, optional + Maximum step size for use in the random displacement. + minimizer_kwargs : dict, optional + Extra keyword arguments to be passed to the local minimizer + `scipy.optimize.minimize` Some important options could be: + + method : str + The minimization method (e.g. ``"L-BFGS-B"``) + args : tuple + Extra arguments passed to the objective function (`func`) and + its derivatives (Jacobian, Hessian). + + take_step : callable ``take_step(x)``, optional + Replace the default step-taking routine with this routine. The default + step-taking routine is a random displacement of the coordinates, but + other step-taking algorithms may be better for some systems. + `take_step` can optionally have the attribute ``take_step.stepsize``. + If this attribute exists, then `basinhopping` will adjust + ``take_step.stepsize`` in order to try to optimize the global minimum + search. + accept_test : callable, ``accept_test(f_new=f_new, x_new=x_new, f_old=fold, x_old=x_old)``, optional + Define a test which will be used to judge whether to accept the + step. This will be used in addition to the Metropolis test based on + "temperature" `T`. The acceptable return values are True, + False, or ``"force accept"``. If any of the tests return False + then the step is rejected. If the latter, then this will override any + other tests in order to accept the step. This can be used, for example, + to forcefully escape from a local minimum that `basinhopping` is + trapped in. + callback : callable, ``callback(x, f, accept)``, optional + A callback function which will be called for all minima found. ``x`` + and ``f`` are the coordinates and function value of the trial minimum, + and ``accept`` is whether that minimum was accepted. This can + be used, for example, to save the lowest N minima found. Also, + `callback` can be used to specify a user defined stop criterion by + optionally returning True to stop the `basinhopping` routine. + interval : integer, optional + interval for how often to update the `stepsize` + disp : bool, optional + Set to True to print status messages + niter_success : integer, optional + Stop the run if the global minimum candidate remains the same for this + number of iterations. + seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Specify `seed` for repeatable minimizations. The random numbers + generated with this seed only affect the default Metropolis + `accept_test` and the default `take_step`. If you supply your own + `take_step` and `accept_test`, and these functions use random + number generation, then those functions are responsible for the state + of their random number generator. + target_accept_rate : float, optional + The target acceptance rate that is used to adjust the `stepsize`. + If the current acceptance rate is greater than the target, + then the `stepsize` is increased. Otherwise, it is decreased. + Range is (0, 1). Default is 0.5. + + .. versionadded:: 1.8.0 + + stepwise_factor : float, optional + The `stepsize` is multiplied or divided by this stepwise factor upon + each update. Range is (0, 1). Default is 0.9. + + .. versionadded:: 1.8.0 + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: ``x`` the solution array, ``fun`` the value + of the function at the solution, and ``message`` which describes the + cause of the termination. The ``OptimizeResult`` object returned by the + selected minimizer at the lowest minimum is also contained within this + object and can be accessed through the ``lowest_optimization_result`` + attribute. See `OptimizeResult` for a description of other attributes. + + See Also + -------- + minimize : + The local minimization function called once for each basinhopping step. + `minimizer_kwargs` is passed to this routine. + + Notes + ----- + Basin-hopping is a stochastic algorithm which attempts to find the global + minimum of a smooth scalar function of one or more variables [1]_ [2]_ [3]_ + [4]_. The algorithm in its current form was described by David Wales and + Jonathan Doye [2]_ http://www-wales.ch.cam.ac.uk/. + + The algorithm is iterative with each cycle composed of the following + features + + 1) random perturbation of the coordinates + + 2) local minimization + + 3) accept or reject the new coordinates based on the minimized function + value + + The acceptance test used here is the Metropolis criterion of standard Monte + Carlo algorithms, although there are many other possibilities [3]_. + + This global minimization method has been shown to be extremely efficient + for a wide variety of problems in physics and chemistry. It is + particularly useful when the function has many minima separated by large + barriers. See the `Cambridge Cluster Database + `_ for databases of molecular + systems that have been optimized primarily using basin-hopping. This + database includes minimization problems exceeding 300 degrees of freedom. + + See the free software program `GMIN `_ + for a Fortran implementation of basin-hopping. This implementation has many + variations of the procedure described above, including more + advanced step taking algorithms and alternate acceptance criterion. + + For stochastic global optimization there is no way to determine if the true + global minimum has actually been found. Instead, as a consistency check, + the algorithm can be run from a number of different random starting points + to ensure the lowest minimum found in each example has converged to the + global minimum. For this reason, `basinhopping` will by default simply + run for the number of iterations `niter` and return the lowest minimum + found. It is left to the user to ensure that this is in fact the global + minimum. + + Choosing `stepsize`: This is a crucial parameter in `basinhopping` and + depends on the problem being solved. The step is chosen uniformly in the + region from x0-stepsize to x0+stepsize, in each dimension. Ideally, it + should be comparable to the typical separation (in argument values) between + local minima of the function being optimized. `basinhopping` will, by + default, adjust `stepsize` to find an optimal value, but this may take + many iterations. You will get quicker results if you set a sensible + initial value for ``stepsize``. + + Choosing `T`: The parameter `T` is the "temperature" used in the + Metropolis criterion. Basinhopping steps are always accepted if + ``func(xnew) < func(xold)``. Otherwise, they are accepted with + probability:: + + exp( -(func(xnew) - func(xold)) / T ) + + So, for best results, `T` should to be comparable to the typical + difference (in function values) between local minima. (The height of + "walls" between local minima is irrelevant.) + + If `T` is 0, the algorithm becomes Monotonic Basin-Hopping, in which all + steps that increase energy are rejected. + + .. versionadded:: 0.12.0 + + References + ---------- + .. [1] Wales, David J. 2003, Energy Landscapes, Cambridge University Press, + Cambridge, UK. + .. [2] Wales, D J, and Doye J P K, Global Optimization by Basin-Hopping and + the Lowest Energy Structures of Lennard-Jones Clusters Containing up to + 110 Atoms. Journal of Physical Chemistry A, 1997, 101, 5111. + .. [3] Li, Z. and Scheraga, H. A., Monte Carlo-minimization approach to the + multiple-minima problem in protein folding, Proc. Natl. Acad. Sci. USA, + 1987, 84, 6611. + .. [4] Wales, D. J. and Scheraga, H. A., Global optimization of clusters, + crystals, and biomolecules, Science, 1999, 285, 1368. + .. [5] Olson, B., Hashmi, I., Molloy, K., and Shehu1, A., Basin Hopping as + a General and Versatile Optimization Framework for the Characterization + of Biological Macromolecules, Advances in Artificial Intelligence, + Volume 2012 (2012), Article ID 674832, :doi:`10.1155/2012/674832` + + Examples + -------- + The following example is a 1-D minimization problem, with many + local minima superimposed on a parabola. + + >>> import numpy as np + >>> from scipy.optimize import basinhopping + >>> func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x + >>> x0 = [1.] + + Basinhopping, internally, uses a local minimization algorithm. We will use + the parameter `minimizer_kwargs` to tell basinhopping which algorithm to + use and how to set up that minimizer. This parameter will be passed to + `scipy.optimize.minimize`. + + >>> minimizer_kwargs = {"method": "BFGS"} + >>> ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs, + ... niter=200) + >>> # the global minimum is: + >>> ret.x, ret.fun + -0.1951, -1.0009 + + Next consider a 2-D minimization problem. Also, this time, we + will use gradient information to significantly speed up the search. + + >>> def func2d(x): + ... f = np.cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] + + ... 0.2) * x[0] + ... df = np.zeros(2) + ... df[0] = -14.5 * np.sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2 + ... df[1] = 2. * x[1] + 0.2 + ... return f, df + + We'll also use a different local minimization algorithm. Also, we must tell + the minimizer that our function returns both energy and gradient (Jacobian). + + >>> minimizer_kwargs = {"method":"L-BFGS-B", "jac":True} + >>> x0 = [1.0, 1.0] + >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs, + ... niter=200) + >>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0], + ... ret.x[1], + ... ret.fun)) + global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109 + + Here is an example using a custom step-taking routine. Imagine you want + the first coordinate to take larger steps than the rest of the coordinates. + This can be implemented like so: + + >>> class MyTakeStep: + ... def __init__(self, stepsize=0.5): + ... self.stepsize = stepsize + ... self.rng = np.random.default_rng() + ... def __call__(self, x): + ... s = self.stepsize + ... x[0] += self.rng.uniform(-2.*s, 2.*s) + ... x[1:] += self.rng.uniform(-s, s, x[1:].shape) + ... return x + + Since ``MyTakeStep.stepsize`` exists basinhopping will adjust the magnitude + of `stepsize` to optimize the search. We'll use the same 2-D function as + before + + >>> mytakestep = MyTakeStep() + >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs, + ... niter=200, take_step=mytakestep) + >>> print("global minimum: x = [%.4f, %.4f], f(x) = %.4f" % (ret.x[0], + ... ret.x[1], + ... ret.fun)) + global minimum: x = [-0.1951, -0.1000], f(x) = -1.0109 + + Now, let's do an example using a custom callback function which prints the + value of every minimum found + + >>> def print_fun(x, f, accepted): + ... print("at minimum %.4f accepted %d" % (f, int(accepted))) + + We'll run it for only 10 basinhopping steps this time. + + >>> rng = np.random.default_rng() + >>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs, + ... niter=10, callback=print_fun, seed=rng) + at minimum 0.4159 accepted 1 + at minimum -0.4317 accepted 1 + at minimum -1.0109 accepted 1 + at minimum -0.9073 accepted 1 + at minimum -0.4317 accepted 0 + at minimum -0.1021 accepted 1 + at minimum -0.7425 accepted 1 + at minimum -0.9073 accepted 1 + at minimum -0.4317 accepted 0 + at minimum -0.7425 accepted 1 + at minimum -0.9073 accepted 1 + + The minimum at -1.0109 is actually the global minimum, found already on the + 8th iteration. + + """ # numpy/numpydoc#87 # noqa: E501 + if target_accept_rate <= 0. or target_accept_rate >= 1.: + raise ValueError('target_accept_rate has to be in range (0, 1)') + if stepwise_factor <= 0. or stepwise_factor >= 1.: + raise ValueError('stepwise_factor has to be in range (0, 1)') + + x0 = np.array(x0) + + # set up the np.random generator + rng = check_random_state(seed) + + # set up minimizer + if minimizer_kwargs is None: + minimizer_kwargs = dict() + wrapped_minimizer = MinimizerWrapper(scipy.optimize.minimize, func, + **minimizer_kwargs) + + # set up step-taking algorithm + if take_step is not None: + if not callable(take_step): + raise TypeError("take_step must be callable") + # if take_step.stepsize exists then use AdaptiveStepsize to control + # take_step.stepsize + if hasattr(take_step, "stepsize"): + take_step_wrapped = AdaptiveStepsize( + take_step, interval=interval, + accept_rate=target_accept_rate, + factor=stepwise_factor, + verbose=disp) + else: + take_step_wrapped = take_step + else: + # use default + displace = RandomDisplacement(stepsize=stepsize, random_gen=rng) + take_step_wrapped = AdaptiveStepsize(displace, interval=interval, + accept_rate=target_accept_rate, + factor=stepwise_factor, + verbose=disp) + + # set up accept tests + accept_tests = [] + if accept_test is not None: + if not callable(accept_test): + raise TypeError("accept_test must be callable") + accept_tests = [accept_test] + + # use default + metropolis = Metropolis(T, random_gen=rng) + accept_tests.append(metropolis) + + if niter_success is None: + niter_success = niter + 2 + + bh = BasinHoppingRunner(x0, wrapped_minimizer, take_step_wrapped, + accept_tests, disp=disp) + + # The wrapped minimizer is called once during construction of + # BasinHoppingRunner, so run the callback + if callable(callback): + callback(bh.storage.minres.x, bh.storage.minres.fun, True) + + # start main iteration loop + count, i = 0, 0 + message = ["requested number of basinhopping iterations completed" + " successfully"] + for i in range(niter): + new_global_min = bh.one_cycle() + + if callable(callback): + # should we pass a copy of x? + val = callback(bh.xtrial, bh.energy_trial, bh.accept) + if val is not None: + if val: + message = ["callback function requested stop early by" + "returning True"] + break + + count += 1 + if new_global_min: + count = 0 + elif count > niter_success: + message = ["success condition satisfied"] + break + + # prepare return object + res = bh.res + res.lowest_optimization_result = bh.storage.get_lowest() + res.x = np.copy(res.lowest_optimization_result.x) + res.fun = res.lowest_optimization_result.fun + res.message = message + res.nit = i + 1 + res.success = res.lowest_optimization_result.success + return res diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_bracket.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_bracket.py new file mode 100644 index 0000000000000000000000000000000000000000..6abfaaa94408ef2ec26b6932a023c6a8aa8ab6fd --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_bracket.py @@ -0,0 +1,666 @@ +import numpy as np +import scipy._lib._elementwise_iterative_method as eim +from scipy._lib._util import _RichResult + +_ELIMITS = -1 # used in _bracket_root +_ESTOPONESIDE = 2 # used in _bracket_root + +def _bracket_root_iv(func, xl0, xr0, xmin, xmax, factor, args, maxiter): + + if not callable(func): + raise ValueError('`func` must be callable.') + + if not np.iterable(args): + args = (args,) + + xl0 = np.asarray(xl0)[()] + if not np.issubdtype(xl0.dtype, np.number) or np.iscomplex(xl0).any(): + raise ValueError('`xl0` must be numeric and real.') + + xr0 = xl0 + 1 if xr0 is None else xr0 + xmin = -np.inf if xmin is None else xmin + xmax = np.inf if xmax is None else xmax + factor = 2. if factor is None else factor + xl0, xr0, xmin, xmax, factor = np.broadcast_arrays(xl0, xr0, xmin, xmax, factor) + + if not np.issubdtype(xr0.dtype, np.number) or np.iscomplex(xr0).any(): + raise ValueError('`xr0` must be numeric and real.') + + if not np.issubdtype(xmin.dtype, np.number) or np.iscomplex(xmin).any(): + raise ValueError('`xmin` must be numeric and real.') + + if not np.issubdtype(xmax.dtype, np.number) or np.iscomplex(xmax).any(): + raise ValueError('`xmax` must be numeric and real.') + + if not np.issubdtype(factor.dtype, np.number) or np.iscomplex(factor).any(): + raise ValueError('`factor` must be numeric and real.') + if not np.all(factor > 1): + raise ValueError('All elements of `factor` must be greater than 1.') + + maxiter = np.asarray(maxiter) + message = '`maxiter` must be a non-negative integer.' + if (not np.issubdtype(maxiter.dtype, np.number) or maxiter.shape != tuple() + or np.iscomplex(maxiter)): + raise ValueError(message) + maxiter_int = int(maxiter[()]) + if not maxiter == maxiter_int or maxiter < 0: + raise ValueError(message) + + return func, xl0, xr0, xmin, xmax, factor, args, maxiter + + +def _bracket_root(func, xl0, xr0=None, *, xmin=None, xmax=None, factor=None, + args=(), maxiter=1000): + """Bracket the root of a monotonic scalar function of one variable + + This function works elementwise when `xl0`, `xr0`, `xmin`, `xmax`, `factor`, and + the elements of `args` are broadcastable arrays. + + Parameters + ---------- + func : callable + The function for which the root is to be bracketed. + The signature must be:: + + func(x: ndarray, *args) -> ndarray + + where each element of ``x`` is a finite real and ``args`` is a tuple, + which may contain an arbitrary number of arrays that are broadcastable + with `x`. ``func`` must be an elementwise function: each element + ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``. + xl0, xr0: float array_like + Starting guess of bracket, which need not contain a root. If `xr0` is + not provided, ``xr0 = xl0 + 1``. Must be broadcastable with one another. + xmin, xmax : float array_like, optional + Minimum and maximum allowable endpoints of the bracket, inclusive. Must + be broadcastable with `xl0` and `xr0`. + factor : float array_like, default: 2 + The factor used to grow the bracket. See notes for details. + args : tuple, optional + Additional positional arguments to be passed to `func`. Must be arrays + broadcastable with `xl0`, `xr0`, `xmin`, and `xmax`. If the callable to be + bracketed requires arguments that are not broadcastable with these + arrays, wrap that callable with `func` such that `func` accepts + only `x` and broadcastable arrays. + maxiter : int, optional + The maximum number of iterations of the algorithm to perform. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. The descriptions are written as though the values will be + scalars; however, if `func` returns an array, the outputs will be + arrays of the same shape. + + xl, xr : float + The lower and upper ends of the bracket, if the algorithm + terminated successfully. + fl, fr : float + The function value at the lower and upper ends of the bracket. + nfev : int + The number of function evaluations required to find the bracket. + This is distinct from the number of times `func` is *called* + because the function may evaluated at multiple points in a single + call. + nit : int + The number of iterations of the algorithm that were performed. + status : int + An integer representing the exit status of the algorithm. + + - ``0`` : The algorithm produced a valid bracket. + - ``-1`` : The bracket expanded to the allowable limits without finding a bracket. + - ``-2`` : The maximum number of iterations was reached. + - ``-3`` : A non-finite value was encountered. + - ``-4`` : Iteration was terminated by `callback`. + - ``-5``: The initial bracket does not satisfy `xmin <= xl0 < xr0 < xmax`. + - ``1`` : The algorithm is proceeding normally (in `callback` only). + - ``2`` : A bracket was found in the opposite search direction (in `callback` only). + + success : bool + ``True`` when the algorithm terminated successfully (status ``0``). + + Notes + ----- + This function generalizes an algorithm found in pieces throughout + `scipy.stats`. The strategy is to iteratively grow the bracket `(l, r)` + until ``func(l) < 0 < func(r)``. The bracket grows to the left as follows. + + - If `xmin` is not provided, the distance between `xl0` and `l` is iteratively + increased by `factor`. + - If `xmin` is provided, the distance between `xmin` and `l` is iteratively + decreased by `factor`. Note that this also *increases* the bracket size. + + Growth of the bracket to the right is analogous. + + Growth of the bracket in one direction stops when the endpoint is no longer + finite, the function value at the endpoint is no longer finite, or the + endpoint reaches its limiting value (`xmin` or `xmax`). Iteration terminates + when the bracket stops growing in both directions, the bracket surrounds + the root, or a root is found (accidentally). + + If two brackets are found - that is, a bracket is found on both sides in + the same iteration, the smaller of the two is returned. + If roots of the function are found, both `l` and `r` are set to the + leftmost root. + + """ # noqa: E501 + # Todo: + # - find bracket with sign change in specified direction + # - Add tolerance + # - allow factor < 1? + + callback = None # works; I just don't want to test it + temp = _bracket_root_iv(func, xl0, xr0, xmin, xmax, factor, args, maxiter) + func, xl0, xr0, xmin, xmax, factor, args, maxiter = temp + + xs = (xl0, xr0) + temp = eim._initialize(func, xs, args) + func, xs, fs, args, shape, dtype, xp = temp # line split for PEP8 + xl0, xr0 = xs + xmin = np.broadcast_to(xmin, shape).astype(dtype, copy=False).ravel() + xmax = np.broadcast_to(xmax, shape).astype(dtype, copy=False).ravel() + invalid_bracket = ~((xmin <= xl0) & (xl0 < xr0) & (xr0 <= xmax)) + + # The approach is to treat the left and right searches as though they were + # (almost) totally independent one-sided bracket searches. (The interaction + # is considered when checking for termination and preparing the result + # object.) + # `x` is the "moving" end of the bracket + x = np.concatenate(xs) + f = np.concatenate(fs) + invalid_bracket = np.concatenate((invalid_bracket, invalid_bracket)) + n = len(x) // 2 + + # `x_last` is the previous location of the moving end of the bracket. If + # the signs of `f` and `f_last` are different, `x` and `x_last` form a + # bracket. + x_last = np.concatenate((x[n:], x[:n])) + f_last = np.concatenate((f[n:], f[:n])) + # `x0` is the "fixed" end of the bracket. + x0 = x_last + # We don't need to retain the corresponding function value, since the + # fixed end of the bracket is only needed to compute the new value of the + # moving end; it is never returned. + limit = np.concatenate((xmin, xmax)) + + factor = np.broadcast_to(factor, shape).astype(dtype, copy=False).ravel() + factor = np.concatenate((factor, factor)) + + active = np.arange(2*n) + args = [np.concatenate((arg, arg)) for arg in args] + + # This is needed due to inner workings of `eim._loop`. + # We're abusing it a tiny bit. + shape = shape + (2,) + + # `d` is for "distance". + # For searches without a limit, the distance between the fixed end of the + # bracket `x0` and the moving end `x` will grow by `factor` each iteration. + # For searches with a limit, the distance between the `limit` and moving + # end of the bracket `x` will shrink by `factor` each iteration. + i = np.isinf(limit) + ni = ~i + d = np.zeros_like(x) + d[i] = x[i] - x0[i] + d[ni] = limit[ni] - x[ni] + + status = np.full_like(x, eim._EINPROGRESS, dtype=int) # in progress + status[invalid_bracket] = eim._EINPUTERR + nit, nfev = 0, 1 # one function evaluation per side performed above + + work = _RichResult(x=x, x0=x0, f=f, limit=limit, factor=factor, + active=active, d=d, x_last=x_last, f_last=f_last, + nit=nit, nfev=nfev, status=status, args=args, + xl=None, xr=None, fl=None, fr=None, n=n) + res_work_pairs = [('status', 'status'), ('xl', 'xl'), ('xr', 'xr'), + ('nit', 'nit'), ('nfev', 'nfev'), ('fl', 'fl'), + ('fr', 'fr'), ('x', 'x'), ('f', 'f'), + ('x_last', 'x_last'), ('f_last', 'f_last')] + + def pre_func_eval(work): + # Initialize moving end of bracket + x = np.zeros_like(work.x) + + # Unlimited brackets grow by `factor` by increasing distance from fixed + # end to moving end. + i = np.isinf(work.limit) # indices of unlimited brackets + work.d[i] *= work.factor[i] + x[i] = work.x0[i] + work.d[i] + + # Limited brackets grow by decreasing the distance from the limit to + # the moving end. + ni = ~i # indices of limited brackets + work.d[ni] /= work.factor[ni] + x[ni] = work.limit[ni] - work.d[ni] + + return x + + def post_func_eval(x, f, work): + # Keep track of the previous location of the moving end so that we can + # return a narrower bracket. (The alternative is to remember the + # original fixed end, but then the bracket would be wider than needed.) + work.x_last = work.x + work.f_last = work.f + work.x = x + work.f = f + + def check_termination(work): + # Condition 0: initial bracket is invalid + stop = (work.status == eim._EINPUTERR) + + # Condition 1: a valid bracket (or the root itself) has been found + sf = np.sign(work.f) + sf_last = np.sign(work.f_last) + i = ((sf_last == -sf) | (sf_last == 0) | (sf == 0)) & ~stop + work.status[i] = eim._ECONVERGED + stop[i] = True + + # Condition 2: the other side's search found a valid bracket. + # (If we just found a bracket with the rightward search, we can stop + # the leftward search, and vice-versa.) + # To do this, we need to set the status of the other side's search; + # this is tricky because `work.status` contains only the *active* + # elements, so we don't immediately know the index of the element we + # need to set - or even if it's still there. (That search may have + # terminated already, e.g. by reaching its `limit`.) + # To facilitate this, `work.active` contains a unit integer index of + # each search. Index `k` (`k < n)` and `k + n` correspond with a + # leftward and rightward search, respectively. Elements are removed + # from `work.active` just as they are removed from `work.status`, so + # we use `work.active` to help find the right location in + # `work.status`. + # Get the integer indices of the elements that can also stop + also_stop = (work.active[i] + work.n) % (2*work.n) + # Check whether they are still active. + # To start, we need to find out where in `work.active` they would + # appear if they are indeed there. + j = np.searchsorted(work.active, also_stop) + # If the location exceeds the length of the `work.active`, they are + # not there. + j = j[j < len(work.active)] + # Check whether they are still there. + j = j[also_stop == work.active[j]] + # Now convert these to boolean indices to use with `work.status`. + i = np.zeros_like(stop) + i[j] = True # boolean indices of elements that can also stop + i = i & ~stop + work.status[i] = _ESTOPONESIDE + stop[i] = True + + # Condition 3: moving end of bracket reaches limit + i = (work.x == work.limit) & ~stop + work.status[i] = _ELIMITS + stop[i] = True + + # Condition 4: non-finite value encountered + i = ~(np.isfinite(work.x) & np.isfinite(work.f)) & ~stop + work.status[i] = eim._EVALUEERR + stop[i] = True + + return stop + + def post_termination_check(work): + pass + + def customize_result(res, shape): + n = len(res['x']) // 2 + + # To avoid ambiguity, below we refer to `xl0`, the initial left endpoint + # as `a` and `xr0`, the initial right endpoint, as `b`. + # Because we treat the two one-sided searches as though they were + # independent, what we keep track of in `work` and what we want to + # return in `res` look quite different. Combine the results from the + # two one-sided searches before reporting the results to the user. + # - "a" refers to the leftward search (the moving end started at `a`) + # - "b" refers to the rightward search (the moving end started at `b`) + # - "l" refers to the left end of the bracket (closer to -oo) + # - "r" refers to the right end of the bracket (closer to +oo) + xal = res['x'][:n] + xar = res['x_last'][:n] + xbl = res['x_last'][n:] + xbr = res['x'][n:] + + fal = res['f'][:n] + far = res['f_last'][:n] + fbl = res['f_last'][n:] + fbr = res['f'][n:] + + # Initialize the brackets and corresponding function values to return + # to the user. Brackets may not be valid (e.g. there is no root, + # there weren't enough iterations, NaN encountered), but we still need + # to return something. One option would be all NaNs, but what I've + # chosen here is the left- and right-most points at which the function + # has been evaluated. This gives the user some information about what + # interval of the real line has been searched and shows that there is + # no sign change between the two ends. + xl = xal.copy() + fl = fal.copy() + xr = xbr.copy() + fr = fbr.copy() + + # `status` indicates whether the bracket is valid or not. If so, + # we want to adjust the bracket we return to be the narrowest possible + # given the points at which we evaluated the function. + # For example if bracket "a" is valid and smaller than bracket "b" OR + # if bracket "a" is valid and bracket "b" is not valid, we want to + # return bracket "a" (and vice versa). + sa = res['status'][:n] + sb = res['status'][n:] + + da = xar - xal + db = xbr - xbl + + i1 = ((da <= db) & (sa == 0)) | ((sa == 0) & (sb != 0)) + i2 = ((db <= da) & (sb == 0)) | ((sb == 0) & (sa != 0)) + + xr[i1] = xar[i1] + fr[i1] = far[i1] + xl[i2] = xbl[i2] + fl[i2] = fbl[i2] + + # Finish assembling the result object + res['xl'] = xl + res['xr'] = xr + res['fl'] = fl + res['fr'] = fr + + res['nit'] = np.maximum(res['nit'][:n], res['nit'][n:]) + res['nfev'] = res['nfev'][:n] + res['nfev'][n:] + # If the status on one side is zero, the status is zero. In any case, + # report the status from one side only. + res['status'] = np.choose(sa == 0, (sb, sa)) + res['success'] = (res['status'] == 0) + + del res['x'] + del res['f'] + del res['x_last'] + del res['f_last'] + + return shape[:-1] + + return eim._loop(work, callback, shape, maxiter, func, args, dtype, + pre_func_eval, post_func_eval, check_termination, + post_termination_check, customize_result, res_work_pairs, + xp) + + +def _bracket_minimum_iv(func, xm0, xl0, xr0, xmin, xmax, factor, args, maxiter): + + if not callable(func): + raise ValueError('`func` must be callable.') + + if not np.iterable(args): + args = (args,) + + xm0 = np.asarray(xm0)[()] + if not np.issubdtype(xm0.dtype, np.number) or np.iscomplex(xm0).any(): + raise ValueError('`xm0` must be numeric and real.') + + xmin = -np.inf if xmin is None else xmin + xmax = np.inf if xmax is None else xmax + + # If xl0 (xr0) is not supplied, fill with a dummy value for the sake + # of broadcasting. We need to wait until xmin (xmax) has been validated + # to compute the default values. + xl0_not_supplied = False + if xl0 is None: + xl0 = np.nan + xl0_not_supplied = True + + xr0_not_supplied = False + if xr0 is None: + xr0 = np.nan + xr0_not_supplied = True + + factor = 2.0 if factor is None else factor + xl0, xm0, xr0, xmin, xmax, factor = np.broadcast_arrays( + xl0, xm0, xr0, xmin, xmax, factor + ) + + if not np.issubdtype(xl0.dtype, np.number) or np.iscomplex(xl0).any(): + raise ValueError('`xl0` must be numeric and real.') + + if not np.issubdtype(xr0.dtype, np.number) or np.iscomplex(xr0).any(): + raise ValueError('`xr0` must be numeric and real.') + + if not np.issubdtype(xmin.dtype, np.number) or np.iscomplex(xmin).any(): + raise ValueError('`xmin` must be numeric and real.') + + if not np.issubdtype(xmax.dtype, np.number) or np.iscomplex(xmax).any(): + raise ValueError('`xmax` must be numeric and real.') + + if not np.issubdtype(factor.dtype, np.number) or np.iscomplex(factor).any(): + raise ValueError('`factor` must be numeric and real.') + if not np.all(factor > 1): + raise ValueError('All elements of `factor` must be greater than 1.') + + # Calculate default values of xl0 and/or xr0 if they have not been supplied + # by the user. We need to be careful to ensure xl0 and xr0 are not outside + # of (xmin, xmax). + if xl0_not_supplied: + xl0 = xm0 - np.minimum((xm0 - xmin)/16, 0.5) + if xr0_not_supplied: + xr0 = xm0 + np.minimum((xmax - xm0)/16, 0.5) + + maxiter = np.asarray(maxiter) + message = '`maxiter` must be a non-negative integer.' + if (not np.issubdtype(maxiter.dtype, np.number) or maxiter.shape != tuple() + or np.iscomplex(maxiter)): + raise ValueError(message) + maxiter_int = int(maxiter[()]) + if not maxiter == maxiter_int or maxiter < 0: + raise ValueError(message) + + return func, xm0, xl0, xr0, xmin, xmax, factor, args, maxiter + + +def _bracket_minimum(func, xm0, *, xl0=None, xr0=None, xmin=None, xmax=None, + factor=None, args=(), maxiter=1000): + """Bracket the minimum of a unimodal scalar function of one variable + + This function works elementwise when `xm0`, `xl0`, `xr0`, `xmin`, `xmax`, + and the elements of `args` are broadcastable arrays. + + Parameters + ---------- + func : callable + The function for which the minimum is to be bracketed. + The signature must be:: + + func(x: ndarray, *args) -> ndarray + + where each element of ``x`` is a finite real and ``args`` is a tuple, + which may contain an arbitrary number of arrays that are broadcastable + with ``x``. `func` must be an elementwise function: each element + ``func(x)[i]`` must equal ``func(x[i])`` for all indices `i`. + xm0: float array_like + Starting guess for middle point of bracket. + xl0, xr0: float array_like, optional + Starting guesses for left and right endpoints of the bracket. Must be + broadcastable with one another and with `xm0`. + xmin, xmax : float array_like, optional + Minimum and maximum allowable endpoints of the bracket, inclusive. Must + be broadcastable with `xl0`, `xm0`, and `xr0`. + factor : float array_like, optional + Controls expansion of bracket endpoint in downhill direction. Works + differently in the cases where a limit is set in the downhill direction + with `xmax` or `xmin`. See Notes. + args : tuple, optional + Additional positional arguments to be passed to `func`. Must be arrays + broadcastable with `xl0`, `xm0`, `xr0`, `xmin`, and `xmax`. If the + callable to be bracketed requires arguments that are not broadcastable + with these arrays, wrap that callable with `func` such that `func` + accepts only ``x`` and broadcastable arrays. + maxiter : int, optional + The maximum number of iterations of the algorithm to perform. The number + of function evaluations is three greater than the number of iterations. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. The descriptions are written as though the values will be + scalars; however, if `func` returns an array, the outputs will be + arrays of the same shape. + + xl, xm, xr : float + The left, middle, and right points of the bracket, if the algorithm + terminated successfully. + fl, fm, fr : float + The function value at the left, middle, and right points of the bracket. + nfev : int + The number of function evaluations required to find the bracket. + nit : int + The number of iterations of the algorithm that were performed. + status : int + An integer representing the exit status of the algorithm. + + - ``0`` : The algorithm produced a valid bracket. + - ``-1`` : The bracket expanded to the allowable limits. Assuming + unimodality, this implies the endpoint at the limit is a + minimizer. + - ``-2`` : The maximum number of iterations was reached. + - ``-3`` : A non-finite value was encountered. + - ``-4`` : ``None`` shall pass. + - ``-5`` : The initial bracket does not satisfy + `xmin <= xl0 < xm0 < xr0 <= xmax`. + + success : bool + ``True`` when the algorithm terminated successfully (status ``0``). + + Notes + ----- + Similar to `scipy.optimize.bracket`, this function seeks to find real + points ``xl < xm < xr`` such that ``f(xl) >= f(xm)`` and ``f(xr) >= f(xm)``, + where at least one of the inequalities is strict. Unlike `scipy.optimize.bracket`, + this function can operate in a vectorized manner on array input, so long as + the input arrays are broadcastable with each other. Also unlike + `scipy.optimize.bracket`, users may specify minimum and maximum endpoints + for the desired bracket. + + Given an initial trio of points ``xl = xl0``, ``xm = xm0``, ``xr = xr0``, + the algorithm checks if these points already give a valid bracket. If not, + a new endpoint, ``w`` is chosen in the "downhill" direction, ``xm`` becomes the new + opposite endpoint, and either `xl` or `xr` becomes the new middle point, + depending on which direction is downhill. The algorithm repeats from here. + + The new endpoint `w` is chosen differently depending on whether or not a + boundary `xmin` or `xmax` has been set in the downhill direction. Without + loss of generality, suppose the downhill direction is to the right, so that + ``f(xl) > f(xm) > f(xr)``. If there is no boundary to the right, then `w` + is chosen to be ``xr + factor * (xr - xm)`` where `factor` is controlled by + the user (defaults to 2.0) so that step sizes increase in geometric proportion. + If there is a boundary, `xmax` in this case, then `w` is chosen to be + ``xmax - (xmax - xr)/factor``, with steps slowing to a stop at + `xmax`. This cautious approach ensures that a minimum near but distinct from + the boundary isn't missed while also detecting whether or not the `xmax` is + a minimizer when `xmax` is reached after a finite number of steps. + """ # noqa: E501 + callback = None # works; I just don't want to test it + + temp = _bracket_minimum_iv(func, xm0, xl0, xr0, xmin, xmax, factor, args, maxiter) + func, xm0, xl0, xr0, xmin, xmax, factor, args, maxiter = temp + + xs = (xl0, xm0, xr0) + temp = eim._initialize(func, xs, args) + func, xs, fs, args, shape, dtype, xp = temp + + xl0, xm0, xr0 = xs + fl0, fm0, fr0 = fs + xmin = np.broadcast_to(xmin, shape).astype(dtype, copy=False).ravel() + xmax = np.broadcast_to(xmax, shape).astype(dtype, copy=False).ravel() + invalid_bracket = ~((xmin <= xl0) & (xl0 < xm0) & (xm0 < xr0) & (xr0 <= xmax)) + # We will modify factor later on so make a copy. np.broadcast_to returns + # a read-only view. + factor = np.broadcast_to(factor, shape).astype(dtype, copy=True).ravel() + + # To simplify the logic, swap xl and xr if f(xl) < f(xr). We should always be + # marching downhill in the direction from xl to xr. + comp = fl0 < fr0 + xl0[comp], xr0[comp] = xr0[comp], xl0[comp] + fl0[comp], fr0[comp] = fr0[comp], fl0[comp] + # We only need the boundary in the direction we're traveling. + limit = np.where(comp, xmin, xmax) + + unlimited = np.isinf(limit) + limited = ~unlimited + step = np.empty_like(xl0) + + step[unlimited] = (xr0[unlimited] - xm0[unlimited]) + step[limited] = (limit[limited] - xr0[limited]) + + # Step size is divided by factor for case where there is a limit. + factor[limited] = 1 / factor[limited] + + status = np.full_like(xl0, eim._EINPROGRESS, dtype=int) + status[invalid_bracket] = eim._EINPUTERR + nit, nfev = 0, 3 + + work = _RichResult(xl=xl0, xm=xm0, xr=xr0, xr0=xr0, fl=fl0, fm=fm0, fr=fr0, + step=step, limit=limit, limited=limited, factor=factor, nit=nit, + nfev=nfev, status=status, args=args) + + res_work_pairs = [('status', 'status'), ('xl', 'xl'), ('xm', 'xm'), ('xr', 'xr'), + ('nit', 'nit'), ('nfev', 'nfev'), ('fl', 'fl'), ('fm', 'fm'), + ('fr', 'fr')] + + def pre_func_eval(work): + work.step *= work.factor + x = np.empty_like(work.xr) + x[~work.limited] = work.xr0[~work.limited] + work.step[~work.limited] + x[work.limited] = work.limit[work.limited] - work.step[work.limited] + # Since the new bracket endpoint is calculated from an offset with the + # limit, it may be the case that the new endpoint equals the old endpoint, + # when the old endpoint is sufficiently close to the limit. We use the + # limit itself as the new endpoint in these cases. + x[work.limited] = np.where( + x[work.limited] == work.xr[work.limited], + work.limit[work.limited], + x[work.limited], + ) + return x + + def post_func_eval(x, f, work): + work.xl, work.xm, work.xr = work.xm, work.xr, x + work.fl, work.fm, work.fr = work.fm, work.fr, f + + def check_termination(work): + # Condition 0: Initial bracket is invalid. + stop = (work.status == eim._EINPUTERR) + + # Condition 1: A valid bracket has been found. + i = ( + (work.fl >= work.fm) & (work.fr > work.fm) + | (work.fl > work.fm) & (work.fr >= work.fm) + ) & ~stop + work.status[i] = eim._ECONVERGED + stop[i] = True + + # Condition 2: Moving end of bracket reaches limit. + i = (work.xr == work.limit) & ~stop + work.status[i] = _ELIMITS + stop[i] = True + + # Condition 3: non-finite value encountered + i = ~(np.isfinite(work.xr) & np.isfinite(work.fr)) & ~stop + work.status[i] = eim._EVALUEERR + stop[i] = True + + return stop + + def post_termination_check(work): + pass + + def customize_result(res, shape): + # Reorder entries of xl and xr if they were swapped due to f(xl0) < f(xr0). + comp = res['xl'] > res['xr'] + res['xl'][comp], res['xr'][comp] = res['xr'][comp], res['xl'][comp] + res['fl'][comp], res['fr'][comp] = res['fr'][comp], res['fl'][comp] + return shape + + return eim._loop(work, callback, shape, + maxiter, func, args, dtype, + pre_func_eval, post_func_eval, + check_termination, post_termination_check, + customize_result, res_work_pairs, xp) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_chandrupatla.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_chandrupatla.py new file mode 100644 index 0000000000000000000000000000000000000000..f1759d6191db209d26bbabc6ebc81a951b43b884 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_chandrupatla.py @@ -0,0 +1,549 @@ +import math +import numpy as np +import scipy._lib._elementwise_iterative_method as eim +from scipy._lib._util import _RichResult +from scipy._lib._array_api import xp_clip, xp_minimum, xp_sign + +# TODO: +# - (maybe?) don't use fancy indexing assignment +# - figure out how to replace the new `try`/`except`s + + +def _chandrupatla(func, a, b, *, args=(), xatol=None, xrtol=None, + fatol=None, frtol=0, maxiter=None, callback=None): + """Find the root of an elementwise function using Chandrupatla's algorithm. + + For each element of the output of `func`, `chandrupatla` seeks the scalar + root that makes the element 0. This function allows for `a`, `b`, and the + output of `func` to be of any broadcastable shapes. + + Parameters + ---------- + func : callable + The function whose root is desired. The signature must be:: + + func(x: ndarray, *args) -> ndarray + + where each element of ``x`` is a finite real and ``args`` is a tuple, + which may contain an arbitrary number of components of any type(s). + ``func`` must be an elementwise function: each element ``func(x)[i]`` + must equal ``func(x[i])`` for all indices ``i``. `_chandrupatla` + seeks an array ``x`` such that ``func(x)`` is an array of zeros. + a, b : array_like + The lower and upper bounds of the root of the function. Must be + broadcastable with one another. + args : tuple, optional + Additional positional arguments to be passed to `func`. + xatol, xrtol, fatol, frtol : float, optional + Absolute and relative tolerances on the root and function value. + See Notes for details. + maxiter : int, optional + The maximum number of iterations of the algorithm to perform. + The default is the maximum possible number of bisections within + the (normal) floating point numbers of the relevant dtype. + callback : callable, optional + An optional user-supplied function to be called before the first + iteration and after each iteration. + Called as ``callback(res)``, where ``res`` is a ``_RichResult`` + similar to that returned by `_chandrupatla` (but containing the current + iterate's values of all variables). If `callback` raises a + ``StopIteration``, the algorithm will terminate immediately and + `_chandrupatla` will return a result. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. The descriptions are written as though the values will be + scalars; however, if `func` returns an array, the outputs will be + arrays of the same shape. + + x : float + The root of the function, if the algorithm terminated successfully. + nfev : int + The number of times the function was called to find the root. + nit : int + The number of iterations of Chandrupatla's algorithm performed. + status : int + An integer representing the exit status of the algorithm. + ``0`` : The algorithm converged to the specified tolerances. + ``-1`` : The algorithm encountered an invalid bracket. + ``-2`` : The maximum number of iterations was reached. + ``-3`` : A non-finite value was encountered. + ``-4`` : Iteration was terminated by `callback`. + ``1`` : The algorithm is proceeding normally (in `callback` only). + success : bool + ``True`` when the algorithm terminated successfully (status ``0``). + fun : float + The value of `func` evaluated at `x`. + xl, xr : float + The lower and upper ends of the bracket. + fl, fr : float + The function value at the lower and upper ends of the bracket. + + Notes + ----- + Implemented based on Chandrupatla's original paper [1]_. + + If ``xl`` and ``xr`` are the left and right ends of the bracket, + ``xmin = xl if abs(func(xl)) <= abs(func(xr)) else xr``, + and ``fmin0 = min(func(a), func(b))``, then the algorithm is considered to + have converged when ``abs(xr - xl) < xatol + abs(xmin) * xrtol`` or + ``fun(xmin) <= fatol + abs(fmin0) * frtol``. This is equivalent to the + termination condition described in [1]_ with ``xrtol = 4e-10``, + ``xatol = 1e-5``, and ``fatol = frtol = 0``. The default values are + ``xatol = 4*tiny``, ``xrtol = 4*eps``, ``frtol = 0``, and ``fatol = tiny``, + where ``eps`` and ``tiny`` are the precision and smallest normal number + of the result ``dtype`` of function inputs and outputs. + + References + ---------- + + .. [1] Chandrupatla, Tirupathi R. + "A new hybrid quadratic/bisection algorithm for finding the zero of a + nonlinear function without using derivatives". + Advances in Engineering Software, 28(3), 145-149. + https://doi.org/10.1016/s0965-9978(96)00051-8 + + See Also + -------- + brentq, brenth, ridder, bisect, newton + + Examples + -------- + >>> from scipy import optimize + >>> def f(x, c): + ... return x**3 - 2*x - c + >>> c = 5 + >>> res = optimize._chandrupatla._chandrupatla(f, 0, 3, args=(c,)) + >>> res.x + 2.0945514818937463 + + >>> c = [3, 4, 5] + >>> res = optimize._chandrupatla._chandrupatla(f, 0, 3, args=(c,)) + >>> res.x + array([1.8932892 , 2. , 2.09455148]) + + """ + res = _chandrupatla_iv(func, args, xatol, xrtol, + fatol, frtol, maxiter, callback) + func, args, xatol, xrtol, fatol, frtol, maxiter, callback = res + + # Initialization + temp = eim._initialize(func, (a, b), args) + func, xs, fs, args, shape, dtype, xp = temp + x1, x2 = xs + f1, f2 = fs + status = xp.full_like(x1, eim._EINPROGRESS, dtype=xp.int32) # in progress + nit, nfev = 0, 2 # two function evaluations performed above + finfo = xp.finfo(dtype) + xatol = 4*finfo.smallest_normal if xatol is None else xatol + xrtol = 4*finfo.eps if xrtol is None else xrtol + fatol = finfo.smallest_normal if fatol is None else fatol + frtol = frtol * xp_minimum(xp.abs(f1), xp.abs(f2)) + maxiter = (math.log2(finfo.max) - math.log2(finfo.smallest_normal) + if maxiter is None else maxiter) + work = _RichResult(x1=x1, f1=f1, x2=x2, f2=f2, x3=None, f3=None, t=0.5, + xatol=xatol, xrtol=xrtol, fatol=fatol, frtol=frtol, + nit=nit, nfev=nfev, status=status) + res_work_pairs = [('status', 'status'), ('x', 'xmin'), ('fun', 'fmin'), + ('nit', 'nit'), ('nfev', 'nfev'), ('xl', 'x1'), + ('fl', 'f1'), ('xr', 'x2'), ('fr', 'f2')] + + def pre_func_eval(work): + # [1] Figure 1 (first box) + x = work.x1 + work.t * (work.x2 - work.x1) + return x + + def post_func_eval(x, f, work): + # [1] Figure 1 (first diamond and boxes) + # Note: y/n are reversed in figure; compare to BASIC in appendix + work.x3, work.f3 = (xp.asarray(work.x2, copy=True), + xp.asarray(work.f2, copy=True)) + j = xp.sign(f) == xp.sign(work.f1) + nj = ~j + work.x3[j], work.f3[j] = work.x1[j], work.f1[j] + work.x2[nj], work.f2[nj] = work.x1[nj], work.f1[nj] + work.x1, work.f1 = x, f + + def check_termination(work): + # [1] Figure 1 (second diamond) + # Check for all terminal conditions and record statuses. + + # See [1] Section 4 (first two sentences) + i = xp.abs(work.f1) < xp.abs(work.f2) + work.xmin = xp.where(i, work.x1, work.x2) + work.fmin = xp.where(i, work.f1, work.f2) + stop = xp.zeros_like(work.x1, dtype=xp.bool) # termination condition met + + # If function value tolerance is met, report successful convergence, + # regardless of other conditions. Note that `frtol` has been redefined + # as `frtol = frtol * minimum(f1, f2)`, where `f1` and `f2` are the + # function evaluated at the original ends of the bracket. + i = xp.abs(work.fmin) <= work.fatol + work.frtol + work.status[i] = eim._ECONVERGED + stop[i] = True + + # If the bracket is no longer valid, report failure (unless a function + # tolerance is met, as detected above). + i = (xp_sign(work.f1) == xp_sign(work.f2)) & ~stop + NaN = xp.asarray(xp.nan, dtype=work.xmin.dtype) + work.xmin[i], work.fmin[i], work.status[i] = NaN, NaN, eim._ESIGNERR + stop[i] = True + + # If the abscissae are non-finite or either function value is NaN, + # report failure. + x_nonfinite = ~(xp.isfinite(work.x1) & xp.isfinite(work.x2)) + f_nan = xp.isnan(work.f1) & xp.isnan(work.f2) + i = (x_nonfinite | f_nan) & ~stop + work.xmin[i], work.fmin[i], work.status[i] = NaN, NaN, eim._EVALUEERR + stop[i] = True + + # This is the convergence criterion used in bisect. Chandrupatla's + # criterion is equivalent to this except with a factor of 4 on `xrtol`. + work.dx = xp.abs(work.x2 - work.x1) + work.tol = xp.abs(work.xmin) * work.xrtol + work.xatol + i = work.dx < work.tol + work.status[i] = eim._ECONVERGED + stop[i] = True + + return stop + + def post_termination_check(work): + # [1] Figure 1 (third diamond and boxes / Equation 1) + xi1 = (work.x1 - work.x2) / (work.x3 - work.x2) + phi1 = (work.f1 - work.f2) / (work.f3 - work.f2) + alpha = (work.x3 - work.x1) / (work.x2 - work.x1) + j = ((1 - xp.sqrt(1 - xi1)) < phi1) & (phi1 < xp.sqrt(xi1)) + + f1j, f2j, f3j, alphaj = work.f1[j], work.f2[j], work.f3[j], alpha[j] + t = xp.full_like(alpha, 0.5) + t[j] = (f1j / (f1j - f2j) * f3j / (f3j - f2j) + - alphaj * f1j / (f3j - f1j) * f2j / (f2j - f3j)) + + # [1] Figure 1 (last box; see also BASIC in appendix with comment + # "Adjust T Away from the Interval Boundary") + tl = 0.5 * work.tol / work.dx + work.t = xp_clip(t, tl, 1 - tl) + + def customize_result(res, shape): + xl, xr, fl, fr = res['xl'], res['xr'], res['fl'], res['fr'] + i = res['xl'] < res['xr'] + res['xl'] = xp.where(i, xl, xr) + res['xr'] = xp.where(i, xr, xl) + res['fl'] = xp.where(i, fl, fr) + res['fr'] = xp.where(i, fr, fl) + return shape + + return eim._loop(work, callback, shape, maxiter, func, args, dtype, + pre_func_eval, post_func_eval, check_termination, + post_termination_check, customize_result, res_work_pairs, + xp=xp) + + +def _chandrupatla_iv(func, args, xatol, xrtol, + fatol, frtol, maxiter, callback): + # Input validation for `_chandrupatla` + + if not callable(func): + raise ValueError('`func` must be callable.') + + if not np.iterable(args): + args = (args,) + + # tolerances are floats, not arrays; OK to use NumPy + tols = np.asarray([xatol if xatol is not None else 1, + xrtol if xrtol is not None else 1, + fatol if fatol is not None else 1, + frtol if frtol is not None else 1]) + if (not np.issubdtype(tols.dtype, np.number) or np.any(tols < 0) + or np.any(np.isnan(tols)) or tols.shape != (4,)): + raise ValueError('Tolerances must be non-negative scalars.') + + if maxiter is not None: + maxiter_int = int(maxiter) + if maxiter != maxiter_int or maxiter < 0: + raise ValueError('`maxiter` must be a non-negative integer.') + + if callback is not None and not callable(callback): + raise ValueError('`callback` must be callable.') + + return func, args, xatol, xrtol, fatol, frtol, maxiter, callback + + +def _chandrupatla_minimize(func, x1, x2, x3, *, args=(), xatol=None, + xrtol=None, fatol=None, frtol=None, maxiter=100, + callback=None): + """Find the minimizer of an elementwise function. + + For each element of the output of `func`, `_chandrupatla_minimize` seeks + the scalar minimizer that minimizes the element. This function allows for + `x1`, `x2`, `x3`, and the elements of `args` to be arrays of any + broadcastable shapes. + + Parameters + ---------- + func : callable + The function whose minimizer is desired. The signature must be:: + + func(x: ndarray, *args) -> ndarray + + where each element of ``x`` is a finite real and ``args`` is a tuple, + which may contain an arbitrary number of arrays that are broadcastable + with `x`. ``func`` must be an elementwise function: each element + ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``. + `_chandrupatla` seeks an array ``x`` such that ``func(x)`` is an array + of minima. + x1, x2, x3 : array_like + The abscissae of a standard scalar minimization bracket. A bracket is + valid if ``x1 < x2 < x3`` and ``func(x1) > func(x2) <= func(x3)``. + Must be broadcastable with one another and `args`. + args : tuple, optional + Additional positional arguments to be passed to `func`. Must be arrays + broadcastable with `x1`, `x2`, and `x3`. If the callable to be + differentiated requires arguments that are not broadcastable with `x`, + wrap that callable with `func` such that `func` accepts only `x` and + broadcastable arrays. + xatol, xrtol, fatol, frtol : float, optional + Absolute and relative tolerances on the minimizer and function value. + See Notes for details. + maxiter : int, optional + The maximum number of iterations of the algorithm to perform. + callback : callable, optional + An optional user-supplied function to be called before the first + iteration and after each iteration. + Called as ``callback(res)``, where ``res`` is a ``_RichResult`` + similar to that returned by `_chandrupatla_minimize` (but containing + the current iterate's values of all variables). If `callback` raises a + ``StopIteration``, the algorithm will terminate immediately and + `_chandrupatla_minimize` will return a result. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. (The descriptions are written as though the values will be + scalars; however, if `func` returns an array, the outputs will be + arrays of the same shape.) + + success : bool + ``True`` when the algorithm terminated successfully (status ``0``). + status : int + An integer representing the exit status of the algorithm. + ``0`` : The algorithm converged to the specified tolerances. + ``-1`` : The algorithm encountered an invalid bracket. + ``-2`` : The maximum number of iterations was reached. + ``-3`` : A non-finite value was encountered. + ``-4`` : Iteration was terminated by `callback`. + ``1`` : The algorithm is proceeding normally (in `callback` only). + x : float + The minimizer of the function, if the algorithm terminated + successfully. + fun : float + The value of `func` evaluated at `x`. + nfev : int + The number of points at which `func` was evaluated. + nit : int + The number of iterations of the algorithm that were performed. + xl, xm, xr : float + The final three-point bracket. + fl, fm, fr : float + The function value at the bracket points. + + Notes + ----- + Implemented based on Chandrupatla's original paper [1]_. + + If ``x1 < x2 < x3`` are the points of the bracket and ``f1 > f2 <= f3`` + are the values of ``func`` at those points, then the algorithm is + considered to have converged when ``x3 - x1 <= abs(x2)*xrtol + xatol`` + or ``(f1 - 2*f2 + f3)/2 <= abs(f2)*frtol + fatol``. Note that first of + these differs from the termination conditions described in [1]_. The + default values of `xrtol` is the square root of the precision of the + appropriate dtype, and ``xatol = fatol = frtol`` is the smallest normal + number of the appropriate dtype. + + References + ---------- + .. [1] Chandrupatla, Tirupathi R. (1998). + "An efficient quadratic fit-sectioning algorithm for minimization + without derivatives". + Computer Methods in Applied Mechanics and Engineering, 152 (1-2), + 211-217. https://doi.org/10.1016/S0045-7825(97)00190-4 + + See Also + -------- + golden, brent, bounded + + Examples + -------- + >>> from scipy.optimize._chandrupatla import _chandrupatla_minimize + >>> def f(x, args=1): + ... return (x - args)**2 + >>> res = _chandrupatla_minimize(f, -5, 0, 5) + >>> res.x + 1.0 + >>> c = [1, 1.5, 2] + >>> res = _chandrupatla_minimize(f, -5, 0, 5, args=(c,)) + >>> res.x + array([1. , 1.5, 2. ]) + """ + res = _chandrupatla_iv(func, args, xatol, xrtol, + fatol, frtol, maxiter, callback) + func, args, xatol, xrtol, fatol, frtol, maxiter, callback = res + + # Initialization + xs = (x1, x2, x3) + temp = eim._initialize(func, xs, args) + func, xs, fs, args, shape, dtype, xp = temp # line split for PEP8 + x1, x2, x3 = xs + f1, f2, f3 = fs + phi = dtype.type(0.5 + 0.5*5**0.5) # golden ratio + status = np.full_like(x1, eim._EINPROGRESS, dtype=int) # in progress + nit, nfev = 0, 3 # three function evaluations performed above + fatol = np.finfo(dtype).tiny if fatol is None else fatol + frtol = np.finfo(dtype).tiny if frtol is None else frtol + xatol = np.finfo(dtype).tiny if xatol is None else xatol + xrtol = np.sqrt(np.finfo(dtype).eps) if xrtol is None else xrtol + + # Ensure that x1 < x2 < x3 initially. + xs, fs = np.vstack((x1, x2, x3)), np.vstack((f1, f2, f3)) + i = np.argsort(xs, axis=0) + x1, x2, x3 = np.take_along_axis(xs, i, axis=0) + f1, f2, f3 = np.take_along_axis(fs, i, axis=0) + q0 = x3.copy() # "At the start, q0 is set at x3..." ([1] after (7)) + + work = _RichResult(x1=x1, f1=f1, x2=x2, f2=f2, x3=x3, f3=f3, phi=phi, + xatol=xatol, xrtol=xrtol, fatol=fatol, frtol=frtol, + nit=nit, nfev=nfev, status=status, q0=q0, args=args) + res_work_pairs = [('status', 'status'), + ('x', 'x2'), ('fun', 'f2'), + ('nit', 'nit'), ('nfev', 'nfev'), + ('xl', 'x1'), ('xm', 'x2'), ('xr', 'x3'), + ('fl', 'f1'), ('fm', 'f2'), ('fr', 'f3')] + + def pre_func_eval(work): + # `_check_termination` is called first -> `x3 - x2 > x2 - x1` + # But let's calculate a few terms that we'll reuse + x21 = work.x2 - work.x1 + x32 = work.x3 - work.x2 + + # [1] Section 3. "The quadratic minimum point Q1 is calculated using + # the relations developed in the previous section." [1] Section 2 (5/6) + A = x21 * (work.f3 - work.f2) + B = x32 * (work.f1 - work.f2) + C = A / (A + B) + # q1 = C * (work.x1 + work.x2) / 2 + (1 - C) * (work.x2 + work.x3) / 2 + q1 = 0.5 * (C*(work.x1 - work.x3) + work.x2 + work.x3) # much faster + # this is an array, so multiplying by 0.5 does not change dtype + + # "If Q1 and Q0 are sufficiently close... Q1 is accepted if it is + # sufficiently away from the inside point x2" + i = abs(q1 - work.q0) < 0.5 * abs(x21) # [1] (7) + xi = q1[i] + # Later, after (9), "If the point Q1 is in a +/- xtol neighborhood of + # x2, the new point is chosen in the larger interval at a distance + # tol away from x2." + # See also QBASIC code after "Accept Ql adjust if close to X2". + j = abs(q1[i] - work.x2[i]) <= work.xtol[i] + xi[j] = work.x2[i][j] + np.sign(x32[i][j]) * work.xtol[i][j] + + # "If condition (7) is not satisfied, golden sectioning of the larger + # interval is carried out to introduce the new point." + # (For simplicity, we go ahead and calculate it for all points, but we + # change the elements for which the condition was satisfied.) + x = work.x2 + (2 - work.phi) * x32 + x[i] = xi + + # "We define Q0 as the value of Q1 at the previous iteration." + work.q0 = q1 + return x + + def post_func_eval(x, f, work): + # Standard logic for updating a three-point bracket based on a new + # point. In QBASIC code, see "IF SGN(X-X2) = SGN(X3-X2) THEN...". + # There is an awful lot of data copying going on here; this would + # probably benefit from code optimization or implementation in Pythran. + i = np.sign(x - work.x2) == np.sign(work.x3 - work.x2) + xi, x1i, x2i, x3i = x[i], work.x1[i], work.x2[i], work.x3[i], + fi, f1i, f2i, f3i = f[i], work.f1[i], work.f2[i], work.f3[i] + j = fi > f2i + x3i[j], f3i[j] = xi[j], fi[j] + j = ~j + x1i[j], f1i[j], x2i[j], f2i[j] = x2i[j], f2i[j], xi[j], fi[j] + + ni = ~i + xni, x1ni, x2ni, x3ni = x[ni], work.x1[ni], work.x2[ni], work.x3[ni], + fni, f1ni, f2ni, f3ni = f[ni], work.f1[ni], work.f2[ni], work.f3[ni] + j = fni > f2ni + x1ni[j], f1ni[j] = xni[j], fni[j] + j = ~j + x3ni[j], f3ni[j], x2ni[j], f2ni[j] = x2ni[j], f2ni[j], xni[j], fni[j] + + work.x1[i], work.x2[i], work.x3[i] = x1i, x2i, x3i + work.f1[i], work.f2[i], work.f3[i] = f1i, f2i, f3i + work.x1[ni], work.x2[ni], work.x3[ni] = x1ni, x2ni, x3ni, + work.f1[ni], work.f2[ni], work.f3[ni] = f1ni, f2ni, f3ni + + def check_termination(work): + # Check for all terminal conditions and record statuses. + stop = np.zeros_like(work.x1, dtype=bool) # termination condition met + + # Bracket is invalid; stop and don't return minimizer/minimum + i = ((work.f2 > work.f1) | (work.f2 > work.f3)) + work.x2[i], work.f2[i] = np.nan, np.nan + stop[i], work.status[i] = True, eim._ESIGNERR + + # Non-finite values; stop and don't return minimizer/minimum + finite = np.isfinite(work.x1+work.x2+work.x3+work.f1+work.f2+work.f3) + i = ~(finite | stop) + work.x2[i], work.f2[i] = np.nan, np.nan + stop[i], work.status[i] = True, eim._EVALUEERR + + # [1] Section 3 "Points 1 and 3 are interchanged if necessary to make + # the (x2, x3) the larger interval." + # Note: I had used np.choose; this is much faster. This would be a good + # place to save e.g. `work.x3 - work.x2` for reuse, but I tried and + # didn't notice a speed boost, so let's keep it simple. + i = abs(work.x3 - work.x2) < abs(work.x2 - work.x1) + temp = work.x1[i] + work.x1[i] = work.x3[i] + work.x3[i] = temp + temp = work.f1[i] + work.f1[i] = work.f3[i] + work.f3[i] = temp + + # [1] Section 3 (bottom of page 212) + # "We set a tolerance value xtol..." + work.xtol = abs(work.x2) * work.xrtol + work.xatol # [1] (8) + # "The convergence based on interval is achieved when..." + # Note: Equality allowed in case of `xtol=0` + i = abs(work.x3 - work.x2) <= 2 * work.xtol # [1] (9) + + # "We define ftol using..." + ftol = abs(work.f2) * work.frtol + work.fatol # [1] (10) + # "The convergence based on function values is achieved when..." + # Note 1: modify in place to incorporate tolerance on function value. + # Note 2: factor of 2 is not in the text; see QBASIC start of DO loop + i |= (work.f1 - 2 * work.f2 + work.f3) <= 2*ftol # [1] (11) + i &= ~stop + stop[i], work.status[i] = True, eim._ECONVERGED + + return stop + + def post_termination_check(work): + pass + + def customize_result(res, shape): + xl, xr, fl, fr = res['xl'], res['xr'], res['fl'], res['fr'] + i = res['xl'] < res['xr'] + res['xl'] = np.choose(i, (xr, xl)) + res['xr'] = np.choose(i, (xl, xr)) + res['fl'] = np.choose(i, (fr, fl)) + res['fr'] = np.choose(i, (fl, fr)) + return shape + + return eim._loop(work, callback, shape, maxiter, func, args, dtype, + pre_func_eval, post_func_eval, check_termination, + post_termination_check, customize_result, res_work_pairs, + xp=xp) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py new file mode 100644 index 0000000000000000000000000000000000000000..9007fe38a06a91fe456e64d74f4c0e37800f0607 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py @@ -0,0 +1,316 @@ +""" +Interface to Constrained Optimization By Linear Approximation + +Functions +--------- +.. autosummary:: + :toctree: generated/ + + fmin_cobyla + +""" + +import functools +from threading import RLock + +import numpy as np +from scipy.optimize import _cobyla as cobyla +from ._optimize import (OptimizeResult, _check_unknown_options, + _prepare_scalar_function) +try: + from itertools import izip +except ImportError: + izip = zip + +__all__ = ['fmin_cobyla'] + +# Workaround as _cobyla.minimize is not threadsafe +# due to an unknown f2py bug and can segfault, +# see gh-9658. +_module_lock = RLock() +def synchronized(func): + @functools.wraps(func) + def wrapper(*args, **kwargs): + with _module_lock: + return func(*args, **kwargs) + return wrapper + +@synchronized +def fmin_cobyla(func, x0, cons, args=(), consargs=None, rhobeg=1.0, + rhoend=1e-4, maxfun=1000, disp=None, catol=2e-4, + *, callback=None): + """ + Minimize a function using the Constrained Optimization By Linear + Approximation (COBYLA) method. This method wraps a FORTRAN + implementation of the algorithm. + + Parameters + ---------- + func : callable + Function to minimize. In the form func(x, \\*args). + x0 : ndarray + Initial guess. + cons : sequence + Constraint functions; must all be ``>=0`` (a single function + if only 1 constraint). Each function takes the parameters `x` + as its first argument, and it can return either a single number or + an array or list of numbers. + args : tuple, optional + Extra arguments to pass to function. + consargs : tuple, optional + Extra arguments to pass to constraint functions (default of None means + use same extra arguments as those passed to func). + Use ``()`` for no extra arguments. + rhobeg : float, optional + Reasonable initial changes to the variables. + rhoend : float, optional + Final accuracy in the optimization (not precisely guaranteed). This + is a lower bound on the size of the trust region. + disp : {0, 1, 2, 3}, optional + Controls the frequency of output; 0 implies no output. + maxfun : int, optional + Maximum number of function evaluations. + catol : float, optional + Absolute tolerance for constraint violations. + callback : callable, optional + Called after each iteration, as ``callback(x)``, where ``x`` is the + current parameter vector. + + Returns + ------- + x : ndarray + The argument that minimises `f`. + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'COBYLA' `method` in particular. + + Notes + ----- + This algorithm is based on linear approximations to the objective + function and each constraint. We briefly describe the algorithm. + + Suppose the function is being minimized over k variables. At the + jth iteration the algorithm has k+1 points v_1, ..., v_(k+1), + an approximate solution x_j, and a radius RHO_j. + (i.e., linear plus a constant) approximations to the objective + function and constraint functions such that their function values + agree with the linear approximation on the k+1 points v_1,.., v_(k+1). + This gives a linear program to solve (where the linear approximations + of the constraint functions are constrained to be non-negative). + + However, the linear approximations are likely only good + approximations near the current simplex, so the linear program is + given the further requirement that the solution, which + will become x_(j+1), must be within RHO_j from x_j. RHO_j only + decreases, never increases. The initial RHO_j is rhobeg and the + final RHO_j is rhoend. In this way COBYLA's iterations behave + like a trust region algorithm. + + Additionally, the linear program may be inconsistent, or the + approximation may give poor improvement. For details about + how these issues are resolved, as well as how the points v_i are + updated, refer to the source code or the references below. + + + References + ---------- + Powell M.J.D. (1994), "A direct search optimization method that models + the objective and constraint functions by linear interpolation.", in + Advances in Optimization and Numerical Analysis, eds. S. Gomez and + J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67 + + Powell M.J.D. (1998), "Direct search algorithms for optimization + calculations", Acta Numerica 7, 287-336 + + Powell M.J.D. (2007), "A view of algorithms for optimization without + derivatives", Cambridge University Technical Report DAMTP 2007/NA03 + + + Examples + -------- + Minimize the objective function f(x,y) = x*y subject + to the constraints x**2 + y**2 < 1 and y > 0:: + + >>> def objective(x): + ... return x[0]*x[1] + ... + >>> def constr1(x): + ... return 1 - (x[0]**2 + x[1]**2) + ... + >>> def constr2(x): + ... return x[1] + ... + >>> from scipy.optimize import fmin_cobyla + >>> fmin_cobyla(objective, [0.0, 0.1], [constr1, constr2], rhoend=1e-7) + array([-0.70710685, 0.70710671]) + + The exact solution is (-sqrt(2)/2, sqrt(2)/2). + + + + """ + err = "cons must be a sequence of callable functions or a single"\ + " callable function." + try: + len(cons) + except TypeError as e: + if callable(cons): + cons = [cons] + else: + raise TypeError(err) from e + else: + for thisfunc in cons: + if not callable(thisfunc): + raise TypeError(err) + + if consargs is None: + consargs = args + + # build constraints + con = tuple({'type': 'ineq', 'fun': c, 'args': consargs} for c in cons) + + # options + opts = {'rhobeg': rhobeg, + 'tol': rhoend, + 'disp': disp, + 'maxiter': maxfun, + 'catol': catol, + 'callback': callback} + + sol = _minimize_cobyla(func, x0, args, constraints=con, + **opts) + if disp and not sol['success']: + print(f"COBYLA failed to find a solution: {sol.message}") + return sol['x'] + + +@synchronized +def _minimize_cobyla(fun, x0, args=(), constraints=(), + rhobeg=1.0, tol=1e-4, maxiter=1000, + disp=False, catol=2e-4, callback=None, bounds=None, + **unknown_options): + """ + Minimize a scalar function of one or more variables using the + Constrained Optimization BY Linear Approximation (COBYLA) algorithm. + + Options + ------- + rhobeg : float + Reasonable initial changes to the variables. + tol : float + Final accuracy in the optimization (not precisely guaranteed). + This is a lower bound on the size of the trust region. + disp : bool + Set to True to print convergence messages. If False, + `verbosity` is ignored as set to 0. + maxiter : int + Maximum number of function evaluations. + catol : float + Tolerance (absolute) for constraint violations + + """ + _check_unknown_options(unknown_options) + maxfun = maxiter + rhoend = tol + iprint = int(bool(disp)) + + # check constraints + if isinstance(constraints, dict): + constraints = (constraints, ) + + if bounds: + i_lb = np.isfinite(bounds.lb) + if np.any(i_lb): + def lb_constraint(x, *args, **kwargs): + return x[i_lb] - bounds.lb[i_lb] + + constraints.append({'type': 'ineq', 'fun': lb_constraint}) + + i_ub = np.isfinite(bounds.ub) + if np.any(i_ub): + def ub_constraint(x): + return bounds.ub[i_ub] - x[i_ub] + + constraints.append({'type': 'ineq', 'fun': ub_constraint}) + + for ic, con in enumerate(constraints): + # check type + try: + ctype = con['type'].lower() + except KeyError as e: + raise KeyError('Constraint %d has no type defined.' % ic) from e + except TypeError as e: + raise TypeError('Constraints must be defined using a ' + 'dictionary.') from e + except AttributeError as e: + raise TypeError("Constraint's type must be a string.") from e + else: + if ctype != 'ineq': + raise ValueError("Constraints of type '%s' not handled by " + "COBYLA." % con['type']) + + # check function + if 'fun' not in con: + raise KeyError('Constraint %d has no function defined.' % ic) + + # check extra arguments + if 'args' not in con: + con['args'] = () + + # m is the total number of constraint values + # it takes into account that some constraints may be vector-valued + cons_lengths = [] + for c in constraints: + f = c['fun'](x0, *c['args']) + try: + cons_length = len(f) + except TypeError: + cons_length = 1 + cons_lengths.append(cons_length) + m = sum(cons_lengths) + + # create the ScalarFunction, cobyla doesn't require derivative function + def _jac(x, *args): + return None + + sf = _prepare_scalar_function(fun, x0, args=args, jac=_jac) + + def calcfc(x, con): + f = sf.fun(x) + i = 0 + for size, c in izip(cons_lengths, constraints): + con[i: i + size] = c['fun'](x, *c['args']) + i += size + return f + + def wrapped_callback(x): + if callback is not None: + callback(np.copy(x)) + + info = np.zeros(4, np.float64) + xopt, info = cobyla.minimize(calcfc, m=m, x=np.copy(x0), rhobeg=rhobeg, + rhoend=rhoend, iprint=iprint, maxfun=maxfun, + dinfo=info, callback=wrapped_callback) + + if info[3] > catol: + # Check constraint violation + info[0] = 4 + + return OptimizeResult(x=xopt, + status=int(info[0]), + success=info[0] == 1, + message={1: 'Optimization terminated successfully.', + 2: 'Maximum number of function evaluations ' + 'has been exceeded.', + 3: 'Rounding errors are becoming damaging ' + 'in COBYLA subroutine.', + 4: 'Did not converge to a solution ' + 'satisfying the constraints. See ' + '`maxcv` for magnitude of violation.', + 5: 'NaN result encountered.' + }.get(info[0], 'Unknown exit status.'), + nfev=int(info[1]), + fun=info[2], + maxcv=info[3]) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyqa_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyqa_py.py new file mode 100644 index 0000000000000000000000000000000000000000..4928fca9c162fe1117451e3325e6a870b5933a6f --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_cobyqa_py.py @@ -0,0 +1,62 @@ +import numpy as np + +from ._optimize import _check_unknown_options + + +def _minimize_cobyqa(fun, x0, args=(), bounds=None, constraints=(), + callback=None, disp=False, maxfev=None, maxiter=None, + f_target=-np.inf, feasibility_tol=1e-8, + initial_tr_radius=1.0, final_tr_radius=1e-6, scale=False, + **unknown_options): + """ + Minimize a scalar function of one or more variables using the + Constrained Optimization BY Quadratic Approximations (COBYQA) algorithm [1]_. + + .. versionadded:: 1.14.0 + + Options + ------- + disp : bool + Set to True to print information about the optimization procedure. + maxfev : int + Maximum number of function evaluations. + maxiter : int + Maximum number of iterations. + f_target : float + Target value for the objective function. The optimization procedure is + terminated when the objective function value of a feasible point (see + `feasibility_tol` below) is less than or equal to this target. + feasibility_tol : float + Absolute tolerance for the constraint violation. + initial_tr_radius : float + Initial trust-region radius. Typically, this value should be in the + order of one tenth of the greatest expected change to the variables. + final_tr_radius : float + Final trust-region radius. It should indicate the accuracy required in + the final values of the variables. If provided, this option overrides + the value of `tol` in the `minimize` function. + scale : bool + Set to True to scale the variables according to the bounds. If True and + if all the lower and upper bounds are finite, the variables are scaled + to be within the range :math:`[-1, 1]`. If any of the lower or upper + bounds is infinite, the variables are not scaled. + + References + ---------- + .. [1] COBYQA + https://www.cobyqa.com/stable/ + """ + from .._lib.cobyqa import minimize # import here to avoid circular imports + + _check_unknown_options(unknown_options) + options = { + 'disp': bool(disp), + 'maxfev': int(maxfev) if maxfev is not None else 500 * len(x0), + 'maxiter': int(maxiter) if maxiter is not None else 1000 * len(x0), + 'target': float(f_target), + 'feasibility_tol': float(feasibility_tol), + 'radius_init': float(initial_tr_radius), + 'radius_final': float(final_tr_radius), + 'scale': bool(scale), + } + return minimize(fun, x0, args, bounds, constraints, callback, options) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_constraints.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_constraints.py new file mode 100644 index 0000000000000000000000000000000000000000..1c7ff5e170b2eb518bc6be0c667ac9f89a073dcf --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_constraints.py @@ -0,0 +1,590 @@ +"""Constraints definition for minimize.""" +import numpy as np +from ._hessian_update_strategy import BFGS +from ._differentiable_functions import ( + VectorFunction, LinearVectorFunction, IdentityVectorFunction) +from ._optimize import OptimizeWarning +from warnings import warn, catch_warnings, simplefilter, filterwarnings +from scipy.sparse import issparse + + +def _arr_to_scalar(x): + # If x is a numpy array, return x.item(). This will + # fail if the array has more than one element. + return x.item() if isinstance(x, np.ndarray) else x + + +class NonlinearConstraint: + """Nonlinear constraint on the variables. + + The constraint has the general inequality form:: + + lb <= fun(x) <= ub + + Here the vector of independent variables x is passed as ndarray of shape + (n,) and ``fun`` returns a vector with m components. + + It is possible to use equal bounds to represent an equality constraint or + infinite bounds to represent a one-sided constraint. + + Parameters + ---------- + fun : callable + The function defining the constraint. + The signature is ``fun(x) -> array_like, shape (m,)``. + lb, ub : array_like + Lower and upper bounds on the constraint. Each array must have the + shape (m,) or be a scalar, in the latter case a bound will be the same + for all components of the constraint. Use ``np.inf`` with an + appropriate sign to specify a one-sided constraint. + Set components of `lb` and `ub` equal to represent an equality + constraint. Note that you can mix constraints of different types: + interval, one-sided or equality, by setting different components of + `lb` and `ub` as necessary. + jac : {callable, '2-point', '3-point', 'cs'}, optional + Method of computing the Jacobian matrix (an m-by-n matrix, + where element (i, j) is the partial derivative of f[i] with + respect to x[j]). The keywords {'2-point', '3-point', + 'cs'} select a finite difference scheme for the numerical estimation. + A callable must have the following signature: + ``jac(x) -> {ndarray, sparse matrix}, shape (m, n)``. + Default is '2-point'. + hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy, None}, optional + Method for computing the Hessian matrix. The keywords + {'2-point', '3-point', 'cs'} select a finite difference scheme for + numerical estimation. Alternatively, objects implementing + `HessianUpdateStrategy` interface can be used to approximate the + Hessian. Currently available implementations are: + + - `BFGS` (default option) + - `SR1` + + A callable must return the Hessian matrix of ``dot(fun, v)`` and + must have the following signature: + ``hess(x, v) -> {LinearOperator, sparse matrix, array_like}, shape (n, n)``. + Here ``v`` is ndarray with shape (m,) containing Lagrange multipliers. + keep_feasible : array_like of bool, optional + Whether to keep the constraint components feasible throughout + iterations. A single value set this property for all components. + Default is False. Has no effect for equality constraints. + finite_diff_rel_step: None or array_like, optional + Relative step size for the finite difference approximation. Default is + None, which will select a reasonable value automatically depending + on a finite difference scheme. + finite_diff_jac_sparsity: {None, array_like, sparse matrix}, optional + Defines the sparsity structure of the Jacobian matrix for finite + difference estimation, its shape must be (m, n). If the Jacobian has + only few non-zero elements in *each* row, providing the sparsity + structure will greatly speed up the computations. A zero entry means + that a corresponding element in the Jacobian is identically zero. + If provided, forces the use of 'lsmr' trust-region solver. + If None (default) then dense differencing will be used. + + Notes + ----- + Finite difference schemes {'2-point', '3-point', 'cs'} may be used for + approximating either the Jacobian or the Hessian. We, however, do not allow + its use for approximating both simultaneously. Hence whenever the Jacobian + is estimated via finite-differences, we require the Hessian to be estimated + using one of the quasi-Newton strategies. + + The scheme 'cs' is potentially the most accurate, but requires the function + to correctly handles complex inputs and be analytically continuable to the + complex plane. The scheme '3-point' is more accurate than '2-point' but + requires twice as many operations. + + Examples + -------- + Constrain ``x[0] < sin(x[1]) + 1.9`` + + >>> from scipy.optimize import NonlinearConstraint + >>> import numpy as np + >>> con = lambda x: x[0] - np.sin(x[1]) + >>> nlc = NonlinearConstraint(con, -np.inf, 1.9) + + """ + def __init__(self, fun, lb, ub, jac='2-point', hess=BFGS(), + keep_feasible=False, finite_diff_rel_step=None, + finite_diff_jac_sparsity=None): + self.fun = fun + self.lb = lb + self.ub = ub + self.finite_diff_rel_step = finite_diff_rel_step + self.finite_diff_jac_sparsity = finite_diff_jac_sparsity + self.jac = jac + self.hess = hess + self.keep_feasible = keep_feasible + + +class LinearConstraint: + """Linear constraint on the variables. + + The constraint has the general inequality form:: + + lb <= A.dot(x) <= ub + + Here the vector of independent variables x is passed as ndarray of shape + (n,) and the matrix A has shape (m, n). + + It is possible to use equal bounds to represent an equality constraint or + infinite bounds to represent a one-sided constraint. + + Parameters + ---------- + A : {array_like, sparse matrix}, shape (m, n) + Matrix defining the constraint. + lb, ub : dense array_like, optional + Lower and upper limits on the constraint. Each array must have the + shape (m,) or be a scalar, in the latter case a bound will be the same + for all components of the constraint. Use ``np.inf`` with an + appropriate sign to specify a one-sided constraint. + Set components of `lb` and `ub` equal to represent an equality + constraint. Note that you can mix constraints of different types: + interval, one-sided or equality, by setting different components of + `lb` and `ub` as necessary. Defaults to ``lb = -np.inf`` + and ``ub = np.inf`` (no limits). + keep_feasible : dense array_like of bool, optional + Whether to keep the constraint components feasible throughout + iterations. A single value set this property for all components. + Default is False. Has no effect for equality constraints. + """ + def _input_validation(self): + if self.A.ndim != 2: + message = "`A` must have exactly two dimensions." + raise ValueError(message) + + try: + shape = self.A.shape[0:1] + self.lb = np.broadcast_to(self.lb, shape) + self.ub = np.broadcast_to(self.ub, shape) + self.keep_feasible = np.broadcast_to(self.keep_feasible, shape) + except ValueError: + message = ("`lb`, `ub`, and `keep_feasible` must be broadcastable " + "to shape `A.shape[0:1]`") + raise ValueError(message) + + def __init__(self, A, lb=-np.inf, ub=np.inf, keep_feasible=False): + if not issparse(A): + # In some cases, if the constraint is not valid, this emits a + # VisibleDeprecationWarning about ragged nested sequences + # before eventually causing an error. `scipy.optimize.milp` would + # prefer that this just error out immediately so it can handle it + # rather than concerning the user. + with catch_warnings(): + simplefilter("error") + self.A = np.atleast_2d(A).astype(np.float64) + else: + self.A = A + if issparse(lb) or issparse(ub): + raise ValueError("Constraint limits must be dense arrays.") + self.lb = np.atleast_1d(lb).astype(np.float64) + self.ub = np.atleast_1d(ub).astype(np.float64) + + if issparse(keep_feasible): + raise ValueError("`keep_feasible` must be a dense array.") + self.keep_feasible = np.atleast_1d(keep_feasible).astype(bool) + self._input_validation() + + def residual(self, x): + """ + Calculate the residual between the constraint function and the limits + + For a linear constraint of the form:: + + lb <= A@x <= ub + + the lower and upper residuals between ``A@x`` and the limits are values + ``sl`` and ``sb`` such that:: + + lb + sl == A@x == ub - sb + + When all elements of ``sl`` and ``sb`` are positive, all elements of + the constraint are satisfied; a negative element in ``sl`` or ``sb`` + indicates that the corresponding element of the constraint is not + satisfied. + + Parameters + ---------- + x: array_like + Vector of independent variables + + Returns + ------- + sl, sb : array-like + The lower and upper residuals + """ + return self.A@x - self.lb, self.ub - self.A@x + + +class Bounds: + """Bounds constraint on the variables. + + The constraint has the general inequality form:: + + lb <= x <= ub + + It is possible to use equal bounds to represent an equality constraint or + infinite bounds to represent a one-sided constraint. + + Parameters + ---------- + lb, ub : dense array_like, optional + Lower and upper bounds on independent variables. `lb`, `ub`, and + `keep_feasible` must be the same shape or broadcastable. + Set components of `lb` and `ub` equal + to fix a variable. Use ``np.inf`` with an appropriate sign to disable + bounds on all or some variables. Note that you can mix constraints of + different types: interval, one-sided or equality, by setting different + components of `lb` and `ub` as necessary. Defaults to ``lb = -np.inf`` + and ``ub = np.inf`` (no bounds). + keep_feasible : dense array_like of bool, optional + Whether to keep the constraint components feasible throughout + iterations. Must be broadcastable with `lb` and `ub`. + Default is False. Has no effect for equality constraints. + """ + def _input_validation(self): + try: + res = np.broadcast_arrays(self.lb, self.ub, self.keep_feasible) + self.lb, self.ub, self.keep_feasible = res + except ValueError: + message = "`lb`, `ub`, and `keep_feasible` must be broadcastable." + raise ValueError(message) + + def __init__(self, lb=-np.inf, ub=np.inf, keep_feasible=False): + if issparse(lb) or issparse(ub): + raise ValueError("Lower and upper bounds must be dense arrays.") + self.lb = np.atleast_1d(lb) + self.ub = np.atleast_1d(ub) + + if issparse(keep_feasible): + raise ValueError("`keep_feasible` must be a dense array.") + self.keep_feasible = np.atleast_1d(keep_feasible).astype(bool) + self._input_validation() + + def __repr__(self): + start = f"{type(self).__name__}({self.lb!r}, {self.ub!r}" + if np.any(self.keep_feasible): + end = f", keep_feasible={self.keep_feasible!r})" + else: + end = ")" + return start + end + + def residual(self, x): + """Calculate the residual (slack) between the input and the bounds + + For a bound constraint of the form:: + + lb <= x <= ub + + the lower and upper residuals between `x` and the bounds are values + ``sl`` and ``sb`` such that:: + + lb + sl == x == ub - sb + + When all elements of ``sl`` and ``sb`` are positive, all elements of + ``x`` lie within the bounds; a negative element in ``sl`` or ``sb`` + indicates that the corresponding element of ``x`` is out of bounds. + + Parameters + ---------- + x: array_like + Vector of independent variables + + Returns + ------- + sl, sb : array-like + The lower and upper residuals + """ + return x - self.lb, self.ub - x + + +class PreparedConstraint: + """Constraint prepared from a user defined constraint. + + On creation it will check whether a constraint definition is valid and + the initial point is feasible. If created successfully, it will contain + the attributes listed below. + + Parameters + ---------- + constraint : {NonlinearConstraint, LinearConstraint`, Bounds} + Constraint to check and prepare. + x0 : array_like + Initial vector of independent variables. + sparse_jacobian : bool or None, optional + If bool, then the Jacobian of the constraint will be converted + to the corresponded format if necessary. If None (default), such + conversion is not made. + finite_diff_bounds : 2-tuple, optional + Lower and upper bounds on the independent variables for the finite + difference approximation, if applicable. Defaults to no bounds. + + Attributes + ---------- + fun : {VectorFunction, LinearVectorFunction, IdentityVectorFunction} + Function defining the constraint wrapped by one of the convenience + classes. + bounds : 2-tuple + Contains lower and upper bounds for the constraints --- lb and ub. + These are converted to ndarray and have a size equal to the number of + the constraints. + keep_feasible : ndarray + Array indicating which components must be kept feasible with a size + equal to the number of the constraints. + """ + def __init__(self, constraint, x0, sparse_jacobian=None, + finite_diff_bounds=(-np.inf, np.inf)): + if isinstance(constraint, NonlinearConstraint): + fun = VectorFunction(constraint.fun, x0, + constraint.jac, constraint.hess, + constraint.finite_diff_rel_step, + constraint.finite_diff_jac_sparsity, + finite_diff_bounds, sparse_jacobian) + elif isinstance(constraint, LinearConstraint): + fun = LinearVectorFunction(constraint.A, x0, sparse_jacobian) + elif isinstance(constraint, Bounds): + fun = IdentityVectorFunction(x0, sparse_jacobian) + else: + raise ValueError("`constraint` of an unknown type is passed.") + + m = fun.m + + lb = np.asarray(constraint.lb, dtype=float) + ub = np.asarray(constraint.ub, dtype=float) + keep_feasible = np.asarray(constraint.keep_feasible, dtype=bool) + + lb = np.broadcast_to(lb, m) + ub = np.broadcast_to(ub, m) + keep_feasible = np.broadcast_to(keep_feasible, m) + + if keep_feasible.shape != (m,): + raise ValueError("`keep_feasible` has a wrong shape.") + + mask = keep_feasible & (lb != ub) + f0 = fun.f + if np.any(f0[mask] < lb[mask]) or np.any(f0[mask] > ub[mask]): + raise ValueError("`x0` is infeasible with respect to some " + "inequality constraint with `keep_feasible` " + "set to True.") + + self.fun = fun + self.bounds = (lb, ub) + self.keep_feasible = keep_feasible + + def violation(self, x): + """How much the constraint is exceeded by. + + Parameters + ---------- + x : array-like + Vector of independent variables + + Returns + ------- + excess : array-like + How much the constraint is exceeded by, for each of the + constraints specified by `PreparedConstraint.fun`. + """ + with catch_warnings(): + # Ignore the following warning, it's not important when + # figuring out total violation + # UserWarning: delta_grad == 0.0. Check if the approximated + # function is linear + filterwarnings("ignore", "delta_grad", UserWarning) + ev = self.fun.fun(np.asarray(x)) + + excess_lb = np.maximum(self.bounds[0] - ev, 0) + excess_ub = np.maximum(ev - self.bounds[1], 0) + + return excess_lb + excess_ub + + +def new_bounds_to_old(lb, ub, n): + """Convert the new bounds representation to the old one. + + The new representation is a tuple (lb, ub) and the old one is a list + containing n tuples, ith containing lower and upper bound on a ith + variable. + If any of the entries in lb/ub are -np.inf/np.inf they are replaced by + None. + """ + lb = np.broadcast_to(lb, n) + ub = np.broadcast_to(ub, n) + + lb = [float(x) if x > -np.inf else None for x in lb] + ub = [float(x) if x < np.inf else None for x in ub] + + return list(zip(lb, ub)) + + +def old_bound_to_new(bounds): + """Convert the old bounds representation to the new one. + + The new representation is a tuple (lb, ub) and the old one is a list + containing n tuples, ith containing lower and upper bound on a ith + variable. + If any of the entries in lb/ub are None they are replaced by + -np.inf/np.inf. + """ + lb, ub = zip(*bounds) + + # Convert occurrences of None to -inf or inf, and replace occurrences of + # any numpy array x with x.item(). Then wrap the results in numpy arrays. + lb = np.array([float(_arr_to_scalar(x)) if x is not None else -np.inf + for x in lb]) + ub = np.array([float(_arr_to_scalar(x)) if x is not None else np.inf + for x in ub]) + + return lb, ub + + +def strict_bounds(lb, ub, keep_feasible, n_vars): + """Remove bounds which are not asked to be kept feasible.""" + strict_lb = np.resize(lb, n_vars).astype(float) + strict_ub = np.resize(ub, n_vars).astype(float) + keep_feasible = np.resize(keep_feasible, n_vars) + strict_lb[~keep_feasible] = -np.inf + strict_ub[~keep_feasible] = np.inf + return strict_lb, strict_ub + + +def new_constraint_to_old(con, x0): + """ + Converts new-style constraint objects to old-style constraint dictionaries. + """ + if isinstance(con, NonlinearConstraint): + if (con.finite_diff_jac_sparsity is not None or + con.finite_diff_rel_step is not None or + not isinstance(con.hess, BFGS) or # misses user specified BFGS + con.keep_feasible): + warn("Constraint options `finite_diff_jac_sparsity`, " + "`finite_diff_rel_step`, `keep_feasible`, and `hess`" + "are ignored by this method.", + OptimizeWarning, stacklevel=3) + + fun = con.fun + if callable(con.jac): + jac = con.jac + else: + jac = None + + else: # LinearConstraint + if np.any(con.keep_feasible): + warn("Constraint option `keep_feasible` is ignored by this method.", + OptimizeWarning, stacklevel=3) + + A = con.A + if issparse(A): + A = A.toarray() + def fun(x): + return np.dot(A, x) + def jac(x): + return A + + # FIXME: when bugs in VectorFunction/LinearVectorFunction are worked out, + # use pcon.fun.fun and pcon.fun.jac. Until then, get fun/jac above. + pcon = PreparedConstraint(con, x0) + lb, ub = pcon.bounds + + i_eq = lb == ub + i_bound_below = np.logical_xor(lb != -np.inf, i_eq) + i_bound_above = np.logical_xor(ub != np.inf, i_eq) + i_unbounded = np.logical_and(lb == -np.inf, ub == np.inf) + + if np.any(i_unbounded): + warn("At least one constraint is unbounded above and below. Such " + "constraints are ignored.", + OptimizeWarning, stacklevel=3) + + ceq = [] + if np.any(i_eq): + def f_eq(x): + y = np.array(fun(x)).flatten() + return y[i_eq] - lb[i_eq] + ceq = [{"type": "eq", "fun": f_eq}] + + if jac is not None: + def j_eq(x): + dy = jac(x) + if issparse(dy): + dy = dy.toarray() + dy = np.atleast_2d(dy) + return dy[i_eq, :] + ceq[0]["jac"] = j_eq + + cineq = [] + n_bound_below = np.sum(i_bound_below) + n_bound_above = np.sum(i_bound_above) + if n_bound_below + n_bound_above: + def f_ineq(x): + y = np.zeros(n_bound_below + n_bound_above) + y_all = np.array(fun(x)).flatten() + y[:n_bound_below] = y_all[i_bound_below] - lb[i_bound_below] + y[n_bound_below:] = -(y_all[i_bound_above] - ub[i_bound_above]) + return y + cineq = [{"type": "ineq", "fun": f_ineq}] + + if jac is not None: + def j_ineq(x): + dy = np.zeros((n_bound_below + n_bound_above, len(x0))) + dy_all = jac(x) + if issparse(dy_all): + dy_all = dy_all.toarray() + dy_all = np.atleast_2d(dy_all) + dy[:n_bound_below, :] = dy_all[i_bound_below] + dy[n_bound_below:, :] = -dy_all[i_bound_above] + return dy + cineq[0]["jac"] = j_ineq + + old_constraints = ceq + cineq + + if len(old_constraints) > 1: + warn("Equality and inequality constraints are specified in the same " + "element of the constraint list. For efficient use with this " + "method, equality and inequality constraints should be specified " + "in separate elements of the constraint list. ", + OptimizeWarning, stacklevel=3) + return old_constraints + + +def old_constraint_to_new(ic, con): + """ + Converts old-style constraint dictionaries to new-style constraint objects. + """ + # check type + try: + ctype = con['type'].lower() + except KeyError as e: + raise KeyError('Constraint %d has no type defined.' % ic) from e + except TypeError as e: + raise TypeError( + 'Constraints must be a sequence of dictionaries.' + ) from e + except AttributeError as e: + raise TypeError("Constraint's type must be a string.") from e + else: + if ctype not in ['eq', 'ineq']: + raise ValueError("Unknown constraint type '%s'." % con['type']) + if 'fun' not in con: + raise ValueError('Constraint %d has no function defined.' % ic) + + lb = 0 + if ctype == 'eq': + ub = 0 + else: + ub = np.inf + + jac = '2-point' + if 'args' in con: + args = con['args'] + def fun(x): + return con["fun"](x, *args) + if 'jac' in con: + def jac(x): + return con["jac"](x, *args) + else: + fun = con['fun'] + if 'jac' in con: + jac = con['jac'] + + return NonlinearConstraint(fun, lb, ub, jac) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dcsrch.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dcsrch.py new file mode 100644 index 0000000000000000000000000000000000000000..f8b4df4763ba4f699869431a0b6528383c2f0328 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dcsrch.py @@ -0,0 +1,728 @@ +import numpy as np + +""" +# 2023 - ported from minpack2.dcsrch, dcstep (Fortran) to Python +c MINPACK-1 Project. June 1983. +c Argonne National Laboratory. +c Jorge J. More' and David J. Thuente. +c +c MINPACK-2 Project. November 1993. +c Argonne National Laboratory and University of Minnesota. +c Brett M. Averick, Richard G. Carter, and Jorge J. More'. +""" + +# NOTE this file was linted by black on first commit, and can be kept that way. + + +class DCSRCH: + """ + Parameters + ---------- + phi : callable phi(alpha) + Function at point `alpha` + derphi : callable phi'(alpha) + Objective function derivative. Returns a scalar. + ftol : float + A nonnegative tolerance for the sufficient decrease condition. + gtol : float + A nonnegative tolerance for the curvature condition. + xtol : float + A nonnegative relative tolerance for an acceptable step. The + subroutine exits with a warning if the relative difference between + sty and stx is less than xtol. + stpmin : float + A nonnegative lower bound for the step. + stpmax : + A nonnegative upper bound for the step. + + Notes + ----- + + This subroutine finds a step that satisfies a sufficient + decrease condition and a curvature condition. + + Each call of the subroutine updates an interval with + endpoints stx and sty. The interval is initially chosen + so that it contains a minimizer of the modified function + + psi(stp) = f(stp) - f(0) - ftol*stp*f'(0). + + If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the + interval is chosen so that it contains a minimizer of f. + + The algorithm is designed to find a step that satisfies + the sufficient decrease condition + + f(stp) <= f(0) + ftol*stp*f'(0), + + and the curvature condition + + abs(f'(stp)) <= gtol*abs(f'(0)). + + If ftol is less than gtol and if, for example, the function + is bounded below, then there is always a step which satisfies + both conditions. + + If no step can be found that satisfies both conditions, then + the algorithm stops with a warning. In this case stp only + satisfies the sufficient decrease condition. + + A typical invocation of dcsrch has the following outline: + + Evaluate the function at stp = 0.0d0; store in f. + Evaluate the gradient at stp = 0.0d0; store in g. + Choose a starting step stp. + + task = 'START' + 10 continue + call dcsrch(stp,f,g,ftol,gtol,xtol,task,stpmin,stpmax, + isave,dsave) + if (task .eq. 'FG') then + Evaluate the function and the gradient at stp + go to 10 + end if + + NOTE: The user must not alter work arrays between calls. + + The subroutine statement is + + subroutine dcsrch(f,g,stp,ftol,gtol,xtol,stpmin,stpmax, + task,isave,dsave) + where + + stp is a double precision variable. + On entry stp is the current estimate of a satisfactory + step. On initial entry, a positive initial estimate + must be provided. + On exit stp is the current estimate of a satisfactory step + if task = 'FG'. If task = 'CONV' then stp satisfies + the sufficient decrease and curvature condition. + + f is a double precision variable. + On initial entry f is the value of the function at 0. + On subsequent entries f is the value of the + function at stp. + On exit f is the value of the function at stp. + + g is a double precision variable. + On initial entry g is the derivative of the function at 0. + On subsequent entries g is the derivative of the + function at stp. + On exit g is the derivative of the function at stp. + + ftol is a double precision variable. + On entry ftol specifies a nonnegative tolerance for the + sufficient decrease condition. + On exit ftol is unchanged. + + gtol is a double precision variable. + On entry gtol specifies a nonnegative tolerance for the + curvature condition. + On exit gtol is unchanged. + + xtol is a double precision variable. + On entry xtol specifies a nonnegative relative tolerance + for an acceptable step. The subroutine exits with a + warning if the relative difference between sty and stx + is less than xtol. + + On exit xtol is unchanged. + + task is a character variable of length at least 60. + On initial entry task must be set to 'START'. + On exit task indicates the required action: + + If task(1:2) = 'FG' then evaluate the function and + derivative at stp and call dcsrch again. + + If task(1:4) = 'CONV' then the search is successful. + + If task(1:4) = 'WARN' then the subroutine is not able + to satisfy the convergence conditions. The exit value of + stp contains the best point found during the search. + + If task(1:5) = 'ERROR' then there is an error in the + input arguments. + + On exit with convergence, a warning or an error, the + variable task contains additional information. + + stpmin is a double precision variable. + On entry stpmin is a nonnegative lower bound for the step. + On exit stpmin is unchanged. + + stpmax is a double precision variable. + On entry stpmax is a nonnegative upper bound for the step. + On exit stpmax is unchanged. + + isave is an integer work array of dimension 2. + + dsave is a double precision work array of dimension 13. + + Subprograms called + + MINPACK-2 ... dcstep + MINPACK-1 Project. June 1983. + Argonne National Laboratory. + Jorge J. More' and David J. Thuente. + + MINPACK-2 Project. November 1993. + Argonne National Laboratory and University of Minnesota. + Brett M. Averick, Richard G. Carter, and Jorge J. More'. + """ + + def __init__(self, phi, derphi, ftol, gtol, xtol, stpmin, stpmax): + self.stage = None + self.ginit = None + self.gtest = None + self.gx = None + self.gy = None + self.finit = None + self.fx = None + self.fy = None + self.stx = None + self.sty = None + self.stmin = None + self.stmax = None + self.width = None + self.width1 = None + + # leave all assessment of tolerances/limits to the first call of + # this object + self.ftol = ftol + self.gtol = gtol + self.xtol = xtol + self.stpmin = stpmin + self.stpmax = stpmax + + self.phi = phi + self.derphi = derphi + + def __call__(self, alpha1, phi0=None, derphi0=None, maxiter=100): + """ + Parameters + ---------- + alpha1 : float + alpha1 is the current estimate of a satisfactory + step. A positive initial estimate must be provided. + phi0 : float + the value of `phi` at 0 (if known). + derphi0 : float + the derivative of `derphi` at 0 (if known). + maxiter : int + + Returns + ------- + alpha : float + Step size, or None if no suitable step was found. + phi : float + Value of `phi` at the new point `alpha`. + phi0 : float + Value of `phi` at `alpha=0`. + task : bytes + On exit task indicates status information. + + If task[:4] == b'CONV' then the search is successful. + + If task[:4] == b'WARN' then the subroutine is not able + to satisfy the convergence conditions. The exit value of + stp contains the best point found during the search. + + If task[:5] == b'ERROR' then there is an error in the + input arguments. + """ + if phi0 is None: + phi0 = self.phi(0.0) + if derphi0 is None: + derphi0 = self.derphi(0.0) + + phi1 = phi0 + derphi1 = derphi0 + + task = b"START" + for i in range(maxiter): + stp, phi1, derphi1, task = self._iterate( + alpha1, phi1, derphi1, task + ) + + if not np.isfinite(stp): + task = b"WARN" + stp = None + break + + if task[:2] == b"FG": + alpha1 = stp + phi1 = self.phi(stp) + derphi1 = self.derphi(stp) + else: + break + else: + # maxiter reached, the line search did not converge + stp = None + task = b"WARNING: dcsrch did not converge within max iterations" + + if task[:5] == b"ERROR" or task[:4] == b"WARN": + stp = None # failed + + return stp, phi1, phi0, task + + def _iterate(self, stp, f, g, task): + """ + Parameters + ---------- + stp : float + The current estimate of a satisfactory step. On initial entry, a + positive initial estimate must be provided. + f : float + On first call f is the value of the function at 0. On subsequent + entries f should be the value of the function at stp. + g : float + On initial entry g is the derivative of the function at 0. On + subsequent entries g is the derivative of the function at stp. + task : bytes + On initial entry task must be set to 'START'. + + On exit with convergence, a warning or an error, the + variable task contains additional information. + + + Returns + ------- + stp, f, g, task: tuple + + stp : float + the current estimate of a satisfactory step if task = 'FG'. If + task = 'CONV' then stp satisfies the sufficient decrease and + curvature condition. + f : float + the value of the function at stp. + g : float + the derivative of the function at stp. + task : bytes + On exit task indicates the required action: + + If task(1:2) == b'FG' then evaluate the function and + derivative at stp and call dcsrch again. + + If task(1:4) == b'CONV' then the search is successful. + + If task(1:4) == b'WARN' then the subroutine is not able + to satisfy the convergence conditions. The exit value of + stp contains the best point found during the search. + + If task(1:5) == b'ERROR' then there is an error in the + input arguments. + """ + p5 = 0.5 + p66 = 0.66 + xtrapl = 1.1 + xtrapu = 4.0 + + if task[:5] == b"START": + if stp < self.stpmin: + task = b"ERROR: STP .LT. STPMIN" + if stp > self.stpmax: + task = b"ERROR: STP .GT. STPMAX" + if g >= 0: + task = b"ERROR: INITIAL G .GE. ZERO" + if self.ftol < 0: + task = b"ERROR: FTOL .LT. ZERO" + if self.gtol < 0: + task = b"ERROR: GTOL .LT. ZERO" + if self.xtol < 0: + task = b"ERROR: XTOL .LT. ZERO" + if self.stpmin < 0: + task = b"ERROR: STPMIN .LT. ZERO" + if self.stpmax < self.stpmin: + task = b"ERROR: STPMAX .LT. STPMIN" + + if task[:5] == b"ERROR": + return stp, f, g, task + + # Initialize local variables. + + self.brackt = False + self.stage = 1 + self.finit = f + self.ginit = g + self.gtest = self.ftol * self.ginit + self.width = self.stpmax - self.stpmin + self.width1 = self.width / p5 + + # The variables stx, fx, gx contain the values of the step, + # function, and derivative at the best step. + # The variables sty, fy, gy contain the value of the step, + # function, and derivative at sty. + # The variables stp, f, g contain the values of the step, + # function, and derivative at stp. + + self.stx = 0.0 + self.fx = self.finit + self.gx = self.ginit + self.sty = 0.0 + self.fy = self.finit + self.gy = self.ginit + self.stmin = 0 + self.stmax = stp + xtrapu * stp + task = b"FG" + return stp, f, g, task + + # in the original Fortran this was a location to restore variables + # we don't need to do that because they're attributes. + + # If psi(stp) <= 0 and f'(stp) >= 0 for some step, then the + # algorithm enters the second stage. + ftest = self.finit + stp * self.gtest + + if self.stage == 1 and f <= ftest and g >= 0: + self.stage = 2 + + # test for warnings + if self.brackt and (stp <= self.stmin or stp >= self.stmax): + task = b"WARNING: ROUNDING ERRORS PREVENT PROGRESS" + if self.brackt and self.stmax - self.stmin <= self.xtol * self.stmax: + task = b"WARNING: XTOL TEST SATISFIED" + if stp == self.stpmax and f <= ftest and g <= self.gtest: + task = b"WARNING: STP = STPMAX" + if stp == self.stpmin and (f > ftest or g >= self.gtest): + task = b"WARNING: STP = STPMIN" + + # test for convergence + if f <= ftest and abs(g) <= self.gtol * -self.ginit: + task = b"CONVERGENCE" + + # test for termination + if task[:4] == b"WARN" or task[:4] == b"CONV": + return stp, f, g, task + + # A modified function is used to predict the step during the + # first stage if a lower function value has been obtained but + # the decrease is not sufficient. + if self.stage == 1 and f <= self.fx and f > ftest: + # Define the modified function and derivative values. + fm = f - stp * self.gtest + fxm = self.fx - self.stx * self.gtest + fym = self.fy - self.sty * self.gtest + gm = g - self.gtest + gxm = self.gx - self.gtest + gym = self.gy - self.gtest + + # Call dcstep to update stx, sty, and to compute the new step. + # dcstep can have several operations which can produce NaN + # e.g. inf/inf. Filter these out. + with np.errstate(invalid="ignore", over="ignore"): + tup = dcstep( + self.stx, + fxm, + gxm, + self.sty, + fym, + gym, + stp, + fm, + gm, + self.brackt, + self.stmin, + self.stmax, + ) + self.stx, fxm, gxm, self.sty, fym, gym, stp, self.brackt = tup + + # Reset the function and derivative values for f + self.fx = fxm + self.stx * self.gtest + self.fy = fym + self.sty * self.gtest + self.gx = gxm + self.gtest + self.gy = gym + self.gtest + + else: + # Call dcstep to update stx, sty, and to compute the new step. + # dcstep can have several operations which can produce NaN + # e.g. inf/inf. Filter these out. + + with np.errstate(invalid="ignore", over="ignore"): + tup = dcstep( + self.stx, + self.fx, + self.gx, + self.sty, + self.fy, + self.gy, + stp, + f, + g, + self.brackt, + self.stmin, + self.stmax, + ) + ( + self.stx, + self.fx, + self.gx, + self.sty, + self.fy, + self.gy, + stp, + self.brackt, + ) = tup + + # Decide if a bisection step is needed + if self.brackt: + if abs(self.sty - self.stx) >= p66 * self.width1: + stp = self.stx + p5 * (self.sty - self.stx) + self.width1 = self.width + self.width = abs(self.sty - self.stx) + + # Set the minimum and maximum steps allowed for stp. + if self.brackt: + self.stmin = min(self.stx, self.sty) + self.stmax = max(self.stx, self.sty) + else: + self.stmin = stp + xtrapl * (stp - self.stx) + self.stmax = stp + xtrapu * (stp - self.stx) + + # Force the step to be within the bounds stpmax and stpmin. + stp = np.clip(stp, self.stpmin, self.stpmax) + + # If further progress is not possible, let stp be the best + # point obtained during the search. + if ( + self.brackt + and (stp <= self.stmin or stp >= self.stmax) + or ( + self.brackt + and self.stmax - self.stmin <= self.xtol * self.stmax + ) + ): + stp = self.stx + + # Obtain another function and derivative + task = b"FG" + return stp, f, g, task + + +def dcstep(stx, fx, dx, sty, fy, dy, stp, fp, dp, brackt, stpmin, stpmax): + """ + Subroutine dcstep + + This subroutine computes a safeguarded step for a search + procedure and updates an interval that contains a step that + satisfies a sufficient decrease and a curvature condition. + + The parameter stx contains the step with the least function + value. If brackt is set to .true. then a minimizer has + been bracketed in an interval with endpoints stx and sty. + The parameter stp contains the current step. + The subroutine assumes that if brackt is set to .true. then + + min(stx,sty) < stp < max(stx,sty), + + and that the derivative at stx is negative in the direction + of the step. + + The subroutine statement is + + subroutine dcstep(stx,fx,dx,sty,fy,dy,stp,fp,dp,brackt, + stpmin,stpmax) + + where + + stx is a double precision variable. + On entry stx is the best step obtained so far and is an + endpoint of the interval that contains the minimizer. + On exit stx is the updated best step. + + fx is a double precision variable. + On entry fx is the function at stx. + On exit fx is the function at stx. + + dx is a double precision variable. + On entry dx is the derivative of the function at + stx. The derivative must be negative in the direction of + the step, that is, dx and stp - stx must have opposite + signs. + On exit dx is the derivative of the function at stx. + + sty is a double precision variable. + On entry sty is the second endpoint of the interval that + contains the minimizer. + On exit sty is the updated endpoint of the interval that + contains the minimizer. + + fy is a double precision variable. + On entry fy is the function at sty. + On exit fy is the function at sty. + + dy is a double precision variable. + On entry dy is the derivative of the function at sty. + On exit dy is the derivative of the function at the exit sty. + + stp is a double precision variable. + On entry stp is the current step. If brackt is set to .true. + then on input stp must be between stx and sty. + On exit stp is a new trial step. + + fp is a double precision variable. + On entry fp is the function at stp + On exit fp is unchanged. + + dp is a double precision variable. + On entry dp is the derivative of the function at stp. + On exit dp is unchanged. + + brackt is an logical variable. + On entry brackt specifies if a minimizer has been bracketed. + Initially brackt must be set to .false. + On exit brackt specifies if a minimizer has been bracketed. + When a minimizer is bracketed brackt is set to .true. + + stpmin is a double precision variable. + On entry stpmin is a lower bound for the step. + On exit stpmin is unchanged. + + stpmax is a double precision variable. + On entry stpmax is an upper bound for the step. + On exit stpmax is unchanged. + + MINPACK-1 Project. June 1983 + Argonne National Laboratory. + Jorge J. More' and David J. Thuente. + + MINPACK-2 Project. November 1993. + Argonne National Laboratory and University of Minnesota. + Brett M. Averick and Jorge J. More'. + + """ + sgn_dp = np.sign(dp) + sgn_dx = np.sign(dx) + + # sgnd = dp * (dx / abs(dx)) + sgnd = sgn_dp * sgn_dx + + # First case: A higher function value. The minimum is bracketed. + # If the cubic step is closer to stx than the quadratic step, the + # cubic step is taken, otherwise the average of the cubic and + # quadratic steps is taken. + if fp > fx: + theta = 3.0 * (fx - fp) / (stp - stx) + dx + dp + s = max(abs(theta), abs(dx), abs(dp)) + gamma = s * np.sqrt((theta / s) ** 2 - (dx / s) * (dp / s)) + if stp < stx: + gamma *= -1 + p = (gamma - dx) + theta + q = ((gamma - dx) + gamma) + dp + r = p / q + stpc = stx + r * (stp - stx) + stpq = stx + ((dx / ((fx - fp) / (stp - stx) + dx)) / 2.0) * (stp - stx) + if abs(stpc - stx) <= abs(stpq - stx): + stpf = stpc + else: + stpf = stpc + (stpq - stpc) / 2.0 + brackt = True + elif sgnd < 0.0: + # Second case: A lower function value and derivatives of opposite + # sign. The minimum is bracketed. If the cubic step is farther from + # stp than the secant step, the cubic step is taken, otherwise the + # secant step is taken. + theta = 3 * (fx - fp) / (stp - stx) + dx + dp + s = max(abs(theta), abs(dx), abs(dp)) + gamma = s * np.sqrt((theta / s) ** 2 - (dx / s) * (dp / s)) + if stp > stx: + gamma *= -1 + p = (gamma - dp) + theta + q = ((gamma - dp) + gamma) + dx + r = p / q + stpc = stp + r * (stx - stp) + stpq = stp + (dp / (dp - dx)) * (stx - stp) + if abs(stpc - stp) > abs(stpq - stp): + stpf = stpc + else: + stpf = stpq + brackt = True + elif abs(dp) < abs(dx): + # Third case: A lower function value, derivatives of the same sign, + # and the magnitude of the derivative decreases. + + # The cubic step is computed only if the cubic tends to infinity + # in the direction of the step or if the minimum of the cubic + # is beyond stp. Otherwise the cubic step is defined to be the + # secant step. + theta = 3 * (fx - fp) / (stp - stx) + dx + dp + s = max(abs(theta), abs(dx), abs(dp)) + + # The case gamma = 0 only arises if the cubic does not tend + # to infinity in the direction of the step. + gamma = s * np.sqrt(max(0, (theta / s) ** 2 - (dx / s) * (dp / s))) + if stp > stx: + gamma = -gamma + p = (gamma - dp) + theta + q = (gamma + (dx - dp)) + gamma + r = p / q + if r < 0 and gamma != 0: + stpc = stp + r * (stx - stp) + elif stp > stx: + stpc = stpmax + else: + stpc = stpmin + stpq = stp + (dp / (dp - dx)) * (stx - stp) + + if brackt: + # A minimizer has been bracketed. If the cubic step is + # closer to stp than the secant step, the cubic step is + # taken, otherwise the secant step is taken. + if abs(stpc - stp) < abs(stpq - stp): + stpf = stpc + else: + stpf = stpq + + if stp > stx: + stpf = min(stp + 0.66 * (sty - stp), stpf) + else: + stpf = max(stp + 0.66 * (sty - stp), stpf) + else: + # A minimizer has not been bracketed. If the cubic step is + # farther from stp than the secant step, the cubic step is + # taken, otherwise the secant step is taken. + if abs(stpc - stp) > abs(stpq - stp): + stpf = stpc + else: + stpf = stpq + stpf = np.clip(stpf, stpmin, stpmax) + + else: + # Fourth case: A lower function value, derivatives of the same sign, + # and the magnitude of the derivative does not decrease. If the + # minimum is not bracketed, the step is either stpmin or stpmax, + # otherwise the cubic step is taken. + if brackt: + theta = 3.0 * (fp - fy) / (sty - stp) + dy + dp + s = max(abs(theta), abs(dy), abs(dp)) + gamma = s * np.sqrt((theta / s) ** 2 - (dy / s) * (dp / s)) + if stp > sty: + gamma = -gamma + p = (gamma - dp) + theta + q = ((gamma - dp) + gamma) + dy + r = p / q + stpc = stp + r * (sty - stp) + stpf = stpc + elif stp > stx: + stpf = stpmax + else: + stpf = stpmin + + # Update the interval which contains a minimizer. + if fp > fx: + sty = stp + fy = fp + dy = dp + else: + if sgnd < 0: + sty = stx + fy = fx + dy = dx + stx = stp + fx = fp + dx = dp + + # Compute the new step. + stp = stpf + + return stx, fx, dx, sty, fy, dy, stp, brackt diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py new file mode 100644 index 0000000000000000000000000000000000000000..9370aff56f7dd428ecb56af31e21f8a5fa181bb4 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py @@ -0,0 +1,693 @@ +import numpy as np +import scipy.sparse as sps +from ._numdiff import approx_derivative, group_columns +from ._hessian_update_strategy import HessianUpdateStrategy +from scipy.sparse.linalg import LinearOperator +from scipy._lib._array_api import atleast_nd, array_namespace + + +FD_METHODS = ('2-point', '3-point', 'cs') + + +def _wrapper_fun(fun, args=()): + ncalls = [0] + + def wrapped(x): + ncalls[0] += 1 + # Send a copy because the user may overwrite it. + # Overwriting results in undefined behaviour because + # fun(self.x) will change self.x, with the two no longer linked. + fx = fun(np.copy(x), *args) + # Make sure the function returns a true scalar + if not np.isscalar(fx): + try: + fx = np.asarray(fx).item() + except (TypeError, ValueError) as e: + raise ValueError( + "The user-provided objective function " + "must return a scalar value." + ) from e + return fx + return wrapped, ncalls + + +def _wrapper_grad(grad, fun=None, args=(), finite_diff_options=None): + ncalls = [0] + + if callable(grad): + def wrapped(x, **kwds): + # kwds present to give function same signature as numdiff variant + ncalls[0] += 1 + return np.atleast_1d(grad(np.copy(x), *args)) + return wrapped, ncalls + + elif grad in FD_METHODS: + def wrapped1(x, f0=None): + ncalls[0] += 1 + return approx_derivative( + fun, x, f0=f0, **finite_diff_options + ) + + return wrapped1, ncalls + + +def _wrapper_hess(hess, grad=None, x0=None, args=(), finite_diff_options=None): + if callable(hess): + H = hess(np.copy(x0), *args) + ncalls = [1] + + if sps.issparse(H): + def wrapped(x, **kwds): + ncalls[0] += 1 + return sps.csr_matrix(hess(np.copy(x), *args)) + + H = sps.csr_matrix(H) + + elif isinstance(H, LinearOperator): + def wrapped(x, **kwds): + ncalls[0] += 1 + return hess(np.copy(x), *args) + + else: # dense + def wrapped(x, **kwds): + ncalls[0] += 1 + return np.atleast_2d(np.asarray(hess(np.copy(x), *args))) + + H = np.atleast_2d(np.asarray(H)) + + return wrapped, ncalls, H + elif hess in FD_METHODS: + ncalls = [0] + + def wrapped1(x, f0=None): + return approx_derivative( + grad, x, f0=f0, **finite_diff_options + ) + + return wrapped1, ncalls, None + + +class ScalarFunction: + """Scalar function and its derivatives. + + This class defines a scalar function F: R^n->R and methods for + computing or approximating its first and second derivatives. + + Parameters + ---------- + fun : callable + evaluates the scalar function. Must be of the form ``fun(x, *args)``, + where ``x`` is the argument in the form of a 1-D array and ``args`` is + a tuple of any additional fixed parameters needed to completely specify + the function. Should return a scalar. + x0 : array-like + Provides an initial set of variables for evaluating fun. Array of real + elements of size (n,), where 'n' is the number of independent + variables. + args : tuple, optional + Any additional fixed parameters needed to completely specify the scalar + function. + grad : {callable, '2-point', '3-point', 'cs'} + Method for computing the gradient vector. + If it is a callable, it should be a function that returns the gradient + vector: + + ``grad(x, *args) -> array_like, shape (n,)`` + + where ``x`` is an array with shape (n,) and ``args`` is a tuple with + the fixed parameters. + Alternatively, the keywords {'2-point', '3-point', 'cs'} can be used + to select a finite difference scheme for numerical estimation of the + gradient with a relative step size. These finite difference schemes + obey any specified `bounds`. + hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy} + Method for computing the Hessian matrix. If it is callable, it should + return the Hessian matrix: + + ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)`` + + where x is a (n,) ndarray and `args` is a tuple with the fixed + parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'} + select a finite difference scheme for numerical estimation. Or, objects + implementing `HessianUpdateStrategy` interface can be used to + approximate the Hessian. + Whenever the gradient is estimated via finite-differences, the Hessian + cannot be estimated with options {'2-point', '3-point', 'cs'} and needs + to be estimated using one of the quasi-Newton strategies. + finite_diff_rel_step : None or array_like + Relative step size to use. The absolute step size is computed as + ``h = finite_diff_rel_step * sign(x0) * max(1, abs(x0))``, possibly + adjusted to fit into the bounds. For ``method='3-point'`` the sign + of `h` is ignored. If None then finite_diff_rel_step is selected + automatically, + finite_diff_bounds : tuple of array_like + Lower and upper bounds on independent variables. Defaults to no bounds, + (-np.inf, np.inf). Each bound must match the size of `x0` or be a + scalar, in the latter case the bound will be the same for all + variables. Use it to limit the range of function evaluation. + epsilon : None or array_like, optional + Absolute step size to use, possibly adjusted to fit into the bounds. + For ``method='3-point'`` the sign of `epsilon` is ignored. By default + relative steps are used, only if ``epsilon is not None`` are absolute + steps used. + + Notes + ----- + This class implements a memoization logic. There are methods `fun`, + `grad`, hess` and corresponding attributes `f`, `g` and `H`. The following + things should be considered: + + 1. Use only public methods `fun`, `grad` and `hess`. + 2. After one of the methods is called, the corresponding attribute + will be set. However, a subsequent call with a different argument + of *any* of the methods may overwrite the attribute. + """ + def __init__(self, fun, x0, args, grad, hess, finite_diff_rel_step, + finite_diff_bounds, epsilon=None): + if not callable(grad) and grad not in FD_METHODS: + raise ValueError( + f"`grad` must be either callable or one of {FD_METHODS}." + ) + + if not (callable(hess) or hess in FD_METHODS + or isinstance(hess, HessianUpdateStrategy)): + raise ValueError( + f"`hess` must be either callable, HessianUpdateStrategy" + f" or one of {FD_METHODS}." + ) + + if grad in FD_METHODS and hess in FD_METHODS: + raise ValueError("Whenever the gradient is estimated via " + "finite-differences, we require the Hessian " + "to be estimated using one of the " + "quasi-Newton strategies.") + + self.xp = xp = array_namespace(x0) + _x = atleast_nd(x0, ndim=1, xp=xp) + _dtype = xp.float64 + if xp.isdtype(_x.dtype, "real floating"): + _dtype = _x.dtype + + # original arguments + self._wrapped_fun, self._nfev = _wrapper_fun(fun, args=args) + self._orig_fun = fun + self._orig_grad = grad + self._orig_hess = hess + self._args = args + + # promotes to floating + self.x = xp.astype(_x, _dtype) + self.x_dtype = _dtype + self.n = self.x.size + self.f_updated = False + self.g_updated = False + self.H_updated = False + + self._lowest_x = None + self._lowest_f = np.inf + + finite_diff_options = {} + if grad in FD_METHODS: + finite_diff_options["method"] = grad + finite_diff_options["rel_step"] = finite_diff_rel_step + finite_diff_options["abs_step"] = epsilon + finite_diff_options["bounds"] = finite_diff_bounds + if hess in FD_METHODS: + finite_diff_options["method"] = hess + finite_diff_options["rel_step"] = finite_diff_rel_step + finite_diff_options["abs_step"] = epsilon + finite_diff_options["as_linear_operator"] = True + + # Initial function evaluation + self._update_fun() + + # Initial gradient evaluation + self._wrapped_grad, self._ngev = _wrapper_grad( + grad, + fun=self._wrapped_fun, + args=args, + finite_diff_options=finite_diff_options + ) + self._update_grad() + + # Hessian evaluation + if callable(hess): + self._wrapped_hess, self._nhev, self.H = _wrapper_hess( + hess, x0=x0, args=args + ) + self.H_updated = True + elif hess in FD_METHODS: + self._wrapped_hess, self._nhev, self.H = _wrapper_hess( + hess, + grad=self._wrapped_grad, + x0=x0, + finite_diff_options=finite_diff_options + ) + self._update_grad() + self.H = self._wrapped_hess(self.x, f0=self.g) + self.H_updated = True + elif isinstance(hess, HessianUpdateStrategy): + self.H = hess + self.H.initialize(self.n, 'hess') + self.H_updated = True + self.x_prev = None + self.g_prev = None + self._nhev = [0] + + @property + def nfev(self): + return self._nfev[0] + + @property + def ngev(self): + return self._ngev[0] + + @property + def nhev(self): + return self._nhev[0] + + def _update_x(self, x): + if isinstance(self._orig_hess, HessianUpdateStrategy): + self._update_grad() + self.x_prev = self.x + self.g_prev = self.g + # ensure that self.x is a copy of x. Don't store a reference + # otherwise the memoization doesn't work properly. + + _x = atleast_nd(x, ndim=1, xp=self.xp) + self.x = self.xp.astype(_x, self.x_dtype) + self.f_updated = False + self.g_updated = False + self.H_updated = False + self._update_hess() + else: + # ensure that self.x is a copy of x. Don't store a reference + # otherwise the memoization doesn't work properly. + _x = atleast_nd(x, ndim=1, xp=self.xp) + self.x = self.xp.astype(_x, self.x_dtype) + self.f_updated = False + self.g_updated = False + self.H_updated = False + + def _update_fun(self): + if not self.f_updated: + fx = self._wrapped_fun(self.x) + if fx < self._lowest_f: + self._lowest_x = self.x + self._lowest_f = fx + + self.f = fx + self.f_updated = True + + def _update_grad(self): + if not self.g_updated: + if self._orig_grad in FD_METHODS: + self._update_fun() + self.g = self._wrapped_grad(self.x, f0=self.f) + self.g_updated = True + + def _update_hess(self): + if not self.H_updated: + if self._orig_hess in FD_METHODS: + self._update_grad() + self.H = self._wrapped_hess(self.x, f0=self.g) + elif isinstance(self._orig_hess, HessianUpdateStrategy): + self._update_grad() + self.H.update(self.x - self.x_prev, self.g - self.g_prev) + else: # should be callable(hess) + self.H = self._wrapped_hess(self.x) + + self.H_updated = True + + def fun(self, x): + if not np.array_equal(x, self.x): + self._update_x(x) + self._update_fun() + return self.f + + def grad(self, x): + if not np.array_equal(x, self.x): + self._update_x(x) + self._update_grad() + return self.g + + def hess(self, x): + if not np.array_equal(x, self.x): + self._update_x(x) + self._update_hess() + return self.H + + def fun_and_grad(self, x): + if not np.array_equal(x, self.x): + self._update_x(x) + self._update_fun() + self._update_grad() + return self.f, self.g + + +class VectorFunction: + """Vector function and its derivatives. + + This class defines a vector function F: R^n->R^m and methods for + computing or approximating its first and second derivatives. + + Notes + ----- + This class implements a memoization logic. There are methods `fun`, + `jac`, hess` and corresponding attributes `f`, `J` and `H`. The following + things should be considered: + + 1. Use only public methods `fun`, `jac` and `hess`. + 2. After one of the methods is called, the corresponding attribute + will be set. However, a subsequent call with a different argument + of *any* of the methods may overwrite the attribute. + """ + def __init__(self, fun, x0, jac, hess, + finite_diff_rel_step, finite_diff_jac_sparsity, + finite_diff_bounds, sparse_jacobian): + if not callable(jac) and jac not in FD_METHODS: + raise ValueError(f"`jac` must be either callable or one of {FD_METHODS}.") + + if not (callable(hess) or hess in FD_METHODS + or isinstance(hess, HessianUpdateStrategy)): + raise ValueError("`hess` must be either callable," + f"HessianUpdateStrategy or one of {FD_METHODS}.") + + if jac in FD_METHODS and hess in FD_METHODS: + raise ValueError("Whenever the Jacobian is estimated via " + "finite-differences, we require the Hessian to " + "be estimated using one of the quasi-Newton " + "strategies.") + + self.xp = xp = array_namespace(x0) + _x = atleast_nd(x0, ndim=1, xp=xp) + _dtype = xp.float64 + if xp.isdtype(_x.dtype, "real floating"): + _dtype = _x.dtype + + # promotes to floating + self.x = xp.astype(_x, _dtype) + self.x_dtype = _dtype + + self.n = self.x.size + self.nfev = 0 + self.njev = 0 + self.nhev = 0 + self.f_updated = False + self.J_updated = False + self.H_updated = False + + finite_diff_options = {} + if jac in FD_METHODS: + finite_diff_options["method"] = jac + finite_diff_options["rel_step"] = finite_diff_rel_step + if finite_diff_jac_sparsity is not None: + sparsity_groups = group_columns(finite_diff_jac_sparsity) + finite_diff_options["sparsity"] = (finite_diff_jac_sparsity, + sparsity_groups) + finite_diff_options["bounds"] = finite_diff_bounds + self.x_diff = np.copy(self.x) + if hess in FD_METHODS: + finite_diff_options["method"] = hess + finite_diff_options["rel_step"] = finite_diff_rel_step + finite_diff_options["as_linear_operator"] = True + self.x_diff = np.copy(self.x) + if jac in FD_METHODS and hess in FD_METHODS: + raise ValueError("Whenever the Jacobian is estimated via " + "finite-differences, we require the Hessian to " + "be estimated using one of the quasi-Newton " + "strategies.") + + # Function evaluation + def fun_wrapped(x): + self.nfev += 1 + return np.atleast_1d(fun(x)) + + def update_fun(): + self.f = fun_wrapped(self.x) + + self._update_fun_impl = update_fun + update_fun() + + self.v = np.zeros_like(self.f) + self.m = self.v.size + + # Jacobian Evaluation + if callable(jac): + self.J = jac(self.x) + self.J_updated = True + self.njev += 1 + + if (sparse_jacobian or + sparse_jacobian is None and sps.issparse(self.J)): + def jac_wrapped(x): + self.njev += 1 + return sps.csr_matrix(jac(x)) + self.J = sps.csr_matrix(self.J) + self.sparse_jacobian = True + + elif sps.issparse(self.J): + def jac_wrapped(x): + self.njev += 1 + return jac(x).toarray() + self.J = self.J.toarray() + self.sparse_jacobian = False + + else: + def jac_wrapped(x): + self.njev += 1 + return np.atleast_2d(jac(x)) + self.J = np.atleast_2d(self.J) + self.sparse_jacobian = False + + def update_jac(): + self.J = jac_wrapped(self.x) + + elif jac in FD_METHODS: + self.J = approx_derivative(fun_wrapped, self.x, f0=self.f, + **finite_diff_options) + self.J_updated = True + + if (sparse_jacobian or + sparse_jacobian is None and sps.issparse(self.J)): + def update_jac(): + self._update_fun() + self.J = sps.csr_matrix( + approx_derivative(fun_wrapped, self.x, f0=self.f, + **finite_diff_options)) + self.J = sps.csr_matrix(self.J) + self.sparse_jacobian = True + + elif sps.issparse(self.J): + def update_jac(): + self._update_fun() + self.J = approx_derivative(fun_wrapped, self.x, f0=self.f, + **finite_diff_options).toarray() + self.J = self.J.toarray() + self.sparse_jacobian = False + + else: + def update_jac(): + self._update_fun() + self.J = np.atleast_2d( + approx_derivative(fun_wrapped, self.x, f0=self.f, + **finite_diff_options)) + self.J = np.atleast_2d(self.J) + self.sparse_jacobian = False + + self._update_jac_impl = update_jac + + # Define Hessian + if callable(hess): + self.H = hess(self.x, self.v) + self.H_updated = True + self.nhev += 1 + + if sps.issparse(self.H): + def hess_wrapped(x, v): + self.nhev += 1 + return sps.csr_matrix(hess(x, v)) + self.H = sps.csr_matrix(self.H) + + elif isinstance(self.H, LinearOperator): + def hess_wrapped(x, v): + self.nhev += 1 + return hess(x, v) + + else: + def hess_wrapped(x, v): + self.nhev += 1 + return np.atleast_2d(np.asarray(hess(x, v))) + self.H = np.atleast_2d(np.asarray(self.H)) + + def update_hess(): + self.H = hess_wrapped(self.x, self.v) + elif hess in FD_METHODS: + def jac_dot_v(x, v): + return jac_wrapped(x).T.dot(v) + + def update_hess(): + self._update_jac() + self.H = approx_derivative(jac_dot_v, self.x, + f0=self.J.T.dot(self.v), + args=(self.v,), + **finite_diff_options) + update_hess() + self.H_updated = True + elif isinstance(hess, HessianUpdateStrategy): + self.H = hess + self.H.initialize(self.n, 'hess') + self.H_updated = True + self.x_prev = None + self.J_prev = None + + def update_hess(): + self._update_jac() + # When v is updated before x was updated, then x_prev and + # J_prev are None and we need this check. + if self.x_prev is not None and self.J_prev is not None: + delta_x = self.x - self.x_prev + delta_g = self.J.T.dot(self.v) - self.J_prev.T.dot(self.v) + self.H.update(delta_x, delta_g) + + self._update_hess_impl = update_hess + + if isinstance(hess, HessianUpdateStrategy): + def update_x(x): + self._update_jac() + self.x_prev = self.x + self.J_prev = self.J + _x = atleast_nd(x, ndim=1, xp=self.xp) + self.x = self.xp.astype(_x, self.x_dtype) + self.f_updated = False + self.J_updated = False + self.H_updated = False + self._update_hess() + else: + def update_x(x): + _x = atleast_nd(x, ndim=1, xp=self.xp) + self.x = self.xp.astype(_x, self.x_dtype) + self.f_updated = False + self.J_updated = False + self.H_updated = False + + self._update_x_impl = update_x + + def _update_v(self, v): + if not np.array_equal(v, self.v): + self.v = v + self.H_updated = False + + def _update_x(self, x): + if not np.array_equal(x, self.x): + self._update_x_impl(x) + + def _update_fun(self): + if not self.f_updated: + self._update_fun_impl() + self.f_updated = True + + def _update_jac(self): + if not self.J_updated: + self._update_jac_impl() + self.J_updated = True + + def _update_hess(self): + if not self.H_updated: + self._update_hess_impl() + self.H_updated = True + + def fun(self, x): + self._update_x(x) + self._update_fun() + return self.f + + def jac(self, x): + self._update_x(x) + self._update_jac() + return self.J + + def hess(self, x, v): + # v should be updated before x. + self._update_v(v) + self._update_x(x) + self._update_hess() + return self.H + + +class LinearVectorFunction: + """Linear vector function and its derivatives. + + Defines a linear function F = A x, where x is N-D vector and + A is m-by-n matrix. The Jacobian is constant and equals to A. The Hessian + is identically zero and it is returned as a csr matrix. + """ + def __init__(self, A, x0, sparse_jacobian): + if sparse_jacobian or sparse_jacobian is None and sps.issparse(A): + self.J = sps.csr_matrix(A) + self.sparse_jacobian = True + elif sps.issparse(A): + self.J = A.toarray() + self.sparse_jacobian = False + else: + # np.asarray makes sure A is ndarray and not matrix + self.J = np.atleast_2d(np.asarray(A)) + self.sparse_jacobian = False + + self.m, self.n = self.J.shape + + self.xp = xp = array_namespace(x0) + _x = atleast_nd(x0, ndim=1, xp=xp) + _dtype = xp.float64 + if xp.isdtype(_x.dtype, "real floating"): + _dtype = _x.dtype + + # promotes to floating + self.x = xp.astype(_x, _dtype) + self.x_dtype = _dtype + + self.f = self.J.dot(self.x) + self.f_updated = True + + self.v = np.zeros(self.m, dtype=float) + self.H = sps.csr_matrix((self.n, self.n)) + + def _update_x(self, x): + if not np.array_equal(x, self.x): + _x = atleast_nd(x, ndim=1, xp=self.xp) + self.x = self.xp.astype(_x, self.x_dtype) + self.f_updated = False + + def fun(self, x): + self._update_x(x) + if not self.f_updated: + self.f = self.J.dot(x) + self.f_updated = True + return self.f + + def jac(self, x): + self._update_x(x) + return self.J + + def hess(self, x, v): + self._update_x(x) + self.v = v + return self.H + + +class IdentityVectorFunction(LinearVectorFunction): + """Identity vector function and its derivatives. + + The Jacobian is the identity matrix, returned as a dense array when + `sparse_jacobian=False` and as a csr matrix otherwise. The Hessian is + identically zero and it is returned as a csr matrix. + """ + def __init__(self, x0, sparse_jacobian): + n = len(x0) + if sparse_jacobian or sparse_jacobian is None: + A = sps.eye(n, format='csr') + sparse_jacobian = True + else: + A = np.eye(n) + sparse_jacobian = False + super().__init__(A, x0, sparse_jacobian) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentialevolution.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentialevolution.py new file mode 100644 index 0000000000000000000000000000000000000000..815d27afd072cd7a114dbc8bb9447ffbc09285f4 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentialevolution.py @@ -0,0 +1,1951 @@ +""" +differential_evolution: The differential evolution global optimization algorithm +Added by Andrew Nelson 2014 +""" +import warnings + +import numpy as np +from scipy.optimize import OptimizeResult, minimize +from scipy.optimize._optimize import _status_message, _wrap_callback +from scipy._lib._util import (check_random_state, MapWrapper, _FunctionWrapper, + rng_integers) + +from scipy.optimize._constraints import (Bounds, new_bounds_to_old, + NonlinearConstraint, LinearConstraint) +from scipy.sparse import issparse + +__all__ = ['differential_evolution'] + + +_MACHEPS = np.finfo(np.float64).eps + + +def differential_evolution(func, bounds, args=(), strategy='best1bin', + maxiter=1000, popsize=15, tol=0.01, + mutation=(0.5, 1), recombination=0.7, seed=None, + callback=None, disp=False, polish=True, + init='latinhypercube', atol=0, updating='immediate', + workers=1, constraints=(), x0=None, *, + integrality=None, vectorized=False): + """Finds the global minimum of a multivariate function. + + The differential evolution method [1]_ is stochastic in nature. It does + not use gradient methods to find the minimum, and can search large areas + of candidate space, but often requires larger numbers of function + evaluations than conventional gradient-based techniques. + + The algorithm is due to Storn and Price [2]_. + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. The number of parameters, N, is equal + to ``len(x)``. + bounds : sequence or `Bounds` + Bounds for variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. ``(min, max)`` pairs for each element in ``x``, defining the + finite lower and upper bounds for the optimizing argument of + `func`. + + The total number of bounds is used to determine the number of + parameters, N. If there are parameters whose bounds are equal the total + number of free parameters is ``N - N_equal``. + + args : tuple, optional + Any additional fixed parameters needed to + completely specify the objective function. + strategy : {str, callable}, optional + The differential evolution strategy to use. Should be one of: + + - 'best1bin' + - 'best1exp' + - 'rand1bin' + - 'rand1exp' + - 'rand2bin' + - 'rand2exp' + - 'randtobest1bin' + - 'randtobest1exp' + - 'currenttobest1bin' + - 'currenttobest1exp' + - 'best2exp' + - 'best2bin' + + The default is 'best1bin'. Strategies that may be implemented are + outlined in 'Notes'. + Alternatively the differential evolution strategy can be customized by + providing a callable that constructs a trial vector. The callable must + have the form ``strategy(candidate: int, population: np.ndarray, rng=None)``, + where ``candidate`` is an integer specifying which entry of the + population is being evolved, ``population`` is an array of shape + ``(S, N)`` containing all the population members (where S is the + total population size), and ``rng`` is the random number generator + being used within the solver. + ``candidate`` will be in the range ``[0, S)``. + ``strategy`` must return a trial vector with shape `(N,)`. The + fitness of this trial vector is compared against the fitness of + ``population[candidate]``. + + .. versionchanged:: 1.12.0 + Customization of evolution strategy via a callable. + + maxiter : int, optional + The maximum number of generations over which the entire population is + evolved. The maximum number of function evaluations (with no polishing) + is: ``(maxiter + 1) * popsize * (N - N_equal)`` + popsize : int, optional + A multiplier for setting the total population size. The population has + ``popsize * (N - N_equal)`` individuals. This keyword is overridden if + an initial population is supplied via the `init` keyword. When using + ``init='sobol'`` the population size is calculated as the next power + of 2 after ``popsize * (N - N_equal)``. + tol : float, optional + Relative tolerance for convergence, the solving stops when + ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, + where and `atol` and `tol` are the absolute and relative tolerance + respectively. + mutation : float or tuple(float, float), optional + The mutation constant. In the literature this is also known as + differential weight, being denoted by F. + If specified as a float it should be in the range [0, 2]. + If specified as a tuple ``(min, max)`` dithering is employed. Dithering + randomly changes the mutation constant on a generation by generation + basis. The mutation constant for that generation is taken from + ``U[min, max)``. Dithering can help speed convergence significantly. + Increasing the mutation constant increases the search radius, but will + slow down convergence. + recombination : float, optional + The recombination constant, should be in the range [0, 1]. In the + literature this is also known as the crossover probability, being + denoted by CR. Increasing this value allows a larger number of mutants + to progress into the next generation, but at the risk of population + stability. + seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Specify `seed` for repeatable minimizations. + disp : bool, optional + Prints the evaluated `func` at every iteration. + callback : callable, optional + A callable called after each iteration. Has the signature: + + ``callback(intermediate_result: OptimizeResult)`` + + where ``intermediate_result`` is a keyword parameter containing an + `OptimizeResult` with attributes ``x`` and ``fun``, the best solution + found so far and the objective function. Note that the name + of the parameter must be ``intermediate_result`` for the callback + to be passed an `OptimizeResult`. + + The callback also supports a signature like: + + ``callback(x, convergence: float=val)`` + + ``val`` represents the fractional value of the population convergence. + When ``val`` is greater than ``1.0``, the function halts. + + Introspection is used to determine which of the signatures is invoked. + + Global minimization will halt if the callback raises ``StopIteration`` + or returns ``True``; any polishing is still carried out. + + .. versionchanged:: 1.12.0 + callback accepts the ``intermediate_result`` keyword. + + polish : bool, optional + If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B` + method is used to polish the best population member at the end, which + can improve the minimization slightly. If a constrained problem is + being studied then the `trust-constr` method is used instead. For large + problems with many constraints, polishing can take a long time due to + the Jacobian computations. + init : str or array-like, optional + Specify which type of population initialization is performed. Should be + one of: + + - 'latinhypercube' + - 'sobol' + - 'halton' + - 'random' + - array specifying the initial population. The array should have + shape ``(S, N)``, where S is the total population size and N is + the number of parameters. + `init` is clipped to `bounds` before use. + + The default is 'latinhypercube'. Latin Hypercube sampling tries to + maximize coverage of the available parameter space. + + 'sobol' and 'halton' are superior alternatives and maximize even more + the parameter space. 'sobol' will enforce an initial population + size which is calculated as the next power of 2 after + ``popsize * (N - N_equal)``. 'halton' has no requirements but is a bit + less efficient. See `scipy.stats.qmc` for more details. + + 'random' initializes the population randomly - this has the drawback + that clustering can occur, preventing the whole of parameter space + being covered. Use of an array to specify a population could be used, + for example, to create a tight bunch of initial guesses in an location + where the solution is known to exist, thereby reducing time for + convergence. + atol : float, optional + Absolute tolerance for convergence, the solving stops when + ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, + where and `atol` and `tol` are the absolute and relative tolerance + respectively. + updating : {'immediate', 'deferred'}, optional + If ``'immediate'``, the best solution vector is continuously updated + within a single generation [4]_. This can lead to faster convergence as + trial vectors can take advantage of continuous improvements in the best + solution. + With ``'deferred'``, the best solution vector is updated once per + generation. Only ``'deferred'`` is compatible with parallelization or + vectorization, and the `workers` and `vectorized` keywords can + over-ride this option. + + .. versionadded:: 1.2.0 + + workers : int or map-like callable, optional + If `workers` is an int the population is subdivided into `workers` + sections and evaluated in parallel + (uses `multiprocessing.Pool `). + Supply -1 to use all available CPU cores. + Alternatively supply a map-like callable, such as + `multiprocessing.Pool.map` for evaluating the population in parallel. + This evaluation is carried out as ``workers(func, iterable)``. + This option will override the `updating` keyword to + ``updating='deferred'`` if ``workers != 1``. + This option overrides the `vectorized` keyword if ``workers != 1``. + Requires that `func` be pickleable. + + .. versionadded:: 1.2.0 + + constraints : {NonLinearConstraint, LinearConstraint, Bounds} + Constraints on the solver, over and above those applied by the `bounds` + kwd. Uses the approach by Lampinen [5]_. + + .. versionadded:: 1.4.0 + + x0 : None or array-like, optional + Provides an initial guess to the minimization. Once the population has + been initialized this vector replaces the first (best) member. This + replacement is done even if `init` is given an initial population. + ``x0.shape == (N,)``. + + .. versionadded:: 1.7.0 + + integrality : 1-D array, optional + For each decision variable, a boolean value indicating whether the + decision variable is constrained to integer values. The array is + broadcast to ``(N,)``. + If any decision variables are constrained to be integral, they will not + be changed during polishing. + Only integer values lying between the lower and upper bounds are used. + If there are no integer values lying between the bounds then a + `ValueError` is raised. + + .. versionadded:: 1.9.0 + + vectorized : bool, optional + If ``vectorized is True``, `func` is sent an `x` array with + ``x.shape == (N, S)``, and is expected to return an array of shape + ``(S,)``, where `S` is the number of solution vectors to be calculated. + If constraints are applied, each of the functions used to construct + a `Constraint` object should accept an `x` array with + ``x.shape == (N, S)``, and return an array of shape ``(M, S)``, where + `M` is the number of constraint components. + This option is an alternative to the parallelization offered by + `workers`, and may help in optimization speed by reducing interpreter + overhead from multiple function calls. This keyword is ignored if + ``workers != 1``. + This option will override the `updating` keyword to + ``updating='deferred'``. + See the notes section for further discussion on when to use + ``'vectorized'``, and when to use ``'workers'``. + + .. versionadded:: 1.9.0 + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully, + ``message`` which describes the cause of the termination, + ``population`` the solution vectors present in the population, and + ``population_energies`` the value of the objective function for each + entry in ``population``. + See `OptimizeResult` for a description of other attributes. If `polish` + was employed, and a lower minimum was obtained by the polishing, then + OptimizeResult also contains the ``jac`` attribute. + If the eventual solution does not satisfy the applied constraints + ``success`` will be `False`. + + Notes + ----- + Differential evolution is a stochastic population based method that is + useful for global optimization problems. At each pass through the + population the algorithm mutates each candidate solution by mixing with + other candidate solutions to create a trial candidate. There are several + strategies [3]_ for creating trial candidates, which suit some problems + more than others. The 'best1bin' strategy is a good starting point for + many systems. In this strategy two members of the population are randomly + chosen. Their difference is used to mutate the best member (the 'best' in + 'best1bin'), :math:`x_0`, so far: + + .. math:: + + b' = x_0 + mutation * (x_{r_0} - x_{r_1}) + + A trial vector is then constructed. Starting with a randomly chosen ith + parameter the trial is sequentially filled (in modulo) with parameters + from ``b'`` or the original candidate. The choice of whether to use ``b'`` + or the original candidate is made with a binomial distribution (the 'bin' + in 'best1bin') - a random number in [0, 1) is generated. If this number is + less than the `recombination` constant then the parameter is loaded from + ``b'``, otherwise it is loaded from the original candidate. The final + parameter is always loaded from ``b'``. Once the trial candidate is built + its fitness is assessed. If the trial is better than the original candidate + then it takes its place. If it is also better than the best overall + candidate it also replaces that. + + The other strategies available are outlined in Qiang and + Mitchell (2014) [3]_. + + .. math:: + rand1* : b' = x_{r_0} + mutation*(x_{r_1} - x_{r_2}) + + rand2* : b' = x_{r_0} + mutation*(x_{r_1} + x_{r_2} + - x_{r_3} - x_{r_4}) + + best1* : b' = x_0 + mutation*(x_{r_0} - x_{r_1}) + + best2* : b' = x_0 + mutation*(x_{r_0} + x_{r_1} + - x_{r_2} - x_{r_3}) + + currenttobest1* : b' = x_i + mutation*(x_0 - x_i + + x_{r_0} - x_{r_1}) + + randtobest1* : b' = x_{r_0} + mutation*(x_0 - x_{r_0} + + x_{r_1} - x_{r_2}) + + where the integers :math:`r_0, r_1, r_2, r_3, r_4` are chosen randomly + from the interval [0, NP) with `NP` being the total population size and + the original candidate having index `i`. The user can fully customize the + generation of the trial candidates by supplying a callable to ``strategy``. + + To improve your chances of finding a global minimum use higher `popsize` + values, with higher `mutation` and (dithering), but lower `recombination` + values. This has the effect of widening the search radius, but slowing + convergence. + + By default the best solution vector is updated continuously within a single + iteration (``updating='immediate'``). This is a modification [4]_ of the + original differential evolution algorithm which can lead to faster + convergence as trial vectors can immediately benefit from improved + solutions. To use the original Storn and Price behaviour, updating the best + solution once per iteration, set ``updating='deferred'``. + The ``'deferred'`` approach is compatible with both parallelization and + vectorization (``'workers'`` and ``'vectorized'`` keywords). These may + improve minimization speed by using computer resources more efficiently. + The ``'workers'`` distribute calculations over multiple processors. By + default the Python `multiprocessing` module is used, but other approaches + are also possible, such as the Message Passing Interface (MPI) used on + clusters [6]_ [7]_. The overhead from these approaches (creating new + Processes, etc) may be significant, meaning that computational speed + doesn't necessarily scale with the number of processors used. + Parallelization is best suited to computationally expensive objective + functions. If the objective function is less expensive, then + ``'vectorized'`` may aid by only calling the objective function once per + iteration, rather than multiple times for all the population members; the + interpreter overhead is reduced. + + .. versionadded:: 0.15.0 + + References + ---------- + .. [1] Differential evolution, Wikipedia, + http://en.wikipedia.org/wiki/Differential_evolution + .. [2] Storn, R and Price, K, Differential Evolution - a Simple and + Efficient Heuristic for Global Optimization over Continuous Spaces, + Journal of Global Optimization, 1997, 11, 341 - 359. + .. [3] Qiang, J., Mitchell, C., A Unified Differential Evolution Algorithm + for Global Optimization, 2014, https://www.osti.gov/servlets/purl/1163659 + .. [4] Wormington, M., Panaccione, C., Matney, K. M., Bowen, D. K., - + Characterization of structures from X-ray scattering data using + genetic algorithms, Phil. Trans. R. Soc. Lond. A, 1999, 357, + 2827-2848 + .. [5] Lampinen, J., A constraint handling approach for the differential + evolution algorithm. Proceedings of the 2002 Congress on + Evolutionary Computation. CEC'02 (Cat. No. 02TH8600). Vol. 2. IEEE, + 2002. + .. [6] https://mpi4py.readthedocs.io/en/stable/ + .. [7] https://schwimmbad.readthedocs.io/en/latest/ + + + Examples + -------- + Let us consider the problem of minimizing the Rosenbrock function. This + function is implemented in `rosen` in `scipy.optimize`. + + >>> import numpy as np + >>> from scipy.optimize import rosen, differential_evolution + >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] + >>> result = differential_evolution(rosen, bounds) + >>> result.x, result.fun + (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19) + + Now repeat, but with parallelization. + + >>> result = differential_evolution(rosen, bounds, updating='deferred', + ... workers=2) + >>> result.x, result.fun + (array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19) + + Let's do a constrained minimization. + + >>> from scipy.optimize import LinearConstraint, Bounds + + We add the constraint that the sum of ``x[0]`` and ``x[1]`` must be less + than or equal to 1.9. This is a linear constraint, which may be written + ``A @ x <= 1.9``, where ``A = array([[1, 1]])``. This can be encoded as + a `LinearConstraint` instance: + + >>> lc = LinearConstraint([[1, 1]], -np.inf, 1.9) + + Specify limits using a `Bounds` object. + + >>> bounds = Bounds([0., 0.], [2., 2.]) + >>> result = differential_evolution(rosen, bounds, constraints=lc, + ... seed=1) + >>> result.x, result.fun + (array([0.96632622, 0.93367155]), 0.0011352416852625719) + + Next find the minimum of the Ackley function + (https://en.wikipedia.org/wiki/Test_functions_for_optimization). + + >>> def ackley(x): + ... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2)) + ... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1])) + ... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e + >>> bounds = [(-5, 5), (-5, 5)] + >>> result = differential_evolution(ackley, bounds, seed=1) + >>> result.x, result.fun + (array([0., 0.]), 4.440892098500626e-16) + + The Ackley function is written in a vectorized manner, so the + ``'vectorized'`` keyword can be employed. Note the reduced number of + function evaluations. + + >>> result = differential_evolution( + ... ackley, bounds, vectorized=True, updating='deferred', seed=1 + ... ) + >>> result.x, result.fun + (array([0., 0.]), 4.440892098500626e-16) + + The following custom strategy function mimics 'best1bin': + + >>> def custom_strategy_fn(candidate, population, rng=None): + ... parameter_count = population.shape(-1) + ... mutation, recombination = 0.7, 0.9 + ... trial = np.copy(population[candidate]) + ... fill_point = rng.choice(parameter_count) + ... + ... pool = np.arange(len(population)) + ... rng.shuffle(pool) + ... + ... # two unique random numbers that aren't the same, and + ... # aren't equal to candidate. + ... idxs = [] + ... while len(idxs) < 2 and len(pool) > 0: + ... idx = pool[0] + ... pool = pool[1:] + ... if idx != candidate: + ... idxs.append(idx) + ... + ... r0, r1 = idxs[:2] + ... + ... bprime = (population[0] + mutation * + ... (population[r0] - population[r1])) + ... + ... crossovers = rng.uniform(size=parameter_count) + ... crossovers = crossovers < recombination + ... crossovers[fill_point] = True + ... trial = np.where(crossovers, bprime, trial) + ... return trial + + """ + + # using a context manager means that any created Pool objects are + # cleared up. + with DifferentialEvolutionSolver(func, bounds, args=args, + strategy=strategy, + maxiter=maxiter, + popsize=popsize, tol=tol, + mutation=mutation, + recombination=recombination, + seed=seed, polish=polish, + callback=callback, + disp=disp, init=init, atol=atol, + updating=updating, + workers=workers, + constraints=constraints, + x0=x0, + integrality=integrality, + vectorized=vectorized) as solver: + ret = solver.solve() + + return ret + + +class DifferentialEvolutionSolver: + + """This class implements the differential evolution solver + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. The number of parameters, N, is equal + to ``len(x)``. + bounds : sequence or `Bounds` + Bounds for variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. ``(min, max)`` pairs for each element in ``x``, defining the + finite lower and upper bounds for the optimizing argument of + `func`. + + The total number of bounds is used to determine the number of + parameters, N. If there are parameters whose bounds are equal the total + number of free parameters is ``N - N_equal``. + args : tuple, optional + Any additional fixed parameters needed to + completely specify the objective function. + strategy : {str, callable}, optional + The differential evolution strategy to use. Should be one of: + + - 'best1bin' + - 'best1exp' + - 'rand1bin' + - 'rand1exp' + - 'rand2bin' + - 'rand2exp' + - 'randtobest1bin' + - 'randtobest1exp' + - 'currenttobest1bin' + - 'currenttobest1exp' + - 'best2exp' + - 'best2bin' + + The default is 'best1bin'. Strategies that may be + implemented are outlined in 'Notes'. + + Alternatively the differential evolution strategy can be customized + by providing a callable that constructs a trial vector. The callable + must have the form + ``strategy(candidate: int, population: np.ndarray, rng=None)``, + where ``candidate`` is an integer specifying which entry of the + population is being evolved, ``population`` is an array of shape + ``(S, N)`` containing all the population members (where S is the + total population size), and ``rng`` is the random number generator + being used within the solver. + ``candidate`` will be in the range ``[0, S)``. + ``strategy`` must return a trial vector with shape `(N,)`. The + fitness of this trial vector is compared against the fitness of + ``population[candidate]``. + maxiter : int, optional + The maximum number of generations over which the entire population is + evolved. The maximum number of function evaluations (with no polishing) + is: ``(maxiter + 1) * popsize * (N - N_equal)`` + popsize : int, optional + A multiplier for setting the total population size. The population has + ``popsize * (N - N_equal)`` individuals. This keyword is overridden if + an initial population is supplied via the `init` keyword. When using + ``init='sobol'`` the population size is calculated as the next power + of 2 after ``popsize * (N - N_equal)``. + tol : float, optional + Relative tolerance for convergence, the solving stops when + ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, + where and `atol` and `tol` are the absolute and relative tolerance + respectively. + mutation : float or tuple(float, float), optional + The mutation constant. In the literature this is also known as + differential weight, being denoted by F. + If specified as a float it should be in the range [0, 2]. + If specified as a tuple ``(min, max)`` dithering is employed. Dithering + randomly changes the mutation constant on a generation by generation + basis. The mutation constant for that generation is taken from + U[min, max). Dithering can help speed convergence significantly. + Increasing the mutation constant increases the search radius, but will + slow down convergence. + recombination : float, optional + The recombination constant, should be in the range [0, 1]. In the + literature this is also known as the crossover probability, being + denoted by CR. Increasing this value allows a larger number of mutants + to progress into the next generation, but at the risk of population + stability. + seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Specify `seed` for repeatable minimizations. + disp : bool, optional + Prints the evaluated `func` at every iteration. + callback : callable, optional + A callable called after each iteration. Has the signature: + + ``callback(intermediate_result: OptimizeResult)`` + + where ``intermediate_result`` is a keyword parameter containing an + `OptimizeResult` with attributes ``x`` and ``fun``, the best solution + found so far and the objective function. Note that the name + of the parameter must be ``intermediate_result`` for the callback + to be passed an `OptimizeResult`. + + The callback also supports a signature like: + + ``callback(x, convergence: float=val)`` + + ``val`` represents the fractional value of the population convergence. + When ``val`` is greater than ``1.0``, the function halts. + + Introspection is used to determine which of the signatures is invoked. + + Global minimization will halt if the callback raises ``StopIteration`` + or returns ``True``; any polishing is still carried out. + + .. versionchanged:: 1.12.0 + callback accepts the ``intermediate_result`` keyword. + + polish : bool, optional + If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B` + method is used to polish the best population member at the end, which + can improve the minimization slightly. If a constrained problem is + being studied then the `trust-constr` method is used instead. For large + problems with many constraints, polishing can take a long time due to + the Jacobian computations. + maxfun : int, optional + Set the maximum number of function evaluations. However, it probably + makes more sense to set `maxiter` instead. + init : str or array-like, optional + Specify which type of population initialization is performed. Should be + one of: + + - 'latinhypercube' + - 'sobol' + - 'halton' + - 'random' + - array specifying the initial population. The array should have + shape ``(S, N)``, where S is the total population size and + N is the number of parameters. + `init` is clipped to `bounds` before use. + + The default is 'latinhypercube'. Latin Hypercube sampling tries to + maximize coverage of the available parameter space. + + 'sobol' and 'halton' are superior alternatives and maximize even more + the parameter space. 'sobol' will enforce an initial population + size which is calculated as the next power of 2 after + ``popsize * (N - N_equal)``. 'halton' has no requirements but is a bit + less efficient. See `scipy.stats.qmc` for more details. + + 'random' initializes the population randomly - this has the drawback + that clustering can occur, preventing the whole of parameter space + being covered. Use of an array to specify a population could be used, + for example, to create a tight bunch of initial guesses in an location + where the solution is known to exist, thereby reducing time for + convergence. + atol : float, optional + Absolute tolerance for convergence, the solving stops when + ``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``, + where and `atol` and `tol` are the absolute and relative tolerance + respectively. + updating : {'immediate', 'deferred'}, optional + If ``'immediate'``, the best solution vector is continuously updated + within a single generation [4]_. This can lead to faster convergence as + trial vectors can take advantage of continuous improvements in the best + solution. + With ``'deferred'``, the best solution vector is updated once per + generation. Only ``'deferred'`` is compatible with parallelization or + vectorization, and the `workers` and `vectorized` keywords can + over-ride this option. + workers : int or map-like callable, optional + If `workers` is an int the population is subdivided into `workers` + sections and evaluated in parallel + (uses `multiprocessing.Pool `). + Supply `-1` to use all cores available to the Process. + Alternatively supply a map-like callable, such as + `multiprocessing.Pool.map` for evaluating the population in parallel. + This evaluation is carried out as ``workers(func, iterable)``. + This option will override the `updating` keyword to + `updating='deferred'` if `workers != 1`. + Requires that `func` be pickleable. + constraints : {NonLinearConstraint, LinearConstraint, Bounds} + Constraints on the solver, over and above those applied by the `bounds` + kwd. Uses the approach by Lampinen. + x0 : None or array-like, optional + Provides an initial guess to the minimization. Once the population has + been initialized this vector replaces the first (best) member. This + replacement is done even if `init` is given an initial population. + ``x0.shape == (N,)``. + integrality : 1-D array, optional + For each decision variable, a boolean value indicating whether the + decision variable is constrained to integer values. The array is + broadcast to ``(N,)``. + If any decision variables are constrained to be integral, they will not + be changed during polishing. + Only integer values lying between the lower and upper bounds are used. + If there are no integer values lying between the bounds then a + `ValueError` is raised. + vectorized : bool, optional + If ``vectorized is True``, `func` is sent an `x` array with + ``x.shape == (N, S)``, and is expected to return an array of shape + ``(S,)``, where `S` is the number of solution vectors to be calculated. + If constraints are applied, each of the functions used to construct + a `Constraint` object should accept an `x` array with + ``x.shape == (N, S)``, and return an array of shape ``(M, S)``, where + `M` is the number of constraint components. + This option is an alternative to the parallelization offered by + `workers`, and may help in optimization speed. This keyword is + ignored if ``workers != 1``. + This option will override the `updating` keyword to + ``updating='deferred'``. + """ + + # Dispatch of mutation strategy method (binomial or exponential). + _binomial = {'best1bin': '_best1', + 'randtobest1bin': '_randtobest1', + 'currenttobest1bin': '_currenttobest1', + 'best2bin': '_best2', + 'rand2bin': '_rand2', + 'rand1bin': '_rand1'} + _exponential = {'best1exp': '_best1', + 'rand1exp': '_rand1', + 'randtobest1exp': '_randtobest1', + 'currenttobest1exp': '_currenttobest1', + 'best2exp': '_best2', + 'rand2exp': '_rand2'} + + __init_error_msg = ("The population initialization method must be one of " + "'latinhypercube' or 'random', or an array of shape " + "(S, N) where N is the number of parameters and S>5") + + def __init__(self, func, bounds, args=(), + strategy='best1bin', maxiter=1000, popsize=15, + tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None, + maxfun=np.inf, callback=None, disp=False, polish=True, + init='latinhypercube', atol=0, updating='immediate', + workers=1, constraints=(), x0=None, *, integrality=None, + vectorized=False): + + if callable(strategy): + # a callable strategy is going to be stored in self.strategy anyway + pass + elif strategy in self._binomial: + self.mutation_func = getattr(self, self._binomial[strategy]) + elif strategy in self._exponential: + self.mutation_func = getattr(self, self._exponential[strategy]) + else: + raise ValueError("Please select a valid mutation strategy") + self.strategy = strategy + + self.callback = _wrap_callback(callback, "differential_evolution") + self.polish = polish + + # set the updating / parallelisation options + if updating in ['immediate', 'deferred']: + self._updating = updating + + self.vectorized = vectorized + + # want to use parallelisation, but updating is immediate + if workers != 1 and updating == 'immediate': + warnings.warn("differential_evolution: the 'workers' keyword has" + " overridden updating='immediate' to" + " updating='deferred'", UserWarning, stacklevel=2) + self._updating = 'deferred' + + if vectorized and workers != 1: + warnings.warn("differential_evolution: the 'workers' keyword" + " overrides the 'vectorized' keyword", stacklevel=2) + self.vectorized = vectorized = False + + if vectorized and updating == 'immediate': + warnings.warn("differential_evolution: the 'vectorized' keyword" + " has overridden updating='immediate' to updating" + "='deferred'", UserWarning, stacklevel=2) + self._updating = 'deferred' + + # an object with a map method. + if vectorized: + def maplike_for_vectorized_func(func, x): + # send an array (N, S) to the user func, + # expect to receive (S,). Transposition is required because + # internally the population is held as (S, N) + return np.atleast_1d(func(x.T)) + workers = maplike_for_vectorized_func + + self._mapwrapper = MapWrapper(workers) + + # relative and absolute tolerances for convergence + self.tol, self.atol = tol, atol + + # Mutation constant should be in [0, 2). If specified as a sequence + # then dithering is performed. + self.scale = mutation + if (not np.all(np.isfinite(mutation)) or + np.any(np.array(mutation) >= 2) or + np.any(np.array(mutation) < 0)): + raise ValueError('The mutation constant must be a float in ' + 'U[0, 2), or specified as a tuple(min, max)' + ' where min < max and min, max are in U[0, 2).') + + self.dither = None + if hasattr(mutation, '__iter__') and len(mutation) > 1: + self.dither = [mutation[0], mutation[1]] + self.dither.sort() + + self.cross_over_probability = recombination + + # we create a wrapped function to allow the use of map (and Pool.map + # in the future) + self.func = _FunctionWrapper(func, args) + self.args = args + + # convert tuple of lower and upper bounds to limits + # [(low_0, high_0), ..., (low_n, high_n] + # -> [[low_0, ..., low_n], [high_0, ..., high_n]] + if isinstance(bounds, Bounds): + self.limits = np.array(new_bounds_to_old(bounds.lb, + bounds.ub, + len(bounds.lb)), + dtype=float).T + else: + self.limits = np.array(bounds, dtype='float').T + + if (np.size(self.limits, 0) != 2 or not + np.all(np.isfinite(self.limits))): + raise ValueError('bounds should be a sequence containing finite ' + 'real valued (min, max) pairs for each value' + ' in x') + + if maxiter is None: # the default used to be None + maxiter = 1000 + self.maxiter = maxiter + if maxfun is None: # the default used to be None + maxfun = np.inf + self.maxfun = maxfun + + # population is scaled to between [0, 1]. + # We have to scale between parameter <-> population + # save these arguments for _scale_parameter and + # _unscale_parameter. This is an optimization + self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1]) + self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1]) + with np.errstate(divide='ignore'): + # if lb == ub then the following line will be 1/0, which is why + # we ignore the divide by zero warning. The result from 1/0 is + # inf, so replace those values by 0. + self.__recip_scale_arg2 = 1 / self.__scale_arg2 + self.__recip_scale_arg2[~np.isfinite(self.__recip_scale_arg2)] = 0 + + self.parameter_count = np.size(self.limits, 1) + + self.random_number_generator = check_random_state(seed) + + # Which parameters are going to be integers? + if np.any(integrality): + # # user has provided a truth value for integer constraints + integrality = np.broadcast_to( + integrality, + self.parameter_count + ) + integrality = np.asarray(integrality, bool) + # For integrality parameters change the limits to only allow + # integer values lying between the limits. + lb, ub = np.copy(self.limits) + + lb = np.ceil(lb) + ub = np.floor(ub) + if not (lb[integrality] <= ub[integrality]).all(): + # there's a parameter that doesn't have an integer value + # lying between the limits + raise ValueError("One of the integrality constraints does not" + " have any possible integer values between" + " the lower/upper bounds.") + nlb = np.nextafter(lb[integrality] - 0.5, np.inf) + nub = np.nextafter(ub[integrality] + 0.5, -np.inf) + + self.integrality = integrality + self.limits[0, self.integrality] = nlb + self.limits[1, self.integrality] = nub + else: + self.integrality = False + + # check for equal bounds + eb = self.limits[0] == self.limits[1] + eb_count = np.count_nonzero(eb) + + # default population initialization is a latin hypercube design, but + # there are other population initializations possible. + # the minimum is 5 because 'best2bin' requires a population that's at + # least 5 long + # 202301 - reduced population size to account for parameters with + # equal bounds. If there are no varying parameters set N to at least 1 + self.num_population_members = max( + 5, + popsize * max(1, self.parameter_count - eb_count) + ) + self.population_shape = (self.num_population_members, + self.parameter_count) + + self._nfev = 0 + # check first str otherwise will fail to compare str with array + if isinstance(init, str): + if init == 'latinhypercube': + self.init_population_lhs() + elif init == 'sobol': + # must be Ns = 2**m for Sobol' + n_s = int(2 ** np.ceil(np.log2(self.num_population_members))) + self.num_population_members = n_s + self.population_shape = (self.num_population_members, + self.parameter_count) + self.init_population_qmc(qmc_engine='sobol') + elif init == 'halton': + self.init_population_qmc(qmc_engine='halton') + elif init == 'random': + self.init_population_random() + else: + raise ValueError(self.__init_error_msg) + else: + self.init_population_array(init) + + if x0 is not None: + # scale to within unit interval and + # ensure parameters are within bounds. + x0_scaled = self._unscale_parameters(np.asarray(x0)) + if ((x0_scaled > 1.0) | (x0_scaled < 0.0)).any(): + raise ValueError( + "Some entries in x0 lay outside the specified bounds" + ) + self.population[0] = x0_scaled + + # infrastructure for constraints + self.constraints = constraints + self._wrapped_constraints = [] + + if hasattr(constraints, '__len__'): + # sequence of constraints, this will also deal with default + # keyword parameter + for c in constraints: + self._wrapped_constraints.append( + _ConstraintWrapper(c, self.x) + ) + else: + self._wrapped_constraints = [ + _ConstraintWrapper(constraints, self.x) + ] + self.total_constraints = np.sum( + [c.num_constr for c in self._wrapped_constraints] + ) + self.constraint_violation = np.zeros((self.num_population_members, 1)) + self.feasible = np.ones(self.num_population_members, bool) + + # an array to shuffle when selecting candidates. Create it here + # rather than repeatedly creating it in _select_samples. + self._random_population_index = np.arange(self.num_population_members) + self.disp = disp + + def init_population_lhs(self): + """ + Initializes the population with Latin Hypercube Sampling. + Latin Hypercube Sampling ensures that each parameter is uniformly + sampled over its range. + """ + rng = self.random_number_generator + + # Each parameter range needs to be sampled uniformly. The scaled + # parameter range ([0, 1)) needs to be split into + # `self.num_population_members` segments, each of which has the following + # size: + segsize = 1.0 / self.num_population_members + + # Within each segment we sample from a uniform random distribution. + # We need to do this sampling for each parameter. + samples = (segsize * rng.uniform(size=self.population_shape) + + # Offset each segment to cover the entire parameter range [0, 1) + + np.linspace(0., 1., self.num_population_members, + endpoint=False)[:, np.newaxis]) + + # Create an array for population of candidate solutions. + self.population = np.zeros_like(samples) + + # Initialize population of candidate solutions by permutation of the + # random samples. + for j in range(self.parameter_count): + order = rng.permutation(range(self.num_population_members)) + self.population[:, j] = samples[order, j] + + # reset population energies + self.population_energies = np.full(self.num_population_members, + np.inf) + + # reset number of function evaluations counter + self._nfev = 0 + + def init_population_qmc(self, qmc_engine): + """Initializes the population with a QMC method. + + QMC methods ensures that each parameter is uniformly + sampled over its range. + + Parameters + ---------- + qmc_engine : str + The QMC method to use for initialization. Can be one of + ``latinhypercube``, ``sobol`` or ``halton``. + + """ + from scipy.stats import qmc + + rng = self.random_number_generator + + # Create an array for population of candidate solutions. + if qmc_engine == 'latinhypercube': + sampler = qmc.LatinHypercube(d=self.parameter_count, seed=rng) + elif qmc_engine == 'sobol': + sampler = qmc.Sobol(d=self.parameter_count, seed=rng) + elif qmc_engine == 'halton': + sampler = qmc.Halton(d=self.parameter_count, seed=rng) + else: + raise ValueError(self.__init_error_msg) + + self.population = sampler.random(n=self.num_population_members) + + # reset population energies + self.population_energies = np.full(self.num_population_members, + np.inf) + + # reset number of function evaluations counter + self._nfev = 0 + + def init_population_random(self): + """ + Initializes the population at random. This type of initialization + can possess clustering, Latin Hypercube sampling is generally better. + """ + rng = self.random_number_generator + self.population = rng.uniform(size=self.population_shape) + + # reset population energies + self.population_energies = np.full(self.num_population_members, + np.inf) + + # reset number of function evaluations counter + self._nfev = 0 + + def init_population_array(self, init): + """ + Initializes the population with a user specified population. + + Parameters + ---------- + init : np.ndarray + Array specifying subset of the initial population. The array should + have shape (S, N), where N is the number of parameters. + The population is clipped to the lower and upper bounds. + """ + # make sure you're using a float array + popn = np.asarray(init, dtype=np.float64) + + if (np.size(popn, 0) < 5 or + popn.shape[1] != self.parameter_count or + len(popn.shape) != 2): + raise ValueError("The population supplied needs to have shape" + " (S, len(x)), where S > 4.") + + # scale values and clip to bounds, assigning to population + self.population = np.clip(self._unscale_parameters(popn), 0, 1) + + self.num_population_members = np.size(self.population, 0) + + self.population_shape = (self.num_population_members, + self.parameter_count) + + # reset population energies + self.population_energies = np.full(self.num_population_members, + np.inf) + + # reset number of function evaluations counter + self._nfev = 0 + + @property + def x(self): + """ + The best solution from the solver + """ + return self._scale_parameters(self.population[0]) + + @property + def convergence(self): + """ + The standard deviation of the population energies divided by their + mean. + """ + if np.any(np.isinf(self.population_energies)): + return np.inf + return (np.std(self.population_energies) / + (np.abs(np.mean(self.population_energies)) + _MACHEPS)) + + def converged(self): + """ + Return True if the solver has converged. + """ + if np.any(np.isinf(self.population_energies)): + return False + + return (np.std(self.population_energies) <= + self.atol + + self.tol * np.abs(np.mean(self.population_energies))) + + def solve(self): + """ + Runs the DifferentialEvolutionSolver. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully, + ``message`` which describes the cause of the termination, + ``population`` the solution vectors present in the population, and + ``population_energies`` the value of the objective function for + each entry in ``population``. + See `OptimizeResult` for a description of other attributes. If + `polish` was employed, and a lower minimum was obtained by the + polishing, then OptimizeResult also contains the ``jac`` attribute. + If the eventual solution does not satisfy the applied constraints + ``success`` will be `False`. + """ + nit, warning_flag = 0, False + status_message = _status_message['success'] + + # The population may have just been initialized (all entries are + # np.inf). If it has you have to calculate the initial energies. + # Although this is also done in the evolve generator it's possible + # that someone can set maxiter=0, at which point we still want the + # initial energies to be calculated (the following loop isn't run). + if np.all(np.isinf(self.population_energies)): + self.feasible, self.constraint_violation = ( + self._calculate_population_feasibilities(self.population)) + + # only work out population energies for feasible solutions + self.population_energies[self.feasible] = ( + self._calculate_population_energies( + self.population[self.feasible])) + + self._promote_lowest_energy() + + # do the optimization. + for nit in range(1, self.maxiter + 1): + # evolve the population by a generation + try: + next(self) + except StopIteration: + warning_flag = True + if self._nfev > self.maxfun: + status_message = _status_message['maxfev'] + elif self._nfev == self.maxfun: + status_message = ('Maximum number of function evaluations' + ' has been reached.') + break + + if self.disp: + print(f"differential_evolution step {nit}: f(x)=" + f" {self.population_energies[0]}" + ) + + if self.callback: + c = self.tol / (self.convergence + _MACHEPS) + res = self._result(nit=nit, message="in progress") + res.convergence = c + try: + warning_flag = bool(self.callback(res)) + except StopIteration: + warning_flag = True + + if warning_flag: + status_message = 'callback function requested stop early' + + # should the solver terminate? + if warning_flag or self.converged(): + break + + else: + status_message = _status_message['maxiter'] + warning_flag = True + + DE_result = self._result( + nit=nit, message=status_message, warning_flag=warning_flag + ) + + if self.polish and not np.all(self.integrality): + # can't polish if all the parameters are integers + if np.any(self.integrality): + # set the lower/upper bounds equal so that any integrality + # constraints work. + limits, integrality = self.limits, self.integrality + limits[0, integrality] = DE_result.x[integrality] + limits[1, integrality] = DE_result.x[integrality] + + polish_method = 'L-BFGS-B' + + if self._wrapped_constraints: + polish_method = 'trust-constr' + + constr_violation = self._constraint_violation_fn(DE_result.x) + if np.any(constr_violation > 0.): + warnings.warn("differential evolution didn't find a " + "solution satisfying the constraints, " + "attempting to polish from the least " + "infeasible solution", + UserWarning, stacklevel=2) + if self.disp: + print(f"Polishing solution with '{polish_method}'") + result = minimize(self.func, + np.copy(DE_result.x), + method=polish_method, + bounds=self.limits.T, + constraints=self.constraints) + + self._nfev += result.nfev + DE_result.nfev = self._nfev + + # Polishing solution is only accepted if there is an improvement in + # cost function, the polishing was successful and the solution lies + # within the bounds. + if (result.fun < DE_result.fun and + result.success and + np.all(result.x <= self.limits[1]) and + np.all(self.limits[0] <= result.x)): + DE_result.fun = result.fun + DE_result.x = result.x + DE_result.jac = result.jac + # to keep internal state consistent + self.population_energies[0] = result.fun + self.population[0] = self._unscale_parameters(result.x) + + if self._wrapped_constraints: + DE_result.constr = [c.violation(DE_result.x) for + c in self._wrapped_constraints] + DE_result.constr_violation = np.max( + np.concatenate(DE_result.constr)) + DE_result.maxcv = DE_result.constr_violation + if DE_result.maxcv > 0: + # if the result is infeasible then success must be False + DE_result.success = False + DE_result.message = ("The solution does not satisfy the " + f"constraints, MAXCV = {DE_result.maxcv}") + + return DE_result + + def _result(self, **kwds): + # form an intermediate OptimizeResult + nit = kwds.get('nit', None) + message = kwds.get('message', None) + warning_flag = kwds.get('warning_flag', False) + result = OptimizeResult( + x=self.x, + fun=self.population_energies[0], + nfev=self._nfev, + nit=nit, + message=message, + success=(warning_flag is not True), + population=self._scale_parameters(self.population), + population_energies=self.population_energies + ) + if self._wrapped_constraints: + result.constr = [c.violation(result.x) + for c in self._wrapped_constraints] + result.constr_violation = np.max(np.concatenate(result.constr)) + result.maxcv = result.constr_violation + if result.maxcv > 0: + result.success = False + + return result + + def _calculate_population_energies(self, population): + """ + Calculate the energies of a population. + + Parameters + ---------- + population : ndarray + An array of parameter vectors normalised to [0, 1] using lower + and upper limits. Has shape ``(np.size(population, 0), N)``. + + Returns + ------- + energies : ndarray + An array of energies corresponding to each population member. If + maxfun will be exceeded during this call, then the number of + function evaluations will be reduced and energies will be + right-padded with np.inf. Has shape ``(np.size(population, 0),)`` + """ + num_members = np.size(population, 0) + # S is the number of function evals left to stay under the + # maxfun budget + S = min(num_members, self.maxfun - self._nfev) + + energies = np.full(num_members, np.inf) + + parameters_pop = self._scale_parameters(population) + try: + calc_energies = list( + self._mapwrapper(self.func, parameters_pop[0:S]) + ) + calc_energies = np.squeeze(calc_energies) + except (TypeError, ValueError) as e: + # wrong number of arguments for _mapwrapper + # or wrong length returned from the mapper + raise RuntimeError( + "The map-like callable must be of the form f(func, iterable), " + "returning a sequence of numbers the same length as 'iterable'" + ) from e + + if calc_energies.size != S: + if self.vectorized: + raise RuntimeError("The vectorized function must return an" + " array of shape (S,) when given an array" + " of shape (len(x), S)") + raise RuntimeError("func(x, *args) must return a scalar value") + + energies[0:S] = calc_energies + + if self.vectorized: + self._nfev += 1 + else: + self._nfev += S + + return energies + + def _promote_lowest_energy(self): + # swaps 'best solution' into first population entry + + idx = np.arange(self.num_population_members) + feasible_solutions = idx[self.feasible] + if feasible_solutions.size: + # find the best feasible solution + idx_t = np.argmin(self.population_energies[feasible_solutions]) + l = feasible_solutions[idx_t] + else: + # no solution was feasible, use 'best' infeasible solution, which + # will violate constraints the least + l = np.argmin(np.sum(self.constraint_violation, axis=1)) + + self.population_energies[[0, l]] = self.population_energies[[l, 0]] + self.population[[0, l], :] = self.population[[l, 0], :] + self.feasible[[0, l]] = self.feasible[[l, 0]] + self.constraint_violation[[0, l], :] = ( + self.constraint_violation[[l, 0], :]) + + def _constraint_violation_fn(self, x): + """ + Calculates total constraint violation for all the constraints, for a + set of solutions. + + Parameters + ---------- + x : ndarray + Solution vector(s). Has shape (S, N), or (N,), where S is the + number of solutions to investigate and N is the number of + parameters. + + Returns + ------- + cv : ndarray + Total violation of constraints. Has shape ``(S, M)``, where M is + the total number of constraint components (which is not necessarily + equal to len(self._wrapped_constraints)). + """ + # how many solution vectors you're calculating constraint violations + # for + S = np.size(x) // self.parameter_count + _out = np.zeros((S, self.total_constraints)) + offset = 0 + for con in self._wrapped_constraints: + # the input/output of the (vectorized) constraint function is + # {(N, S), (N,)} --> (M, S) + # The input to _constraint_violation_fn is (S, N) or (N,), so + # transpose to pass it to the constraint. The output is transposed + # from (M, S) to (S, M) for further use. + c = con.violation(x.T).T + + # The shape of c should be (M,), (1, M), or (S, M). Check for + # those shapes, as an incorrect shape indicates that the + # user constraint function didn't return the right thing, and + # the reshape operation will fail. Intercept the wrong shape + # to give a reasonable error message. I'm not sure what failure + # modes an inventive user will come up with. + if c.shape[-1] != con.num_constr or (S > 1 and c.shape[0] != S): + raise RuntimeError("An array returned from a Constraint has" + " the wrong shape. If `vectorized is False`" + " the Constraint should return an array of" + " shape (M,). If `vectorized is True` then" + " the Constraint must return an array of" + " shape (M, S), where S is the number of" + " solution vectors and M is the number of" + " constraint components in a given" + " Constraint object.") + + # the violation function may return a 1D array, but is it a + # sequence of constraints for one solution (S=1, M>=1), or the + # value of a single constraint for a sequence of solutions + # (S>=1, M=1) + c = np.reshape(c, (S, con.num_constr)) + _out[:, offset:offset + con.num_constr] = c + offset += con.num_constr + + return _out + + def _calculate_population_feasibilities(self, population): + """ + Calculate the feasibilities of a population. + + Parameters + ---------- + population : ndarray + An array of parameter vectors normalised to [0, 1] using lower + and upper limits. Has shape ``(np.size(population, 0), N)``. + + Returns + ------- + feasible, constraint_violation : ndarray, ndarray + Boolean array of feasibility for each population member, and an + array of the constraint violation for each population member. + constraint_violation has shape ``(np.size(population, 0), M)``, + where M is the number of constraints. + """ + num_members = np.size(population, 0) + if not self._wrapped_constraints: + # shortcut for no constraints + return np.ones(num_members, bool), np.zeros((num_members, 1)) + + # (S, N) + parameters_pop = self._scale_parameters(population) + + if self.vectorized: + # (S, M) + constraint_violation = np.array( + self._constraint_violation_fn(parameters_pop) + ) + else: + # (S, 1, M) + constraint_violation = np.array([self._constraint_violation_fn(x) + for x in parameters_pop]) + # if you use the list comprehension in the line above it will + # create an array of shape (S, 1, M), because each iteration + # generates an array of (1, M). In comparison the vectorized + # version returns (S, M). It's therefore necessary to remove axis 1 + constraint_violation = constraint_violation[:, 0] + + feasible = ~(np.sum(constraint_violation, axis=1) > 0) + + return feasible, constraint_violation + + def __iter__(self): + return self + + def __enter__(self): + return self + + def __exit__(self, *args): + return self._mapwrapper.__exit__(*args) + + def _accept_trial(self, energy_trial, feasible_trial, cv_trial, + energy_orig, feasible_orig, cv_orig): + """ + Trial is accepted if: + * it satisfies all constraints and provides a lower or equal objective + function value, while both the compared solutions are feasible + - or - + * it is feasible while the original solution is infeasible, + - or - + * it is infeasible, but provides a lower or equal constraint violation + for all constraint functions. + + This test corresponds to section III of Lampinen [1]_. + + Parameters + ---------- + energy_trial : float + Energy of the trial solution + feasible_trial : float + Feasibility of trial solution + cv_trial : array-like + Excess constraint violation for the trial solution + energy_orig : float + Energy of the original solution + feasible_orig : float + Feasibility of original solution + cv_orig : array-like + Excess constraint violation for the original solution + + Returns + ------- + accepted : bool + + """ + if feasible_orig and feasible_trial: + return energy_trial <= energy_orig + elif feasible_trial and not feasible_orig: + return True + elif not feasible_trial and (cv_trial <= cv_orig).all(): + # cv_trial < cv_orig would imply that both trial and orig are not + # feasible + return True + + return False + + def __next__(self): + """ + Evolve the population by a single generation + + Returns + ------- + x : ndarray + The best solution from the solver. + fun : float + Value of objective function obtained from the best solution. + """ + # the population may have just been initialized (all entries are + # np.inf). If it has you have to calculate the initial energies + if np.all(np.isinf(self.population_energies)): + self.feasible, self.constraint_violation = ( + self._calculate_population_feasibilities(self.population)) + + # only need to work out population energies for those that are + # feasible + self.population_energies[self.feasible] = ( + self._calculate_population_energies( + self.population[self.feasible])) + + self._promote_lowest_energy() + + if self.dither is not None: + self.scale = self.random_number_generator.uniform(self.dither[0], + self.dither[1]) + + if self._updating == 'immediate': + # update best solution immediately + for candidate in range(self.num_population_members): + if self._nfev > self.maxfun: + raise StopIteration + + # create a trial solution + trial = self._mutate(candidate) + + # ensuring that it's in the range [0, 1) + self._ensure_constraint(trial) + + # scale from [0, 1) to the actual parameter value + parameters = self._scale_parameters(trial) + + # determine the energy of the objective function + if self._wrapped_constraints: + cv = self._constraint_violation_fn(parameters) + feasible = False + energy = np.inf + if not np.sum(cv) > 0: + # solution is feasible + feasible = True + energy = self.func(parameters) + self._nfev += 1 + else: + feasible = True + cv = np.atleast_2d([0.]) + energy = self.func(parameters) + self._nfev += 1 + + # compare trial and population member + if self._accept_trial(energy, feasible, cv, + self.population_energies[candidate], + self.feasible[candidate], + self.constraint_violation[candidate]): + self.population[candidate] = trial + self.population_energies[candidate] = np.squeeze(energy) + self.feasible[candidate] = feasible + self.constraint_violation[candidate] = cv + + # if the trial candidate is also better than the best + # solution then promote it. + if self._accept_trial(energy, feasible, cv, + self.population_energies[0], + self.feasible[0], + self.constraint_violation[0]): + self._promote_lowest_energy() + + elif self._updating == 'deferred': + # update best solution once per generation + if self._nfev >= self.maxfun: + raise StopIteration + + # 'deferred' approach, vectorised form. + # create trial solutions + trial_pop = self._mutate_many( + np.arange(self.num_population_members) + ) + + # enforce bounds + self._ensure_constraint(trial_pop) + + # determine the energies of the objective function, but only for + # feasible trials + feasible, cv = self._calculate_population_feasibilities(trial_pop) + trial_energies = np.full(self.num_population_members, np.inf) + + # only calculate for feasible entries + trial_energies[feasible] = self._calculate_population_energies( + trial_pop[feasible]) + + # which solutions are 'improved'? + loc = [self._accept_trial(*val) for val in + zip(trial_energies, feasible, cv, self.population_energies, + self.feasible, self.constraint_violation)] + loc = np.array(loc) + self.population = np.where(loc[:, np.newaxis], + trial_pop, + self.population) + self.population_energies = np.where(loc, + trial_energies, + self.population_energies) + self.feasible = np.where(loc, + feasible, + self.feasible) + self.constraint_violation = np.where(loc[:, np.newaxis], + cv, + self.constraint_violation) + + # make sure the best solution is updated if updating='deferred'. + # put the lowest energy into the best solution position. + self._promote_lowest_energy() + + return self.x, self.population_energies[0] + + def _scale_parameters(self, trial): + """Scale from a number between 0 and 1 to parameters.""" + # trial either has shape (N, ) or (L, N), where L is the number of + # solutions being scaled + scaled = self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2 + if np.count_nonzero(self.integrality): + i = np.broadcast_to(self.integrality, scaled.shape) + scaled[i] = np.round(scaled[i]) + return scaled + + def _unscale_parameters(self, parameters): + """Scale from parameters to a number between 0 and 1.""" + return (parameters - self.__scale_arg1) * self.__recip_scale_arg2 + 0.5 + + def _ensure_constraint(self, trial): + """Make sure the parameters lie between the limits.""" + mask = np.bitwise_or(trial > 1, trial < 0) + if oob := np.count_nonzero(mask): + trial[mask] = self.random_number_generator.uniform(size=oob) + + def _mutate_custom(self, candidate): + rng = self.random_number_generator + msg = ( + "strategy must have signature" + " f(candidate: int, population: np.ndarray, rng=None) returning an" + " array of shape (N,)" + ) + _population = self._scale_parameters(self.population) + if not len(np.shape(candidate)): + # single entry in population + trial = self.strategy(candidate, _population, rng=rng) + if trial.shape != (self.parameter_count,): + raise RuntimeError(msg) + else: + S = candidate.shape[0] + trial = np.array( + [self.strategy(c, _population, rng=rng) for c in candidate], + dtype=float + ) + if trial.shape != (S, self.parameter_count): + raise RuntimeError(msg) + return self._unscale_parameters(trial) + + def _mutate_many(self, candidates): + """Create trial vectors based on a mutation strategy.""" + rng = self.random_number_generator + + S = len(candidates) + if callable(self.strategy): + return self._mutate_custom(candidates) + + trial = np.copy(self.population[candidates]) + samples = np.array([self._select_samples(c, 5) for c in candidates]) + + if self.strategy in ['currenttobest1exp', 'currenttobest1bin']: + bprime = self.mutation_func(candidates, samples) + else: + bprime = self.mutation_func(samples) + + fill_point = rng_integers(rng, self.parameter_count, size=S) + crossovers = rng.uniform(size=(S, self.parameter_count)) + crossovers = crossovers < self.cross_over_probability + if self.strategy in self._binomial: + # the last one is always from the bprime vector for binomial + # If you fill in modulo with a loop you have to set the last one to + # true. If you don't use a loop then you can have any random entry + # be True. + i = np.arange(S) + crossovers[i, fill_point[i]] = True + trial = np.where(crossovers, bprime, trial) + return trial + + elif self.strategy in self._exponential: + crossovers[..., 0] = True + for j in range(S): + i = 0 + init_fill = fill_point[j] + while (i < self.parameter_count and crossovers[j, i]): + trial[j, init_fill] = bprime[j, init_fill] + init_fill = (init_fill + 1) % self.parameter_count + i += 1 + + return trial + + def _mutate(self, candidate): + """Create a trial vector based on a mutation strategy.""" + rng = self.random_number_generator + + if callable(self.strategy): + return self._mutate_custom(candidate) + + fill_point = rng_integers(rng, self.parameter_count) + samples = self._select_samples(candidate, 5) + + trial = np.copy(self.population[candidate]) + + if self.strategy in ['currenttobest1exp', 'currenttobest1bin']: + bprime = self.mutation_func(candidate, samples) + else: + bprime = self.mutation_func(samples) + + crossovers = rng.uniform(size=self.parameter_count) + crossovers = crossovers < self.cross_over_probability + if self.strategy in self._binomial: + # the last one is always from the bprime vector for binomial + # If you fill in modulo with a loop you have to set the last one to + # true. If you don't use a loop then you can have any random entry + # be True. + crossovers[fill_point] = True + trial = np.where(crossovers, bprime, trial) + return trial + + elif self.strategy in self._exponential: + i = 0 + crossovers[0] = True + while i < self.parameter_count and crossovers[i]: + trial[fill_point] = bprime[fill_point] + fill_point = (fill_point + 1) % self.parameter_count + i += 1 + + return trial + + def _best1(self, samples): + """best1bin, best1exp""" + # samples.shape == (S, 5) + # or + # samples.shape(5,) + r0, r1 = samples[..., :2].T + return (self.population[0] + self.scale * + (self.population[r0] - self.population[r1])) + + def _rand1(self, samples): + """rand1bin, rand1exp""" + r0, r1, r2 = samples[..., :3].T + return (self.population[r0] + self.scale * + (self.population[r1] - self.population[r2])) + + def _randtobest1(self, samples): + """randtobest1bin, randtobest1exp""" + r0, r1, r2 = samples[..., :3].T + bprime = np.copy(self.population[r0]) + bprime += self.scale * (self.population[0] - bprime) + bprime += self.scale * (self.population[r1] - + self.population[r2]) + return bprime + + def _currenttobest1(self, candidate, samples): + """currenttobest1bin, currenttobest1exp""" + r0, r1 = samples[..., :2].T + bprime = (self.population[candidate] + self.scale * + (self.population[0] - self.population[candidate] + + self.population[r0] - self.population[r1])) + return bprime + + def _best2(self, samples): + """best2bin, best2exp""" + r0, r1, r2, r3 = samples[..., :4].T + bprime = (self.population[0] + self.scale * + (self.population[r0] + self.population[r1] - + self.population[r2] - self.population[r3])) + + return bprime + + def _rand2(self, samples): + """rand2bin, rand2exp""" + r0, r1, r2, r3, r4 = samples[..., :5].T + bprime = (self.population[r0] + self.scale * + (self.population[r1] + self.population[r2] - + self.population[r3] - self.population[r4])) + + return bprime + + def _select_samples(self, candidate, number_samples): + """ + obtain random integers from range(self.num_population_members), + without replacement. You can't have the original candidate either. + """ + self.random_number_generator.shuffle(self._random_population_index) + idxs = self._random_population_index[:number_samples + 1] + return idxs[idxs != candidate][:number_samples] + + +class _ConstraintWrapper: + """Object to wrap/evaluate user defined constraints. + + Very similar in practice to `PreparedConstraint`, except that no evaluation + of jac/hess is performed (explicit or implicit). + + If created successfully, it will contain the attributes listed below. + + Parameters + ---------- + constraint : {`NonlinearConstraint`, `LinearConstraint`, `Bounds`} + Constraint to check and prepare. + x0 : array_like + Initial vector of independent variables, shape (N,) + + Attributes + ---------- + fun : callable + Function defining the constraint wrapped by one of the convenience + classes. + bounds : 2-tuple + Contains lower and upper bounds for the constraints --- lb and ub. + These are converted to ndarray and have a size equal to the number of + the constraints. + + Notes + ----- + _ConstraintWrapper.fun and _ConstraintWrapper.violation can get sent + arrays of shape (N, S) or (N,), where S is the number of vectors of shape + (N,) to consider constraints for. + """ + def __init__(self, constraint, x0): + self.constraint = constraint + + if isinstance(constraint, NonlinearConstraint): + def fun(x): + x = np.asarray(x) + return np.atleast_1d(constraint.fun(x)) + elif isinstance(constraint, LinearConstraint): + def fun(x): + if issparse(constraint.A): + A = constraint.A + else: + A = np.atleast_2d(constraint.A) + + res = A.dot(x) + # x either has shape (N, S) or (N) + # (M, N) x (N, S) --> (M, S) + # (M, N) x (N,) --> (M,) + # However, if (M, N) is a matrix then: + # (M, N) * (N,) --> (M, 1), we need this to be (M,) + if x.ndim == 1 and res.ndim == 2: + # deal with case that constraint.A is an np.matrix + # see gh20041 + res = np.asarray(res)[:, 0] + + return res + elif isinstance(constraint, Bounds): + def fun(x): + return np.asarray(x) + else: + raise ValueError("`constraint` of an unknown type is passed.") + + self.fun = fun + + lb = np.asarray(constraint.lb, dtype=float) + ub = np.asarray(constraint.ub, dtype=float) + + x0 = np.asarray(x0) + + # find out the number of constraints + f0 = fun(x0) + self.num_constr = m = f0.size + self.parameter_count = x0.size + + if lb.ndim == 0: + lb = np.resize(lb, m) + if ub.ndim == 0: + ub = np.resize(ub, m) + + self.bounds = (lb, ub) + + def __call__(self, x): + return np.atleast_1d(self.fun(x)) + + def violation(self, x): + """How much the constraint is exceeded by. + + Parameters + ---------- + x : array-like + Vector of independent variables, (N, S), where N is number of + parameters and S is the number of solutions to be investigated. + + Returns + ------- + excess : array-like + How much the constraint is exceeded by, for each of the + constraints specified by `_ConstraintWrapper.fun`. + Has shape (M, S) where M is the number of constraint components. + """ + # expect ev to have shape (num_constr, S) or (num_constr,) + ev = self.fun(np.asarray(x)) + + try: + excess_lb = np.maximum(self.bounds[0] - ev.T, 0) + excess_ub = np.maximum(ev.T - self.bounds[1], 0) + except ValueError as e: + raise RuntimeError("An array returned from a Constraint has" + " the wrong shape. If `vectorized is False`" + " the Constraint should return an array of" + " shape (M,). If `vectorized is True` then" + " the Constraint must return an array of" + " shape (M, S), where S is the number of" + " solution vectors and M is the number of" + " constraint components in a given" + " Constraint object.") from e + + v = (excess_lb + excess_ub).T + return v diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiate.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiate.py new file mode 100644 index 0000000000000000000000000000000000000000..959c17e3ffaedf960ebffe7984aa25aa32d9eb6c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_differentiate.py @@ -0,0 +1,856 @@ +# mypy: disable-error-code="attr-defined" +import numpy as np +import scipy._lib._elementwise_iterative_method as eim +from scipy._lib._util import _RichResult + +_EERRORINCREASE = -1 # used in _differentiate + +def _differentiate_iv(func, x, args, atol, rtol, maxiter, order, initial_step, + step_factor, step_direction, preserve_shape, callback): + # Input validation for `_differentiate` + + if not callable(func): + raise ValueError('`func` must be callable.') + + # x has more complex IV that is taken care of during initialization + x = np.asarray(x) + dtype = x.dtype if np.issubdtype(x.dtype, np.inexact) else np.float64 + + if not np.iterable(args): + args = (args,) + + if atol is None: + atol = np.finfo(dtype).tiny + + if rtol is None: + rtol = np.sqrt(np.finfo(dtype).eps) + + message = 'Tolerances and step parameters must be non-negative scalars.' + tols = np.asarray([atol, rtol, initial_step, step_factor]) + if (not np.issubdtype(tols.dtype, np.number) + or np.any(tols < 0) + or tols.shape != (4,)): + raise ValueError(message) + initial_step, step_factor = tols[2:].astype(dtype) + + maxiter_int = int(maxiter) + if maxiter != maxiter_int or maxiter <= 0: + raise ValueError('`maxiter` must be a positive integer.') + + order_int = int(order) + if order_int != order or order <= 0: + raise ValueError('`order` must be a positive integer.') + + step_direction = np.sign(step_direction).astype(dtype) + x, step_direction = np.broadcast_arrays(x, step_direction) + x, step_direction = x[()], step_direction[()] + + message = '`preserve_shape` must be True or False.' + if preserve_shape not in {True, False}: + raise ValueError(message) + + if callback is not None and not callable(callback): + raise ValueError('`callback` must be callable.') + + return (func, x, args, atol, rtol, maxiter_int, order_int, initial_step, + step_factor, step_direction, preserve_shape, callback) + + +def _differentiate(func, x, *, args=(), atol=None, rtol=None, maxiter=10, + order=8, initial_step=0.5, step_factor=2.0, + step_direction=0, preserve_shape=False, callback=None): + """Evaluate the derivative of an elementwise scalar function numerically. + + Parameters + ---------- + func : callable + The function whose derivative is desired. The signature must be:: + + func(x: ndarray, *fargs) -> ndarray + + where each element of ``x`` is a finite real number and ``fargs`` is a tuple, + which may contain an arbitrary number of arrays that are broadcastable + with `x`. ``func`` must be an elementwise function: each element + ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``. + x : array_like + Abscissae at which to evaluate the derivative. + args : tuple, optional + Additional positional arguments to be passed to `func`. Must be arrays + broadcastable with `x`. If the callable to be differentiated requires + arguments that are not broadcastable with `x`, wrap that callable with + `func`. See Examples. + atol, rtol : float, optional + Absolute and relative tolerances for the stopping condition: iteration + will stop when ``res.error < atol + rtol * abs(res.df)``. The default + `atol` is the smallest normal number of the appropriate dtype, and + the default `rtol` is the square root of the precision of the + appropriate dtype. + order : int, default: 8 + The (positive integer) order of the finite difference formula to be + used. Odd integers will be rounded up to the next even integer. + initial_step : float, default: 0.5 + The (absolute) initial step size for the finite difference derivative + approximation. + step_factor : float, default: 2.0 + The factor by which the step size is *reduced* in each iteration; i.e. + the step size in iteration 1 is ``initial_step/step_factor``. If + ``step_factor < 1``, subsequent steps will be greater than the initial + step; this may be useful if steps smaller than some threshold are + undesirable (e.g. due to subtractive cancellation error). + maxiter : int, default: 10 + The maximum number of iterations of the algorithm to perform. See + notes. + step_direction : array_like + An array representing the direction of the finite difference steps (for + use when `x` lies near to the boundary of the domain of the function.) + Must be broadcastable with `x` and all `args`. + Where 0 (default), central differences are used; where negative (e.g. + -1), steps are non-positive; and where positive (e.g. 1), all steps are + non-negative. + preserve_shape : bool, default: False + In the following, "arguments of `func`" refers to the array ``x`` and + any arrays within ``fargs``. Let ``shape`` be the broadcasted shape + of `x` and all elements of `args` (which is conceptually + distinct from ``fargs`` passed into `f`). + + - When ``preserve_shape=False`` (default), `f` must accept arguments + of *any* broadcastable shapes. + + - When ``preserve_shape=True``, `f` must accept arguments of shape + ``shape`` *or* ``shape + (n,)``, where ``(n,)`` is the number of + abscissae at which the function is being evaluated. + + In either case, for each scalar element ``xi`` within `x`, the array + returned by `f` must include the scalar ``f(xi)`` at the same index. + Consequently, the shape of the output is always the shape of the input + ``x``. + + See Examples. + callback : callable, optional + An optional user-supplied function to be called before the first + iteration and after each iteration. + Called as ``callback(res)``, where ``res`` is a ``_RichResult`` + similar to that returned by `_differentiate` (but containing the + current iterate's values of all variables). If `callback` raises a + ``StopIteration``, the algorithm will terminate immediately and + `_differentiate` will return a result. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. (The descriptions are written as though the values will be + scalars; however, if `func` returns an array, the outputs will be + arrays of the same shape.) + + success : bool + ``True`` when the algorithm terminated successfully (status ``0``). + status : int + An integer representing the exit status of the algorithm. + ``0`` : The algorithm converged to the specified tolerances. + ``-1`` : The error estimate increased, so iteration was terminated. + ``-2`` : The maximum number of iterations was reached. + ``-3`` : A non-finite value was encountered. + ``-4`` : Iteration was terminated by `callback`. + ``1`` : The algorithm is proceeding normally (in `callback` only). + df : float + The derivative of `func` at `x`, if the algorithm terminated + successfully. + error : float + An estimate of the error: the magnitude of the difference between + the current estimate of the derivative and the estimate in the + previous iteration. + nit : int + The number of iterations performed. + nfev : int + The number of points at which `func` was evaluated. + x : float + The value at which the derivative of `func` was evaluated + (after broadcasting with `args` and `step_direction`). + + Notes + ----- + The implementation was inspired by jacobi [1]_, numdifftools [2]_, and + DERIVEST [3]_, but the implementation follows the theory of Taylor series + more straightforwardly (and arguably naively so). + In the first iteration, the derivative is estimated using a finite + difference formula of order `order` with maximum step size `initial_step`. + Each subsequent iteration, the maximum step size is reduced by + `step_factor`, and the derivative is estimated again until a termination + condition is reached. The error estimate is the magnitude of the difference + between the current derivative approximation and that of the previous + iteration. + + The stencils of the finite difference formulae are designed such that + abscissae are "nested": after `func` is evaluated at ``order + 1`` + points in the first iteration, `func` is evaluated at only two new points + in each subsequent iteration; ``order - 1`` previously evaluated function + values required by the finite difference formula are reused, and two + function values (evaluations at the points furthest from `x`) are unused. + + Step sizes are absolute. When the step size is small relative to the + magnitude of `x`, precision is lost; for example, if `x` is ``1e20``, the + default initial step size of ``0.5`` cannot be resolved. Accordingly, + consider using larger initial step sizes for large magnitudes of `x`. + + The default tolerances are challenging to satisfy at points where the + true derivative is exactly zero. If the derivative may be exactly zero, + consider specifying an absolute tolerance (e.g. ``atol=1e-16``) to + improve convergence. + + References + ---------- + [1]_ Hans Dembinski (@HDembinski). jacobi. + https://github.com/HDembinski/jacobi + [2]_ Per A. Brodtkorb and John D'Errico. numdifftools. + https://numdifftools.readthedocs.io/en/latest/ + [3]_ John D'Errico. DERIVEST: Adaptive Robust Numerical Differentiation. + https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation + [4]_ Numerical Differentition. Wikipedia. + https://en.wikipedia.org/wiki/Numerical_differentiation + + Examples + -------- + Evaluate the derivative of ``np.exp`` at several points ``x``. + + >>> import numpy as np + >>> from scipy.optimize._differentiate import _differentiate + >>> f = np.exp + >>> df = np.exp # true derivative + >>> x = np.linspace(1, 2, 5) + >>> res = _differentiate(f, x) + >>> res.df # approximation of the derivative + array([2.71828183, 3.49034296, 4.48168907, 5.75460268, 7.3890561 ]) + >>> res.error # estimate of the error + array( + [7.12940817e-12, 9.16688947e-12, 1.17594823e-11, 1.50972568e-11, 1.93942640e-11] + ) + >>> abs(res.df - df(x)) # true error + array( + [3.06421555e-14, 3.01980663e-14, 5.06261699e-14, 6.30606678e-14, 8.34887715e-14] + ) + + Show the convergence of the approximation as the step size is reduced. + Each iteration, the step size is reduced by `step_factor`, so for + sufficiently small initial step, each iteration reduces the error by a + factor of ``1/step_factor**order`` until finite precision arithmetic + inhibits further improvement. + + >>> iter = list(range(1, 12)) # maximum iterations + >>> hfac = 2 # step size reduction per iteration + >>> hdir = [-1, 0, 1] # compare left-, central-, and right- steps + >>> order = 4 # order of differentiation formula + >>> x = 1 + >>> ref = df(x) + >>> errors = [] # true error + >>> for i in iter: + ... res = _differentiate(f, x, maxiter=i, step_factor=hfac, + ... step_direction=hdir, order=order, + ... atol=0, rtol=0) # prevent early termination + ... errors.append(abs(res.df - ref)) + >>> errors = np.array(errors) + >>> plt.semilogy(iter, errors[:, 0], label='left differences') + >>> plt.semilogy(iter, errors[:, 1], label='central differences') + >>> plt.semilogy(iter, errors[:, 2], label='right differences') + >>> plt.xlabel('iteration') + >>> plt.ylabel('error') + >>> plt.legend() + >>> plt.show() + >>> (errors[1, 1] / errors[0, 1], 1 / hfac**order) + (0.06215223140159822, 0.0625) + + The implementation is vectorized over `x`, `step_direction`, and `args`. + The function is evaluated once before the first iteration to perform input + validation and standardization, and once per iteration thereafter. + + >>> def f(x, p): + ... print('here') + ... f.nit += 1 + ... return x**p + >>> f.nit = 0 + >>> def df(x, p): + ... return p*x**(p-1) + >>> x = np.arange(1, 5) + >>> p = np.arange(1, 6).reshape((-1, 1)) + >>> hdir = np.arange(-1, 2).reshape((-1, 1, 1)) + >>> res = _differentiate(f, x, args=(p,), step_direction=hdir, maxiter=1) + >>> np.allclose(res.df, df(x, p)) + True + >>> res.df.shape + (3, 5, 4) + >>> f.nit + 2 + + By default, `preserve_shape` is False, and therefore the callable + `f` may be called with arrays of any broadcastable shapes. + For example: + + >>> shapes = [] + >>> def f(x, c): + ... shape = np.broadcast_shapes(x.shape, c.shape) + ... shapes.append(shape) + ... return np.sin(c*x) + >>> + >>> c = [1, 5, 10, 20] + >>> res = _differentiate(f, 0, args=(c,)) + >>> shapes + [(4,), (4, 8), (4, 2), (3, 2), (2, 2), (1, 2)] + + To understand where these shapes are coming from - and to better + understand how `_differentiate` computes accurate results - note that + higher values of ``c`` correspond with higher frequency sinusoids. + The higher frequency sinusoids make the function's derivative change + faster, so more function evaluations are required to achieve the target + accuracy: + + >>> res.nfev + array([11, 13, 15, 17]) + + The initial ``shape``, ``(4,)``, corresponds with evaluating the + function at a single abscissa and all four frequencies; this is used + for input validation and to determine the size and dtype of the arrays + that store results. The next shape corresponds with evaluating the + function at an initial grid of abscissae and all four frequencies. + Successive calls to the function evaluate the function at two more + abscissae, increasing the effective order of the approximation by two. + However, in later function evaluations, the function is evaluated at + fewer frequencies because the corresponding derivative has already + converged to the required tolerance. This saves function evaluations to + improve performance, but it requires the function to accept arguments of + any shape. + + "Vector-valued" functions are unlikely to satisfy this requirement. + For example, consider + + >>> def f(x): + ... return [x, np.sin(3*x), x+np.sin(10*x), np.sin(20*x)*(x-1)**2] + + This integrand is not compatible with `_differentiate` as written; for instance, + the shape of the output will not be the same as the shape of ``x``. Such a + function *could* be converted to a compatible form with the introduction of + additional parameters, but this would be inconvenient. In such cases, + a simpler solution would be to use `preserve_shape`. + + >>> shapes = [] + >>> def f(x): + ... shapes.append(x.shape) + ... x0, x1, x2, x3 = x + ... return [x0, np.sin(3*x1), x2+np.sin(10*x2), np.sin(20*x3)*(x3-1)**2] + >>> + >>> x = np.zeros(4) + >>> res = _differentiate(f, x, preserve_shape=True) + >>> shapes + [(4,), (4, 8), (4, 2), (4, 2), (4, 2), (4, 2)] + + Here, the shape of ``x`` is ``(4,)``. With ``preserve_shape=True``, the + function may be called with argument ``x`` of shape ``(4,)`` or ``(4, n)``, + and this is what we observe. + + """ + # TODO (followup): + # - investigate behavior at saddle points + # - array initial_step / step_factor? + # - multivariate functions? + + res = _differentiate_iv(func, x, args, atol, rtol, maxiter, order, initial_step, + step_factor, step_direction, preserve_shape, callback) + (func, x, args, atol, rtol, maxiter, order, + h0, fac, hdir, preserve_shape, callback) = res + + # Initialization + # Since f(x) (no step) is not needed for central differences, it may be + # possible to eliminate this function evaluation. However, it's useful for + # input validation and standardization, and everything else is designed to + # reduce function calls, so let's keep it simple. + temp = eim._initialize(func, (x,), args, preserve_shape=preserve_shape) + func, xs, fs, args, shape, dtype, xp = temp + x, f = xs[0], fs[0] + df = np.full_like(f, np.nan) + # Ideally we'd broadcast the shape of `hdir` in `_elementwise_algo_init`, but + # it's simpler to do it here than to generalize `_elementwise_algo_init` further. + # `hdir` and `x` are already broadcasted in `_differentiate_iv`, so we know + # that `hdir` can be broadcasted to the final shape. + hdir = np.broadcast_to(hdir, shape).flatten() + + status = np.full_like(x, eim._EINPROGRESS, dtype=int) # in progress + nit, nfev = 0, 1 # one function evaluations performed above + # Boolean indices of left, central, right, and (all) one-sided steps + il = hdir < 0 + ic = hdir == 0 + ir = hdir > 0 + io = il | ir + + # Most of these attributes are reasonably obvious, but: + # - `fs` holds all the function values of all active `x`. The zeroth + # axis corresponds with active points `x`, the first axis corresponds + # with the different steps (in the order described in + # `_differentiate_weights`). + # - `terms` (which could probably use a better name) is half the `order`, + # which is always even. + work = _RichResult(x=x, df=df, fs=f[:, np.newaxis], error=np.nan, h=h0, + df_last=np.nan, error_last=np.nan, h0=h0, fac=fac, + atol=atol, rtol=rtol, nit=nit, nfev=nfev, + status=status, dtype=dtype, terms=(order+1)//2, + hdir=hdir, il=il, ic=ic, ir=ir, io=io) + # This is the correspondence between terms in the `work` object and the + # final result. In this case, the mapping is trivial. Note that `success` + # is prepended automatically. + res_work_pairs = [('status', 'status'), ('df', 'df'), ('error', 'error'), + ('nit', 'nit'), ('nfev', 'nfev'), ('x', 'x')] + + def pre_func_eval(work): + """Determine the abscissae at which the function needs to be evaluated. + + See `_differentiate_weights` for a description of the stencil (pattern + of the abscissae). + + In the first iteration, there is only one stored function value in + `work.fs`, `f(x)`, so we need to evaluate at `order` new points. In + subsequent iterations, we evaluate at two new points. Note that + `work.x` is always flattened into a 1D array after broadcasting with + all `args`, so we add a new axis at the end and evaluate all point + in one call to the function. + + For improvement: + - Consider measuring the step size actually taken, since `(x + h) - x` + is not identically equal to `h` with floating point arithmetic. + - Adjust the step size automatically if `x` is too big to resolve the + step. + - We could probably save some work if there are no central difference + steps or no one-sided steps. + """ + n = work.terms # half the order + h = work.h # step size + c = work.fac # step reduction factor + d = c**0.5 # square root of step reduction factor (one-sided stencil) + # Note - no need to be careful about dtypes until we allocate `x_eval` + + if work.nit == 0: + hc = h / c**np.arange(n) + hc = np.concatenate((-hc[::-1], hc)) + else: + hc = np.asarray([-h, h]) / c**(n-1) + + if work.nit == 0: + hr = h / d**np.arange(2*n) + else: + hr = np.asarray([h, h/d]) / c**(n-1) + + n_new = 2*n if work.nit == 0 else 2 # number of new abscissae + x_eval = np.zeros((len(work.hdir), n_new), dtype=work.dtype) + il, ic, ir = work.il, work.ic, work.ir + x_eval[ir] = work.x[ir, np.newaxis] + hr + x_eval[ic] = work.x[ic, np.newaxis] + hc + x_eval[il] = work.x[il, np.newaxis] - hr + return x_eval + + def post_func_eval(x, f, work): + """ Estimate the derivative and error from the function evaluations + + As in `pre_func_eval`: in the first iteration, there is only one stored + function value in `work.fs`, `f(x)`, so we need to add the `order` new + points. In subsequent iterations, we add two new points. The tricky + part is getting the order to match that of the weights, which is + described in `_differentiate_weights`. + + For improvement: + - Change the order of the weights (and steps in `pre_func_eval`) to + simplify `work_fc` concatenation and eliminate `fc` concatenation. + - It would be simple to do one-step Richardson extrapolation with `df` + and `df_last` to increase the order of the estimate and/or improve + the error estimate. + - Process the function evaluations in a more numerically favorable + way. For instance, combining the pairs of central difference evals + into a second-order approximation and using Richardson extrapolation + to produce a higher order approximation seemed to retain accuracy up + to very high order. + - Alternatively, we could use `polyfit` like Jacobi. An advantage of + fitting polynomial to more points than necessary is improved noise + tolerance. + """ + n = work.terms + n_new = n if work.nit == 0 else 1 + il, ic, io = work.il, work.ic, work.io + + # Central difference + # `work_fc` is *all* the points at which the function has been evaluated + # `fc` is the points we're using *this iteration* to produce the estimate + work_fc = (f[ic, :n_new], work.fs[ic, :], f[ic, -n_new:]) + work_fc = np.concatenate(work_fc, axis=-1) + if work.nit == 0: + fc = work_fc + else: + fc = (work_fc[:, :n], work_fc[:, n:n+1], work_fc[:, -n:]) + fc = np.concatenate(fc, axis=-1) + + # One-sided difference + work_fo = np.concatenate((work.fs[io, :], f[io, :]), axis=-1) + if work.nit == 0: + fo = work_fo + else: + fo = np.concatenate((work_fo[:, 0:1], work_fo[:, -2*n:]), axis=-1) + + work.fs = np.zeros((len(ic), work.fs.shape[-1] + 2*n_new)) + work.fs[ic] = work_fc + work.fs[io] = work_fo + + wc, wo = _differentiate_weights(work, n) + work.df_last = work.df.copy() + work.df[ic] = fc @ wc / work.h + work.df[io] = fo @ wo / work.h + work.df[il] *= -1 + + work.h /= work.fac + work.error_last = work.error + # Simple error estimate - the difference in derivative estimates between + # this iteration and the last. This is typically conservative because if + # convergence has begin, the true error is much closer to the difference + # between the current estimate and the *next* error estimate. However, + # we could use Richarson extrapolation to produce an error estimate that + # is one order higher, and take the difference between that and + # `work.df` (which would just be constant factor that depends on `fac`.) + work.error = abs(work.df - work.df_last) + + def check_termination(work): + """Terminate due to convergence, non-finite values, or error increase""" + stop = np.zeros_like(work.df).astype(bool) + + i = work.error < work.atol + work.rtol*abs(work.df) + work.status[i] = eim._ECONVERGED + stop[i] = True + + if work.nit > 0: + i = ~((np.isfinite(work.x) & np.isfinite(work.df)) | stop) + work.df[i], work.status[i] = np.nan, eim._EVALUEERR + stop[i] = True + + # With infinite precision, there is a step size below which + # all smaller step sizes will reduce the error. But in floating point + # arithmetic, catastrophic cancellation will begin to cause the error + # to increase again. This heuristic tries to avoid step sizes that are + # too small. There may be more theoretically sound approaches for + # detecting a step size that minimizes the total error, but this + # heuristic seems simple and effective. + i = (work.error > work.error_last*10) & ~stop + work.status[i] = _EERRORINCREASE + stop[i] = True + + return stop + + def post_termination_check(work): + return + + def customize_result(res, shape): + return shape + + return eim._loop(work, callback, shape, maxiter, func, args, dtype, + pre_func_eval, post_func_eval, check_termination, + post_termination_check, customize_result, res_work_pairs, + xp, preserve_shape) + + +def _differentiate_weights(work, n): + # This produces the weights of the finite difference formula for a given + # stencil. In experiments, use of a second-order central difference formula + # with Richardson extrapolation was more accurate numerically, but it was + # more complicated, and it would have become even more complicated when + # adding support for one-sided differences. However, now that all the + # function evaluation values are stored, they can be processed in whatever + # way is desired to produce the derivative estimate. We leave alternative + # approaches to future work. To be more self-contained, here is the theory + # for deriving the weights below. + # + # Recall that the Taylor expansion of a univariate, scalar-values function + # about a point `x` may be expressed as: + # f(x + h) = f(x) + f'(x)*h + f''(x)/2!*h**2 + O(h**3) + # Suppose we evaluate f(x), f(x+h), and f(x-h). We have: + # f(x) = f(x) + # f(x + h) = f(x) + f'(x)*h + f''(x)/2!*h**2 + O(h**3) + # f(x - h) = f(x) - f'(x)*h + f''(x)/2!*h**2 + O(h**3) + # We can solve for weights `wi` such that: + # w1*f(x) = w1*(f(x)) + # + w2*f(x + h) = w2*(f(x) + f'(x)*h + f''(x)/2!*h**2) + O(h**3) + # + w3*f(x - h) = w3*(f(x) - f'(x)*h + f''(x)/2!*h**2) + O(h**3) + # = 0 + f'(x)*h + 0 + O(h**3) + # Then + # f'(x) ~ (w1*f(x) + w2*f(x+h) + w3*f(x-h))/h + # is a finite difference derivative approximation with error O(h**2), + # and so it is said to be a "second-order" approximation. Under certain + # conditions (e.g. well-behaved function, `h` sufficiently small), the + # error in the approximation will decrease with h**2; that is, if `h` is + # reduced by a factor of 2, the error is reduced by a factor of 4. + # + # By default, we use eighth-order formulae. Our central-difference formula + # uses abscissae: + # x-h/c**3, x-h/c**2, x-h/c, x-h, x, x+h, x+h/c, x+h/c**2, x+h/c**3 + # where `c` is the step factor. (Typically, the step factor is greater than + # one, so the outermost points - as written above - are actually closest to + # `x`.) This "stencil" is chosen so that each iteration, the step can be + # reduced by the factor `c`, and most of the function evaluations can be + # reused with the new step size. For example, in the next iteration, we + # will have: + # x-h/c**4, x-h/c**3, x-h/c**2, x-h/c, x, x+h/c, x+h/c**2, x+h/c**3, x+h/c**4 + # We do not reuse `x-h` and `x+h` for the new derivative estimate. + # While this would increase the order of the formula and thus the + # theoretical convergence rate, it is also less stable numerically. + # (As noted above, there are other ways of processing the values that are + # more stable. Thus, even now we store `f(x-h)` and `f(x+h)` in `work.fs` + # to simplify future development of this sort of improvement.) + # + # The (right) one-sided formula is produced similarly using abscissae + # x, x+h, x+h/d, x+h/d**2, ..., x+h/d**6, x+h/d**7, x+h/d**7 + # where `d` is the square root of `c`. (The left one-sided formula simply + # uses -h.) When the step size is reduced by factor `c = d**2`, we have + # abscissae: + # x, x+h/d**2, x+h/d**3..., x+h/d**8, x+h/d**9, x+h/d**9 + # `d` is chosen as the square root of `c` so that the rate of the step-size + # reduction is the same per iteration as in the central difference case. + # Note that because the central difference formulas are inherently of even + # order, for simplicity, we use only even-order formulas for one-sided + # differences, too. + + # It's possible for the user to specify `fac` in, say, double precision but + # `x` and `args` in single precision. `fac` gets converted to single + # precision, but we should always use double precision for the intermediate + # calculations here to avoid additional error in the weights. + fac = work.fac.astype(np.float64) + + # Note that if the user switches back to floating point precision with + # `x` and `args`, then `fac` will not necessarily equal the (lower + # precision) cached `_differentiate_weights.fac`, and the weights will + # need to be recalculated. This could be fixed, but it's late, and of + # low consequence. + if fac != _differentiate_weights.fac: + _differentiate_weights.central = [] + _differentiate_weights.right = [] + _differentiate_weights.fac = fac + + if len(_differentiate_weights.central) != 2*n + 1: + # Central difference weights. Consider refactoring this; it could + # probably be more compact. + i = np.arange(-n, n + 1) + p = np.abs(i) - 1. # center point has power `p` -1, but sign `s` is 0 + s = np.sign(i) + + h = s / fac ** p + A = np.vander(h, increasing=True).T + b = np.zeros(2*n + 1) + b[1] = 1 + weights = np.linalg.solve(A, b) + + # Enforce identities to improve accuracy + weights[n] = 0 + for i in range(n): + weights[-i-1] = -weights[i] + + # Cache the weights. We only need to calculate them once unless + # the step factor changes. + _differentiate_weights.central = weights + + # One-sided difference weights. The left one-sided weights (with + # negative steps) are simply the negative of the right one-sided + # weights, so no need to compute them separately. + i = np.arange(2*n + 1) + p = i - 1. + s = np.sign(i) + + h = s / np.sqrt(fac) ** p + A = np.vander(h, increasing=True).T + b = np.zeros(2 * n + 1) + b[1] = 1 + weights = np.linalg.solve(A, b) + + _differentiate_weights.right = weights + + return (_differentiate_weights.central.astype(work.dtype, copy=False), + _differentiate_weights.right.astype(work.dtype, copy=False)) +_differentiate_weights.central = [] +_differentiate_weights.right = [] +_differentiate_weights.fac = None + + +def _jacobian(func, x, *, atol=None, rtol=None, maxiter=10, + order=8, initial_step=0.5, step_factor=2.0): + r"""Evaluate the Jacobian of a function numerically. + + Parameters + ---------- + func : callable + The function whose Jacobian is desired. The signature must be:: + + func(x: ndarray) -> ndarray + + where each element of ``x`` is a finite real. If the function to be + differentiated accepts additional, arguments wrap it (e.g. using + `functools.partial` or ``lambda``) and pass the wrapped callable + into `_jacobian`. See Notes regarding vectorization and the dimensionality + of the input and output. + x : array_like + Points at which to evaluate the Jacobian. Must have at least one dimension. + See Notes regarding the dimensionality and vectorization. + atol, rtol : float, optional + Absolute and relative tolerances for the stopping condition: iteration + will stop for each element of the Jacobian when + ``res.error < atol + rtol * abs(res.df)``. The default `atol` is the + smallest normal number of the appropriate dtype, and the default `rtol` + is the square root of the precision of the appropriate dtype. + order : int, default: 8 + The (positive integer) order of the finite difference formula to be + used. Odd integers will be rounded up to the next even integer. + initial_step : float, default: 0.5 + The (absolute) initial step size for the finite difference derivative + approximation. + step_factor : float, default: 2.0 + The factor by which the step size is *reduced* in each iteration; i.e. + the step size in iteration 1 is ``initial_step/step_factor``. If + ``step_factor < 1``, subsequent steps will be greater than the initial + step; this may be useful if steps smaller than some threshold are + undesirable (e.g. due to subtractive cancellation error). + maxiter : int, default: 10 + The maximum number of iterations of the algorithm to perform. + + Returns + ------- + res : _RichResult + An instance of `scipy._lib._util._RichResult` with the following + attributes. + + success : bool array + ``True`` when the algorithm terminated successfully (status ``0``). + status : int array + An integer representing the exit status of the algorithm. + ``0`` : The algorithm converged to the specified tolerances. + ``-1`` : The error estimate increased, so iteration was terminated. + ``-2`` : The maximum number of iterations was reached. + ``-3`` : A non-finite value was encountered. + ``-4`` : Iteration was terminated by `callback`. + ``1`` : The algorithm is proceeding normally (in `callback` only). + df : float array + The Jacobian of `func` at `x`, if the algorithm terminated + successfully. + error : float array + An estimate of the error: the magnitude of the difference between + the current estimate of the derivative and the estimate in the + previous iteration. + nit : int array + The number of iterations performed. + nfev : int array + The number of points at which `func` was evaluated. + x : float array + The value at which the derivative of `func` was evaluated. + + See Also + -------- + _differentiate + + Notes + ----- + Suppose we wish to evaluate the Jacobian of a function + :math:`f: \mathbf{R^m} \rightarrow \mathbf{R^n}`, and assign to variables + ``m`` and ``n`` the positive integer values of :math:`m` and :math:`n`, + respectively. If we wish to evaluate the Jacobian at a single point, + then: + + - argument `x` must be an array of shape ``(m,)`` + - argument `func` must be vectorized to accept an array of shape ``(m, p)``. + The first axis represents the :math:`m` inputs of :math:`f`; the second + is for evaluating the function at multiple points in a single call. + - argument `func` must return an array of shape ``(n, p)``. The first + axis represents the :math:`n` outputs of :math:`f`; the second + is for the result of evaluating the function at multiple points. + - attribute ``df`` of the result object will be an array of shape ``(n, m)``, + the Jacobian. + + This function is also vectorized in the sense that the Jacobian can be + evaluated at ``k`` points in a single call. In this case, `x` would be an + array of shape ``(m, k)``, `func` would accept an array of shape + ``(m, k, p)`` and return an array of shape ``(n, k, p)``, and the ``df`` + attribute of the result would have shape ``(n, m, k)``. + + References + ---------- + .. [1] Jacobian matrix and determinant, *Wikipedia*, + https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant + + Examples + -------- + The Rosenbrock function maps from :math:`\mathbf{R}^m \righarrow \mathbf{R}`; + the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an + array of shape ``(m, p)`` and return an array of shape ``m``. Suppose we wish + to evaluate the Jacobian (AKA the gradient because the function returns a scalar) + at ``[0.5, 0.5, 0.5]``. + + >>> import numpy as np + >>> from scipy.optimize._differentiate import _jacobian as jacobian + >>> from scipy.optimize import rosen, rosen_der + >>> m = 3 + >>> x = np.full(m, 0.5) + >>> res = jacobian(rosen, x) + >>> ref = rosen_der(x) # reference value of the gradient + >>> res.df, ref + (array([-51., -1., 50.]), array([-51., -1., 50.])) + + As an example of a function with multiple outputs, consider Example 4 + from [1]_. + + >>> def f(x): + ... x1, x2, x3 = x ... + ... return [x1, 5*x3, 4*x2**2 - 2*x3, x3*np.sin(x1)] + + The true Jacobian is given by: + + >>> def df(x): + ... x1, x2, x3 = x + ... one = np.ones_like(x1) + ... return [[one, 0*one, 0*one], + ... [0*one, 0*one, 5*one], + ... [0*one, 8*x2, -2*one], + ... [x3*np.cos(x1), 0*one, np.sin(x1)]] + + Evaluate the Jacobian at an arbitrary point. + + >>> rng = np.random.default_rng(389252938452) + >>> x = rng.random(size=3) + >>> res = jacobian(f, x) + >>> ref = df(x) + >>> res.df.shape == (4, 3) + True + >>> np.allclose(res.df, ref) + True + + Evaluate the Jacobian at 10 arbitrary points in a single call. + + >>> x = rng.random(size=(3, 10)) + >>> res = jacobian(f, x) + >>> ref = df(x) + >>> res.df.shape == (4, 3, 10) + True + >>> np.allclose(res.df, ref) + True + + """ + x = np.asarray(x) + int_dtype = np.issubdtype(x.dtype, np.integer) + x0 = np.asarray(x, dtype=float) if int_dtype else x + + if x0.ndim < 1: + message = "Argument `x` must be at least 1-D." + raise ValueError(message) + + m = x0.shape[0] + i = np.arange(m) + + def wrapped(x): + p = () if x.ndim == x0.ndim else (x.shape[-1],) # number of abscissae + new_dims = (1,) if x.ndim == x0.ndim else (1, -1) + new_shape = (m, m) + x0.shape[1:] + p + xph = np.expand_dims(x0, new_dims) + xph = np.broadcast_to(xph, new_shape).copy() + xph[i, i] = x + return func(xph) + + res = _differentiate(wrapped, x, atol=atol, rtol=rtol, + maxiter=maxiter, order=order, initial_step=initial_step, + step_factor=step_factor, preserve_shape=True) + del res.x # the user knows `x`, and the way it gets broadcasted is meaningless here + return res diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..fe89bac4a6f6b828def53da54b5eac17d45a4019 Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct_py.py new file mode 100644 index 0000000000000000000000000000000000000000..440cbb5ae866462b6299b1e12d4a6ba1e407fd62 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_direct_py.py @@ -0,0 +1,278 @@ +from __future__ import annotations +from typing import ( # noqa: UP035 + Any, Callable, Iterable, TYPE_CHECKING +) + +import numpy as np +from scipy.optimize import OptimizeResult +from ._constraints import old_bound_to_new, Bounds +from ._direct import direct as _direct # type: ignore + +if TYPE_CHECKING: + import numpy.typing as npt + +__all__ = ['direct'] + +ERROR_MESSAGES = ( + "Number of function evaluations done is larger than maxfun={}", + "Number of iterations is larger than maxiter={}", + "u[i] < l[i] for some i", + "maxfun is too large", + "Initialization failed", + "There was an error in the creation of the sample points", + "An error occurred while the function was sampled", + "Maximum number of levels has been reached.", + "Forced stop", + "Invalid arguments", + "Out of memory", +) + +SUCCESS_MESSAGES = ( + ("The best function value found is within a relative error={} " + "of the (known) global optimum f_min"), + ("The volume of the hyperrectangle containing the lowest function value " + "found is below vol_tol={}"), + ("The side length measure of the hyperrectangle containing the lowest " + "function value found is below len_tol={}"), +) + + +def direct( + func: Callable[[npt.ArrayLike, tuple[Any]], float], + bounds: Iterable | Bounds, + *, + args: tuple = (), + eps: float = 1e-4, + maxfun: int | None = None, + maxiter: int = 1000, + locally_biased: bool = True, + f_min: float = -np.inf, + f_min_rtol: float = 1e-4, + vol_tol: float = 1e-16, + len_tol: float = 1e-6, + callback: Callable[[npt.ArrayLike], None] | None = None +) -> OptimizeResult: + """ + Finds the global minimum of a function using the + DIRECT algorithm. + + Parameters + ---------- + func : callable + The objective function to be minimized. + ``func(x, *args) -> float`` + where ``x`` is an 1-D array with shape (n,) and ``args`` is a tuple of + the fixed parameters needed to completely specify the function. + bounds : sequence or `Bounds` + Bounds for variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. ``(min, max)`` pairs for each element in ``x``. + + args : tuple, optional + Any additional fixed parameters needed to + completely specify the objective function. + eps : float, optional + Minimal required difference of the objective function values + between the current best hyperrectangle and the next potentially + optimal hyperrectangle to be divided. In consequence, `eps` serves as a + tradeoff between local and global search: the smaller, the more local + the search becomes. Default is 1e-4. + maxfun : int or None, optional + Approximate upper bound on objective function evaluations. + If `None`, will be automatically set to ``1000 * N`` where ``N`` + represents the number of dimensions. Will be capped if necessary to + limit DIRECT's RAM usage to app. 1GiB. This will only occur for very + high dimensional problems and excessive `max_fun`. Default is `None`. + maxiter : int, optional + Maximum number of iterations. Default is 1000. + locally_biased : bool, optional + If `True` (default), use the locally biased variant of the + algorithm known as DIRECT_L. If `False`, use the original unbiased + DIRECT algorithm. For hard problems with many local minima, + `False` is recommended. + f_min : float, optional + Function value of the global optimum. Set this value only if the + global optimum is known. Default is ``-np.inf``, so that this + termination criterion is deactivated. + f_min_rtol : float, optional + Terminate the optimization once the relative error between the + current best minimum `f` and the supplied global minimum `f_min` + is smaller than `f_min_rtol`. This parameter is only used if + `f_min` is also set. Must lie between 0 and 1. Default is 1e-4. + vol_tol : float, optional + Terminate the optimization once the volume of the hyperrectangle + containing the lowest function value is smaller than `vol_tol` + of the complete search space. Must lie between 0 and 1. + Default is 1e-16. + len_tol : float, optional + If `locally_biased=True`, terminate the optimization once half of + the normalized maximal side length of the hyperrectangle containing + the lowest function value is smaller than `len_tol`. + If `locally_biased=False`, terminate the optimization once half of + the normalized diagonal of the hyperrectangle containing the lowest + function value is smaller than `len_tol`. Must lie between 0 and 1. + Default is 1e-6. + callback : callable, optional + A callback function with signature ``callback(xk)`` where ``xk`` + represents the best function value found so far. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. + + Notes + ----- + DIviding RECTangles (DIRECT) is a deterministic global + optimization algorithm capable of minimizing a black box function with + its variables subject to lower and upper bound constraints by sampling + potential solutions in the search space [1]_. The algorithm starts by + normalising the search space to an n-dimensional unit hypercube. + It samples the function at the center of this hypercube and at 2n + (n is the number of variables) more points, 2 in each coordinate + direction. Using these function values, DIRECT then divides the + domain into hyperrectangles, each having exactly one of the sampling + points as its center. In each iteration, DIRECT chooses, using the `eps` + parameter which defaults to 1e-4, some of the existing hyperrectangles + to be further divided. This division process continues until either the + maximum number of iterations or maximum function evaluations allowed + are exceeded, or the hyperrectangle containing the minimal value found + so far becomes small enough. If `f_min` is specified, the optimization + will stop once this function value is reached within a relative tolerance. + The locally biased variant of DIRECT (originally called DIRECT_L) [2]_ is + used by default. It makes the search more locally biased and more + efficient for cases with only a few local minima. + + A note about termination criteria: `vol_tol` refers to the volume of the + hyperrectangle containing the lowest function value found so far. This + volume decreases exponentially with increasing dimensionality of the + problem. Therefore `vol_tol` should be decreased to avoid premature + termination of the algorithm for higher dimensions. This does not hold + for `len_tol`: it refers either to half of the maximal side length + (for ``locally_biased=True``) or half of the diagonal of the + hyperrectangle (for ``locally_biased=False``). + + This code is based on the DIRECT 2.0.4 Fortran code by Gablonsky et al. at + https://ctk.math.ncsu.edu/SOFTWARE/DIRECTv204.tar.gz . + This original version was initially converted via f2c and then cleaned up + and reorganized by Steven G. Johnson, August 2007, for the NLopt project. + The `direct` function wraps the C implementation. + + .. versionadded:: 1.9.0 + + References + ---------- + .. [1] Jones, D.R., Perttunen, C.D. & Stuckman, B.E. Lipschitzian + optimization without the Lipschitz constant. J Optim Theory Appl + 79, 157-181 (1993). + .. [2] Gablonsky, J., Kelley, C. A Locally-Biased form of the DIRECT + Algorithm. Journal of Global Optimization 21, 27-37 (2001). + + Examples + -------- + The following example is a 2-D problem with four local minima: minimizing + the Styblinski-Tang function + (https://en.wikipedia.org/wiki/Test_functions_for_optimization). + + >>> from scipy.optimize import direct, Bounds + >>> def styblinski_tang(pos): + ... x, y = pos + ... return 0.5 * (x**4 - 16*x**2 + 5*x + y**4 - 16*y**2 + 5*y) + >>> bounds = Bounds([-4., -4.], [4., 4.]) + >>> result = direct(styblinski_tang, bounds) + >>> result.x, result.fun, result.nfev + array([-2.90321597, -2.90321597]), -78.3323279095383, 2011 + + The correct global minimum was found but with a huge number of function + evaluations (2011). Loosening the termination tolerances `vol_tol` and + `len_tol` can be used to stop DIRECT earlier. + + >>> result = direct(styblinski_tang, bounds, len_tol=1e-3) + >>> result.x, result.fun, result.nfev + array([-2.9044353, -2.9044353]), -78.33230330754142, 207 + + """ + # convert bounds to new Bounds class if necessary + if not isinstance(bounds, Bounds): + if isinstance(bounds, list) or isinstance(bounds, tuple): + lb, ub = old_bound_to_new(bounds) + bounds = Bounds(lb, ub) + else: + message = ("bounds must be a sequence or " + "instance of Bounds class") + raise ValueError(message) + + lb = np.ascontiguousarray(bounds.lb, dtype=np.float64) + ub = np.ascontiguousarray(bounds.ub, dtype=np.float64) + + # validate bounds + # check that lower bounds are smaller than upper bounds + if not np.all(lb < ub): + raise ValueError('Bounds are not consistent min < max') + # check for infs + if (np.any(np.isinf(lb)) or np.any(np.isinf(ub))): + raise ValueError("Bounds must not be inf.") + + # validate tolerances + if (vol_tol < 0 or vol_tol > 1): + raise ValueError("vol_tol must be between 0 and 1.") + if (len_tol < 0 or len_tol > 1): + raise ValueError("len_tol must be between 0 and 1.") + if (f_min_rtol < 0 or f_min_rtol > 1): + raise ValueError("f_min_rtol must be between 0 and 1.") + + # validate maxfun and maxiter + if maxfun is None: + maxfun = 1000 * lb.shape[0] + if not isinstance(maxfun, int): + raise ValueError("maxfun must be of type int.") + if maxfun < 0: + raise ValueError("maxfun must be > 0.") + if not isinstance(maxiter, int): + raise ValueError("maxiter must be of type int.") + if maxiter < 0: + raise ValueError("maxiter must be > 0.") + + # validate boolean parameters + if not isinstance(locally_biased, bool): + raise ValueError("locally_biased must be True or False.") + + def _func_wrap(x, args=None): + x = np.asarray(x) + if args is None: + f = func(x) + else: + f = func(x, *args) + # always return a float + return np.asarray(f).item() + + # TODO: fix disp argument + x, fun, ret_code, nfev, nit = _direct( + _func_wrap, + np.asarray(lb), np.asarray(ub), + args, + False, eps, maxfun, maxiter, + locally_biased, + f_min, f_min_rtol, + vol_tol, len_tol, callback + ) + + format_val = (maxfun, maxiter, f_min_rtol, vol_tol, len_tol) + if ret_code > 2: + message = SUCCESS_MESSAGES[ret_code - 3].format( + format_val[ret_code - 1]) + elif 0 < ret_code <= 2: + message = ERROR_MESSAGES[ret_code - 1].format(format_val[ret_code - 1]) + elif 0 > ret_code > -100: + message = ERROR_MESSAGES[abs(ret_code) + 1] + else: + message = ERROR_MESSAGES[ret_code + 99] + + return OptimizeResult(x=np.asarray(x), fun=fun, status=ret_code, + success=ret_code > 2, message=message, + nfev=nfev, nit=nit) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dual_annealing.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dual_annealing.py new file mode 100644 index 0000000000000000000000000000000000000000..9645c7967b96772463d4cbe41e905195273ba1ae --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_dual_annealing.py @@ -0,0 +1,732 @@ +# Dual Annealing implementation. +# Copyright (c) 2018 Sylvain Gubian , +# Yang Xiang +# Author: Sylvain Gubian, Yang Xiang, PMP S.A. + +""" +A Dual Annealing global optimization algorithm +""" + +import numpy as np +from scipy.optimize import OptimizeResult +from scipy.optimize import minimize, Bounds +from scipy.special import gammaln +from scipy._lib._util import check_random_state +from scipy.optimize._constraints import new_bounds_to_old + +__all__ = ['dual_annealing'] + + +class VisitingDistribution: + """ + Class used to generate new coordinates based on the distorted + Cauchy-Lorentz distribution. Depending on the steps within the strategy + chain, the class implements the strategy for generating new location + changes. + + Parameters + ---------- + lb : array_like + A 1-D NumPy ndarray containing lower bounds of the generated + components. Neither NaN or inf are allowed. + ub : array_like + A 1-D NumPy ndarray containing upper bounds for the generated + components. Neither NaN or inf are allowed. + visiting_param : float + Parameter for visiting distribution. Default value is 2.62. + Higher values give the visiting distribution a heavier tail, this + makes the algorithm jump to a more distant region. + The value range is (1, 3]. Its value is fixed for the life of the + object. + rand_gen : {`~numpy.random.RandomState`, `~numpy.random.Generator`} + A `~numpy.random.RandomState`, `~numpy.random.Generator` object + for using the current state of the created random generator container. + + """ + TAIL_LIMIT = 1.e8 + MIN_VISIT_BOUND = 1.e-10 + + def __init__(self, lb, ub, visiting_param, rand_gen): + # if you wish to make _visiting_param adjustable during the life of + # the object then _factor2, _factor3, _factor5, _d1, _factor6 will + # have to be dynamically calculated in `visit_fn`. They're factored + # out here so they don't need to be recalculated all the time. + self._visiting_param = visiting_param + self.rand_gen = rand_gen + self.lower = lb + self.upper = ub + self.bound_range = ub - lb + + # these are invariant numbers unless visiting_param changes + self._factor2 = np.exp((4.0 - self._visiting_param) * np.log( + self._visiting_param - 1.0)) + self._factor3 = np.exp((2.0 - self._visiting_param) * np.log(2.0) + / (self._visiting_param - 1.0)) + self._factor4_p = np.sqrt(np.pi) * self._factor2 / (self._factor3 * ( + 3.0 - self._visiting_param)) + + self._factor5 = 1.0 / (self._visiting_param - 1.0) - 0.5 + self._d1 = 2.0 - self._factor5 + self._factor6 = np.pi * (1.0 - self._factor5) / np.sin( + np.pi * (1.0 - self._factor5)) / np.exp(gammaln(self._d1)) + + def visiting(self, x, step, temperature): + """ Based on the step in the strategy chain, new coordinates are + generated by changing all components is the same time or only + one of them, the new values are computed with visit_fn method + """ + dim = x.size + if step < dim: + # Changing all coordinates with a new visiting value + visits = self.visit_fn(temperature, dim) + upper_sample, lower_sample = self.rand_gen.uniform(size=2) + visits[visits > self.TAIL_LIMIT] = self.TAIL_LIMIT * upper_sample + visits[visits < -self.TAIL_LIMIT] = -self.TAIL_LIMIT * lower_sample + x_visit = visits + x + a = x_visit - self.lower + b = np.fmod(a, self.bound_range) + self.bound_range + x_visit = np.fmod(b, self.bound_range) + self.lower + x_visit[np.fabs( + x_visit - self.lower) < self.MIN_VISIT_BOUND] += 1.e-10 + else: + # Changing only one coordinate at a time based on strategy + # chain step + x_visit = np.copy(x) + visit = self.visit_fn(temperature, 1)[0] + if visit > self.TAIL_LIMIT: + visit = self.TAIL_LIMIT * self.rand_gen.uniform() + elif visit < -self.TAIL_LIMIT: + visit = -self.TAIL_LIMIT * self.rand_gen.uniform() + index = step - dim + x_visit[index] = visit + x[index] + a = x_visit[index] - self.lower[index] + b = np.fmod(a, self.bound_range[index]) + self.bound_range[index] + x_visit[index] = np.fmod(b, self.bound_range[ + index]) + self.lower[index] + if np.fabs(x_visit[index] - self.lower[ + index]) < self.MIN_VISIT_BOUND: + x_visit[index] += self.MIN_VISIT_BOUND + return x_visit + + def visit_fn(self, temperature, dim): + """ Formula Visita from p. 405 of reference [2] """ + x, y = self.rand_gen.normal(size=(dim, 2)).T + + factor1 = np.exp(np.log(temperature) / (self._visiting_param - 1.0)) + factor4 = self._factor4_p * factor1 + + # sigmax + x *= np.exp(-(self._visiting_param - 1.0) * np.log( + self._factor6 / factor4) / (3.0 - self._visiting_param)) + + den = np.exp((self._visiting_param - 1.0) * np.log(np.fabs(y)) / + (3.0 - self._visiting_param)) + + return x / den + + +class EnergyState: + """ + Class used to record the energy state. At any time, it knows what is the + currently used coordinates and the most recent best location. + + Parameters + ---------- + lower : array_like + A 1-D NumPy ndarray containing lower bounds for generating an initial + random components in the `reset` method. + upper : array_like + A 1-D NumPy ndarray containing upper bounds for generating an initial + random components in the `reset` method + components. Neither NaN or inf are allowed. + callback : callable, ``callback(x, f, context)``, optional + A callback function which will be called for all minima found. + ``x`` and ``f`` are the coordinates and function value of the + latest minimum found, and `context` has value in [0, 1, 2] + """ + # Maximum number of trials for generating a valid starting point + MAX_REINIT_COUNT = 1000 + + def __init__(self, lower, upper, callback=None): + self.ebest = None + self.current_energy = None + self.current_location = None + self.xbest = None + self.lower = lower + self.upper = upper + self.callback = callback + + def reset(self, func_wrapper, rand_gen, x0=None): + """ + Initialize current location is the search domain. If `x0` is not + provided, a random location within the bounds is generated. + """ + if x0 is None: + self.current_location = rand_gen.uniform(self.lower, self.upper, + size=len(self.lower)) + else: + self.current_location = np.copy(x0) + init_error = True + reinit_counter = 0 + while init_error: + self.current_energy = func_wrapper.fun(self.current_location) + if self.current_energy is None: + raise ValueError('Objective function is returning None') + if (not np.isfinite(self.current_energy) or np.isnan( + self.current_energy)): + if reinit_counter >= EnergyState.MAX_REINIT_COUNT: + init_error = False + message = ( + 'Stopping algorithm because function ' + 'create NaN or (+/-) infinity values even with ' + 'trying new random parameters' + ) + raise ValueError(message) + self.current_location = rand_gen.uniform(self.lower, + self.upper, + size=self.lower.size) + reinit_counter += 1 + else: + init_error = False + # If first time reset, initialize ebest and xbest + if self.ebest is None and self.xbest is None: + self.ebest = self.current_energy + self.xbest = np.copy(self.current_location) + # Otherwise, we keep them in case of reannealing reset + + def update_best(self, e, x, context): + self.ebest = e + self.xbest = np.copy(x) + if self.callback is not None: + val = self.callback(x, e, context) + if val is not None: + if val: + return ('Callback function requested to stop early by ' + 'returning True') + + def update_current(self, e, x): + self.current_energy = e + self.current_location = np.copy(x) + + +class StrategyChain: + """ + Class that implements within a Markov chain the strategy for location + acceptance and local search decision making. + + Parameters + ---------- + acceptance_param : float + Parameter for acceptance distribution. It is used to control the + probability of acceptance. The lower the acceptance parameter, the + smaller the probability of acceptance. Default value is -5.0 with + a range (-1e4, -5]. + visit_dist : VisitingDistribution + Instance of `VisitingDistribution` class. + func_wrapper : ObjectiveFunWrapper + Instance of `ObjectiveFunWrapper` class. + minimizer_wrapper: LocalSearchWrapper + Instance of `LocalSearchWrapper` class. + rand_gen : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + energy_state: EnergyState + Instance of `EnergyState` class. + + """ + + def __init__(self, acceptance_param, visit_dist, func_wrapper, + minimizer_wrapper, rand_gen, energy_state): + # Local strategy chain minimum energy and location + self.emin = energy_state.current_energy + self.xmin = np.array(energy_state.current_location) + # Global optimizer state + self.energy_state = energy_state + # Acceptance parameter + self.acceptance_param = acceptance_param + # Visiting distribution instance + self.visit_dist = visit_dist + # Wrapper to objective function + self.func_wrapper = func_wrapper + # Wrapper to the local minimizer + self.minimizer_wrapper = minimizer_wrapper + self.not_improved_idx = 0 + self.not_improved_max_idx = 1000 + self._rand_gen = rand_gen + self.temperature_step = 0 + self.K = 100 * len(energy_state.current_location) + + def accept_reject(self, j, e, x_visit): + r = self._rand_gen.uniform() + pqv_temp = 1.0 - ((1.0 - self.acceptance_param) * + (e - self.energy_state.current_energy) / self.temperature_step) + if pqv_temp <= 0.: + pqv = 0. + else: + pqv = np.exp(np.log(pqv_temp) / ( + 1. - self.acceptance_param)) + + if r <= pqv: + # We accept the new location and update state + self.energy_state.update_current(e, x_visit) + self.xmin = np.copy(self.energy_state.current_location) + + # No improvement for a long time + if self.not_improved_idx >= self.not_improved_max_idx: + if j == 0 or self.energy_state.current_energy < self.emin: + self.emin = self.energy_state.current_energy + self.xmin = np.copy(self.energy_state.current_location) + + def run(self, step, temperature): + self.temperature_step = temperature / float(step + 1) + self.not_improved_idx += 1 + for j in range(self.energy_state.current_location.size * 2): + if j == 0: + if step == 0: + self.energy_state_improved = True + else: + self.energy_state_improved = False + x_visit = self.visit_dist.visiting( + self.energy_state.current_location, j, temperature) + # Calling the objective function + e = self.func_wrapper.fun(x_visit) + if e < self.energy_state.current_energy: + # We have got a better energy value + self.energy_state.update_current(e, x_visit) + if e < self.energy_state.ebest: + val = self.energy_state.update_best(e, x_visit, 0) + if val is not None: + if val: + return val + self.energy_state_improved = True + self.not_improved_idx = 0 + else: + # We have not improved but do we accept the new location? + self.accept_reject(j, e, x_visit) + if self.func_wrapper.nfev >= self.func_wrapper.maxfun: + return ('Maximum number of function call reached ' + 'during annealing') + # End of StrategyChain loop + + def local_search(self): + # Decision making for performing a local search + # based on strategy chain results + # If energy has been improved or no improvement since too long, + # performing a local search with the best strategy chain location + if self.energy_state_improved: + # Global energy has improved, let's see if LS improves further + e, x = self.minimizer_wrapper.local_search(self.energy_state.xbest, + self.energy_state.ebest) + if e < self.energy_state.ebest: + self.not_improved_idx = 0 + val = self.energy_state.update_best(e, x, 1) + if val is not None: + if val: + return val + self.energy_state.update_current(e, x) + if self.func_wrapper.nfev >= self.func_wrapper.maxfun: + return ('Maximum number of function call reached ' + 'during local search') + # Check probability of a need to perform a LS even if no improvement + do_ls = False + if self.K < 90 * len(self.energy_state.current_location): + pls = np.exp(self.K * ( + self.energy_state.ebest - self.energy_state.current_energy) / + self.temperature_step) + if pls >= self._rand_gen.uniform(): + do_ls = True + # Global energy not improved, let's see what LS gives + # on the best strategy chain location + if self.not_improved_idx >= self.not_improved_max_idx: + do_ls = True + if do_ls: + e, x = self.minimizer_wrapper.local_search(self.xmin, self.emin) + self.xmin = np.copy(x) + self.emin = e + self.not_improved_idx = 0 + self.not_improved_max_idx = self.energy_state.current_location.size + if e < self.energy_state.ebest: + val = self.energy_state.update_best( + self.emin, self.xmin, 2) + if val is not None: + if val: + return val + self.energy_state.update_current(e, x) + if self.func_wrapper.nfev >= self.func_wrapper.maxfun: + return ('Maximum number of function call reached ' + 'during dual annealing') + + +class ObjectiveFunWrapper: + + def __init__(self, func, maxfun=1e7, *args): + self.func = func + self.args = args + # Number of objective function evaluations + self.nfev = 0 + # Number of gradient function evaluation if used + self.ngev = 0 + # Number of hessian of the objective function if used + self.nhev = 0 + self.maxfun = maxfun + + def fun(self, x): + self.nfev += 1 + return self.func(x, *self.args) + + +class LocalSearchWrapper: + """ + Class used to wrap around the minimizer used for local search + Default local minimizer is SciPy minimizer L-BFGS-B + """ + + LS_MAXITER_RATIO = 6 + LS_MAXITER_MIN = 100 + LS_MAXITER_MAX = 1000 + + def __init__(self, search_bounds, func_wrapper, *args, **kwargs): + self.func_wrapper = func_wrapper + self.kwargs = kwargs + self.jac = self.kwargs.get('jac', None) + self.hess = self.kwargs.get('hess', None) + self.hessp = self.kwargs.get('hessp', None) + self.kwargs.pop("args", None) + self.minimizer = minimize + bounds_list = list(zip(*search_bounds)) + self.lower = np.array(bounds_list[0]) + self.upper = np.array(bounds_list[1]) + + # If no minimizer specified, use SciPy minimize with 'L-BFGS-B' method + if not self.kwargs: + n = len(self.lower) + ls_max_iter = min(max(n * self.LS_MAXITER_RATIO, + self.LS_MAXITER_MIN), + self.LS_MAXITER_MAX) + self.kwargs['method'] = 'L-BFGS-B' + self.kwargs['options'] = { + 'maxiter': ls_max_iter, + } + self.kwargs['bounds'] = list(zip(self.lower, self.upper)) + else: + if callable(self.jac): + def wrapped_jac(x): + return self.jac(x, *args) + self.kwargs['jac'] = wrapped_jac + if callable(self.hess): + def wrapped_hess(x): + return self.hess(x, *args) + self.kwargs['hess'] = wrapped_hess + if callable(self.hessp): + def wrapped_hessp(x, p): + return self.hessp(x, p, *args) + self.kwargs['hessp'] = wrapped_hessp + + def local_search(self, x, e): + # Run local search from the given x location where energy value is e + x_tmp = np.copy(x) + mres = self.minimizer(self.func_wrapper.fun, x, **self.kwargs) + if 'njev' in mres: + self.func_wrapper.ngev += mres.njev + if 'nhev' in mres: + self.func_wrapper.nhev += mres.nhev + # Check if is valid value + is_finite = np.all(np.isfinite(mres.x)) and np.isfinite(mres.fun) + in_bounds = np.all(mres.x >= self.lower) and np.all( + mres.x <= self.upper) + is_valid = is_finite and in_bounds + + # Use the new point only if it is valid and return a better results + if is_valid and mres.fun < e: + return mres.fun, mres.x + else: + return e, x_tmp + + +def dual_annealing(func, bounds, args=(), maxiter=1000, + minimizer_kwargs=None, initial_temp=5230., + restart_temp_ratio=2.e-5, visit=2.62, accept=-5.0, + maxfun=1e7, seed=None, no_local_search=False, + callback=None, x0=None): + """ + Find the global minimum of a function using Dual Annealing. + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. + bounds : sequence or `Bounds` + Bounds for variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. Sequence of ``(min, max)`` pairs for each element in `x`. + + args : tuple, optional + Any additional fixed parameters needed to completely specify the + objective function. + maxiter : int, optional + The maximum number of global search iterations. Default value is 1000. + minimizer_kwargs : dict, optional + Keyword arguments to be passed to the local minimizer + (`minimize`). An important option could be ``method`` for the minimizer + method to use. + If no keyword arguments are provided, the local minimizer defaults to + 'L-BFGS-B' and uses the already supplied bounds. If `minimizer_kwargs` + is specified, then the dict must contain all parameters required to + control the local minimization. `args` is ignored in this dict, as it is + passed automatically. `bounds` is not automatically passed on to the + local minimizer as the method may not support them. + initial_temp : float, optional + The initial temperature, use higher values to facilitates a wider + search of the energy landscape, allowing dual_annealing to escape + local minima that it is trapped in. Default value is 5230. Range is + (0.01, 5.e4]. + restart_temp_ratio : float, optional + During the annealing process, temperature is decreasing, when it + reaches ``initial_temp * restart_temp_ratio``, the reannealing process + is triggered. Default value of the ratio is 2e-5. Range is (0, 1). + visit : float, optional + Parameter for visiting distribution. Default value is 2.62. Higher + values give the visiting distribution a heavier tail, this makes + the algorithm jump to a more distant region. The value range is (1, 3]. + accept : float, optional + Parameter for acceptance distribution. It is used to control the + probability of acceptance. The lower the acceptance parameter, the + smaller the probability of acceptance. Default value is -5.0 with + a range (-1e4, -5]. + maxfun : int, optional + Soft limit for the number of objective function calls. If the + algorithm is in the middle of a local search, this number will be + exceeded, the algorithm will stop just after the local search is + done. Default value is 1e7. + seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Specify `seed` for repeatable minimizations. The random numbers + generated with this seed only affect the visiting distribution function + and new coordinates generation. + no_local_search : bool, optional + If `no_local_search` is set to True, a traditional Generalized + Simulated Annealing will be performed with no local search + strategy applied. + callback : callable, optional + A callback function with signature ``callback(x, f, context)``, + which will be called for all minima found. + ``x`` and ``f`` are the coordinates and function value of the + latest minimum found, and ``context`` has value in [0, 1, 2], with the + following meaning: + + - 0: minimum detected in the annealing process. + - 1: detection occurred in the local search process. + - 2: detection done in the dual annealing process. + + If the callback implementation returns True, the algorithm will stop. + x0 : ndarray, shape(n,), optional + Coordinates of a single N-D starting point. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: ``x`` the solution array, ``fun`` the value + of the function at the solution, and ``message`` which describes the + cause of the termination. + See `OptimizeResult` for a description of other attributes. + + Notes + ----- + This function implements the Dual Annealing optimization. This stochastic + approach derived from [3]_ combines the generalization of CSA (Classical + Simulated Annealing) and FSA (Fast Simulated Annealing) [1]_ [2]_ coupled + to a strategy for applying a local search on accepted locations [4]_. + An alternative implementation of this same algorithm is described in [5]_ + and benchmarks are presented in [6]_. This approach introduces an advanced + method to refine the solution found by the generalized annealing + process. This algorithm uses a distorted Cauchy-Lorentz visiting + distribution, with its shape controlled by the parameter :math:`q_{v}` + + .. math:: + + g_{q_{v}}(\\Delta x(t)) \\propto \\frac{ \\ + \\left[T_{q_{v}}(t) \\right]^{-\\frac{D}{3-q_{v}}}}{ \\ + \\left[{1+(q_{v}-1)\\frac{(\\Delta x(t))^{2}} { \\ + \\left[T_{q_{v}}(t)\\right]^{\\frac{2}{3-q_{v}}}}}\\right]^{ \\ + \\frac{1}{q_{v}-1}+\\frac{D-1}{2}}} + + Where :math:`t` is the artificial time. This visiting distribution is used + to generate a trial jump distance :math:`\\Delta x(t)` of variable + :math:`x(t)` under artificial temperature :math:`T_{q_{v}}(t)`. + + From the starting point, after calling the visiting distribution + function, the acceptance probability is computed as follows: + + .. math:: + + p_{q_{a}} = \\min{\\{1,\\left[1-(1-q_{a}) \\beta \\Delta E \\right]^{ \\ + \\frac{1}{1-q_{a}}}\\}} + + Where :math:`q_{a}` is a acceptance parameter. For :math:`q_{a}<1`, zero + acceptance probability is assigned to the cases where + + .. math:: + + [1-(1-q_{a}) \\beta \\Delta E] < 0 + + The artificial temperature :math:`T_{q_{v}}(t)` is decreased according to + + .. math:: + + T_{q_{v}}(t) = T_{q_{v}}(1) \\frac{2^{q_{v}-1}-1}{\\left( \\ + 1 + t\\right)^{q_{v}-1}-1} + + Where :math:`q_{v}` is the visiting parameter. + + .. versionadded:: 1.2.0 + + References + ---------- + .. [1] Tsallis C. Possible generalization of Boltzmann-Gibbs + statistics. Journal of Statistical Physics, 52, 479-487 (1998). + .. [2] Tsallis C, Stariolo DA. Generalized Simulated Annealing. + Physica A, 233, 395-406 (1996). + .. [3] Xiang Y, Sun DY, Fan W, Gong XG. Generalized Simulated + Annealing Algorithm and Its Application to the Thomson Model. + Physics Letters A, 233, 216-220 (1997). + .. [4] Xiang Y, Gong XG. Efficiency of Generalized Simulated + Annealing. Physical Review E, 62, 4473 (2000). + .. [5] Xiang Y, Gubian S, Suomela B, Hoeng J. Generalized + Simulated Annealing for Efficient Global Optimization: the GenSA + Package for R. The R Journal, Volume 5/1 (2013). + .. [6] Mullen, K. Continuous Global Optimization in R. Journal of + Statistical Software, 60(6), 1 - 45, (2014). + :doi:`10.18637/jss.v060.i06` + + Examples + -------- + The following example is a 10-D problem, with many local minima. + The function involved is called Rastrigin + (https://en.wikipedia.org/wiki/Rastrigin_function) + + >>> import numpy as np + >>> from scipy.optimize import dual_annealing + >>> func = lambda x: np.sum(x*x - 10*np.cos(2*np.pi*x)) + 10*np.size(x) + >>> lw = [-5.12] * 10 + >>> up = [5.12] * 10 + >>> ret = dual_annealing(func, bounds=list(zip(lw, up))) + >>> ret.x + array([-4.26437714e-09, -3.91699361e-09, -1.86149218e-09, -3.97165720e-09, + -6.29151648e-09, -6.53145322e-09, -3.93616815e-09, -6.55623025e-09, + -6.05775280e-09, -5.00668935e-09]) # random + >>> ret.fun + 0.000000 + + """ + + if isinstance(bounds, Bounds): + bounds = new_bounds_to_old(bounds.lb, bounds.ub, len(bounds.lb)) + + if x0 is not None and not len(x0) == len(bounds): + raise ValueError('Bounds size does not match x0') + + lu = list(zip(*bounds)) + lower = np.array(lu[0]) + upper = np.array(lu[1]) + # Check that restart temperature ratio is correct + if restart_temp_ratio <= 0. or restart_temp_ratio >= 1.: + raise ValueError('Restart temperature ratio has to be in range (0, 1)') + # Checking bounds are valid + if (np.any(np.isinf(lower)) or np.any(np.isinf(upper)) or np.any( + np.isnan(lower)) or np.any(np.isnan(upper))): + raise ValueError('Some bounds values are inf values or nan values') + # Checking that bounds are consistent + if not np.all(lower < upper): + raise ValueError('Bounds are not consistent min < max') + # Checking that bounds are the same length + if not len(lower) == len(upper): + raise ValueError('Bounds do not have the same dimensions') + + # Wrapper for the objective function + func_wrapper = ObjectiveFunWrapper(func, maxfun, *args) + + # minimizer_kwargs has to be a dict, not None + minimizer_kwargs = minimizer_kwargs or {} + + minimizer_wrapper = LocalSearchWrapper( + bounds, func_wrapper, *args, **minimizer_kwargs) + + # Initialization of random Generator for reproducible runs if seed provided + rand_state = check_random_state(seed) + # Initialization of the energy state + energy_state = EnergyState(lower, upper, callback) + energy_state.reset(func_wrapper, rand_state, x0) + # Minimum value of annealing temperature reached to perform + # re-annealing + temperature_restart = initial_temp * restart_temp_ratio + # VisitingDistribution instance + visit_dist = VisitingDistribution(lower, upper, visit, rand_state) + # Strategy chain instance + strategy_chain = StrategyChain(accept, visit_dist, func_wrapper, + minimizer_wrapper, rand_state, energy_state) + need_to_stop = False + iteration = 0 + message = [] + # OptimizeResult object to be returned + optimize_res = OptimizeResult() + optimize_res.success = True + optimize_res.status = 0 + + t1 = np.exp((visit - 1) * np.log(2.0)) - 1.0 + # Run the search loop + while not need_to_stop: + for i in range(maxiter): + # Compute temperature for this step + s = float(i) + 2.0 + t2 = np.exp((visit - 1) * np.log(s)) - 1.0 + temperature = initial_temp * t1 / t2 + if iteration >= maxiter: + message.append("Maximum number of iteration reached") + need_to_stop = True + break + # Need a re-annealing process? + if temperature < temperature_restart: + energy_state.reset(func_wrapper, rand_state) + break + # starting strategy chain + val = strategy_chain.run(i, temperature) + if val is not None: + message.append(val) + need_to_stop = True + optimize_res.success = False + break + # Possible local search at the end of the strategy chain + if not no_local_search: + val = strategy_chain.local_search() + if val is not None: + message.append(val) + need_to_stop = True + optimize_res.success = False + break + iteration += 1 + + # Setting the OptimizeResult values + optimize_res.x = energy_state.xbest + optimize_res.fun = energy_state.ebest + optimize_res.nit = iteration + optimize_res.nfev = func_wrapper.nfev + optimize_res.njev = func_wrapper.ngev + optimize_res.nhev = func_wrapper.nhev + optimize_res.message = message + return optimize_res diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_group_columns.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_group_columns.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..6bf365e82423d10a4e2fe926977e1e1167aab4e5 Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_group_columns.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_hessian_update_strategy.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_hessian_update_strategy.py new file mode 100644 index 0000000000000000000000000000000000000000..c72d1159314e0ea449085df44ef80d1d0dbb1ebb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_hessian_update_strategy.py @@ -0,0 +1,475 @@ +"""Hessian update strategies for quasi-Newton optimization methods.""" +import numpy as np +from numpy.linalg import norm +from scipy.linalg import get_blas_funcs, issymmetric +from warnings import warn + + +__all__ = ['HessianUpdateStrategy', 'BFGS', 'SR1'] + + +class HessianUpdateStrategy: + """Interface for implementing Hessian update strategies. + + Many optimization methods make use of Hessian (or inverse Hessian) + approximations, such as the quasi-Newton methods BFGS, SR1, L-BFGS. + Some of these approximations, however, do not actually need to store + the entire matrix or can compute the internal matrix product with a + given vector in a very efficiently manner. This class serves as an + abstract interface between the optimization algorithm and the + quasi-Newton update strategies, giving freedom of implementation + to store and update the internal matrix as efficiently as possible. + Different choices of initialization and update procedure will result + in different quasi-Newton strategies. + + Four methods should be implemented in derived classes: ``initialize``, + ``update``, ``dot`` and ``get_matrix``. + + Notes + ----- + Any instance of a class that implements this interface, + can be accepted by the method ``minimize`` and used by + the compatible solvers to approximate the Hessian (or + inverse Hessian) used by the optimization algorithms. + """ + + def initialize(self, n, approx_type): + """Initialize internal matrix. + + Allocate internal memory for storing and updating + the Hessian or its inverse. + + Parameters + ---------- + n : int + Problem dimension. + approx_type : {'hess', 'inv_hess'} + Selects either the Hessian or the inverse Hessian. + When set to 'hess' the Hessian will be stored and updated. + When set to 'inv_hess' its inverse will be used instead. + """ + raise NotImplementedError("The method ``initialize(n, approx_type)``" + " is not implemented.") + + def update(self, delta_x, delta_grad): + """Update internal matrix. + + Update Hessian matrix or its inverse (depending on how 'approx_type' + is defined) using information about the last evaluated points. + + Parameters + ---------- + delta_x : ndarray + The difference between two points the gradient + function have been evaluated at: ``delta_x = x2 - x1``. + delta_grad : ndarray + The difference between the gradients: + ``delta_grad = grad(x2) - grad(x1)``. + """ + raise NotImplementedError("The method ``update(delta_x, delta_grad)``" + " is not implemented.") + + def dot(self, p): + """Compute the product of the internal matrix with the given vector. + + Parameters + ---------- + p : array_like + 1-D array representing a vector. + + Returns + ------- + Hp : array + 1-D represents the result of multiplying the approximation matrix + by vector p. + """ + raise NotImplementedError("The method ``dot(p)``" + " is not implemented.") + + def get_matrix(self): + """Return current internal matrix. + + Returns + ------- + H : ndarray, shape (n, n) + Dense matrix containing either the Hessian + or its inverse (depending on how 'approx_type' + is defined). + """ + raise NotImplementedError("The method ``get_matrix(p)``" + " is not implemented.") + + +class FullHessianUpdateStrategy(HessianUpdateStrategy): + """Hessian update strategy with full dimensional internal representation. + """ + _syr = get_blas_funcs('syr', dtype='d') # Symmetric rank 1 update + _syr2 = get_blas_funcs('syr2', dtype='d') # Symmetric rank 2 update + # Symmetric matrix-vector product + _symv = get_blas_funcs('symv', dtype='d') + + def __init__(self, init_scale='auto'): + self.init_scale = init_scale + # Until initialize is called we can't really use the class, + # so it makes sense to set everything to None. + self.first_iteration = None + self.approx_type = None + self.B = None + self.H = None + + def initialize(self, n, approx_type): + """Initialize internal matrix. + + Allocate internal memory for storing and updating + the Hessian or its inverse. + + Parameters + ---------- + n : int + Problem dimension. + approx_type : {'hess', 'inv_hess'} + Selects either the Hessian or the inverse Hessian. + When set to 'hess' the Hessian will be stored and updated. + When set to 'inv_hess' its inverse will be used instead. + """ + self.first_iteration = True + self.n = n + self.approx_type = approx_type + if approx_type not in ('hess', 'inv_hess'): + raise ValueError("`approx_type` must be 'hess' or 'inv_hess'.") + # Create matrix + if self.approx_type == 'hess': + self.B = np.eye(n, dtype=float) + else: + self.H = np.eye(n, dtype=float) + + def _auto_scale(self, delta_x, delta_grad): + # Heuristic to scale matrix at first iteration. + # Described in Nocedal and Wright "Numerical Optimization" + # p.143 formula (6.20). + s_norm2 = np.dot(delta_x, delta_x) + y_norm2 = np.dot(delta_grad, delta_grad) + ys = np.abs(np.dot(delta_grad, delta_x)) + if ys == 0.0 or y_norm2 == 0 or s_norm2 == 0: + return 1 + if self.approx_type == 'hess': + return y_norm2 / ys + else: + return ys / y_norm2 + + def _update_implementation(self, delta_x, delta_grad): + raise NotImplementedError("The method ``_update_implementation``" + " is not implemented.") + + def update(self, delta_x, delta_grad): + """Update internal matrix. + + Update Hessian matrix or its inverse (depending on how 'approx_type' + is defined) using information about the last evaluated points. + + Parameters + ---------- + delta_x : ndarray + The difference between two points the gradient + function have been evaluated at: ``delta_x = x2 - x1``. + delta_grad : ndarray + The difference between the gradients: + ``delta_grad = grad(x2) - grad(x1)``. + """ + if np.all(delta_x == 0.0): + return + if np.all(delta_grad == 0.0): + warn('delta_grad == 0.0. Check if the approximated ' + 'function is linear. If the function is linear ' + 'better results can be obtained by defining the ' + 'Hessian as zero instead of using quasi-Newton ' + 'approximations.', + UserWarning, stacklevel=2) + return + if self.first_iteration: + # Get user specific scale + if isinstance(self.init_scale, str) and self.init_scale == "auto": + scale = self._auto_scale(delta_x, delta_grad) + else: + scale = self.init_scale + + # Check for complex: numpy will silently cast a complex array to + # a real one but not so for scalar as it raises a TypeError. + # Checking here brings a consistent behavior. + replace = False + if np.size(scale) == 1: + # to account for the legacy behavior having the exact same cast + scale = float(scale) + elif np.iscomplexobj(scale): + raise TypeError("init_scale contains complex elements, " + "must be real.") + else: # test explicitly for allowed shapes and values + replace = True + if self.approx_type == 'hess': + shape = np.shape(self.B) + dtype = self.B.dtype + else: + shape = np.shape(self.H) + dtype = self.H.dtype + # copy, will replace the original + scale = np.array(scale, dtype=dtype, copy=True) + + # it has to match the shape of the matrix for the multiplication, + # no implicit broadcasting is allowed + if shape != (init_shape := np.shape(scale)): + raise ValueError("If init_scale is an array, it must have the " + f"dimensions of the hess/inv_hess: {shape}." + f" Got {init_shape}.") + if not issymmetric(scale): + raise ValueError("If init_scale is an array, it must be" + " symmetric (passing scipy.linalg.issymmetric)" + " to be an approximation of a hess/inv_hess.") + + # Scale initial matrix with ``scale * np.eye(n)`` or replace + # This is not ideal, we could assign the scale directly in + # initialize, but we would need to + if self.approx_type == 'hess': + if replace: + self.B = scale + else: + self.B *= scale + else: + if replace: + self.H = scale + else: + self.H *= scale + self.first_iteration = False + self._update_implementation(delta_x, delta_grad) + + def dot(self, p): + """Compute the product of the internal matrix with the given vector. + + Parameters + ---------- + p : array_like + 1-D array representing a vector. + + Returns + ------- + Hp : array + 1-D represents the result of multiplying the approximation matrix + by vector p. + """ + if self.approx_type == 'hess': + return self._symv(1, self.B, p) + else: + return self._symv(1, self.H, p) + + def get_matrix(self): + """Return the current internal matrix. + + Returns + ------- + M : ndarray, shape (n, n) + Dense matrix containing either the Hessian or its inverse + (depending on how `approx_type` was defined). + """ + if self.approx_type == 'hess': + M = np.copy(self.B) + else: + M = np.copy(self.H) + li = np.tril_indices_from(M, k=-1) + M[li] = M.T[li] + return M + + +class BFGS(FullHessianUpdateStrategy): + """Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy. + + Parameters + ---------- + exception_strategy : {'skip_update', 'damp_update'}, optional + Define how to proceed when the curvature condition is violated. + Set it to 'skip_update' to just skip the update. Or, alternatively, + set it to 'damp_update' to interpolate between the actual BFGS + result and the unmodified matrix. Both exceptions strategies + are explained in [1]_, p.536-537. + min_curvature : float + This number, scaled by a normalization factor, defines the + minimum curvature ``dot(delta_grad, delta_x)`` allowed to go + unaffected by the exception strategy. By default is equal to + 1e-8 when ``exception_strategy = 'skip_update'`` and equal + to 0.2 when ``exception_strategy = 'damp_update'``. + init_scale : {float, np.array, 'auto'} + This parameter can be used to initialize the Hessian or its + inverse. When a float is given, the relevant array is initialized + to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension. + Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given, + this array will be used. Otherwise an error is generated. + Set it to 'auto' in order to use an automatic heuristic for choosing + the initial scale. The heuristic is described in [1]_, p.143. + The default is 'auto'. + + Notes + ----- + The update is based on the description in [1]_, p.140. + + References + ---------- + .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" + Second Edition (2006). + """ + + def __init__(self, exception_strategy='skip_update', min_curvature=None, + init_scale='auto'): + if exception_strategy == 'skip_update': + if min_curvature is not None: + self.min_curvature = min_curvature + else: + self.min_curvature = 1e-8 + elif exception_strategy == 'damp_update': + if min_curvature is not None: + self.min_curvature = min_curvature + else: + self.min_curvature = 0.2 + else: + raise ValueError("`exception_strategy` must be 'skip_update' " + "or 'damp_update'.") + + super().__init__(init_scale) + self.exception_strategy = exception_strategy + + def _update_inverse_hessian(self, ys, Hy, yHy, s): + """Update the inverse Hessian matrix. + + BFGS update using the formula: + + ``H <- H + ((H*y).T*y + s.T*y)/(s.T*y)^2 * (s*s.T) + - 1/(s.T*y) * ((H*y)*s.T + s*(H*y).T)`` + + where ``s = delta_x`` and ``y = delta_grad``. This formula is + equivalent to (6.17) in [1]_ written in a more efficient way + for implementation. + + References + ---------- + .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" + Second Edition (2006). + """ + self.H = self._syr2(-1.0 / ys, s, Hy, a=self.H) + self.H = self._syr((ys + yHy) / ys ** 2, s, a=self.H) + + def _update_hessian(self, ys, Bs, sBs, y): + """Update the Hessian matrix. + + BFGS update using the formula: + + ``B <- B - (B*s)*(B*s).T/s.T*(B*s) + y*y^T/s.T*y`` + + where ``s`` is short for ``delta_x`` and ``y`` is short + for ``delta_grad``. Formula (6.19) in [1]_. + + References + ---------- + .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" + Second Edition (2006). + """ + self.B = self._syr(1.0 / ys, y, a=self.B) + self.B = self._syr(-1.0 / sBs, Bs, a=self.B) + + def _update_implementation(self, delta_x, delta_grad): + # Auxiliary variables w and z + if self.approx_type == 'hess': + w = delta_x + z = delta_grad + else: + w = delta_grad + z = delta_x + # Do some common operations + wz = np.dot(w, z) + Mw = self.dot(w) + wMw = Mw.dot(w) + # Guarantee that wMw > 0 by reinitializing matrix. + # While this is always true in exact arithmetic, + # indefinite matrix may appear due to roundoff errors. + if wMw <= 0.0: + scale = self._auto_scale(delta_x, delta_grad) + # Reinitialize matrix + if self.approx_type == 'hess': + self.B = scale * np.eye(self.n, dtype=float) + else: + self.H = scale * np.eye(self.n, dtype=float) + # Do common operations for new matrix + Mw = self.dot(w) + wMw = Mw.dot(w) + # Check if curvature condition is violated + if wz <= self.min_curvature * wMw: + # If the option 'skip_update' is set + # we just skip the update when the condition + # is violated. + if self.exception_strategy == 'skip_update': + return + # If the option 'damp_update' is set we + # interpolate between the actual BFGS + # result and the unmodified matrix. + elif self.exception_strategy == 'damp_update': + update_factor = (1-self.min_curvature) / (1 - wz/wMw) + z = update_factor*z + (1-update_factor)*Mw + wz = np.dot(w, z) + # Update matrix + if self.approx_type == 'hess': + self._update_hessian(wz, Mw, wMw, z) + else: + self._update_inverse_hessian(wz, Mw, wMw, z) + + +class SR1(FullHessianUpdateStrategy): + """Symmetric-rank-1 Hessian update strategy. + + Parameters + ---------- + min_denominator : float + This number, scaled by a normalization factor, + defines the minimum denominator magnitude allowed + in the update. When the condition is violated we skip + the update. By default uses ``1e-8``. + init_scale : {float, np.array, 'auto'}, optional + This parameter can be used to initialize the Hessian or its + inverse. When a float is given, the relevant array is initialized + to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension. + Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given, + this array will be used. Otherwise an error is generated. + Set it to 'auto' in order to use an automatic heuristic for choosing + the initial scale. The heuristic is described in [1]_, p.143. + The default is 'auto'. + + Notes + ----- + The update is based on the description in [1]_, p.144-146. + + References + ---------- + .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" + Second Edition (2006). + """ + + def __init__(self, min_denominator=1e-8, init_scale='auto'): + self.min_denominator = min_denominator + super().__init__(init_scale) + + def _update_implementation(self, delta_x, delta_grad): + # Auxiliary variables w and z + if self.approx_type == 'hess': + w = delta_x + z = delta_grad + else: + w = delta_grad + z = delta_x + # Do some common operations + Mw = self.dot(w) + z_minus_Mw = z - Mw + denominator = np.dot(w, z_minus_Mw) + # If the denominator is too small + # we just skip the update. + if np.abs(denominator) <= self.min_denominator*norm(w)*norm(z_minus_Mw): + return + # Update matrix + if self.approx_type == 'hess': + self.B = self._syr(1/denominator, z_minus_Mw, a=self.B) + else: + self.H = self._syr(1/denominator, z_minus_Mw, a=self.H) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_isotonic.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_isotonic.py new file mode 100644 index 0000000000000000000000000000000000000000..bbbce625a7e5f9befd53bd4b5a1d043e71537bee --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_isotonic.py @@ -0,0 +1,158 @@ +from __future__ import annotations +from typing import TYPE_CHECKING + +import numpy as np + +from ._optimize import OptimizeResult +from ._pava_pybind import pava + +if TYPE_CHECKING: + import numpy.typing as npt + + +__all__ = ["isotonic_regression"] + + +def isotonic_regression( + y: npt.ArrayLike, + *, + weights: npt.ArrayLike | None = None, + increasing: bool = True, +) -> OptimizeResult: + r"""Nonparametric isotonic regression. + + A (not strictly) monotonically increasing array `x` with the same length + as `y` is calculated by the pool adjacent violators algorithm (PAVA), see + [1]_. See the Notes section for more details. + + Parameters + ---------- + y : (N,) array_like + Response variable. + weights : (N,) array_like or None + Case weights. + increasing : bool + If True, fit monotonic increasing, i.e. isotonic, regression. + If False, fit a monotonic decreasing, i.e. antitonic, regression. + Default is True. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: + + - ``x``: The isotonic regression solution, i.e. an increasing (or + decreasing) array of the same length than y, with elements in the + range from min(y) to max(y). + - ``weights`` : Array with the sum of case weights for each block + (or pool) B. + - ``blocks``: Array of length B+1 with the indices of the start + positions of each block (or pool) B. The j-th block is given by + ``x[blocks[j]:blocks[j+1]]`` for which all values are the same. + + Notes + ----- + Given data :math:`y` and case weights :math:`w`, the isotonic regression + solves the following optimization problem: + + .. math:: + + \operatorname{argmin}_{x_i} \sum_i w_i (y_i - x_i)^2 \quad + \text{subject to } x_i \leq x_j \text{ whenever } i \leq j \,. + + For every input value :math:`y_i`, it generates a value :math:`x_i` such + that :math:`x` is increasing (but not strictly), i.e. + :math:`x_i \leq x_{i+1}`. This is accomplished by the PAVA. + The solution consists of pools or blocks, i.e. neighboring elements of + :math:`x`, e.g. :math:`x_i` and :math:`x_{i+1}`, that all have the same + value. + + Most interestingly, the solution stays the same if the squared loss is + replaced by the wide class of Bregman functions which are the unique + class of strictly consistent scoring functions for the mean, see [2]_ + and references therein. + + The implemented version of PAVA according to [1]_ has a computational + complexity of O(N) with input size N. + + References + ---------- + .. [1] Busing, F. M. T. A. (2022). + Monotone Regression: A Simple and Fast O(n) PAVA Implementation. + Journal of Statistical Software, Code Snippets, 102(1), 1-25. + :doi:`10.18637/jss.v102.c01` + .. [2] Jordan, A.I., Mühlemann, A. & Ziegel, J.F. + Characterizing the optimal solutions to the isotonic regression + problem for identifiable functionals. + Ann Inst Stat Math 74, 489-514 (2022). + :doi:`10.1007/s10463-021-00808-0` + + Examples + -------- + This example demonstrates that ``isotonic_regression`` really solves a + constrained optimization problem. + + >>> import numpy as np + >>> from scipy.optimize import isotonic_regression, minimize + >>> y = [1.5, 1.0, 4.0, 6.0, 5.7, 5.0, 7.8, 9.0, 7.5, 9.5, 9.0] + >>> def objective(yhat, y): + ... return np.sum((yhat - y)**2) + >>> def constraint(yhat, y): + ... # This is for a monotonically increasing regression. + ... return np.diff(yhat) + >>> result = minimize(objective, x0=y, args=(y,), + ... constraints=[{'type': 'ineq', + ... 'fun': lambda x: constraint(x, y)}]) + >>> result.x + array([1.25 , 1.25 , 4. , 5.56666667, 5.56666667, + 5.56666667, 7.8 , 8.25 , 8.25 , 9.25 , + 9.25 ]) + >>> result = isotonic_regression(y) + >>> result.x + array([1.25 , 1.25 , 4. , 5.56666667, 5.56666667, + 5.56666667, 7.8 , 8.25 , 8.25 , 9.25 , + 9.25 ]) + + The big advantage of ``isotonic_regression`` compared to calling + ``minimize`` is that it is more user friendly, i.e. one does not need to + define objective and constraint functions, and that it is orders of + magnitudes faster. On commodity hardware (in 2023), for normal distributed + input y of length 1000, the minimizer takes about 4 seconds, while + ``isotonic_regression`` takes about 200 microseconds. + """ + yarr = np.atleast_1d(y) # Check yarr.ndim == 1 is implicit (pybind11) in pava. + order = slice(None) if increasing else slice(None, None, -1) + x = np.array(yarr[order], order="C", dtype=np.float64, copy=True) + if weights is None: + wx = np.ones_like(yarr, dtype=np.float64) + else: + warr = np.atleast_1d(weights) + + if not (yarr.ndim == warr.ndim == 1 and yarr.shape[0] == warr.shape[0]): + raise ValueError( + "Input arrays y and w must have one dimension of equal length." + ) + if np.any(warr <= 0): + raise ValueError("Weights w must be strictly positive.") + + wx = np.array(warr[order], order="C", dtype=np.float64, copy=True) + n = x.shape[0] + r = np.full(shape=n + 1, fill_value=-1, dtype=np.intp) + x, wx, r, b = pava(x, wx, r) + # Now that we know the number of blocks b, we only keep the relevant part + # of r and wx. + # As information: Due to the pava implementation, after the last block + # index, there might be smaller numbers appended to r, e.g. + # r = [0, 10, 8, 7] which in the end should be r = [0, 10]. + r = r[:b + 1] + wx = wx[:b] + if not increasing: + x = x[::-1] + wx = wx[::-1] + r = r[-1] - r[::-1] + return OptimizeResult( + x=x, + weights=wx, + blocks=r, + ) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lbfgsb_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lbfgsb_py.py new file mode 100644 index 0000000000000000000000000000000000000000..42ad9038ef0ce4c29b0cf22c5c9d2a1c029827c3 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lbfgsb_py.py @@ -0,0 +1,543 @@ +""" +Functions +--------- +.. autosummary:: + :toctree: generated/ + + fmin_l_bfgs_b + +""" + +## License for the Python wrapper +## ============================== + +## Copyright (c) 2004 David M. Cooke + +## Permission is hereby granted, free of charge, to any person obtaining a +## copy of this software and associated documentation files (the "Software"), +## to deal in the Software without restriction, including without limitation +## the rights to use, copy, modify, merge, publish, distribute, sublicense, +## and/or sell copies of the Software, and to permit persons to whom the +## Software is furnished to do so, subject to the following conditions: + +## The above copyright notice and this permission notice shall be included in +## all copies or substantial portions of the Software. + +## THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +## IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +## FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +## AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +## LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +## FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +## DEALINGS IN THE SOFTWARE. + +## Modifications by Travis Oliphant and Enthought, Inc. for inclusion in SciPy + +import numpy as np +from numpy import array, asarray, float64, zeros +from . import _lbfgsb +from ._optimize import (MemoizeJac, OptimizeResult, _call_callback_maybe_halt, + _wrap_callback, _check_unknown_options, + _prepare_scalar_function) +from ._constraints import old_bound_to_new + +from scipy.sparse.linalg import LinearOperator + +__all__ = ['fmin_l_bfgs_b', 'LbfgsInvHessProduct'] + + +def fmin_l_bfgs_b(func, x0, fprime=None, args=(), + approx_grad=0, + bounds=None, m=10, factr=1e7, pgtol=1e-5, + epsilon=1e-8, + iprint=-1, maxfun=15000, maxiter=15000, disp=None, + callback=None, maxls=20): + """ + Minimize a function func using the L-BFGS-B algorithm. + + Parameters + ---------- + func : callable f(x,*args) + Function to minimize. + x0 : ndarray + Initial guess. + fprime : callable fprime(x,*args), optional + The gradient of `func`. If None, then `func` returns the function + value and the gradient (``f, g = func(x, *args)``), unless + `approx_grad` is True in which case `func` returns only ``f``. + args : sequence, optional + Arguments to pass to `func` and `fprime`. + approx_grad : bool, optional + Whether to approximate the gradient numerically (in which case + `func` returns only the function value). + bounds : list, optional + ``(min, max)`` pairs for each element in ``x``, defining + the bounds on that parameter. Use None or +-inf for one of ``min`` or + ``max`` when there is no bound in that direction. + m : int, optional + The maximum number of variable metric corrections + used to define the limited memory matrix. (The limited memory BFGS + method does not store the full hessian but uses this many terms in an + approximation to it.) + factr : float, optional + The iteration stops when + ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``, + where ``eps`` is the machine precision, which is automatically + generated by the code. Typical values for `factr` are: 1e12 for + low accuracy; 1e7 for moderate accuracy; 10.0 for extremely + high accuracy. See Notes for relationship to `ftol`, which is exposed + (instead of `factr`) by the `scipy.optimize.minimize` interface to + L-BFGS-B. + pgtol : float, optional + The iteration will stop when + ``max{|proj g_i | i = 1, ..., n} <= pgtol`` + where ``proj g_i`` is the i-th component of the projected gradient. + epsilon : float, optional + Step size used when `approx_grad` is True, for numerically + calculating the gradient + iprint : int, optional + Controls the frequency of output. ``iprint < 0`` means no output; + ``iprint = 0`` print only one line at the last iteration; + ``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations; + ``iprint = 99`` print details of every iteration except n-vectors; + ``iprint = 100`` print also the changes of active set and final x; + ``iprint > 100`` print details of every iteration including x and g. + disp : int, optional + If zero, then no output. If a positive number, then this over-rides + `iprint` (i.e., `iprint` gets the value of `disp`). + maxfun : int, optional + Maximum number of function evaluations. Note that this function + may violate the limit because of evaluating gradients by numerical + differentiation. + maxiter : int, optional + Maximum number of iterations. + callback : callable, optional + Called after each iteration, as ``callback(xk)``, where ``xk`` is the + current parameter vector. + maxls : int, optional + Maximum number of line search steps (per iteration). Default is 20. + + Returns + ------- + x : array_like + Estimated position of the minimum. + f : float + Value of `func` at the minimum. + d : dict + Information dictionary. + + * d['warnflag'] is + + - 0 if converged, + - 1 if too many function evaluations or too many iterations, + - 2 if stopped for another reason, given in d['task'] + + * d['grad'] is the gradient at the minimum (should be 0 ish) + * d['funcalls'] is the number of function calls made. + * d['nit'] is the number of iterations. + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'L-BFGS-B' `method` in particular. Note that the + `ftol` option is made available via that interface, while `factr` is + provided via this interface, where `factr` is the factor multiplying + the default machine floating-point precision to arrive at `ftol`: + ``ftol = factr * numpy.finfo(float).eps``. + + Notes + ----- + License of L-BFGS-B (FORTRAN code): + + The version included here (in fortran code) is 3.0 + (released April 25, 2011). It was written by Ciyou Zhu, Richard Byrd, + and Jorge Nocedal . It carries the following + condition for use: + + This software is freely available, but we expect that all publications + describing work using this software, or all commercial products using it, + quote at least one of the references given below. This software is released + under the BSD License. + + References + ---------- + * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound + Constrained Optimization, (1995), SIAM Journal on Scientific and + Statistical Computing, 16, 5, pp. 1190-1208. + * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, + FORTRAN routines for large scale bound constrained optimization (1997), + ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560. + * J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, + FORTRAN routines for large scale bound constrained optimization (2011), + ACM Transactions on Mathematical Software, 38, 1. + + Examples + -------- + Solve a linear regression problem via `fmin_l_bfgs_b`. To do this, first we define + an objective function ``f(m, b) = (y - y_model)**2``, where `y` describes the + observations and `y_model` the prediction of the linear model as + ``y_model = m*x + b``. The bounds for the parameters, ``m`` and ``b``, are arbitrarily + chosen as ``(0,5)`` and ``(5,10)`` for this example. + + >>> import numpy as np + >>> from scipy.optimize import fmin_l_bfgs_b + >>> X = np.arange(0, 10, 1) + >>> M = 2 + >>> B = 3 + >>> Y = M * X + B + >>> def func(parameters, *args): + ... x = args[0] + ... y = args[1] + ... m, b = parameters + ... y_model = m*x + b + ... error = sum(np.power((y - y_model), 2)) + ... return error + + >>> initial_values = np.array([0.0, 1.0]) + + >>> x_opt, f_opt, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y), + ... approx_grad=True) + >>> x_opt, f_opt + array([1.99999999, 3.00000006]), 1.7746231151323805e-14 # may vary + + The optimized parameters in ``x_opt`` agree with the ground truth parameters + ``m`` and ``b``. Next, let us perform a bound contrained optimization using the `bounds` + parameter. + + >>> bounds = [(0, 5), (5, 10)] + >>> x_opt, f_op, info = fmin_l_bfgs_b(func, x0=initial_values, args=(X, Y), + ... approx_grad=True, bounds=bounds) + >>> x_opt, f_opt + array([1.65990508, 5.31649385]), 15.721334516453945 # may vary + """ + # handle fprime/approx_grad + if approx_grad: + fun = func + jac = None + elif fprime is None: + fun = MemoizeJac(func) + jac = fun.derivative + else: + fun = func + jac = fprime + + # build options + callback = _wrap_callback(callback) + opts = {'disp': disp, + 'iprint': iprint, + 'maxcor': m, + 'ftol': factr * np.finfo(float).eps, + 'gtol': pgtol, + 'eps': epsilon, + 'maxfun': maxfun, + 'maxiter': maxiter, + 'callback': callback, + 'maxls': maxls} + + res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds, + **opts) + d = {'grad': res['jac'], + 'task': res['message'], + 'funcalls': res['nfev'], + 'nit': res['nit'], + 'warnflag': res['status']} + f = res['fun'] + x = res['x'] + + return x, f, d + + +def _minimize_lbfgsb(fun, x0, args=(), jac=None, bounds=None, + disp=None, maxcor=10, ftol=2.2204460492503131e-09, + gtol=1e-5, eps=1e-8, maxfun=15000, maxiter=15000, + iprint=-1, callback=None, maxls=20, + finite_diff_rel_step=None, **unknown_options): + """ + Minimize a scalar function of one or more variables using the L-BFGS-B + algorithm. + + Options + ------- + disp : None or int + If `disp is None` (the default), then the supplied version of `iprint` + is used. If `disp is not None`, then it overrides the supplied version + of `iprint` with the behaviour you outlined. + maxcor : int + The maximum number of variable metric corrections used to + define the limited memory matrix. (The limited memory BFGS + method does not store the full hessian but uses this many terms + in an approximation to it.) + ftol : float + The iteration stops when ``(f^k - + f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol``. + gtol : float + The iteration will stop when ``max{|proj g_i | i = 1, ..., n} + <= gtol`` where ``proj g_i`` is the i-th component of the + projected gradient. + eps : float or ndarray + If `jac is None` the absolute step size used for numerical + approximation of the jacobian via forward differences. + maxfun : int + Maximum number of function evaluations. Note that this function + may violate the limit because of evaluating gradients by numerical + differentiation. + maxiter : int + Maximum number of iterations. + iprint : int, optional + Controls the frequency of output. ``iprint < 0`` means no output; + ``iprint = 0`` print only one line at the last iteration; + ``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations; + ``iprint = 99`` print details of every iteration except n-vectors; + ``iprint = 100`` print also the changes of active set and final x; + ``iprint > 100`` print details of every iteration including x and g. + maxls : int, optional + Maximum number of line search steps (per iteration). Default is 20. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of the jacobian. The absolute step + size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, + possibly adjusted to fit into the bounds. For ``method='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + + Notes + ----- + The option `ftol` is exposed via the `scipy.optimize.minimize` interface, + but calling `scipy.optimize.fmin_l_bfgs_b` directly exposes `factr`. The + relationship between the two is ``ftol = factr * numpy.finfo(float).eps``. + I.e., `factr` multiplies the default machine floating-point precision to + arrive at `ftol`. + + """ + _check_unknown_options(unknown_options) + m = maxcor + pgtol = gtol + factr = ftol / np.finfo(float).eps + + x0 = asarray(x0).ravel() + n, = x0.shape + + # historically old-style bounds were/are expected by lbfgsb. + # That's still the case but we'll deal with new-style from here on, + # it's easier + if bounds is None: + pass + elif len(bounds) != n: + raise ValueError('length of x0 != length of bounds') + else: + bounds = np.array(old_bound_to_new(bounds)) + + # check bounds + if (bounds[0] > bounds[1]).any(): + raise ValueError( + "LBFGSB - one of the lower bounds is greater than an upper bound." + ) + + # initial vector must lie within the bounds. Otherwise ScalarFunction and + # approx_derivative will cause problems + x0 = np.clip(x0, bounds[0], bounds[1]) + + if disp is not None: + if disp == 0: + iprint = -1 + else: + iprint = disp + + # _prepare_scalar_function can use bounds=None to represent no bounds + sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps, + bounds=bounds, + finite_diff_rel_step=finite_diff_rel_step) + + func_and_grad = sf.fun_and_grad + + fortran_int = _lbfgsb.types.intvar.dtype + + nbd = zeros(n, fortran_int) + low_bnd = zeros(n, float64) + upper_bnd = zeros(n, float64) + bounds_map = {(-np.inf, np.inf): 0, + (1, np.inf): 1, + (1, 1): 2, + (-np.inf, 1): 3} + + if bounds is not None: + for i in range(0, n): + l, u = bounds[0, i], bounds[1, i] + if not np.isinf(l): + low_bnd[i] = l + l = 1 + if not np.isinf(u): + upper_bnd[i] = u + u = 1 + nbd[i] = bounds_map[l, u] + + if not maxls > 0: + raise ValueError('maxls must be positive.') + + x = array(x0, float64) + f = array(0.0, float64) + g = zeros((n,), float64) + wa = zeros(2*m*n + 5*n + 11*m*m + 8*m, float64) + iwa = zeros(3*n, fortran_int) + task = zeros(1, 'S60') + csave = zeros(1, 'S60') + lsave = zeros(4, fortran_int) + isave = zeros(44, fortran_int) + dsave = zeros(29, float64) + + task[:] = 'START' + + n_iterations = 0 + + while 1: + # g may become float32 if a user provides a function that calculates + # the Jacobian in float32 (see gh-18730). The underlying Fortran code + # expects float64, so upcast it + g = g.astype(np.float64) + # x, f, g, wa, iwa, task, csave, lsave, isave, dsave = \ + _lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr, + pgtol, wa, iwa, task, iprint, csave, lsave, + isave, dsave, maxls) + task_str = task.tobytes() + if task_str.startswith(b'FG'): + # The minimization routine wants f and g at the current x. + # Note that interruptions due to maxfun are postponed + # until the completion of the current minimization iteration. + # Overwrite f and g: + f, g = func_and_grad(x) + elif task_str.startswith(b'NEW_X'): + # new iteration + n_iterations += 1 + + intermediate_result = OptimizeResult(x=x, fun=f) + if _call_callback_maybe_halt(callback, intermediate_result): + task[:] = 'STOP: CALLBACK REQUESTED HALT' + if n_iterations >= maxiter: + task[:] = 'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT' + elif sf.nfev > maxfun: + task[:] = ('STOP: TOTAL NO. of f AND g EVALUATIONS ' + 'EXCEEDS LIMIT') + else: + break + + task_str = task.tobytes().strip(b'\x00').strip() + if task_str.startswith(b'CONV'): + warnflag = 0 + elif sf.nfev > maxfun or n_iterations >= maxiter: + warnflag = 1 + else: + warnflag = 2 + + # These two portions of the workspace are described in the mainlb + # subroutine in lbfgsb.f. See line 363. + s = wa[0: m*n].reshape(m, n) + y = wa[m*n: 2*m*n].reshape(m, n) + + # See lbfgsb.f line 160 for this portion of the workspace. + # isave(31) = the total number of BFGS updates prior the current iteration; + n_bfgs_updates = isave[30] + + n_corrs = min(n_bfgs_updates, maxcor) + hess_inv = LbfgsInvHessProduct(s[:n_corrs], y[:n_corrs]) + + task_str = task_str.decode() + return OptimizeResult(fun=f, jac=g, nfev=sf.nfev, + njev=sf.ngev, + nit=n_iterations, status=warnflag, message=task_str, + x=x, success=(warnflag == 0), hess_inv=hess_inv) + + +class LbfgsInvHessProduct(LinearOperator): + """Linear operator for the L-BFGS approximate inverse Hessian. + + This operator computes the product of a vector with the approximate inverse + of the Hessian of the objective function, using the L-BFGS limited + memory approximation to the inverse Hessian, accumulated during the + optimization. + + Objects of this class implement the ``scipy.sparse.linalg.LinearOperator`` + interface. + + Parameters + ---------- + sk : array_like, shape=(n_corr, n) + Array of `n_corr` most recent updates to the solution vector. + (See [1]). + yk : array_like, shape=(n_corr, n) + Array of `n_corr` most recent updates to the gradient. (See [1]). + + References + ---------- + .. [1] Nocedal, Jorge. "Updating quasi-Newton matrices with limited + storage." Mathematics of computation 35.151 (1980): 773-782. + + """ + + def __init__(self, sk, yk): + """Construct the operator.""" + if sk.shape != yk.shape or sk.ndim != 2: + raise ValueError('sk and yk must have matching shape, (n_corrs, n)') + n_corrs, n = sk.shape + + super().__init__(dtype=np.float64, shape=(n, n)) + + self.sk = sk + self.yk = yk + self.n_corrs = n_corrs + self.rho = 1 / np.einsum('ij,ij->i', sk, yk) + + def _matvec(self, x): + """Efficient matrix-vector multiply with the BFGS matrices. + + This calculation is described in Section (4) of [1]. + + Parameters + ---------- + x : ndarray + An array with shape (n,) or (n,1). + + Returns + ------- + y : ndarray + The matrix-vector product + + """ + s, y, n_corrs, rho = self.sk, self.yk, self.n_corrs, self.rho + q = np.array(x, dtype=self.dtype, copy=True) + if q.ndim == 2 and q.shape[1] == 1: + q = q.reshape(-1) + + alpha = np.empty(n_corrs) + + for i in range(n_corrs-1, -1, -1): + alpha[i] = rho[i] * np.dot(s[i], q) + q = q - alpha[i]*y[i] + + r = q + for i in range(n_corrs): + beta = rho[i] * np.dot(y[i], r) + r = r + s[i] * (alpha[i] - beta) + + return r + + def todense(self): + """Return a dense array representation of this operator. + + Returns + ------- + arr : ndarray, shape=(n, n) + An array with the same shape and containing + the same data represented by this `LinearOperator`. + + """ + s, y, n_corrs, rho = self.sk, self.yk, self.n_corrs, self.rho + I = np.eye(*self.shape, dtype=self.dtype) + Hk = I + + for i in range(n_corrs): + A1 = I - s[i][:, np.newaxis] * y[i][np.newaxis, :] * rho[i] + A2 = I - y[i][:, np.newaxis] * s[i][np.newaxis, :] * rho[i] + + Hk = np.dot(A1, np.dot(Hk, A2)) + (rho[i] * s[i][:, np.newaxis] * + s[i][np.newaxis, :]) + return Hk diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linesearch.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linesearch.py new file mode 100644 index 0000000000000000000000000000000000000000..39e0b3826d5f2cb6390e01cb0f8b2f63ee8cf77e --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linesearch.py @@ -0,0 +1,896 @@ +""" +Functions +--------- +.. autosummary:: + :toctree: generated/ + + line_search_armijo + line_search_wolfe1 + line_search_wolfe2 + scalar_search_wolfe1 + scalar_search_wolfe2 + +""" +from warnings import warn + +from ._dcsrch import DCSRCH +import numpy as np + +__all__ = ['LineSearchWarning', 'line_search_wolfe1', 'line_search_wolfe2', + 'scalar_search_wolfe1', 'scalar_search_wolfe2', + 'line_search_armijo'] + +class LineSearchWarning(RuntimeWarning): + pass + + +def _check_c1_c2(c1, c2): + if not (0 < c1 < c2 < 1): + raise ValueError("'c1' and 'c2' do not satisfy" + "'0 < c1 < c2 < 1'.") + + +#------------------------------------------------------------------------------ +# Minpack's Wolfe line and scalar searches +#------------------------------------------------------------------------------ + +def line_search_wolfe1(f, fprime, xk, pk, gfk=None, + old_fval=None, old_old_fval=None, + args=(), c1=1e-4, c2=0.9, amax=50, amin=1e-8, + xtol=1e-14): + """ + As `scalar_search_wolfe1` but do a line search to direction `pk` + + Parameters + ---------- + f : callable + Function `f(x)` + fprime : callable + Gradient of `f` + xk : array_like + Current point + pk : array_like + Search direction + gfk : array_like, optional + Gradient of `f` at point `xk` + old_fval : float, optional + Value of `f` at point `xk` + old_old_fval : float, optional + Value of `f` at point preceding `xk` + + The rest of the parameters are the same as for `scalar_search_wolfe1`. + + Returns + ------- + stp, f_count, g_count, fval, old_fval + As in `line_search_wolfe1` + gval : array + Gradient of `f` at the final point + + Notes + ----- + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + + """ + if gfk is None: + gfk = fprime(xk, *args) + + gval = [gfk] + gc = [0] + fc = [0] + + def phi(s): + fc[0] += 1 + return f(xk + s*pk, *args) + + def derphi(s): + gval[0] = fprime(xk + s*pk, *args) + gc[0] += 1 + return np.dot(gval[0], pk) + + derphi0 = np.dot(gfk, pk) + + stp, fval, old_fval = scalar_search_wolfe1( + phi, derphi, old_fval, old_old_fval, derphi0, + c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol) + + return stp, fc[0], gc[0], fval, old_fval, gval[0] + + +def scalar_search_wolfe1(phi, derphi, phi0=None, old_phi0=None, derphi0=None, + c1=1e-4, c2=0.9, + amax=50, amin=1e-8, xtol=1e-14): + """ + Scalar function search for alpha that satisfies strong Wolfe conditions + + alpha > 0 is assumed to be a descent direction. + + Parameters + ---------- + phi : callable phi(alpha) + Function at point `alpha` + derphi : callable phi'(alpha) + Objective function derivative. Returns a scalar. + phi0 : float, optional + Value of phi at 0 + old_phi0 : float, optional + Value of phi at previous point + derphi0 : float, optional + Value derphi at 0 + c1 : float, optional + Parameter for Armijo condition rule. + c2 : float, optional + Parameter for curvature condition rule. + amax, amin : float, optional + Maximum and minimum step size + xtol : float, optional + Relative tolerance for an acceptable step. + + Returns + ------- + alpha : float + Step size, or None if no suitable step was found + phi : float + Value of `phi` at the new point `alpha` + phi0 : float + Value of `phi` at `alpha=0` + + Notes + ----- + Uses routine DCSRCH from MINPACK. + + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1`` as described in [1]_. + + References + ---------- + + .. [1] Nocedal, J., & Wright, S. J. (2006). Numerical optimization. + In Springer Series in Operations Research and Financial Engineering. + (Springer Series in Operations Research and Financial Engineering). + Springer Nature. + + """ + _check_c1_c2(c1, c2) + + if phi0 is None: + phi0 = phi(0.) + if derphi0 is None: + derphi0 = derphi(0.) + + if old_phi0 is not None and derphi0 != 0: + alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0) + if alpha1 < 0: + alpha1 = 1.0 + else: + alpha1 = 1.0 + + maxiter = 100 + + dcsrch = DCSRCH(phi, derphi, c1, c2, xtol, amin, amax) + stp, phi1, phi0, task = dcsrch( + alpha1, phi0=phi0, derphi0=derphi0, maxiter=maxiter + ) + + return stp, phi1, phi0 + + +line_search = line_search_wolfe1 + + +#------------------------------------------------------------------------------ +# Pure-Python Wolfe line and scalar searches +#------------------------------------------------------------------------------ + +# Note: `line_search_wolfe2` is the public `scipy.optimize.line_search` + +def line_search_wolfe2(f, myfprime, xk, pk, gfk=None, old_fval=None, + old_old_fval=None, args=(), c1=1e-4, c2=0.9, amax=None, + extra_condition=None, maxiter=10): + """Find alpha that satisfies strong Wolfe conditions. + + Parameters + ---------- + f : callable f(x,*args) + Objective function. + myfprime : callable f'(x,*args) + Objective function gradient. + xk : ndarray + Starting point. + pk : ndarray + Search direction. The search direction must be a descent direction + for the algorithm to converge. + gfk : ndarray, optional + Gradient value for x=xk (xk being the current parameter + estimate). Will be recomputed if omitted. + old_fval : float, optional + Function value for x=xk. Will be recomputed if omitted. + old_old_fval : float, optional + Function value for the point preceding x=xk. + args : tuple, optional + Additional arguments passed to objective function. + c1 : float, optional + Parameter for Armijo condition rule. + c2 : float, optional + Parameter for curvature condition rule. + amax : float, optional + Maximum step size + extra_condition : callable, optional + A callable of the form ``extra_condition(alpha, x, f, g)`` + returning a boolean. Arguments are the proposed step ``alpha`` + and the corresponding ``x``, ``f`` and ``g`` values. The line search + accepts the value of ``alpha`` only if this + callable returns ``True``. If the callable returns ``False`` + for the step length, the algorithm will continue with + new iterates. The callable is only called for iterates + satisfying the strong Wolfe conditions. + maxiter : int, optional + Maximum number of iterations to perform. + + Returns + ------- + alpha : float or None + Alpha for which ``x_new = x0 + alpha * pk``, + or None if the line search algorithm did not converge. + fc : int + Number of function evaluations made. + gc : int + Number of gradient evaluations made. + new_fval : float or None + New function value ``f(x_new)=f(x0+alpha*pk)``, + or None if the line search algorithm did not converge. + old_fval : float + Old function value ``f(x0)``. + new_slope : float or None + The local slope along the search direction at the + new value ````, + or None if the line search algorithm did not converge. + + + Notes + ----- + Uses the line search algorithm to enforce strong Wolfe + conditions. See Wright and Nocedal, 'Numerical Optimization', + 1999, pp. 59-61. + + The search direction `pk` must be a descent direction (e.g. + ``-myfprime(xk)``) to find a step length that satisfies the strong Wolfe + conditions. If the search direction is not a descent direction (e.g. + ``myfprime(xk)``), then `alpha`, `new_fval`, and `new_slope` will be None. + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import line_search + + A objective function and its gradient are defined. + + >>> def obj_func(x): + ... return (x[0])**2+(x[1])**2 + >>> def obj_grad(x): + ... return [2*x[0], 2*x[1]] + + We can find alpha that satisfies strong Wolfe conditions. + + >>> start_point = np.array([1.8, 1.7]) + >>> search_gradient = np.array([-1.0, -1.0]) + >>> line_search(obj_func, obj_grad, start_point, search_gradient) + (1.0, 2, 1, 1.1300000000000001, 6.13, [1.6, 1.4]) + + """ + fc = [0] + gc = [0] + gval = [None] + gval_alpha = [None] + + def phi(alpha): + fc[0] += 1 + return f(xk + alpha * pk, *args) + + fprime = myfprime + + def derphi(alpha): + gc[0] += 1 + gval[0] = fprime(xk + alpha * pk, *args) # store for later use + gval_alpha[0] = alpha + return np.dot(gval[0], pk) + + if gfk is None: + gfk = fprime(xk, *args) + derphi0 = np.dot(gfk, pk) + + if extra_condition is not None: + # Add the current gradient as argument, to avoid needless + # re-evaluation + def extra_condition2(alpha, phi): + if gval_alpha[0] != alpha: + derphi(alpha) + x = xk + alpha * pk + return extra_condition(alpha, x, phi, gval[0]) + else: + extra_condition2 = None + + alpha_star, phi_star, old_fval, derphi_star = scalar_search_wolfe2( + phi, derphi, old_fval, old_old_fval, derphi0, c1, c2, amax, + extra_condition2, maxiter=maxiter) + + if derphi_star is None: + warn('The line search algorithm did not converge', + LineSearchWarning, stacklevel=2) + else: + # derphi_star is a number (derphi) -- so use the most recently + # calculated gradient used in computing it derphi = gfk*pk + # this is the gradient at the next step no need to compute it + # again in the outer loop. + derphi_star = gval[0] + + return alpha_star, fc[0], gc[0], phi_star, old_fval, derphi_star + + +def scalar_search_wolfe2(phi, derphi, phi0=None, + old_phi0=None, derphi0=None, + c1=1e-4, c2=0.9, amax=None, + extra_condition=None, maxiter=10): + """Find alpha that satisfies strong Wolfe conditions. + + alpha > 0 is assumed to be a descent direction. + + Parameters + ---------- + phi : callable phi(alpha) + Objective scalar function. + derphi : callable phi'(alpha) + Objective function derivative. Returns a scalar. + phi0 : float, optional + Value of phi at 0. + old_phi0 : float, optional + Value of phi at previous point. + derphi0 : float, optional + Value of derphi at 0 + c1 : float, optional + Parameter for Armijo condition rule. + c2 : float, optional + Parameter for curvature condition rule. + amax : float, optional + Maximum step size. + extra_condition : callable, optional + A callable of the form ``extra_condition(alpha, phi_value)`` + returning a boolean. The line search accepts the value + of ``alpha`` only if this callable returns ``True``. + If the callable returns ``False`` for the step length, + the algorithm will continue with new iterates. + The callable is only called for iterates satisfying + the strong Wolfe conditions. + maxiter : int, optional + Maximum number of iterations to perform. + + Returns + ------- + alpha_star : float or None + Best alpha, or None if the line search algorithm did not converge. + phi_star : float + phi at alpha_star. + phi0 : float + phi at 0. + derphi_star : float or None + derphi at alpha_star, or None if the line search algorithm + did not converge. + + Notes + ----- + Uses the line search algorithm to enforce strong Wolfe + conditions. See Wright and Nocedal, 'Numerical Optimization', + 1999, pp. 59-61. + + """ + _check_c1_c2(c1, c2) + + if phi0 is None: + phi0 = phi(0.) + + if derphi0 is None: + derphi0 = derphi(0.) + + alpha0 = 0 + if old_phi0 is not None and derphi0 != 0: + alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0) + else: + alpha1 = 1.0 + + if alpha1 < 0: + alpha1 = 1.0 + + if amax is not None: + alpha1 = min(alpha1, amax) + + phi_a1 = phi(alpha1) + #derphi_a1 = derphi(alpha1) evaluated below + + phi_a0 = phi0 + derphi_a0 = derphi0 + + if extra_condition is None: + def extra_condition(alpha, phi): + return True + + for i in range(maxiter): + if alpha1 == 0 or (amax is not None and alpha0 > amax): + # alpha1 == 0: This shouldn't happen. Perhaps the increment has + # slipped below machine precision? + alpha_star = None + phi_star = phi0 + phi0 = old_phi0 + derphi_star = None + + if alpha1 == 0: + msg = 'Rounding errors prevent the line search from converging' + else: + msg = "The line search algorithm could not find a solution " + \ + "less than or equal to amax: %s" % amax + + warn(msg, LineSearchWarning, stacklevel=2) + break + + not_first_iteration = i > 0 + if (phi_a1 > phi0 + c1 * alpha1 * derphi0) or \ + ((phi_a1 >= phi_a0) and not_first_iteration): + alpha_star, phi_star, derphi_star = \ + _zoom(alpha0, alpha1, phi_a0, + phi_a1, derphi_a0, phi, derphi, + phi0, derphi0, c1, c2, extra_condition) + break + + derphi_a1 = derphi(alpha1) + if (abs(derphi_a1) <= -c2*derphi0): + if extra_condition(alpha1, phi_a1): + alpha_star = alpha1 + phi_star = phi_a1 + derphi_star = derphi_a1 + break + + if (derphi_a1 >= 0): + alpha_star, phi_star, derphi_star = \ + _zoom(alpha1, alpha0, phi_a1, + phi_a0, derphi_a1, phi, derphi, + phi0, derphi0, c1, c2, extra_condition) + break + + alpha2 = 2 * alpha1 # increase by factor of two on each iteration + if amax is not None: + alpha2 = min(alpha2, amax) + alpha0 = alpha1 + alpha1 = alpha2 + phi_a0 = phi_a1 + phi_a1 = phi(alpha1) + derphi_a0 = derphi_a1 + + else: + # stopping test maxiter reached + alpha_star = alpha1 + phi_star = phi_a1 + derphi_star = None + warn('The line search algorithm did not converge', + LineSearchWarning, stacklevel=2) + + return alpha_star, phi_star, phi0, derphi_star + + +def _cubicmin(a, fa, fpa, b, fb, c, fc): + """ + Finds the minimizer for a cubic polynomial that goes through the + points (a,fa), (b,fb), and (c,fc) with derivative at a of fpa. + + If no minimizer can be found, return None. + + """ + # f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D + + with np.errstate(divide='raise', over='raise', invalid='raise'): + try: + C = fpa + db = b - a + dc = c - a + denom = (db * dc) ** 2 * (db - dc) + d1 = np.empty((2, 2)) + d1[0, 0] = dc ** 2 + d1[0, 1] = -db ** 2 + d1[1, 0] = -dc ** 3 + d1[1, 1] = db ** 3 + [A, B] = np.dot(d1, np.asarray([fb - fa - C * db, + fc - fa - C * dc]).flatten()) + A /= denom + B /= denom + radical = B * B - 3 * A * C + xmin = a + (-B + np.sqrt(radical)) / (3 * A) + except ArithmeticError: + return None + if not np.isfinite(xmin): + return None + return xmin + + +def _quadmin(a, fa, fpa, b, fb): + """ + Finds the minimizer for a quadratic polynomial that goes through + the points (a,fa), (b,fb) with derivative at a of fpa. + + """ + # f(x) = B*(x-a)^2 + C*(x-a) + D + with np.errstate(divide='raise', over='raise', invalid='raise'): + try: + D = fa + C = fpa + db = b - a * 1.0 + B = (fb - D - C * db) / (db * db) + xmin = a - C / (2.0 * B) + except ArithmeticError: + return None + if not np.isfinite(xmin): + return None + return xmin + + +def _zoom(a_lo, a_hi, phi_lo, phi_hi, derphi_lo, + phi, derphi, phi0, derphi0, c1, c2, extra_condition): + """Zoom stage of approximate linesearch satisfying strong Wolfe conditions. + + Part of the optimization algorithm in `scalar_search_wolfe2`. + + Notes + ----- + Implements Algorithm 3.6 (zoom) in Wright and Nocedal, + 'Numerical Optimization', 1999, pp. 61. + + """ + + maxiter = 10 + i = 0 + delta1 = 0.2 # cubic interpolant check + delta2 = 0.1 # quadratic interpolant check + phi_rec = phi0 + a_rec = 0 + while True: + # interpolate to find a trial step length between a_lo and + # a_hi Need to choose interpolation here. Use cubic + # interpolation and then if the result is within delta * + # dalpha or outside of the interval bounded by a_lo or a_hi + # then use quadratic interpolation, if the result is still too + # close, then use bisection + + dalpha = a_hi - a_lo + if dalpha < 0: + a, b = a_hi, a_lo + else: + a, b = a_lo, a_hi + + # minimizer of cubic interpolant + # (uses phi_lo, derphi_lo, phi_hi, and the most recent value of phi) + # + # if the result is too close to the end points (or out of the + # interval), then use quadratic interpolation with phi_lo, + # derphi_lo and phi_hi if the result is still too close to the + # end points (or out of the interval) then use bisection + + if (i > 0): + cchk = delta1 * dalpha + a_j = _cubicmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi, + a_rec, phi_rec) + if (i == 0) or (a_j is None) or (a_j > b - cchk) or (a_j < a + cchk): + qchk = delta2 * dalpha + a_j = _quadmin(a_lo, phi_lo, derphi_lo, a_hi, phi_hi) + if (a_j is None) or (a_j > b-qchk) or (a_j < a+qchk): + a_j = a_lo + 0.5*dalpha + + # Check new value of a_j + + phi_aj = phi(a_j) + if (phi_aj > phi0 + c1*a_j*derphi0) or (phi_aj >= phi_lo): + phi_rec = phi_hi + a_rec = a_hi + a_hi = a_j + phi_hi = phi_aj + else: + derphi_aj = derphi(a_j) + if abs(derphi_aj) <= -c2*derphi0 and extra_condition(a_j, phi_aj): + a_star = a_j + val_star = phi_aj + valprime_star = derphi_aj + break + if derphi_aj*(a_hi - a_lo) >= 0: + phi_rec = phi_hi + a_rec = a_hi + a_hi = a_lo + phi_hi = phi_lo + else: + phi_rec = phi_lo + a_rec = a_lo + a_lo = a_j + phi_lo = phi_aj + derphi_lo = derphi_aj + i += 1 + if (i > maxiter): + # Failed to find a conforming step size + a_star = None + val_star = None + valprime_star = None + break + return a_star, val_star, valprime_star + + +#------------------------------------------------------------------------------ +# Armijo line and scalar searches +#------------------------------------------------------------------------------ + +def line_search_armijo(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1): + """Minimize over alpha, the function ``f(xk+alpha pk)``. + + Parameters + ---------- + f : callable + Function to be minimized. + xk : array_like + Current point. + pk : array_like + Search direction. + gfk : array_like + Gradient of `f` at point `xk`. + old_fval : float + Value of `f` at point `xk`. + args : tuple, optional + Optional arguments. + c1 : float, optional + Value to control stopping criterion. + alpha0 : scalar, optional + Value of `alpha` at start of the optimization. + + Returns + ------- + alpha + f_count + f_val_at_alpha + + Notes + ----- + Uses the interpolation algorithm (Armijo backtracking) as suggested by + Wright and Nocedal in 'Numerical Optimization', 1999, pp. 56-57 + + """ + xk = np.atleast_1d(xk) + fc = [0] + + def phi(alpha1): + fc[0] += 1 + return f(xk + alpha1*pk, *args) + + if old_fval is None: + phi0 = phi(0.) + else: + phi0 = old_fval # compute f(xk) -- done in past loop + + derphi0 = np.dot(gfk, pk) + alpha, phi1 = scalar_search_armijo(phi, phi0, derphi0, c1=c1, + alpha0=alpha0) + return alpha, fc[0], phi1 + + +def line_search_BFGS(f, xk, pk, gfk, old_fval, args=(), c1=1e-4, alpha0=1): + """ + Compatibility wrapper for `line_search_armijo` + """ + r = line_search_armijo(f, xk, pk, gfk, old_fval, args=args, c1=c1, + alpha0=alpha0) + return r[0], r[1], 0, r[2] + + +def scalar_search_armijo(phi, phi0, derphi0, c1=1e-4, alpha0=1, amin=0): + """Minimize over alpha, the function ``phi(alpha)``. + + Uses the interpolation algorithm (Armijo backtracking) as suggested by + Wright and Nocedal in 'Numerical Optimization', 1999, pp. 56-57 + + alpha > 0 is assumed to be a descent direction. + + Returns + ------- + alpha + phi1 + + """ + phi_a0 = phi(alpha0) + if phi_a0 <= phi0 + c1*alpha0*derphi0: + return alpha0, phi_a0 + + # Otherwise, compute the minimizer of a quadratic interpolant: + + alpha1 = -(derphi0) * alpha0**2 / 2.0 / (phi_a0 - phi0 - derphi0 * alpha0) + phi_a1 = phi(alpha1) + + if (phi_a1 <= phi0 + c1*alpha1*derphi0): + return alpha1, phi_a1 + + # Otherwise, loop with cubic interpolation until we find an alpha which + # satisfies the first Wolfe condition (since we are backtracking, we will + # assume that the value of alpha is not too small and satisfies the second + # condition. + + while alpha1 > amin: # we are assuming alpha>0 is a descent direction + factor = alpha0**2 * alpha1**2 * (alpha1-alpha0) + a = alpha0**2 * (phi_a1 - phi0 - derphi0*alpha1) - \ + alpha1**2 * (phi_a0 - phi0 - derphi0*alpha0) + a = a / factor + b = -alpha0**3 * (phi_a1 - phi0 - derphi0*alpha1) + \ + alpha1**3 * (phi_a0 - phi0 - derphi0*alpha0) + b = b / factor + + alpha2 = (-b + np.sqrt(abs(b**2 - 3 * a * derphi0))) / (3.0*a) + phi_a2 = phi(alpha2) + + if (phi_a2 <= phi0 + c1*alpha2*derphi0): + return alpha2, phi_a2 + + if (alpha1 - alpha2) > alpha1 / 2.0 or (1 - alpha2/alpha1) < 0.96: + alpha2 = alpha1 / 2.0 + + alpha0 = alpha1 + alpha1 = alpha2 + phi_a0 = phi_a1 + phi_a1 = phi_a2 + + # Failed to find a suitable step length + return None, phi_a1 + + +#------------------------------------------------------------------------------ +# Non-monotone line search for DF-SANE +#------------------------------------------------------------------------------ + +def _nonmonotone_line_search_cruz(f, x_k, d, prev_fs, eta, + gamma=1e-4, tau_min=0.1, tau_max=0.5): + """ + Nonmonotone backtracking line search as described in [1]_ + + Parameters + ---------- + f : callable + Function returning a tuple ``(f, F)`` where ``f`` is the value + of a merit function and ``F`` the residual. + x_k : ndarray + Initial position. + d : ndarray + Search direction. + prev_fs : float + List of previous merit function values. Should have ``len(prev_fs) <= M`` + where ``M`` is the nonmonotonicity window parameter. + eta : float + Allowed merit function increase, see [1]_ + gamma, tau_min, tau_max : float, optional + Search parameters, see [1]_ + + Returns + ------- + alpha : float + Step length + xp : ndarray + Next position + fp : float + Merit function value at next position + Fp : ndarray + Residual at next position + + References + ---------- + [1] "Spectral residual method without gradient information for solving + large-scale nonlinear systems of equations." W. La Cruz, + J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006). + + """ + f_k = prev_fs[-1] + f_bar = max(prev_fs) + + alpha_p = 1 + alpha_m = 1 + alpha = 1 + + while True: + xp = x_k + alpha_p * d + fp, Fp = f(xp) + + if fp <= f_bar + eta - gamma * alpha_p**2 * f_k: + alpha = alpha_p + break + + alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k) + + xp = x_k - alpha_m * d + fp, Fp = f(xp) + + if fp <= f_bar + eta - gamma * alpha_m**2 * f_k: + alpha = -alpha_m + break + + alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k) + + alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p) + alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m) + + return alpha, xp, fp, Fp + + +def _nonmonotone_line_search_cheng(f, x_k, d, f_k, C, Q, eta, + gamma=1e-4, tau_min=0.1, tau_max=0.5, + nu=0.85): + """ + Nonmonotone line search from [1] + + Parameters + ---------- + f : callable + Function returning a tuple ``(f, F)`` where ``f`` is the value + of a merit function and ``F`` the residual. + x_k : ndarray + Initial position. + d : ndarray + Search direction. + f_k : float + Initial merit function value. + C, Q : float + Control parameters. On the first iteration, give values + Q=1.0, C=f_k + eta : float + Allowed merit function increase, see [1]_ + nu, gamma, tau_min, tau_max : float, optional + Search parameters, see [1]_ + + Returns + ------- + alpha : float + Step length + xp : ndarray + Next position + fp : float + Merit function value at next position + Fp : ndarray + Residual at next position + C : float + New value for the control parameter C + Q : float + New value for the control parameter Q + + References + ---------- + .. [1] W. Cheng & D.-H. Li, ''A derivative-free nonmonotone line + search and its application to the spectral residual + method'', IMA J. Numer. Anal. 29, 814 (2009). + + """ + alpha_p = 1 + alpha_m = 1 + alpha = 1 + + while True: + xp = x_k + alpha_p * d + fp, Fp = f(xp) + + if fp <= C + eta - gamma * alpha_p**2 * f_k: + alpha = alpha_p + break + + alpha_tp = alpha_p**2 * f_k / (fp + (2*alpha_p - 1)*f_k) + + xp = x_k - alpha_m * d + fp, Fp = f(xp) + + if fp <= C + eta - gamma * alpha_m**2 * f_k: + alpha = -alpha_m + break + + alpha_tm = alpha_m**2 * f_k / (fp + (2*alpha_m - 1)*f_k) + + alpha_p = np.clip(alpha_tp, tau_min * alpha_p, tau_max * alpha_p) + alpha_m = np.clip(alpha_tm, tau_min * alpha_m, tau_max * alpha_m) + + # Update C and Q + Q_next = nu * Q + 1 + C = (nu * Q * (C + eta) + fp) / Q_next + Q = Q_next + + return alpha, xp, fp, Fp, C, Q diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog.py new file mode 100644 index 0000000000000000000000000000000000000000..1812182171961f16f69fe85f40d07bf0ae790e03 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog.py @@ -0,0 +1,716 @@ +""" +A top-level linear programming interface. + +.. versionadded:: 0.15.0 + +Functions +--------- +.. autosummary:: + :toctree: generated/ + + linprog + linprog_verbose_callback + linprog_terse_callback + +""" + +import numpy as np + +from ._optimize import OptimizeResult, OptimizeWarning +from warnings import warn +from ._linprog_highs import _linprog_highs +from ._linprog_ip import _linprog_ip +from ._linprog_simplex import _linprog_simplex +from ._linprog_rs import _linprog_rs +from ._linprog_doc import (_linprog_highs_doc, _linprog_ip_doc, # noqa: F401 + _linprog_rs_doc, _linprog_simplex_doc, + _linprog_highs_ipm_doc, _linprog_highs_ds_doc) +from ._linprog_util import ( + _parse_linprog, _presolve, _get_Abc, _LPProblem, _autoscale, + _postsolve, _check_result, _display_summary) +from copy import deepcopy + +__all__ = ['linprog', 'linprog_verbose_callback', 'linprog_terse_callback'] + +__docformat__ = "restructuredtext en" + +LINPROG_METHODS = [ + 'simplex', 'revised simplex', 'interior-point', 'highs', 'highs-ds', 'highs-ipm' +] + + +def linprog_verbose_callback(res): + """ + A sample callback function demonstrating the linprog callback interface. + This callback produces detailed output to sys.stdout before each iteration + and after the final iteration of the simplex algorithm. + + Parameters + ---------- + res : A `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + The independent variable vector which optimizes the linear + programming problem. + fun : float + Value of the objective function. + success : bool + True if the algorithm succeeded in finding an optimal solution. + slack : 1-D array + The values of the slack variables. Each slack variable corresponds + to an inequality constraint. If the slack is zero, then the + corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, that is, + ``b - A_eq @ x`` + phase : int + The phase of the optimization being executed. In phase 1 a basic + feasible solution is sought and the T has an additional row + representing an alternate objective function. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + """ + x = res['x'] + fun = res['fun'] + phase = res['phase'] + status = res['status'] + nit = res['nit'] + message = res['message'] + complete = res['complete'] + + saved_printoptions = np.get_printoptions() + np.set_printoptions(linewidth=500, + formatter={'float': lambda x: f"{x: 12.4f}"}) + if status: + print('--------- Simplex Early Exit -------\n') + print(f'The simplex method exited early with status {status:d}') + print(message) + elif complete: + print('--------- Simplex Complete --------\n') + print(f'Iterations required: {nit}') + else: + print(f'--------- Iteration {nit:d} ---------\n') + + if nit > 0: + if phase == 1: + print('Current Pseudo-Objective Value:') + else: + print('Current Objective Value:') + print('f = ', fun) + print() + print('Current Solution Vector:') + print('x = ', x) + print() + + np.set_printoptions(**saved_printoptions) + + +def linprog_terse_callback(res): + """ + A sample callback function demonstrating the linprog callback interface. + This callback produces brief output to sys.stdout before each iteration + and after the final iteration of the simplex algorithm. + + Parameters + ---------- + res : A `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + The independent variable vector which optimizes the linear + programming problem. + fun : float + Value of the objective function. + success : bool + True if the algorithm succeeded in finding an optimal solution. + slack : 1-D array + The values of the slack variables. Each slack variable corresponds + to an inequality constraint. If the slack is zero, then the + corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, that is, + ``b - A_eq @ x``. + phase : int + The phase of the optimization being executed. In phase 1 a basic + feasible solution is sought and the T has an additional row + representing an alternate objective function. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + """ + nit = res['nit'] + x = res['x'] + + if nit == 0: + print("Iter: X:") + print(f"{nit: <5d} ", end="") + print(x) + + +def linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=(0, None), method='highs', callback=None, + options=None, x0=None, integrality=None): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + - minimize :: + + c @ x + + - such that :: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None``. Other bounds can be + specified with ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. + If a single tuple ``(min, max)`` is provided, then ``min`` and ``max`` + will serve as bounds for all decision variables. + Use ``None`` to indicate that there is no bound. For instance, the + default bound ``(0, None)`` means that all decision variables are + non-negative, and the pair ``(None, None)`` means no bounds at all, + i.e. all variables are allowed to be any real. + method : str, optional + The algorithm used to solve the standard form problem. + :ref:`'highs' ` (default), + :ref:`'highs-ds' `, + :ref:`'highs-ipm' `, + :ref:`'interior-point' ` (legacy), + :ref:`'revised simplex' ` (legacy), + and + :ref:`'simplex' ` (legacy) are supported. + The legacy methods are deprecated and will be removed in SciPy 1.11.0. + callback : callable, optional + If a callback function is provided, it will be called at least once per + iteration of the algorithm. The callback function must accept a single + `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + The current solution vector. + fun : float + The current value of the objective function ``c @ x``. + success : bool + ``True`` when the algorithm has completed successfully. + slack : 1-D array + The (nominally positive) values of the slack, + ``b_ub - A_ub @ x``. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + phase : int + The phase of the algorithm being executed. + status : int + An integer representing the status of the algorithm. + + ``0`` : Optimization proceeding nominally. + + ``1`` : Iteration limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : Numerical difficulties encountered. + + nit : int + The current iteration number. + message : str + A string descriptor of the algorithm status. + + Callback functions are not currently supported by the HiGHS methods. + + options : dict, optional + A dictionary of solver options. All methods accept the following + options: + + maxiter : int + Maximum number of iterations to perform. + Default: see method-specific documentation. + disp : bool + Set to ``True`` to print convergence messages. + Default: ``False``. + presolve : bool + Set to ``False`` to disable automatic presolve. + Default: ``True``. + + All methods except the HiGHS solvers also accept: + + tol : float + A tolerance which determines when a residual is "close enough" to + zero to be considered exactly zero. + autoscale : bool + Set to ``True`` to automatically perform equilibration. + Consider using this option if the numerical values in the + constraints are separated by several orders of magnitude. + Default: ``False``. + rr : bool + Set to ``False`` to disable automatic redundancy removal. + Default: ``True``. + rr_method : string + Method used to identify and remove redundant rows from the + equality constraint matrix after presolve. For problems with + dense input, the available methods for redundancy removal are: + + "SVD": + Repeatedly performs singular value decomposition on + the matrix, detecting redundant rows based on nonzeros + in the left singular vectors that correspond with + zero singular values. May be fast when the matrix is + nearly full rank. + "pivot": + Uses the algorithm presented in [5]_ to identify + redundant rows. + "ID": + Uses a randomized interpolative decomposition. + Identifies columns of the matrix transpose not used in + a full-rank interpolative decomposition of the matrix. + None: + Uses "svd" if the matrix is nearly full rank, that is, + the difference between the matrix rank and the number + of rows is less than five. If not, uses "pivot". The + behavior of this default is subject to change without + prior notice. + + Default: None. + For problems with sparse input, this option is ignored, and the + pivot-based algorithm presented in [5]_ is used. + + For method-specific options, see + :func:`show_options('linprog') `. + + x0 : 1-D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + integrality : 1-D array or int, optional + Indicates the type of integrality constraint on each decision variable. + + ``0`` : Continuous variable; no integrality constraint. + + ``1`` : Integer variable; decision variable must be an integer + within `bounds`. + + ``2`` : Semi-continuous variable; decision variable must be within + `bounds` or take value ``0``. + + ``3`` : Semi-integer variable; decision variable must be an integer + within `bounds` or take value ``0``. + + By default, all variables are continuous. + + For mixed integrality constraints, supply an array of shape `c.shape`. + To infer a constraint on each decision variable from shorter inputs, + the argument will be broadcasted to `c.shape` using `np.broadcast_to`. + + This argument is currently used only by the ``'highs'`` method and + ignored otherwise. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields + below. Note that the return types of the fields may depend on whether + the optimization was successful, therefore it is recommended to check + `OptimizeResult.status` before relying on the other fields: + + x : 1-D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1-D array + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : Numerical difficulties encountered. + + nit : int + The total number of iterations performed in all phases. + message : str + A string descriptor of the exit status of the algorithm. + + See Also + -------- + show_options : Additional options accepted by the solvers. + + Notes + ----- + This section describes the available solvers that can be selected by the + 'method' parameter. + + `'highs-ds'` and + `'highs-ipm'` are interfaces to the + HiGHS simplex and interior-point method solvers [13]_, respectively. + `'highs'` (default) chooses between + the two automatically. These are the fastest linear + programming solvers in SciPy, especially for large, sparse problems; + which of these two is faster is problem-dependent. + The other solvers (`'interior-point'`, `'revised simplex'`, and + `'simplex'`) are legacy methods and will be removed in SciPy 1.11.0. + + Method *highs-ds* is a wrapper of the C++ high performance dual + revised simplex implementation (HSOL) [13]_, [14]_. Method *highs-ipm* + is a wrapper of a C++ implementation of an **i**\ nterior-\ **p**\ oint + **m**\ ethod [13]_; it features a crossover routine, so it is as accurate + as a simplex solver. Method *highs* chooses between the two automatically. + For new code involving `linprog`, we recommend explicitly choosing one of + these three method values. + + .. versionadded:: 1.6.0 + + Method *interior-point* uses the primal-dual path following algorithm + as outlined in [4]_. This algorithm supports sparse constraint matrices and + is typically faster than the simplex methods, especially for large, sparse + problems. Note, however, that the solution returned may be slightly less + accurate than those of the simplex methods and will not, in general, + correspond with a vertex of the polytope defined by the constraints. + + .. versionadded:: 1.0.0 + + Method *revised simplex* uses the revised simplex method as described in + [9]_, except that a factorization [11]_ of the basis matrix, rather than + its inverse, is efficiently maintained and used to solve the linear systems + at each iteration of the algorithm. + + .. versionadded:: 1.3.0 + + Method *simplex* uses a traditional, full-tableau implementation of + Dantzig's simplex algorithm [1]_, [2]_ (*not* the + Nelder-Mead simplex). This algorithm is included for backwards + compatibility and educational purposes. + + .. versionadded:: 0.15.0 + + Before applying *interior-point*, *revised simplex*, or *simplex*, + a presolve procedure based on [8]_ attempts + to identify trivial infeasibilities, trivial unboundedness, and potential + problem simplifications. Specifically, it checks for: + + - rows of zeros in ``A_eq`` or ``A_ub``, representing trivial constraints; + - columns of zeros in ``A_eq`` `and` ``A_ub``, representing unconstrained + variables; + - column singletons in ``A_eq``, representing fixed variables; and + - column singletons in ``A_ub``, representing simple bounds. + + If presolve reveals that the problem is unbounded (e.g. an unconstrained + and unbounded variable has negative cost) or infeasible (e.g., a row of + zeros in ``A_eq`` corresponds with a nonzero in ``b_eq``), the solver + terminates with the appropriate status code. Note that presolve terminates + as soon as any sign of unboundedness is detected; consequently, a problem + may be reported as unbounded when in reality the problem is infeasible + (but infeasibility has not been detected yet). Therefore, if it is + important to know whether the problem is actually infeasible, solve the + problem again with option ``presolve=False``. + + If neither infeasibility nor unboundedness are detected in a single pass + of the presolve, bounds are tightened where possible and fixed + variables are removed from the problem. Then, linearly dependent rows + of the ``A_eq`` matrix are removed, (unless they represent an + infeasibility) to avoid numerical difficulties in the primary solve + routine. Note that rows that are nearly linearly dependent (within a + prescribed tolerance) may also be removed, which can change the optimal + solution in rare cases. If this is a concern, eliminate redundancy from + your problem formulation and run with option ``rr=False`` or + ``presolve=False``. + + Several potential improvements can be made here: additional presolve + checks outlined in [8]_ should be implemented, the presolve routine should + be run multiple times (until no further simplifications can be made), and + more of the efficiency improvements from [5]_ should be implemented in the + redundancy removal routines. + + After presolve, the problem is transformed to standard form by converting + the (tightened) simple bounds to upper bound constraints, introducing + non-negative slack variables for inequality constraints, and expressing + unbounded variables as the difference between two non-negative variables. + Optionally, the problem is automatically scaled via equilibration [12]_. + The selected algorithm solves the standard form problem, and a + postprocessing routine converts the result to a solution to the original + problem. + + References + ---------- + .. [1] Dantzig, George B., Linear programming and extensions. Rand + Corporation Research Study Princeton Univ. Press, Princeton, NJ, + 1963 + .. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to + Mathematical Programming", McGraw-Hill, Chapter 4. + .. [3] Bland, Robert G. New finite pivoting rules for the simplex method. + Mathematics of Operations Research (2), 1977: pp. 103-107. + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + .. [5] Andersen, Erling D. "Finding all linearly dependent rows in + large-scale linear programming." Optimization Methods and Software + 6.3 (1995): 219-227. + .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear + Programming based on Newton's Method." Unpublished Course Notes, + March 2004. Available 2/25/2017 at + https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf + .. [7] Fourer, Robert. "Solving Linear Programs by Interior-Point Methods." + Unpublished Course Notes, August 26, 2005. Available 2/25/2017 at + http://www.4er.org/CourseNotes/Book%20B/B-III.pdf + .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear + programming." Mathematical Programming 71.2 (1995): 221-245. + .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. + .. [10] Andersen, Erling D., et al. Implementation of interior point + methods for large scale linear programming. HEC/Universite de + Geneve, 1996. + .. [11] Bartels, Richard H. "A stabilization of the simplex method." + Journal in Numerische Mathematik 16.5 (1971): 414-434. + .. [12] Tomlin, J. A. "On scaling linear programming problems." + Mathematical Programming Study 4 (1975): 146-166. + .. [13] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. + "HiGHS - high performance software for linear optimization." + https://highs.dev/ + .. [14] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised + simplex method." Mathematical Programming Computation, 10 (1), + 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 + + Examples + -------- + Consider the following problem: + + .. math:: + + \min_{x_0, x_1} \ -x_0 + 4x_1 & \\ + \mbox{such that} \ -3x_0 + x_1 & \leq 6,\\ + -x_0 - 2x_1 & \geq -4,\\ + x_1 & \geq -3. + + The problem is not presented in the form accepted by `linprog`. This is + easily remedied by converting the "greater than" inequality + constraint to a "less than" inequality constraint by + multiplying both sides by a factor of :math:`-1`. Note also that the last + constraint is really the simple bound :math:`-3 \leq x_1 \leq \infty`. + Finally, since there are no bounds on :math:`x_0`, we must explicitly + specify the bounds :math:`-\infty \leq x_0 \leq \infty`, as the + default is for variables to be non-negative. After collecting coeffecients + into arrays and tuples, the input for this problem is: + + >>> from scipy.optimize import linprog + >>> c = [-1, 4] + >>> A = [[-3, 1], [1, 2]] + >>> b = [6, 4] + >>> x0_bounds = (None, None) + >>> x1_bounds = (-3, None) + >>> res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds]) + >>> res.fun + -22.0 + >>> res.x + array([10., -3.]) + >>> res.message + 'Optimization terminated successfully. (HiGHS Status 7: Optimal)' + + The marginals (AKA dual values / shadow prices / Lagrange multipliers) + and residuals (slacks) are also available. + + >>> res.ineqlin + residual: [ 3.900e+01 0.000e+00] + marginals: [-0.000e+00 -1.000e+00] + + For example, because the marginal associated with the second inequality + constraint is -1, we expect the optimal value of the objective function + to decrease by ``eps`` if we add a small amount ``eps`` to the right hand + side of the second inequality constraint: + + >>> eps = 0.05 + >>> b[1] += eps + >>> linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds]).fun + -22.05 + + Also, because the residual on the first inequality constraint is 39, we + can decrease the right hand side of the first constraint by 39 without + affecting the optimal solution. + + >>> b = [6, 4] # reset to original values + >>> b[0] -= 39 + >>> linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds]).fun + -22.0 + + """ + + meth = method.lower() + methods = {"highs", "highs-ds", "highs-ipm", + "simplex", "revised simplex", "interior-point"} + + if meth not in methods: + raise ValueError(f"Unknown solver '{method}'") + + if x0 is not None and meth != "revised simplex": + warning_message = "x0 is used only when method is 'revised simplex'. " + warn(warning_message, OptimizeWarning, stacklevel=2) + + if np.any(integrality) and not meth == "highs": + integrality = None + warning_message = ("Only `method='highs'` supports integer " + "constraints. Ignoring `integrality`.") + warn(warning_message, OptimizeWarning, stacklevel=2) + elif np.any(integrality): + integrality = np.broadcast_to(integrality, np.shape(c)) + else: + integrality = None + + lp = _LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality) + lp, solver_options = _parse_linprog(lp, options, meth) + tol = solver_options.get('tol', 1e-9) + + # Give unmodified problem to HiGHS + if meth.startswith('highs'): + if callback is not None: + raise NotImplementedError("HiGHS solvers do not support the " + "callback interface.") + highs_solvers = {'highs-ipm': 'ipm', 'highs-ds': 'simplex', + 'highs': None} + + sol = _linprog_highs(lp, solver=highs_solvers[meth], + **solver_options) + sol['status'], sol['message'] = ( + _check_result(sol['x'], sol['fun'], sol['status'], sol['slack'], + sol['con'], lp.bounds, tol, sol['message'], + integrality)) + sol['success'] = sol['status'] == 0 + return OptimizeResult(sol) + + warn(f"`method='{meth}'` is deprecated and will be removed in SciPy " + "1.11.0. Please use one of the HiGHS solvers (e.g. " + "`method='highs'`) in new code.", DeprecationWarning, stacklevel=2) + + iteration = 0 + complete = False # will become True if solved in presolve + undo = [] + + # Keep the original arrays to calculate slack/residuals for original + # problem. + lp_o = deepcopy(lp) + + # Solve trivial problem, eliminate variables, tighten bounds, etc. + rr_method = solver_options.pop('rr_method', None) # need to pop these; + rr = solver_options.pop('rr', True) # they're not passed to methods + c0 = 0 # we might get a constant term in the objective + if solver_options.pop('presolve', True): + (lp, c0, x, undo, complete, status, message) = _presolve(lp, rr, + rr_method, + tol) + + C, b_scale = 1, 1 # for trivial unscaling if autoscale is not used + postsolve_args = (lp_o._replace(bounds=lp.bounds), undo, C, b_scale) + + if not complete: + A, b, c, c0, x0 = _get_Abc(lp, c0) + if solver_options.pop('autoscale', False): + A, b, c, x0, C, b_scale = _autoscale(A, b, c, x0) + postsolve_args = postsolve_args[:-2] + (C, b_scale) + + if meth == 'simplex': + x, status, message, iteration = _linprog_simplex( + c, c0=c0, A=A, b=b, callback=callback, + postsolve_args=postsolve_args, **solver_options) + elif meth == 'interior-point': + x, status, message, iteration = _linprog_ip( + c, c0=c0, A=A, b=b, callback=callback, + postsolve_args=postsolve_args, **solver_options) + elif meth == 'revised simplex': + x, status, message, iteration = _linprog_rs( + c, c0=c0, A=A, b=b, x0=x0, callback=callback, + postsolve_args=postsolve_args, **solver_options) + + # Eliminate artificial variables, re-introduce presolved variables, etc. + disp = solver_options.get('disp', False) + + x, fun, slack, con = _postsolve(x, postsolve_args, complete) + + status, message = _check_result(x, fun, status, slack, con, lp_o.bounds, + tol, message, integrality) + + if disp: + _display_summary(message, status, fun, iteration) + + sol = { + 'x': x, + 'fun': fun, + 'slack': slack, + 'con': con, + 'status': status, + 'message': message, + 'nit': iteration, + 'success': status == 0} + + return OptimizeResult(sol) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_doc.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_doc.py new file mode 100644 index 0000000000000000000000000000000000000000..56c914134bdef816c8eb00eb4ab011475cd5b4ea --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_doc.py @@ -0,0 +1,1434 @@ +""" +Created on Sat Aug 22 19:49:17 2020 + +@author: matth +""" + + +def _linprog_highs_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='highs', callback=None, + maxiter=None, disp=False, presolve=True, + time_limit=None, + dual_feasibility_tolerance=None, + primal_feasibility_tolerance=None, + ipm_optimality_tolerance=None, + simplex_dual_edge_weight_strategy=None, + mip_rel_gap=None, + **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using one of the HiGHS solvers. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + + This is the method-specific documentation for 'highs', which chooses + automatically between + :ref:`'highs-ds' ` and + :ref:`'highs-ipm' `. + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy) + are also available. + integrality : 1-D array or int, optional + Indicates the type of integrality constraint on each decision variable. + + ``0`` : Continuous variable; no integrality constraint. + + ``1`` : Integer variable; decision variable must be an integer + within `bounds`. + + ``2`` : Semi-continuous variable; decision variable must be within + `bounds` or take value ``0``. + + ``3`` : Semi-integer variable; decision variable must be an integer + within `bounds` or take value ``0``. + + By default, all variables are continuous. + + For mixed integrality constraints, supply an array of shape `c.shape`. + To infer a constraint on each decision variable from shorter inputs, + the argument will be broadcasted to `c.shape` using `np.broadcast_to`. + + This argument is currently used only by the ``'highs'`` method and + ignored otherwise. + + Options + ------- + maxiter : int + The maximum number of iterations to perform in either phase. + For :ref:`'highs-ipm' `, this does not + include the number of crossover iterations. Default is the largest + possible value for an ``int`` on the platform. + disp : bool (default: ``False``) + Set to ``True`` if indicators of optimization status are to be + printed to the console during optimization. + presolve : bool (default: ``True``) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + time_limit : float + The maximum time in seconds allotted to solve the problem; + default is the largest possible value for a ``double`` on the + platform. + dual_feasibility_tolerance : double (default: 1e-07) + Dual feasibility tolerance for + :ref:`'highs-ds' `. + The minimum of this and ``primal_feasibility_tolerance`` + is used for the feasibility tolerance of + :ref:`'highs-ipm' `. + primal_feasibility_tolerance : double (default: 1e-07) + Primal feasibility tolerance for + :ref:`'highs-ds' `. + The minimum of this and ``dual_feasibility_tolerance`` + is used for the feasibility tolerance of + :ref:`'highs-ipm' `. + ipm_optimality_tolerance : double (default: ``1e-08``) + Optimality tolerance for + :ref:`'highs-ipm' `. + Minimum allowable value is 1e-12. + simplex_dual_edge_weight_strategy : str (default: None) + Strategy for simplex dual edge weights. The default, ``None``, + automatically selects one of the following. + + ``'dantzig'`` uses Dantzig's original strategy of choosing the most + negative reduced cost. + + ``'devex'`` uses the strategy described in [15]_. + + ``steepest`` uses the exact steepest edge strategy as described in + [16]_. + + ``'steepest-devex'`` begins with the exact steepest edge strategy + until the computation is too costly or inexact and then switches to + the devex method. + + Currently, ``None`` always selects ``'steepest-devex'``, but this + may change as new options become available. + mip_rel_gap : double (default: None) + Termination criterion for MIP solver: solver will terminate when the + gap between the primal objective value and the dual objective bound, + scaled by the primal objective value, is <= mip_rel_gap. + unknown_options : dict + Optional arguments not used by this particular solver. If + ``unknown_options`` is non-empty, a warning is issued listing + all unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1D array + The (nominally positive) values of the slack, + ``b_ub - A_ub @ x``. + con : 1D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration or time limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : The HiGHS solver ran into a problem. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed. + For the HiGHS simplex method, this includes iterations in all + phases. For the HiGHS interior-point method, this does not include + crossover iterations. + crossover_nit : int + The number of primal/dual pushes performed during the + crossover routine for the HiGHS interior-point method. + This is ``0`` for the HiGHS simplex method. + ineqlin : OptimizeResult + Solution and sensitivity information corresponding to the + inequality constraints, `b_ub`. A dictionary consisting of the + fields: + + residual : np.ndnarray + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. This quantity is also commonly + referred to as "slack". + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + inequality constraints, `b_ub`. + + eqlin : OptimizeResult + Solution and sensitivity information corresponding to the + equality constraints, `b_eq`. A dictionary consisting of the + fields: + + residual : np.ndarray + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + equality constraints, `b_eq`. + + lower, upper : OptimizeResult + Solution and sensitivity information corresponding to the + lower and upper bounds on decision variables, `bounds`. + + residual : np.ndarray + The (nominally positive) values of the quantity + ``x - lb`` (lower) or ``ub - x`` (upper). + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the lower and upper + `bounds`. + + Notes + ----- + + Method :ref:`'highs-ds' ` is a wrapper + of the C++ high performance dual revised simplex implementation (HSOL) + [13]_, [14]_. Method :ref:`'highs-ipm' ` + is a wrapper of a C++ implementation of an **i**\ nterior-\ **p**\ oint + **m**\ ethod [13]_; it features a crossover routine, so it is as accurate + as a simplex solver. Method :ref:`'highs' ` chooses + between the two automatically. For new code involving `linprog`, we + recommend explicitly choosing one of these three method values instead of + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy). + + The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain + `marginals`, or partial derivatives of the objective function with respect + to the right-hand side of each constraint. These partial derivatives are + also referred to as "Lagrange multipliers", "dual values", and + "shadow prices". The sign convention of `marginals` is opposite that + of Lagrange multipliers produced by many nonlinear solvers. + + References + ---------- + .. [13] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. + "HiGHS - high performance software for linear optimization." + https://highs.dev/ + .. [14] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised + simplex method." Mathematical Programming Computation, 10 (1), + 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 + .. [15] Harris, Paula MJ. "Pivot selection methods of the Devex LP code." + Mathematical programming 5.1 (1973): 1-28. + .. [16] Goldfarb, Donald, and John Ker Reid. "A practicable steepest-edge + simplex algorithm." Mathematical Programming 12.1 (1977): 361-371. + """ + pass + + +def _linprog_highs_ds_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='highs-ds', callback=None, + maxiter=None, disp=False, presolve=True, + time_limit=None, + dual_feasibility_tolerance=None, + primal_feasibility_tolerance=None, + simplex_dual_edge_weight_strategy=None, + **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using the HiGHS dual simplex solver. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + + This is the method-specific documentation for 'highs-ds'. + :ref:`'highs' `, + :ref:`'highs-ipm' `, + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy) + are also available. + + Options + ------- + maxiter : int + The maximum number of iterations to perform in either phase. + Default is the largest possible value for an ``int`` on the platform. + disp : bool (default: ``False``) + Set to ``True`` if indicators of optimization status are to be + printed to the console during optimization. + presolve : bool (default: ``True``) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + time_limit : float + The maximum time in seconds allotted to solve the problem; + default is the largest possible value for a ``double`` on the + platform. + dual_feasibility_tolerance : double (default: 1e-07) + Dual feasibility tolerance for + :ref:`'highs-ds' `. + primal_feasibility_tolerance : double (default: 1e-07) + Primal feasibility tolerance for + :ref:`'highs-ds' `. + simplex_dual_edge_weight_strategy : str (default: None) + Strategy for simplex dual edge weights. The default, ``None``, + automatically selects one of the following. + + ``'dantzig'`` uses Dantzig's original strategy of choosing the most + negative reduced cost. + + ``'devex'`` uses the strategy described in [15]_. + + ``steepest`` uses the exact steepest edge strategy as described in + [16]_. + + ``'steepest-devex'`` begins with the exact steepest edge strategy + until the computation is too costly or inexact and then switches to + the devex method. + + Currently, ``None`` always selects ``'steepest-devex'``, but this + may change as new options become available. + unknown_options : dict + Optional arguments not used by this particular solver. If + ``unknown_options`` is non-empty, a warning is issued listing + all unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1D array + The (nominally positive) values of the slack, + ``b_ub - A_ub @ x``. + con : 1D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration or time limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : The HiGHS solver ran into a problem. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed. This includes iterations + in all phases. + crossover_nit : int + This is always ``0`` for the HiGHS simplex method. + For the HiGHS interior-point method, this is the number of + primal/dual pushes performed during the crossover routine. + ineqlin : OptimizeResult + Solution and sensitivity information corresponding to the + inequality constraints, `b_ub`. A dictionary consisting of the + fields: + + residual : np.ndnarray + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. This quantity is also commonly + referred to as "slack". + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + inequality constraints, `b_ub`. + + eqlin : OptimizeResult + Solution and sensitivity information corresponding to the + equality constraints, `b_eq`. A dictionary consisting of the + fields: + + residual : np.ndarray + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + equality constraints, `b_eq`. + + lower, upper : OptimizeResult + Solution and sensitivity information corresponding to the + lower and upper bounds on decision variables, `bounds`. + + residual : np.ndarray + The (nominally positive) values of the quantity + ``x - lb`` (lower) or ``ub - x`` (upper). + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the lower and upper + `bounds`. + + Notes + ----- + + Method :ref:`'highs-ds' ` is a wrapper + of the C++ high performance dual revised simplex implementation (HSOL) + [13]_, [14]_. Method :ref:`'highs-ipm' ` + is a wrapper of a C++ implementation of an **i**\ nterior-\ **p**\ oint + **m**\ ethod [13]_; it features a crossover routine, so it is as accurate + as a simplex solver. Method :ref:`'highs' ` chooses + between the two automatically. For new code involving `linprog`, we + recommend explicitly choosing one of these three method values instead of + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy). + + The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain + `marginals`, or partial derivatives of the objective function with respect + to the right-hand side of each constraint. These partial derivatives are + also referred to as "Lagrange multipliers", "dual values", and + "shadow prices". The sign convention of `marginals` is opposite that + of Lagrange multipliers produced by many nonlinear solvers. + + References + ---------- + .. [13] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. + "HiGHS - high performance software for linear optimization." + https://highs.dev/ + .. [14] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised + simplex method." Mathematical Programming Computation, 10 (1), + 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 + .. [15] Harris, Paula MJ. "Pivot selection methods of the Devex LP code." + Mathematical programming 5.1 (1973): 1-28. + .. [16] Goldfarb, Donald, and John Ker Reid. "A practicable steepest-edge + simplex algorithm." Mathematical Programming 12.1 (1977): 361-371. + """ + pass + + +def _linprog_highs_ipm_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='highs-ipm', callback=None, + maxiter=None, disp=False, presolve=True, + time_limit=None, + dual_feasibility_tolerance=None, + primal_feasibility_tolerance=None, + ipm_optimality_tolerance=None, + **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using the HiGHS interior point solver. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + + This is the method-specific documentation for 'highs-ipm'. + :ref:`'highs-ipm' `, + :ref:`'highs-ds' `, + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy) + are also available. + + Options + ------- + maxiter : int + The maximum number of iterations to perform in either phase. + For :ref:`'highs-ipm' `, this does not + include the number of crossover iterations. Default is the largest + possible value for an ``int`` on the platform. + disp : bool (default: ``False``) + Set to ``True`` if indicators of optimization status are to be + printed to the console during optimization. + presolve : bool (default: ``True``) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + time_limit : float + The maximum time in seconds allotted to solve the problem; + default is the largest possible value for a ``double`` on the + platform. + dual_feasibility_tolerance : double (default: 1e-07) + The minimum of this and ``primal_feasibility_tolerance`` + is used for the feasibility tolerance of + :ref:`'highs-ipm' `. + primal_feasibility_tolerance : double (default: 1e-07) + The minimum of this and ``dual_feasibility_tolerance`` + is used for the feasibility tolerance of + :ref:`'highs-ipm' `. + ipm_optimality_tolerance : double (default: ``1e-08``) + Optimality tolerance for + :ref:`'highs-ipm' `. + Minimum allowable value is 1e-12. + unknown_options : dict + Optional arguments not used by this particular solver. If + ``unknown_options`` is non-empty, a warning is issued listing + all unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1D array + The (nominally positive) values of the slack, + ``b_ub - A_ub @ x``. + con : 1D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration or time limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : The HiGHS solver ran into a problem. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed. + For the HiGHS interior-point method, this does not include + crossover iterations. + crossover_nit : int + The number of primal/dual pushes performed during the + crossover routine for the HiGHS interior-point method. + ineqlin : OptimizeResult + Solution and sensitivity information corresponding to the + inequality constraints, `b_ub`. A dictionary consisting of the + fields: + + residual : np.ndnarray + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. This quantity is also commonly + referred to as "slack". + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + inequality constraints, `b_ub`. + + eqlin : OptimizeResult + Solution and sensitivity information corresponding to the + equality constraints, `b_eq`. A dictionary consisting of the + fields: + + residual : np.ndarray + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + equality constraints, `b_eq`. + + lower, upper : OptimizeResult + Solution and sensitivity information corresponding to the + lower and upper bounds on decision variables, `bounds`. + + residual : np.ndarray + The (nominally positive) values of the quantity + ``x - lb`` (lower) or ``ub - x`` (upper). + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the lower and upper + `bounds`. + + Notes + ----- + + Method :ref:`'highs-ipm' ` + is a wrapper of a C++ implementation of an **i**\ nterior-\ **p**\ oint + **m**\ ethod [13]_; it features a crossover routine, so it is as accurate + as a simplex solver. + Method :ref:`'highs-ds' ` is a wrapper + of the C++ high performance dual revised simplex implementation (HSOL) + [13]_, [14]_. Method :ref:`'highs' ` chooses + between the two automatically. For new code involving `linprog`, we + recommend explicitly choosing one of these three method values instead of + :ref:`'interior-point' ` (default), + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy). + + The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain + `marginals`, or partial derivatives of the objective function with respect + to the right-hand side of each constraint. These partial derivatives are + also referred to as "Lagrange multipliers", "dual values", and + "shadow prices". The sign convention of `marginals` is opposite that + of Lagrange multipliers produced by many nonlinear solvers. + + References + ---------- + .. [13] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. + "HiGHS - high performance software for linear optimization." + https://highs.dev/ + .. [14] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised + simplex method." Mathematical Programming Computation, 10 (1), + 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 + """ + pass + + +def _linprog_ip_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='interior-point', callback=None, + maxiter=1000, disp=False, presolve=True, + tol=1e-8, autoscale=False, rr=True, + alpha0=.99995, beta=0.1, sparse=False, + lstsq=False, sym_pos=True, cholesky=True, pc=True, + ip=False, permc_spec='MMD_AT_PLUS_A', **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using the interior-point method of + [4]_. + + .. deprecated:: 1.9.0 + `method='interior-point'` will be removed in SciPy 1.11.0. + It is replaced by `method='highs'` because the latter is + faster and more robust. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + This is the method-specific documentation for 'interior-point'. + :ref:`'highs' `, + :ref:`'highs-ds' `, + :ref:`'highs-ipm' `, + :ref:`'revised simplex' `, and + :ref:`'simplex' ` (legacy) + are also available. + callback : callable, optional + Callback function to be executed once per iteration. + + Options + ------- + maxiter : int (default: 1000) + The maximum number of iterations of the algorithm. + disp : bool (default: False) + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + presolve : bool (default: True) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + tol : float (default: 1e-8) + Termination tolerance to be used for all termination criteria; + see [4]_ Section 4.5. + autoscale : bool (default: False) + Set to ``True`` to automatically perform equilibration. + Consider using this option if the numerical values in the + constraints are separated by several orders of magnitude. + rr : bool (default: True) + Set to ``False`` to disable automatic redundancy removal. + alpha0 : float (default: 0.99995) + The maximal step size for Mehrota's predictor-corrector search + direction; see :math:`\beta_{3}` of [4]_ Table 8.1. + beta : float (default: 0.1) + The desired reduction of the path parameter :math:`\mu` (see [6]_) + when Mehrota's predictor-corrector is not in use (uncommon). + sparse : bool (default: False) + Set to ``True`` if the problem is to be treated as sparse after + presolve. If either ``A_eq`` or ``A_ub`` is a sparse matrix, + this option will automatically be set ``True``, and the problem + will be treated as sparse even during presolve. If your constraint + matrices contain mostly zeros and the problem is not very small (less + than about 100 constraints or variables), consider setting ``True`` + or providing ``A_eq`` and ``A_ub`` as sparse matrices. + lstsq : bool (default: ``False``) + Set to ``True`` if the problem is expected to be very poorly + conditioned. This should always be left ``False`` unless severe + numerical difficulties are encountered. Leave this at the default + unless you receive a warning message suggesting otherwise. + sym_pos : bool (default: True) + Leave ``True`` if the problem is expected to yield a well conditioned + symmetric positive definite normal equation matrix + (almost always). Leave this at the default unless you receive + a warning message suggesting otherwise. + cholesky : bool (default: True) + Set to ``True`` if the normal equations are to be solved by explicit + Cholesky decomposition followed by explicit forward/backward + substitution. This is typically faster for problems + that are numerically well-behaved. + pc : bool (default: True) + Leave ``True`` if the predictor-corrector method of Mehrota is to be + used. This is almost always (if not always) beneficial. + ip : bool (default: False) + Set to ``True`` if the improved initial point suggestion due to [4]_ + Section 4.3 is desired. Whether this is beneficial or not + depends on the problem. + permc_spec : str (default: 'MMD_AT_PLUS_A') + (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos = + True``, and no SuiteSparse.) + A matrix is factorized in each iteration of the algorithm. + This option specifies how to permute the columns of the matrix for + sparsity preservation. Acceptable values are: + + - ``NATURAL``: natural ordering. + - ``MMD_ATA``: minimum degree ordering on the structure of A^T A. + - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A. + - ``COLAMD``: approximate minimum degree column ordering. + + This option can impact the convergence of the + interior point algorithm; test different values to determine which + performs best for your problem. For more information, refer to + ``scipy.sparse.linalg.splu``. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1-D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1-D array + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : Numerical difficulties encountered. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed in all phases. + + + Notes + ----- + This method implements the algorithm outlined in [4]_ with ideas from [8]_ + and a structure inspired by the simpler methods of [6]_. + + The primal-dual path following method begins with initial 'guesses' of + the primal and dual variables of the standard form problem and iteratively + attempts to solve the (nonlinear) Karush-Kuhn-Tucker conditions for the + problem with a gradually reduced logarithmic barrier term added to the + objective. This particular implementation uses a homogeneous self-dual + formulation, which provides certificates of infeasibility or unboundedness + where applicable. + + The default initial point for the primal and dual variables is that + defined in [4]_ Section 4.4 Equation 8.22. Optionally (by setting initial + point option ``ip=True``), an alternate (potentially improved) starting + point can be calculated according to the additional recommendations of + [4]_ Section 4.4. + + A search direction is calculated using the predictor-corrector method + (single correction) proposed by Mehrota and detailed in [4]_ Section 4.1. + (A potential improvement would be to implement the method of multiple + corrections described in [4]_ Section 4.2.) In practice, this is + accomplished by solving the normal equations, [4]_ Section 5.1 Equations + 8.31 and 8.32, derived from the Newton equations [4]_ Section 5 Equations + 8.25 (compare to [4]_ Section 4 Equations 8.6-8.8). The advantage of + solving the normal equations rather than 8.25 directly is that the + matrices involved are symmetric positive definite, so Cholesky + decomposition can be used rather than the more expensive LU factorization. + + With default options, the solver used to perform the factorization depends + on third-party software availability and the conditioning of the problem. + + For dense problems, solvers are tried in the following order: + + 1. ``scipy.linalg.cho_factor`` + + 2. ``scipy.linalg.solve`` with option ``sym_pos=True`` + + 3. ``scipy.linalg.solve`` with option ``sym_pos=False`` + + 4. ``scipy.linalg.lstsq`` + + For sparse problems: + + 1. ``sksparse.cholmod.cholesky`` (if scikit-sparse and SuiteSparse are + installed) + + 2. ``scipy.sparse.linalg.factorized`` (if scikit-umfpack and SuiteSparse + are installed) + + 3. ``scipy.sparse.linalg.splu`` (which uses SuperLU distributed with SciPy) + + 4. ``scipy.sparse.linalg.lsqr`` + + If the solver fails for any reason, successively more robust (but slower) + solvers are attempted in the order indicated. Attempting, failing, and + re-starting factorization can be time consuming, so if the problem is + numerically challenging, options can be set to bypass solvers that are + failing. Setting ``cholesky=False`` skips to solver 2, + ``sym_pos=False`` skips to solver 3, and ``lstsq=True`` skips + to solver 4 for both sparse and dense problems. + + Potential improvements for combatting issues associated with dense + columns in otherwise sparse problems are outlined in [4]_ Section 5.3 and + [10]_ Section 4.1-4.2; the latter also discusses the alleviation of + accuracy issues associated with the substitution approach to free + variables. + + After calculating the search direction, the maximum possible step size + that does not activate the non-negativity constraints is calculated, and + the smaller of this step size and unity is applied (as in [4]_ Section + 4.1.) [4]_ Section 4.3 suggests improvements for choosing the step size. + + The new point is tested according to the termination conditions of [4]_ + Section 4.5. The same tolerance, which can be set using the ``tol`` option, + is used for all checks. (A potential improvement would be to expose + the different tolerances to be set independently.) If optimality, + unboundedness, or infeasibility is detected, the solve procedure + terminates; otherwise it repeats. + + Whereas the top level ``linprog`` module expects a problem of form: + + Minimize:: + + c @ x + + Subject to:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + where ``lb = 0`` and ``ub = None`` unless set in ``bounds``. The problem + is automatically converted to the form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + for solution. That is, the original problem contains equality, upper-bound + and variable constraints whereas the method specific solver requires + equality constraints and variable non-negativity. ``linprog`` converts the + original problem to standard form by converting the simple bounds to upper + bound constraints, introducing non-negative slack variables for inequality + constraints, and expressing unbounded variables as the difference between + two non-negative variables. The problem is converted back to the original + form before results are reported. + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear + Programming based on Newton's Method." Unpublished Course Notes, + March 2004. Available 2/25/2017 at + https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf + .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear + programming." Mathematical Programming 71.2 (1995): 221-245. + .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. + .. [10] Andersen, Erling D., et al. Implementation of interior point + methods for large scale linear programming. HEC/Universite de + Geneve, 1996. + """ + pass + + +def _linprog_rs_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='interior-point', callback=None, + x0=None, maxiter=5000, disp=False, presolve=True, + tol=1e-12, autoscale=False, rr=True, maxupdate=10, + mast=False, pivot="mrc", **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using the revised simplex method. + + .. deprecated:: 1.9.0 + `method='revised simplex'` will be removed in SciPy 1.11.0. + It is replaced by `method='highs'` because the latter is + faster and more robust. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + This is the method-specific documentation for 'revised simplex'. + :ref:`'highs' `, + :ref:`'highs-ds' `, + :ref:`'highs-ipm' `, + :ref:`'interior-point' ` (default), + and :ref:`'simplex' ` (legacy) + are also available. + callback : callable, optional + Callback function to be executed once per iteration. + x0 : 1-D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + Options + ------- + maxiter : int (default: 5000) + The maximum number of iterations to perform in either phase. + disp : bool (default: False) + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + presolve : bool (default: True) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + tol : float (default: 1e-12) + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + autoscale : bool (default: False) + Set to ``True`` to automatically perform equilibration. + Consider using this option if the numerical values in the + constraints are separated by several orders of magnitude. + rr : bool (default: True) + Set to ``False`` to disable automatic redundancy removal. + maxupdate : int (default: 10) + The maximum number of updates performed on the LU factorization. + After this many updates is reached, the basis matrix is factorized + from scratch. + mast : bool (default: False) + Minimize Amortized Solve Time. If enabled, the average time to solve + a linear system using the basis factorization is measured. Typically, + the average solve time will decrease with each successive solve after + initial factorization, as factorization takes much more time than the + solve operation (and updates). Eventually, however, the updated + factorization becomes sufficiently complex that the average solve time + begins to increase. When this is detected, the basis is refactorized + from scratch. Enable this option to maximize speed at the risk of + nondeterministic behavior. Ignored if ``maxupdate`` is 0. + pivot : "mrc" or "bland" (default: "mrc") + Pivot rule: Minimum Reduced Cost ("mrc") or Bland's rule ("bland"). + Choose Bland's rule if iteration limit is reached and cycling is + suspected. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1-D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1-D array + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : Numerical difficulties encountered. + + ``5`` : Problem has no constraints; turn presolve on. + + ``6`` : Invalid guess provided. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed in all phases. + + + Notes + ----- + Method *revised simplex* uses the revised simplex method as described in + [9]_, except that a factorization [11]_ of the basis matrix, rather than + its inverse, is efficiently maintained and used to solve the linear systems + at each iteration of the algorithm. + + References + ---------- + .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. + .. [11] Bartels, Richard H. "A stabilization of the simplex method." + Journal in Numerische Mathematik 16.5 (1971): 414-434. + """ + pass + + +def _linprog_simplex_doc(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, + bounds=None, method='interior-point', callback=None, + maxiter=5000, disp=False, presolve=True, + tol=1e-12, autoscale=False, rr=True, bland=False, + **unknown_options): + r""" + Linear programming: minimize a linear objective function subject to linear + equality and inequality constraints using the tableau-based simplex method. + + .. deprecated:: 1.9.0 + `method='simplex'` will be removed in SciPy 1.11.0. + It is replaced by `method='highs'` because the latter is + faster and more robust. + + Linear programming solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ + & A_{eq} x = b_{eq},\\ + & l \leq x \leq u , + + where :math:`x` is a vector of decision variables; :math:`c`, + :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and + :math:`A_{ub}` and :math:`A_{eq}` are matrices. + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + Note that by default ``lb = 0`` and ``ub = None`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1-D array + The coefficients of the linear objective function to be minimized. + A_ub : 2-D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1-D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2-D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1-D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : sequence, optional + A sequence of ``(min, max)`` pairs for each element in ``x``, defining + the minimum and maximum values of that decision variable. Use ``None`` + to indicate that there is no bound. By default, bounds are + ``(0, None)`` (all decision variables are non-negative). + If a single tuple ``(min, max)`` is provided, then ``min`` and + ``max`` will serve as bounds for all decision variables. + method : str + This is the method-specific documentation for 'simplex'. + :ref:`'highs' `, + :ref:`'highs-ds' `, + :ref:`'highs-ipm' `, + :ref:`'interior-point' ` (default), + and :ref:`'revised simplex' ` + are also available. + callback : callable, optional + Callback function to be executed once per iteration. + + Options + ------- + maxiter : int (default: 5000) + The maximum number of iterations to perform in either phase. + disp : bool (default: False) + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + presolve : bool (default: True) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if + presolve is to be disabled. + tol : float (default: 1e-12) + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + autoscale : bool (default: False) + Set to ``True`` to automatically perform equilibration. + Consider using this option if the numerical values in the + constraints are separated by several orders of magnitude. + rr : bool (default: True) + Set to ``False`` to disable automatic redundancy removal. + bland : bool + If True, use Bland's anti-cycling rule [3]_ to choose pivots to + prevent cycling. If False, choose pivots which should lead to a + converged solution more quickly. The latter method is subject to + cycling (non-convergence) in rare instances. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + res : OptimizeResult + A :class:`scipy.optimize.OptimizeResult` consisting of the fields: + + x : 1-D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1-D array + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : Numerical difficulties encountered. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed in all phases. + + References + ---------- + .. [1] Dantzig, George B., Linear programming and extensions. Rand + Corporation Research Study Princeton Univ. Press, Princeton, NJ, + 1963 + .. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to + Mathematical Programming", McGraw-Hill, Chapter 4. + .. [3] Bland, Robert G. New finite pivoting rules for the simplex method. + Mathematics of Operations Research (2), 1977: pp. 103-107. + """ + pass diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_highs.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_highs.py new file mode 100644 index 0000000000000000000000000000000000000000..eb07443bb255471e6e0ac487bd6749253bf5d133 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_highs.py @@ -0,0 +1,440 @@ +"""HiGHS Linear Optimization Methods + +Interface to HiGHS linear optimization software. +https://highs.dev/ + +.. versionadded:: 1.5.0 + +References +---------- +.. [1] Q. Huangfu and J.A.J. Hall. "Parallelizing the dual revised simplex + method." Mathematical Programming Computation, 10 (1), 119-142, + 2018. DOI: 10.1007/s12532-017-0130-5 + +""" + +import inspect +import numpy as np +from ._optimize import OptimizeWarning, OptimizeResult +from warnings import warn +from ._highs._highs_wrapper import _highs_wrapper +from ._highs._highs_constants import ( + CONST_INF, + MESSAGE_LEVEL_NONE, + HIGHS_OBJECTIVE_SENSE_MINIMIZE, + + MODEL_STATUS_NOTSET, + MODEL_STATUS_LOAD_ERROR, + MODEL_STATUS_MODEL_ERROR, + MODEL_STATUS_PRESOLVE_ERROR, + MODEL_STATUS_SOLVE_ERROR, + MODEL_STATUS_POSTSOLVE_ERROR, + MODEL_STATUS_MODEL_EMPTY, + MODEL_STATUS_OPTIMAL, + MODEL_STATUS_INFEASIBLE, + MODEL_STATUS_UNBOUNDED_OR_INFEASIBLE, + MODEL_STATUS_UNBOUNDED, + MODEL_STATUS_REACHED_DUAL_OBJECTIVE_VALUE_UPPER_BOUND + as MODEL_STATUS_RDOVUB, + MODEL_STATUS_REACHED_OBJECTIVE_TARGET, + MODEL_STATUS_REACHED_TIME_LIMIT, + MODEL_STATUS_REACHED_ITERATION_LIMIT, + + HIGHS_SIMPLEX_STRATEGY_DUAL, + + HIGHS_SIMPLEX_CRASH_STRATEGY_OFF, + + HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_CHOOSE, + HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DANTZIG, + HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DEVEX, + HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE, +) +from scipy.sparse import csc_matrix, vstack, issparse + + +def _highs_to_scipy_status_message(highs_status, highs_message): + """Converts HiGHS status number/message to SciPy status number/message""" + + scipy_statuses_messages = { + None: (4, "HiGHS did not provide a status code. "), + MODEL_STATUS_NOTSET: (4, ""), + MODEL_STATUS_LOAD_ERROR: (4, ""), + MODEL_STATUS_MODEL_ERROR: (2, ""), + MODEL_STATUS_PRESOLVE_ERROR: (4, ""), + MODEL_STATUS_SOLVE_ERROR: (4, ""), + MODEL_STATUS_POSTSOLVE_ERROR: (4, ""), + MODEL_STATUS_MODEL_EMPTY: (4, ""), + MODEL_STATUS_RDOVUB: (4, ""), + MODEL_STATUS_REACHED_OBJECTIVE_TARGET: (4, ""), + MODEL_STATUS_OPTIMAL: (0, "Optimization terminated successfully. "), + MODEL_STATUS_REACHED_TIME_LIMIT: (1, "Time limit reached. "), + MODEL_STATUS_REACHED_ITERATION_LIMIT: (1, "Iteration limit reached. "), + MODEL_STATUS_INFEASIBLE: (2, "The problem is infeasible. "), + MODEL_STATUS_UNBOUNDED: (3, "The problem is unbounded. "), + MODEL_STATUS_UNBOUNDED_OR_INFEASIBLE: (4, "The problem is unbounded " + "or infeasible. ")} + unrecognized = (4, "The HiGHS status code was not recognized. ") + scipy_status, scipy_message = ( + scipy_statuses_messages.get(highs_status, unrecognized)) + scipy_message = (f"{scipy_message}" + f"(HiGHS Status {highs_status}: {highs_message})") + return scipy_status, scipy_message + + +def _replace_inf(x): + # Replace `np.inf` with CONST_INF + infs = np.isinf(x) + with np.errstate(invalid="ignore"): + x[infs] = np.sign(x[infs])*CONST_INF + return x + + +def _convert_to_highs_enum(option, option_str, choices): + # If option is in the choices we can look it up, if not use + # the default value taken from function signature and warn: + try: + return choices[option.lower()] + except AttributeError: + return choices[option] + except KeyError: + sig = inspect.signature(_linprog_highs) + default_str = sig.parameters[option_str].default + warn(f"Option {option_str} is {option}, but only values in " + f"{set(choices.keys())} are allowed. Using default: " + f"{default_str}.", + OptimizeWarning, stacklevel=3) + return choices[default_str] + + +def _linprog_highs(lp, solver, time_limit=None, presolve=True, + disp=False, maxiter=None, + dual_feasibility_tolerance=None, + primal_feasibility_tolerance=None, + ipm_optimality_tolerance=None, + simplex_dual_edge_weight_strategy=None, + mip_rel_gap=None, + mip_max_nodes=None, + **unknown_options): + r""" + Solve the following linear programming problem using one of the HiGHS + solvers: + + User-facing documentation is in _linprog_doc.py. + + Parameters + ---------- + lp : _LPProblem + A ``scipy.optimize._linprog_util._LPProblem`` ``namedtuple``. + solver : "ipm" or "simplex" or None + Which HiGHS solver to use. If ``None``, "simplex" will be used. + + Options + ------- + maxiter : int + The maximum number of iterations to perform in either phase. For + ``solver='ipm'``, this does not include the number of crossover + iterations. Default is the largest possible value for an ``int`` + on the platform. + disp : bool + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration; default ``False``. + time_limit : float + The maximum time in seconds allotted to solve the problem; default is + the largest possible value for a ``double`` on the platform. + presolve : bool + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. It is generally recommended + to keep the default setting ``True``; set to ``False`` if presolve is + to be disabled. + dual_feasibility_tolerance : double + Dual feasibility tolerance. Default is 1e-07. + The minimum of this and ``primal_feasibility_tolerance`` + is used for the feasibility tolerance when ``solver='ipm'``. + primal_feasibility_tolerance : double + Primal feasibility tolerance. Default is 1e-07. + The minimum of this and ``dual_feasibility_tolerance`` + is used for the feasibility tolerance when ``solver='ipm'``. + ipm_optimality_tolerance : double + Optimality tolerance for ``solver='ipm'``. Default is 1e-08. + Minimum possible value is 1e-12 and must be smaller than the largest + possible value for a ``double`` on the platform. + simplex_dual_edge_weight_strategy : str (default: None) + Strategy for simplex dual edge weights. The default, ``None``, + automatically selects one of the following. + + ``'dantzig'`` uses Dantzig's original strategy of choosing the most + negative reduced cost. + + ``'devex'`` uses the strategy described in [15]_. + + ``steepest`` uses the exact steepest edge strategy as described in + [16]_. + + ``'steepest-devex'`` begins with the exact steepest edge strategy + until the computation is too costly or inexact and then switches to + the devex method. + + Currently, using ``None`` always selects ``'steepest-devex'``, but this + may change as new options become available. + + mip_max_nodes : int + The maximum number of nodes allotted to solve the problem; default is + the largest possible value for a ``HighsInt`` on the platform. + Ignored if not using the MIP solver. + unknown_options : dict + Optional arguments not used by this particular solver. If + ``unknown_options`` is non-empty, a warning is issued listing all + unused options. + + Returns + ------- + sol : dict + A dictionary consisting of the fields: + + x : 1D array + The values of the decision variables that minimizes the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + slack : 1D array + The (nominally positive) values of the slack, + ``b_ub - A_ub @ x``. + con : 1D array + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + success : bool + ``True`` when the algorithm succeeds in finding an optimal + solution. + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimization terminated successfully. + + ``1`` : Iteration or time limit reached. + + ``2`` : Problem appears to be infeasible. + + ``3`` : Problem appears to be unbounded. + + ``4`` : The HiGHS solver ran into a problem. + + message : str + A string descriptor of the exit status of the algorithm. + nit : int + The total number of iterations performed. + For ``solver='simplex'``, this includes iterations in all + phases. For ``solver='ipm'``, this does not include + crossover iterations. + crossover_nit : int + The number of primal/dual pushes performed during the + crossover routine for ``solver='ipm'``. This is ``0`` + for ``solver='simplex'``. + ineqlin : OptimizeResult + Solution and sensitivity information corresponding to the + inequality constraints, `b_ub`. A dictionary consisting of the + fields: + + residual : np.ndnarray + The (nominally positive) values of the slack variables, + ``b_ub - A_ub @ x``. This quantity is also commonly + referred to as "slack". + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + inequality constraints, `b_ub`. + + eqlin : OptimizeResult + Solution and sensitivity information corresponding to the + equality constraints, `b_eq`. A dictionary consisting of the + fields: + + residual : np.ndarray + The (nominally zero) residuals of the equality constraints, + ``b_eq - A_eq @ x``. + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the right-hand side of the + equality constraints, `b_eq`. + + lower, upper : OptimizeResult + Solution and sensitivity information corresponding to the + lower and upper bounds on decision variables, `bounds`. + + residual : np.ndarray + The (nominally positive) values of the quantity + ``x - lb`` (lower) or ``ub - x`` (upper). + + marginals : np.ndarray + The sensitivity (partial derivative) of the objective + function with respect to the lower and upper + `bounds`. + + mip_node_count : int + The number of subproblems or "nodes" solved by the MILP + solver. Only present when `integrality` is not `None`. + + mip_dual_bound : float + The MILP solver's final estimate of the lower bound on the + optimal solution. Only present when `integrality` is not + `None`. + + mip_gap : float + The difference between the final objective function value + and the final dual bound, scaled by the final objective + function value. Only present when `integrality` is not + `None`. + + Notes + ----- + The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain + `marginals`, or partial derivatives of the objective function with respect + to the right-hand side of each constraint. These partial derivatives are + also referred to as "Lagrange multipliers", "dual values", and + "shadow prices". The sign convention of `marginals` is opposite that + of Lagrange multipliers produced by many nonlinear solvers. + + References + ---------- + .. [15] Harris, Paula MJ. "Pivot selection methods of the Devex LP code." + Mathematical programming 5.1 (1973): 1-28. + .. [16] Goldfarb, Donald, and John Ker Reid. "A practicable steepest-edge + simplex algorithm." Mathematical Programming 12.1 (1977): 361-371. + """ + if unknown_options: + message = (f"Unrecognized options detected: {unknown_options}. " + "These will be passed to HiGHS verbatim.") + warn(message, OptimizeWarning, stacklevel=3) + + # Map options to HiGHS enum values + simplex_dual_edge_weight_strategy_enum = _convert_to_highs_enum( + simplex_dual_edge_weight_strategy, + 'simplex_dual_edge_weight_strategy', + choices={'dantzig': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DANTZIG, + 'devex': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_DEVEX, + 'steepest-devex': HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_CHOOSE, + 'steepest': + HIGHS_SIMPLEX_EDGE_WEIGHT_STRATEGY_STEEPEST_EDGE, + None: None}) + + c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp + + lb, ub = bounds.T.copy() # separate bounds, copy->C-cntgs + # highs_wrapper solves LHS <= A*x <= RHS, not equality constraints + with np.errstate(invalid="ignore"): + lhs_ub = -np.ones_like(b_ub)*np.inf # LHS of UB constraints is -inf + rhs_ub = b_ub # RHS of UB constraints is b_ub + lhs_eq = b_eq # Equality constraint is inequality + rhs_eq = b_eq # constraint with LHS=RHS + lhs = np.concatenate((lhs_ub, lhs_eq)) + rhs = np.concatenate((rhs_ub, rhs_eq)) + + if issparse(A_ub) or issparse(A_eq): + A = vstack((A_ub, A_eq)) + else: + A = np.vstack((A_ub, A_eq)) + A = csc_matrix(A) + + options = { + 'presolve': presolve, + 'sense': HIGHS_OBJECTIVE_SENSE_MINIMIZE, + 'solver': solver, + 'time_limit': time_limit, + 'highs_debug_level': MESSAGE_LEVEL_NONE, + 'dual_feasibility_tolerance': dual_feasibility_tolerance, + 'ipm_optimality_tolerance': ipm_optimality_tolerance, + 'log_to_console': disp, + 'mip_max_nodes': mip_max_nodes, + 'output_flag': disp, + 'primal_feasibility_tolerance': primal_feasibility_tolerance, + 'simplex_dual_edge_weight_strategy': + simplex_dual_edge_weight_strategy_enum, + 'simplex_strategy': HIGHS_SIMPLEX_STRATEGY_DUAL, + 'simplex_crash_strategy': HIGHS_SIMPLEX_CRASH_STRATEGY_OFF, + 'ipm_iteration_limit': maxiter, + 'simplex_iteration_limit': maxiter, + 'mip_rel_gap': mip_rel_gap, + } + options.update(unknown_options) + + # np.inf doesn't work; use very large constant + rhs = _replace_inf(rhs) + lhs = _replace_inf(lhs) + lb = _replace_inf(lb) + ub = _replace_inf(ub) + + if integrality is None or np.sum(integrality) == 0: + integrality = np.empty(0) + else: + integrality = np.array(integrality) + + res = _highs_wrapper(c, A.indptr, A.indices, A.data, lhs, rhs, + lb, ub, integrality.astype(np.uint8), options) + + # HiGHS represents constraints as lhs/rhs, so + # Ax + s = b => Ax = b - s + # and we need to split up s by A_ub and A_eq + if 'slack' in res: + slack = res['slack'] + con = np.array(slack[len(b_ub):]) + slack = np.array(slack[:len(b_ub)]) + else: + slack, con = None, None + + # lagrange multipliers for equalities/inequalities and upper/lower bounds + if 'lambda' in res: + lamda = res['lambda'] + marg_ineqlin = np.array(lamda[:len(b_ub)]) + marg_eqlin = np.array(lamda[len(b_ub):]) + marg_upper = np.array(res['marg_bnds'][1, :]) + marg_lower = np.array(res['marg_bnds'][0, :]) + else: + marg_ineqlin, marg_eqlin = None, None + marg_upper, marg_lower = None, None + + # this needs to be updated if we start choosing the solver intelligently + + # Convert to scipy-style status and message + highs_status = res.get('status', None) + highs_message = res.get('message', None) + status, message = _highs_to_scipy_status_message(highs_status, + highs_message) + + x = np.array(res['x']) if 'x' in res else None + sol = {'x': x, + 'slack': slack, + 'con': con, + 'ineqlin': OptimizeResult({ + 'residual': slack, + 'marginals': marg_ineqlin, + }), + 'eqlin': OptimizeResult({ + 'residual': con, + 'marginals': marg_eqlin, + }), + 'lower': OptimizeResult({ + 'residual': None if x is None else x - lb, + 'marginals': marg_lower, + }), + 'upper': OptimizeResult({ + 'residual': None if x is None else ub - x, + 'marginals': marg_upper + }), + 'fun': res.get('fun'), + 'status': status, + 'success': res['status'] == MODEL_STATUS_OPTIMAL, + 'message': message, + 'nit': res.get('simplex_nit', 0) or res.get('ipm_nit', 0), + 'crossover_nit': res.get('crossover_nit'), + } + + if np.any(x) and integrality is not None: + sol.update({ + 'mip_node_count': res.get('mip_node_count', 0), + 'mip_dual_bound': res.get('mip_dual_bound', 0.0), + 'mip_gap': res.get('mip_gap', 0.0), + }) + + return sol diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_ip.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_ip.py new file mode 100644 index 0000000000000000000000000000000000000000..73bca3037f0e548f2420ba6be220446e94ddeb69 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_ip.py @@ -0,0 +1,1126 @@ +"""Interior-point method for linear programming + +The *interior-point* method uses the primal-dual path following algorithm +outlined in [1]_. This algorithm supports sparse constraint matrices and +is typically faster than the simplex methods, especially for large, sparse +problems. Note, however, that the solution returned may be slightly less +accurate than those of the simplex methods and will not, in general, +correspond with a vertex of the polytope defined by the constraints. + + .. versionadded:: 1.0.0 + +References +---------- +.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. +""" +# Author: Matt Haberland + +import numpy as np +import scipy as sp +import scipy.sparse as sps +from warnings import warn +from scipy.linalg import LinAlgError +from ._optimize import OptimizeWarning, OptimizeResult, _check_unknown_options +from ._linprog_util import _postsolve +has_umfpack = True +has_cholmod = True +try: + import sksparse # noqa: F401 + from sksparse.cholmod import cholesky as cholmod # noqa: F401 + from sksparse.cholmod import analyze as cholmod_analyze +except ImportError: + has_cholmod = False +try: + import scikits.umfpack # test whether to use factorized # noqa: F401 +except ImportError: + has_umfpack = False + + +def _get_solver(M, sparse=False, lstsq=False, sym_pos=True, + cholesky=True, permc_spec='MMD_AT_PLUS_A'): + """ + Given solver options, return a handle to the appropriate linear system + solver. + + Parameters + ---------- + M : 2-D array + As defined in [4] Equation 8.31 + sparse : bool (default = False) + True if the system to be solved is sparse. This is typically set + True when the original ``A_ub`` and ``A_eq`` arrays are sparse. + lstsq : bool (default = False) + True if the system is ill-conditioned and/or (nearly) singular and + thus a more robust least-squares solver is desired. This is sometimes + needed as the solution is approached. + sym_pos : bool (default = True) + True if the system matrix is symmetric positive definite + Sometimes this needs to be set false as the solution is approached, + even when the system should be symmetric positive definite, due to + numerical difficulties. + cholesky : bool (default = True) + True if the system is to be solved by Cholesky, rather than LU, + decomposition. This is typically faster unless the problem is very + small or prone to numerical difficulties. + permc_spec : str (default = 'MMD_AT_PLUS_A') + Sparsity preservation strategy used by SuperLU. Acceptable values are: + + - ``NATURAL``: natural ordering. + - ``MMD_ATA``: minimum degree ordering on the structure of A^T A. + - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A. + - ``COLAMD``: approximate minimum degree column ordering. + + See SuperLU documentation. + + Returns + ------- + solve : function + Handle to the appropriate solver function + + """ + try: + if sparse: + if lstsq: + def solve(r, sym_pos=False): + return sps.linalg.lsqr(M, r)[0] + elif cholesky: + try: + # Will raise an exception in the first call, + # or when the matrix changes due to a new problem + _get_solver.cholmod_factor.cholesky_inplace(M) + except Exception: + _get_solver.cholmod_factor = cholmod_analyze(M) + _get_solver.cholmod_factor.cholesky_inplace(M) + solve = _get_solver.cholmod_factor + else: + if has_umfpack and sym_pos: + solve = sps.linalg.factorized(M) + else: # factorized doesn't pass permc_spec + solve = sps.linalg.splu(M, permc_spec=permc_spec).solve + + else: + if lstsq: # sometimes necessary as solution is approached + def solve(r): + return sp.linalg.lstsq(M, r)[0] + elif cholesky: + L = sp.linalg.cho_factor(M) + + def solve(r): + return sp.linalg.cho_solve(L, r) + else: + # this seems to cache the matrix factorization, so solving + # with multiple right hand sides is much faster + def solve(r, sym_pos=sym_pos): + if sym_pos: + return sp.linalg.solve(M, r, assume_a="pos") + else: + return sp.linalg.solve(M, r) + # There are many things that can go wrong here, and it's hard to say + # what all of them are. It doesn't really matter: if the matrix can't be + # factorized, return None. get_solver will be called again with different + # inputs, and a new routine will try to factorize the matrix. + except KeyboardInterrupt: + raise + except Exception: + return None + return solve + + +def _get_delta(A, b, c, x, y, z, tau, kappa, gamma, eta, sparse=False, + lstsq=False, sym_pos=True, cholesky=True, pc=True, ip=False, + permc_spec='MMD_AT_PLUS_A'): + """ + Given standard form problem defined by ``A``, ``b``, and ``c``; + current variable estimates ``x``, ``y``, ``z``, ``tau``, and ``kappa``; + algorithmic parameters ``gamma and ``eta; + and options ``sparse``, ``lstsq``, ``sym_pos``, ``cholesky``, ``pc`` + (predictor-corrector), and ``ip`` (initial point improvement), + get the search direction for increments to the variable estimates. + + Parameters + ---------- + As defined in [4], except: + sparse : bool + True if the system to be solved is sparse. This is typically set + True when the original ``A_ub`` and ``A_eq`` arrays are sparse. + lstsq : bool + True if the system is ill-conditioned and/or (nearly) singular and + thus a more robust least-squares solver is desired. This is sometimes + needed as the solution is approached. + sym_pos : bool + True if the system matrix is symmetric positive definite + Sometimes this needs to be set false as the solution is approached, + even when the system should be symmetric positive definite, due to + numerical difficulties. + cholesky : bool + True if the system is to be solved by Cholesky, rather than LU, + decomposition. This is typically faster unless the problem is very + small or prone to numerical difficulties. + pc : bool + True if the predictor-corrector method of Mehrota is to be used. This + is almost always (if not always) beneficial. Even though it requires + the solution of an additional linear system, the factorization + is typically (implicitly) reused so solution is efficient, and the + number of algorithm iterations is typically reduced. + ip : bool + True if the improved initial point suggestion due to [4] section 4.3 + is desired. It's unclear whether this is beneficial. + permc_spec : str (default = 'MMD_AT_PLUS_A') + (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos = + True``.) A matrix is factorized in each iteration of the algorithm. + This option specifies how to permute the columns of the matrix for + sparsity preservation. Acceptable values are: + + - ``NATURAL``: natural ordering. + - ``MMD_ATA``: minimum degree ordering on the structure of A^T A. + - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A. + - ``COLAMD``: approximate minimum degree column ordering. + + This option can impact the convergence of the + interior point algorithm; test different values to determine which + performs best for your problem. For more information, refer to + ``scipy.sparse.linalg.splu``. + + Returns + ------- + Search directions as defined in [4] + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + if A.shape[0] == 0: + # If there are no constraints, some solvers fail (understandably) + # rather than returning empty solution. This gets the job done. + sparse, lstsq, sym_pos, cholesky = False, False, True, False + n_x = len(x) + + # [4] Equation 8.8 + r_P = b * tau - A.dot(x) + r_D = c * tau - A.T.dot(y) - z + r_G = c.dot(x) - b.transpose().dot(y) + kappa + mu = (x.dot(z) + tau * kappa) / (n_x + 1) + + # Assemble M from [4] Equation 8.31 + Dinv = x / z + + if sparse: + M = A.dot(sps.diags(Dinv, 0, format="csc").dot(A.T)) + else: + M = A.dot(Dinv.reshape(-1, 1) * A.T) + solve = _get_solver(M, sparse, lstsq, sym_pos, cholesky, permc_spec) + + # pc: "predictor-corrector" [4] Section 4.1 + # In development this option could be turned off + # but it always seems to improve performance substantially + n_corrections = 1 if pc else 0 + + i = 0 + alpha, d_x, d_z, d_tau, d_kappa = 0, 0, 0, 0, 0 + while i <= n_corrections: + # Reference [4] Eq. 8.6 + rhatp = eta(gamma) * r_P + rhatd = eta(gamma) * r_D + rhatg = eta(gamma) * r_G + + # Reference [4] Eq. 8.7 + rhatxs = gamma * mu - x * z + rhattk = gamma * mu - tau * kappa + + if i == 1: + if ip: # if the correction is to get "initial point" + # Reference [4] Eq. 8.23 + rhatxs = ((1 - alpha) * gamma * mu - + x * z - alpha**2 * d_x * d_z) + rhattk = ((1 - alpha) * gamma * mu - + tau * kappa - + alpha**2 * d_tau * d_kappa) + else: # if the correction is for "predictor-corrector" + # Reference [4] Eq. 8.13 + rhatxs -= d_x * d_z + rhattk -= d_tau * d_kappa + + # sometimes numerical difficulties arise as the solution is approached + # this loop tries to solve the equations using a sequence of functions + # for solve. For dense systems, the order is: + # 1. scipy.linalg.cho_factor/scipy.linalg.cho_solve, + # 2. scipy.linalg.solve w/ sym_pos = True, + # 3. scipy.linalg.solve w/ sym_pos = False, and if all else fails + # 4. scipy.linalg.lstsq + # For sparse systems, the order is: + # 1. sksparse.cholmod.cholesky (if available) + # 2. scipy.sparse.linalg.factorized (if umfpack available) + # 3. scipy.sparse.linalg.splu + # 4. scipy.sparse.linalg.lsqr + solved = False + while not solved: + try: + # [4] Equation 8.28 + p, q = _sym_solve(Dinv, A, c, b, solve) + # [4] Equation 8.29 + u, v = _sym_solve(Dinv, A, rhatd - + (1 / x) * rhatxs, rhatp, solve) + if np.any(np.isnan(p)) or np.any(np.isnan(q)): + raise LinAlgError + solved = True + except (LinAlgError, ValueError, TypeError) as e: + # Usually this doesn't happen. If it does, it happens when + # there are redundant constraints or when approaching the + # solution. If so, change solver. + if cholesky: + cholesky = False + warn( + "Solving system with option 'cholesky':True " + "failed. It is normal for this to happen " + "occasionally, especially as the solution is " + "approached. However, if you see this frequently, " + "consider setting option 'cholesky' to False.", + OptimizeWarning, stacklevel=5) + elif sym_pos: + sym_pos = False + warn( + "Solving system with option 'sym_pos':True " + "failed. It is normal for this to happen " + "occasionally, especially as the solution is " + "approached. However, if you see this frequently, " + "consider setting option 'sym_pos' to False.", + OptimizeWarning, stacklevel=5) + elif not lstsq: + lstsq = True + warn( + "Solving system with option 'sym_pos':False " + "failed. This may happen occasionally, " + "especially as the solution is " + "approached. However, if you see this frequently, " + "your problem may be numerically challenging. " + "If you cannot improve the formulation, consider " + "setting 'lstsq' to True. Consider also setting " + "`presolve` to True, if it is not already.", + OptimizeWarning, stacklevel=5) + else: + raise e + solve = _get_solver(M, sparse, lstsq, sym_pos, + cholesky, permc_spec) + # [4] Results after 8.29 + d_tau = ((rhatg + 1 / tau * rhattk - (-c.dot(u) + b.dot(v))) / + (1 / tau * kappa + (-c.dot(p) + b.dot(q)))) + d_x = u + p * d_tau + d_y = v + q * d_tau + + # [4] Relations between after 8.25 and 8.26 + d_z = (1 / x) * (rhatxs - z * d_x) + d_kappa = 1 / tau * (rhattk - kappa * d_tau) + + # [4] 8.12 and "Let alpha be the maximal possible step..." before 8.23 + alpha = _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, 1) + if ip: # initial point - see [4] 4.4 + gamma = 10 + else: # predictor-corrector, [4] definition after 8.12 + beta1 = 0.1 # [4] pg. 220 (Table 8.1) + gamma = (1 - alpha)**2 * min(beta1, (1 - alpha)) + i += 1 + + return d_x, d_y, d_z, d_tau, d_kappa + + +def _sym_solve(Dinv, A, r1, r2, solve): + """ + An implementation of [4] equation 8.31 and 8.32 + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + # [4] 8.31 + r = r2 + A.dot(Dinv * r1) + v = solve(r) + # [4] 8.32 + u = Dinv * (A.T.dot(v) - r1) + return u, v + + +def _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, alpha0): + """ + An implementation of [4] equation 8.21 + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + # [4] 4.3 Equation 8.21, ignoring 8.20 requirement + # same step is taken in primal and dual spaces + # alpha0 is basically beta3 from [4] Table 8.1, but instead of beta3 + # the value 1 is used in Mehrota corrector and initial point correction + i_x = d_x < 0 + i_z = d_z < 0 + alpha_x = alpha0 * np.min(x[i_x] / -d_x[i_x]) if np.any(i_x) else 1 + alpha_tau = alpha0 * tau / -d_tau if d_tau < 0 else 1 + alpha_z = alpha0 * np.min(z[i_z] / -d_z[i_z]) if np.any(i_z) else 1 + alpha_kappa = alpha0 * kappa / -d_kappa if d_kappa < 0 else 1 + alpha = np.min([1, alpha_x, alpha_tau, alpha_z, alpha_kappa]) + return alpha + + +def _get_message(status): + """ + Given problem status code, return a more detailed message. + + Parameters + ---------- + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + Returns + ------- + message : str + A string descriptor of the exit status of the optimization. + + """ + messages = ( + ["Optimization terminated successfully.", + "The iteration limit was reached before the algorithm converged.", + "The algorithm terminated successfully and determined that the " + "problem is infeasible.", + "The algorithm terminated successfully and determined that the " + "problem is unbounded.", + "Numerical difficulties were encountered before the problem " + "converged. Please check your problem formulation for errors, " + "independence of linear equality constraints, and reasonable " + "scaling and matrix condition numbers. If you continue to " + "encounter this error, please submit a bug report." + ]) + return messages[status] + + +def _do_step(x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha): + """ + An implementation of [4] Equation 8.9 + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + x = x + alpha * d_x + tau = tau + alpha * d_tau + z = z + alpha * d_z + kappa = kappa + alpha * d_kappa + y = y + alpha * d_y + return x, y, z, tau, kappa + + +def _get_blind_start(shape): + """ + Return the starting point from [4] 4.4 + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + m, n = shape + x0 = np.ones(n) + y0 = np.zeros(m) + z0 = np.ones(n) + tau0 = 1 + kappa0 = 1 + return x0, y0, z0, tau0, kappa0 + + +def _indicators(A, b, c, c0, x, y, z, tau, kappa): + """ + Implementation of several equations from [4] used as indicators of + the status of optimization. + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + + # residuals for termination are relative to initial values + x0, y0, z0, tau0, kappa0 = _get_blind_start(A.shape) + + # See [4], Section 4 - The Homogeneous Algorithm, Equation 8.8 + def r_p(x, tau): + return b * tau - A.dot(x) + + def r_d(y, z, tau): + return c * tau - A.T.dot(y) - z + + def r_g(x, y, kappa): + return kappa + c.dot(x) - b.dot(y) + + # np.dot unpacks if they are arrays of size one + def mu(x, tau, z, kappa): + return (x.dot(z) + np.dot(tau, kappa)) / (len(x) + 1) + + obj = c.dot(x / tau) + c0 + + def norm(a): + return np.linalg.norm(a) + + # See [4], Section 4.5 - The Stopping Criteria + r_p0 = r_p(x0, tau0) + r_d0 = r_d(y0, z0, tau0) + r_g0 = r_g(x0, y0, kappa0) + mu_0 = mu(x0, tau0, z0, kappa0) + rho_A = norm(c.T.dot(x) - b.T.dot(y)) / (tau + norm(b.T.dot(y))) + rho_p = norm(r_p(x, tau)) / max(1, norm(r_p0)) + rho_d = norm(r_d(y, z, tau)) / max(1, norm(r_d0)) + rho_g = norm(r_g(x, y, kappa)) / max(1, norm(r_g0)) + rho_mu = mu(x, tau, z, kappa) / mu_0 + return rho_p, rho_d, rho_A, rho_g, rho_mu, obj + + +def _display_iter(rho_p, rho_d, rho_g, alpha, rho_mu, obj, header=False): + """ + Print indicators of optimization status to the console. + + Parameters + ---------- + rho_p : float + The (normalized) primal feasibility, see [4] 4.5 + rho_d : float + The (normalized) dual feasibility, see [4] 4.5 + rho_g : float + The (normalized) duality gap, see [4] 4.5 + alpha : float + The step size, see [4] 4.3 + rho_mu : float + The (normalized) path parameter, see [4] 4.5 + obj : float + The objective function value of the current iterate + header : bool + True if a header is to be printed + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + + """ + if header: + print("Primal Feasibility ", + "Dual Feasibility ", + "Duality Gap ", + "Step ", + "Path Parameter ", + "Objective ") + + # no clue why this works + fmt = '{0:<20.13}{1:<20.13}{2:<20.13}{3:<17.13}{4:<20.13}{5:<20.13}' + print(fmt.format( + float(rho_p), + float(rho_d), + float(rho_g), + alpha if isinstance(alpha, str) else float(alpha), + float(rho_mu), + float(obj))) + + +def _ip_hsd(A, b, c, c0, alpha0, beta, maxiter, disp, tol, sparse, lstsq, + sym_pos, cholesky, pc, ip, permc_spec, callback, postsolve_args): + r""" + Solve a linear programming problem in standard form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + using the interior point method of [4]. + + Parameters + ---------- + A : 2-D array + 2-D array such that ``A @ x``, gives the values of the equality + constraints at ``x``. + b : 1-D array + 1-D array of values representing the RHS of each equality constraint + (row) in ``A`` (for standard form problem). + c : 1-D array + Coefficients of the linear objective function to be minimized (for + standard form problem). + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. (Purely for display.) + alpha0 : float + The maximal step size for Mehrota's predictor-corrector search + direction; see :math:`\beta_3`of [4] Table 8.1 + beta : float + The desired reduction of the path parameter :math:`\mu` (see [6]_) + maxiter : int + The maximum number of iterations of the algorithm. + disp : bool + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + tol : float + Termination tolerance; see [4]_ Section 4.5. + sparse : bool + Set to ``True`` if the problem is to be treated as sparse. However, + the inputs ``A_eq`` and ``A_ub`` should nonetheless be provided as + (dense) arrays rather than sparse matrices. + lstsq : bool + Set to ``True`` if the problem is expected to be very poorly + conditioned. This should always be left as ``False`` unless severe + numerical difficulties are frequently encountered, and a better option + would be to improve the formulation of the problem. + sym_pos : bool + Leave ``True`` if the problem is expected to yield a well conditioned + symmetric positive definite normal equation matrix (almost always). + cholesky : bool + Set to ``True`` if the normal equations are to be solved by explicit + Cholesky decomposition followed by explicit forward/backward + substitution. This is typically faster for moderate, dense problems + that are numerically well-behaved. + pc : bool + Leave ``True`` if the predictor-corrector method of Mehrota is to be + used. This is almost always (if not always) beneficial. + ip : bool + Set to ``True`` if the improved initial point suggestion due to [4]_ + Section 4.3 is desired. It's unclear whether this is beneficial. + permc_spec : str (default = 'MMD_AT_PLUS_A') + (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos = + True``.) A matrix is factorized in each iteration of the algorithm. + This option specifies how to permute the columns of the matrix for + sparsity preservation. Acceptable values are: + + - ``NATURAL``: natural ordering. + - ``MMD_ATA``: minimum degree ordering on the structure of A^T A. + - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A. + - ``COLAMD``: approximate minimum degree column ordering. + + This option can impact the convergence of the + interior point algorithm; test different values to determine which + performs best for your problem. For more information, refer to + ``scipy.sparse.linalg.splu``. + callback : callable, optional + If a callback function is provided, it will be called within each + iteration of the algorithm. The callback function must accept a single + `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + Current solution vector + fun : float + Current value of the objective function + success : bool + True only when an algorithm has completed successfully, + so this is always False as the callback function is called + only while the algorithm is still iterating. + slack : 1-D array + The values of the slack variables. Each slack variable + corresponds to an inequality constraint. If the slack is zero, + the corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + that is, ``b - A_eq @ x`` + phase : int + The phase of the algorithm being executed. This is always + 1 for the interior-point method because it has only one phase. + status : int + For revised simplex, this is always 0 because if a different + status is detected, the algorithm terminates. + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem. + + Returns + ------- + x_hat : float + Solution vector (for standard form problem). + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + message : str + A string descriptor of the exit status of the optimization. + iteration : int + The number of iterations taken to solve the problem + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear + Programming based on Newton's Method." Unpublished Course Notes, + March 2004. Available 2/25/2017 at: + https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf + + """ + + iteration = 0 + + # default initial point + x, y, z, tau, kappa = _get_blind_start(A.shape) + + # first iteration is special improvement of initial point + ip = ip if pc else False + + # [4] 4.5 + rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators( + A, b, c, c0, x, y, z, tau, kappa) + go = rho_p > tol or rho_d > tol or rho_A > tol # we might get lucky : ) + + if disp: + _display_iter(rho_p, rho_d, rho_g, "-", rho_mu, obj, header=True) + if callback is not None: + x_o, fun, slack, con = _postsolve(x/tau, postsolve_args) + res = OptimizeResult({'x': x_o, 'fun': fun, 'slack': slack, + 'con': con, 'nit': iteration, 'phase': 1, + 'complete': False, 'status': 0, + 'message': "", 'success': False}) + callback(res) + + status = 0 + message = "Optimization terminated successfully." + + if sparse: + A = sps.csc_matrix(A) + + while go: + + iteration += 1 + + if ip: # initial point + # [4] Section 4.4 + gamma = 1 + + def eta(g): + return 1 + else: + # gamma = 0 in predictor step according to [4] 4.1 + # if predictor/corrector is off, use mean of complementarity [6] + # 5.1 / [4] Below Figure 10-4 + gamma = 0 if pc else beta * np.mean(z * x) + # [4] Section 4.1 + + def eta(g=gamma): + return 1 - g + + try: + # Solve [4] 8.6 and 8.7/8.13/8.23 + d_x, d_y, d_z, d_tau, d_kappa = _get_delta( + A, b, c, x, y, z, tau, kappa, gamma, eta, + sparse, lstsq, sym_pos, cholesky, pc, ip, permc_spec) + + if ip: # initial point + # [4] 4.4 + # Formula after 8.23 takes a full step regardless if this will + # take it negative + alpha = 1.0 + x, y, z, tau, kappa = _do_step( + x, y, z, tau, kappa, d_x, d_y, + d_z, d_tau, d_kappa, alpha) + x[x < 1] = 1 + z[z < 1] = 1 + tau = max(1, tau) + kappa = max(1, kappa) + ip = False # done with initial point + else: + # [4] Section 4.3 + alpha = _get_step(x, d_x, z, d_z, tau, + d_tau, kappa, d_kappa, alpha0) + # [4] Equation 8.9 + x, y, z, tau, kappa = _do_step( + x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha) + + except (LinAlgError, FloatingPointError, + ValueError, ZeroDivisionError): + # this can happen when sparse solver is used and presolve + # is turned off. Also observed ValueError in AppVeyor Python 3.6 + # Win32 build (PR #8676). I've never seen it otherwise. + status = 4 + message = _get_message(status) + break + + # [4] 4.5 + rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators( + A, b, c, c0, x, y, z, tau, kappa) + go = rho_p > tol or rho_d > tol or rho_A > tol + + if disp: + _display_iter(rho_p, rho_d, rho_g, alpha, rho_mu, obj) + if callback is not None: + x_o, fun, slack, con = _postsolve(x/tau, postsolve_args) + res = OptimizeResult({'x': x_o, 'fun': fun, 'slack': slack, + 'con': con, 'nit': iteration, 'phase': 1, + 'complete': False, 'status': 0, + 'message': "", 'success': False}) + callback(res) + + # [4] 4.5 + inf1 = (rho_p < tol and rho_d < tol and rho_g < tol and tau < tol * + max(1, kappa)) + inf2 = rho_mu < tol and tau < tol * min(1, kappa) + if inf1 or inf2: + # [4] Lemma 8.4 / Theorem 8.3 + if b.transpose().dot(y) > tol: + status = 2 + else: # elif c.T.dot(x) < tol: ? Probably not necessary. + status = 3 + message = _get_message(status) + break + elif iteration >= maxiter: + status = 1 + message = _get_message(status) + break + + x_hat = x / tau + # [4] Statement after Theorem 8.2 + return x_hat, status, message, iteration + + +def _linprog_ip(c, c0, A, b, callback, postsolve_args, maxiter=1000, tol=1e-8, + disp=False, alpha0=.99995, beta=0.1, sparse=False, lstsq=False, + sym_pos=True, cholesky=None, pc=True, ip=False, + permc_spec='MMD_AT_PLUS_A', **unknown_options): + r""" + Minimize a linear objective function subject to linear + equality and non-negativity constraints using the interior point method + of [4]_. Linear programming is intended to solve problems + of the following form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + User-facing documentation is in _linprog_doc.py. + + Parameters + ---------- + c : 1-D array + Coefficients of the linear objective function to be minimized. + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. (Purely for display.) + A : 2-D array + 2-D array such that ``A @ x``, gives the values of the equality + constraints at ``x``. + b : 1-D array + 1-D array of values representing the right hand side of each equality + constraint (row) in ``A``. + callback : callable, optional + Callback function to be executed once per iteration. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem. + + Options + ------- + maxiter : int (default = 1000) + The maximum number of iterations of the algorithm. + tol : float (default = 1e-8) + Termination tolerance to be used for all termination criteria; + see [4]_ Section 4.5. + disp : bool (default = False) + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + alpha0 : float (default = 0.99995) + The maximal step size for Mehrota's predictor-corrector search + direction; see :math:`\beta_{3}` of [4]_ Table 8.1. + beta : float (default = 0.1) + The desired reduction of the path parameter :math:`\mu` (see [6]_) + when Mehrota's predictor-corrector is not in use (uncommon). + sparse : bool (default = False) + Set to ``True`` if the problem is to be treated as sparse after + presolve. If either ``A_eq`` or ``A_ub`` is a sparse matrix, + this option will automatically be set ``True``, and the problem + will be treated as sparse even during presolve. If your constraint + matrices contain mostly zeros and the problem is not very small (less + than about 100 constraints or variables), consider setting ``True`` + or providing ``A_eq`` and ``A_ub`` as sparse matrices. + lstsq : bool (default = False) + Set to ``True`` if the problem is expected to be very poorly + conditioned. This should always be left ``False`` unless severe + numerical difficulties are encountered. Leave this at the default + unless you receive a warning message suggesting otherwise. + sym_pos : bool (default = True) + Leave ``True`` if the problem is expected to yield a well conditioned + symmetric positive definite normal equation matrix + (almost always). Leave this at the default unless you receive + a warning message suggesting otherwise. + cholesky : bool (default = True) + Set to ``True`` if the normal equations are to be solved by explicit + Cholesky decomposition followed by explicit forward/backward + substitution. This is typically faster for problems + that are numerically well-behaved. + pc : bool (default = True) + Leave ``True`` if the predictor-corrector method of Mehrota is to be + used. This is almost always (if not always) beneficial. + ip : bool (default = False) + Set to ``True`` if the improved initial point suggestion due to [4]_ + Section 4.3 is desired. Whether this is beneficial or not + depends on the problem. + permc_spec : str (default = 'MMD_AT_PLUS_A') + (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos = + True``, and no SuiteSparse.) + A matrix is factorized in each iteration of the algorithm. + This option specifies how to permute the columns of the matrix for + sparsity preservation. Acceptable values are: + + - ``NATURAL``: natural ordering. + - ``MMD_ATA``: minimum degree ordering on the structure of A^T A. + - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A. + - ``COLAMD``: approximate minimum degree column ordering. + + This option can impact the convergence of the + interior point algorithm; test different values to determine which + performs best for your problem. For more information, refer to + ``scipy.sparse.linalg.splu``. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + x : 1-D array + Solution vector. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + message : str + A string descriptor of the exit status of the optimization. + iteration : int + The number of iterations taken to solve the problem. + + Notes + ----- + This method implements the algorithm outlined in [4]_ with ideas from [8]_ + and a structure inspired by the simpler methods of [6]_. + + The primal-dual path following method begins with initial 'guesses' of + the primal and dual variables of the standard form problem and iteratively + attempts to solve the (nonlinear) Karush-Kuhn-Tucker conditions for the + problem with a gradually reduced logarithmic barrier term added to the + objective. This particular implementation uses a homogeneous self-dual + formulation, which provides certificates of infeasibility or unboundedness + where applicable. + + The default initial point for the primal and dual variables is that + defined in [4]_ Section 4.4 Equation 8.22. Optionally (by setting initial + point option ``ip=True``), an alternate (potentially improved) starting + point can be calculated according to the additional recommendations of + [4]_ Section 4.4. + + A search direction is calculated using the predictor-corrector method + (single correction) proposed by Mehrota and detailed in [4]_ Section 4.1. + (A potential improvement would be to implement the method of multiple + corrections described in [4]_ Section 4.2.) In practice, this is + accomplished by solving the normal equations, [4]_ Section 5.1 Equations + 8.31 and 8.32, derived from the Newton equations [4]_ Section 5 Equations + 8.25 (compare to [4]_ Section 4 Equations 8.6-8.8). The advantage of + solving the normal equations rather than 8.25 directly is that the + matrices involved are symmetric positive definite, so Cholesky + decomposition can be used rather than the more expensive LU factorization. + + With default options, the solver used to perform the factorization depends + on third-party software availability and the conditioning of the problem. + + For dense problems, solvers are tried in the following order: + + 1. ``scipy.linalg.cho_factor`` + + 2. ``scipy.linalg.solve`` with option ``sym_pos=True`` + + 3. ``scipy.linalg.solve`` with option ``sym_pos=False`` + + 4. ``scipy.linalg.lstsq`` + + For sparse problems: + + 1. ``sksparse.cholmod.cholesky`` (if scikit-sparse and SuiteSparse are installed) + + 2. ``scipy.sparse.linalg.factorized`` + (if scikit-umfpack and SuiteSparse are installed) + + 3. ``scipy.sparse.linalg.splu`` (which uses SuperLU distributed with SciPy) + + 4. ``scipy.sparse.linalg.lsqr`` + + If the solver fails for any reason, successively more robust (but slower) + solvers are attempted in the order indicated. Attempting, failing, and + re-starting factorization can be time consuming, so if the problem is + numerically challenging, options can be set to bypass solvers that are + failing. Setting ``cholesky=False`` skips to solver 2, + ``sym_pos=False`` skips to solver 3, and ``lstsq=True`` skips + to solver 4 for both sparse and dense problems. + + Potential improvements for combatting issues associated with dense + columns in otherwise sparse problems are outlined in [4]_ Section 5.3 and + [10]_ Section 4.1-4.2; the latter also discusses the alleviation of + accuracy issues associated with the substitution approach to free + variables. + + After calculating the search direction, the maximum possible step size + that does not activate the non-negativity constraints is calculated, and + the smaller of this step size and unity is applied (as in [4]_ Section + 4.1.) [4]_ Section 4.3 suggests improvements for choosing the step size. + + The new point is tested according to the termination conditions of [4]_ + Section 4.5. The same tolerance, which can be set using the ``tol`` option, + is used for all checks. (A potential improvement would be to expose + the different tolerances to be set independently.) If optimality, + unboundedness, or infeasibility is detected, the solve procedure + terminates; otherwise it repeats. + + The expected problem formulation differs between the top level ``linprog`` + module and the method specific solvers. The method specific solvers expect a + problem in standard form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + Whereas the top level ``linprog`` module expects a problem of form: + + Minimize:: + + c @ x + + Subject to:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + where ``lb = 0`` and ``ub = None`` unless set in ``bounds``. + + The original problem contains equality, upper-bound and variable constraints + whereas the method specific solver requires equality constraints and + variable non-negativity. + + ``linprog`` module converts the original problem to standard form by + converting the simple bounds to upper bound constraints, introducing + non-negative slack variables for inequality constraints, and expressing + unbounded variables as the difference between two non-negative variables. + + + References + ---------- + .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point + optimizer for linear programming: an implementation of the + homogeneous algorithm." High performance optimization. Springer US, + 2000. 197-232. + .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear + Programming based on Newton's Method." Unpublished Course Notes, + March 2004. Available 2/25/2017 at + https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf + .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear + programming." Mathematical Programming 71.2 (1995): 221-245. + .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. + .. [10] Andersen, Erling D., et al. Implementation of interior point methods + for large scale linear programming. HEC/Universite de Geneve, 1996. + + """ + + _check_unknown_options(unknown_options) + + # These should be warnings, not errors + if (cholesky or cholesky is None) and sparse and not has_cholmod: + if cholesky: + warn("Sparse cholesky is only available with scikit-sparse. " + "Setting `cholesky = False`", + OptimizeWarning, stacklevel=3) + cholesky = False + + if sparse and lstsq: + warn("Option combination 'sparse':True and 'lstsq':True " + "is not recommended.", + OptimizeWarning, stacklevel=3) + + if lstsq and cholesky: + warn("Invalid option combination 'lstsq':True " + "and 'cholesky':True; option 'cholesky' has no effect when " + "'lstsq' is set True.", + OptimizeWarning, stacklevel=3) + + valid_permc_spec = ('NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', 'COLAMD') + if permc_spec.upper() not in valid_permc_spec: + warn("Invalid permc_spec option: '" + str(permc_spec) + "'. " + "Acceptable values are 'NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', " + "and 'COLAMD'. Reverting to default.", + OptimizeWarning, stacklevel=3) + permc_spec = 'MMD_AT_PLUS_A' + + # This can be an error + if not sym_pos and cholesky: + raise ValueError( + "Invalid option combination 'sym_pos':False " + "and 'cholesky':True: Cholesky decomposition is only possible " + "for symmetric positive definite matrices.") + + cholesky = cholesky or (cholesky is None and sym_pos and not lstsq) + + x, status, message, iteration = _ip_hsd(A, b, c, c0, alpha0, beta, + maxiter, disp, tol, sparse, + lstsq, sym_pos, cholesky, + pc, ip, permc_spec, callback, + postsolve_args) + + return x, status, message, iteration diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_rs.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_rs.py new file mode 100644 index 0000000000000000000000000000000000000000..826ceffce398a6f58bdfcd6264e2f14fc5f6f8ee --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_rs.py @@ -0,0 +1,572 @@ +"""Revised simplex method for linear programming + +The *revised simplex* method uses the method described in [1]_, except +that a factorization [2]_ of the basis matrix, rather than its inverse, +is efficiently maintained and used to solve the linear systems at each +iteration of the algorithm. + +.. versionadded:: 1.3.0 + +References +---------- +.. [1] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. +.. [2] Bartels, Richard H. "A stabilization of the simplex method." + Journal in Numerische Mathematik 16.5 (1971): 414-434. + +""" +# Author: Matt Haberland + +import numpy as np +from numpy.linalg import LinAlgError + +from scipy.linalg import solve +from ._optimize import _check_unknown_options +from ._bglu_dense import LU +from ._bglu_dense import BGLU as BGLU +from ._linprog_util import _postsolve +from ._optimize import OptimizeResult + + +def _phase_one(A, b, x0, callback, postsolve_args, maxiter, tol, disp, + maxupdate, mast, pivot): + """ + The purpose of phase one is to find an initial basic feasible solution + (BFS) to the original problem. + + Generates an auxiliary problem with a trivial BFS and an objective that + minimizes infeasibility of the original problem. Solves the auxiliary + problem using the main simplex routine (phase two). This either yields + a BFS to the original problem or determines that the original problem is + infeasible. If feasible, phase one detects redundant rows in the original + constraint matrix and removes them, then chooses additional indices as + necessary to complete a basis/BFS for the original problem. + """ + + m, n = A.shape + status = 0 + + # generate auxiliary problem to get initial BFS + A, b, c, basis, x, status = _generate_auxiliary_problem(A, b, x0, tol) + + if status == 6: + residual = c.dot(x) + iter_k = 0 + return x, basis, A, b, residual, status, iter_k + + # solve auxiliary problem + phase_one_n = n + iter_k = 0 + x, basis, status, iter_k = _phase_two(c, A, x, basis, callback, + postsolve_args, + maxiter, tol, disp, + maxupdate, mast, pivot, + iter_k, phase_one_n) + + # check for infeasibility + residual = c.dot(x) + if status == 0 and residual > tol: + status = 2 + + # drive artificial variables out of basis + # TODO: test redundant row removal better + # TODO: make solve more efficient with BGLU? This could take a while. + keep_rows = np.ones(m, dtype=bool) + for basis_column in basis[basis >= n]: + B = A[:, basis] + try: + basis_finder = np.abs(solve(B, A)) # inefficient + pertinent_row = np.argmax(basis_finder[:, basis_column]) + eligible_columns = np.ones(n, dtype=bool) + eligible_columns[basis[basis < n]] = 0 + eligible_column_indices = np.where(eligible_columns)[0] + index = np.argmax(basis_finder[:, :n] + [pertinent_row, eligible_columns]) + new_basis_column = eligible_column_indices[index] + if basis_finder[pertinent_row, new_basis_column] < tol: + keep_rows[pertinent_row] = False + else: + basis[basis == basis_column] = new_basis_column + except LinAlgError: + status = 4 + + # form solution to original problem + A = A[keep_rows, :n] + basis = basis[keep_rows] + x = x[:n] + m = A.shape[0] + return x, basis, A, b, residual, status, iter_k + + +def _get_more_basis_columns(A, basis): + """ + Called when the auxiliary problem terminates with artificial columns in + the basis, which must be removed and replaced with non-artificial + columns. Finds additional columns that do not make the matrix singular. + """ + m, n = A.shape + + # options for inclusion are those that aren't already in the basis + a = np.arange(m+n) + bl = np.zeros(len(a), dtype=bool) + bl[basis] = 1 + options = a[~bl] + options = options[options < n] # and they have to be non-artificial + + # form basis matrix + B = np.zeros((m, m)) + B[:, 0:len(basis)] = A[:, basis] + + if (basis.size > 0 and + np.linalg.matrix_rank(B[:, :len(basis)]) < len(basis)): + raise Exception("Basis has dependent columns") + + rank = 0 # just enter the loop + for i in range(n): # somewhat arbitrary, but we need another way out + # permute the options, and take as many as needed + new_basis = np.random.permutation(options)[:m-len(basis)] + B[:, len(basis):] = A[:, new_basis] # update the basis matrix + rank = np.linalg.matrix_rank(B) # check the rank + if rank == m: + break + + return np.concatenate((basis, new_basis)) + + +def _generate_auxiliary_problem(A, b, x0, tol): + """ + Modifies original problem to create an auxiliary problem with a trivial + initial basic feasible solution and an objective that minimizes + infeasibility in the original problem. + + Conceptually, this is done by stacking an identity matrix on the right of + the original constraint matrix, adding artificial variables to correspond + with each of these new columns, and generating a cost vector that is all + zeros except for ones corresponding with each of the new variables. + + A initial basic feasible solution is trivial: all variables are zero + except for the artificial variables, which are set equal to the + corresponding element of the right hand side `b`. + + Running the simplex method on this auxiliary problem drives all of the + artificial variables - and thus the cost - to zero if the original problem + is feasible. The original problem is declared infeasible otherwise. + + Much of the complexity below is to improve efficiency by using singleton + columns in the original problem where possible, thus generating artificial + variables only as necessary, and using an initial 'guess' basic feasible + solution. + """ + status = 0 + m, n = A.shape + + if x0 is not None: + x = x0 + else: + x = np.zeros(n) + + r = b - A@x # residual; this must be all zeros for feasibility + + A[r < 0] = -A[r < 0] # express problem with RHS positive for trivial BFS + b[r < 0] = -b[r < 0] # to the auxiliary problem + r[r < 0] *= -1 + + # Rows which we will need to find a trivial way to zero. + # This should just be the rows where there is a nonzero residual. + # But then we would not necessarily have a column singleton in every row. + # This makes it difficult to find an initial basis. + if x0 is None: + nonzero_constraints = np.arange(m) + else: + nonzero_constraints = np.where(r > tol)[0] + + # these are (at least some of) the initial basis columns + basis = np.where(np.abs(x) > tol)[0] + + if len(nonzero_constraints) == 0 and len(basis) <= m: # already a BFS + c = np.zeros(n) + basis = _get_more_basis_columns(A, basis) + return A, b, c, basis, x, status + elif (len(nonzero_constraints) > m - len(basis) or + np.any(x < 0)): # can't get trivial BFS + c = np.zeros(n) + status = 6 + return A, b, c, basis, x, status + + # chooses existing columns appropriate for inclusion in initial basis + cols, rows = _select_singleton_columns(A, r) + + # find the rows we need to zero that we _can_ zero with column singletons + i_tofix = np.isin(rows, nonzero_constraints) + # these columns can't already be in the basis, though + # we are going to add them to the basis and change the corresponding x val + i_notinbasis = np.logical_not(np.isin(cols, basis)) + i_fix_without_aux = np.logical_and(i_tofix, i_notinbasis) + rows = rows[i_fix_without_aux] + cols = cols[i_fix_without_aux] + + # indices of the rows we can only zero with auxiliary variable + # these rows will get a one in each auxiliary column + arows = nonzero_constraints[np.logical_not( + np.isin(nonzero_constraints, rows))] + n_aux = len(arows) + acols = n + np.arange(n_aux) # indices of auxiliary columns + + basis_ng = np.concatenate((cols, acols)) # basis columns not from guess + basis_ng_rows = np.concatenate((rows, arows)) # rows we need to zero + + # add auxiliary singleton columns + A = np.hstack((A, np.zeros((m, n_aux)))) + A[arows, acols] = 1 + + # generate initial BFS + x = np.concatenate((x, np.zeros(n_aux))) + x[basis_ng] = r[basis_ng_rows]/A[basis_ng_rows, basis_ng] + + # generate costs to minimize infeasibility + c = np.zeros(n_aux + n) + c[acols] = 1 + + # basis columns correspond with nonzeros in guess, those with column + # singletons we used to zero remaining constraints, and any additional + # columns to get a full set (m columns) + basis = np.concatenate((basis, basis_ng)) + basis = _get_more_basis_columns(A, basis) # add columns as needed + + return A, b, c, basis, x, status + + +def _select_singleton_columns(A, b): + """ + Finds singleton columns for which the singleton entry is of the same sign + as the right-hand side; these columns are eligible for inclusion in an + initial basis. Determines the rows in which the singleton entries are + located. For each of these rows, returns the indices of the one singleton + column and its corresponding row. + """ + # find indices of all singleton columns and corresponding row indices + column_indices = np.nonzero(np.sum(np.abs(A) != 0, axis=0) == 1)[0] + columns = A[:, column_indices] # array of singleton columns + row_indices = np.zeros(len(column_indices), dtype=int) + nonzero_rows, nonzero_columns = np.nonzero(columns) + row_indices[nonzero_columns] = nonzero_rows # corresponding row indices + + # keep only singletons with entries that have same sign as RHS + # this is necessary because all elements of BFS must be non-negative + same_sign = A[row_indices, column_indices]*b[row_indices] >= 0 + column_indices = column_indices[same_sign][::-1] + row_indices = row_indices[same_sign][::-1] + # Reversing the order so that steps below select rightmost columns + # for initial basis, which will tend to be slack variables. (If the + # guess corresponds with a basic feasible solution but a constraint + # is not satisfied with the corresponding slack variable zero, the slack + # variable must be basic.) + + # for each row, keep rightmost singleton column with an entry in that row + unique_row_indices, first_columns = np.unique(row_indices, + return_index=True) + return column_indices[first_columns], unique_row_indices + + +def _find_nonzero_rows(A, tol): + """ + Returns logical array indicating the locations of rows with at least + one nonzero element. + """ + return np.any(np.abs(A) > tol, axis=1) + + +def _select_enter_pivot(c_hat, bl, a, rule="bland", tol=1e-12): + """ + Selects a pivot to enter the basis. Currently Bland's rule - the smallest + index that has a negative reduced cost - is the default. + """ + if rule.lower() == "mrc": # index with minimum reduced cost + return a[~bl][np.argmin(c_hat)] + else: # smallest index w/ negative reduced cost + return a[~bl][c_hat < -tol][0] + + +def _display_iter(phase, iteration, slack, con, fun): + """ + Print indicators of optimization status to the console. + """ + header = True if not iteration % 20 else False + + if header: + print("Phase", + "Iteration", + "Minimum Slack ", + "Constraint Residual", + "Objective ") + + # := -tol): # all reduced costs positive -> terminate + break + + j = _select_enter_pivot(c_hat, bl, a, rule=pivot, tol=tol) + u = B.solve(A[:, j]) # similar to u = solve(B, A[:, j]) + + i = u > tol # if none of the u are positive, unbounded + if not np.any(i): + status = 3 + break + + th = xb[i]/u[i] + l = np.argmin(th) # implicitly selects smallest subscript + th_star = th[l] # step size + + x[b] = x[b] - th_star*u # take step + x[j] = th_star + B.update(ab[i][l], j) # modify basis + b = B.b # similar to b[ab[i][l]] = + + else: + # If the end of the for loop is reached (without a break statement), + # then another step has been taken, so the iteration counter should + # increment, info should be displayed, and callback should be called. + iteration += 1 + status = 1 + if disp or callback is not None: + _display_and_callback(phase_one_n, x, postsolve_args, status, + iteration, disp, callback) + + return x, b, status, iteration + + +def _linprog_rs(c, c0, A, b, x0, callback, postsolve_args, + maxiter=5000, tol=1e-12, disp=False, + maxupdate=10, mast=False, pivot="mrc", + **unknown_options): + """ + Solve the following linear programming problem via a two-phase + revised simplex algorithm.:: + + minimize: c @ x + + subject to: A @ x == b + 0 <= x < oo + + User-facing documentation is in _linprog_doc.py. + + Parameters + ---------- + c : 1-D array + Coefficients of the linear objective function to be minimized. + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. (Currently unused.) + A : 2-D array + 2-D array which, when matrix-multiplied by ``x``, gives the values of + the equality constraints at ``x``. + b : 1-D array + 1-D array of values representing the RHS of each equality constraint + (row) in ``A_eq``. + x0 : 1-D array, optional + Starting values of the independent variables, which will be refined by + the optimization algorithm. For the revised simplex method, these must + correspond with a basic feasible solution. + callback : callable, optional + If a callback function is provided, it will be called within each + iteration of the algorithm. The callback function must accept a single + `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + Current solution vector. + fun : float + Current value of the objective function ``c @ x``. + success : bool + True only when an algorithm has completed successfully, + so this is always False as the callback function is called + only while the algorithm is still iterating. + slack : 1-D array + The values of the slack variables. Each slack variable + corresponds to an inequality constraint. If the slack is zero, + the corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + that is, ``b - A_eq @ x``. + phase : int + The phase of the algorithm being executed. + status : int + For revised simplex, this is always 0 because if a different + status is detected, the algorithm terminates. + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem. + + Options + ------- + maxiter : int + The maximum number of iterations to perform in either phase. + tol : float + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + disp : bool + Set to ``True`` if indicators of optimization status are to be printed + to the console each iteration. + maxupdate : int + The maximum number of updates performed on the LU factorization. + After this many updates is reached, the basis matrix is factorized + from scratch. + mast : bool + Minimize Amortized Solve Time. If enabled, the average time to solve + a linear system using the basis factorization is measured. Typically, + the average solve time will decrease with each successive solve after + initial factorization, as factorization takes much more time than the + solve operation (and updates). Eventually, however, the updated + factorization becomes sufficiently complex that the average solve time + begins to increase. When this is detected, the basis is refactorized + from scratch. Enable this option to maximize speed at the risk of + nondeterministic behavior. Ignored if ``maxupdate`` is 0. + pivot : "mrc" or "bland" + Pivot rule: Minimum Reduced Cost (default) or Bland's rule. Choose + Bland's rule if iteration limit is reached and cycling is suspected. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + x : 1-D array + Solution vector. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Numerical difficulties encountered + 5 : No constraints; turn presolve on + 6 : Guess x0 cannot be converted to a basic feasible solution + + message : str + A string descriptor of the exit status of the optimization. + iteration : int + The number of iterations taken to solve the problem. + """ + + _check_unknown_options(unknown_options) + + messages = ["Optimization terminated successfully.", + "Iteration limit reached.", + "The problem appears infeasible, as the phase one auxiliary " + "problem terminated successfully with a residual of {0:.1e}, " + "greater than the tolerance {1} required for the solution to " + "be considered feasible. Consider increasing the tolerance to " + "be greater than {0:.1e}. If this tolerance is unnaceptably " + "large, the problem is likely infeasible.", + "The problem is unbounded, as the simplex algorithm found " + "a basic feasible solution from which there is a direction " + "with negative reduced cost in which all decision variables " + "increase.", + "Numerical difficulties encountered; consider trying " + "method='interior-point'.", + "Problems with no constraints are trivially solved; please " + "turn presolve on.", + "The guess x0 cannot be converted to a basic feasible " + "solution. " + ] + + if A.size == 0: # address test_unbounded_below_no_presolve_corrected + return np.zeros(c.shape), 5, messages[5], 0 + + x, basis, A, b, residual, status, iteration = ( + _phase_one(A, b, x0, callback, postsolve_args, + maxiter, tol, disp, maxupdate, mast, pivot)) + + if status == 0: + x, basis, status, iteration = _phase_two(c, A, x, basis, callback, + postsolve_args, + maxiter, tol, disp, + maxupdate, mast, pivot, + iteration) + + return x, status, messages[status].format(residual, tol), iteration diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_simplex.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_simplex.py new file mode 100644 index 0000000000000000000000000000000000000000..b13418c369864ca528efe76d9f45c07da2bcf680 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_simplex.py @@ -0,0 +1,661 @@ +"""Simplex method for linear programming + +The *simplex* method uses a traditional, full-tableau implementation of +Dantzig's simplex algorithm [1]_, [2]_ (*not* the Nelder-Mead simplex). +This algorithm is included for backwards compatibility and educational +purposes. + + .. versionadded:: 0.15.0 + +Warnings +-------- + +The simplex method may encounter numerical difficulties when pivot +values are close to the specified tolerance. If encountered try +remove any redundant constraints, change the pivot strategy to Bland's +rule or increase the tolerance value. + +Alternatively, more robust methods maybe be used. See +:ref:`'interior-point' ` and +:ref:`'revised simplex' `. + +References +---------- +.. [1] Dantzig, George B., Linear programming and extensions. Rand + Corporation Research Study Princeton Univ. Press, Princeton, NJ, + 1963 +.. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to + Mathematical Programming", McGraw-Hill, Chapter 4. +""" + +import numpy as np +from warnings import warn +from ._optimize import OptimizeResult, OptimizeWarning, _check_unknown_options +from ._linprog_util import _postsolve + + +def _pivot_col(T, tol=1e-9, bland=False): + """ + Given a linear programming simplex tableau, determine the column + of the variable to enter the basis. + + Parameters + ---------- + T : 2-D array + A 2-D array representing the simplex tableau, T, corresponding to the + linear programming problem. It should have the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0]] + + for a Phase 2 problem, or the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0], + [c'[0], c'[1], ..., c'[n_total], 0]] + + for a Phase 1 problem (a problem in which a basic feasible solution is + sought prior to maximizing the actual objective. ``T`` is modified in + place by ``_solve_simplex``. + tol : float + Elements in the objective row larger than -tol will not be considered + for pivoting. Nominally this value is zero, but numerical issues + cause a tolerance about zero to be necessary. + bland : bool + If True, use Bland's rule for selection of the column (select the + first column with a negative coefficient in the objective row, + regardless of magnitude). + + Returns + ------- + status: bool + True if a suitable pivot column was found, otherwise False. + A return of False indicates that the linear programming simplex + algorithm is complete. + col: int + The index of the column of the pivot element. + If status is False, col will be returned as nan. + """ + ma = np.ma.masked_where(T[-1, :-1] >= -tol, T[-1, :-1], copy=False) + if ma.count() == 0: + return False, np.nan + if bland: + # ma.mask is sometimes 0d + return True, np.nonzero(np.logical_not(np.atleast_1d(ma.mask)))[0][0] + return True, np.ma.nonzero(ma == ma.min())[0][0] + + +def _pivot_row(T, basis, pivcol, phase, tol=1e-9, bland=False): + """ + Given a linear programming simplex tableau, determine the row for the + pivot operation. + + Parameters + ---------- + T : 2-D array + A 2-D array representing the simplex tableau, T, corresponding to the + linear programming problem. It should have the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0]] + + for a Phase 2 problem, or the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0], + [c'[0], c'[1], ..., c'[n_total], 0]] + + for a Phase 1 problem (a Problem in which a basic feasible solution is + sought prior to maximizing the actual objective. ``T`` is modified in + place by ``_solve_simplex``. + basis : array + A list of the current basic variables. + pivcol : int + The index of the pivot column. + phase : int + The phase of the simplex algorithm (1 or 2). + tol : float + Elements in the pivot column smaller than tol will not be considered + for pivoting. Nominally this value is zero, but numerical issues + cause a tolerance about zero to be necessary. + bland : bool + If True, use Bland's rule for selection of the row (if more than one + row can be used, choose the one with the lowest variable index). + + Returns + ------- + status: bool + True if a suitable pivot row was found, otherwise False. A return + of False indicates that the linear programming problem is unbounded. + row: int + The index of the row of the pivot element. If status is False, row + will be returned as nan. + """ + if phase == 1: + k = 2 + else: + k = 1 + ma = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, pivcol], copy=False) + if ma.count() == 0: + return False, np.nan + mb = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, -1], copy=False) + q = mb / ma + min_rows = np.ma.nonzero(q == q.min())[0] + if bland: + return True, min_rows[np.argmin(np.take(basis, min_rows))] + return True, min_rows[0] + + +def _apply_pivot(T, basis, pivrow, pivcol, tol=1e-9): + """ + Pivot the simplex tableau inplace on the element given by (pivrow, pivol). + The entering variable corresponds to the column given by pivcol forcing + the variable basis[pivrow] to leave the basis. + + Parameters + ---------- + T : 2-D array + A 2-D array representing the simplex tableau, T, corresponding to the + linear programming problem. It should have the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0]] + + for a Phase 2 problem, or the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0], + [c'[0], c'[1], ..., c'[n_total], 0]] + + for a Phase 1 problem (a problem in which a basic feasible solution is + sought prior to maximizing the actual objective. ``T`` is modified in + place by ``_solve_simplex``. + basis : 1-D array + An array of the indices of the basic variables, such that basis[i] + contains the column corresponding to the basic variable for row i. + Basis is modified in place by _apply_pivot. + pivrow : int + Row index of the pivot. + pivcol : int + Column index of the pivot. + """ + basis[pivrow] = pivcol + pivval = T[pivrow, pivcol] + T[pivrow] = T[pivrow] / pivval + for irow in range(T.shape[0]): + if irow != pivrow: + T[irow] = T[irow] - T[pivrow] * T[irow, pivcol] + + # The selected pivot should never lead to a pivot value less than the tol. + if np.isclose(pivval, tol, atol=0, rtol=1e4): + message = ( + f"The pivot operation produces a pivot value of:{pivval: .1e}, " + "which is only slightly greater than the specified " + f"tolerance{tol: .1e}. This may lead to issues regarding the " + "numerical stability of the simplex method. " + "Removing redundant constraints, changing the pivot strategy " + "via Bland's rule or increasing the tolerance may " + "help reduce the issue.") + warn(message, OptimizeWarning, stacklevel=5) + + +def _solve_simplex(T, n, basis, callback, postsolve_args, + maxiter=1000, tol=1e-9, phase=2, bland=False, nit0=0, + ): + """ + Solve a linear programming problem in "standard form" using the Simplex + Method. Linear Programming is intended to solve the following problem form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + Parameters + ---------- + T : 2-D array + A 2-D array representing the simplex tableau, T, corresponding to the + linear programming problem. It should have the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0]] + + for a Phase 2 problem, or the form: + + [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]], + [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]], + . + . + . + [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]], + [c[0], c[1], ..., c[n_total], 0], + [c'[0], c'[1], ..., c'[n_total], 0]] + + for a Phase 1 problem (a problem in which a basic feasible solution is + sought prior to maximizing the actual objective. ``T`` is modified in + place by ``_solve_simplex``. + n : int + The number of true variables in the problem. + basis : 1-D array + An array of the indices of the basic variables, such that basis[i] + contains the column corresponding to the basic variable for row i. + Basis is modified in place by _solve_simplex + callback : callable, optional + If a callback function is provided, it will be called within each + iteration of the algorithm. The callback must accept a + `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + Current solution vector + fun : float + Current value of the objective function + success : bool + True only when a phase has completed successfully. This + will be False for most iterations. + slack : 1-D array + The values of the slack variables. Each slack variable + corresponds to an inequality constraint. If the slack is zero, + the corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + that is, ``b - A_eq @ x`` + phase : int + The phase of the optimization being executed. In phase 1 a basic + feasible solution is sought and the T has an additional row + representing an alternate objective function. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem. + maxiter : int + The maximum number of iterations to perform before aborting the + optimization. + tol : float + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + phase : int + The phase of the optimization being executed. In phase 1 a basic + feasible solution is sought and the T has an additional row + representing an alternate objective function. + bland : bool + If True, choose pivots using Bland's rule [3]_. In problems which + fail to converge due to cycling, using Bland's rule can provide + convergence at the expense of a less optimal path about the simplex. + nit0 : int + The initial iteration number used to keep an accurate iteration total + in a two-phase problem. + + Returns + ------- + nit : int + The number of iterations. Used to keep an accurate iteration total + in the two-phase problem. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + """ + nit = nit0 + status = 0 + message = '' + complete = False + + if phase == 1: + m = T.shape[1]-2 + elif phase == 2: + m = T.shape[1]-1 + else: + raise ValueError("Argument 'phase' to _solve_simplex must be 1 or 2") + + if phase == 2: + # Check if any artificial variables are still in the basis. + # If yes, check if any coefficients from this row and a column + # corresponding to one of the non-artificial variable is non-zero. + # If found, pivot at this term. If not, start phase 2. + # Do this for all artificial variables in the basis. + # Ref: "An Introduction to Linear Programming and Game Theory" + # by Paul R. Thie, Gerard E. Keough, 3rd Ed, + # Chapter 3.7 Redundant Systems (pag 102) + for pivrow in [row for row in range(basis.size) + if basis[row] > T.shape[1] - 2]: + non_zero_row = [col for col in range(T.shape[1] - 1) + if abs(T[pivrow, col]) > tol] + if len(non_zero_row) > 0: + pivcol = non_zero_row[0] + _apply_pivot(T, basis, pivrow, pivcol, tol) + nit += 1 + + if len(basis[:m]) == 0: + solution = np.empty(T.shape[1] - 1, dtype=np.float64) + else: + solution = np.empty(max(T.shape[1] - 1, max(basis[:m]) + 1), + dtype=np.float64) + + while not complete: + # Find the pivot column + pivcol_found, pivcol = _pivot_col(T, tol, bland) + if not pivcol_found: + pivcol = np.nan + pivrow = np.nan + status = 0 + complete = True + else: + # Find the pivot row + pivrow_found, pivrow = _pivot_row(T, basis, pivcol, phase, tol, bland) + if not pivrow_found: + status = 3 + complete = True + + if callback is not None: + solution[:] = 0 + solution[basis[:n]] = T[:n, -1] + x = solution[:m] + x, fun, slack, con = _postsolve( + x, postsolve_args + ) + res = OptimizeResult({ + 'x': x, + 'fun': fun, + 'slack': slack, + 'con': con, + 'status': status, + 'message': message, + 'nit': nit, + 'success': status == 0 and complete, + 'phase': phase, + 'complete': complete, + }) + callback(res) + + if not complete: + if nit >= maxiter: + # Iteration limit exceeded + status = 1 + complete = True + else: + _apply_pivot(T, basis, pivrow, pivcol, tol) + nit += 1 + return nit, status + + +def _linprog_simplex(c, c0, A, b, callback, postsolve_args, + maxiter=1000, tol=1e-9, disp=False, bland=False, + **unknown_options): + """ + Minimize a linear objective function subject to linear equality and + non-negativity constraints using the two phase simplex method. + Linear programming is intended to solve problems of the following form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + User-facing documentation is in _linprog_doc.py. + + Parameters + ---------- + c : 1-D array + Coefficients of the linear objective function to be minimized. + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. (Purely for display.) + A : 2-D array + 2-D array such that ``A @ x``, gives the values of the equality + constraints at ``x``. + b : 1-D array + 1-D array of values representing the right hand side of each equality + constraint (row) in ``A``. + callback : callable, optional + If a callback function is provided, it will be called within each + iteration of the algorithm. The callback function must accept a single + `scipy.optimize.OptimizeResult` consisting of the following fields: + + x : 1-D array + Current solution vector + fun : float + Current value of the objective function + success : bool + True when an algorithm has completed successfully. + slack : 1-D array + The values of the slack variables. Each slack variable + corresponds to an inequality constraint. If the slack is zero, + the corresponding constraint is active. + con : 1-D array + The (nominally zero) residuals of the equality constraints, + that is, ``b - A_eq @ x`` + phase : int + The phase of the algorithm being executed. + status : int + An integer representing the status of the optimization:: + + 0 : Algorithm proceeding nominally + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + nit : int + The number of iterations performed. + message : str + A string descriptor of the exit status of the optimization. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem. + + Options + ------- + maxiter : int + The maximum number of iterations to perform. + disp : bool + If True, print exit status message to sys.stdout + tol : float + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + bland : bool + If True, use Bland's anti-cycling rule [3]_ to choose pivots to + prevent cycling. If False, choose pivots which should lead to a + converged solution more quickly. The latter method is subject to + cycling (non-convergence) in rare instances. + unknown_options : dict + Optional arguments not used by this particular solver. If + `unknown_options` is non-empty a warning is issued listing all + unused options. + + Returns + ------- + x : 1-D array + Solution vector. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + message : str + A string descriptor of the exit status of the optimization. + iteration : int + The number of iterations taken to solve the problem. + + References + ---------- + .. [1] Dantzig, George B., Linear programming and extensions. Rand + Corporation Research Study Princeton Univ. Press, Princeton, NJ, + 1963 + .. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to + Mathematical Programming", McGraw-Hill, Chapter 4. + .. [3] Bland, Robert G. New finite pivoting rules for the simplex method. + Mathematics of Operations Research (2), 1977: pp. 103-107. + + + Notes + ----- + The expected problem formulation differs between the top level ``linprog`` + module and the method specific solvers. The method specific solvers expect a + problem in standard form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + Whereas the top level ``linprog`` module expects a problem of form: + + Minimize:: + + c @ x + + Subject to:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + where ``lb = 0`` and ``ub = None`` unless set in ``bounds``. + + The original problem contains equality, upper-bound and variable constraints + whereas the method specific solver requires equality constraints and + variable non-negativity. + + ``linprog`` module converts the original problem to standard form by + converting the simple bounds to upper bound constraints, introducing + non-negative slack variables for inequality constraints, and expressing + unbounded variables as the difference between two non-negative variables. + """ + _check_unknown_options(unknown_options) + + status = 0 + messages = {0: "Optimization terminated successfully.", + 1: "Iteration limit reached.", + 2: "Optimization failed. Unable to find a feasible" + " starting point.", + 3: "Optimization failed. The problem appears to be unbounded.", + 4: "Optimization failed. Singular matrix encountered."} + + n, m = A.shape + + # All constraints must have b >= 0. + is_negative_constraint = np.less(b, 0) + A[is_negative_constraint] *= -1 + b[is_negative_constraint] *= -1 + + # As all constraints are equality constraints the artificial variables + # will also be basic variables. + av = np.arange(n) + m + basis = av.copy() + + # Format the phase one tableau by adding artificial variables and stacking + # the constraints, the objective row and pseudo-objective row. + row_constraints = np.hstack((A, np.eye(n), b[:, np.newaxis])) + row_objective = np.hstack((c, np.zeros(n), c0)) + row_pseudo_objective = -row_constraints.sum(axis=0) + row_pseudo_objective[av] = 0 + T = np.vstack((row_constraints, row_objective, row_pseudo_objective)) + + nit1, status = _solve_simplex(T, n, basis, callback=callback, + postsolve_args=postsolve_args, + maxiter=maxiter, tol=tol, phase=1, + bland=bland + ) + # if pseudo objective is zero, remove the last row from the tableau and + # proceed to phase 2 + nit2 = nit1 + if abs(T[-1, -1]) < tol: + # Remove the pseudo-objective row from the tableau + T = T[:-1, :] + # Remove the artificial variable columns from the tableau + T = np.delete(T, av, 1) + else: + # Failure to find a feasible starting point + status = 2 + messages[status] = ( + "Phase 1 of the simplex method failed to find a feasible " + "solution. The pseudo-objective function evaluates to {0:.1e} " + "which exceeds the required tolerance of {1} for a solution to be " + "considered 'close enough' to zero to be a basic solution. " + "Consider increasing the tolerance to be greater than {0:.1e}. " + "If this tolerance is unacceptably large the problem may be " + "infeasible.".format(abs(T[-1, -1]), tol) + ) + + if status == 0: + # Phase 2 + nit2, status = _solve_simplex(T, n, basis, callback=callback, + postsolve_args=postsolve_args, + maxiter=maxiter, tol=tol, phase=2, + bland=bland, nit0=nit1 + ) + + solution = np.zeros(n + m) + solution[basis[:n]] = T[:n, -1] + x = solution[:m] + + return x, status, messages[status], int(nit2) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_util.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_util.py new file mode 100644 index 0000000000000000000000000000000000000000..3d25cee4d9ce6b1c5a40cc474d97ec13474ebafc --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_linprog_util.py @@ -0,0 +1,1522 @@ +""" +Method agnostic utility functions for linear programming +""" + +import numpy as np +import scipy.sparse as sps +from warnings import warn +from ._optimize import OptimizeWarning +from scipy.optimize._remove_redundancy import ( + _remove_redundancy_svd, _remove_redundancy_pivot_sparse, + _remove_redundancy_pivot_dense, _remove_redundancy_id + ) +from collections import namedtuple + +_LPProblem = namedtuple('_LPProblem', + 'c A_ub b_ub A_eq b_eq bounds x0 integrality') +_LPProblem.__new__.__defaults__ = (None,) * 7 # make c the only required arg +_LPProblem.__doc__ = \ + """ Represents a linear-programming problem. + + Attributes + ---------- + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : various valid formats, optional + The bounds of ``x``, as ``min`` and ``max`` pairs. + If bounds are specified for all N variables separately, valid formats + are: + * a 2D array (N x 2); + * a sequence of N sequences, each with 2 values. + If all variables have the same bounds, the bounds can be specified as + a 1-D or 2-D array or sequence with 2 scalar values. + If all variables have a lower bound of 0 and no upper bound, the bounds + parameter can be omitted (or given as None). + Absent lower and/or upper bounds can be specified as -numpy.inf (no + lower bound), numpy.inf (no upper bound) or None (both). + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + integrality : 1-D array or int, optional + Indicates the type of integrality constraint on each decision variable. + + ``0`` : Continuous variable; no integrality constraint. + + ``1`` : Integer variable; decision variable must be an integer + within `bounds`. + + ``2`` : Semi-continuous variable; decision variable must be within + `bounds` or take value ``0``. + + ``3`` : Semi-integer variable; decision variable must be an integer + within `bounds` or take value ``0``. + + By default, all variables are continuous. + + For mixed integrality constraints, supply an array of shape `c.shape`. + To infer a constraint on each decision variable from shorter inputs, + the argument will be broadcasted to `c.shape` using `np.broadcast_to`. + + This argument is currently used only by the ``'highs'`` method and + ignored otherwise. + + Notes + ----- + This namedtuple supports 2 ways of initialization: + >>> lp1 = _LPProblem(c=[-1, 4], A_ub=[[-3, 1], [1, 2]], b_ub=[6, 4]) + >>> lp2 = _LPProblem([-1, 4], [[-3, 1], [1, 2]], [6, 4]) + + Note that only ``c`` is a required argument here, whereas all other arguments + ``A_ub``, ``b_ub``, ``A_eq``, ``b_eq``, ``bounds``, ``x0`` are optional with + default values of None. + For example, ``A_eq`` and ``b_eq`` can be set without ``A_ub`` or ``b_ub``: + >>> lp3 = _LPProblem(c=[-1, 4], A_eq=[[2, 1]], b_eq=[10]) + """ + + +def _check_sparse_inputs(options, meth, A_ub, A_eq): + """ + Check the provided ``A_ub`` and ``A_eq`` matrices conform to the specified + optional sparsity variables. + + Parameters + ---------- + A_ub : 2-D array, optional + 2-D array such that ``A_ub @ x`` gives the values of the upper-bound + inequality constraints at ``x``. + A_eq : 2-D array, optional + 2-D array such that ``A_eq @ x`` gives the values of the equality + constraints at ``x``. + options : dict + A dictionary of solver options. All methods accept the following + generic options: + + maxiter : int + Maximum number of iterations to perform. + disp : bool + Set to True to print convergence messages. + + For method-specific options, see :func:`show_options('linprog')`. + method : str, optional + The algorithm used to solve the standard form problem. + + Returns + ------- + A_ub : 2-D array, optional + 2-D array such that ``A_ub @ x`` gives the values of the upper-bound + inequality constraints at ``x``. + A_eq : 2-D array, optional + 2-D array such that ``A_eq @ x`` gives the values of the equality + constraints at ``x``. + options : dict + A dictionary of solver options. All methods accept the following + generic options: + + maxiter : int + Maximum number of iterations to perform. + disp : bool + Set to True to print convergence messages. + + For method-specific options, see :func:`show_options('linprog')`. + """ + # This is an undocumented option for unit testing sparse presolve + _sparse_presolve = options.pop('_sparse_presolve', False) + if _sparse_presolve and A_eq is not None: + A_eq = sps.coo_matrix(A_eq) + if _sparse_presolve and A_ub is not None: + A_ub = sps.coo_matrix(A_ub) + + sparse_constraint = sps.issparse(A_eq) or sps.issparse(A_ub) + + preferred_methods = {"highs", "highs-ds", "highs-ipm"} + dense_methods = {"simplex", "revised simplex"} + if meth in dense_methods and sparse_constraint: + raise ValueError(f"Method '{meth}' does not support sparse " + "constraint matrices. Please consider using one of " + f"{preferred_methods}.") + + sparse = options.get('sparse', False) + if not sparse and sparse_constraint and meth == 'interior-point': + options['sparse'] = True + warn("Sparse constraint matrix detected; setting 'sparse':True.", + OptimizeWarning, stacklevel=4) + return options, A_ub, A_eq + + +def _format_A_constraints(A, n_x, sparse_lhs=False): + """Format the left hand side of the constraints to a 2-D array + + Parameters + ---------- + A : 2-D array + 2-D array such that ``A @ x`` gives the values of the upper-bound + (in)equality constraints at ``x``. + n_x : int + The number of variables in the linear programming problem. + sparse_lhs : bool + Whether either of `A_ub` or `A_eq` are sparse. If true return a + coo_matrix instead of a numpy array. + + Returns + ------- + np.ndarray or sparse.coo_matrix + 2-D array such that ``A @ x`` gives the values of the upper-bound + (in)equality constraints at ``x``. + + """ + if sparse_lhs: + return sps.coo_matrix( + (0, n_x) if A is None else A, dtype=float, copy=True + ) + elif A is None: + return np.zeros((0, n_x), dtype=float) + else: + return np.array(A, dtype=float, copy=True) + + +def _format_b_constraints(b): + """Format the upper bounds of the constraints to a 1-D array + + Parameters + ---------- + b : 1-D array + 1-D array of values representing the upper-bound of each (in)equality + constraint (row) in ``A``. + + Returns + ------- + 1-D np.array + 1-D array of values representing the upper-bound of each (in)equality + constraint (row) in ``A``. + + """ + if b is None: + return np.array([], dtype=float) + b = np.array(b, dtype=float, copy=True).squeeze() + return b if b.size != 1 else b.reshape(-1) + + +def _clean_inputs(lp): + """ + Given user inputs for a linear programming problem, return the + objective vector, upper bound constraints, equality constraints, + and simple bounds in a preferred format. + + Parameters + ---------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : various valid formats, optional + The bounds of ``x``, as ``min`` and ``max`` pairs. + If bounds are specified for all N variables separately, valid formats are: + * a 2D array (2 x N or N x 2); + * a sequence of N sequences, each with 2 values. + If all variables have the same bounds, a single pair of values can + be specified. Valid formats are: + * a sequence with 2 scalar values; + * a sequence with a single element containing 2 scalar values. + If all variables have a lower bound of 0 and no upper bound, the bounds + parameter can be omitted (or given as None). + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + Returns + ------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N + elements of ``x``. The N x 2 array contains lower bounds in the first + column and upper bounds in the 2nd. Unbounded variables have lower + bound -np.inf and/or upper bound np.inf. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + """ + c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp + + if c is None: + raise TypeError + + try: + c = np.array(c, dtype=np.float64, copy=True).squeeze() + except ValueError as e: + raise TypeError( + "Invalid input for linprog: c must be a 1-D array of numerical " + "coefficients") from e + else: + # If c is a single value, convert it to a 1-D array. + if c.size == 1: + c = c.reshape(-1) + + n_x = len(c) + if n_x == 0 or len(c.shape) != 1: + raise ValueError( + "Invalid input for linprog: c must be a 1-D array and must " + "not have more than one non-singleton dimension") + if not np.isfinite(c).all(): + raise ValueError( + "Invalid input for linprog: c must not contain values " + "inf, nan, or None") + + sparse_lhs = sps.issparse(A_eq) or sps.issparse(A_ub) + try: + A_ub = _format_A_constraints(A_ub, n_x, sparse_lhs=sparse_lhs) + except ValueError as e: + raise TypeError( + "Invalid input for linprog: A_ub must be a 2-D array " + "of numerical values") from e + else: + n_ub = A_ub.shape[0] + if len(A_ub.shape) != 2 or A_ub.shape[1] != n_x: + raise ValueError( + "Invalid input for linprog: A_ub must have exactly two " + "dimensions, and the number of columns in A_ub must be " + "equal to the size of c") + if (sps.issparse(A_ub) and not np.isfinite(A_ub.data).all() + or not sps.issparse(A_ub) and not np.isfinite(A_ub).all()): + raise ValueError( + "Invalid input for linprog: A_ub must not contain values " + "inf, nan, or None") + + try: + b_ub = _format_b_constraints(b_ub) + except ValueError as e: + raise TypeError( + "Invalid input for linprog: b_ub must be a 1-D array of " + "numerical values, each representing the upper bound of an " + "inequality constraint (row) in A_ub") from e + else: + if b_ub.shape != (n_ub,): + raise ValueError( + "Invalid input for linprog: b_ub must be a 1-D array; b_ub " + "must not have more than one non-singleton dimension and " + "the number of rows in A_ub must equal the number of values " + "in b_ub") + if not np.isfinite(b_ub).all(): + raise ValueError( + "Invalid input for linprog: b_ub must not contain values " + "inf, nan, or None") + + try: + A_eq = _format_A_constraints(A_eq, n_x, sparse_lhs=sparse_lhs) + except ValueError as e: + raise TypeError( + "Invalid input for linprog: A_eq must be a 2-D array " + "of numerical values") from e + else: + n_eq = A_eq.shape[0] + if len(A_eq.shape) != 2 or A_eq.shape[1] != n_x: + raise ValueError( + "Invalid input for linprog: A_eq must have exactly two " + "dimensions, and the number of columns in A_eq must be " + "equal to the size of c") + + if (sps.issparse(A_eq) and not np.isfinite(A_eq.data).all() + or not sps.issparse(A_eq) and not np.isfinite(A_eq).all()): + raise ValueError( + "Invalid input for linprog: A_eq must not contain values " + "inf, nan, or None") + + try: + b_eq = _format_b_constraints(b_eq) + except ValueError as e: + raise TypeError( + "Invalid input for linprog: b_eq must be a dense, 1-D array of " + "numerical values, each representing the right hand side of an " + "equality constraint (row) in A_eq") from e + else: + if b_eq.shape != (n_eq,): + raise ValueError( + "Invalid input for linprog: b_eq must be a 1-D array; b_eq " + "must not have more than one non-singleton dimension and " + "the number of rows in A_eq must equal the number of values " + "in b_eq") + if not np.isfinite(b_eq).all(): + raise ValueError( + "Invalid input for linprog: b_eq must not contain values " + "inf, nan, or None") + + # x0 gives a (optional) starting solution to the solver. If x0 is None, + # skip the checks. Initial solution will be generated automatically. + if x0 is not None: + try: + x0 = np.array(x0, dtype=float, copy=True).squeeze() + except ValueError as e: + raise TypeError( + "Invalid input for linprog: x0 must be a 1-D array of " + "numerical coefficients") from e + if x0.ndim == 0: + x0 = x0.reshape(-1) + if len(x0) == 0 or x0.ndim != 1: + raise ValueError( + "Invalid input for linprog: x0 should be a 1-D array; it " + "must not have more than one non-singleton dimension") + if not x0.size == c.size: + raise ValueError( + "Invalid input for linprog: x0 and c should contain the " + "same number of elements") + if not np.isfinite(x0).all(): + raise ValueError( + "Invalid input for linprog: x0 must not contain values " + "inf, nan, or None") + + # Bounds can be one of these formats: + # (1) a 2-D array or sequence, with shape N x 2 + # (2) a 1-D or 2-D sequence or array with 2 scalars + # (3) None (or an empty sequence or array) + # Unspecified bounds can be represented by None or (-)np.inf. + # All formats are converted into a N x 2 np.array with (-)np.inf where + # bounds are unspecified. + + # Prepare clean bounds array + bounds_clean = np.zeros((n_x, 2), dtype=float) + + # Convert to a numpy array. + # np.array(..,dtype=float) raises an error if dimensions are inconsistent + # or if there are invalid data types in bounds. Just add a linprog prefix + # to the error and re-raise. + # Creating at least a 2-D array simplifies the cases to distinguish below. + if bounds is None or np.array_equal(bounds, []) or np.array_equal(bounds, [[]]): + bounds = (0, np.inf) + try: + bounds_conv = np.atleast_2d(np.array(bounds, dtype=float)) + except ValueError as e: + raise ValueError( + "Invalid input for linprog: unable to interpret bounds, " + "check values and dimensions: " + e.args[0]) from e + except TypeError as e: + raise TypeError( + "Invalid input for linprog: unable to interpret bounds, " + "check values and dimensions: " + e.args[0]) from e + + # Check bounds options + bsh = bounds_conv.shape + if len(bsh) > 2: + # Do not try to handle multidimensional bounds input + raise ValueError( + "Invalid input for linprog: provide a 2-D array for bounds, " + f"not a {len(bsh):d}-D array.") + elif np.all(bsh == (n_x, 2)): + # Regular N x 2 array + bounds_clean = bounds_conv + elif (np.all(bsh == (2, 1)) or np.all(bsh == (1, 2))): + # 2 values: interpret as overall lower and upper bound + bounds_flat = bounds_conv.flatten() + bounds_clean[:, 0] = bounds_flat[0] + bounds_clean[:, 1] = bounds_flat[1] + elif np.all(bsh == (2, n_x)): + # Reject a 2 x N array + raise ValueError( + f"Invalid input for linprog: provide a {n_x:d} x 2 array for bounds, " + f"not a 2 x {n_x:d} array.") + else: + raise ValueError( + "Invalid input for linprog: unable to interpret bounds with this " + f"dimension tuple: {bsh}.") + + # The process above creates nan-s where the input specified None + # Convert the nan-s in the 1st column to -np.inf and in the 2nd column + # to np.inf + i_none = np.isnan(bounds_clean[:, 0]) + bounds_clean[i_none, 0] = -np.inf + i_none = np.isnan(bounds_clean[:, 1]) + bounds_clean[i_none, 1] = np.inf + + return _LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds_clean, x0, integrality) + + +def _presolve(lp, rr, rr_method, tol=1e-9): + """ + Given inputs for a linear programming problem in preferred format, + presolve the problem: identify trivial infeasibilities, redundancies, + and unboundedness, tighten bounds where possible, and eliminate fixed + variables. + + Parameters + ---------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N + elements of ``x``. The N x 2 array contains lower bounds in the first + column and upper bounds in the 2nd. Unbounded variables have lower + bound -np.inf and/or upper bound np.inf. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + rr : bool + If ``True`` attempts to eliminate any redundant rows in ``A_eq``. + Set False if ``A_eq`` is known to be of full row rank, or if you are + looking for a potential speedup (at the expense of reliability). + rr_method : string + Method used to identify and remove redundant rows from the + equality constraint matrix after presolve. + tol : float + The tolerance which determines when a solution is "close enough" to + zero in Phase 1 to be considered a basic feasible solution or close + enough to positive to serve as an optimal solution. + + Returns + ------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, as ``min`` and ``max`` pairs, possibly tightened. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + c0 : 1D array + Constant term in objective function due to fixed (and eliminated) + variables. + x : 1D array + Solution vector (when the solution is trivial and can be determined + in presolve) + revstack: list of functions + the functions in the list reverse the operations of _presolve() + the function signature is x_org = f(x_mod), where x_mod is the result + of a presolve step and x_org the value at the start of the step + (currently, the revstack contains only one function) + complete: bool + Whether the solution is complete (solved or determined to be infeasible + or unbounded in presolve) + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + message : str + A string descriptor of the exit status of the optimization. + + References + ---------- + .. [5] Andersen, Erling D. "Finding all linearly dependent rows in + large-scale linear programming." Optimization Methods and Software + 6.3 (1995): 219-227. + .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear + programming." Mathematical Programming 71.2 (1995): 221-245. + + """ + # ideas from Reference [5] by Andersen and Andersen + # however, unlike the reference, this is performed before converting + # problem to standard form + # There are a few advantages: + # * artificial variables have not been added, so matrices are smaller + # * bounds have not been converted to constraints yet. (It is better to + # do that after presolve because presolve may adjust the simple bounds.) + # There are many improvements that can be made, namely: + # * implement remaining checks from [5] + # * loop presolve until no additional changes are made + # * implement additional efficiency improvements in redundancy removal [2] + + c, A_ub, b_ub, A_eq, b_eq, bounds, x0, _ = lp + + revstack = [] # record of variables eliminated from problem + # constant term in cost function may be added if variables are eliminated + c0 = 0 + complete = False # complete is True if detected infeasible/unbounded + x = np.zeros(c.shape) # this is solution vector if completed in presolve + + status = 0 # all OK unless determined otherwise + message = "" + + # Lower and upper bounds. Copy to prevent feedback. + lb = bounds[:, 0].copy() + ub = bounds[:, 1].copy() + + m_eq, n = A_eq.shape + m_ub, n = A_ub.shape + + if (rr_method is not None + and rr_method.lower() not in {"svd", "pivot", "id"}): + message = ("'" + str(rr_method) + "' is not a valid option " + "for redundancy removal. Valid options are 'SVD', " + "'pivot', and 'ID'.") + raise ValueError(message) + + if sps.issparse(A_eq): + A_eq = A_eq.tocsr() + A_ub = A_ub.tocsr() + + def where(A): + return A.nonzero() + + vstack = sps.vstack + else: + where = np.where + vstack = np.vstack + + # upper bounds > lower bounds + if np.any(ub < lb) or np.any(lb == np.inf) or np.any(ub == -np.inf): + status = 2 + message = ("The problem is (trivially) infeasible since one " + "or more upper bounds are smaller than the corresponding " + "lower bounds, a lower bound is np.inf or an upper bound " + "is -np.inf.") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + + # zero row in equality constraints + zero_row = np.array(np.sum(A_eq != 0, axis=1) == 0).flatten() + if np.any(zero_row): + if np.any( + np.logical_and( + zero_row, + np.abs(b_eq) > tol)): # test_zero_row_1 + # infeasible if RHS is not zero + status = 2 + message = ("The problem is (trivially) infeasible due to a row " + "of zeros in the equality constraint matrix with a " + "nonzero corresponding constraint value.") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + else: # test_zero_row_2 + # if RHS is zero, we can eliminate this equation entirely + A_eq = A_eq[np.logical_not(zero_row), :] + b_eq = b_eq[np.logical_not(zero_row)] + + # zero row in inequality constraints + zero_row = np.array(np.sum(A_ub != 0, axis=1) == 0).flatten() + if np.any(zero_row): + if np.any(np.logical_and(zero_row, b_ub < -tol)): # test_zero_row_1 + # infeasible if RHS is less than zero (because LHS is zero) + status = 2 + message = ("The problem is (trivially) infeasible due to a row " + "of zeros in the equality constraint matrix with a " + "nonzero corresponding constraint value.") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + else: # test_zero_row_2 + # if LHS is >= 0, we can eliminate this constraint entirely + A_ub = A_ub[np.logical_not(zero_row), :] + b_ub = b_ub[np.logical_not(zero_row)] + + # zero column in (both) constraints + # this indicates that a variable isn't constrained and can be removed + A = vstack((A_eq, A_ub)) + if A.shape[0] > 0: + zero_col = np.array(np.sum(A != 0, axis=0) == 0).flatten() + # variable will be at upper or lower bound, depending on objective + x[np.logical_and(zero_col, c < 0)] = ub[ + np.logical_and(zero_col, c < 0)] + x[np.logical_and(zero_col, c > 0)] = lb[ + np.logical_and(zero_col, c > 0)] + if np.any(np.isinf(x)): # if an unconstrained variable has no bound + status = 3 + message = ("If feasible, the problem is (trivially) unbounded " + "due to a zero column in the constraint matrices. If " + "you wish to check whether the problem is infeasible, " + "turn presolve off.") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + # variables will equal upper/lower bounds will be removed later + lb[np.logical_and(zero_col, c < 0)] = ub[ + np.logical_and(zero_col, c < 0)] + ub[np.logical_and(zero_col, c > 0)] = lb[ + np.logical_and(zero_col, c > 0)] + + # row singleton in equality constraints + # this fixes a variable and removes the constraint + singleton_row = np.array(np.sum(A_eq != 0, axis=1) == 1).flatten() + rows = where(singleton_row)[0] + cols = where(A_eq[rows, :])[1] + if len(rows) > 0: + for row, col in zip(rows, cols): + val = b_eq[row] / A_eq[row, col] + if not lb[col] - tol <= val <= ub[col] + tol: + # infeasible if fixed value is not within bounds + status = 2 + message = ("The problem is (trivially) infeasible because a " + "singleton row in the equality constraints is " + "inconsistent with the bounds.") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + else: + # sets upper and lower bounds at that fixed value - variable + # will be removed later + lb[col] = val + ub[col] = val + A_eq = A_eq[np.logical_not(singleton_row), :] + b_eq = b_eq[np.logical_not(singleton_row)] + + # row singleton in inequality constraints + # this indicates a simple bound and the constraint can be removed + # simple bounds may be adjusted here + # After all of the simple bound information is combined here, get_Abc will + # turn the simple bounds into constraints + singleton_row = np.array(np.sum(A_ub != 0, axis=1) == 1).flatten() + cols = where(A_ub[singleton_row, :])[1] + rows = where(singleton_row)[0] + if len(rows) > 0: + for row, col in zip(rows, cols): + val = b_ub[row] / A_ub[row, col] + if A_ub[row, col] > 0: # upper bound + if val < lb[col] - tol: # infeasible + complete = True + elif val < ub[col]: # new upper bound + ub[col] = val + else: # lower bound + if val > ub[col] + tol: # infeasible + complete = True + elif val > lb[col]: # new lower bound + lb[col] = val + if complete: + status = 2 + message = ("The problem is (trivially) infeasible because a " + "singleton row in the upper bound constraints is " + "inconsistent with the bounds.") + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + A_ub = A_ub[np.logical_not(singleton_row), :] + b_ub = b_ub[np.logical_not(singleton_row)] + + # identical bounds indicate that variable can be removed + i_f = np.abs(lb - ub) < tol # indices of "fixed" variables + i_nf = np.logical_not(i_f) # indices of "not fixed" variables + + # test_bounds_equal_but_infeasible + if np.all(i_f): # if bounds define solution, check for consistency + residual = b_eq - A_eq.dot(lb) + slack = b_ub - A_ub.dot(lb) + if ((A_ub.size > 0 and np.any(slack < 0)) or + (A_eq.size > 0 and not np.allclose(residual, 0))): + status = 2 + message = ("The problem is (trivially) infeasible because the " + "bounds fix all variables to values inconsistent with " + "the constraints") + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + + ub_mod = ub + lb_mod = lb + if np.any(i_f): + c0 += c[i_f].dot(lb[i_f]) + b_eq = b_eq - A_eq[:, i_f].dot(lb[i_f]) + b_ub = b_ub - A_ub[:, i_f].dot(lb[i_f]) + c = c[i_nf] + x_undo = lb[i_f] # not x[i_f], x is just zeroes + x = x[i_nf] + # user guess x0 stays separate from presolve solution x + if x0 is not None: + x0 = x0[i_nf] + A_eq = A_eq[:, i_nf] + A_ub = A_ub[:, i_nf] + # modify bounds + lb_mod = lb[i_nf] + ub_mod = ub[i_nf] + + def rev(x_mod): + # Function to restore x: insert x_undo into x_mod. + # When elements have been removed at positions k1, k2, k3, ... + # then these must be replaced at (after) positions k1-1, k2-2, + # k3-3, ... in the modified array to recreate the original + i = np.flatnonzero(i_f) + # Number of variables to restore + N = len(i) + index_offset = np.arange(N) + # Create insert indices + insert_indices = i - index_offset + x_rev = np.insert(x_mod.astype(float), insert_indices, x_undo) + return x_rev + + # Use revstack as a list of functions, currently just this one. + revstack.append(rev) + + # no constraints indicates that problem is trivial + if A_eq.size == 0 and A_ub.size == 0: + b_eq = np.array([]) + b_ub = np.array([]) + # test_empty_constraint_1 + if c.size == 0: + status = 0 + message = ("The solution was determined in presolve as there are " + "no non-trivial constraints.") + elif (np.any(np.logical_and(c < 0, ub_mod == np.inf)) or + np.any(np.logical_and(c > 0, lb_mod == -np.inf))): + # test_no_constraints() + # test_unbounded_no_nontrivial_constraints_1 + # test_unbounded_no_nontrivial_constraints_2 + status = 3 + message = ("The problem is (trivially) unbounded " + "because there are no non-trivial constraints and " + "a) at least one decision variable is unbounded " + "above and its corresponding cost is negative, or " + "b) at least one decision variable is unbounded below " + "and its corresponding cost is positive. ") + else: # test_empty_constraint_2 + status = 0 + message = ("The solution was determined in presolve as there are " + "no non-trivial constraints.") + complete = True + x[c < 0] = ub_mod[c < 0] + x[c > 0] = lb_mod[c > 0] + # where c is zero, set x to a finite bound or zero + x_zero_c = ub_mod[c == 0] + x_zero_c[np.isinf(x_zero_c)] = ub_mod[c == 0][np.isinf(x_zero_c)] + x_zero_c[np.isinf(x_zero_c)] = 0 + x[c == 0] = x_zero_c + # if this is not the last step of presolve, should convert bounds back + # to array and return here + + # Convert modified lb and ub back into N x 2 bounds + bounds = np.hstack((lb_mod[:, np.newaxis], ub_mod[:, np.newaxis])) + + # remove redundant (linearly dependent) rows from equality constraints + n_rows_A = A_eq.shape[0] + redundancy_warning = ("A_eq does not appear to be of full row rank. To " + "improve performance, check the problem formulation " + "for redundant equality constraints.") + if (sps.issparse(A_eq)): + if rr and A_eq.size > 0: # TODO: Fast sparse rank check? + rr_res = _remove_redundancy_pivot_sparse(A_eq, b_eq) + A_eq, b_eq, status, message = rr_res + if A_eq.shape[0] < n_rows_A: + warn(redundancy_warning, OptimizeWarning, stacklevel=1) + if status != 0: + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + + # This is a wild guess for which redundancy removal algorithm will be + # faster. More testing would be good. + small_nullspace = 5 + if rr and A_eq.size > 0: + try: # TODO: use results of first SVD in _remove_redundancy_svd + rank = np.linalg.matrix_rank(A_eq) + # oh well, we'll have to go with _remove_redundancy_pivot_dense + except Exception: + rank = 0 + if rr and A_eq.size > 0 and rank < A_eq.shape[0]: + warn(redundancy_warning, OptimizeWarning, stacklevel=3) + dim_row_nullspace = A_eq.shape[0]-rank + if rr_method is None: + if dim_row_nullspace <= small_nullspace: + rr_res = _remove_redundancy_svd(A_eq, b_eq) + A_eq, b_eq, status, message = rr_res + if dim_row_nullspace > small_nullspace or status == 4: + rr_res = _remove_redundancy_pivot_dense(A_eq, b_eq) + A_eq, b_eq, status, message = rr_res + + else: + rr_method = rr_method.lower() + if rr_method == "svd": + rr_res = _remove_redundancy_svd(A_eq, b_eq) + A_eq, b_eq, status, message = rr_res + elif rr_method == "pivot": + rr_res = _remove_redundancy_pivot_dense(A_eq, b_eq) + A_eq, b_eq, status, message = rr_res + elif rr_method == "id": + rr_res = _remove_redundancy_id(A_eq, b_eq, rank) + A_eq, b_eq, status, message = rr_res + else: # shouldn't get here; option validity checked above + pass + if A_eq.shape[0] < rank: + message = ("Due to numerical issues, redundant equality " + "constraints could not be removed automatically. " + "Try providing your constraint matrices as sparse " + "matrices to activate sparse presolve, try turning " + "off redundancy removal, or try turning off presolve " + "altogether.") + status = 4 + if status != 0: + complete = True + return (_LPProblem(c, A_ub, b_ub, A_eq, b_eq, bounds, x0), + c0, x, revstack, complete, status, message) + + +def _parse_linprog(lp, options, meth): + """ + Parse the provided linear programming problem + + ``_parse_linprog`` employs two main steps ``_check_sparse_inputs`` and + ``_clean_inputs``. ``_check_sparse_inputs`` checks for sparsity in the + provided constraints (``A_ub`` and ``A_eq) and if these match the provided + sparsity optional values. + + ``_clean inputs`` checks of the provided inputs. If no violations are + identified the objective vector, upper bound constraints, equality + constraints, and simple bounds are returned in the expected format. + + Parameters + ---------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : various valid formats, optional + The bounds of ``x``, as ``min`` and ``max`` pairs. + If bounds are specified for all N variables separately, valid formats are: + * a 2D array (2 x N or N x 2); + * a sequence of N sequences, each with 2 values. + If all variables have the same bounds, a single pair of values can + be specified. Valid formats are: + * a sequence with 2 scalar values; + * a sequence with a single element containing 2 scalar values. + If all variables have a lower bound of 0 and no upper bound, the bounds + parameter can be omitted (or given as None). + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + options : dict + A dictionary of solver options. All methods accept the following + generic options: + + maxiter : int + Maximum number of iterations to perform. + disp : bool + Set to True to print convergence messages. + + For method-specific options, see :func:`show_options('linprog')`. + + Returns + ------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, as ``min`` and ``max`` pairs, one for each of the N + elements of ``x``. The N x 2 array contains lower bounds in the first + column and upper bounds in the 2nd. Unbounded variables have lower + bound -np.inf and/or upper bound np.inf. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + options : dict, optional + A dictionary of solver options. All methods accept the following + generic options: + + maxiter : int + Maximum number of iterations to perform. + disp : bool + Set to True to print convergence messages. + + For method-specific options, see :func:`show_options('linprog')`. + + """ + if options is None: + options = {} + + solver_options = {k: v for k, v in options.items()} + solver_options, A_ub, A_eq = _check_sparse_inputs(solver_options, meth, + lp.A_ub, lp.A_eq) + # Convert lists to numpy arrays, etc... + lp = _clean_inputs(lp._replace(A_ub=A_ub, A_eq=A_eq)) + return lp, solver_options + + +def _get_Abc(lp, c0): + """ + Given a linear programming problem of the form: + + Minimize:: + + c @ x + + Subject to:: + + A_ub @ x <= b_ub + A_eq @ x == b_eq + lb <= x <= ub + + where ``lb = 0`` and ``ub = None`` unless set in ``bounds``. + + Return the problem in standard form: + + Minimize:: + + c @ x + + Subject to:: + + A @ x == b + x >= 0 + + by adding slack variables and making variable substitutions as necessary. + + Parameters + ---------- + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, lower bounds in the 1st column, upper + bounds in the 2nd column. The bounds are possibly tightened + by the presolve procedure. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. + + Returns + ------- + A : 2-D array + 2-D array such that ``A`` @ ``x``, gives the values of the equality + constraints at ``x``. + b : 1-D array + 1-D array of values representing the RHS of each equality constraint + (row) in A (for standard form problem). + c : 1-D array + Coefficients of the linear objective function to be minimized (for + standard form problem). + c0 : float + Constant term in objective function due to fixed (and eliminated) + variables. + x0 : 1-D array + Starting values of the independent variables, which will be refined by + the optimization algorithm + + References + ---------- + .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear + programming." Athena Scientific 1 (1997): 997. + + """ + c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = lp + + if sps.issparse(A_eq): + sparse = True + A_eq = sps.csr_matrix(A_eq) + A_ub = sps.csr_matrix(A_ub) + + def hstack(blocks): + return sps.hstack(blocks, format="csr") + + def vstack(blocks): + return sps.vstack(blocks, format="csr") + + zeros = sps.csr_matrix + eye = sps.eye + else: + sparse = False + hstack = np.hstack + vstack = np.vstack + zeros = np.zeros + eye = np.eye + + # Variables lbs and ubs (see below) may be changed, which feeds back into + # bounds, so copy. + bounds = np.array(bounds, copy=True) + + # modify problem such that all variables have only non-negativity bounds + lbs = bounds[:, 0] + ubs = bounds[:, 1] + m_ub, n_ub = A_ub.shape + + lb_none = np.equal(lbs, -np.inf) + ub_none = np.equal(ubs, np.inf) + lb_some = np.logical_not(lb_none) + ub_some = np.logical_not(ub_none) + + # unbounded below: substitute xi = -xi' (unbounded above) + # if -inf <= xi <= ub, then -ub <= -xi <= inf, so swap and invert bounds + l_nolb_someub = np.logical_and(lb_none, ub_some) + i_nolb = np.nonzero(l_nolb_someub)[0] + lbs[l_nolb_someub], ubs[l_nolb_someub] = ( + -ubs[l_nolb_someub], -lbs[l_nolb_someub]) + lb_none = np.equal(lbs, -np.inf) + ub_none = np.equal(ubs, np.inf) + lb_some = np.logical_not(lb_none) + ub_some = np.logical_not(ub_none) + c[i_nolb] *= -1 + if x0 is not None: + x0[i_nolb] *= -1 + if len(i_nolb) > 0: + if A_ub.shape[0] > 0: # sometimes needed for sparse arrays... weird + A_ub[:, i_nolb] *= -1 + if A_eq.shape[0] > 0: + A_eq[:, i_nolb] *= -1 + + # upper bound: add inequality constraint + i_newub, = ub_some.nonzero() + ub_newub = ubs[ub_some] + n_bounds = len(i_newub) + if n_bounds > 0: + shape = (n_bounds, A_ub.shape[1]) + if sparse: + idxs = (np.arange(n_bounds), i_newub) + A_ub = vstack((A_ub, sps.csr_matrix((np.ones(n_bounds), idxs), + shape=shape))) + else: + A_ub = vstack((A_ub, np.zeros(shape))) + A_ub[np.arange(m_ub, A_ub.shape[0]), i_newub] = 1 + b_ub = np.concatenate((b_ub, np.zeros(n_bounds))) + b_ub[m_ub:] = ub_newub + + A1 = vstack((A_ub, A_eq)) + b = np.concatenate((b_ub, b_eq)) + c = np.concatenate((c, np.zeros((A_ub.shape[0],)))) + if x0 is not None: + x0 = np.concatenate((x0, np.zeros((A_ub.shape[0],)))) + # unbounded: substitute xi = xi+ + xi- + l_free = np.logical_and(lb_none, ub_none) + i_free = np.nonzero(l_free)[0] + n_free = len(i_free) + c = np.concatenate((c, np.zeros(n_free))) + if x0 is not None: + x0 = np.concatenate((x0, np.zeros(n_free))) + A1 = hstack((A1[:, :n_ub], -A1[:, i_free])) + c[n_ub:n_ub+n_free] = -c[i_free] + if x0 is not None: + i_free_neg = x0[i_free] < 0 + x0[np.arange(n_ub, A1.shape[1])[i_free_neg]] = -x0[i_free[i_free_neg]] + x0[i_free[i_free_neg]] = 0 + + # add slack variables + A2 = vstack([eye(A_ub.shape[0]), zeros((A_eq.shape[0], A_ub.shape[0]))]) + + A = hstack([A1, A2]) + + # lower bound: substitute xi = xi' + lb + # now there is a constant term in objective + i_shift = np.nonzero(lb_some)[0] + lb_shift = lbs[lb_some].astype(float) + c0 += np.sum(lb_shift * c[i_shift]) + if sparse: + b = b.reshape(-1, 1) + A = A.tocsc() + b -= (A[:, i_shift] * sps.diags(lb_shift)).sum(axis=1) + b = b.ravel() + else: + b -= (A[:, i_shift] * lb_shift).sum(axis=1) + if x0 is not None: + x0[i_shift] -= lb_shift + + return A, b, c, c0, x0 + + +def _round_to_power_of_two(x): + """ + Round elements of the array to the nearest power of two. + """ + return 2**np.around(np.log2(x)) + + +def _autoscale(A, b, c, x0): + """ + Scales the problem according to equilibration from [12]. + Also normalizes the right hand side vector by its maximum element. + """ + m, n = A.shape + + C = 1 + R = 1 + + if A.size > 0: + + R = np.max(np.abs(A), axis=1) + if sps.issparse(A): + R = R.toarray().flatten() + R[R == 0] = 1 + R = 1/_round_to_power_of_two(R) + A = sps.diags(R)*A if sps.issparse(A) else A*R.reshape(m, 1) + b = b*R + + C = np.max(np.abs(A), axis=0) + if sps.issparse(A): + C = C.toarray().flatten() + C[C == 0] = 1 + C = 1/_round_to_power_of_two(C) + A = A*sps.diags(C) if sps.issparse(A) else A*C + c = c*C + + b_scale = np.max(np.abs(b)) if b.size > 0 else 1 + if b_scale == 0: + b_scale = 1. + b = b/b_scale + + if x0 is not None: + x0 = x0/b_scale*(1/C) + return A, b, c, x0, C, b_scale + + +def _unscale(x, C, b_scale): + """ + Converts solution to _autoscale problem -> solution to original problem. + """ + + try: + n = len(C) + # fails if sparse or scalar; that's OK. + # this is only needed for original simplex (never sparse) + except TypeError: + n = len(x) + + return x[:n]*b_scale*C + + +def _display_summary(message, status, fun, iteration): + """ + Print the termination summary of the linear program + + Parameters + ---------- + message : str + A string descriptor of the exit status of the optimization. + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + fun : float + Value of the objective function. + iteration : iteration + The number of iterations performed. + """ + print(message) + if status in (0, 1): + print(f" Current function value: {fun: <12.6f}") + print(f" Iterations: {iteration:d}") + + +def _postsolve(x, postsolve_args, complete=False): + """ + Given solution x to presolved, standard form linear program x, add + fixed variables back into the problem and undo the variable substitutions + to get solution to original linear program. Also, calculate the objective + function value, slack in original upper bound constraints, and residuals + in original equality constraints. + + Parameters + ---------- + x : 1-D array + Solution vector to the standard-form problem. + postsolve_args : tuple + Data needed by _postsolve to convert the solution to the standard-form + problem into the solution to the original problem, including: + + lp : A `scipy.optimize._linprog_util._LPProblem` consisting of the following fields: + + c : 1D array + The coefficients of the linear objective function to be minimized. + A_ub : 2D array, optional + The inequality constraint matrix. Each row of ``A_ub`` specifies the + coefficients of a linear inequality constraint on ``x``. + b_ub : 1D array, optional + The inequality constraint vector. Each element represents an + upper bound on the corresponding value of ``A_ub @ x``. + A_eq : 2D array, optional + The equality constraint matrix. Each row of ``A_eq`` specifies the + coefficients of a linear equality constraint on ``x``. + b_eq : 1D array, optional + The equality constraint vector. Each element of ``A_eq @ x`` must equal + the corresponding element of ``b_eq``. + bounds : 2D array + The bounds of ``x``, lower bounds in the 1st column, upper + bounds in the 2nd column. The bounds are possibly tightened + by the presolve procedure. + x0 : 1D array, optional + Guess values of the decision variables, which will be refined by + the optimization algorithm. This argument is currently used only by the + 'revised simplex' method, and can only be used if `x0` represents a + basic feasible solution. + + revstack: list of functions + the functions in the list reverse the operations of _presolve() + the function signature is x_org = f(x_mod), where x_mod is the result + of a presolve step and x_org the value at the start of the step + complete : bool + Whether the solution is was determined in presolve (``True`` if so) + + Returns + ------- + x : 1-D array + Solution vector to original linear programming problem + fun: float + optimal objective value for original problem + slack : 1-D array + The (non-negative) slack in the upper bound constraints, that is, + ``b_ub - A_ub @ x`` + con : 1-D array + The (nominally zero) residuals of the equality constraints, that is, + ``b - A_eq @ x`` + """ + # note that all the inputs are the ORIGINAL, unmodified versions + # no rows, columns have been removed + + c, A_ub, b_ub, A_eq, b_eq, bounds, x0, integrality = postsolve_args[0] + revstack, C, b_scale = postsolve_args[1:] + + x = _unscale(x, C, b_scale) + + # Undo variable substitutions of _get_Abc() + # if "complete", problem was solved in presolve; don't do anything here + n_x = bounds.shape[0] + if not complete and bounds is not None: # bounds are never none, probably + n_unbounded = 0 + for i, bi in enumerate(bounds): + lbi = bi[0] + ubi = bi[1] + if lbi == -np.inf and ubi == np.inf: + n_unbounded += 1 + x[i] = x[i] - x[n_x + n_unbounded - 1] + else: + if lbi == -np.inf: + x[i] = ubi - x[i] + else: + x[i] += lbi + # all the rest of the variables were artificial + x = x[:n_x] + + # If there were variables removed from the problem, add them back into the + # solution vector + # Apply the functions in revstack (reverse direction) + for rev in reversed(revstack): + x = rev(x) + + fun = x.dot(c) + slack = b_ub - A_ub.dot(x) # report slack for ORIGINAL UB constraints + # report residuals of ORIGINAL EQ constraints + con = b_eq - A_eq.dot(x) + + return x, fun, slack, con + + +def _check_result(x, fun, status, slack, con, bounds, tol, message, + integrality): + """ + Check the validity of the provided solution. + + A valid (optimal) solution satisfies all bounds, all slack variables are + negative and all equality constraint residuals are strictly non-zero. + Further, the lower-bounds, upper-bounds, slack and residuals contain + no nan values. + + Parameters + ---------- + x : 1-D array + Solution vector to original linear programming problem + fun: float + optimal objective value for original problem + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + slack : 1-D array + The (non-negative) slack in the upper bound constraints, that is, + ``b_ub - A_ub @ x`` + con : 1-D array + The (nominally zero) residuals of the equality constraints, that is, + ``b - A_eq @ x`` + bounds : 2D array + The bounds on the original variables ``x`` + message : str + A string descriptor of the exit status of the optimization. + tol : float + Termination tolerance; see [1]_ Section 4.5. + + Returns + ------- + status : int + An integer representing the exit status of the optimization:: + + 0 : Optimization terminated successfully + 1 : Iteration limit reached + 2 : Problem appears to be infeasible + 3 : Problem appears to be unbounded + 4 : Serious numerical difficulties encountered + + message : str + A string descriptor of the exit status of the optimization. + """ + # Somewhat arbitrary + tol = np.sqrt(tol) * 10 + + if x is None: + # HiGHS does not provide x if infeasible/unbounded + if status == 0: # Observed with HiGHS Simplex Primal + status = 4 + message = ("The solver did not provide a solution nor did it " + "report a failure. Please submit a bug report.") + return status, message + + contains_nans = ( + np.isnan(x).any() + or np.isnan(fun) + or np.isnan(slack).any() + or np.isnan(con).any() + ) + + if contains_nans: + is_feasible = False + else: + if integrality is None: + integrality = 0 + valid_bounds = (x >= bounds[:, 0] - tol) & (x <= bounds[:, 1] + tol) + # When integrality is 2 or 3, x must be within bounds OR take value 0 + valid_bounds |= (integrality > 1) & np.isclose(x, 0, atol=tol) + invalid_bounds = not np.all(valid_bounds) + + invalid_slack = status != 3 and (slack < -tol).any() + invalid_con = status != 3 and (np.abs(con) > tol).any() + is_feasible = not (invalid_bounds or invalid_slack or invalid_con) + + if status == 0 and not is_feasible: + status = 4 + message = ("The solution does not satisfy the constraints within the " + "required tolerance of " + f"{tol:.2E}" + ", yet " + "no errors were raised and there is no certificate of " + "infeasibility or unboundedness. Check whether " + "the slack and constraint residuals are acceptable; " + "if not, consider enabling presolve, adjusting the " + "tolerance option(s), and/or using a different method. " + "Please consider submitting a bug report.") + elif status == 2 and is_feasible: + # Occurs if the simplex method exits after phase one with a very + # nearly basic feasible solution. Postsolving can make the solution + # basic, however, this solution is NOT optimal + status = 4 + message = ("The solution is feasible, but the solver did not report " + "that the solution was optimal. Please try a different " + "method.") + + return status, message diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lsap.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lsap.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..b2ea39a10549d1346bada989f573981804d22006 Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_lsap.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_milp.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_milp.py new file mode 100644 index 0000000000000000000000000000000000000000..5ec771eba471e37aac5aa3008b642f68167fbafb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_milp.py @@ -0,0 +1,392 @@ +import warnings +import numpy as np +from scipy.sparse import csc_array, vstack, issparse +from scipy._lib._util import VisibleDeprecationWarning +from ._highs._highs_wrapper import _highs_wrapper # type: ignore[import-not-found,import-untyped] +from ._constraints import LinearConstraint, Bounds +from ._optimize import OptimizeResult +from ._linprog_highs import _highs_to_scipy_status_message + + +def _constraints_to_components(constraints): + """ + Convert sequence of constraints to a single set of components A, b_l, b_u. + + `constraints` could be + + 1. A LinearConstraint + 2. A tuple representing a LinearConstraint + 3. An invalid object + 4. A sequence of composed entirely of objects of type 1/2 + 5. A sequence containing at least one object of type 3 + + We want to accept 1, 2, and 4 and reject 3 and 5. + """ + message = ("`constraints` (or each element within `constraints`) must be " + "convertible into an instance of " + "`scipy.optimize.LinearConstraint`.") + As = [] + b_ls = [] + b_us = [] + + # Accept case 1 by standardizing as case 4 + if isinstance(constraints, LinearConstraint): + constraints = [constraints] + else: + # Reject case 3 + try: + iter(constraints) + except TypeError as exc: + raise ValueError(message) from exc + + # Accept case 2 by standardizing as case 4 + if len(constraints) == 3: + # argument could be a single tuple representing a LinearConstraint + try: + constraints = [LinearConstraint(*constraints)] + except (TypeError, ValueError, VisibleDeprecationWarning): + # argument was not a tuple representing a LinearConstraint + pass + + # Address cases 4/5 + for constraint in constraints: + # if it's not a LinearConstraint or something that represents a + # LinearConstraint at this point, it's invalid + if not isinstance(constraint, LinearConstraint): + try: + constraint = LinearConstraint(*constraint) + except TypeError as exc: + raise ValueError(message) from exc + As.append(csc_array(constraint.A)) + b_ls.append(np.atleast_1d(constraint.lb).astype(np.float64)) + b_us.append(np.atleast_1d(constraint.ub).astype(np.float64)) + + if len(As) > 1: + A = vstack(As, format="csc") + b_l = np.concatenate(b_ls) + b_u = np.concatenate(b_us) + else: # avoid unnecessary copying + A = As[0] + b_l = b_ls[0] + b_u = b_us[0] + + return A, b_l, b_u + + +def _milp_iv(c, integrality, bounds, constraints, options): + # objective IV + if issparse(c): + raise ValueError("`c` must be a dense array.") + c = np.atleast_1d(c).astype(np.float64) + if c.ndim != 1 or c.size == 0 or not np.all(np.isfinite(c)): + message = ("`c` must be a one-dimensional array of finite numbers " + "with at least one element.") + raise ValueError(message) + + # integrality IV + if issparse(integrality): + raise ValueError("`integrality` must be a dense array.") + message = ("`integrality` must contain integers 0-3 and be broadcastable " + "to `c.shape`.") + if integrality is None: + integrality = 0 + try: + integrality = np.broadcast_to(integrality, c.shape).astype(np.uint8) + except ValueError: + raise ValueError(message) + if integrality.min() < 0 or integrality.max() > 3: + raise ValueError(message) + + # bounds IV + if bounds is None: + bounds = Bounds(0, np.inf) + elif not isinstance(bounds, Bounds): + message = ("`bounds` must be convertible into an instance of " + "`scipy.optimize.Bounds`.") + try: + bounds = Bounds(*bounds) + except TypeError as exc: + raise ValueError(message) from exc + + try: + lb = np.broadcast_to(bounds.lb, c.shape).astype(np.float64) + ub = np.broadcast_to(bounds.ub, c.shape).astype(np.float64) + except (ValueError, TypeError) as exc: + message = ("`bounds.lb` and `bounds.ub` must contain reals and " + "be broadcastable to `c.shape`.") + raise ValueError(message) from exc + + # constraints IV + if not constraints: + constraints = [LinearConstraint(np.empty((0, c.size)), + np.empty((0,)), np.empty((0,)))] + try: + A, b_l, b_u = _constraints_to_components(constraints) + except ValueError as exc: + message = ("`constraints` (or each element within `constraints`) must " + "be convertible into an instance of " + "`scipy.optimize.LinearConstraint`.") + raise ValueError(message) from exc + + if A.shape != (b_l.size, c.size): + message = "The shape of `A` must be (len(b_l), len(c))." + raise ValueError(message) + indptr, indices, data = A.indptr, A.indices, A.data.astype(np.float64) + + # options IV + options = options or {} + supported_options = {'disp', 'presolve', 'time_limit', 'node_limit', + 'mip_rel_gap'} + unsupported_options = set(options).difference(supported_options) + if unsupported_options: + message = (f"Unrecognized options detected: {unsupported_options}. " + "These will be passed to HiGHS verbatim.") + warnings.warn(message, RuntimeWarning, stacklevel=3) + options_iv = {'log_to_console': options.pop("disp", False), + 'mip_max_nodes': options.pop("node_limit", None)} + options_iv.update(options) + + return c, integrality, lb, ub, indptr, indices, data, b_l, b_u, options_iv + + +def milp(c, *, integrality=None, bounds=None, constraints=None, options=None): + r""" + Mixed-integer linear programming + + Solves problems of the following form: + + .. math:: + + \min_x \ & c^T x \\ + \mbox{such that} \ & b_l \leq A x \leq b_u,\\ + & l \leq x \leq u, \\ + & x_i \in \mathbb{Z}, i \in X_i + + where :math:`x` is a vector of decision variables; + :math:`c`, :math:`b_l`, :math:`b_u`, :math:`l`, and :math:`u` are vectors; + :math:`A` is a matrix, and :math:`X_i` is the set of indices of + decision variables that must be integral. (In this context, a + variable that can assume only integer values is said to be "integral"; + it has an "integrality" constraint.) + + Alternatively, that's: + + minimize:: + + c @ x + + such that:: + + b_l <= A @ x <= b_u + l <= x <= u + Specified elements of x must be integers + + By default, ``l = 0`` and ``u = np.inf`` unless specified with + ``bounds``. + + Parameters + ---------- + c : 1D dense array_like + The coefficients of the linear objective function to be minimized. + `c` is converted to a double precision array before the problem is + solved. + integrality : 1D dense array_like, optional + Indicates the type of integrality constraint on each decision variable. + + ``0`` : Continuous variable; no integrality constraint. + + ``1`` : Integer variable; decision variable must be an integer + within `bounds`. + + ``2`` : Semi-continuous variable; decision variable must be within + `bounds` or take value ``0``. + + ``3`` : Semi-integer variable; decision variable must be an integer + within `bounds` or take value ``0``. + + By default, all variables are continuous. `integrality` is converted + to an array of integers before the problem is solved. + + bounds : scipy.optimize.Bounds, optional + Bounds on the decision variables. Lower and upper bounds are converted + to double precision arrays before the problem is solved. The + ``keep_feasible`` parameter of the `Bounds` object is ignored. If + not specified, all decision variables are constrained to be + non-negative. + constraints : sequence of scipy.optimize.LinearConstraint, optional + Linear constraints of the optimization problem. Arguments may be + one of the following: + + 1. A single `LinearConstraint` object + 2. A single tuple that can be converted to a `LinearConstraint` object + as ``LinearConstraint(*constraints)`` + 3. A sequence composed entirely of objects of type 1. and 2. + + Before the problem is solved, all values are converted to double + precision, and the matrices of constraint coefficients are converted to + instances of `scipy.sparse.csc_array`. The ``keep_feasible`` parameter + of `LinearConstraint` objects is ignored. + options : dict, optional + A dictionary of solver options. The following keys are recognized. + + disp : bool (default: ``False``) + Set to ``True`` if indicators of optimization status are to be + printed to the console during optimization. + node_limit : int, optional + The maximum number of nodes (linear program relaxations) to solve + before stopping. Default is no maximum number of nodes. + presolve : bool (default: ``True``) + Presolve attempts to identify trivial infeasibilities, + identify trivial unboundedness, and simplify the problem before + sending it to the main solver. + time_limit : float, optional + The maximum number of seconds allotted to solve the problem. + Default is no time limit. + mip_rel_gap : float, optional + Termination criterion for MIP solver: solver will terminate when + the gap between the primal objective value and the dual objective + bound, scaled by the primal objective value, is <= mip_rel_gap. + + Returns + ------- + res : OptimizeResult + An instance of :class:`scipy.optimize.OptimizeResult`. The object + is guaranteed to have the following attributes. + + status : int + An integer representing the exit status of the algorithm. + + ``0`` : Optimal solution found. + + ``1`` : Iteration or time limit reached. + + ``2`` : Problem is infeasible. + + ``3`` : Problem is unbounded. + + ``4`` : Other; see message for details. + + success : bool + ``True`` when an optimal solution is found and ``False`` otherwise. + + message : str + A string descriptor of the exit status of the algorithm. + + The following attributes will also be present, but the values may be + ``None``, depending on the solution status. + + x : ndarray + The values of the decision variables that minimize the + objective function while satisfying the constraints. + fun : float + The optimal value of the objective function ``c @ x``. + mip_node_count : int + The number of subproblems or "nodes" solved by the MILP solver. + mip_dual_bound : float + The MILP solver's final estimate of the lower bound on the optimal + solution. + mip_gap : float + The difference between the primal objective value and the dual + objective bound, scaled by the primal objective value. + + Notes + ----- + `milp` is a wrapper of the HiGHS linear optimization software [1]_. The + algorithm is deterministic, and it typically finds the global optimum of + moderately challenging mixed-integer linear programs (when it exists). + + References + ---------- + .. [1] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. + "HiGHS - high performance software for linear optimization." + https://highs.dev/ + .. [2] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised + simplex method." Mathematical Programming Computation, 10 (1), + 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 + + Examples + -------- + Consider the problem at + https://en.wikipedia.org/wiki/Integer_programming#Example, which is + expressed as a maximization problem of two variables. Since `milp` requires + that the problem be expressed as a minimization problem, the objective + function coefficients on the decision variables are: + + >>> import numpy as np + >>> c = -np.array([0, 1]) + + Note the negative sign: we maximize the original objective function + by minimizing the negative of the objective function. + + We collect the coefficients of the constraints into arrays like: + + >>> A = np.array([[-1, 1], [3, 2], [2, 3]]) + >>> b_u = np.array([1, 12, 12]) + >>> b_l = np.full_like(b_u, -np.inf, dtype=float) + + Because there is no lower limit on these constraints, we have defined a + variable ``b_l`` full of values representing negative infinity. This may + be unfamiliar to users of `scipy.optimize.linprog`, which only accepts + "less than" (or "upper bound") inequality constraints of the form + ``A_ub @ x <= b_u``. By accepting both ``b_l`` and ``b_u`` of constraints + ``b_l <= A_ub @ x <= b_u``, `milp` makes it easy to specify "greater than" + inequality constraints, "less than" inequality constraints, and equality + constraints concisely. + + These arrays are collected into a single `LinearConstraint` object like: + + >>> from scipy.optimize import LinearConstraint + >>> constraints = LinearConstraint(A, b_l, b_u) + + The non-negativity bounds on the decision variables are enforced by + default, so we do not need to provide an argument for `bounds`. + + Finally, the problem states that both decision variables must be integers: + + >>> integrality = np.ones_like(c) + + We solve the problem like: + + >>> from scipy.optimize import milp + >>> res = milp(c=c, constraints=constraints, integrality=integrality) + >>> res.x + [2.0, 2.0] + + Note that had we solved the relaxed problem (without integrality + constraints): + + >>> res = milp(c=c, constraints=constraints) # OR: + >>> # from scipy.optimize import linprog; res = linprog(c, A, b_u) + >>> res.x + [1.8, 2.8] + + we would not have obtained the correct solution by rounding to the nearest + integers. + + Other examples are given :ref:`in the tutorial `. + + """ + args_iv = _milp_iv(c, integrality, bounds, constraints, options) + c, integrality, lb, ub, indptr, indices, data, b_l, b_u, options = args_iv + + highs_res = _highs_wrapper(c, indptr, indices, data, b_l, b_u, + lb, ub, integrality, options) + + res = {} + + # Convert to scipy-style status and message + highs_status = highs_res.get('status', None) + highs_message = highs_res.get('message', None) + status, message = _highs_to_scipy_status_message(highs_status, + highs_message) + res['status'] = status + res['message'] = message + res['success'] = (status == 0) + x = highs_res.get('x', None) + res['x'] = np.array(x) if x is not None else None + res['fun'] = highs_res.get('fun', None) + res['mip_node_count'] = highs_res.get('mip_node_count', None) + res['mip_dual_bound'] = highs_res.get('mip_dual_bound', None) + res['mip_gap'] = highs_res.get('mip_gap', None) + + return OptimizeResult(res) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minimize.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minimize.py new file mode 100644 index 0000000000000000000000000000000000000000..195e31f23e227155040c6c54d7552e11bba7b1c0 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minimize.py @@ -0,0 +1,1116 @@ +""" +Unified interfaces to minimization algorithms. + +Functions +--------- +- minimize : minimization of a function of several variables. +- minimize_scalar : minimization of a function of one variable. +""" + +__all__ = ['minimize', 'minimize_scalar'] + + +from warnings import warn + +import numpy as np + +# unconstrained minimization +from ._optimize import (_minimize_neldermead, _minimize_powell, _minimize_cg, + _minimize_bfgs, _minimize_newtoncg, + _minimize_scalar_brent, _minimize_scalar_bounded, + _minimize_scalar_golden, MemoizeJac, OptimizeResult, + _wrap_callback, _recover_from_bracket_error) +from ._trustregion_dogleg import _minimize_dogleg +from ._trustregion_ncg import _minimize_trust_ncg +from ._trustregion_krylov import _minimize_trust_krylov +from ._trustregion_exact import _minimize_trustregion_exact +from ._trustregion_constr import _minimize_trustregion_constr + +# constrained minimization +from ._lbfgsb_py import _minimize_lbfgsb +from ._tnc import _minimize_tnc +from ._cobyla_py import _minimize_cobyla +from ._cobyqa_py import _minimize_cobyqa +from ._slsqp_py import _minimize_slsqp +from ._constraints import (old_bound_to_new, new_bounds_to_old, + old_constraint_to_new, new_constraint_to_old, + NonlinearConstraint, LinearConstraint, Bounds, + PreparedConstraint) +from ._differentiable_functions import FD_METHODS + +MINIMIZE_METHODS = ['nelder-mead', 'powell', 'cg', 'bfgs', 'newton-cg', + 'l-bfgs-b', 'tnc', 'cobyla', 'cobyqa', 'slsqp', + 'trust-constr', 'dogleg', 'trust-ncg', 'trust-exact', + 'trust-krylov'] + +# These methods support the new callback interface (passed an OptimizeResult) +MINIMIZE_METHODS_NEW_CB = ['nelder-mead', 'powell', 'cg', 'bfgs', 'newton-cg', + 'l-bfgs-b', 'trust-constr', 'dogleg', 'trust-ncg', + 'trust-exact', 'trust-krylov', 'cobyqa'] + +MINIMIZE_SCALAR_METHODS = ['brent', 'bounded', 'golden'] + +def minimize(fun, x0, args=(), method=None, jac=None, hess=None, + hessp=None, bounds=None, constraints=(), tol=None, + callback=None, options=None): + """Minimization of scalar function of one or more variables. + + Parameters + ---------- + fun : callable + The objective function to be minimized. + + ``fun(x, *args) -> float`` + + where ``x`` is a 1-D array with shape (n,) and ``args`` + is a tuple of the fixed parameters needed to completely + specify the function. + x0 : ndarray, shape (n,) + Initial guess. Array of real elements of size (n,), + where ``n`` is the number of independent variables. + args : tuple, optional + Extra arguments passed to the objective function and its + derivatives (`fun`, `jac` and `hess` functions). + method : str or callable, optional + Type of solver. Should be one of + + - 'Nelder-Mead' :ref:`(see here) ` + - 'Powell' :ref:`(see here) ` + - 'CG' :ref:`(see here) ` + - 'BFGS' :ref:`(see here) ` + - 'Newton-CG' :ref:`(see here) ` + - 'L-BFGS-B' :ref:`(see here) ` + - 'TNC' :ref:`(see here) ` + - 'COBYLA' :ref:`(see here) ` + - 'COBYQA' :ref:`(see here) ` + - 'SLSQP' :ref:`(see here) ` + - 'trust-constr':ref:`(see here) ` + - 'dogleg' :ref:`(see here) ` + - 'trust-ncg' :ref:`(see here) ` + - 'trust-exact' :ref:`(see here) ` + - 'trust-krylov' :ref:`(see here) ` + - custom - a callable object, see below for description. + + If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``, + depending on whether or not the problem has constraints or bounds. + jac : {callable, '2-point', '3-point', 'cs', bool}, optional + Method for computing the gradient vector. Only for CG, BFGS, + Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov, + trust-exact and trust-constr. + If it is a callable, it should be a function that returns the gradient + vector: + + ``jac(x, *args) -> array_like, shape (n,)`` + + where ``x`` is an array with shape (n,) and ``args`` is a tuple with + the fixed parameters. If `jac` is a Boolean and is True, `fun` is + assumed to return a tuple ``(f, g)`` containing the objective + function and the gradient. + Methods 'Newton-CG', 'trust-ncg', 'dogleg', 'trust-exact', and + 'trust-krylov' require that either a callable be supplied, or that + `fun` return the objective and gradient. + If None or False, the gradient will be estimated using 2-point finite + difference estimation with an absolute step size. + Alternatively, the keywords {'2-point', '3-point', 'cs'} can be used + to select a finite difference scheme for numerical estimation of the + gradient with a relative step size. These finite difference schemes + obey any specified `bounds`. + hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional + Method for computing the Hessian matrix. Only for Newton-CG, dogleg, + trust-ncg, trust-krylov, trust-exact and trust-constr. + If it is callable, it should return the Hessian matrix: + + ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)`` + + where ``x`` is a (n,) ndarray and ``args`` is a tuple with the fixed + parameters. + The keywords {'2-point', '3-point', 'cs'} can also be used to select + a finite difference scheme for numerical estimation of the hessian. + Alternatively, objects implementing the `HessianUpdateStrategy` + interface can be used to approximate the Hessian. Available + quasi-Newton methods implementing this interface are: + + - `BFGS`; + - `SR1`. + + Not all of the options are available for each of the methods; for + availability refer to the notes. + hessp : callable, optional + Hessian of objective function times an arbitrary vector p. Only for + Newton-CG, trust-ncg, trust-krylov, trust-constr. + Only one of `hessp` or `hess` needs to be given. If `hess` is + provided, then `hessp` will be ignored. `hessp` must compute the + Hessian times an arbitrary vector: + + ``hessp(x, p, *args) -> ndarray shape (n,)`` + + where ``x`` is a (n,) ndarray, ``p`` is an arbitrary vector with + dimension (n,) and ``args`` is a tuple with the fixed + parameters. + bounds : sequence or `Bounds`, optional + Bounds on variables for Nelder-Mead, L-BFGS-B, TNC, SLSQP, Powell, + trust-constr, COBYLA, and COBYQA methods. There are two ways to specify + the bounds: + + 1. Instance of `Bounds` class. + 2. Sequence of ``(min, max)`` pairs for each element in `x`. None + is used to specify no bound. + + constraints : {Constraint, dict} or List of {Constraint, dict}, optional + Constraints definition. Only for COBYLA, COBYQA, SLSQP and trust-constr. + + Constraints for 'trust-constr' and 'cobyqa' are defined as a single object + or a list of objects specifying constraints to the optimization problem. + Available constraints are: + + - `LinearConstraint` + - `NonlinearConstraint` + + Constraints for COBYLA, SLSQP are defined as a list of dictionaries. + Each dictionary with fields: + + type : str + Constraint type: 'eq' for equality, 'ineq' for inequality. + fun : callable + The function defining the constraint. + jac : callable, optional + The Jacobian of `fun` (only for SLSQP). + args : sequence, optional + Extra arguments to be passed to the function and Jacobian. + + Equality constraint means that the constraint function result is to + be zero whereas inequality means that it is to be non-negative. + Note that COBYLA only supports inequality constraints. + + tol : float, optional + Tolerance for termination. When `tol` is specified, the selected + minimization algorithm sets some relevant solver-specific tolerance(s) + equal to `tol`. For detailed control, use solver-specific + options. + options : dict, optional + A dictionary of solver options. All methods except `TNC` accept the + following generic options: + + maxiter : int + Maximum number of iterations to perform. Depending on the + method each iteration may use several function evaluations. + + For `TNC` use `maxfun` instead of `maxiter`. + disp : bool + Set to True to print convergence messages. + + For method-specific options, see :func:`show_options()`. + callback : callable, optional + A callable called after each iteration. + + All methods except TNC, SLSQP, and COBYLA support a callable with + the signature: + + ``callback(intermediate_result: OptimizeResult)`` + + where ``intermediate_result`` is a keyword parameter containing an + `OptimizeResult` with attributes ``x`` and ``fun``, the present values + of the parameter vector and objective function. Note that the name + of the parameter must be ``intermediate_result`` for the callback + to be passed an `OptimizeResult`. These methods will also terminate if + the callback raises ``StopIteration``. + + All methods except trust-constr (also) support a signature like: + + ``callback(xk)`` + + where ``xk`` is the current parameter vector. + + Introspection is used to determine which of the signatures above to + invoke. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. + + See also + -------- + minimize_scalar : Interface to minimization algorithms for scalar + univariate functions + show_options : Additional options accepted by the solvers + + Notes + ----- + This section describes the available solvers that can be selected by the + 'method' parameter. The default method is *BFGS*. + + **Unconstrained minimization** + + Method :ref:`CG ` uses a nonlinear conjugate + gradient algorithm by Polak and Ribiere, a variant of the + Fletcher-Reeves method described in [5]_ pp.120-122. Only the + first derivatives are used. + + Method :ref:`BFGS ` uses the quasi-Newton + method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [5]_ + pp. 136. It uses the first derivatives only. BFGS has proven good + performance even for non-smooth optimizations. This method also + returns an approximation of the Hessian inverse, stored as + `hess_inv` in the OptimizeResult object. + + Method :ref:`Newton-CG ` uses a + Newton-CG algorithm [5]_ pp. 168 (also known as the truncated + Newton method). It uses a CG method to the compute the search + direction. See also *TNC* method for a box-constrained + minimization with a similar algorithm. Suitable for large-scale + problems. + + Method :ref:`dogleg ` uses the dog-leg + trust-region algorithm [5]_ for unconstrained minimization. This + algorithm requires the gradient and Hessian; furthermore the + Hessian is required to be positive definite. + + Method :ref:`trust-ncg ` uses the + Newton conjugate gradient trust-region algorithm [5]_ for + unconstrained minimization. This algorithm requires the gradient + and either the Hessian or a function that computes the product of + the Hessian with a given vector. Suitable for large-scale problems. + + Method :ref:`trust-krylov ` uses + the Newton GLTR trust-region algorithm [14]_, [15]_ for unconstrained + minimization. This algorithm requires the gradient + and either the Hessian or a function that computes the product of + the Hessian with a given vector. Suitable for large-scale problems. + On indefinite problems it requires usually less iterations than the + `trust-ncg` method and is recommended for medium and large-scale problems. + + Method :ref:`trust-exact ` + is a trust-region method for unconstrained minimization in which + quadratic subproblems are solved almost exactly [13]_. This + algorithm requires the gradient and the Hessian (which is + *not* required to be positive definite). It is, in many + situations, the Newton method to converge in fewer iterations + and the most recommended for small and medium-size problems. + + **Bound-Constrained minimization** + + Method :ref:`Nelder-Mead ` uses the + Simplex algorithm [1]_, [2]_. This algorithm is robust in many + applications. However, if numerical computation of derivative can be + trusted, other algorithms using the first and/or second derivatives + information might be preferred for their better performance in + general. + + Method :ref:`L-BFGS-B ` uses the L-BFGS-B + algorithm [6]_, [7]_ for bound constrained minimization. + + Method :ref:`Powell ` is a modification + of Powell's method [3]_, [4]_ which is a conjugate direction + method. It performs sequential one-dimensional minimizations along + each vector of the directions set (`direc` field in `options` and + `info`), which is updated at each iteration of the main + minimization loop. The function need not be differentiable, and no + derivatives are taken. If bounds are not provided, then an + unbounded line search will be used. If bounds are provided and + the initial guess is within the bounds, then every function + evaluation throughout the minimization procedure will be within + the bounds. If bounds are provided, the initial guess is outside + the bounds, and `direc` is full rank (default has full rank), then + some function evaluations during the first iteration may be + outside the bounds, but every function evaluation after the first + iteration will be within the bounds. If `direc` is not full rank, + then some parameters may not be optimized and the solution is not + guaranteed to be within the bounds. + + Method :ref:`TNC ` uses a truncated Newton + algorithm [5]_, [8]_ to minimize a function with variables subject + to bounds. This algorithm uses gradient information; it is also + called Newton Conjugate-Gradient. It differs from the *Newton-CG* + method described above as it wraps a C implementation and allows + each variable to be given upper and lower bounds. + + **Constrained Minimization** + + Method :ref:`COBYLA ` uses the + Constrained Optimization BY Linear Approximation (COBYLA) method + [9]_, [10]_, [11]_. The algorithm is based on linear + approximations to the objective function and each constraint. The + method wraps a FORTRAN implementation of the algorithm. The + constraints functions 'fun' may return either a single number + or an array or list of numbers. + + Method :ref:`COBYQA ` uses the Constrained + Optimization BY Quadratic Approximations (COBYQA) method [18]_. The + algorithm is a derivative-free trust-region SQP method based on quadratic + approximations to the objective function and each nonlinear constraint. The + bounds are treated as unrelaxable constraints, in the sense that the + algorithm always respects them throughout the optimization process. + + Method :ref:`SLSQP ` uses Sequential + Least SQuares Programming to minimize a function of several + variables with any combination of bounds, equality and inequality + constraints. The method wraps the SLSQP Optimization subroutine + originally implemented by Dieter Kraft [12]_. Note that the + wrapper handles infinite values in bounds by converting them into + large floating values. + + Method :ref:`trust-constr ` is a + trust-region algorithm for constrained optimization. It switches + between two implementations depending on the problem definition. + It is the most versatile constrained minimization algorithm + implemented in SciPy and the most appropriate for large-scale problems. + For equality constrained problems it is an implementation of Byrd-Omojokun + Trust-Region SQP method described in [17]_ and in [5]_, p. 549. When + inequality constraints are imposed as well, it switches to the trust-region + interior point method described in [16]_. This interior point algorithm, + in turn, solves inequality constraints by introducing slack variables + and solving a sequence of equality-constrained barrier problems + for progressively smaller values of the barrier parameter. + The previously described equality constrained SQP method is + used to solve the subproblems with increasing levels of accuracy + as the iterate gets closer to a solution. + + **Finite-Difference Options** + + For Method :ref:`trust-constr ` + the gradient and the Hessian may be approximated using + three finite-difference schemes: {'2-point', '3-point', 'cs'}. + The scheme 'cs' is, potentially, the most accurate but it + requires the function to correctly handle complex inputs and to + be differentiable in the complex plane. The scheme '3-point' is more + accurate than '2-point' but requires twice as many operations. If the + gradient is estimated via finite-differences the Hessian must be + estimated using one of the quasi-Newton strategies. + + **Method specific options for the** `hess` **keyword** + + +--------------+------+----------+-------------------------+-----+ + | method/Hess | None | callable | '2-point/'3-point'/'cs' | HUS | + +==============+======+==========+=========================+=====+ + | Newton-CG | x | (n, n) | x | x | + | | | LO | | | + +--------------+------+----------+-------------------------+-----+ + | dogleg | | (n, n) | | | + +--------------+------+----------+-------------------------+-----+ + | trust-ncg | | (n, n) | x | x | + +--------------+------+----------+-------------------------+-----+ + | trust-krylov | | (n, n) | x | x | + +--------------+------+----------+-------------------------+-----+ + | trust-exact | | (n, n) | | | + +--------------+------+----------+-------------------------+-----+ + | trust-constr | x | (n, n) | x | x | + | | | LO | | | + | | | sp | | | + +--------------+------+----------+-------------------------+-----+ + + where LO=LinearOperator, sp=Sparse matrix, HUS=HessianUpdateStrategy + + **Custom minimizers** + + It may be useful to pass a custom minimization method, for example + when using a frontend to this method such as `scipy.optimize.basinhopping` + or a different library. You can simply pass a callable as the ``method`` + parameter. + + The callable is called as ``method(fun, x0, args, **kwargs, **options)`` + where ``kwargs`` corresponds to any other parameters passed to `minimize` + (such as `callback`, `hess`, etc.), except the `options` dict, which has + its contents also passed as `method` parameters pair by pair. Also, if + `jac` has been passed as a bool type, `jac` and `fun` are mangled so that + `fun` returns just the function values and `jac` is converted to a function + returning the Jacobian. The method shall return an `OptimizeResult` + object. + + The provided `method` callable must be able to accept (and possibly ignore) + arbitrary parameters; the set of parameters accepted by `minimize` may + expand in future versions and then these parameters will be passed to + the method. You can find an example in the scipy.optimize tutorial. + + References + ---------- + .. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function + Minimization. The Computer Journal 7: 308-13. + .. [2] Wright M H. 1996. Direct search methods: Once scorned, now + respectable, in Numerical Analysis 1995: Proceedings of the 1995 + Dundee Biennial Conference in Numerical Analysis (Eds. D F + Griffiths and G A Watson). Addison Wesley Longman, Harlow, UK. + 191-208. + .. [3] Powell, M J D. 1964. An efficient method for finding the minimum of + a function of several variables without calculating derivatives. The + Computer Journal 7: 155-162. + .. [4] Press W, S A Teukolsky, W T Vetterling and B P Flannery. + Numerical Recipes (any edition), Cambridge University Press. + .. [5] Nocedal, J, and S J Wright. 2006. Numerical Optimization. + Springer New York. + .. [6] Byrd, R H and P Lu and J. Nocedal. 1995. A Limited Memory + Algorithm for Bound Constrained Optimization. SIAM Journal on + Scientific and Statistical Computing 16 (5): 1190-1208. + .. [7] Zhu, C and R H Byrd and J Nocedal. 1997. L-BFGS-B: Algorithm + 778: L-BFGS-B, FORTRAN routines for large scale bound constrained + optimization. ACM Transactions on Mathematical Software 23 (4): + 550-560. + .. [8] Nash, S G. Newton-Type Minimization Via the Lanczos Method. + 1984. SIAM Journal of Numerical Analysis 21: 770-778. + .. [9] Powell, M J D. A direct search optimization method that models + the objective and constraint functions by linear interpolation. + 1994. Advances in Optimization and Numerical Analysis, eds. S. Gomez + and J-P Hennart, Kluwer Academic (Dordrecht), 51-67. + .. [10] Powell M J D. Direct search algorithms for optimization + calculations. 1998. Acta Numerica 7: 287-336. + .. [11] Powell M J D. A view of algorithms for optimization without + derivatives. 2007.Cambridge University Technical Report DAMTP + 2007/NA03 + .. [12] Kraft, D. A software package for sequential quadratic + programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace + Center -- Institute for Flight Mechanics, Koln, Germany. + .. [13] Conn, A. R., Gould, N. I., and Toint, P. L. + Trust region methods. 2000. Siam. pp. 169-200. + .. [14] F. Lenders, C. Kirches, A. Potschka: "trlib: A vector-free + implementation of the GLTR method for iterative solution of + the trust region problem", :arxiv:`1611.04718` + .. [15] N. Gould, S. Lucidi, M. Roma, P. Toint: "Solving the + Trust-Region Subproblem using the Lanczos Method", + SIAM J. Optim., 9(2), 504--525, (1999). + .. [16] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. 1999. + An interior point algorithm for large-scale nonlinear programming. + SIAM Journal on Optimization 9.4: 877-900. + .. [17] Lalee, Marucha, Jorge Nocedal, and Todd Plantega. 1998. On the + implementation of an algorithm for large-scale equality constrained + optimization. SIAM Journal on Optimization 8.3: 682-706. + .. [18] Ragonneau, T. M. *Model-Based Derivative-Free Optimization Methods + and Software*. PhD thesis, Department of Applied Mathematics, The Hong + Kong Polytechnic University, Hong Kong, China, 2022. URL: + https://theses.lib.polyu.edu.hk/handle/200/12294. + + Examples + -------- + Let us consider the problem of minimizing the Rosenbrock function. This + function (and its respective derivatives) is implemented in `rosen` + (resp. `rosen_der`, `rosen_hess`) in the `scipy.optimize`. + + >>> from scipy.optimize import minimize, rosen, rosen_der + + A simple application of the *Nelder-Mead* method is: + + >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2] + >>> res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6) + >>> res.x + array([ 1., 1., 1., 1., 1.]) + + Now using the *BFGS* algorithm, using the first derivative and a few + options: + + >>> res = minimize(rosen, x0, method='BFGS', jac=rosen_der, + ... options={'gtol': 1e-6, 'disp': True}) + Optimization terminated successfully. + Current function value: 0.000000 + Iterations: 26 + Function evaluations: 31 + Gradient evaluations: 31 + >>> res.x + array([ 1., 1., 1., 1., 1.]) + >>> print(res.message) + Optimization terminated successfully. + >>> res.hess_inv + array([ + [ 0.00749589, 0.01255155, 0.02396251, 0.04750988, 0.09495377], # may vary + [ 0.01255155, 0.02510441, 0.04794055, 0.09502834, 0.18996269], + [ 0.02396251, 0.04794055, 0.09631614, 0.19092151, 0.38165151], + [ 0.04750988, 0.09502834, 0.19092151, 0.38341252, 0.7664427 ], + [ 0.09495377, 0.18996269, 0.38165151, 0.7664427, 1.53713523] + ]) + + + Next, consider a minimization problem with several constraints (namely + Example 16.4 from [5]_). The objective function is: + + >>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2 + + There are three constraints defined as: + + >>> cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2}, + ... {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6}, + ... {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2}) + + And variables must be positive, hence the following bounds: + + >>> bnds = ((0, None), (0, None)) + + The optimization problem is solved using the SLSQP method as: + + >>> res = minimize(fun, (2, 0), method='SLSQP', bounds=bnds, + ... constraints=cons) + + It should converge to the theoretical solution (1.4 ,1.7). + + """ + x0 = np.atleast_1d(np.asarray(x0)) + + if x0.ndim != 1: + raise ValueError("'x0' must only have one dimension.") + + if x0.dtype.kind in np.typecodes["AllInteger"]: + x0 = np.asarray(x0, dtype=float) + + if not isinstance(args, tuple): + args = (args,) + + if method is None: + # Select automatically + if constraints: + method = 'SLSQP' + elif bounds is not None: + method = 'L-BFGS-B' + else: + method = 'BFGS' + + if callable(method): + meth = "_custom" + else: + meth = method.lower() + + if options is None: + options = {} + # check if optional parameters are supported by the selected method + # - jac + if meth in ('nelder-mead', 'powell', 'cobyla', 'cobyqa') and bool(jac): + warn('Method %s does not use gradient information (jac).' % method, + RuntimeWarning, stacklevel=2) + # - hess + if meth not in ('newton-cg', 'dogleg', 'trust-ncg', 'trust-constr', + 'trust-krylov', 'trust-exact', '_custom') and hess is not None: + warn('Method %s does not use Hessian information (hess).' % method, + RuntimeWarning, stacklevel=2) + # - hessp + if meth not in ('newton-cg', 'trust-ncg', 'trust-constr', + 'trust-krylov', '_custom') \ + and hessp is not None: + warn('Method %s does not use Hessian-vector product ' + 'information (hessp).' % method, + RuntimeWarning, stacklevel=2) + # - constraints or bounds + if (meth not in ('cobyla', 'cobyqa', 'slsqp', 'trust-constr', '_custom') and + np.any(constraints)): + warn('Method %s cannot handle constraints.' % method, + RuntimeWarning, stacklevel=2) + if meth not in ( + 'nelder-mead', 'powell', 'l-bfgs-b', 'cobyla', 'cobyqa', 'slsqp', + 'tnc', 'trust-constr', '_custom') and bounds is not None: + warn('Method %s cannot handle bounds.' % method, + RuntimeWarning, stacklevel=2) + # - return_all + if (meth in ('l-bfgs-b', 'tnc', 'cobyla', 'cobyqa', 'slsqp') and + options.get('return_all', False)): + warn('Method %s does not support the return_all option.' % method, + RuntimeWarning, stacklevel=2) + + # check gradient vector + if callable(jac): + pass + elif jac is True: + # fun returns func and grad + fun = MemoizeJac(fun) + jac = fun.derivative + elif (jac in FD_METHODS and + meth in ['trust-constr', 'bfgs', 'cg', 'l-bfgs-b', 'tnc', 'slsqp']): + # finite differences with relative step + pass + elif meth in ['trust-constr']: + # default jac calculation for this method + jac = '2-point' + elif jac is None or bool(jac) is False: + # this will cause e.g. LBFGS to use forward difference, absolute step + jac = None + else: + # default if jac option is not understood + jac = None + + # set default tolerances + if tol is not None: + options = dict(options) + if meth == 'nelder-mead': + options.setdefault('xatol', tol) + options.setdefault('fatol', tol) + if meth in ('newton-cg', 'powell', 'tnc'): + options.setdefault('xtol', tol) + if meth in ('powell', 'l-bfgs-b', 'tnc', 'slsqp'): + options.setdefault('ftol', tol) + if meth in ('bfgs', 'cg', 'l-bfgs-b', 'tnc', 'dogleg', + 'trust-ncg', 'trust-exact', 'trust-krylov'): + options.setdefault('gtol', tol) + if meth in ('cobyla', '_custom'): + options.setdefault('tol', tol) + if meth == 'cobyqa': + options.setdefault('final_tr_radius', tol) + if meth == 'trust-constr': + options.setdefault('xtol', tol) + options.setdefault('gtol', tol) + options.setdefault('barrier_tol', tol) + + if meth == '_custom': + # custom method called before bounds and constraints are 'standardised' + # custom method should be able to accept whatever bounds/constraints + # are provided to it. + return method(fun, x0, args=args, jac=jac, hess=hess, hessp=hessp, + bounds=bounds, constraints=constraints, + callback=callback, **options) + + constraints = standardize_constraints(constraints, x0, meth) + + remove_vars = False + if bounds is not None: + # convert to new-style bounds so we only have to consider one case + bounds = standardize_bounds(bounds, x0, 'new') + bounds = _validate_bounds(bounds, x0, meth) + + if meth in {"tnc", "slsqp", "l-bfgs-b"}: + # These methods can't take the finite-difference derivatives they + # need when a variable is fixed by the bounds. To avoid this issue, + # remove fixed variables from the problem. + # NOTE: if this list is expanded, then be sure to update the + # accompanying tests and test_optimize.eb_data. Consider also if + # default OptimizeResult will need updating. + + # determine whether any variables are fixed + i_fixed = (bounds.lb == bounds.ub) + + if np.all(i_fixed): + # all the parameters are fixed, a minimizer is not able to do + # anything + return _optimize_result_for_equal_bounds( + fun, bounds, meth, args=args, constraints=constraints + ) + + # determine whether finite differences are needed for any grad/jac + fd_needed = (not callable(jac)) + for con in constraints: + if not callable(con.get('jac', None)): + fd_needed = True + + # If finite differences are ever used, remove all fixed variables + # Always remove fixed variables for TNC; see gh-14565 + remove_vars = i_fixed.any() and (fd_needed or meth == "tnc") + if remove_vars: + x_fixed = (bounds.lb)[i_fixed] + x0 = x0[~i_fixed] + bounds = _remove_from_bounds(bounds, i_fixed) + fun = _remove_from_func(fun, i_fixed, x_fixed) + if callable(callback): + callback = _remove_from_func(callback, i_fixed, x_fixed) + if callable(jac): + jac = _remove_from_func(jac, i_fixed, x_fixed, remove=1) + + # make a copy of the constraints so the user's version doesn't + # get changed. (Shallow copy is ok) + constraints = [con.copy() for con in constraints] + for con in constraints: # yes, guaranteed to be a list + con['fun'] = _remove_from_func(con['fun'], i_fixed, + x_fixed, min_dim=1, + remove=0) + if callable(con.get('jac', None)): + con['jac'] = _remove_from_func(con['jac'], i_fixed, + x_fixed, min_dim=2, + remove=1) + bounds = standardize_bounds(bounds, x0, meth) + + callback = _wrap_callback(callback, meth) + + if meth == 'nelder-mead': + res = _minimize_neldermead(fun, x0, args, callback, bounds=bounds, + **options) + elif meth == 'powell': + res = _minimize_powell(fun, x0, args, callback, bounds, **options) + elif meth == 'cg': + res = _minimize_cg(fun, x0, args, jac, callback, **options) + elif meth == 'bfgs': + res = _minimize_bfgs(fun, x0, args, jac, callback, **options) + elif meth == 'newton-cg': + res = _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback, + **options) + elif meth == 'l-bfgs-b': + res = _minimize_lbfgsb(fun, x0, args, jac, bounds, + callback=callback, **options) + elif meth == 'tnc': + res = _minimize_tnc(fun, x0, args, jac, bounds, callback=callback, + **options) + elif meth == 'cobyla': + res = _minimize_cobyla(fun, x0, args, constraints, callback=callback, + bounds=bounds, **options) + elif meth == 'cobyqa': + res = _minimize_cobyqa(fun, x0, args, bounds, constraints, callback, + **options) + elif meth == 'slsqp': + res = _minimize_slsqp(fun, x0, args, jac, bounds, + constraints, callback=callback, **options) + elif meth == 'trust-constr': + res = _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp, + bounds, constraints, + callback=callback, **options) + elif meth == 'dogleg': + res = _minimize_dogleg(fun, x0, args, jac, hess, + callback=callback, **options) + elif meth == 'trust-ncg': + res = _minimize_trust_ncg(fun, x0, args, jac, hess, hessp, + callback=callback, **options) + elif meth == 'trust-krylov': + res = _minimize_trust_krylov(fun, x0, args, jac, hess, hessp, + callback=callback, **options) + elif meth == 'trust-exact': + res = _minimize_trustregion_exact(fun, x0, args, jac, hess, + callback=callback, **options) + else: + raise ValueError('Unknown solver %s' % method) + + if remove_vars: + res.x = _add_to_array(res.x, i_fixed, x_fixed) + res.jac = _add_to_array(res.jac, i_fixed, np.nan) + if "hess_inv" in res: + res.hess_inv = None # unknown + + if getattr(callback, 'stop_iteration', False): + res.success = False + res.status = 99 + res.message = "`callback` raised `StopIteration`." + + return res + + +def minimize_scalar(fun, bracket=None, bounds=None, args=(), + method=None, tol=None, options=None): + """Local minimization of scalar function of one variable. + + Parameters + ---------- + fun : callable + Objective function. + Scalar function, must return a scalar. + bracket : sequence, optional + For methods 'brent' and 'golden', `bracket` defines the bracketing + interval and is required. + Either a triple ``(xa, xb, xc)`` satisfying ``xa < xb < xc`` and + ``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair + ``(xa, xb)`` to be used as initial points for a downhill bracket search + (see `scipy.optimize.bracket`). + The minimizer ``res.x`` will not necessarily satisfy + ``xa <= res.x <= xb``. + bounds : sequence, optional + For method 'bounded', `bounds` is mandatory and must have two finite + items corresponding to the optimization bounds. + args : tuple, optional + Extra arguments passed to the objective function. + method : str or callable, optional + Type of solver. Should be one of: + + - :ref:`Brent ` + - :ref:`Bounded ` + - :ref:`Golden ` + - custom - a callable object (added in version 0.14.0), see below + + Default is "Bounded" if bounds are provided and "Brent" otherwise. + See the 'Notes' section for details of each solver. + + tol : float, optional + Tolerance for termination. For detailed control, use solver-specific + options. + options : dict, optional + A dictionary of solver options. + + maxiter : int + Maximum number of iterations to perform. + disp : bool + Set to True to print convergence messages. + + See :func:`show_options()` for solver-specific options. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. + + See also + -------- + minimize : Interface to minimization algorithms for scalar multivariate + functions + show_options : Additional options accepted by the solvers + + Notes + ----- + This section describes the available solvers that can be selected by the + 'method' parameter. The default method is the ``"Bounded"`` Brent method if + `bounds` are passed and unbounded ``"Brent"`` otherwise. + + Method :ref:`Brent ` uses Brent's + algorithm [1]_ to find a local minimum. The algorithm uses inverse + parabolic interpolation when possible to speed up convergence of + the golden section method. + + Method :ref:`Golden ` uses the + golden section search technique [1]_. It uses analog of the bisection + method to decrease the bracketed interval. It is usually + preferable to use the *Brent* method. + + Method :ref:`Bounded ` can + perform bounded minimization [2]_ [3]_. It uses the Brent method to find a + local minimum in the interval x1 < xopt < x2. + + Note that the Brent and Golden methods do not guarantee success unless a + valid ``bracket`` triple is provided. If a three-point bracket cannot be + found, consider `scipy.optimize.minimize`. Also, all methods are intended + only for local minimization. When the function of interest has more than + one local minimum, consider :ref:`global_optimization`. + + **Custom minimizers** + + It may be useful to pass a custom minimization method, for example + when using some library frontend to minimize_scalar. You can simply + pass a callable as the ``method`` parameter. + + The callable is called as ``method(fun, args, **kwargs, **options)`` + where ``kwargs`` corresponds to any other parameters passed to `minimize` + (such as `bracket`, `tol`, etc.), except the `options` dict, which has + its contents also passed as `method` parameters pair by pair. The method + shall return an `OptimizeResult` object. + + The provided `method` callable must be able to accept (and possibly ignore) + arbitrary parameters; the set of parameters accepted by `minimize` may + expand in future versions and then these parameters will be passed to + the method. You can find an example in the scipy.optimize tutorial. + + .. versionadded:: 0.11.0 + + References + ---------- + .. [1] Press, W., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. + Numerical Recipes in C. Cambridge University Press. + .. [2] Forsythe, G.E., M. A. Malcolm, and C. B. Moler. "Computer Methods + for Mathematical Computations." Prentice-Hall Series in Automatic + Computation 259 (1977). + .. [3] Brent, Richard P. Algorithms for Minimization Without Derivatives. + Courier Corporation, 2013. + + Examples + -------- + Consider the problem of minimizing the following function. + + >>> def f(x): + ... return (x - 2) * x * (x + 2)**2 + + Using the *Brent* method, we find the local minimum as: + + >>> from scipy.optimize import minimize_scalar + >>> res = minimize_scalar(f) + >>> res.fun + -9.9149495908 + + The minimizer is: + + >>> res.x + 1.28077640403 + + Using the *Bounded* method, we find a local minimum with specified + bounds as: + + >>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded') + >>> res.fun # minimum + 3.28365179850e-13 + >>> res.x # minimizer + -2.0000002026 + + """ + if not isinstance(args, tuple): + args = (args,) + + if callable(method): + meth = "_custom" + elif method is None: + meth = 'brent' if bounds is None else 'bounded' + else: + meth = method.lower() + if options is None: + options = {} + + if bounds is not None and meth in {'brent', 'golden'}: + message = f"Use of `bounds` is incompatible with 'method={method}'." + raise ValueError(message) + + if tol is not None: + options = dict(options) + if meth == 'bounded' and 'xatol' not in options: + warn("Method 'bounded' does not support relative tolerance in x; " + "defaulting to absolute tolerance.", + RuntimeWarning, stacklevel=2) + options['xatol'] = tol + elif meth == '_custom': + options.setdefault('tol', tol) + else: + options.setdefault('xtol', tol) + + # replace boolean "disp" option, if specified, by an integer value. + disp = options.get('disp') + if isinstance(disp, bool): + options['disp'] = 2 * int(disp) + + if meth == '_custom': + res = method(fun, args=args, bracket=bracket, bounds=bounds, **options) + elif meth == 'brent': + res = _recover_from_bracket_error(_minimize_scalar_brent, + fun, bracket, args, **options) + elif meth == 'bounded': + if bounds is None: + raise ValueError('The `bounds` parameter is mandatory for ' + 'method `bounded`.') + res = _minimize_scalar_bounded(fun, bounds, args, **options) + elif meth == 'golden': + res = _recover_from_bracket_error(_minimize_scalar_golden, + fun, bracket, args, **options) + else: + raise ValueError('Unknown solver %s' % method) + + # gh-16196 reported inconsistencies in the output shape of `res.x`. While + # fixing this, future-proof it for when the function is vectorized: + # the shape of `res.x` should match that of `res.fun`. + res.fun = np.asarray(res.fun)[()] + res.x = np.reshape(res.x, res.fun.shape)[()] + return res + + +def _remove_from_bounds(bounds, i_fixed): + """Removes fixed variables from a `Bounds` instance""" + lb = bounds.lb[~i_fixed] + ub = bounds.ub[~i_fixed] + return Bounds(lb, ub) # don't mutate original Bounds object + + +def _remove_from_func(fun_in, i_fixed, x_fixed, min_dim=None, remove=0): + """Wraps a function such that fixed variables need not be passed in""" + def fun_out(x_in, *args, **kwargs): + x_out = np.zeros_like(i_fixed, dtype=x_in.dtype) + x_out[i_fixed] = x_fixed + x_out[~i_fixed] = x_in + y_out = fun_in(x_out, *args, **kwargs) + y_out = np.array(y_out) + + if min_dim == 1: + y_out = np.atleast_1d(y_out) + elif min_dim == 2: + y_out = np.atleast_2d(y_out) + + if remove == 1: + y_out = y_out[..., ~i_fixed] + elif remove == 2: + y_out = y_out[~i_fixed, ~i_fixed] + + return y_out + return fun_out + + +def _add_to_array(x_in, i_fixed, x_fixed): + """Adds fixed variables back to an array""" + i_free = ~i_fixed + if x_in.ndim == 2: + i_free = i_free[:, None] @ i_free[None, :] + x_out = np.zeros_like(i_free, dtype=x_in.dtype) + x_out[~i_free] = x_fixed + x_out[i_free] = x_in.ravel() + return x_out + + +def _validate_bounds(bounds, x0, meth): + """Check that bounds are valid.""" + + msg = "An upper bound is less than the corresponding lower bound." + if np.any(bounds.ub < bounds.lb): + raise ValueError(msg) + + msg = "The number of bounds is not compatible with the length of `x0`." + try: + bounds.lb = np.broadcast_to(bounds.lb, x0.shape) + bounds.ub = np.broadcast_to(bounds.ub, x0.shape) + except Exception as e: + raise ValueError(msg) from e + + return bounds + +def standardize_bounds(bounds, x0, meth): + """Converts bounds to the form required by the solver.""" + if meth in {'trust-constr', 'powell', 'nelder-mead', 'cobyla', 'cobyqa', + 'new'}: + if not isinstance(bounds, Bounds): + lb, ub = old_bound_to_new(bounds) + bounds = Bounds(lb, ub) + elif meth in ('l-bfgs-b', 'tnc', 'slsqp', 'old'): + if isinstance(bounds, Bounds): + bounds = new_bounds_to_old(bounds.lb, bounds.ub, x0.shape[0]) + return bounds + + +def standardize_constraints(constraints, x0, meth): + """Converts constraints to the form required by the solver.""" + all_constraint_types = (NonlinearConstraint, LinearConstraint, dict) + new_constraint_types = all_constraint_types[:-1] + if constraints is None: + constraints = [] + elif isinstance(constraints, all_constraint_types): + constraints = [constraints] + else: + constraints = list(constraints) # ensure it's a mutable sequence + + if meth in ['trust-constr', 'cobyqa', 'new']: + for i, con in enumerate(constraints): + if not isinstance(con, new_constraint_types): + constraints[i] = old_constraint_to_new(i, con) + else: + # iterate over copy, changing original + for i, con in enumerate(list(constraints)): + if isinstance(con, new_constraint_types): + old_constraints = new_constraint_to_old(con, x0) + constraints[i] = old_constraints[0] + constraints.extend(old_constraints[1:]) # appends 1 if present + + return constraints + + +def _optimize_result_for_equal_bounds( + fun, bounds, method, args=(), constraints=() +): + """ + Provides a default OptimizeResult for when a bounded minimization method + has (lb == ub).all(). + + Parameters + ---------- + fun: callable + bounds: Bounds + method: str + constraints: Constraint + """ + success = True + message = 'All independent variables were fixed by bounds.' + + # bounds is new-style + x0 = bounds.lb + + if constraints: + message = ("All independent variables were fixed by bounds at values" + " that satisfy the constraints.") + constraints = standardize_constraints(constraints, x0, 'new') + + maxcv = 0 + for c in constraints: + pc = PreparedConstraint(c, x0) + violation = pc.violation(x0) + if np.sum(violation): + maxcv = max(maxcv, np.max(violation)) + success = False + message = (f"All independent variables were fixed by bounds, but " + f"the independent variables do not satisfy the " + f"constraints exactly. (Maximum violation: {maxcv}).") + + return OptimizeResult( + x=x0, fun=fun(x0, *args), success=success, message=message, nfev=1, + njev=0, nhev=0, + ) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..f747929147c24b2502a9738995f0a74f8753db99 Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack2.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack2.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..f816e37ac89a947c5086a2a48830b8e73956382b Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack2.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack_py.py new file mode 100644 index 0000000000000000000000000000000000000000..b67a17ae41b4db6633918aa0b318fae88d56d5f7 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_minpack_py.py @@ -0,0 +1,1164 @@ +import warnings +from . import _minpack + +import numpy as np +from numpy import (atleast_1d, triu, shape, transpose, zeros, prod, greater, + asarray, inf, + finfo, inexact, issubdtype, dtype) +from scipy import linalg +from scipy.linalg import svd, cholesky, solve_triangular, LinAlgError +from scipy._lib._util import _asarray_validated, _lazywhere, _contains_nan +from scipy._lib._util import getfullargspec_no_self as _getfullargspec +from ._optimize import OptimizeResult, _check_unknown_options, OptimizeWarning +from ._lsq import least_squares +# from ._lsq.common import make_strictly_feasible +from ._lsq.least_squares import prepare_bounds +from scipy.optimize._minimize import Bounds + +__all__ = ['fsolve', 'leastsq', 'fixed_point', 'curve_fit'] + + +def _check_func(checker, argname, thefunc, x0, args, numinputs, + output_shape=None): + res = atleast_1d(thefunc(*((x0[:numinputs],) + args))) + if (output_shape is not None) and (shape(res) != output_shape): + if (output_shape[0] != 1): + if len(output_shape) > 1: + if output_shape[1] == 1: + return shape(res) + msg = f"{checker}: there is a mismatch between the input and output " \ + f"shape of the '{argname}' argument" + func_name = getattr(thefunc, '__name__', None) + if func_name: + msg += " '%s'." % func_name + else: + msg += "." + msg += f'Shape should be {output_shape} but it is {shape(res)}.' + raise TypeError(msg) + if issubdtype(res.dtype, inexact): + dt = res.dtype + else: + dt = dtype(float) + return shape(res), dt + + +def fsolve(func, x0, args=(), fprime=None, full_output=0, + col_deriv=0, xtol=1.49012e-8, maxfev=0, band=None, + epsfcn=None, factor=100, diag=None): + """ + Find the roots of a function. + + Return the roots of the (non-linear) equations defined by + ``func(x) = 0`` given a starting estimate. + + Parameters + ---------- + func : callable ``f(x, *args)`` + A function that takes at least one (possibly vector) argument, + and returns a value of the same length. + x0 : ndarray + The starting estimate for the roots of ``func(x) = 0``. + args : tuple, optional + Any extra arguments to `func`. + fprime : callable ``f(x, *args)``, optional + A function to compute the Jacobian of `func` with derivatives + across the rows. By default, the Jacobian will be estimated. + full_output : bool, optional + If True, return optional outputs. + col_deriv : bool, optional + Specify whether the Jacobian function computes derivatives down + the columns (faster, because there is no transpose operation). + xtol : float, optional + The calculation will terminate if the relative error between two + consecutive iterates is at most `xtol`. + maxfev : int, optional + The maximum number of calls to the function. If zero, then + ``100*(N+1)`` is the maximum where N is the number of elements + in `x0`. + band : tuple, optional + If set to a two-sequence containing the number of sub- and + super-diagonals within the band of the Jacobi matrix, the + Jacobi matrix is considered banded (only for ``fprime=None``). + epsfcn : float, optional + A suitable step length for the forward-difference + approximation of the Jacobian (for ``fprime=None``). If + `epsfcn` is less than the machine precision, it is assumed + that the relative errors in the functions are of the order of + the machine precision. + factor : float, optional + A parameter determining the initial step bound + (``factor * || diag * x||``). Should be in the interval + ``(0.1, 100)``. + diag : sequence, optional + N positive entries that serve as a scale factors for the + variables. + + Returns + ------- + x : ndarray + The solution (or the result of the last iteration for + an unsuccessful call). + infodict : dict + A dictionary of optional outputs with the keys: + + ``nfev`` + number of function calls + ``njev`` + number of Jacobian calls + ``fvec`` + function evaluated at the output + ``fjac`` + the orthogonal matrix, q, produced by the QR + factorization of the final approximate Jacobian + matrix, stored column wise + ``r`` + upper triangular matrix produced by QR factorization + of the same matrix + ``qtf`` + the vector ``(transpose(q) * fvec)`` + + ier : int + An integer flag. Set to 1 if a solution was found, otherwise refer + to `mesg` for more information. + mesg : str + If no solution is found, `mesg` details the cause of failure. + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See the ``method='hybr'`` in particular. + + Notes + ----- + ``fsolve`` is a wrapper around MINPACK's hybrd and hybrj algorithms. + + Examples + -------- + Find a solution to the system of equations: + ``x0*cos(x1) = 4, x1*x0 - x1 = 5``. + + >>> import numpy as np + >>> from scipy.optimize import fsolve + >>> def func(x): + ... return [x[0] * np.cos(x[1]) - 4, + ... x[1] * x[0] - x[1] - 5] + >>> root = fsolve(func, [1, 1]) + >>> root + array([6.50409711, 0.90841421]) + >>> np.isclose(func(root), [0.0, 0.0]) # func(root) should be almost 0.0. + array([ True, True]) + + """ + def _wrapped_func(*fargs): + """ + Wrapped `func` to track the number of times + the function has been called. + """ + _wrapped_func.nfev += 1 + return func(*fargs) + + _wrapped_func.nfev = 0 + + options = {'col_deriv': col_deriv, + 'xtol': xtol, + 'maxfev': maxfev, + 'band': band, + 'eps': epsfcn, + 'factor': factor, + 'diag': diag} + + res = _root_hybr(_wrapped_func, x0, args, jac=fprime, **options) + res.nfev = _wrapped_func.nfev + + if full_output: + x = res['x'] + info = {k: res.get(k) + for k in ('nfev', 'njev', 'fjac', 'r', 'qtf') if k in res} + info['fvec'] = res['fun'] + return x, info, res['status'], res['message'] + else: + status = res['status'] + msg = res['message'] + if status == 0: + raise TypeError(msg) + elif status == 1: + pass + elif status in [2, 3, 4, 5]: + warnings.warn(msg, RuntimeWarning, stacklevel=2) + else: + raise TypeError(msg) + return res['x'] + + +def _root_hybr(func, x0, args=(), jac=None, + col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, eps=None, + factor=100, diag=None, **unknown_options): + """ + Find the roots of a multivariate function using MINPACK's hybrd and + hybrj routines (modified Powell method). + + Options + ------- + col_deriv : bool + Specify whether the Jacobian function computes derivatives down + the columns (faster, because there is no transpose operation). + xtol : float + The calculation will terminate if the relative error between two + consecutive iterates is at most `xtol`. + maxfev : int + The maximum number of calls to the function. If zero, then + ``100*(N+1)`` is the maximum where N is the number of elements + in `x0`. + band : tuple + If set to a two-sequence containing the number of sub- and + super-diagonals within the band of the Jacobi matrix, the + Jacobi matrix is considered banded (only for ``fprime=None``). + eps : float + A suitable step length for the forward-difference + approximation of the Jacobian (for ``fprime=None``). If + `eps` is less than the machine precision, it is assumed + that the relative errors in the functions are of the order of + the machine precision. + factor : float + A parameter determining the initial step bound + (``factor * || diag * x||``). Should be in the interval + ``(0.1, 100)``. + diag : sequence + N positive entries that serve as a scale factors for the + variables. + + """ + _check_unknown_options(unknown_options) + epsfcn = eps + + x0 = asarray(x0).flatten() + n = len(x0) + if not isinstance(args, tuple): + args = (args,) + shape, dtype = _check_func('fsolve', 'func', func, x0, args, n, (n,)) + if epsfcn is None: + epsfcn = finfo(dtype).eps + Dfun = jac + if Dfun is None: + if band is None: + ml, mu = -10, -10 + else: + ml, mu = band[:2] + if maxfev == 0: + maxfev = 200 * (n + 1) + retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev, + ml, mu, epsfcn, factor, diag) + else: + _check_func('fsolve', 'fprime', Dfun, x0, args, n, (n, n)) + if (maxfev == 0): + maxfev = 100 * (n + 1) + retval = _minpack._hybrj(func, Dfun, x0, args, 1, + col_deriv, xtol, maxfev, factor, diag) + + x, status = retval[0], retval[-1] + + errors = {0: "Improper input parameters were entered.", + 1: "The solution converged.", + 2: "The number of calls to function has " + "reached maxfev = %d." % maxfev, + 3: "xtol=%f is too small, no further improvement " + "in the approximate\n solution " + "is possible." % xtol, + 4: "The iteration is not making good progress, as measured " + "by the \n improvement from the last five " + "Jacobian evaluations.", + 5: "The iteration is not making good progress, " + "as measured by the \n improvement from the last " + "ten iterations.", + 'unknown': "An error occurred."} + + info = retval[1] + info['fun'] = info.pop('fvec') + sol = OptimizeResult(x=x, success=(status == 1), status=status, + method="hybr") + sol.update(info) + try: + sol['message'] = errors[status] + except KeyError: + sol['message'] = errors['unknown'] + + return sol + + +LEASTSQ_SUCCESS = [1, 2, 3, 4] +LEASTSQ_FAILURE = [5, 6, 7, 8] + + +def leastsq(func, x0, args=(), Dfun=None, full_output=False, + col_deriv=False, ftol=1.49012e-8, xtol=1.49012e-8, + gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None): + """ + Minimize the sum of squares of a set of equations. + + :: + + x = arg min(sum(func(y)**2,axis=0)) + y + + Parameters + ---------- + func : callable + Should take at least one (possibly length ``N`` vector) argument and + returns ``M`` floating point numbers. It must not return NaNs or + fitting might fail. ``M`` must be greater than or equal to ``N``. + x0 : ndarray + The starting estimate for the minimization. + args : tuple, optional + Any extra arguments to func are placed in this tuple. + Dfun : callable, optional + A function or method to compute the Jacobian of func with derivatives + across the rows. If this is None, the Jacobian will be estimated. + full_output : bool, optional + If ``True``, return all optional outputs (not just `x` and `ier`). + col_deriv : bool, optional + If ``True``, specify that the Jacobian function computes derivatives + down the columns (faster, because there is no transpose operation). + ftol : float, optional + Relative error desired in the sum of squares. + xtol : float, optional + Relative error desired in the approximate solution. + gtol : float, optional + Orthogonality desired between the function vector and the columns of + the Jacobian. + maxfev : int, optional + The maximum number of calls to the function. If `Dfun` is provided, + then the default `maxfev` is 100*(N+1) where N is the number of elements + in x0, otherwise the default `maxfev` is 200*(N+1). + epsfcn : float, optional + A variable used in determining a suitable step length for the forward- + difference approximation of the Jacobian (for Dfun=None). + Normally the actual step length will be sqrt(epsfcn)*x + If epsfcn is less than the machine precision, it is assumed that the + relative errors are of the order of the machine precision. + factor : float, optional + A parameter determining the initial step bound + (``factor * || diag * x||``). Should be in interval ``(0.1, 100)``. + diag : sequence, optional + N positive entries that serve as a scale factors for the variables. + + Returns + ------- + x : ndarray + The solution (or the result of the last iteration for an unsuccessful + call). + cov_x : ndarray + The inverse of the Hessian. `fjac` and `ipvt` are used to construct an + estimate of the Hessian. A value of None indicates a singular matrix, + which means the curvature in parameters `x` is numerically flat. To + obtain the covariance matrix of the parameters `x`, `cov_x` must be + multiplied by the variance of the residuals -- see curve_fit. Only + returned if `full_output` is ``True``. + infodict : dict + a dictionary of optional outputs with the keys: + + ``nfev`` + The number of function calls + ``fvec`` + The function evaluated at the output + ``fjac`` + A permutation of the R matrix of a QR + factorization of the final approximate + Jacobian matrix, stored column wise. + Together with ipvt, the covariance of the + estimate can be approximated. + ``ipvt`` + An integer array of length N which defines + a permutation matrix, p, such that + fjac*p = q*r, where r is upper triangular + with diagonal elements of nonincreasing + magnitude. Column j of p is column ipvt(j) + of the identity matrix. + ``qtf`` + The vector (transpose(q) * fvec). + + Only returned if `full_output` is ``True``. + mesg : str + A string message giving information about the cause of failure. + Only returned if `full_output` is ``True``. + ier : int + An integer flag. If it is equal to 1, 2, 3 or 4, the solution was + found. Otherwise, the solution was not found. In either case, the + optional output variable 'mesg' gives more information. + + See Also + -------- + least_squares : Newer interface to solve nonlinear least-squares problems + with bounds on the variables. See ``method='lm'`` in particular. + + Notes + ----- + "leastsq" is a wrapper around MINPACK's lmdif and lmder algorithms. + + cov_x is a Jacobian approximation to the Hessian of the least squares + objective function. + This approximation assumes that the objective function is based on the + difference between some observed target data (ydata) and a (non-linear) + function of the parameters `f(xdata, params)` :: + + func(params) = ydata - f(xdata, params) + + so that the objective function is :: + + min sum((ydata - f(xdata, params))**2, axis=0) + params + + The solution, `x`, is always a 1-D array, regardless of the shape of `x0`, + or whether `x0` is a scalar. + + Examples + -------- + >>> from scipy.optimize import leastsq + >>> def func(x): + ... return 2*(x-3)**2+1 + >>> leastsq(func, 0) + (array([2.99999999]), 1) + + """ + x0 = asarray(x0).flatten() + n = len(x0) + if not isinstance(args, tuple): + args = (args,) + shape, dtype = _check_func('leastsq', 'func', func, x0, args, n) + m = shape[0] + + if n > m: + raise TypeError(f"Improper input: func input vector length N={n} must" + f" not exceed func output vector length M={m}") + + if epsfcn is None: + epsfcn = finfo(dtype).eps + + if Dfun is None: + if maxfev == 0: + maxfev = 200*(n + 1) + retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol, + gtol, maxfev, epsfcn, factor, diag) + else: + if col_deriv: + _check_func('leastsq', 'Dfun', Dfun, x0, args, n, (n, m)) + else: + _check_func('leastsq', 'Dfun', Dfun, x0, args, n, (m, n)) + if maxfev == 0: + maxfev = 100 * (n + 1) + retval = _minpack._lmder(func, Dfun, x0, args, full_output, + col_deriv, ftol, xtol, gtol, maxfev, + factor, diag) + + errors = {0: ["Improper input parameters.", TypeError], + 1: ["Both actual and predicted relative reductions " + "in the sum of squares\n are at most %f" % ftol, None], + 2: ["The relative error between two consecutive " + "iterates is at most %f" % xtol, None], + 3: ["Both actual and predicted relative reductions in " + f"the sum of squares\n are at most {ftol:f} and the " + "relative error between two consecutive " + f"iterates is at \n most {xtol:f}", None], + 4: ["The cosine of the angle between func(x) and any " + "column of the\n Jacobian is at most %f in " + "absolute value" % gtol, None], + 5: ["Number of calls to function has reached " + "maxfev = %d." % maxfev, ValueError], + 6: ["ftol=%f is too small, no further reduction " + "in the sum of squares\n is possible." % ftol, + ValueError], + 7: ["xtol=%f is too small, no further improvement in " + "the approximate\n solution is possible." % xtol, + ValueError], + 8: ["gtol=%f is too small, func(x) is orthogonal to the " + "columns of\n the Jacobian to machine " + "precision." % gtol, ValueError]} + + # The FORTRAN return value (possible return values are >= 0 and <= 8) + info = retval[-1] + + if full_output: + cov_x = None + if info in LEASTSQ_SUCCESS: + # This was + # perm = take(eye(n), retval[1]['ipvt'] - 1, 0) + # r = triu(transpose(retval[1]['fjac'])[:n, :]) + # R = dot(r, perm) + # cov_x = inv(dot(transpose(R), R)) + # but the explicit dot product was not necessary and sometimes + # the result was not symmetric positive definite. See gh-4555. + perm = retval[1]['ipvt'] - 1 + n = len(perm) + r = triu(transpose(retval[1]['fjac'])[:n, :]) + inv_triu = linalg.get_lapack_funcs('trtri', (r,)) + try: + # inverse of permuted matrix is a permutation of matrix inverse + invR, trtri_info = inv_triu(r) # default: upper, non-unit diag + if trtri_info != 0: # explicit comparison for readability + raise LinAlgError(f'trtri returned info {trtri_info}') + invR[perm] = invR.copy() + cov_x = invR @ invR.T + except (LinAlgError, ValueError): + pass + return (retval[0], cov_x) + retval[1:-1] + (errors[info][0], info) + else: + if info in LEASTSQ_FAILURE: + warnings.warn(errors[info][0], RuntimeWarning, stacklevel=2) + elif info == 0: + raise errors[info][1](errors[info][0]) + return retval[0], info + + +def _lightweight_memoizer(f): + # very shallow memoization to address gh-13670: only remember the first set + # of parameters and corresponding function value, and only attempt to use + # them twice (the number of times the function is evaluated at x0). + def _memoized_func(params): + if _memoized_func.skip_lookup: + return f(params) + + if np.all(_memoized_func.last_params == params): + return _memoized_func.last_val + elif _memoized_func.last_params is not None: + _memoized_func.skip_lookup = True + + val = f(params) + + if _memoized_func.last_params is None: + _memoized_func.last_params = np.copy(params) + _memoized_func.last_val = val + + return val + + _memoized_func.last_params = None + _memoized_func.last_val = None + _memoized_func.skip_lookup = False + return _memoized_func + + +def _wrap_func(func, xdata, ydata, transform): + if transform is None: + def func_wrapped(params): + return func(xdata, *params) - ydata + elif transform.size == 1 or transform.ndim == 1: + def func_wrapped(params): + return transform * (func(xdata, *params) - ydata) + else: + # Chisq = (y - yd)^T C^{-1} (y-yd) + # transform = L such that C = L L^T + # C^{-1} = L^{-T} L^{-1} + # Chisq = (y - yd)^T L^{-T} L^{-1} (y-yd) + # Define (y-yd)' = L^{-1} (y-yd) + # by solving + # L (y-yd)' = (y-yd) + # and minimize (y-yd)'^T (y-yd)' + def func_wrapped(params): + return solve_triangular(transform, func(xdata, *params) - ydata, lower=True) + return func_wrapped + + +def _wrap_jac(jac, xdata, transform): + if transform is None: + def jac_wrapped(params): + return jac(xdata, *params) + elif transform.ndim == 1: + def jac_wrapped(params): + return transform[:, np.newaxis] * np.asarray(jac(xdata, *params)) + else: + def jac_wrapped(params): + return solve_triangular(transform, + np.asarray(jac(xdata, *params)), + lower=True) + return jac_wrapped + + +def _initialize_feasible(lb, ub): + p0 = np.ones_like(lb) + lb_finite = np.isfinite(lb) + ub_finite = np.isfinite(ub) + + mask = lb_finite & ub_finite + p0[mask] = 0.5 * (lb[mask] + ub[mask]) + + mask = lb_finite & ~ub_finite + p0[mask] = lb[mask] + 1 + + mask = ~lb_finite & ub_finite + p0[mask] = ub[mask] - 1 + + return p0 + + +def curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, + check_finite=None, bounds=(-np.inf, np.inf), method=None, + jac=None, *, full_output=False, nan_policy=None, + **kwargs): + """ + Use non-linear least squares to fit a function, f, to data. + + Assumes ``ydata = f(xdata, *params) + eps``. + + Parameters + ---------- + f : callable + The model function, f(x, ...). It must take the independent + variable as the first argument and the parameters to fit as + separate remaining arguments. + xdata : array_like + The independent variable where the data is measured. + Should usually be an M-length sequence or an (k,M)-shaped array for + functions with k predictors, and each element should be float + convertible if it is an array like object. + ydata : array_like + The dependent data, a length M array - nominally ``f(xdata, ...)``. + p0 : array_like, optional + Initial guess for the parameters (length N). If None, then the + initial values will all be 1 (if the number of parameters for the + function can be determined using introspection, otherwise a + ValueError is raised). + sigma : None or scalar or M-length sequence or MxM array, optional + Determines the uncertainty in `ydata`. If we define residuals as + ``r = ydata - f(xdata, *popt)``, then the interpretation of `sigma` + depends on its number of dimensions: + + - A scalar or 1-D `sigma` should contain values of standard deviations of + errors in `ydata`. In this case, the optimized function is + ``chisq = sum((r / sigma) ** 2)``. + + - A 2-D `sigma` should contain the covariance matrix of + errors in `ydata`. In this case, the optimized function is + ``chisq = r.T @ inv(sigma) @ r``. + + .. versionadded:: 0.19 + + None (default) is equivalent of 1-D `sigma` filled with ones. + absolute_sigma : bool, optional + If True, `sigma` is used in an absolute sense and the estimated parameter + covariance `pcov` reflects these absolute values. + + If False (default), only the relative magnitudes of the `sigma` values matter. + The returned parameter covariance matrix `pcov` is based on scaling + `sigma` by a constant factor. This constant is set by demanding that the + reduced `chisq` for the optimal parameters `popt` when using the + *scaled* `sigma` equals unity. In other words, `sigma` is scaled to + match the sample variance of the residuals after the fit. Default is False. + Mathematically, + ``pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)`` + check_finite : bool, optional + If True, check that the input arrays do not contain nans of infs, + and raise a ValueError if they do. Setting this parameter to + False may silently produce nonsensical results if the input arrays + do contain nans. Default is True if `nan_policy` is not specified + explicitly and False otherwise. + bounds : 2-tuple of array_like or `Bounds`, optional + Lower and upper bounds on parameters. Defaults to no bounds. + There are two ways to specify the bounds: + + - Instance of `Bounds` class. + + - 2-tuple of array_like: Each element of the tuple must be either + an array with the length equal to the number of parameters, or a + scalar (in which case the bound is taken to be the same for all + parameters). Use ``np.inf`` with an appropriate sign to disable + bounds on all or some parameters. + + method : {'lm', 'trf', 'dogbox'}, optional + Method to use for optimization. See `least_squares` for more details. + Default is 'lm' for unconstrained problems and 'trf' if `bounds` are + provided. The method 'lm' won't work when the number of observations + is less than the number of variables, use 'trf' or 'dogbox' in this + case. + + .. versionadded:: 0.17 + jac : callable, string or None, optional + Function with signature ``jac(x, ...)`` which computes the Jacobian + matrix of the model function with respect to parameters as a dense + array_like structure. It will be scaled according to provided `sigma`. + If None (default), the Jacobian will be estimated numerically. + String keywords for 'trf' and 'dogbox' methods can be used to select + a finite difference scheme, see `least_squares`. + + .. versionadded:: 0.18 + full_output : boolean, optional + If True, this function returns additioal information: `infodict`, + `mesg`, and `ier`. + + .. versionadded:: 1.9 + nan_policy : {'raise', 'omit', None}, optional + Defines how to handle when input contains nan. + The following options are available (default is None): + + * 'raise': throws an error + * 'omit': performs the calculations ignoring nan values + * None: no special handling of NaNs is performed + (except what is done by check_finite); the behavior when NaNs + are present is implementation-dependent and may change. + + Note that if this value is specified explicitly (not None), + `check_finite` will be set as False. + + .. versionadded:: 1.11 + **kwargs + Keyword arguments passed to `leastsq` for ``method='lm'`` or + `least_squares` otherwise. + + Returns + ------- + popt : array + Optimal values for the parameters so that the sum of the squared + residuals of ``f(xdata, *popt) - ydata`` is minimized. + pcov : 2-D array + The estimated approximate covariance of popt. The diagonals provide + the variance of the parameter estimate. To compute one standard + deviation errors on the parameters, use + ``perr = np.sqrt(np.diag(pcov))``. Note that the relationship between + `cov` and parameter error estimates is derived based on a linear + approximation to the model function around the optimum [1]. + When this approximation becomes inaccurate, `cov` may not provide an + accurate measure of uncertainty. + + How the `sigma` parameter affects the estimated covariance + depends on `absolute_sigma` argument, as described above. + + If the Jacobian matrix at the solution doesn't have a full rank, then + 'lm' method returns a matrix filled with ``np.inf``, on the other hand + 'trf' and 'dogbox' methods use Moore-Penrose pseudoinverse to compute + the covariance matrix. Covariance matrices with large condition numbers + (e.g. computed with `numpy.linalg.cond`) may indicate that results are + unreliable. + infodict : dict (returned only if `full_output` is True) + a dictionary of optional outputs with the keys: + + ``nfev`` + The number of function calls. Methods 'trf' and 'dogbox' do not + count function calls for numerical Jacobian approximation, + as opposed to 'lm' method. + ``fvec`` + The residual values evaluated at the solution, for a 1-D `sigma` + this is ``(f(x, *popt) - ydata)/sigma``. + ``fjac`` + A permutation of the R matrix of a QR + factorization of the final approximate + Jacobian matrix, stored column wise. + Together with ipvt, the covariance of the + estimate can be approximated. + Method 'lm' only provides this information. + ``ipvt`` + An integer array of length N which defines + a permutation matrix, p, such that + fjac*p = q*r, where r is upper triangular + with diagonal elements of nonincreasing + magnitude. Column j of p is column ipvt(j) + of the identity matrix. + Method 'lm' only provides this information. + ``qtf`` + The vector (transpose(q) * fvec). + Method 'lm' only provides this information. + + .. versionadded:: 1.9 + mesg : str (returned only if `full_output` is True) + A string message giving information about the solution. + + .. versionadded:: 1.9 + ier : int (returned only if `full_output` is True) + An integer flag. If it is equal to 1, 2, 3 or 4, the solution was + found. Otherwise, the solution was not found. In either case, the + optional output variable `mesg` gives more information. + + .. versionadded:: 1.9 + + Raises + ------ + ValueError + if either `ydata` or `xdata` contain NaNs, or if incompatible options + are used. + + RuntimeError + if the least-squares minimization fails. + + OptimizeWarning + if covariance of the parameters can not be estimated. + + See Also + -------- + least_squares : Minimize the sum of squares of nonlinear functions. + scipy.stats.linregress : Calculate a linear least squares regression for + two sets of measurements. + + Notes + ----- + Users should ensure that inputs `xdata`, `ydata`, and the output of `f` + are ``float64``, or else the optimization may return incorrect results. + + With ``method='lm'``, the algorithm uses the Levenberg-Marquardt algorithm + through `leastsq`. Note that this algorithm can only deal with + unconstrained problems. + + Box constraints can be handled by methods 'trf' and 'dogbox'. Refer to + the docstring of `least_squares` for more information. + + Parameters to be fitted must have similar scale. Differences of multiple + orders of magnitude can lead to incorrect results. For the 'trf' and + 'dogbox' methods, the `x_scale` keyword argument can be used to scale + the parameters. + + References + ---------- + [1] K. Vugrin et al. Confidence region estimation techniques for nonlinear + regression in groundwater flow: Three case studies. Water Resources + Research, Vol. 43, W03423, :doi:`10.1029/2005WR004804` + + Examples + -------- + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.optimize import curve_fit + + >>> def func(x, a, b, c): + ... return a * np.exp(-b * x) + c + + Define the data to be fit with some noise: + + >>> xdata = np.linspace(0, 4, 50) + >>> y = func(xdata, 2.5, 1.3, 0.5) + >>> rng = np.random.default_rng() + >>> y_noise = 0.2 * rng.normal(size=xdata.size) + >>> ydata = y + y_noise + >>> plt.plot(xdata, ydata, 'b-', label='data') + + Fit for the parameters a, b, c of the function `func`: + + >>> popt, pcov = curve_fit(func, xdata, ydata) + >>> popt + array([2.56274217, 1.37268521, 0.47427475]) + >>> plt.plot(xdata, func(xdata, *popt), 'r-', + ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt)) + + Constrain the optimization to the region of ``0 <= a <= 3``, + ``0 <= b <= 1`` and ``0 <= c <= 0.5``: + + >>> popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5])) + >>> popt + array([2.43736712, 1. , 0.34463856]) + >>> plt.plot(xdata, func(xdata, *popt), 'g--', + ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt)) + + >>> plt.xlabel('x') + >>> plt.ylabel('y') + >>> plt.legend() + >>> plt.show() + + For reliable results, the model `func` should not be overparametrized; + redundant parameters can cause unreliable covariance matrices and, in some + cases, poorer quality fits. As a quick check of whether the model may be + overparameterized, calculate the condition number of the covariance matrix: + + >>> np.linalg.cond(pcov) + 34.571092161547405 # may vary + + The value is small, so it does not raise much concern. If, however, we were + to add a fourth parameter ``d`` to `func` with the same effect as ``a``: + + >>> def func2(x, a, b, c, d): + ... return a * d * np.exp(-b * x) + c # a and d are redundant + >>> popt, pcov = curve_fit(func2, xdata, ydata) + >>> np.linalg.cond(pcov) + 1.13250718925596e+32 # may vary + + Such a large value is cause for concern. The diagonal elements of the + covariance matrix, which is related to uncertainty of the fit, gives more + information: + + >>> np.diag(pcov) + array([1.48814742e+29, 3.78596560e-02, 5.39253738e-03, 2.76417220e+28]) # may vary + + Note that the first and last terms are much larger than the other elements, + suggesting that the optimal values of these parameters are ambiguous and + that only one of these parameters is needed in the model. + + If the optimal parameters of `f` differ by multiple orders of magnitude, the + resulting fit can be inaccurate. Sometimes, `curve_fit` can fail to find any + results: + + >>> ydata = func(xdata, 500000, 0.01, 15) + >>> try: + ... popt, pcov = curve_fit(func, xdata, ydata, method = 'trf') + ... except RuntimeError as e: + ... print(e) + Optimal parameters not found: The maximum number of function evaluations is + exceeded. + + If parameter scale is roughly known beforehand, it can be defined in + `x_scale` argument: + + >>> popt, pcov = curve_fit(func, xdata, ydata, method = 'trf', + ... x_scale = [1000, 1, 1]) + >>> popt + array([5.00000000e+05, 1.00000000e-02, 1.49999999e+01]) + """ + if p0 is None: + # determine number of parameters by inspecting the function + sig = _getfullargspec(f) + args = sig.args + if len(args) < 2: + raise ValueError("Unable to determine number of fit parameters.") + n = len(args) - 1 + else: + p0 = np.atleast_1d(p0) + n = p0.size + + if isinstance(bounds, Bounds): + lb, ub = bounds.lb, bounds.ub + else: + lb, ub = prepare_bounds(bounds, n) + if p0 is None: + p0 = _initialize_feasible(lb, ub) + + bounded_problem = np.any((lb > -np.inf) | (ub < np.inf)) + if method is None: + if bounded_problem: + method = 'trf' + else: + method = 'lm' + + if method == 'lm' and bounded_problem: + raise ValueError("Method 'lm' only works for unconstrained problems. " + "Use 'trf' or 'dogbox' instead.") + + if check_finite is None: + check_finite = True if nan_policy is None else False + + # optimization may produce garbage for float32 inputs, cast them to float64 + if check_finite: + ydata = np.asarray_chkfinite(ydata, float) + else: + ydata = np.asarray(ydata, float) + + if isinstance(xdata, (list, tuple, np.ndarray)): + # `xdata` is passed straight to the user-defined `f`, so allow + # non-array_like `xdata`. + if check_finite: + xdata = np.asarray_chkfinite(xdata, float) + else: + xdata = np.asarray(xdata, float) + + if ydata.size == 0: + raise ValueError("`ydata` must not be empty!") + + # nan handling is needed only if check_finite is False because if True, + # the x-y data are already checked, and they don't contain nans. + if not check_finite and nan_policy is not None: + if nan_policy == "propagate": + raise ValueError("`nan_policy='propagate'` is not supported " + "by this function.") + + policies = [None, 'raise', 'omit'] + x_contains_nan, nan_policy = _contains_nan(xdata, nan_policy, + policies=policies) + y_contains_nan, nan_policy = _contains_nan(ydata, nan_policy, + policies=policies) + + if (x_contains_nan or y_contains_nan) and nan_policy == 'omit': + # ignore NaNs for N dimensional arrays + has_nan = np.isnan(xdata) + has_nan = has_nan.any(axis=tuple(range(has_nan.ndim-1))) + has_nan |= np.isnan(ydata) + + xdata = xdata[..., ~has_nan] + ydata = ydata[~has_nan] + + # Determine type of sigma + if sigma is not None: + sigma = np.asarray(sigma) + + # if 1-D or a scalar, sigma are errors, define transform = 1/sigma + if sigma.size == 1 or sigma.shape == (ydata.size, ): + transform = 1.0 / sigma + # if 2-D, sigma is the covariance matrix, + # define transform = L such that L L^T = C + elif sigma.shape == (ydata.size, ydata.size): + try: + # scipy.linalg.cholesky requires lower=True to return L L^T = A + transform = cholesky(sigma, lower=True) + except LinAlgError as e: + raise ValueError("`sigma` must be positive definite.") from e + else: + raise ValueError("`sigma` has incorrect shape.") + else: + transform = None + + func = _lightweight_memoizer(_wrap_func(f, xdata, ydata, transform)) + + if callable(jac): + jac = _lightweight_memoizer(_wrap_jac(jac, xdata, transform)) + elif jac is None and method != 'lm': + jac = '2-point' + + if 'args' in kwargs: + # The specification for the model function `f` does not support + # additional arguments. Refer to the `curve_fit` docstring for + # acceptable call signatures of `f`. + raise ValueError("'args' is not a supported keyword argument.") + + if method == 'lm': + # if ydata.size == 1, this might be used for broadcast. + if ydata.size != 1 and n > ydata.size: + raise TypeError(f"The number of func parameters={n} must not" + f" exceed the number of data points={ydata.size}") + res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs) + popt, pcov, infodict, errmsg, ier = res + ysize = len(infodict['fvec']) + cost = np.sum(infodict['fvec'] ** 2) + if ier not in [1, 2, 3, 4]: + raise RuntimeError("Optimal parameters not found: " + errmsg) + else: + # Rename maxfev (leastsq) to max_nfev (least_squares), if specified. + if 'max_nfev' not in kwargs: + kwargs['max_nfev'] = kwargs.pop('maxfev', None) + + res = least_squares(func, p0, jac=jac, bounds=bounds, method=method, + **kwargs) + + if not res.success: + raise RuntimeError("Optimal parameters not found: " + res.message) + + infodict = dict(nfev=res.nfev, fvec=res.fun) + ier = res.status + errmsg = res.message + + ysize = len(res.fun) + cost = 2 * res.cost # res.cost is half sum of squares! + popt = res.x + + # Do Moore-Penrose inverse discarding zero singular values. + _, s, VT = svd(res.jac, full_matrices=False) + threshold = np.finfo(float).eps * max(res.jac.shape) * s[0] + s = s[s > threshold] + VT = VT[:s.size] + pcov = np.dot(VT.T / s**2, VT) + + warn_cov = False + if pcov is None or np.isnan(pcov).any(): + # indeterminate covariance + pcov = zeros((len(popt), len(popt)), dtype=float) + pcov.fill(inf) + warn_cov = True + elif not absolute_sigma: + if ysize > p0.size: + s_sq = cost / (ysize - p0.size) + pcov = pcov * s_sq + else: + pcov.fill(inf) + warn_cov = True + + if warn_cov: + warnings.warn('Covariance of the parameters could not be estimated', + category=OptimizeWarning, stacklevel=2) + + if full_output: + return popt, pcov, infodict, errmsg, ier + else: + return popt, pcov + + +def check_gradient(fcn, Dfcn, x0, args=(), col_deriv=0): + """Perform a simple check on the gradient for correctness. + + """ + + x = atleast_1d(x0) + n = len(x) + x = x.reshape((n,)) + fvec = atleast_1d(fcn(x, *args)) + m = len(fvec) + fvec = fvec.reshape((m,)) + ldfjac = m + fjac = atleast_1d(Dfcn(x, *args)) + fjac = fjac.reshape((m, n)) + if col_deriv == 0: + fjac = transpose(fjac) + + xp = zeros((n,), float) + err = zeros((m,), float) + fvecp = None + _minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 1, err) + + fvecp = atleast_1d(fcn(xp, *args)) + fvecp = fvecp.reshape((m,)) + _minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 2, err) + + good = (prod(greater(err, 0.5), axis=0)) + + return (good, err) + + +def _del2(p0, p1, d): + return p0 - np.square(p1 - p0) / d + + +def _relerr(actual, desired): + return (actual - desired) / desired + + +def _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel): + p0 = x0 + for i in range(maxiter): + p1 = func(p0, *args) + if use_accel: + p2 = func(p1, *args) + d = p2 - 2.0 * p1 + p0 + p = _lazywhere(d != 0, (p0, p1, d), f=_del2, fillvalue=p2) + else: + p = p1 + relerr = _lazywhere(p0 != 0, (p, p0), f=_relerr, fillvalue=p) + if np.all(np.abs(relerr) < xtol): + return p + p0 = p + msg = "Failed to converge after %d iterations, value is %s" % (maxiter, p) + raise RuntimeError(msg) + + +def fixed_point(func, x0, args=(), xtol=1e-8, maxiter=500, method='del2'): + """ + Find a fixed point of the function. + + Given a function of one or more variables and a starting point, find a + fixed point of the function: i.e., where ``func(x0) == x0``. + + Parameters + ---------- + func : function + Function to evaluate. + x0 : array_like + Fixed point of function. + args : tuple, optional + Extra arguments to `func`. + xtol : float, optional + Convergence tolerance, defaults to 1e-08. + maxiter : int, optional + Maximum number of iterations, defaults to 500. + method : {"del2", "iteration"}, optional + Method of finding the fixed-point, defaults to "del2", + which uses Steffensen's Method with Aitken's ``Del^2`` + convergence acceleration [1]_. The "iteration" method simply iterates + the function until convergence is detected, without attempting to + accelerate the convergence. + + References + ---------- + .. [1] Burden, Faires, "Numerical Analysis", 5th edition, pg. 80 + + Examples + -------- + >>> import numpy as np + >>> from scipy import optimize + >>> def func(x, c1, c2): + ... return np.sqrt(c1/(x+c2)) + >>> c1 = np.array([10,12.]) + >>> c2 = np.array([3, 5.]) + >>> optimize.fixed_point(func, [1.2, 1.3], args=(c1,c2)) + array([ 1.4920333 , 1.37228132]) + + """ + use_accel = {'del2': True, 'iteration': False}[method] + x0 = _asarray_validated(x0, as_inexact=True) + return _fixed_point_helper(func, x0, args, xtol, maxiter, use_accel) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nnls.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nnls.py new file mode 100644 index 0000000000000000000000000000000000000000..17fcdc9e4cc52b1839cd938f21a78256cfb19436 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nnls.py @@ -0,0 +1,164 @@ +import numpy as np +from scipy.linalg import solve, LinAlgWarning +import warnings + +__all__ = ['nnls'] + + +def nnls(A, b, maxiter=None, *, atol=None): + """ + Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. + + This problem, often called as NonNegative Least Squares, is a convex + optimization problem with convex constraints. It typically arises when + the ``x`` models quantities for which only nonnegative values are + attainable; weight of ingredients, component costs and so on. + + Parameters + ---------- + A : (m, n) ndarray + Coefficient array + b : (m,) ndarray, float + Right-hand side vector. + maxiter: int, optional + Maximum number of iterations, optional. Default value is ``3 * n``. + atol: float + Tolerance value used in the algorithm to assess closeness to zero in + the projected residual ``(A.T @ (A x - b)`` entries. Increasing this + value relaxes the solution constraints. A typical relaxation value can + be selected as ``max(m, n) * np.linalg.norm(a, 1) * np.spacing(1.)``. + This value is not set as default since the norm operation becomes + expensive for large problems hence can be used only when necessary. + + Returns + ------- + x : ndarray + Solution vector. + rnorm : float + The 2-norm of the residual, ``|| Ax-b ||_2``. + + See Also + -------- + lsq_linear : Linear least squares with bounds on the variables + + Notes + ----- + The code is based on [2]_ which is an improved version of the classical + algorithm of [1]_. It utilizes an active set method and solves the KKT + (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem. + + References + ---------- + .. [1] : Lawson C., Hanson R.J., "Solving Least Squares Problems", SIAM, + 1995, :doi:`10.1137/1.9781611971217` + .. [2] : Bro, Rasmus and de Jong, Sijmen, "A Fast Non-Negativity- + Constrained Least Squares Algorithm", Journal Of Chemometrics, 1997, + :doi:`10.1002/(SICI)1099-128X(199709/10)11:5<393::AID-CEM483>3.0.CO;2-L` + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import nnls + ... + >>> A = np.array([[1, 0], [1, 0], [0, 1]]) + >>> b = np.array([2, 1, 1]) + >>> nnls(A, b) + (array([1.5, 1. ]), 0.7071067811865475) + + >>> b = np.array([-1, -1, -1]) + >>> nnls(A, b) + (array([0., 0.]), 1.7320508075688772) + + """ + + A = np.asarray_chkfinite(A) + b = np.asarray_chkfinite(b) + + if len(A.shape) != 2: + raise ValueError("Expected a two-dimensional array (matrix)" + + f", but the shape of A is {A.shape}") + if len(b.shape) != 1: + raise ValueError("Expected a one-dimensional array (vector)" + + f", but the shape of b is {b.shape}") + + m, n = A.shape + + if m != b.shape[0]: + raise ValueError( + "Incompatible dimensions. The first dimension of " + + f"A is {m}, while the shape of b is {(b.shape[0], )}") + + x, rnorm, mode = _nnls(A, b, maxiter, tol=atol) + if mode != 1: + raise RuntimeError("Maximum number of iterations reached.") + + return x, rnorm + + +def _nnls(A, b, maxiter=None, tol=None): + """ + This is a single RHS algorithm from ref [2] above. For multiple RHS + support, the algorithm is given in :doi:`10.1002/cem.889` + """ + m, n = A.shape + + AtA = A.T @ A + Atb = b @ A # Result is 1D - let NumPy figure it out + + if not maxiter: + maxiter = 3*n + if tol is None: + tol = 10 * max(m, n) * np.spacing(1.) + + # Initialize vars + x = np.zeros(n, dtype=np.float64) + s = np.zeros(n, dtype=np.float64) + # Inactive constraint switches + P = np.zeros(n, dtype=bool) + + # Projected residual + w = Atb.copy().astype(np.float64) # x=0. Skip (-AtA @ x) term + + # Overall iteration counter + # Outer loop is not counted, inner iter is counted across outer spins + iter = 0 + + while (not P.all()) and (w[~P] > tol).any(): # B + # Get the "most" active coeff index and move to inactive set + k = np.argmax(w * (~P)) # B.2 + P[k] = True # B.3 + + # Iteration solution + s[:] = 0. + # B.4 + with warnings.catch_warnings(): + warnings.filterwarnings('ignore', message='Ill-conditioned matrix', + category=LinAlgWarning) + s[P] = solve(AtA[np.ix_(P, P)], Atb[P], assume_a='sym', check_finite=False) + + # Inner loop + while (iter < maxiter) and (s[P].min() < 0): # C.1 + iter += 1 + inds = P * (s < 0) + alpha = (x[inds] / (x[inds] - s[inds])).min() # C.2 + x *= (1 - alpha) + x += alpha*s + P[x <= tol] = False + with warnings.catch_warnings(): + warnings.filterwarnings('ignore', message='Ill-conditioned matrix', + category=LinAlgWarning) + s[P] = solve(AtA[np.ix_(P, P)], Atb[P], assume_a='sym', + check_finite=False) + s[~P] = 0 # C.6 + + x[:] = s[:] + w[:] = Atb - AtA @ x + + if iter == maxiter: + # Typically following line should return + # return x, np.linalg.norm(A@x - b), -1 + # however at the top level, -1 raises an exception wasting norm + # Instead return dummy number 0. + return x, 0., -1 + + return x, np.linalg.norm(A@x - b), 1 diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nonlin.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nonlin.py new file mode 100644 index 0000000000000000000000000000000000000000..cbaa3d4ced448df492e965cffe39e99f593c8895 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_nonlin.py @@ -0,0 +1,1585 @@ +# Copyright (C) 2009, Pauli Virtanen +# Distributed under the same license as SciPy. + +import inspect +import sys +import warnings + +import numpy as np +from numpy import asarray, dot, vdot + +from scipy.linalg import norm, solve, inv, qr, svd, LinAlgError +import scipy.sparse.linalg +import scipy.sparse +from scipy.linalg import get_blas_funcs +from scipy._lib._util import copy_if_needed +from scipy._lib._util import getfullargspec_no_self as _getfullargspec +from ._linesearch import scalar_search_wolfe1, scalar_search_armijo + + +__all__ = [ + 'broyden1', 'broyden2', 'anderson', 'linearmixing', + 'diagbroyden', 'excitingmixing', 'newton_krylov', + 'BroydenFirst', 'KrylovJacobian', 'InverseJacobian', 'NoConvergence'] + +#------------------------------------------------------------------------------ +# Utility functions +#------------------------------------------------------------------------------ + + +class NoConvergence(Exception): + """Exception raised when nonlinear solver fails to converge within the specified + `maxiter`.""" + pass + + +def maxnorm(x): + return np.absolute(x).max() + + +def _as_inexact(x): + """Return `x` as an array, of either floats or complex floats""" + x = asarray(x) + if not np.issubdtype(x.dtype, np.inexact): + return asarray(x, dtype=np.float64) + return x + + +def _array_like(x, x0): + """Return ndarray `x` as same array subclass and shape as `x0`""" + x = np.reshape(x, np.shape(x0)) + wrap = getattr(x0, '__array_wrap__', x.__array_wrap__) + return wrap(x) + + +def _safe_norm(v): + if not np.isfinite(v).all(): + return np.array(np.inf) + return norm(v) + +#------------------------------------------------------------------------------ +# Generic nonlinear solver machinery +#------------------------------------------------------------------------------ + + +_doc_parts = dict( + params_basic=""" + F : function(x) -> f + Function whose root to find; should take and return an array-like + object. + xin : array_like + Initial guess for the solution + """.strip(), + params_extra=""" + iter : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + verbose : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. If more are needed to + meet convergence, `NoConvergence` is raised. + f_tol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + f_rtol : float, optional + Relative tolerance for the residual. If omitted, not used. + x_tol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + x_rtol : float, optional + Relative minimum step size. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in the + direction given by the Jacobian approximation. Defaults to 'armijo'. + callback : function, optional + Optional callback function. It is called on every iteration as + ``callback(x, f)`` where `x` is the current solution and `f` + the corresponding residual. + + Returns + ------- + sol : ndarray + An array (of similar array type as `x0`) containing the final solution. + + Raises + ------ + NoConvergence + When a solution was not found. + + """.strip() +) + + +def _set_doc(obj): + if obj.__doc__: + obj.__doc__ = obj.__doc__ % _doc_parts + + +def nonlin_solve(F, x0, jacobian='krylov', iter=None, verbose=False, + maxiter=None, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, + tol_norm=None, line_search='armijo', callback=None, + full_output=False, raise_exception=True): + """ + Find a root of a function, in a way suitable for large-scale problems. + + Parameters + ---------- + %(params_basic)s + jacobian : Jacobian + A Jacobian approximation: `Jacobian` object or something that + `asjacobian` can transform to one. Alternatively, a string specifying + which of the builtin Jacobian approximations to use: + + krylov, broyden1, broyden2, anderson + diagbroyden, linearmixing, excitingmixing + + %(params_extra)s + full_output : bool + If true, returns a dictionary `info` containing convergence + information. + raise_exception : bool + If True, a `NoConvergence` exception is raise if no solution is found. + + See Also + -------- + asjacobian, Jacobian + + Notes + ----- + This algorithm implements the inexact Newton method, with + backtracking or full line searches. Several Jacobian + approximations are available, including Krylov and Quasi-Newton + methods. + + References + ---------- + .. [KIM] C. T. Kelley, \"Iterative Methods for Linear and Nonlinear + Equations\". Society for Industrial and Applied Mathematics. (1995) + https://archive.siam.org/books/kelley/fr16/ + + """ + # Can't use default parameters because it's being explicitly passed as None + # from the calling function, so we need to set it here. + tol_norm = maxnorm if tol_norm is None else tol_norm + condition = TerminationCondition(f_tol=f_tol, f_rtol=f_rtol, + x_tol=x_tol, x_rtol=x_rtol, + iter=iter, norm=tol_norm) + + x0 = _as_inexact(x0) + def func(z): + return _as_inexact(F(_array_like(z, x0))).flatten() + x = x0.flatten() + + dx = np.full_like(x, np.inf) + Fx = func(x) + Fx_norm = norm(Fx) + + jacobian = asjacobian(jacobian) + jacobian.setup(x.copy(), Fx, func) + + if maxiter is None: + if iter is not None: + maxiter = iter + 1 + else: + maxiter = 100*(x.size+1) + + if line_search is True: + line_search = 'armijo' + elif line_search is False: + line_search = None + + if line_search not in (None, 'armijo', 'wolfe'): + raise ValueError("Invalid line search") + + # Solver tolerance selection + gamma = 0.9 + eta_max = 0.9999 + eta_treshold = 0.1 + eta = 1e-3 + + for n in range(maxiter): + status = condition.check(Fx, x, dx) + if status: + break + + # The tolerance, as computed for scipy.sparse.linalg.* routines + tol = min(eta, eta*Fx_norm) + dx = -jacobian.solve(Fx, tol=tol) + + if norm(dx) == 0: + raise ValueError("Jacobian inversion yielded zero vector. " + "This indicates a bug in the Jacobian " + "approximation.") + + # Line search, or Newton step + if line_search: + s, x, Fx, Fx_norm_new = _nonlin_line_search(func, x, Fx, dx, + line_search) + else: + s = 1.0 + x = x + dx + Fx = func(x) + Fx_norm_new = norm(Fx) + + jacobian.update(x.copy(), Fx) + + if callback: + callback(x, Fx) + + # Adjust forcing parameters for inexact methods + eta_A = gamma * Fx_norm_new**2 / Fx_norm**2 + if gamma * eta**2 < eta_treshold: + eta = min(eta_max, eta_A) + else: + eta = min(eta_max, max(eta_A, gamma*eta**2)) + + Fx_norm = Fx_norm_new + + # Print status + if verbose: + sys.stdout.write("%d: |F(x)| = %g; step %g\n" % ( + n, tol_norm(Fx), s)) + sys.stdout.flush() + else: + if raise_exception: + raise NoConvergence(_array_like(x, x0)) + else: + status = 2 + + if full_output: + info = {'nit': condition.iteration, + 'fun': Fx, + 'status': status, + 'success': status == 1, + 'message': {1: 'A solution was found at the specified ' + 'tolerance.', + 2: 'The maximum number of iterations allowed ' + 'has been reached.' + }[status] + } + return _array_like(x, x0), info + else: + return _array_like(x, x0) + + +_set_doc(nonlin_solve) + + +def _nonlin_line_search(func, x, Fx, dx, search_type='armijo', rdiff=1e-8, + smin=1e-2): + tmp_s = [0] + tmp_Fx = [Fx] + tmp_phi = [norm(Fx)**2] + s_norm = norm(x) / norm(dx) + + def phi(s, store=True): + if s == tmp_s[0]: + return tmp_phi[0] + xt = x + s*dx + v = func(xt) + p = _safe_norm(v)**2 + if store: + tmp_s[0] = s + tmp_phi[0] = p + tmp_Fx[0] = v + return p + + def derphi(s): + ds = (abs(s) + s_norm + 1) * rdiff + return (phi(s+ds, store=False) - phi(s)) / ds + + if search_type == 'wolfe': + s, phi1, phi0 = scalar_search_wolfe1(phi, derphi, tmp_phi[0], + xtol=1e-2, amin=smin) + elif search_type == 'armijo': + s, phi1 = scalar_search_armijo(phi, tmp_phi[0], -tmp_phi[0], + amin=smin) + + if s is None: + # XXX: No suitable step length found. Take the full Newton step, + # and hope for the best. + s = 1.0 + + x = x + s*dx + if s == tmp_s[0]: + Fx = tmp_Fx[0] + else: + Fx = func(x) + Fx_norm = norm(Fx) + + return s, x, Fx, Fx_norm + + +class TerminationCondition: + """ + Termination condition for an iteration. It is terminated if + + - |F| < f_rtol*|F_0|, AND + - |F| < f_tol + + AND + + - |dx| < x_rtol*|x|, AND + - |dx| < x_tol + + """ + def __init__(self, f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, + iter=None, norm=maxnorm): + + if f_tol is None: + f_tol = np.finfo(np.float64).eps ** (1./3) + if f_rtol is None: + f_rtol = np.inf + if x_tol is None: + x_tol = np.inf + if x_rtol is None: + x_rtol = np.inf + + self.x_tol = x_tol + self.x_rtol = x_rtol + self.f_tol = f_tol + self.f_rtol = f_rtol + + self.norm = norm + + self.iter = iter + + self.f0_norm = None + self.iteration = 0 + + def check(self, f, x, dx): + self.iteration += 1 + f_norm = self.norm(f) + x_norm = self.norm(x) + dx_norm = self.norm(dx) + + if self.f0_norm is None: + self.f0_norm = f_norm + + if f_norm == 0: + return 1 + + if self.iter is not None: + # backwards compatibility with SciPy 0.6.0 + return 2 * (self.iteration > self.iter) + + # NB: condition must succeed for rtol=inf even if norm == 0 + return int((f_norm <= self.f_tol + and f_norm/self.f_rtol <= self.f0_norm) + and (dx_norm <= self.x_tol + and dx_norm/self.x_rtol <= x_norm)) + + +#------------------------------------------------------------------------------ +# Generic Jacobian approximation +#------------------------------------------------------------------------------ + +class Jacobian: + """ + Common interface for Jacobians or Jacobian approximations. + + The optional methods come useful when implementing trust region + etc., algorithms that often require evaluating transposes of the + Jacobian. + + Methods + ------- + solve + Returns J^-1 * v + update + Updates Jacobian to point `x` (where the function has residual `Fx`) + + matvec : optional + Returns J * v + rmatvec : optional + Returns A^H * v + rsolve : optional + Returns A^-H * v + matmat : optional + Returns A * V, where V is a dense matrix with dimensions (N,K). + todense : optional + Form the dense Jacobian matrix. Necessary for dense trust region + algorithms, and useful for testing. + + Attributes + ---------- + shape + Matrix dimensions (M, N) + dtype + Data type of the matrix. + func : callable, optional + Function the Jacobian corresponds to + + """ + + def __init__(self, **kw): + names = ["solve", "update", "matvec", "rmatvec", "rsolve", + "matmat", "todense", "shape", "dtype"] + for name, value in kw.items(): + if name not in names: + raise ValueError("Unknown keyword argument %s" % name) + if value is not None: + setattr(self, name, kw[name]) + + + if hasattr(self, "todense"): + def __array__(self, dtype=None, copy=None): + if dtype is not None: + raise ValueError(f"`dtype` must be None, was {dtype}") + return self.todense() + + def aspreconditioner(self): + return InverseJacobian(self) + + def solve(self, v, tol=0): + raise NotImplementedError + + def update(self, x, F): + pass + + def setup(self, x, F, func): + self.func = func + self.shape = (F.size, x.size) + self.dtype = F.dtype + if self.__class__.setup is Jacobian.setup: + # Call on the first point unless overridden + self.update(x, F) + + +class InverseJacobian: + def __init__(self, jacobian): + self.jacobian = jacobian + self.matvec = jacobian.solve + self.update = jacobian.update + if hasattr(jacobian, 'setup'): + self.setup = jacobian.setup + if hasattr(jacobian, 'rsolve'): + self.rmatvec = jacobian.rsolve + + @property + def shape(self): + return self.jacobian.shape + + @property + def dtype(self): + return self.jacobian.dtype + + +def asjacobian(J): + """ + Convert given object to one suitable for use as a Jacobian. + """ + spsolve = scipy.sparse.linalg.spsolve + if isinstance(J, Jacobian): + return J + elif inspect.isclass(J) and issubclass(J, Jacobian): + return J() + elif isinstance(J, np.ndarray): + if J.ndim > 2: + raise ValueError('array must have rank <= 2') + J = np.atleast_2d(np.asarray(J)) + if J.shape[0] != J.shape[1]: + raise ValueError('array must be square') + + return Jacobian(matvec=lambda v: dot(J, v), + rmatvec=lambda v: dot(J.conj().T, v), + solve=lambda v, tol=0: solve(J, v), + rsolve=lambda v, tol=0: solve(J.conj().T, v), + dtype=J.dtype, shape=J.shape) + elif scipy.sparse.issparse(J): + if J.shape[0] != J.shape[1]: + raise ValueError('matrix must be square') + return Jacobian(matvec=lambda v: J @ v, + rmatvec=lambda v: J.conj().T @ v, + solve=lambda v, tol=0: spsolve(J, v), + rsolve=lambda v, tol=0: spsolve(J.conj().T, v), + dtype=J.dtype, shape=J.shape) + elif hasattr(J, 'shape') and hasattr(J, 'dtype') and hasattr(J, 'solve'): + return Jacobian(matvec=getattr(J, 'matvec'), + rmatvec=getattr(J, 'rmatvec'), + solve=J.solve, + rsolve=getattr(J, 'rsolve'), + update=getattr(J, 'update'), + setup=getattr(J, 'setup'), + dtype=J.dtype, + shape=J.shape) + elif callable(J): + # Assume it's a function J(x) that returns the Jacobian + class Jac(Jacobian): + def update(self, x, F): + self.x = x + + def solve(self, v, tol=0): + m = J(self.x) + if isinstance(m, np.ndarray): + return solve(m, v) + elif scipy.sparse.issparse(m): + return spsolve(m, v) + else: + raise ValueError("Unknown matrix type") + + def matvec(self, v): + m = J(self.x) + if isinstance(m, np.ndarray): + return dot(m, v) + elif scipy.sparse.issparse(m): + return m @ v + else: + raise ValueError("Unknown matrix type") + + def rsolve(self, v, tol=0): + m = J(self.x) + if isinstance(m, np.ndarray): + return solve(m.conj().T, v) + elif scipy.sparse.issparse(m): + return spsolve(m.conj().T, v) + else: + raise ValueError("Unknown matrix type") + + def rmatvec(self, v): + m = J(self.x) + if isinstance(m, np.ndarray): + return dot(m.conj().T, v) + elif scipy.sparse.issparse(m): + return m.conj().T @ v + else: + raise ValueError("Unknown matrix type") + return Jac() + elif isinstance(J, str): + return dict(broyden1=BroydenFirst, + broyden2=BroydenSecond, + anderson=Anderson, + diagbroyden=DiagBroyden, + linearmixing=LinearMixing, + excitingmixing=ExcitingMixing, + krylov=KrylovJacobian)[J]() + else: + raise TypeError('Cannot convert object to a Jacobian') + + +#------------------------------------------------------------------------------ +# Broyden +#------------------------------------------------------------------------------ + +class GenericBroyden(Jacobian): + def setup(self, x0, f0, func): + Jacobian.setup(self, x0, f0, func) + self.last_f = f0 + self.last_x = x0 + + if hasattr(self, 'alpha') and self.alpha is None: + # Autoscale the initial Jacobian parameter + # unless we have already guessed the solution. + normf0 = norm(f0) + if normf0: + self.alpha = 0.5*max(norm(x0), 1) / normf0 + else: + self.alpha = 1.0 + + def _update(self, x, f, dx, df, dx_norm, df_norm): + raise NotImplementedError + + def update(self, x, f): + df = f - self.last_f + dx = x - self.last_x + self._update(x, f, dx, df, norm(dx), norm(df)) + self.last_f = f + self.last_x = x + + +class LowRankMatrix: + r""" + A matrix represented as + + .. math:: \alpha I + \sum_{n=0}^{n=M} c_n d_n^\dagger + + However, if the rank of the matrix reaches the dimension of the vectors, + full matrix representation will be used thereon. + + """ + + def __init__(self, alpha, n, dtype): + self.alpha = alpha + self.cs = [] + self.ds = [] + self.n = n + self.dtype = dtype + self.collapsed = None + + @staticmethod + def _matvec(v, alpha, cs, ds): + axpy, scal, dotc = get_blas_funcs(['axpy', 'scal', 'dotc'], + cs[:1] + [v]) + w = alpha * v + for c, d in zip(cs, ds): + a = dotc(d, v) + w = axpy(c, w, w.size, a) + return w + + @staticmethod + def _solve(v, alpha, cs, ds): + """Evaluate w = M^-1 v""" + if len(cs) == 0: + return v/alpha + + # (B + C D^H)^-1 = B^-1 - B^-1 C (I + D^H B^-1 C)^-1 D^H B^-1 + + axpy, dotc = get_blas_funcs(['axpy', 'dotc'], cs[:1] + [v]) + + c0 = cs[0] + A = alpha * np.identity(len(cs), dtype=c0.dtype) + for i, d in enumerate(ds): + for j, c in enumerate(cs): + A[i,j] += dotc(d, c) + + q = np.zeros(len(cs), dtype=c0.dtype) + for j, d in enumerate(ds): + q[j] = dotc(d, v) + q /= alpha + q = solve(A, q) + + w = v/alpha + for c, qc in zip(cs, q): + w = axpy(c, w, w.size, -qc) + + return w + + def matvec(self, v): + """Evaluate w = M v""" + if self.collapsed is not None: + return np.dot(self.collapsed, v) + return LowRankMatrix._matvec(v, self.alpha, self.cs, self.ds) + + def rmatvec(self, v): + """Evaluate w = M^H v""" + if self.collapsed is not None: + return np.dot(self.collapsed.T.conj(), v) + return LowRankMatrix._matvec(v, np.conj(self.alpha), self.ds, self.cs) + + def solve(self, v, tol=0): + """Evaluate w = M^-1 v""" + if self.collapsed is not None: + return solve(self.collapsed, v) + return LowRankMatrix._solve(v, self.alpha, self.cs, self.ds) + + def rsolve(self, v, tol=0): + """Evaluate w = M^-H v""" + if self.collapsed is not None: + return solve(self.collapsed.T.conj(), v) + return LowRankMatrix._solve(v, np.conj(self.alpha), self.ds, self.cs) + + def append(self, c, d): + if self.collapsed is not None: + self.collapsed += c[:,None] * d[None,:].conj() + return + + self.cs.append(c) + self.ds.append(d) + + if len(self.cs) > c.size: + self.collapse() + + def __array__(self, dtype=None, copy=None): + if dtype is not None: + warnings.warn("LowRankMatrix is scipy-internal code, `dtype` " + f"should only be None but was {dtype} (not handled)", + stacklevel=3) + if copy is not None: + warnings.warn("LowRankMatrix is scipy-internal code, `copy` " + f"should only be None but was {copy} (not handled)", + stacklevel=3) + if self.collapsed is not None: + return self.collapsed + + Gm = self.alpha*np.identity(self.n, dtype=self.dtype) + for c, d in zip(self.cs, self.ds): + Gm += c[:,None]*d[None,:].conj() + return Gm + + def collapse(self): + """Collapse the low-rank matrix to a full-rank one.""" + self.collapsed = np.array(self, copy=copy_if_needed) + self.cs = None + self.ds = None + self.alpha = None + + def restart_reduce(self, rank): + """ + Reduce the rank of the matrix by dropping all vectors. + """ + if self.collapsed is not None: + return + assert rank > 0 + if len(self.cs) > rank: + del self.cs[:] + del self.ds[:] + + def simple_reduce(self, rank): + """ + Reduce the rank of the matrix by dropping oldest vectors. + """ + if self.collapsed is not None: + return + assert rank > 0 + while len(self.cs) > rank: + del self.cs[0] + del self.ds[0] + + def svd_reduce(self, max_rank, to_retain=None): + """ + Reduce the rank of the matrix by retaining some SVD components. + + This corresponds to the \"Broyden Rank Reduction Inverse\" + algorithm described in [1]_. + + Note that the SVD decomposition can be done by solving only a + problem whose size is the effective rank of this matrix, which + is viable even for large problems. + + Parameters + ---------- + max_rank : int + Maximum rank of this matrix after reduction. + to_retain : int, optional + Number of SVD components to retain when reduction is done + (ie. rank > max_rank). Default is ``max_rank - 2``. + + References + ---------- + .. [1] B.A. van der Rotten, PhD thesis, + \"A limited memory Broyden method to solve high-dimensional + systems of nonlinear equations\". Mathematisch Instituut, + Universiteit Leiden, The Netherlands (2003). + + https://web.archive.org/web/20161022015821/http://www.math.leidenuniv.nl/scripties/Rotten.pdf + + """ + if self.collapsed is not None: + return + + p = max_rank + if to_retain is not None: + q = to_retain + else: + q = p - 2 + + if self.cs: + p = min(p, len(self.cs[0])) + q = max(0, min(q, p-1)) + + m = len(self.cs) + if m < p: + # nothing to do + return + + C = np.array(self.cs).T + D = np.array(self.ds).T + + D, R = qr(D, mode='economic') + C = dot(C, R.T.conj()) + + U, S, WH = svd(C, full_matrices=False) + + C = dot(C, inv(WH)) + D = dot(D, WH.T.conj()) + + for k in range(q): + self.cs[k] = C[:,k].copy() + self.ds[k] = D[:,k].copy() + + del self.cs[q:] + del self.ds[q:] + + +_doc_parts['broyden_params'] = """ + alpha : float, optional + Initial guess for the Jacobian is ``(-1/alpha)``. + reduction_method : str or tuple, optional + Method used in ensuring that the rank of the Broyden matrix + stays low. Can either be a string giving the name of the method, + or a tuple of the form ``(method, param1, param2, ...)`` + that gives the name of the method and values for additional parameters. + + Methods available: + + - ``restart``: drop all matrix columns. Has no extra parameters. + - ``simple``: drop oldest matrix column. Has no extra parameters. + - ``svd``: keep only the most significant SVD components. + Takes an extra parameter, ``to_retain``, which determines the + number of SVD components to retain when rank reduction is done. + Default is ``max_rank - 2``. + + max_rank : int, optional + Maximum rank for the Broyden matrix. + Default is infinity (i.e., no rank reduction). + """.strip() + + +class BroydenFirst(GenericBroyden): + r""" + Find a root of a function, using Broyden's first Jacobian approximation. + + This method is also known as \"Broyden's good method\". + + Parameters + ---------- + %(params_basic)s + %(broyden_params)s + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='broyden1'`` in particular. + + Notes + ----- + This algorithm implements the inverse Jacobian Quasi-Newton update + + .. math:: H_+ = H + (dx - H df) dx^\dagger H / ( dx^\dagger H df) + + which corresponds to Broyden's first Jacobian update + + .. math:: J_+ = J + (df - J dx) dx^\dagger / dx^\dagger dx + + + References + ---------- + .. [1] B.A. van der Rotten, PhD thesis, + \"A limited memory Broyden method to solve high-dimensional + systems of nonlinear equations\". Mathematisch Instituut, + Universiteit Leiden, The Netherlands (2003). + + https://web.archive.org/web/20161022015821/http://www.math.leidenuniv.nl/scripties/Rotten.pdf + + Examples + -------- + The following functions define a system of nonlinear equations + + >>> def fun(x): + ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, + ... 0.5 * (x[1] - x[0])**3 + x[1]] + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.broyden1(fun, [0, 0]) + >>> sol + array([0.84116396, 0.15883641]) + + """ + + def __init__(self, alpha=None, reduction_method='restart', max_rank=None): + GenericBroyden.__init__(self) + self.alpha = alpha + self.Gm = None + + if max_rank is None: + max_rank = np.inf + self.max_rank = max_rank + + if isinstance(reduction_method, str): + reduce_params = () + else: + reduce_params = reduction_method[1:] + reduction_method = reduction_method[0] + reduce_params = (max_rank - 1,) + reduce_params + + if reduction_method == 'svd': + self._reduce = lambda: self.Gm.svd_reduce(*reduce_params) + elif reduction_method == 'simple': + self._reduce = lambda: self.Gm.simple_reduce(*reduce_params) + elif reduction_method == 'restart': + self._reduce = lambda: self.Gm.restart_reduce(*reduce_params) + else: + raise ValueError("Unknown rank reduction method '%s'" % + reduction_method) + + def setup(self, x, F, func): + GenericBroyden.setup(self, x, F, func) + self.Gm = LowRankMatrix(-self.alpha, self.shape[0], self.dtype) + + def todense(self): + return inv(self.Gm) + + def solve(self, f, tol=0): + r = self.Gm.matvec(f) + if not np.isfinite(r).all(): + # singular; reset the Jacobian approximation + self.setup(self.last_x, self.last_f, self.func) + return self.Gm.matvec(f) + return r + + def matvec(self, f): + return self.Gm.solve(f) + + def rsolve(self, f, tol=0): + return self.Gm.rmatvec(f) + + def rmatvec(self, f): + return self.Gm.rsolve(f) + + def _update(self, x, f, dx, df, dx_norm, df_norm): + self._reduce() # reduce first to preserve secant condition + + v = self.Gm.rmatvec(dx) + c = dx - self.Gm.matvec(df) + d = v / vdot(df, v) + + self.Gm.append(c, d) + + +class BroydenSecond(BroydenFirst): + """ + Find a root of a function, using Broyden\'s second Jacobian approximation. + + This method is also known as \"Broyden's bad method\". + + Parameters + ---------- + %(params_basic)s + %(broyden_params)s + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='broyden2'`` in particular. + + Notes + ----- + This algorithm implements the inverse Jacobian Quasi-Newton update + + .. math:: H_+ = H + (dx - H df) df^\\dagger / ( df^\\dagger df) + + corresponding to Broyden's second method. + + References + ---------- + .. [1] B.A. van der Rotten, PhD thesis, + \"A limited memory Broyden method to solve high-dimensional + systems of nonlinear equations\". Mathematisch Instituut, + Universiteit Leiden, The Netherlands (2003). + + https://web.archive.org/web/20161022015821/http://www.math.leidenuniv.nl/scripties/Rotten.pdf + + Examples + -------- + The following functions define a system of nonlinear equations + + >>> def fun(x): + ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, + ... 0.5 * (x[1] - x[0])**3 + x[1]] + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.broyden2(fun, [0, 0]) + >>> sol + array([0.84116365, 0.15883529]) + + """ + + def _update(self, x, f, dx, df, dx_norm, df_norm): + self._reduce() # reduce first to preserve secant condition + + v = df + c = dx - self.Gm.matvec(df) + d = v / df_norm**2 + self.Gm.append(c, d) + + +#------------------------------------------------------------------------------ +# Broyden-like (restricted memory) +#------------------------------------------------------------------------------ + +class Anderson(GenericBroyden): + """ + Find a root of a function, using (extended) Anderson mixing. + + The Jacobian is formed by for a 'best' solution in the space + spanned by last `M` vectors. As a result, only a MxM matrix + inversions and MxN multiplications are required. [Ey]_ + + Parameters + ---------- + %(params_basic)s + alpha : float, optional + Initial guess for the Jacobian is (-1/alpha). + M : float, optional + Number of previous vectors to retain. Defaults to 5. + w0 : float, optional + Regularization parameter for numerical stability. + Compared to unity, good values of the order of 0.01. + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='anderson'`` in particular. + + References + ---------- + .. [Ey] V. Eyert, J. Comp. Phys., 124, 271 (1996). + + Examples + -------- + The following functions define a system of nonlinear equations + + >>> def fun(x): + ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, + ... 0.5 * (x[1] - x[0])**3 + x[1]] + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.anderson(fun, [0, 0]) + >>> sol + array([0.84116588, 0.15883789]) + + """ + + # Note: + # + # Anderson method maintains a rank M approximation of the inverse Jacobian, + # + # J^-1 v ~ -v*alpha + (dX + alpha dF) A^-1 dF^H v + # A = W + dF^H dF + # W = w0^2 diag(dF^H dF) + # + # so that for w0 = 0 the secant condition applies for last M iterates, i.e., + # + # J^-1 df_j = dx_j + # + # for all j = 0 ... M-1. + # + # Moreover, (from Sherman-Morrison-Woodbury formula) + # + # J v ~ [ b I - b^2 C (I + b dF^H A^-1 C)^-1 dF^H ] v + # C = (dX + alpha dF) A^-1 + # b = -1/alpha + # + # and after simplification + # + # J v ~ -v/alpha + (dX/alpha + dF) (dF^H dX - alpha W)^-1 dF^H v + # + + def __init__(self, alpha=None, w0=0.01, M=5): + GenericBroyden.__init__(self) + self.alpha = alpha + self.M = M + self.dx = [] + self.df = [] + self.gamma = None + self.w0 = w0 + + def solve(self, f, tol=0): + dx = -self.alpha*f + + n = len(self.dx) + if n == 0: + return dx + + df_f = np.empty(n, dtype=f.dtype) + for k in range(n): + df_f[k] = vdot(self.df[k], f) + + try: + gamma = solve(self.a, df_f) + except LinAlgError: + # singular; reset the Jacobian approximation + del self.dx[:] + del self.df[:] + return dx + + for m in range(n): + dx += gamma[m]*(self.dx[m] + self.alpha*self.df[m]) + return dx + + def matvec(self, f): + dx = -f/self.alpha + + n = len(self.dx) + if n == 0: + return dx + + df_f = np.empty(n, dtype=f.dtype) + for k in range(n): + df_f[k] = vdot(self.df[k], f) + + b = np.empty((n, n), dtype=f.dtype) + for i in range(n): + for j in range(n): + b[i,j] = vdot(self.df[i], self.dx[j]) + if i == j and self.w0 != 0: + b[i,j] -= vdot(self.df[i], self.df[i])*self.w0**2*self.alpha + gamma = solve(b, df_f) + + for m in range(n): + dx += gamma[m]*(self.df[m] + self.dx[m]/self.alpha) + return dx + + def _update(self, x, f, dx, df, dx_norm, df_norm): + if self.M == 0: + return + + self.dx.append(dx) + self.df.append(df) + + while len(self.dx) > self.M: + self.dx.pop(0) + self.df.pop(0) + + n = len(self.dx) + a = np.zeros((n, n), dtype=f.dtype) + + for i in range(n): + for j in range(i, n): + if i == j: + wd = self.w0**2 + else: + wd = 0 + a[i,j] = (1+wd)*vdot(self.df[i], self.df[j]) + + a += np.triu(a, 1).T.conj() + self.a = a + +#------------------------------------------------------------------------------ +# Simple iterations +#------------------------------------------------------------------------------ + + +class DiagBroyden(GenericBroyden): + """ + Find a root of a function, using diagonal Broyden Jacobian approximation. + + The Jacobian approximation is derived from previous iterations, by + retaining only the diagonal of Broyden matrices. + + .. warning:: + + This algorithm may be useful for specific problems, but whether + it will work may depend strongly on the problem. + + Parameters + ---------- + %(params_basic)s + alpha : float, optional + Initial guess for the Jacobian is (-1/alpha). + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='diagbroyden'`` in particular. + + Examples + -------- + The following functions define a system of nonlinear equations + + >>> def fun(x): + ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, + ... 0.5 * (x[1] - x[0])**3 + x[1]] + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.diagbroyden(fun, [0, 0]) + >>> sol + array([0.84116403, 0.15883384]) + + """ + + def __init__(self, alpha=None): + GenericBroyden.__init__(self) + self.alpha = alpha + + def setup(self, x, F, func): + GenericBroyden.setup(self, x, F, func) + self.d = np.full((self.shape[0],), 1 / self.alpha, dtype=self.dtype) + + def solve(self, f, tol=0): + return -f / self.d + + def matvec(self, f): + return -f * self.d + + def rsolve(self, f, tol=0): + return -f / self.d.conj() + + def rmatvec(self, f): + return -f * self.d.conj() + + def todense(self): + return np.diag(-self.d) + + def _update(self, x, f, dx, df, dx_norm, df_norm): + self.d -= (df + self.d*dx)*dx/dx_norm**2 + + +class LinearMixing(GenericBroyden): + """ + Find a root of a function, using a scalar Jacobian approximation. + + .. warning:: + + This algorithm may be useful for specific problems, but whether + it will work may depend strongly on the problem. + + Parameters + ---------- + %(params_basic)s + alpha : float, optional + The Jacobian approximation is (-1/alpha). + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='linearmixing'`` in particular. + + """ + + def __init__(self, alpha=None): + GenericBroyden.__init__(self) + self.alpha = alpha + + def solve(self, f, tol=0): + return -f*self.alpha + + def matvec(self, f): + return -f/self.alpha + + def rsolve(self, f, tol=0): + return -f*np.conj(self.alpha) + + def rmatvec(self, f): + return -f/np.conj(self.alpha) + + def todense(self): + return np.diag(np.full(self.shape[0], -1/self.alpha)) + + def _update(self, x, f, dx, df, dx_norm, df_norm): + pass + + +class ExcitingMixing(GenericBroyden): + """ + Find a root of a function, using a tuned diagonal Jacobian approximation. + + The Jacobian matrix is diagonal and is tuned on each iteration. + + .. warning:: + + This algorithm may be useful for specific problems, but whether + it will work may depend strongly on the problem. + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='excitingmixing'`` in particular. + + Parameters + ---------- + %(params_basic)s + alpha : float, optional + Initial Jacobian approximation is (-1/alpha). + alphamax : float, optional + The entries of the diagonal Jacobian are kept in the range + ``[alpha, alphamax]``. + %(params_extra)s + """ + + def __init__(self, alpha=None, alphamax=1.0): + GenericBroyden.__init__(self) + self.alpha = alpha + self.alphamax = alphamax + self.beta = None + + def setup(self, x, F, func): + GenericBroyden.setup(self, x, F, func) + self.beta = np.full((self.shape[0],), self.alpha, dtype=self.dtype) + + def solve(self, f, tol=0): + return -f*self.beta + + def matvec(self, f): + return -f/self.beta + + def rsolve(self, f, tol=0): + return -f*self.beta.conj() + + def rmatvec(self, f): + return -f/self.beta.conj() + + def todense(self): + return np.diag(-1/self.beta) + + def _update(self, x, f, dx, df, dx_norm, df_norm): + incr = f*self.last_f > 0 + self.beta[incr] += self.alpha + self.beta[~incr] = self.alpha + np.clip(self.beta, 0, self.alphamax, out=self.beta) + + +#------------------------------------------------------------------------------ +# Iterative/Krylov approximated Jacobians +#------------------------------------------------------------------------------ + +class KrylovJacobian(Jacobian): + r""" + Find a root of a function, using Krylov approximation for inverse Jacobian. + + This method is suitable for solving large-scale problems. + + Parameters + ---------- + %(params_basic)s + rdiff : float, optional + Relative step size to use in numerical differentiation. + method : str or callable, optional + Krylov method to use to approximate the Jacobian. Can be a string, + or a function implementing the same interface as the iterative + solvers in `scipy.sparse.linalg`. If a string, needs to be one of: + ``'lgmres'``, ``'gmres'``, ``'bicgstab'``, ``'cgs'``, ``'minres'``, + ``'tfqmr'``. + + The default is `scipy.sparse.linalg.lgmres`. + inner_maxiter : int, optional + Parameter to pass to the "inner" Krylov solver: maximum number of + iterations. Iteration will stop after maxiter steps even if the + specified tolerance has not been achieved. + inner_M : LinearOperator or InverseJacobian + Preconditioner for the inner Krylov iteration. + Note that you can use also inverse Jacobians as (adaptive) + preconditioners. For example, + + >>> from scipy.optimize import BroydenFirst, KrylovJacobian + >>> from scipy.optimize import InverseJacobian + >>> jac = BroydenFirst() + >>> kjac = KrylovJacobian(inner_M=InverseJacobian(jac)) + + If the preconditioner has a method named 'update', it will be called + as ``update(x, f)`` after each nonlinear step, with ``x`` giving + the current point, and ``f`` the current function value. + outer_k : int, optional + Size of the subspace kept across LGMRES nonlinear iterations. + See `scipy.sparse.linalg.lgmres` for details. + inner_kwargs : kwargs + Keyword parameters for the "inner" Krylov solver + (defined with `method`). Parameter names must start with + the `inner_` prefix which will be stripped before passing on + the inner method. See, e.g., `scipy.sparse.linalg.gmres` for details. + %(params_extra)s + + See Also + -------- + root : Interface to root finding algorithms for multivariate + functions. See ``method='krylov'`` in particular. + scipy.sparse.linalg.gmres + scipy.sparse.linalg.lgmres + + Notes + ----- + This function implements a Newton-Krylov solver. The basic idea is + to compute the inverse of the Jacobian with an iterative Krylov + method. These methods require only evaluating the Jacobian-vector + products, which are conveniently approximated by a finite difference: + + .. math:: J v \approx (f(x + \omega*v/|v|) - f(x)) / \omega + + Due to the use of iterative matrix inverses, these methods can + deal with large nonlinear problems. + + SciPy's `scipy.sparse.linalg` module offers a selection of Krylov + solvers to choose from. The default here is `lgmres`, which is a + variant of restarted GMRES iteration that reuses some of the + information obtained in the previous Newton steps to invert + Jacobians in subsequent steps. + + For a review on Newton-Krylov methods, see for example [1]_, + and for the LGMRES sparse inverse method, see [2]_. + + References + ---------- + .. [1] C. T. Kelley, Solving Nonlinear Equations with Newton's Method, + SIAM, pp.57-83, 2003. + :doi:`10.1137/1.9780898718898.ch3` + .. [2] D.A. Knoll and D.E. Keyes, J. Comp. Phys. 193, 357 (2004). + :doi:`10.1016/j.jcp.2003.08.010` + .. [3] A.H. Baker and E.R. Jessup and T. Manteuffel, + SIAM J. Matrix Anal. Appl. 26, 962 (2005). + :doi:`10.1137/S0895479803422014` + + Examples + -------- + The following functions define a system of nonlinear equations + + >>> def fun(x): + ... return [x[0] + 0.5 * x[1] - 1.0, + ... 0.5 * (x[1] - x[0]) ** 2] + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.newton_krylov(fun, [0, 0]) + >>> sol + array([0.66731771, 0.66536458]) + + """ + + def __init__(self, rdiff=None, method='lgmres', inner_maxiter=20, + inner_M=None, outer_k=10, **kw): + self.preconditioner = inner_M + self.rdiff = rdiff + # Note that this retrieves one of the named functions, or otherwise + # uses `method` as is (i.e., for a user-provided callable). + self.method = dict( + bicgstab=scipy.sparse.linalg.bicgstab, + gmres=scipy.sparse.linalg.gmres, + lgmres=scipy.sparse.linalg.lgmres, + cgs=scipy.sparse.linalg.cgs, + minres=scipy.sparse.linalg.minres, + tfqmr=scipy.sparse.linalg.tfqmr, + ).get(method, method) + + self.method_kw = dict(maxiter=inner_maxiter, M=self.preconditioner) + + if self.method is scipy.sparse.linalg.gmres: + # Replace GMRES's outer iteration with Newton steps + self.method_kw['restart'] = inner_maxiter + self.method_kw['maxiter'] = 1 + self.method_kw.setdefault('atol', 0) + elif self.method in (scipy.sparse.linalg.gcrotmk, + scipy.sparse.linalg.bicgstab, + scipy.sparse.linalg.cgs): + self.method_kw.setdefault('atol', 0) + elif self.method is scipy.sparse.linalg.lgmres: + self.method_kw['outer_k'] = outer_k + # Replace LGMRES's outer iteration with Newton steps + self.method_kw['maxiter'] = 1 + # Carry LGMRES's `outer_v` vectors across nonlinear iterations + self.method_kw.setdefault('outer_v', []) + self.method_kw.setdefault('prepend_outer_v', True) + # But don't carry the corresponding Jacobian*v products, in case + # the Jacobian changes a lot in the nonlinear step + # + # XXX: some trust-region inspired ideas might be more efficient... + # See e.g., Brown & Saad. But needs to be implemented separately + # since it's not an inexact Newton method. + self.method_kw.setdefault('store_outer_Av', False) + self.method_kw.setdefault('atol', 0) + + for key, value in kw.items(): + if not key.startswith('inner_'): + raise ValueError("Unknown parameter %s" % key) + self.method_kw[key[6:]] = value + + def _update_diff_step(self): + mx = abs(self.x0).max() + mf = abs(self.f0).max() + self.omega = self.rdiff * max(1, mx) / max(1, mf) + + def matvec(self, v): + nv = norm(v) + if nv == 0: + return 0*v + sc = self.omega / nv + r = (self.func(self.x0 + sc*v) - self.f0) / sc + if not np.all(np.isfinite(r)) and np.all(np.isfinite(v)): + raise ValueError('Function returned non-finite results') + return r + + def solve(self, rhs, tol=0): + if 'rtol' in self.method_kw: + sol, info = self.method(self.op, rhs, **self.method_kw) + else: + sol, info = self.method(self.op, rhs, rtol=tol, **self.method_kw) + return sol + + def update(self, x, f): + self.x0 = x + self.f0 = f + self._update_diff_step() + + # Update also the preconditioner, if possible + if self.preconditioner is not None: + if hasattr(self.preconditioner, 'update'): + self.preconditioner.update(x, f) + + def setup(self, x, f, func): + Jacobian.setup(self, x, f, func) + self.x0 = x + self.f0 = f + self.op = scipy.sparse.linalg.aslinearoperator(self) + + if self.rdiff is None: + self.rdiff = np.finfo(x.dtype).eps ** (1./2) + + self._update_diff_step() + + # Setup also the preconditioner, if possible + if self.preconditioner is not None: + if hasattr(self.preconditioner, 'setup'): + self.preconditioner.setup(x, f, func) + + +#------------------------------------------------------------------------------ +# Wrapper functions +#------------------------------------------------------------------------------ + +def _nonlin_wrapper(name, jac): + """ + Construct a solver wrapper with given name and Jacobian approx. + + It inspects the keyword arguments of ``jac.__init__``, and allows to + use the same arguments in the wrapper function, in addition to the + keyword arguments of `nonlin_solve` + + """ + signature = _getfullargspec(jac.__init__) + args, varargs, varkw, defaults, kwonlyargs, kwdefaults, _ = signature + kwargs = list(zip(args[-len(defaults):], defaults)) + kw_str = ", ".join([f"{k}={v!r}" for k, v in kwargs]) + if kw_str: + kw_str = ", " + kw_str + kwkw_str = ", ".join([f"{k}={k}" for k, v in kwargs]) + if kwkw_str: + kwkw_str = kwkw_str + ", " + if kwonlyargs: + raise ValueError('Unexpected signature %s' % signature) + + # Construct the wrapper function so that its keyword arguments + # are visible in pydoc.help etc. + wrapper = """ +def %(name)s(F, xin, iter=None %(kw)s, verbose=False, maxiter=None, + f_tol=None, f_rtol=None, x_tol=None, x_rtol=None, + tol_norm=None, line_search='armijo', callback=None, **kw): + jac = %(jac)s(%(kwkw)s **kw) + return nonlin_solve(F, xin, jac, iter, verbose, maxiter, + f_tol, f_rtol, x_tol, x_rtol, tol_norm, line_search, + callback) +""" + + wrapper = wrapper % dict(name=name, kw=kw_str, jac=jac.__name__, + kwkw=kwkw_str) + ns = {} + ns.update(globals()) + exec(wrapper, ns) + func = ns[name] + func.__doc__ = jac.__doc__ + _set_doc(func) + return func + + +broyden1 = _nonlin_wrapper('broyden1', BroydenFirst) +broyden2 = _nonlin_wrapper('broyden2', BroydenSecond) +anderson = _nonlin_wrapper('anderson', Anderson) +linearmixing = _nonlin_wrapper('linearmixing', LinearMixing) +diagbroyden = _nonlin_wrapper('diagbroyden', DiagBroyden) +excitingmixing = _nonlin_wrapper('excitingmixing', ExcitingMixing) +newton_krylov = _nonlin_wrapper('newton_krylov', KrylovJacobian) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_numdiff.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_numdiff.py new file mode 100644 index 0000000000000000000000000000000000000000..b5cb5724d8636bd149906a6356ac97bae169e289 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_numdiff.py @@ -0,0 +1,779 @@ +"""Routines for numerical differentiation.""" +import functools +import numpy as np +from numpy.linalg import norm + +from scipy.sparse.linalg import LinearOperator +from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find +from ._group_columns import group_dense, group_sparse +from scipy._lib._array_api import atleast_nd, array_namespace + + +def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub): + """Adjust final difference scheme to the presence of bounds. + + Parameters + ---------- + x0 : ndarray, shape (n,) + Point at which we wish to estimate derivative. + h : ndarray, shape (n,) + Desired absolute finite difference steps. + num_steps : int + Number of `h` steps in one direction required to implement finite + difference scheme. For example, 2 means that we need to evaluate + f(x0 + 2 * h) or f(x0 - 2 * h) + scheme : {'1-sided', '2-sided'} + Whether steps in one or both directions are required. In other + words '1-sided' applies to forward and backward schemes, '2-sided' + applies to center schemes. + lb : ndarray, shape (n,) + Lower bounds on independent variables. + ub : ndarray, shape (n,) + Upper bounds on independent variables. + + Returns + ------- + h_adjusted : ndarray, shape (n,) + Adjusted absolute step sizes. Step size decreases only if a sign flip + or switching to one-sided scheme doesn't allow to take a full step. + use_one_sided : ndarray of bool, shape (n,) + Whether to switch to one-sided scheme. Informative only for + ``scheme='2-sided'``. + """ + if scheme == '1-sided': + use_one_sided = np.ones_like(h, dtype=bool) + elif scheme == '2-sided': + h = np.abs(h) + use_one_sided = np.zeros_like(h, dtype=bool) + else: + raise ValueError("`scheme` must be '1-sided' or '2-sided'.") + + if np.all((lb == -np.inf) & (ub == np.inf)): + return h, use_one_sided + + h_total = h * num_steps + h_adjusted = h.copy() + + lower_dist = x0 - lb + upper_dist = ub - x0 + + if scheme == '1-sided': + x = x0 + h_total + violated = (x < lb) | (x > ub) + fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist) + h_adjusted[violated & fitting] *= -1 + + forward = (upper_dist >= lower_dist) & ~fitting + h_adjusted[forward] = upper_dist[forward] / num_steps + backward = (upper_dist < lower_dist) & ~fitting + h_adjusted[backward] = -lower_dist[backward] / num_steps + elif scheme == '2-sided': + central = (lower_dist >= h_total) & (upper_dist >= h_total) + + forward = (upper_dist >= lower_dist) & ~central + h_adjusted[forward] = np.minimum( + h[forward], 0.5 * upper_dist[forward] / num_steps) + use_one_sided[forward] = True + + backward = (upper_dist < lower_dist) & ~central + h_adjusted[backward] = -np.minimum( + h[backward], 0.5 * lower_dist[backward] / num_steps) + use_one_sided[backward] = True + + min_dist = np.minimum(upper_dist, lower_dist) / num_steps + adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist)) + h_adjusted[adjusted_central] = min_dist[adjusted_central] + use_one_sided[adjusted_central] = False + + return h_adjusted, use_one_sided + + +@functools.lru_cache +def _eps_for_method(x0_dtype, f0_dtype, method): + """ + Calculates relative EPS step to use for a given data type + and numdiff step method. + + Progressively smaller steps are used for larger floating point types. + + Parameters + ---------- + f0_dtype: np.dtype + dtype of function evaluation + + x0_dtype: np.dtype + dtype of parameter vector + + method: {'2-point', '3-point', 'cs'} + + Returns + ------- + EPS: float + relative step size. May be np.float16, np.float32, np.float64 + + Notes + ----- + The default relative step will be np.float64. However, if x0 or f0 are + smaller floating point types (np.float16, np.float32), then the smallest + floating point type is chosen. + """ + # the default EPS value + EPS = np.finfo(np.float64).eps + + x0_is_fp = False + if np.issubdtype(x0_dtype, np.inexact): + # if you're a floating point type then over-ride the default EPS + EPS = np.finfo(x0_dtype).eps + x0_itemsize = np.dtype(x0_dtype).itemsize + x0_is_fp = True + + if np.issubdtype(f0_dtype, np.inexact): + f0_itemsize = np.dtype(f0_dtype).itemsize + # choose the smallest itemsize between x0 and f0 + if x0_is_fp and f0_itemsize < x0_itemsize: + EPS = np.finfo(f0_dtype).eps + + if method in ["2-point", "cs"]: + return EPS**0.5 + elif method in ["3-point"]: + return EPS**(1/3) + else: + raise RuntimeError("Unknown step method, should be one of " + "{'2-point', '3-point', 'cs'}") + + +def _compute_absolute_step(rel_step, x0, f0, method): + """ + Computes an absolute step from a relative step for finite difference + calculation. + + Parameters + ---------- + rel_step: None or array-like + Relative step for the finite difference calculation + x0 : np.ndarray + Parameter vector + f0 : np.ndarray or scalar + method : {'2-point', '3-point', 'cs'} + + Returns + ------- + h : float + The absolute step size + + Notes + ----- + `h` will always be np.float64. However, if `x0` or `f0` are + smaller floating point dtypes (e.g. np.float32), then the absolute + step size will be calculated from the smallest floating point size. + """ + # this is used instead of np.sign(x0) because we need + # sign_x0 to be 1 when x0 == 0. + sign_x0 = (x0 >= 0).astype(float) * 2 - 1 + + rstep = _eps_for_method(x0.dtype, f0.dtype, method) + + if rel_step is None: + abs_step = rstep * sign_x0 * np.maximum(1.0, np.abs(x0)) + else: + # User has requested specific relative steps. + # Don't multiply by max(1, abs(x0) because if x0 < 1 then their + # requested step is not used. + abs_step = rel_step * sign_x0 * np.abs(x0) + + # however we don't want an abs_step of 0, which can happen if + # rel_step is 0, or x0 is 0. Instead, substitute a realistic step + dx = ((x0 + abs_step) - x0) + abs_step = np.where(dx == 0, + rstep * sign_x0 * np.maximum(1.0, np.abs(x0)), + abs_step) + + return abs_step + + +def _prepare_bounds(bounds, x0): + """ + Prepares new-style bounds from a two-tuple specifying the lower and upper + limits for values in x0. If a value is not bound then the lower/upper bound + will be expected to be -np.inf/np.inf. + + Examples + -------- + >>> _prepare_bounds([(0, 1, 2), (1, 2, np.inf)], [0.5, 1.5, 2.5]) + (array([0., 1., 2.]), array([ 1., 2., inf])) + """ + lb, ub = (np.asarray(b, dtype=float) for b in bounds) + if lb.ndim == 0: + lb = np.resize(lb, x0.shape) + + if ub.ndim == 0: + ub = np.resize(ub, x0.shape) + + return lb, ub + + +def group_columns(A, order=0): + """Group columns of a 2-D matrix for sparse finite differencing [1]_. + + Two columns are in the same group if in each row at least one of them + has zero. A greedy sequential algorithm is used to construct groups. + + Parameters + ---------- + A : array_like or sparse matrix, shape (m, n) + Matrix of which to group columns. + order : int, iterable of int with shape (n,) or None + Permutation array which defines the order of columns enumeration. + If int or None, a random permutation is used with `order` used as + a random seed. Default is 0, that is use a random permutation but + guarantee repeatability. + + Returns + ------- + groups : ndarray of int, shape (n,) + Contains values from 0 to n_groups-1, where n_groups is the number + of found groups. Each value ``groups[i]`` is an index of a group to + which ith column assigned. The procedure was helpful only if + n_groups is significantly less than n. + + References + ---------- + .. [1] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of + sparse Jacobian matrices", Journal of the Institute of Mathematics + and its Applications, 13 (1974), pp. 117-120. + """ + if issparse(A): + A = csc_matrix(A) + else: + A = np.atleast_2d(A) + A = (A != 0).astype(np.int32) + + if A.ndim != 2: + raise ValueError("`A` must be 2-dimensional.") + + m, n = A.shape + + if order is None or np.isscalar(order): + rng = np.random.RandomState(order) + order = rng.permutation(n) + else: + order = np.asarray(order) + if order.shape != (n,): + raise ValueError("`order` has incorrect shape.") + + A = A[:, order] + + if issparse(A): + groups = group_sparse(m, n, A.indices, A.indptr) + else: + groups = group_dense(m, n, A) + + groups[order] = groups.copy() + + return groups + + +def approx_derivative(fun, x0, method='3-point', rel_step=None, abs_step=None, + f0=None, bounds=(-np.inf, np.inf), sparsity=None, + as_linear_operator=False, args=(), kwargs={}): + """Compute finite difference approximation of the derivatives of a + vector-valued function. + + If a function maps from R^n to R^m, its derivatives form m-by-n matrix + called the Jacobian, where an element (i, j) is a partial derivative of + f[i] with respect to x[j]. + + Parameters + ---------- + fun : callable + Function of which to estimate the derivatives. The argument x + passed to this function is ndarray of shape (n,) (never a scalar + even if n=1). It must return 1-D array_like of shape (m,) or a scalar. + x0 : array_like of shape (n,) or float + Point at which to estimate the derivatives. Float will be converted + to a 1-D array. + method : {'3-point', '2-point', 'cs'}, optional + Finite difference method to use: + - '2-point' - use the first order accuracy forward or backward + difference. + - '3-point' - use central difference in interior points and the + second order accuracy forward or backward difference + near the boundary. + - 'cs' - use a complex-step finite difference scheme. This assumes + that the user function is real-valued and can be + analytically continued to the complex plane. Otherwise, + produces bogus results. + rel_step : None or array_like, optional + Relative step size to use. If None (default) the absolute step size is + computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, with + `rel_step` being selected automatically, see Notes. Otherwise + ``h = rel_step * sign(x0) * abs(x0)``. For ``method='3-point'`` the + sign of `h` is ignored. The calculated step size is possibly adjusted + to fit into the bounds. + abs_step : array_like, optional + Absolute step size to use, possibly adjusted to fit into the bounds. + For ``method='3-point'`` the sign of `abs_step` is ignored. By default + relative steps are used, only if ``abs_step is not None`` are absolute + steps used. + f0 : None or array_like, optional + If not None it is assumed to be equal to ``fun(x0)``, in this case + the ``fun(x0)`` is not called. Default is None. + bounds : tuple of array_like, optional + Lower and upper bounds on independent variables. Defaults to no bounds. + Each bound must match the size of `x0` or be a scalar, in the latter + case the bound will be the same for all variables. Use it to limit the + range of function evaluation. Bounds checking is not implemented + when `as_linear_operator` is True. + sparsity : {None, array_like, sparse matrix, 2-tuple}, optional + Defines a sparsity structure of the Jacobian matrix. If the Jacobian + matrix is known to have only few non-zero elements in each row, then + it's possible to estimate its several columns by a single function + evaluation [3]_. To perform such economic computations two ingredients + are required: + + * structure : array_like or sparse matrix of shape (m, n). A zero + element means that a corresponding element of the Jacobian + identically equals to zero. + * groups : array_like of shape (n,). A column grouping for a given + sparsity structure, use `group_columns` to obtain it. + + A single array or a sparse matrix is interpreted as a sparsity + structure, and groups are computed inside the function. A tuple is + interpreted as (structure, groups). If None (default), a standard + dense differencing will be used. + + Note, that sparse differencing makes sense only for large Jacobian + matrices where each row contains few non-zero elements. + as_linear_operator : bool, optional + When True the function returns an `scipy.sparse.linalg.LinearOperator`. + Otherwise it returns a dense array or a sparse matrix depending on + `sparsity`. The linear operator provides an efficient way of computing + ``J.dot(p)`` for any vector ``p`` of shape (n,), but does not allow + direct access to individual elements of the matrix. By default + `as_linear_operator` is False. + args, kwargs : tuple and dict, optional + Additional arguments passed to `fun`. Both empty by default. + The calling signature is ``fun(x, *args, **kwargs)``. + + Returns + ------- + J : {ndarray, sparse matrix, LinearOperator} + Finite difference approximation of the Jacobian matrix. + If `as_linear_operator` is True returns a LinearOperator + with shape (m, n). Otherwise it returns a dense array or sparse + matrix depending on how `sparsity` is defined. If `sparsity` + is None then a ndarray with shape (m, n) is returned. If + `sparsity` is not None returns a csr_matrix with shape (m, n). + For sparse matrices and linear operators it is always returned as + a 2-D structure, for ndarrays, if m=1 it is returned + as a 1-D gradient array with shape (n,). + + See Also + -------- + check_derivative : Check correctness of a function computing derivatives. + + Notes + ----- + If `rel_step` is not provided, it assigned as ``EPS**(1/s)``, where EPS is + determined from the smallest floating point dtype of `x0` or `fun(x0)`, + ``np.finfo(x0.dtype).eps``, s=2 for '2-point' method and + s=3 for '3-point' method. Such relative step approximately minimizes a sum + of truncation and round-off errors, see [1]_. Relative steps are used by + default. However, absolute steps are used when ``abs_step is not None``. + If any of the absolute or relative steps produces an indistinguishable + difference from the original `x0`, ``(x0 + dx) - x0 == 0``, then a + automatic step size is substituted for that particular entry. + + A finite difference scheme for '3-point' method is selected automatically. + The well-known central difference scheme is used for points sufficiently + far from the boundary, and 3-point forward or backward scheme is used for + points near the boundary. Both schemes have the second-order accuracy in + terms of Taylor expansion. Refer to [2]_ for the formulas of 3-point + forward and backward difference schemes. + + For dense differencing when m=1 Jacobian is returned with a shape (n,), + on the other hand when n=1 Jacobian is returned with a shape (m, 1). + Our motivation is the following: a) It handles a case of gradient + computation (m=1) in a conventional way. b) It clearly separates these two + different cases. b) In all cases np.atleast_2d can be called to get 2-D + Jacobian with correct dimensions. + + References + ---------- + .. [1] W. H. Press et. al. "Numerical Recipes. The Art of Scientific + Computing. 3rd edition", sec. 5.7. + + .. [2] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of + sparse Jacobian matrices", Journal of the Institute of Mathematics + and its Applications, 13 (1974), pp. 117-120. + + .. [3] B. Fornberg, "Generation of Finite Difference Formulas on + Arbitrarily Spaced Grids", Mathematics of Computation 51, 1988. + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize._numdiff import approx_derivative + >>> + >>> def f(x, c1, c2): + ... return np.array([x[0] * np.sin(c1 * x[1]), + ... x[0] * np.cos(c2 * x[1])]) + ... + >>> x0 = np.array([1.0, 0.5 * np.pi]) + >>> approx_derivative(f, x0, args=(1, 2)) + array([[ 1., 0.], + [-1., 0.]]) + + Bounds can be used to limit the region of function evaluation. + In the example below we compute left and right derivative at point 1.0. + + >>> def g(x): + ... return x**2 if x >= 1 else x + ... + >>> x0 = 1.0 + >>> approx_derivative(g, x0, bounds=(-np.inf, 1.0)) + array([ 1.]) + >>> approx_derivative(g, x0, bounds=(1.0, np.inf)) + array([ 2.]) + """ + if method not in ['2-point', '3-point', 'cs']: + raise ValueError("Unknown method '%s'. " % method) + + xp = array_namespace(x0) + _x = atleast_nd(x0, ndim=1, xp=xp) + _dtype = xp.float64 + if xp.isdtype(_x.dtype, "real floating"): + _dtype = _x.dtype + + # promotes to floating + x0 = xp.astype(_x, _dtype) + + if x0.ndim > 1: + raise ValueError("`x0` must have at most 1 dimension.") + + lb, ub = _prepare_bounds(bounds, x0) + + if lb.shape != x0.shape or ub.shape != x0.shape: + raise ValueError("Inconsistent shapes between bounds and `x0`.") + + if as_linear_operator and not (np.all(np.isinf(lb)) + and np.all(np.isinf(ub))): + raise ValueError("Bounds not supported when " + "`as_linear_operator` is True.") + + def fun_wrapped(x): + # send user function same fp type as x0. (but only if cs is not being + # used + if xp.isdtype(x.dtype, "real floating"): + x = xp.astype(x, x0.dtype) + + f = np.atleast_1d(fun(x, *args, **kwargs)) + if f.ndim > 1: + raise RuntimeError("`fun` return value has " + "more than 1 dimension.") + return f + + if f0 is None: + f0 = fun_wrapped(x0) + else: + f0 = np.atleast_1d(f0) + if f0.ndim > 1: + raise ValueError("`f0` passed has more than 1 dimension.") + + if np.any((x0 < lb) | (x0 > ub)): + raise ValueError("`x0` violates bound constraints.") + + if as_linear_operator: + if rel_step is None: + rel_step = _eps_for_method(x0.dtype, f0.dtype, method) + + return _linear_operator_difference(fun_wrapped, x0, + f0, rel_step, method) + else: + # by default we use rel_step + if abs_step is None: + h = _compute_absolute_step(rel_step, x0, f0, method) + else: + # user specifies an absolute step + sign_x0 = (x0 >= 0).astype(float) * 2 - 1 + h = abs_step + + # cannot have a zero step. This might happen if x0 is very large + # or small. In which case fall back to relative step. + dx = ((x0 + h) - x0) + h = np.where(dx == 0, + _eps_for_method(x0.dtype, f0.dtype, method) * + sign_x0 * np.maximum(1.0, np.abs(x0)), + h) + + if method == '2-point': + h, use_one_sided = _adjust_scheme_to_bounds( + x0, h, 1, '1-sided', lb, ub) + elif method == '3-point': + h, use_one_sided = _adjust_scheme_to_bounds( + x0, h, 1, '2-sided', lb, ub) + elif method == 'cs': + use_one_sided = False + + if sparsity is None: + return _dense_difference(fun_wrapped, x0, f0, h, + use_one_sided, method) + else: + if not issparse(sparsity) and len(sparsity) == 2: + structure, groups = sparsity + else: + structure = sparsity + groups = group_columns(sparsity) + + if issparse(structure): + structure = csc_matrix(structure) + else: + structure = np.atleast_2d(structure) + + groups = np.atleast_1d(groups) + return _sparse_difference(fun_wrapped, x0, f0, h, + use_one_sided, structure, + groups, method) + + +def _linear_operator_difference(fun, x0, f0, h, method): + m = f0.size + n = x0.size + + if method == '2-point': + def matvec(p): + if np.array_equal(p, np.zeros_like(p)): + return np.zeros(m) + dx = h / norm(p) + x = x0 + dx*p + df = fun(x) - f0 + return df / dx + + elif method == '3-point': + def matvec(p): + if np.array_equal(p, np.zeros_like(p)): + return np.zeros(m) + dx = 2*h / norm(p) + x1 = x0 - (dx/2)*p + x2 = x0 + (dx/2)*p + f1 = fun(x1) + f2 = fun(x2) + df = f2 - f1 + return df / dx + + elif method == 'cs': + def matvec(p): + if np.array_equal(p, np.zeros_like(p)): + return np.zeros(m) + dx = h / norm(p) + x = x0 + dx*p*1.j + f1 = fun(x) + df = f1.imag + return df / dx + + else: + raise RuntimeError("Never be here.") + + return LinearOperator((m, n), matvec) + + +def _dense_difference(fun, x0, f0, h, use_one_sided, method): + m = f0.size + n = x0.size + J_transposed = np.empty((n, m)) + x1 = x0.copy() + x2 = x0.copy() + xc = x0.astype(complex, copy=True) + + for i in range(h.size): + if method == '2-point': + x1[i] += h[i] + dx = x1[i] - x0[i] # Recompute dx as exactly representable number. + df = fun(x1) - f0 + elif method == '3-point' and use_one_sided[i]: + x1[i] += h[i] + x2[i] += 2 * h[i] + dx = x2[i] - x0[i] + f1 = fun(x1) + f2 = fun(x2) + df = -3.0 * f0 + 4 * f1 - f2 + elif method == '3-point' and not use_one_sided[i]: + x1[i] -= h[i] + x2[i] += h[i] + dx = x2[i] - x1[i] + f1 = fun(x1) + f2 = fun(x2) + df = f2 - f1 + elif method == 'cs': + xc[i] += h[i] * 1.j + f1 = fun(xc) + df = f1.imag + dx = h[i] + else: + raise RuntimeError("Never be here.") + + J_transposed[i] = df / dx + x1[i] = x2[i] = xc[i] = x0[i] + + if m == 1: + J_transposed = np.ravel(J_transposed) + + return J_transposed.T + + +def _sparse_difference(fun, x0, f0, h, use_one_sided, + structure, groups, method): + m = f0.size + n = x0.size + row_indices = [] + col_indices = [] + fractions = [] + + n_groups = np.max(groups) + 1 + for group in range(n_groups): + # Perturb variables which are in the same group simultaneously. + e = np.equal(group, groups) + h_vec = h * e + if method == '2-point': + x = x0 + h_vec + dx = x - x0 + df = fun(x) - f0 + # The result is written to columns which correspond to perturbed + # variables. + cols, = np.nonzero(e) + # Find all non-zero elements in selected columns of Jacobian. + i, j, _ = find(structure[:, cols]) + # Restore column indices in the full array. + j = cols[j] + elif method == '3-point': + # Here we do conceptually the same but separate one-sided + # and two-sided schemes. + x1 = x0.copy() + x2 = x0.copy() + + mask_1 = use_one_sided & e + x1[mask_1] += h_vec[mask_1] + x2[mask_1] += 2 * h_vec[mask_1] + + mask_2 = ~use_one_sided & e + x1[mask_2] -= h_vec[mask_2] + x2[mask_2] += h_vec[mask_2] + + dx = np.zeros(n) + dx[mask_1] = x2[mask_1] - x0[mask_1] + dx[mask_2] = x2[mask_2] - x1[mask_2] + + f1 = fun(x1) + f2 = fun(x2) + + cols, = np.nonzero(e) + i, j, _ = find(structure[:, cols]) + j = cols[j] + + mask = use_one_sided[j] + df = np.empty(m) + + rows = i[mask] + df[rows] = -3 * f0[rows] + 4 * f1[rows] - f2[rows] + + rows = i[~mask] + df[rows] = f2[rows] - f1[rows] + elif method == 'cs': + f1 = fun(x0 + h_vec*1.j) + df = f1.imag + dx = h_vec + cols, = np.nonzero(e) + i, j, _ = find(structure[:, cols]) + j = cols[j] + else: + raise ValueError("Never be here.") + + # All that's left is to compute the fraction. We store i, j and + # fractions as separate arrays and later construct coo_matrix. + row_indices.append(i) + col_indices.append(j) + fractions.append(df[i] / dx[j]) + + row_indices = np.hstack(row_indices) + col_indices = np.hstack(col_indices) + fractions = np.hstack(fractions) + J = coo_matrix((fractions, (row_indices, col_indices)), shape=(m, n)) + return csr_matrix(J) + + +def check_derivative(fun, jac, x0, bounds=(-np.inf, np.inf), args=(), + kwargs={}): + """Check correctness of a function computing derivatives (Jacobian or + gradient) by comparison with a finite difference approximation. + + Parameters + ---------- + fun : callable + Function of which to estimate the derivatives. The argument x + passed to this function is ndarray of shape (n,) (never a scalar + even if n=1). It must return 1-D array_like of shape (m,) or a scalar. + jac : callable + Function which computes Jacobian matrix of `fun`. It must work with + argument x the same way as `fun`. The return value must be array_like + or sparse matrix with an appropriate shape. + x0 : array_like of shape (n,) or float + Point at which to estimate the derivatives. Float will be converted + to 1-D array. + bounds : 2-tuple of array_like, optional + Lower and upper bounds on independent variables. Defaults to no bounds. + Each bound must match the size of `x0` or be a scalar, in the latter + case the bound will be the same for all variables. Use it to limit the + range of function evaluation. + args, kwargs : tuple and dict, optional + Additional arguments passed to `fun` and `jac`. Both empty by default. + The calling signature is ``fun(x, *args, **kwargs)`` and the same + for `jac`. + + Returns + ------- + accuracy : float + The maximum among all relative errors for elements with absolute values + higher than 1 and absolute errors for elements with absolute values + less or equal than 1. If `accuracy` is on the order of 1e-6 or lower, + then it is likely that your `jac` implementation is correct. + + See Also + -------- + approx_derivative : Compute finite difference approximation of derivative. + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize._numdiff import check_derivative + >>> + >>> + >>> def f(x, c1, c2): + ... return np.array([x[0] * np.sin(c1 * x[1]), + ... x[0] * np.cos(c2 * x[1])]) + ... + >>> def jac(x, c1, c2): + ... return np.array([ + ... [np.sin(c1 * x[1]), c1 * x[0] * np.cos(c1 * x[1])], + ... [np.cos(c2 * x[1]), -c2 * x[0] * np.sin(c2 * x[1])] + ... ]) + ... + >>> + >>> x0 = np.array([1.0, 0.5 * np.pi]) + >>> check_derivative(f, jac, x0, args=(1, 2)) + 2.4492935982947064e-16 + """ + J_to_test = jac(x0, *args, **kwargs) + if issparse(J_to_test): + J_diff = approx_derivative(fun, x0, bounds=bounds, sparsity=J_to_test, + args=args, kwargs=kwargs) + J_to_test = csr_matrix(J_to_test) + abs_err = J_to_test - J_diff + i, j, abs_err_data = find(abs_err) + J_diff_data = np.asarray(J_diff[i, j]).ravel() + return np.max(np.abs(abs_err_data) / + np.maximum(1, np.abs(J_diff_data))) + else: + J_diff = approx_derivative(fun, x0, bounds=bounds, + args=args, kwargs=kwargs) + abs_err = np.abs(J_to_test - J_diff) + return np.max(abs_err / np.maximum(1, np.abs(J_diff))) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_optimize.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_optimize.py new file mode 100644 index 0000000000000000000000000000000000000000..37472486fd53ca6ae6bb6c64a3fc0a36eb6fac7e --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_optimize.py @@ -0,0 +1,4093 @@ +#__docformat__ = "restructuredtext en" +# ******NOTICE*************** +# optimize.py module by Travis E. Oliphant +# +# You may copy and use this module as you see fit with no +# guarantee implied provided you keep this notice in all copies. +# *****END NOTICE************ + +# A collection of optimization algorithms. Version 0.5 +# CHANGES +# Added fminbound (July 2001) +# Added brute (Aug. 2002) +# Finished line search satisfying strong Wolfe conditions (Mar. 2004) +# Updated strong Wolfe conditions line search to use +# cubic-interpolation (Mar. 2004) + + +# Minimization routines + +__all__ = ['fmin', 'fmin_powell', 'fmin_bfgs', 'fmin_ncg', 'fmin_cg', + 'fminbound', 'brent', 'golden', 'bracket', 'rosen', 'rosen_der', + 'rosen_hess', 'rosen_hess_prod', 'brute', 'approx_fprime', + 'line_search', 'check_grad', 'OptimizeResult', 'show_options', + 'OptimizeWarning'] + +__docformat__ = "restructuredtext en" + +import math +import warnings +import sys +import inspect +from numpy import (atleast_1d, eye, argmin, zeros, shape, squeeze, + asarray, sqrt) +import numpy as np +from scipy.linalg import cholesky, issymmetric, LinAlgError +from scipy.sparse.linalg import LinearOperator +from ._linesearch import (line_search_wolfe1, line_search_wolfe2, + line_search_wolfe2 as line_search, + LineSearchWarning) +from ._numdiff import approx_derivative +from scipy._lib._util import getfullargspec_no_self as _getfullargspec +from scipy._lib._util import (MapWrapper, check_random_state, _RichResult, + _call_callback_maybe_halt) +from scipy.optimize._differentiable_functions import ScalarFunction, FD_METHODS + + +# standard status messages of optimizers +_status_message = {'success': 'Optimization terminated successfully.', + 'maxfev': 'Maximum number of function evaluations has ' + 'been exceeded.', + 'maxiter': 'Maximum number of iterations has been ' + 'exceeded.', + 'pr_loss': 'Desired error not necessarily achieved due ' + 'to precision loss.', + 'nan': 'NaN result encountered.', + 'out_of_bounds': 'The result is outside of the provided ' + 'bounds.'} + + +class MemoizeJac: + """ Decorator that caches the return values of a function returning `(fun, grad)` + each time it is called. """ + + def __init__(self, fun): + self.fun = fun + self.jac = None + self._value = None + self.x = None + + def _compute_if_needed(self, x, *args): + if not np.all(x == self.x) or self._value is None or self.jac is None: + self.x = np.asarray(x).copy() + fg = self.fun(x, *args) + self.jac = fg[1] + self._value = fg[0] + + def __call__(self, x, *args): + """ returns the function value """ + self._compute_if_needed(x, *args) + return self._value + + def derivative(self, x, *args): + self._compute_if_needed(x, *args) + return self.jac + + +def _wrap_callback(callback, method=None): + """Wrap a user-provided callback so that attributes can be attached.""" + if callback is None or method in {'tnc', 'slsqp', 'cobyla', 'cobyqa'}: + return callback # don't wrap + + sig = inspect.signature(callback) + + if set(sig.parameters) == {'intermediate_result'}: + def wrapped_callback(res): + return callback(intermediate_result=res) + elif method == 'trust-constr': + def wrapped_callback(res): + return callback(np.copy(res.x), res) + elif method == 'differential_evolution': + def wrapped_callback(res): + return callback(np.copy(res.x), res.convergence) + else: + def wrapped_callback(res): + return callback(np.copy(res.x)) + + wrapped_callback.stop_iteration = False + return wrapped_callback + + +class OptimizeResult(_RichResult): + """ + Represents the optimization result. + + Attributes + ---------- + x : ndarray + The solution of the optimization. + success : bool + Whether or not the optimizer exited successfully. + status : int + Termination status of the optimizer. Its value depends on the + underlying solver. Refer to `message` for details. + message : str + Description of the cause of the termination. + fun, jac, hess: ndarray + Values of objective function, its Jacobian and its Hessian (if + available). The Hessians may be approximations, see the documentation + of the function in question. + hess_inv : object + Inverse of the objective function's Hessian; may be an approximation. + Not available for all solvers. The type of this attribute may be + either np.ndarray or scipy.sparse.linalg.LinearOperator. + nfev, njev, nhev : int + Number of evaluations of the objective functions and of its + Jacobian and Hessian. + nit : int + Number of iterations performed by the optimizer. + maxcv : float + The maximum constraint violation. + + Notes + ----- + Depending on the specific solver being used, `OptimizeResult` may + not have all attributes listed here, and they may have additional + attributes not listed here. Since this class is essentially a + subclass of dict with attribute accessors, one can see which + attributes are available using the `OptimizeResult.keys` method. + + """ + pass + + +class OptimizeWarning(UserWarning): + pass + +def _check_positive_definite(Hk): + def is_pos_def(A): + if issymmetric(A): + try: + cholesky(A) + return True + except LinAlgError: + return False + else: + return False + if Hk is not None: + if not is_pos_def(Hk): + raise ValueError("'hess_inv0' matrix isn't positive definite.") + + +def _check_unknown_options(unknown_options): + if unknown_options: + msg = ", ".join(map(str, unknown_options.keys())) + # Stack level 4: this is called from _minimize_*, which is + # called from another function in SciPy. Level 4 is the first + # level in user code. + warnings.warn("Unknown solver options: %s" % msg, OptimizeWarning, stacklevel=4) + + +def is_finite_scalar(x): + """Test whether `x` is either a finite scalar or a finite array scalar. + + """ + return np.size(x) == 1 and np.isfinite(x) + + +_epsilon = sqrt(np.finfo(float).eps) + + +def vecnorm(x, ord=2): + if ord == np.inf: + return np.amax(np.abs(x)) + elif ord == -np.inf: + return np.amin(np.abs(x)) + else: + return np.sum(np.abs(x)**ord, axis=0)**(1.0 / ord) + + +def _prepare_scalar_function(fun, x0, jac=None, args=(), bounds=None, + epsilon=None, finite_diff_rel_step=None, + hess=None): + """ + Creates a ScalarFunction object for use with scalar minimizers + (BFGS/LBFGSB/SLSQP/TNC/CG/etc). + + Parameters + ---------- + fun : callable + The objective function to be minimized. + + ``fun(x, *args) -> float`` + + where ``x`` is an 1-D array with shape (n,) and ``args`` + is a tuple of the fixed parameters needed to completely + specify the function. + x0 : ndarray, shape (n,) + Initial guess. Array of real elements of size (n,), + where 'n' is the number of independent variables. + jac : {callable, '2-point', '3-point', 'cs', None}, optional + Method for computing the gradient vector. If it is a callable, it + should be a function that returns the gradient vector: + + ``jac(x, *args) -> array_like, shape (n,)`` + + If one of `{'2-point', '3-point', 'cs'}` is selected then the gradient + is calculated with a relative step for finite differences. If `None`, + then two-point finite differences with an absolute step is used. + args : tuple, optional + Extra arguments passed to the objective function and its + derivatives (`fun`, `jac` functions). + bounds : sequence, optional + Bounds on variables. 'new-style' bounds are required. + eps : float or ndarray + If `jac is None` the absolute step size used for numerical + approximation of the jacobian via forward differences. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of the jacobian. The absolute step + size is computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, + possibly adjusted to fit into the bounds. For ``jac='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + hess : {callable, '2-point', '3-point', 'cs', None} + Computes the Hessian matrix. If it is callable, it should return the + Hessian matrix: + + ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)`` + + Alternatively, the keywords {'2-point', '3-point', 'cs'} select a + finite difference scheme for numerical estimation. + Whenever the gradient is estimated via finite-differences, the Hessian + cannot be estimated with options {'2-point', '3-point', 'cs'} and needs + to be estimated using one of the quasi-Newton strategies. + + Returns + ------- + sf : ScalarFunction + """ + if callable(jac): + grad = jac + elif jac in FD_METHODS: + # epsilon is set to None so that ScalarFunction is made to use + # rel_step + epsilon = None + grad = jac + else: + # default (jac is None) is to do 2-point finite differences with + # absolute step size. ScalarFunction has to be provided an + # epsilon value that is not None to use absolute steps. This is + # normally the case from most _minimize* methods. + grad = '2-point' + epsilon = epsilon + + if hess is None: + # ScalarFunction requires something for hess, so we give a dummy + # implementation here if nothing is provided, return a value of None + # so that downstream minimisers halt. The results of `fun.hess` + # should not be used. + def hess(x, *args): + return None + + if bounds is None: + bounds = (-np.inf, np.inf) + + # ScalarFunction caches. Reuse of fun(x) during grad + # calculation reduces overall function evaluations. + sf = ScalarFunction(fun, x0, args, grad, hess, + finite_diff_rel_step, bounds, epsilon=epsilon) + + return sf + + +def _clip_x_for_func(func, bounds): + # ensures that x values sent to func are clipped to bounds + + # this is used as a mitigation for gh11403, slsqp/tnc sometimes + # suggest a move that is outside the limits by 1 or 2 ULP. This + # unclean fix makes sure x is strictly within bounds. + def eval(x): + x = _check_clip_x(x, bounds) + return func(x) + + return eval + + +def _check_clip_x(x, bounds): + if (x < bounds[0]).any() or (x > bounds[1]).any(): + warnings.warn("Values in x were outside bounds during a " + "minimize step, clipping to bounds", + RuntimeWarning, stacklevel=3) + x = np.clip(x, bounds[0], bounds[1]) + return x + + return x + + +def rosen(x): + """ + The Rosenbrock function. + + The function computed is:: + + sum(100.0*(x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0) + + Parameters + ---------- + x : array_like + 1-D array of points at which the Rosenbrock function is to be computed. + + Returns + ------- + f : float + The value of the Rosenbrock function. + + See Also + -------- + rosen_der, rosen_hess, rosen_hess_prod + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import rosen + >>> X = 0.1 * np.arange(10) + >>> rosen(X) + 76.56 + + For higher-dimensional input ``rosen`` broadcasts. + In the following example, we use this to plot a 2D landscape. + Note that ``rosen_hess`` does not broadcast in this manner. + + >>> import matplotlib.pyplot as plt + >>> from mpl_toolkits.mplot3d import Axes3D + >>> x = np.linspace(-1, 1, 50) + >>> X, Y = np.meshgrid(x, x) + >>> ax = plt.subplot(111, projection='3d') + >>> ax.plot_surface(X, Y, rosen([X, Y])) + >>> plt.show() + """ + x = asarray(x) + r = np.sum(100.0 * (x[1:] - x[:-1]**2.0)**2.0 + (1 - x[:-1])**2.0, + axis=0) + return r + + +def rosen_der(x): + """ + The derivative (i.e. gradient) of the Rosenbrock function. + + Parameters + ---------- + x : array_like + 1-D array of points at which the derivative is to be computed. + + Returns + ------- + rosen_der : (N,) ndarray + The gradient of the Rosenbrock function at `x`. + + See Also + -------- + rosen, rosen_hess, rosen_hess_prod + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import rosen_der + >>> X = 0.1 * np.arange(9) + >>> rosen_der(X) + array([ -2. , 10.6, 15.6, 13.4, 6.4, -3. , -12.4, -19.4, 62. ]) + + """ + x = asarray(x) + xm = x[1:-1] + xm_m1 = x[:-2] + xm_p1 = x[2:] + der = np.zeros_like(x) + der[1:-1] = (200 * (xm - xm_m1**2) - + 400 * (xm_p1 - xm**2) * xm - 2 * (1 - xm)) + der[0] = -400 * x[0] * (x[1] - x[0]**2) - 2 * (1 - x[0]) + der[-1] = 200 * (x[-1] - x[-2]**2) + return der + + +def rosen_hess(x): + """ + The Hessian matrix of the Rosenbrock function. + + Parameters + ---------- + x : array_like + 1-D array of points at which the Hessian matrix is to be computed. + + Returns + ------- + rosen_hess : ndarray + The Hessian matrix of the Rosenbrock function at `x`. + + See Also + -------- + rosen, rosen_der, rosen_hess_prod + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import rosen_hess + >>> X = 0.1 * np.arange(4) + >>> rosen_hess(X) + array([[-38., 0., 0., 0.], + [ 0., 134., -40., 0.], + [ 0., -40., 130., -80.], + [ 0., 0., -80., 200.]]) + + """ + x = atleast_1d(x) + H = np.diag(-400 * x[:-1], 1) - np.diag(400 * x[:-1], -1) + diagonal = np.zeros(len(x), dtype=x.dtype) + diagonal[0] = 1200 * x[0]**2 - 400 * x[1] + 2 + diagonal[-1] = 200 + diagonal[1:-1] = 202 + 1200 * x[1:-1]**2 - 400 * x[2:] + H = H + np.diag(diagonal) + return H + + +def rosen_hess_prod(x, p): + """ + Product of the Hessian matrix of the Rosenbrock function with a vector. + + Parameters + ---------- + x : array_like + 1-D array of points at which the Hessian matrix is to be computed. + p : array_like + 1-D array, the vector to be multiplied by the Hessian matrix. + + Returns + ------- + rosen_hess_prod : ndarray + The Hessian matrix of the Rosenbrock function at `x` multiplied + by the vector `p`. + + See Also + -------- + rosen, rosen_der, rosen_hess + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import rosen_hess_prod + >>> X = 0.1 * np.arange(9) + >>> p = 0.5 * np.arange(9) + >>> rosen_hess_prod(X, p) + array([ -0., 27., -10., -95., -192., -265., -278., -195., -180.]) + + """ + x = atleast_1d(x) + Hp = np.zeros(len(x), dtype=x.dtype) + Hp[0] = (1200 * x[0]**2 - 400 * x[1] + 2) * p[0] - 400 * x[0] * p[1] + Hp[1:-1] = (-400 * x[:-2] * p[:-2] + + (202 + 1200 * x[1:-1]**2 - 400 * x[2:]) * p[1:-1] - + 400 * x[1:-1] * p[2:]) + Hp[-1] = -400 * x[-2] * p[-2] + 200*p[-1] + return Hp + + +def _wrap_scalar_function(function, args): + # wraps a minimizer function to count number of evaluations + # and to easily provide an args kwd. + ncalls = [0] + if function is None: + return ncalls, None + + def function_wrapper(x, *wrapper_args): + ncalls[0] += 1 + # A copy of x is sent to the user function (gh13740) + fx = function(np.copy(x), *(wrapper_args + args)) + # Ideally, we'd like to a have a true scalar returned from f(x). For + # backwards-compatibility, also allow np.array([1.3]), np.array([[1.3]]) etc. + if not np.isscalar(fx): + try: + fx = np.asarray(fx).item() + except (TypeError, ValueError) as e: + raise ValueError("The user-provided objective function " + "must return a scalar value.") from e + return fx + + return ncalls, function_wrapper + + +class _MaxFuncCallError(RuntimeError): + pass + + +def _wrap_scalar_function_maxfun_validation(function, args, maxfun): + # wraps a minimizer function to count number of evaluations + # and to easily provide an args kwd. + ncalls = [0] + if function is None: + return ncalls, None + + def function_wrapper(x, *wrapper_args): + if ncalls[0] >= maxfun: + raise _MaxFuncCallError("Too many function calls") + ncalls[0] += 1 + # A copy of x is sent to the user function (gh13740) + fx = function(np.copy(x), *(wrapper_args + args)) + # Ideally, we'd like to a have a true scalar returned from f(x). For + # backwards-compatibility, also allow np.array([1.3]), + # np.array([[1.3]]) etc. + if not np.isscalar(fx): + try: + fx = np.asarray(fx).item() + except (TypeError, ValueError) as e: + raise ValueError("The user-provided objective function " + "must return a scalar value.") from e + return fx + + return ncalls, function_wrapper + + +def fmin(func, x0, args=(), xtol=1e-4, ftol=1e-4, maxiter=None, maxfun=None, + full_output=0, disp=1, retall=0, callback=None, initial_simplex=None): + """ + Minimize a function using the downhill simplex algorithm. + + This algorithm only uses function values, not derivatives or second + derivatives. + + Parameters + ---------- + func : callable func(x,*args) + The objective function to be minimized. + x0 : ndarray + Initial guess. + args : tuple, optional + Extra arguments passed to func, i.e., ``f(x,*args)``. + xtol : float, optional + Absolute error in xopt between iterations that is acceptable for + convergence. + ftol : number, optional + Absolute error in func(xopt) between iterations that is acceptable for + convergence. + maxiter : int, optional + Maximum number of iterations to perform. + maxfun : number, optional + Maximum number of function evaluations to make. + full_output : bool, optional + Set to True if fopt and warnflag outputs are desired. + disp : bool, optional + Set to True to print convergence messages. + retall : bool, optional + Set to True to return list of solutions at each iteration. + callback : callable, optional + Called after each iteration, as callback(xk), where xk is the + current parameter vector. + initial_simplex : array_like of shape (N + 1, N), optional + Initial simplex. If given, overrides `x0`. + ``initial_simplex[j,:]`` should contain the coordinates of + the jth vertex of the ``N+1`` vertices in the simplex, where + ``N`` is the dimension. + + Returns + ------- + xopt : ndarray + Parameter that minimizes function. + fopt : float + Value of function at minimum: ``fopt = func(xopt)``. + iter : int + Number of iterations performed. + funcalls : int + Number of function calls made. + warnflag : int + 1 : Maximum number of function evaluations made. + 2 : Maximum number of iterations reached. + allvecs : list + Solution at each iteration. + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'Nelder-Mead' `method` in particular. + + Notes + ----- + Uses a Nelder-Mead simplex algorithm to find the minimum of function of + one or more variables. + + This algorithm has a long history of successful use in applications. + But it will usually be slower than an algorithm that uses first or + second derivative information. In practice, it can have poor + performance in high-dimensional problems and is not robust to + minimizing complicated functions. Additionally, there currently is no + complete theory describing when the algorithm will successfully + converge to the minimum, or how fast it will if it does. Both the ftol and + xtol criteria must be met for convergence. + + Examples + -------- + >>> def f(x): + ... return x**2 + + >>> from scipy import optimize + + >>> minimum = optimize.fmin(f, 1) + Optimization terminated successfully. + Current function value: 0.000000 + Iterations: 17 + Function evaluations: 34 + >>> minimum[0] + -8.8817841970012523e-16 + + References + ---------- + .. [1] Nelder, J.A. and Mead, R. (1965), "A simplex method for function + minimization", The Computer Journal, 7, pp. 308-313 + + .. [2] Wright, M.H. (1996), "Direct Search Methods: Once Scorned, Now + Respectable", in Numerical Analysis 1995, Proceedings of the + 1995 Dundee Biennial Conference in Numerical Analysis, D.F. + Griffiths and G.A. Watson (Eds.), Addison Wesley Longman, + Harlow, UK, pp. 191-208. + + """ + opts = {'xatol': xtol, + 'fatol': ftol, + 'maxiter': maxiter, + 'maxfev': maxfun, + 'disp': disp, + 'return_all': retall, + 'initial_simplex': initial_simplex} + + callback = _wrap_callback(callback) + res = _minimize_neldermead(func, x0, args, callback=callback, **opts) + if full_output: + retlist = res['x'], res['fun'], res['nit'], res['nfev'], res['status'] + if retall: + retlist += (res['allvecs'], ) + return retlist + else: + if retall: + return res['x'], res['allvecs'] + else: + return res['x'] + + +def _minimize_neldermead(func, x0, args=(), callback=None, + maxiter=None, maxfev=None, disp=False, + return_all=False, initial_simplex=None, + xatol=1e-4, fatol=1e-4, adaptive=False, bounds=None, + **unknown_options): + """ + Minimization of scalar function of one or more variables using the + Nelder-Mead algorithm. + + Options + ------- + disp : bool + Set to True to print convergence messages. + maxiter, maxfev : int + Maximum allowed number of iterations and function evaluations. + Will default to ``N*200``, where ``N`` is the number of + variables, if neither `maxiter` or `maxfev` is set. If both + `maxiter` and `maxfev` are set, minimization will stop at the + first reached. + return_all : bool, optional + Set to True to return a list of the best solution at each of the + iterations. + initial_simplex : array_like of shape (N + 1, N) + Initial simplex. If given, overrides `x0`. + ``initial_simplex[j,:]`` should contain the coordinates of + the jth vertex of the ``N+1`` vertices in the simplex, where + ``N`` is the dimension. + xatol : float, optional + Absolute error in xopt between iterations that is acceptable for + convergence. + fatol : number, optional + Absolute error in func(xopt) between iterations that is acceptable for + convergence. + adaptive : bool, optional + Adapt algorithm parameters to dimensionality of problem. Useful for + high-dimensional minimization [1]_. + bounds : sequence or `Bounds`, optional + Bounds on variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. Sequence of ``(min, max)`` pairs for each element in `x`. None + is used to specify no bound. + + Note that this just clips all vertices in simplex based on + the bounds. + + References + ---------- + .. [1] Gao, F. and Han, L. + Implementing the Nelder-Mead simplex algorithm with adaptive + parameters. 2012. Computational Optimization and Applications. + 51:1, pp. 259-277 + + """ + _check_unknown_options(unknown_options) + maxfun = maxfev + retall = return_all + + x0 = np.atleast_1d(x0).flatten() + dtype = x0.dtype if np.issubdtype(x0.dtype, np.inexact) else np.float64 + x0 = np.asarray(x0, dtype=dtype) + + if adaptive: + dim = float(len(x0)) + rho = 1 + chi = 1 + 2/dim + psi = 0.75 - 1/(2*dim) + sigma = 1 - 1/dim + else: + rho = 1 + chi = 2 + psi = 0.5 + sigma = 0.5 + + nonzdelt = 0.05 + zdelt = 0.00025 + + if bounds is not None: + lower_bound, upper_bound = bounds.lb, bounds.ub + # check bounds + if (lower_bound > upper_bound).any(): + raise ValueError("Nelder Mead - one of the lower bounds " + "is greater than an upper bound.") + if np.any(lower_bound > x0) or np.any(x0 > upper_bound): + warnings.warn("Initial guess is not within the specified bounds", + OptimizeWarning, stacklevel=3) + + if bounds is not None: + x0 = np.clip(x0, lower_bound, upper_bound) + + if initial_simplex is None: + N = len(x0) + + sim = np.empty((N + 1, N), dtype=x0.dtype) + sim[0] = x0 + for k in range(N): + y = np.array(x0, copy=True) + if y[k] != 0: + y[k] = (1 + nonzdelt)*y[k] + else: + y[k] = zdelt + sim[k + 1] = y + else: + sim = np.atleast_2d(initial_simplex).copy() + dtype = sim.dtype if np.issubdtype(sim.dtype, np.inexact) else np.float64 + sim = np.asarray(sim, dtype=dtype) + if sim.ndim != 2 or sim.shape[0] != sim.shape[1] + 1: + raise ValueError("`initial_simplex` should be an array of shape (N+1,N)") + if len(x0) != sim.shape[1]: + raise ValueError("Size of `initial_simplex` is not consistent with `x0`") + N = sim.shape[1] + + if retall: + allvecs = [sim[0]] + + # If neither are set, then set both to default + if maxiter is None and maxfun is None: + maxiter = N * 200 + maxfun = N * 200 + elif maxiter is None: + # Convert remaining Nones, to np.inf, unless the other is np.inf, in + # which case use the default to avoid unbounded iteration + if maxfun == np.inf: + maxiter = N * 200 + else: + maxiter = np.inf + elif maxfun is None: + if maxiter == np.inf: + maxfun = N * 200 + else: + maxfun = np.inf + + if bounds is not None: + # The default simplex construction may make all entries (for a given + # parameter) greater than an upper bound if x0 is very close to the + # upper bound. If one simply clips the simplex to the bounds this could + # make the simplex entries degenerate. If that occurs reflect into the + # interior. + msk = sim > upper_bound + # reflect into the interior + sim = np.where(msk, 2*upper_bound - sim, sim) + # but make sure the reflection is no less than the lower_bound + sim = np.clip(sim, lower_bound, upper_bound) + + one2np1 = list(range(1, N + 1)) + fsim = np.full((N + 1,), np.inf, dtype=float) + + fcalls, func = _wrap_scalar_function_maxfun_validation(func, args, maxfun) + + try: + for k in range(N + 1): + fsim[k] = func(sim[k]) + except _MaxFuncCallError: + pass + finally: + ind = np.argsort(fsim) + sim = np.take(sim, ind, 0) + fsim = np.take(fsim, ind, 0) + + ind = np.argsort(fsim) + fsim = np.take(fsim, ind, 0) + # sort so sim[0,:] has the lowest function value + sim = np.take(sim, ind, 0) + + iterations = 1 + + while (fcalls[0] < maxfun and iterations < maxiter): + try: + if (np.max(np.ravel(np.abs(sim[1:] - sim[0]))) <= xatol and + np.max(np.abs(fsim[0] - fsim[1:])) <= fatol): + break + + xbar = np.add.reduce(sim[:-1], 0) / N + xr = (1 + rho) * xbar - rho * sim[-1] + if bounds is not None: + xr = np.clip(xr, lower_bound, upper_bound) + fxr = func(xr) + doshrink = 0 + + if fxr < fsim[0]: + xe = (1 + rho * chi) * xbar - rho * chi * sim[-1] + if bounds is not None: + xe = np.clip(xe, lower_bound, upper_bound) + fxe = func(xe) + + if fxe < fxr: + sim[-1] = xe + fsim[-1] = fxe + else: + sim[-1] = xr + fsim[-1] = fxr + else: # fsim[0] <= fxr + if fxr < fsim[-2]: + sim[-1] = xr + fsim[-1] = fxr + else: # fxr >= fsim[-2] + # Perform contraction + if fxr < fsim[-1]: + xc = (1 + psi * rho) * xbar - psi * rho * sim[-1] + if bounds is not None: + xc = np.clip(xc, lower_bound, upper_bound) + fxc = func(xc) + + if fxc <= fxr: + sim[-1] = xc + fsim[-1] = fxc + else: + doshrink = 1 + else: + # Perform an inside contraction + xcc = (1 - psi) * xbar + psi * sim[-1] + if bounds is not None: + xcc = np.clip(xcc, lower_bound, upper_bound) + fxcc = func(xcc) + + if fxcc < fsim[-1]: + sim[-1] = xcc + fsim[-1] = fxcc + else: + doshrink = 1 + + if doshrink: + for j in one2np1: + sim[j] = sim[0] + sigma * (sim[j] - sim[0]) + if bounds is not None: + sim[j] = np.clip( + sim[j], lower_bound, upper_bound) + fsim[j] = func(sim[j]) + iterations += 1 + except _MaxFuncCallError: + pass + finally: + ind = np.argsort(fsim) + sim = np.take(sim, ind, 0) + fsim = np.take(fsim, ind, 0) + if retall: + allvecs.append(sim[0]) + intermediate_result = OptimizeResult(x=sim[0], fun=fsim[0]) + if _call_callback_maybe_halt(callback, intermediate_result): + break + + x = sim[0] + fval = np.min(fsim) + warnflag = 0 + + if fcalls[0] >= maxfun: + warnflag = 1 + msg = _status_message['maxfev'] + if disp: + warnings.warn(msg, RuntimeWarning, stacklevel=3) + elif iterations >= maxiter: + warnflag = 2 + msg = _status_message['maxiter'] + if disp: + warnings.warn(msg, RuntimeWarning, stacklevel=3) + else: + msg = _status_message['success'] + if disp: + print(msg) + print(" Current function value: %f" % fval) + print(" Iterations: %d" % iterations) + print(" Function evaluations: %d" % fcalls[0]) + + result = OptimizeResult(fun=fval, nit=iterations, nfev=fcalls[0], + status=warnflag, success=(warnflag == 0), + message=msg, x=x, final_simplex=(sim, fsim)) + if retall: + result['allvecs'] = allvecs + return result + + +def approx_fprime(xk, f, epsilon=_epsilon, *args): + """Finite difference approximation of the derivatives of a + scalar or vector-valued function. + + If a function maps from :math:`R^n` to :math:`R^m`, its derivatives form + an m-by-n matrix + called the Jacobian, where an element :math:`(i, j)` is a partial + derivative of f[i] with respect to ``xk[j]``. + + Parameters + ---------- + xk : array_like + The coordinate vector at which to determine the gradient of `f`. + f : callable + Function of which to estimate the derivatives of. Has the signature + ``f(xk, *args)`` where `xk` is the argument in the form of a 1-D array + and `args` is a tuple of any additional fixed parameters needed to + completely specify the function. The argument `xk` passed to this + function is an ndarray of shape (n,) (never a scalar even if n=1). + It must return a 1-D array_like of shape (m,) or a scalar. + + .. versionchanged:: 1.9.0 + `f` is now able to return a 1-D array-like, with the :math:`(m, n)` + Jacobian being estimated. + + epsilon : {float, array_like}, optional + Increment to `xk` to use for determining the function gradient. + If a scalar, uses the same finite difference delta for all partial + derivatives. If an array, should contain one value per element of + `xk`. Defaults to ``sqrt(np.finfo(float).eps)``, which is approximately + 1.49e-08. + \\*args : args, optional + Any other arguments that are to be passed to `f`. + + Returns + ------- + jac : ndarray + The partial derivatives of `f` to `xk`. + + See Also + -------- + check_grad : Check correctness of gradient function against approx_fprime. + + Notes + ----- + The function gradient is determined by the forward finite difference + formula:: + + f(xk[i] + epsilon[i]) - f(xk[i]) + f'[i] = --------------------------------- + epsilon[i] + + Examples + -------- + >>> import numpy as np + >>> from scipy import optimize + >>> def func(x, c0, c1): + ... "Coordinate vector `x` should be an array of size two." + ... return c0 * x[0]**2 + c1*x[1]**2 + + >>> x = np.ones(2) + >>> c0, c1 = (1, 200) + >>> eps = np.sqrt(np.finfo(float).eps) + >>> optimize.approx_fprime(x, func, [eps, np.sqrt(200) * eps], c0, c1) + array([ 2. , 400.00004208]) + + """ + xk = np.asarray(xk, float) + f0 = f(xk, *args) + + return approx_derivative(f, xk, method='2-point', abs_step=epsilon, + args=args, f0=f0) + + +def check_grad(func, grad, x0, *args, epsilon=_epsilon, + direction='all', seed=None): + """Check the correctness of a gradient function by comparing it against a + (forward) finite-difference approximation of the gradient. + + Parameters + ---------- + func : callable ``func(x0, *args)`` + Function whose derivative is to be checked. + grad : callable ``grad(x0, *args)`` + Jacobian of `func`. + x0 : ndarray + Points to check `grad` against forward difference approximation of grad + using `func`. + args : \\*args, optional + Extra arguments passed to `func` and `grad`. + epsilon : float, optional + Step size used for the finite difference approximation. It defaults to + ``sqrt(np.finfo(float).eps)``, which is approximately 1.49e-08. + direction : str, optional + If set to ``'random'``, then gradients along a random vector + are used to check `grad` against forward difference approximation + using `func`. By default it is ``'all'``, in which case, all + the one hot direction vectors are considered to check `grad`. + If `func` is a vector valued function then only ``'all'`` can be used. + seed : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + Specify `seed` for reproducing the return value from this function. + The random numbers generated with this seed affect the random vector + along which gradients are computed to check ``grad``. Note that `seed` + is only used when `direction` argument is set to `'random'`. + + Returns + ------- + err : float + The square root of the sum of squares (i.e., the 2-norm) of the + difference between ``grad(x0, *args)`` and the finite difference + approximation of `grad` using func at the points `x0`. + + See Also + -------- + approx_fprime + + Examples + -------- + >>> import numpy as np + >>> def func(x): + ... return x[0]**2 - 0.5 * x[1]**3 + >>> def grad(x): + ... return [2 * x[0], -1.5 * x[1]**2] + >>> from scipy.optimize import check_grad + >>> check_grad(func, grad, [1.5, -1.5]) + 2.9802322387695312e-08 # may vary + >>> rng = np.random.default_rng() + >>> check_grad(func, grad, [1.5, -1.5], + ... direction='random', seed=rng) + 2.9802322387695312e-08 + + """ + step = epsilon + x0 = np.asarray(x0) + + def g(w, func, x0, v, *args): + return func(x0 + w*v, *args) + + if direction == 'random': + _grad = np.asanyarray(grad(x0, *args)) + if _grad.ndim > 1: + raise ValueError("'random' can only be used with scalar valued" + " func") + random_state = check_random_state(seed) + v = random_state.normal(0, 1, size=(x0.shape)) + _args = (func, x0, v) + args + _func = g + vars = np.zeros((1,)) + analytical_grad = np.dot(_grad, v) + elif direction == 'all': + _args = args + _func = func + vars = x0 + analytical_grad = grad(x0, *args) + else: + raise ValueError(f"{direction} is not a valid string for " + "``direction`` argument") + + return np.sqrt(np.sum(np.abs( + (analytical_grad - approx_fprime(vars, _func, step, *_args))**2 + ))) + + +def approx_fhess_p(x0, p, fprime, epsilon, *args): + # calculate fprime(x0) first, as this may be cached by ScalarFunction + f1 = fprime(*((x0,) + args)) + f2 = fprime(*((x0 + epsilon*p,) + args)) + return (f2 - f1) / epsilon + + +class _LineSearchError(RuntimeError): + pass + + +def _line_search_wolfe12(f, fprime, xk, pk, gfk, old_fval, old_old_fval, + **kwargs): + """ + Same as line_search_wolfe1, but fall back to line_search_wolfe2 if + suitable step length is not found, and raise an exception if a + suitable step length is not found. + + Raises + ------ + _LineSearchError + If no suitable step size is found + + """ + + extra_condition = kwargs.pop('extra_condition', None) + + ret = line_search_wolfe1(f, fprime, xk, pk, gfk, + old_fval, old_old_fval, + **kwargs) + + if ret[0] is not None and extra_condition is not None: + xp1 = xk + ret[0] * pk + if not extra_condition(ret[0], xp1, ret[3], ret[5]): + # Reject step if extra_condition fails + ret = (None,) + + if ret[0] is None: + # line search failed: try different one. + with warnings.catch_warnings(): + warnings.simplefilter('ignore', LineSearchWarning) + kwargs2 = {} + for key in ('c1', 'c2', 'amax'): + if key in kwargs: + kwargs2[key] = kwargs[key] + ret = line_search_wolfe2(f, fprime, xk, pk, gfk, + old_fval, old_old_fval, + extra_condition=extra_condition, + **kwargs2) + + if ret[0] is None: + raise _LineSearchError() + + return ret + + +def fmin_bfgs(f, x0, fprime=None, args=(), gtol=1e-5, norm=np.inf, + epsilon=_epsilon, maxiter=None, full_output=0, disp=1, + retall=0, callback=None, xrtol=0, c1=1e-4, c2=0.9, + hess_inv0=None): + """ + Minimize a function using the BFGS algorithm. + + Parameters + ---------- + f : callable ``f(x,*args)`` + Objective function to be minimized. + x0 : ndarray + Initial guess, shape (n,) + fprime : callable ``f'(x,*args)``, optional + Gradient of f. + args : tuple, optional + Extra arguments passed to f and fprime. + gtol : float, optional + Terminate successfully if gradient norm is less than `gtol` + norm : float, optional + Order of norm (Inf is max, -Inf is min) + epsilon : int or ndarray, optional + If `fprime` is approximated, use this value for the step size. + callback : callable, optional + An optional user-supplied function to call after each + iteration. Called as ``callback(xk)``, where ``xk`` is the + current parameter vector. + maxiter : int, optional + Maximum number of iterations to perform. + full_output : bool, optional + If True, return ``fopt``, ``func_calls``, ``grad_calls``, and + ``warnflag`` in addition to ``xopt``. + disp : bool, optional + Print convergence message if True. + retall : bool, optional + Return a list of results at each iteration if True. + xrtol : float, default: 0 + Relative tolerance for `x`. Terminate successfully if step + size is less than ``xk * xrtol`` where ``xk`` is the current + parameter vector. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.9 + Parameter for curvature condition rule. + hess_inv0 : None or ndarray, optional`` + Initial inverse hessian estimate, shape (n, n). If None (default) then + the identity matrix is used. + + Returns + ------- + xopt : ndarray + Parameters which minimize f, i.e., ``f(xopt) == fopt``. + fopt : float + Minimum value. + gopt : ndarray + Value of gradient at minimum, f'(xopt), which should be near 0. + Bopt : ndarray + Value of 1/f''(xopt), i.e., the inverse Hessian matrix. + func_calls : int + Number of function_calls made. + grad_calls : int + Number of gradient calls made. + warnflag : integer + 1 : Maximum number of iterations exceeded. + 2 : Gradient and/or function calls not changing. + 3 : NaN result encountered. + allvecs : list + The value of `xopt` at each iteration. Only returned if `retall` is + True. + + Notes + ----- + Optimize the function, `f`, whose gradient is given by `fprime` + using the quasi-Newton method of Broyden, Fletcher, Goldfarb, + and Shanno (BFGS). + + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + + See Also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See ``method='BFGS'`` in particular. + + References + ---------- + Wright, and Nocedal 'Numerical Optimization', 1999, p. 198. + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import fmin_bfgs + >>> def quadratic_cost(x, Q): + ... return x @ Q @ x + ... + >>> x0 = np.array([-3, -4]) + >>> cost_weight = np.diag([1., 10.]) + >>> # Note that a trailing comma is necessary for a tuple with single element + >>> fmin_bfgs(quadratic_cost, x0, args=(cost_weight,)) + Optimization terminated successfully. + Current function value: 0.000000 + Iterations: 7 # may vary + Function evaluations: 24 # may vary + Gradient evaluations: 8 # may vary + array([ 2.85169950e-06, -4.61820139e-07]) + + >>> def quadratic_cost_grad(x, Q): + ... return 2 * Q @ x + ... + >>> fmin_bfgs(quadratic_cost, x0, quadratic_cost_grad, args=(cost_weight,)) + Optimization terminated successfully. + Current function value: 0.000000 + Iterations: 7 + Function evaluations: 8 + Gradient evaluations: 8 + array([ 2.85916637e-06, -4.54371951e-07]) + + """ + opts = {'gtol': gtol, + 'norm': norm, + 'eps': epsilon, + 'disp': disp, + 'maxiter': maxiter, + 'return_all': retall, + 'xrtol': xrtol, + 'c1': c1, + 'c2': c2, + 'hess_inv0': hess_inv0} + + callback = _wrap_callback(callback) + res = _minimize_bfgs(f, x0, args, fprime, callback=callback, **opts) + + if full_output: + retlist = (res['x'], res['fun'], res['jac'], res['hess_inv'], + res['nfev'], res['njev'], res['status']) + if retall: + retlist += (res['allvecs'], ) + return retlist + else: + if retall: + return res['x'], res['allvecs'] + else: + return res['x'] + + +def _minimize_bfgs(fun, x0, args=(), jac=None, callback=None, + gtol=1e-5, norm=np.inf, eps=_epsilon, maxiter=None, + disp=False, return_all=False, finite_diff_rel_step=None, + xrtol=0, c1=1e-4, c2=0.9, + hess_inv0=None, **unknown_options): + """ + Minimization of scalar function of one or more variables using the + BFGS algorithm. + + Options + ------- + disp : bool + Set to True to print convergence messages. + maxiter : int + Maximum number of iterations to perform. + gtol : float + Terminate successfully if gradient norm is less than `gtol`. + norm : float + Order of norm (Inf is max, -Inf is min). + eps : float or ndarray + If `jac is None` the absolute step size used for numerical + approximation of the jacobian via forward differences. + return_all : bool, optional + Set to True to return a list of the best solution at each of the + iterations. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of the jacobian. The absolute step + size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, + possibly adjusted to fit into the bounds. For ``jac='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + xrtol : float, default: 0 + Relative tolerance for `x`. Terminate successfully if step size is + less than ``xk * xrtol`` where ``xk`` is the current parameter vector. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.9 + Parameter for curvature condition rule. + hess_inv0 : None or ndarray, optional + Initial inverse hessian estimate, shape (n, n). If None (default) then + the identity matrix is used. + + Notes + ----- + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + + If minimization doesn't complete successfully, with an error message of + ``Desired error not necessarily achieved due to precision loss``, then + consider setting `gtol` to a higher value. This precision loss typically + occurs when the (finite difference) numerical differentiation cannot provide + sufficient precision to satisfy the `gtol` termination criterion. + This can happen when working in single precision and a callable jac is not + provided. For single precision problems a `gtol` of 1e-3 seems to work. + """ + _check_unknown_options(unknown_options) + _check_positive_definite(hess_inv0) + retall = return_all + + x0 = asarray(x0).flatten() + if x0.ndim == 0: + x0.shape = (1,) + if maxiter is None: + maxiter = len(x0) * 200 + + sf = _prepare_scalar_function(fun, x0, jac, args=args, epsilon=eps, + finite_diff_rel_step=finite_diff_rel_step) + + f = sf.fun + myfprime = sf.grad + + old_fval = f(x0) + gfk = myfprime(x0) + + k = 0 + N = len(x0) + I = np.eye(N, dtype=int) + Hk = I if hess_inv0 is None else hess_inv0 + + # Sets the initial step guess to dx ~ 1 + old_old_fval = old_fval + np.linalg.norm(gfk) / 2 + + xk = x0 + if retall: + allvecs = [x0] + warnflag = 0 + gnorm = vecnorm(gfk, ord=norm) + while (gnorm > gtol) and (k < maxiter): + pk = -np.dot(Hk, gfk) + try: + alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \ + _line_search_wolfe12(f, myfprime, xk, pk, gfk, + old_fval, old_old_fval, amin=1e-100, + amax=1e100, c1=c1, c2=c2) + except _LineSearchError: + # Line search failed to find a better solution. + warnflag = 2 + break + + sk = alpha_k * pk + xkp1 = xk + sk + + if retall: + allvecs.append(xkp1) + xk = xkp1 + if gfkp1 is None: + gfkp1 = myfprime(xkp1) + + yk = gfkp1 - gfk + gfk = gfkp1 + k += 1 + intermediate_result = OptimizeResult(x=xk, fun=old_fval) + if _call_callback_maybe_halt(callback, intermediate_result): + break + gnorm = vecnorm(gfk, ord=norm) + if (gnorm <= gtol): + break + + # See Chapter 5 in P.E. Frandsen, K. Jonasson, H.B. Nielsen, + # O. Tingleff: "Unconstrained Optimization", IMM, DTU. 1999. + # These notes are available here: + # http://www2.imm.dtu.dk/documents/ftp/publlec.html + if (alpha_k*vecnorm(pk) <= xrtol*(xrtol + vecnorm(xk))): + break + + if not np.isfinite(old_fval): + # We correctly found +-Inf as optimal value, or something went + # wrong. + warnflag = 2 + break + + rhok_inv = np.dot(yk, sk) + # this was handled in numeric, let it remains for more safety + # Cryptic comment above is preserved for posterity. Future reader: + # consider change to condition below proposed in gh-1261/gh-17345. + if rhok_inv == 0.: + rhok = 1000.0 + if disp: + msg = "Divide-by-zero encountered: rhok assumed large" + _print_success_message_or_warn(True, msg) + else: + rhok = 1. / rhok_inv + + A1 = I - sk[:, np.newaxis] * yk[np.newaxis, :] * rhok + A2 = I - yk[:, np.newaxis] * sk[np.newaxis, :] * rhok + Hk = np.dot(A1, np.dot(Hk, A2)) + (rhok * sk[:, np.newaxis] * + sk[np.newaxis, :]) + + fval = old_fval + + if warnflag == 2: + msg = _status_message['pr_loss'] + elif k >= maxiter: + warnflag = 1 + msg = _status_message['maxiter'] + elif np.isnan(gnorm) or np.isnan(fval) or np.isnan(xk).any(): + warnflag = 3 + msg = _status_message['nan'] + else: + msg = _status_message['success'] + + if disp: + _print_success_message_or_warn(warnflag, msg) + print(" Current function value: %f" % fval) + print(" Iterations: %d" % k) + print(" Function evaluations: %d" % sf.nfev) + print(" Gradient evaluations: %d" % sf.ngev) + + result = OptimizeResult(fun=fval, jac=gfk, hess_inv=Hk, nfev=sf.nfev, + njev=sf.ngev, status=warnflag, + success=(warnflag == 0), message=msg, x=xk, + nit=k) + if retall: + result['allvecs'] = allvecs + return result + + +def _print_success_message_or_warn(warnflag, message, warntype=None): + if not warnflag: + print(message) + else: + warnings.warn(message, warntype or OptimizeWarning, stacklevel=3) + + +def fmin_cg(f, x0, fprime=None, args=(), gtol=1e-5, norm=np.inf, + epsilon=_epsilon, maxiter=None, full_output=0, disp=1, retall=0, + callback=None, c1=1e-4, c2=0.4): + """ + Minimize a function using a nonlinear conjugate gradient algorithm. + + Parameters + ---------- + f : callable, ``f(x, *args)`` + Objective function to be minimized. Here `x` must be a 1-D array of + the variables that are to be changed in the search for a minimum, and + `args` are the other (fixed) parameters of `f`. + x0 : ndarray + A user-supplied initial estimate of `xopt`, the optimal value of `x`. + It must be a 1-D array of values. + fprime : callable, ``fprime(x, *args)``, optional + A function that returns the gradient of `f` at `x`. Here `x` and `args` + are as described above for `f`. The returned value must be a 1-D array. + Defaults to None, in which case the gradient is approximated + numerically (see `epsilon`, below). + args : tuple, optional + Parameter values passed to `f` and `fprime`. Must be supplied whenever + additional fixed parameters are needed to completely specify the + functions `f` and `fprime`. + gtol : float, optional + Stop when the norm of the gradient is less than `gtol`. + norm : float, optional + Order to use for the norm of the gradient + (``-np.inf`` is min, ``np.inf`` is max). + epsilon : float or ndarray, optional + Step size(s) to use when `fprime` is approximated numerically. Can be a + scalar or a 1-D array. Defaults to ``sqrt(eps)``, with eps the + floating point machine precision. Usually ``sqrt(eps)`` is about + 1.5e-8. + maxiter : int, optional + Maximum number of iterations to perform. Default is ``200 * len(x0)``. + full_output : bool, optional + If True, return `fopt`, `func_calls`, `grad_calls`, and `warnflag` in + addition to `xopt`. See the Returns section below for additional + information on optional return values. + disp : bool, optional + If True, return a convergence message, followed by `xopt`. + retall : bool, optional + If True, add to the returned values the results of each iteration. + callback : callable, optional + An optional user-supplied function, called after each iteration. + Called as ``callback(xk)``, where ``xk`` is the current value of `x0`. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.4 + Parameter for curvature condition rule. + + Returns + ------- + xopt : ndarray + Parameters which minimize f, i.e., ``f(xopt) == fopt``. + fopt : float, optional + Minimum value found, f(xopt). Only returned if `full_output` is True. + func_calls : int, optional + The number of function_calls made. Only returned if `full_output` + is True. + grad_calls : int, optional + The number of gradient calls made. Only returned if `full_output` is + True. + warnflag : int, optional + Integer value with warning status, only returned if `full_output` is + True. + + 0 : Success. + + 1 : The maximum number of iterations was exceeded. + + 2 : Gradient and/or function calls were not changing. May indicate + that precision was lost, i.e., the routine did not converge. + + 3 : NaN result encountered. + + allvecs : list of ndarray, optional + List of arrays, containing the results at each iteration. + Only returned if `retall` is True. + + See Also + -------- + minimize : common interface to all `scipy.optimize` algorithms for + unconstrained and constrained minimization of multivariate + functions. It provides an alternative way to call + ``fmin_cg``, by specifying ``method='CG'``. + + Notes + ----- + This conjugate gradient algorithm is based on that of Polak and Ribiere + [1]_. + + Conjugate gradient methods tend to work better when: + + 1. `f` has a unique global minimizing point, and no local minima or + other stationary points, + 2. `f` is, at least locally, reasonably well approximated by a + quadratic function of the variables, + 3. `f` is continuous and has a continuous gradient, + 4. `fprime` is not too large, e.g., has a norm less than 1000, + 5. The initial guess, `x0`, is reasonably close to `f` 's global + minimizing point, `xopt`. + + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + + References + ---------- + .. [1] Wright & Nocedal, "Numerical Optimization", 1999, pp. 120-122. + + Examples + -------- + Example 1: seek the minimum value of the expression + ``a*u**2 + b*u*v + c*v**2 + d*u + e*v + f`` for given values + of the parameters and an initial guess ``(u, v) = (0, 0)``. + + >>> import numpy as np + >>> args = (2, 3, 7, 8, 9, 10) # parameter values + >>> def f(x, *args): + ... u, v = x + ... a, b, c, d, e, f = args + ... return a*u**2 + b*u*v + c*v**2 + d*u + e*v + f + >>> def gradf(x, *args): + ... u, v = x + ... a, b, c, d, e, f = args + ... gu = 2*a*u + b*v + d # u-component of the gradient + ... gv = b*u + 2*c*v + e # v-component of the gradient + ... return np.asarray((gu, gv)) + >>> x0 = np.asarray((0, 0)) # Initial guess. + >>> from scipy import optimize + >>> res1 = optimize.fmin_cg(f, x0, fprime=gradf, args=args) + Optimization terminated successfully. + Current function value: 1.617021 + Iterations: 4 + Function evaluations: 8 + Gradient evaluations: 8 + >>> res1 + array([-1.80851064, -0.25531915]) + + Example 2: solve the same problem using the `minimize` function. + (This `myopts` dictionary shows all of the available options, + although in practice only non-default values would be needed. + The returned value will be a dictionary.) + + >>> opts = {'maxiter' : None, # default value. + ... 'disp' : True, # non-default value. + ... 'gtol' : 1e-5, # default value. + ... 'norm' : np.inf, # default value. + ... 'eps' : 1.4901161193847656e-08} # default value. + >>> res2 = optimize.minimize(f, x0, jac=gradf, args=args, + ... method='CG', options=opts) + Optimization terminated successfully. + Current function value: 1.617021 + Iterations: 4 + Function evaluations: 8 + Gradient evaluations: 8 + >>> res2.x # minimum found + array([-1.80851064, -0.25531915]) + + """ + opts = {'gtol': gtol, + 'norm': norm, + 'eps': epsilon, + 'disp': disp, + 'maxiter': maxiter, + 'return_all': retall} + + callback = _wrap_callback(callback) + res = _minimize_cg(f, x0, args, fprime, callback=callback, c1=c1, c2=c2, + **opts) + + if full_output: + retlist = res['x'], res['fun'], res['nfev'], res['njev'], res['status'] + if retall: + retlist += (res['allvecs'], ) + return retlist + else: + if retall: + return res['x'], res['allvecs'] + else: + return res['x'] + + +def _minimize_cg(fun, x0, args=(), jac=None, callback=None, + gtol=1e-5, norm=np.inf, eps=_epsilon, maxiter=None, + disp=False, return_all=False, finite_diff_rel_step=None, + c1=1e-4, c2=0.4, **unknown_options): + """ + Minimization of scalar function of one or more variables using the + conjugate gradient algorithm. + + Options + ------- + disp : bool + Set to True to print convergence messages. + maxiter : int + Maximum number of iterations to perform. + gtol : float + Gradient norm must be less than `gtol` before successful + termination. + norm : float + Order of norm (Inf is max, -Inf is min). + eps : float or ndarray + If `jac is None` the absolute step size used for numerical + approximation of the jacobian via forward differences. + return_all : bool, optional + Set to True to return a list of the best solution at each of the + iterations. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of the jacobian. The absolute step + size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, + possibly adjusted to fit into the bounds. For ``jac='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.4 + Parameter for curvature condition rule. + + Notes + ----- + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + """ + _check_unknown_options(unknown_options) + + retall = return_all + + x0 = asarray(x0).flatten() + if maxiter is None: + maxiter = len(x0) * 200 + + sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps, + finite_diff_rel_step=finite_diff_rel_step) + + f = sf.fun + myfprime = sf.grad + + old_fval = f(x0) + gfk = myfprime(x0) + + k = 0 + xk = x0 + # Sets the initial step guess to dx ~ 1 + old_old_fval = old_fval + np.linalg.norm(gfk) / 2 + + if retall: + allvecs = [xk] + warnflag = 0 + pk = -gfk + gnorm = vecnorm(gfk, ord=norm) + + sigma_3 = 0.01 + + while (gnorm > gtol) and (k < maxiter): + deltak = np.dot(gfk, gfk) + + cached_step = [None] + + def polak_ribiere_powell_step(alpha, gfkp1=None): + xkp1 = xk + alpha * pk + if gfkp1 is None: + gfkp1 = myfprime(xkp1) + yk = gfkp1 - gfk + beta_k = max(0, np.dot(yk, gfkp1) / deltak) + pkp1 = -gfkp1 + beta_k * pk + gnorm = vecnorm(gfkp1, ord=norm) + return (alpha, xkp1, pkp1, gfkp1, gnorm) + + def descent_condition(alpha, xkp1, fp1, gfkp1): + # Polak-Ribiere+ needs an explicit check of a sufficient + # descent condition, which is not guaranteed by strong Wolfe. + # + # See Gilbert & Nocedal, "Global convergence properties of + # conjugate gradient methods for optimization", + # SIAM J. Optimization 2, 21 (1992). + cached_step[:] = polak_ribiere_powell_step(alpha, gfkp1) + alpha, xk, pk, gfk, gnorm = cached_step + + # Accept step if it leads to convergence. + if gnorm <= gtol: + return True + + # Accept step if sufficient descent condition applies. + return np.dot(pk, gfk) <= -sigma_3 * np.dot(gfk, gfk) + + try: + alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \ + _line_search_wolfe12(f, myfprime, xk, pk, gfk, old_fval, + old_old_fval, c1=c1, c2=c2, amin=1e-100, + amax=1e100, extra_condition=descent_condition) + except _LineSearchError: + # Line search failed to find a better solution. + warnflag = 2 + break + + # Reuse already computed results if possible + if alpha_k == cached_step[0]: + alpha_k, xk, pk, gfk, gnorm = cached_step + else: + alpha_k, xk, pk, gfk, gnorm = polak_ribiere_powell_step(alpha_k, gfkp1) + + if retall: + allvecs.append(xk) + k += 1 + intermediate_result = OptimizeResult(x=xk, fun=old_fval) + if _call_callback_maybe_halt(callback, intermediate_result): + break + + fval = old_fval + if warnflag == 2: + msg = _status_message['pr_loss'] + elif k >= maxiter: + warnflag = 1 + msg = _status_message['maxiter'] + elif np.isnan(gnorm) or np.isnan(fval) or np.isnan(xk).any(): + warnflag = 3 + msg = _status_message['nan'] + else: + msg = _status_message['success'] + + if disp: + _print_success_message_or_warn(warnflag, msg) + print(" Current function value: %f" % fval) + print(" Iterations: %d" % k) + print(" Function evaluations: %d" % sf.nfev) + print(" Gradient evaluations: %d" % sf.ngev) + + result = OptimizeResult(fun=fval, jac=gfk, nfev=sf.nfev, + njev=sf.ngev, status=warnflag, + success=(warnflag == 0), message=msg, x=xk, + nit=k) + if retall: + result['allvecs'] = allvecs + return result + + +def fmin_ncg(f, x0, fprime, fhess_p=None, fhess=None, args=(), avextol=1e-5, + epsilon=_epsilon, maxiter=None, full_output=0, disp=1, retall=0, + callback=None, c1=1e-4, c2=0.9): + """ + Unconstrained minimization of a function using the Newton-CG method. + + Parameters + ---------- + f : callable ``f(x, *args)`` + Objective function to be minimized. + x0 : ndarray + Initial guess. + fprime : callable ``f'(x, *args)`` + Gradient of f. + fhess_p : callable ``fhess_p(x, p, *args)``, optional + Function which computes the Hessian of f times an + arbitrary vector, p. + fhess : callable ``fhess(x, *args)``, optional + Function to compute the Hessian matrix of f. + args : tuple, optional + Extra arguments passed to f, fprime, fhess_p, and fhess + (the same set of extra arguments is supplied to all of + these functions). + epsilon : float or ndarray, optional + If fhess is approximated, use this value for the step size. + callback : callable, optional + An optional user-supplied function which is called after + each iteration. Called as callback(xk), where xk is the + current parameter vector. + avextol : float, optional + Convergence is assumed when the average relative error in + the minimizer falls below this amount. + maxiter : int, optional + Maximum number of iterations to perform. + full_output : bool, optional + If True, return the optional outputs. + disp : bool, optional + If True, print convergence message. + retall : bool, optional + If True, return a list of results at each iteration. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.9 + Parameter for curvature condition rule + + Returns + ------- + xopt : ndarray + Parameters which minimize f, i.e., ``f(xopt) == fopt``. + fopt : float + Value of the function at xopt, i.e., ``fopt = f(xopt)``. + fcalls : int + Number of function calls made. + gcalls : int + Number of gradient calls made. + hcalls : int + Number of Hessian calls made. + warnflag : int + Warnings generated by the algorithm. + 1 : Maximum number of iterations exceeded. + 2 : Line search failure (precision loss). + 3 : NaN result encountered. + allvecs : list + The result at each iteration, if retall is True (see below). + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'Newton-CG' `method` in particular. + + Notes + ----- + Only one of `fhess_p` or `fhess` need to be given. If `fhess` + is provided, then `fhess_p` will be ignored. If neither `fhess` + nor `fhess_p` is provided, then the hessian product will be + approximated using finite differences on `fprime`. `fhess_p` + must compute the hessian times an arbitrary vector. If it is not + given, finite-differences on `fprime` are used to compute + it. + + Newton-CG methods are also called truncated Newton methods. This + function differs from scipy.optimize.fmin_tnc because + + 1. scipy.optimize.fmin_ncg is written purely in Python using NumPy + and scipy while scipy.optimize.fmin_tnc calls a C function. + 2. scipy.optimize.fmin_ncg is only for unconstrained minimization + while scipy.optimize.fmin_tnc is for unconstrained minimization + or box constrained minimization. (Box constraints give + lower and upper bounds for each variable separately.) + + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + + References + ---------- + Wright & Nocedal, 'Numerical Optimization', 1999, p. 140. + + """ + opts = {'xtol': avextol, + 'eps': epsilon, + 'maxiter': maxiter, + 'disp': disp, + 'return_all': retall} + + callback = _wrap_callback(callback) + res = _minimize_newtoncg(f, x0, args, fprime, fhess, fhess_p, + callback=callback, c1=c1, c2=c2, **opts) + + if full_output: + retlist = (res['x'], res['fun'], res['nfev'], res['njev'], + res['nhev'], res['status']) + if retall: + retlist += (res['allvecs'], ) + return retlist + else: + if retall: + return res['x'], res['allvecs'] + else: + return res['x'] + + +def _minimize_newtoncg(fun, x0, args=(), jac=None, hess=None, hessp=None, + callback=None, xtol=1e-5, eps=_epsilon, maxiter=None, + disp=False, return_all=False, c1=1e-4, c2=0.9, + **unknown_options): + """ + Minimization of scalar function of one or more variables using the + Newton-CG algorithm. + + Note that the `jac` parameter (Jacobian) is required. + + Options + ------- + disp : bool + Set to True to print convergence messages. + xtol : float + Average relative error in solution `xopt` acceptable for + convergence. + maxiter : int + Maximum number of iterations to perform. + eps : float or ndarray + If `hessp` is approximated, use this value for the step size. + return_all : bool, optional + Set to True to return a list of the best solution at each of the + iterations. + c1 : float, default: 1e-4 + Parameter for Armijo condition rule. + c2 : float, default: 0.9 + Parameter for curvature condition rule. + + Notes + ----- + Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. + """ + _check_unknown_options(unknown_options) + if jac is None: + raise ValueError('Jacobian is required for Newton-CG method') + fhess_p = hessp + fhess = hess + avextol = xtol + epsilon = eps + retall = return_all + + x0 = asarray(x0).flatten() + # TODO: add hessp (callable or FD) to ScalarFunction? + sf = _prepare_scalar_function( + fun, x0, jac, args=args, epsilon=eps, hess=hess + ) + f = sf.fun + fprime = sf.grad + _h = sf.hess(x0) + + # Logic for hess/hessp + # - If a callable(hess) is provided, then use that + # - If hess is a FD_METHOD, or the output from hess(x) is a LinearOperator + # then create a hessp function using those. + # - If hess is None but you have callable(hessp) then use the hessp. + # - If hess and hessp are None then approximate hessp using the grad/jac. + + if (hess in FD_METHODS or isinstance(_h, LinearOperator)): + fhess = None + + def _hessp(x, p, *args): + return sf.hess(x).dot(p) + + fhess_p = _hessp + + def terminate(warnflag, msg): + if disp: + _print_success_message_or_warn(warnflag, msg) + print(" Current function value: %f" % old_fval) + print(" Iterations: %d" % k) + print(" Function evaluations: %d" % sf.nfev) + print(" Gradient evaluations: %d" % sf.ngev) + print(" Hessian evaluations: %d" % hcalls) + fval = old_fval + result = OptimizeResult(fun=fval, jac=gfk, nfev=sf.nfev, + njev=sf.ngev, nhev=hcalls, status=warnflag, + success=(warnflag == 0), message=msg, x=xk, + nit=k) + if retall: + result['allvecs'] = allvecs + return result + + hcalls = 0 + if maxiter is None: + maxiter = len(x0)*200 + cg_maxiter = 20*len(x0) + + xtol = len(x0) * avextol + # Make sure we enter the while loop. + update_l1norm = np.finfo(float).max + xk = np.copy(x0) + if retall: + allvecs = [xk] + k = 0 + gfk = None + old_fval = f(x0) + old_old_fval = None + float64eps = np.finfo(np.float64).eps + while update_l1norm > xtol: + if k >= maxiter: + msg = "Warning: " + _status_message['maxiter'] + return terminate(1, msg) + # Compute a search direction pk by applying the CG method to + # del2 f(xk) p = - grad f(xk) starting from 0. + b = -fprime(xk) + maggrad = np.linalg.norm(b, ord=1) + eta = min(0.5, math.sqrt(maggrad)) + termcond = eta * maggrad + xsupi = zeros(len(x0), dtype=x0.dtype) + ri = -b + psupi = -ri + i = 0 + dri0 = np.dot(ri, ri) + + if fhess is not None: # you want to compute hessian once. + A = sf.hess(xk) + hcalls += 1 + + for k2 in range(cg_maxiter): + if np.add.reduce(np.abs(ri)) <= termcond: + break + if fhess is None: + if fhess_p is None: + Ap = approx_fhess_p(xk, psupi, fprime, epsilon) + else: + Ap = fhess_p(xk, psupi, *args) + hcalls += 1 + else: + # hess was supplied as a callable or hessian update strategy, so + # A is a dense numpy array or sparse matrix + Ap = A.dot(psupi) + # check curvature + Ap = asarray(Ap).squeeze() # get rid of matrices... + curv = np.dot(psupi, Ap) + if 0 <= curv <= 3 * float64eps: + break + elif curv < 0: + if (i > 0): + break + else: + # fall back to steepest descent direction + xsupi = dri0 / (-curv) * b + break + alphai = dri0 / curv + xsupi += alphai * psupi + ri += alphai * Ap + dri1 = np.dot(ri, ri) + betai = dri1 / dri0 + psupi = -ri + betai * psupi + i += 1 + dri0 = dri1 # update np.dot(ri,ri) for next time. + else: + # curvature keeps increasing, bail out + msg = ("Warning: CG iterations didn't converge. The Hessian is not " + "positive definite.") + return terminate(3, msg) + + pk = xsupi # search direction is solution to system. + gfk = -b # gradient at xk + + try: + alphak, fc, gc, old_fval, old_old_fval, gfkp1 = \ + _line_search_wolfe12(f, fprime, xk, pk, gfk, + old_fval, old_old_fval, c1=c1, c2=c2) + except _LineSearchError: + # Line search failed to find a better solution. + msg = "Warning: " + _status_message['pr_loss'] + return terminate(2, msg) + + update = alphak * pk + xk += update # upcast if necessary + if retall: + allvecs.append(xk) + k += 1 + intermediate_result = OptimizeResult(x=xk, fun=old_fval) + if _call_callback_maybe_halt(callback, intermediate_result): + return terminate(5, "") + update_l1norm = np.linalg.norm(update, ord=1) + + else: + if np.isnan(old_fval) or np.isnan(update_l1norm): + return terminate(3, _status_message['nan']) + + msg = _status_message['success'] + return terminate(0, msg) + + +def fminbound(func, x1, x2, args=(), xtol=1e-5, maxfun=500, + full_output=0, disp=1): + """Bounded minimization for scalar functions. + + Parameters + ---------- + func : callable f(x,*args) + Objective function to be minimized (must accept and return scalars). + x1, x2 : float or array scalar + Finite optimization bounds. + args : tuple, optional + Extra arguments passed to function. + xtol : float, optional + The convergence tolerance. + maxfun : int, optional + Maximum number of function evaluations allowed. + full_output : bool, optional + If True, return optional outputs. + disp : int, optional + If non-zero, print messages. + 0 : no message printing. + 1 : non-convergence notification messages only. + 2 : print a message on convergence too. + 3 : print iteration results. + + + Returns + ------- + xopt : ndarray + Parameters (over given interval) which minimize the + objective function. + fval : number + (Optional output) The function value evaluated at the minimizer. + ierr : int + (Optional output) An error flag (0 if converged, 1 if maximum number of + function calls reached). + numfunc : int + (Optional output) The number of function calls made. + + See also + -------- + minimize_scalar: Interface to minimization algorithms for scalar + univariate functions. See the 'Bounded' `method` in particular. + + Notes + ----- + Finds a local minimizer of the scalar function `func` in the + interval x1 < xopt < x2 using Brent's method. (See `brent` + for auto-bracketing.) + + References + ---------- + .. [1] Forsythe, G.E., M. A. Malcolm, and C. B. Moler. "Computer Methods + for Mathematical Computations." Prentice-Hall Series in Automatic + Computation 259 (1977). + .. [2] Brent, Richard P. Algorithms for Minimization Without Derivatives. + Courier Corporation, 2013. + + Examples + -------- + `fminbound` finds the minimizer of the function in the given range. + The following examples illustrate this. + + >>> from scipy import optimize + >>> def f(x): + ... return (x-1)**2 + >>> minimizer = optimize.fminbound(f, -4, 4) + >>> minimizer + 1.0 + >>> minimum = f(minimizer) + >>> minimum + 0.0 + >>> res = optimize.fminbound(f, 3, 4, full_output=True) + >>> minimizer, fval, ierr, numfunc = res + >>> minimizer + 3.000005960860986 + >>> minimum = f(minimizer) + >>> minimum, fval + (4.000023843479476, 4.000023843479476) + """ + options = {'xatol': xtol, + 'maxiter': maxfun, + 'disp': disp} + + res = _minimize_scalar_bounded(func, (x1, x2), args, **options) + if full_output: + return res['x'], res['fun'], res['status'], res['nfev'] + else: + return res['x'] + + +def _minimize_scalar_bounded(func, bounds, args=(), + xatol=1e-5, maxiter=500, disp=0, + **unknown_options): + """ + Options + ------- + maxiter : int + Maximum number of iterations to perform. + disp: int, optional + If non-zero, print messages. + 0 : no message printing. + 1 : non-convergence notification messages only. + 2 : print a message on convergence too. + 3 : print iteration results. + xatol : float + Absolute error in solution `xopt` acceptable for convergence. + + """ + _check_unknown_options(unknown_options) + maxfun = maxiter + # Test bounds are of correct form + if len(bounds) != 2: + raise ValueError('bounds must have two elements.') + x1, x2 = bounds + + if not (is_finite_scalar(x1) and is_finite_scalar(x2)): + raise ValueError("Optimization bounds must be finite scalars.") + + if x1 > x2: + raise ValueError("The lower bound exceeds the upper bound.") + + flag = 0 + header = ' Func-count x f(x) Procedure' + step = ' initial' + + sqrt_eps = sqrt(2.2e-16) + golden_mean = 0.5 * (3.0 - sqrt(5.0)) + a, b = x1, x2 + fulc = a + golden_mean * (b - a) + nfc, xf = fulc, fulc + rat = e = 0.0 + x = xf + fx = func(x, *args) + num = 1 + fmin_data = (1, xf, fx) + fu = np.inf + + ffulc = fnfc = fx + xm = 0.5 * (a + b) + tol1 = sqrt_eps * np.abs(xf) + xatol / 3.0 + tol2 = 2.0 * tol1 + + if disp > 2: + print(" ") + print(header) + print("%5.0f %12.6g %12.6g %s" % (fmin_data + (step,))) + + while (np.abs(xf - xm) > (tol2 - 0.5 * (b - a))): + golden = 1 + # Check for parabolic fit + if np.abs(e) > tol1: + golden = 0 + r = (xf - nfc) * (fx - ffulc) + q = (xf - fulc) * (fx - fnfc) + p = (xf - fulc) * q - (xf - nfc) * r + q = 2.0 * (q - r) + if q > 0.0: + p = -p + q = np.abs(q) + r = e + e = rat + + # Check for acceptability of parabola + if ((np.abs(p) < np.abs(0.5*q*r)) and (p > q*(a - xf)) and + (p < q * (b - xf))): + rat = (p + 0.0) / q + x = xf + rat + step = ' parabolic' + + if ((x - a) < tol2) or ((b - x) < tol2): + si = np.sign(xm - xf) + ((xm - xf) == 0) + rat = tol1 * si + else: # do a golden-section step + golden = 1 + + if golden: # do a golden-section step + if xf >= xm: + e = a - xf + else: + e = b - xf + rat = golden_mean*e + step = ' golden' + + si = np.sign(rat) + (rat == 0) + x = xf + si * np.maximum(np.abs(rat), tol1) + fu = func(x, *args) + num += 1 + fmin_data = (num, x, fu) + if disp > 2: + print("%5.0f %12.6g %12.6g %s" % (fmin_data + (step,))) + + if fu <= fx: + if x >= xf: + a = xf + else: + b = xf + fulc, ffulc = nfc, fnfc + nfc, fnfc = xf, fx + xf, fx = x, fu + else: + if x < xf: + a = x + else: + b = x + if (fu <= fnfc) or (nfc == xf): + fulc, ffulc = nfc, fnfc + nfc, fnfc = x, fu + elif (fu <= ffulc) or (fulc == xf) or (fulc == nfc): + fulc, ffulc = x, fu + + xm = 0.5 * (a + b) + tol1 = sqrt_eps * np.abs(xf) + xatol / 3.0 + tol2 = 2.0 * tol1 + + if num >= maxfun: + flag = 1 + break + + if np.isnan(xf) or np.isnan(fx) or np.isnan(fu): + flag = 2 + + fval = fx + if disp > 0: + _endprint(x, flag, fval, maxfun, xatol, disp) + + result = OptimizeResult(fun=fval, status=flag, success=(flag == 0), + message={0: 'Solution found.', + 1: 'Maximum number of function calls ' + 'reached.', + 2: _status_message['nan']}.get(flag, ''), + x=xf, nfev=num, nit=num) + + return result + + +class Brent: + #need to rethink design of __init__ + def __init__(self, func, args=(), tol=1.48e-8, maxiter=500, + full_output=0, disp=0): + self.func = func + self.args = args + self.tol = tol + self.maxiter = maxiter + self._mintol = 1.0e-11 + self._cg = 0.3819660 + self.xmin = None + self.fval = None + self.iter = 0 + self.funcalls = 0 + self.disp = disp + + # need to rethink design of set_bracket (new options, etc.) + def set_bracket(self, brack=None): + self.brack = brack + + def get_bracket_info(self): + #set up + func = self.func + args = self.args + brack = self.brack + ### BEGIN core bracket_info code ### + ### carefully DOCUMENT any CHANGES in core ## + if brack is None: + xa, xb, xc, fa, fb, fc, funcalls = bracket(func, args=args) + elif len(brack) == 2: + xa, xb, xc, fa, fb, fc, funcalls = bracket(func, xa=brack[0], + xb=brack[1], args=args) + elif len(brack) == 3: + xa, xb, xc = brack + if (xa > xc): # swap so xa < xc can be assumed + xc, xa = xa, xc + if not ((xa < xb) and (xb < xc)): + raise ValueError( + "Bracketing values (xa, xb, xc) do not" + " fulfill this requirement: (xa < xb) and (xb < xc)" + ) + fa = func(*((xa,) + args)) + fb = func(*((xb,) + args)) + fc = func(*((xc,) + args)) + if not ((fb < fa) and (fb < fc)): + raise ValueError( + "Bracketing values (xa, xb, xc) do not fulfill" + " this requirement: (f(xb) < f(xa)) and (f(xb) < f(xc))" + ) + + funcalls = 3 + else: + raise ValueError("Bracketing interval must be " + "length 2 or 3 sequence.") + ### END core bracket_info code ### + + return xa, xb, xc, fa, fb, fc, funcalls + + def optimize(self): + # set up for optimization + func = self.func + xa, xb, xc, fa, fb, fc, funcalls = self.get_bracket_info() + _mintol = self._mintol + _cg = self._cg + ################################# + #BEGIN CORE ALGORITHM + ################################# + x = w = v = xb + fw = fv = fx = fb + if (xa < xc): + a = xa + b = xc + else: + a = xc + b = xa + deltax = 0.0 + iter = 0 + + if self.disp > 2: + print(" ") + print(f"{'Func-count':^12} {'x':^12} {'f(x)': ^12}") + print(f"{funcalls:^12g} {x:^12.6g} {fx:^12.6g}") + + while (iter < self.maxiter): + tol1 = self.tol * np.abs(x) + _mintol + tol2 = 2.0 * tol1 + xmid = 0.5 * (a + b) + # check for convergence + if np.abs(x - xmid) < (tol2 - 0.5 * (b - a)): + break + # XXX In the first iteration, rat is only bound in the true case + # of this conditional. This used to cause an UnboundLocalError + # (gh-4140). It should be set before the if (but to what?). + if (np.abs(deltax) <= tol1): + if (x >= xmid): + deltax = a - x # do a golden section step + else: + deltax = b - x + rat = _cg * deltax + else: # do a parabolic step + tmp1 = (x - w) * (fx - fv) + tmp2 = (x - v) * (fx - fw) + p = (x - v) * tmp2 - (x - w) * tmp1 + tmp2 = 2.0 * (tmp2 - tmp1) + if (tmp2 > 0.0): + p = -p + tmp2 = np.abs(tmp2) + dx_temp = deltax + deltax = rat + # check parabolic fit + if ((p > tmp2 * (a - x)) and (p < tmp2 * (b - x)) and + (np.abs(p) < np.abs(0.5 * tmp2 * dx_temp))): + rat = p * 1.0 / tmp2 # if parabolic step is useful. + u = x + rat + if ((u - a) < tol2 or (b - u) < tol2): + if xmid - x >= 0: + rat = tol1 + else: + rat = -tol1 + else: + if (x >= xmid): + deltax = a - x # if it's not do a golden section step + else: + deltax = b - x + rat = _cg * deltax + + if (np.abs(rat) < tol1): # update by at least tol1 + if rat >= 0: + u = x + tol1 + else: + u = x - tol1 + else: + u = x + rat + fu = func(*((u,) + self.args)) # calculate new output value + funcalls += 1 + + if (fu > fx): # if it's bigger than current + if (u < x): + a = u + else: + b = u + if (fu <= fw) or (w == x): + v = w + w = u + fv = fw + fw = fu + elif (fu <= fv) or (v == x) or (v == w): + v = u + fv = fu + else: + if (u >= x): + a = x + else: + b = x + v = w + w = x + x = u + fv = fw + fw = fx + fx = fu + + if self.disp > 2: + print(f"{funcalls:^12g} {x:^12.6g} {fx:^12.6g}") + + iter += 1 + ################################# + #END CORE ALGORITHM + ################################# + + self.xmin = x + self.fval = fx + self.iter = iter + self.funcalls = funcalls + + def get_result(self, full_output=False): + if full_output: + return self.xmin, self.fval, self.iter, self.funcalls + else: + return self.xmin + + +def brent(func, args=(), brack=None, tol=1.48e-8, full_output=0, maxiter=500): + """ + Given a function of one variable and a possible bracket, return + a local minimizer of the function isolated to a fractional precision + of tol. + + Parameters + ---------- + func : callable f(x,*args) + Objective function. + args : tuple, optional + Additional arguments (if present). + brack : tuple, optional + Either a triple ``(xa, xb, xc)`` satisfying ``xa < xb < xc`` and + ``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair + ``(xa, xb)`` to be used as initial points for a downhill bracket search + (see `scipy.optimize.bracket`). + The minimizer ``x`` will not necessarily satisfy ``xa <= x <= xb``. + tol : float, optional + Relative error in solution `xopt` acceptable for convergence. + full_output : bool, optional + If True, return all output args (xmin, fval, iter, + funcalls). + maxiter : int, optional + Maximum number of iterations in solution. + + Returns + ------- + xmin : ndarray + Optimum point. + fval : float + (Optional output) Optimum function value. + iter : int + (Optional output) Number of iterations. + funcalls : int + (Optional output) Number of objective function evaluations made. + + See also + -------- + minimize_scalar: Interface to minimization algorithms for scalar + univariate functions. See the 'Brent' `method` in particular. + + Notes + ----- + Uses inverse parabolic interpolation when possible to speed up + convergence of golden section method. + + Does not ensure that the minimum lies in the range specified by + `brack`. See `scipy.optimize.fminbound`. + + Examples + -------- + We illustrate the behaviour of the function when `brack` is of + size 2 and 3 respectively. In the case where `brack` is of the + form ``(xa, xb)``, we can see for the given values, the output does + not necessarily lie in the range ``(xa, xb)``. + + >>> def f(x): + ... return (x-1)**2 + + >>> from scipy import optimize + + >>> minimizer = optimize.brent(f, brack=(1, 2)) + >>> minimizer + 1 + >>> res = optimize.brent(f, brack=(-1, 0.5, 2), full_output=True) + >>> xmin, fval, iter, funcalls = res + >>> f(xmin), fval + (0.0, 0.0) + + """ + options = {'xtol': tol, + 'maxiter': maxiter} + res = _minimize_scalar_brent(func, brack, args, **options) + if full_output: + return res['x'], res['fun'], res['nit'], res['nfev'] + else: + return res['x'] + + +def _minimize_scalar_brent(func, brack=None, args=(), xtol=1.48e-8, + maxiter=500, disp=0, + **unknown_options): + """ + Options + ------- + maxiter : int + Maximum number of iterations to perform. + xtol : float + Relative error in solution `xopt` acceptable for convergence. + disp: int, optional + If non-zero, print messages. + 0 : no message printing. + 1 : non-convergence notification messages only. + 2 : print a message on convergence too. + 3 : print iteration results. + Notes + ----- + Uses inverse parabolic interpolation when possible to speed up + convergence of golden section method. + + """ + _check_unknown_options(unknown_options) + tol = xtol + if tol < 0: + raise ValueError('tolerance should be >= 0, got %r' % tol) + + brent = Brent(func=func, args=args, tol=tol, + full_output=True, maxiter=maxiter, disp=disp) + brent.set_bracket(brack) + brent.optimize() + x, fval, nit, nfev = brent.get_result(full_output=True) + + success = nit < maxiter and not (np.isnan(x) or np.isnan(fval)) + + if success: + message = ("\nOptimization terminated successfully;\n" + "The returned value satisfies the termination criteria\n" + f"(using xtol = {xtol} )") + else: + if nit >= maxiter: + message = "\nMaximum number of iterations exceeded" + if np.isnan(x) or np.isnan(fval): + message = f"{_status_message['nan']}" + + if disp: + _print_success_message_or_warn(not success, message) + + return OptimizeResult(fun=fval, x=x, nit=nit, nfev=nfev, + success=success, message=message) + + +def golden(func, args=(), brack=None, tol=_epsilon, + full_output=0, maxiter=5000): + """ + Return the minimizer of a function of one variable using the golden section + method. + + Given a function of one variable and a possible bracketing interval, + return a minimizer of the function isolated to a fractional precision of + tol. + + Parameters + ---------- + func : callable func(x,*args) + Objective function to minimize. + args : tuple, optional + Additional arguments (if present), passed to func. + brack : tuple, optional + Either a triple ``(xa, xb, xc)`` where ``xa < xb < xc`` and + ``func(xb) < func(xa) and func(xb) < func(xc)``, or a pair (xa, xb) + to be used as initial points for a downhill bracket search (see + `scipy.optimize.bracket`). + The minimizer ``x`` will not necessarily satisfy ``xa <= x <= xb``. + tol : float, optional + x tolerance stop criterion + full_output : bool, optional + If True, return optional outputs. + maxiter : int + Maximum number of iterations to perform. + + Returns + ------- + xmin : ndarray + Optimum point. + fval : float + (Optional output) Optimum function value. + funcalls : int + (Optional output) Number of objective function evaluations made. + + See also + -------- + minimize_scalar: Interface to minimization algorithms for scalar + univariate functions. See the 'Golden' `method` in particular. + + Notes + ----- + Uses analog of bisection method to decrease the bracketed + interval. + + Examples + -------- + We illustrate the behaviour of the function when `brack` is of + size 2 and 3, respectively. In the case where `brack` is of the + form (xa,xb), we can see for the given values, the output need + not necessarily lie in the range ``(xa, xb)``. + + >>> def f(x): + ... return (x-1)**2 + + >>> from scipy import optimize + + >>> minimizer = optimize.golden(f, brack=(1, 2)) + >>> minimizer + 1 + >>> res = optimize.golden(f, brack=(-1, 0.5, 2), full_output=True) + >>> xmin, fval, funcalls = res + >>> f(xmin), fval + (9.925165290385052e-18, 9.925165290385052e-18) + + """ + options = {'xtol': tol, 'maxiter': maxiter} + res = _minimize_scalar_golden(func, brack, args, **options) + if full_output: + return res['x'], res['fun'], res['nfev'] + else: + return res['x'] + + +def _minimize_scalar_golden(func, brack=None, args=(), + xtol=_epsilon, maxiter=5000, disp=0, + **unknown_options): + """ + Options + ------- + xtol : float + Relative error in solution `xopt` acceptable for convergence. + maxiter : int + Maximum number of iterations to perform. + disp: int, optional + If non-zero, print messages. + 0 : no message printing. + 1 : non-convergence notification messages only. + 2 : print a message on convergence too. + 3 : print iteration results. + """ + _check_unknown_options(unknown_options) + tol = xtol + if brack is None: + xa, xb, xc, fa, fb, fc, funcalls = bracket(func, args=args) + elif len(brack) == 2: + xa, xb, xc, fa, fb, fc, funcalls = bracket(func, xa=brack[0], + xb=brack[1], args=args) + elif len(brack) == 3: + xa, xb, xc = brack + if (xa > xc): # swap so xa < xc can be assumed + xc, xa = xa, xc + if not ((xa < xb) and (xb < xc)): + raise ValueError( + "Bracketing values (xa, xb, xc) do not" + " fulfill this requirement: (xa < xb) and (xb < xc)" + ) + fa = func(*((xa,) + args)) + fb = func(*((xb,) + args)) + fc = func(*((xc,) + args)) + if not ((fb < fa) and (fb < fc)): + raise ValueError( + "Bracketing values (xa, xb, xc) do not fulfill" + " this requirement: (f(xb) < f(xa)) and (f(xb) < f(xc))" + ) + funcalls = 3 + else: + raise ValueError("Bracketing interval must be length 2 or 3 sequence.") + + _gR = 0.61803399 # golden ratio conjugate: 2.0/(1.0+sqrt(5.0)) + _gC = 1.0 - _gR + x3 = xc + x0 = xa + if (np.abs(xc - xb) > np.abs(xb - xa)): + x1 = xb + x2 = xb + _gC * (xc - xb) + else: + x2 = xb + x1 = xb - _gC * (xb - xa) + f1 = func(*((x1,) + args)) + f2 = func(*((x2,) + args)) + funcalls += 2 + nit = 0 + + if disp > 2: + print(" ") + print(f"{'Func-count':^12} {'x':^12} {'f(x)': ^12}") + + for i in range(maxiter): + if np.abs(x3 - x0) <= tol * (np.abs(x1) + np.abs(x2)): + break + if (f2 < f1): + x0 = x1 + x1 = x2 + x2 = _gR * x1 + _gC * x3 + f1 = f2 + f2 = func(*((x2,) + args)) + else: + x3 = x2 + x2 = x1 + x1 = _gR * x2 + _gC * x0 + f2 = f1 + f1 = func(*((x1,) + args)) + funcalls += 1 + if disp > 2: + if (f1 < f2): + xmin, fval = x1, f1 + else: + xmin, fval = x2, f2 + print(f"{funcalls:^12g} {xmin:^12.6g} {fval:^12.6g}") + + nit += 1 + # end of iteration loop + + if (f1 < f2): + xmin = x1 + fval = f1 + else: + xmin = x2 + fval = f2 + + success = nit < maxiter and not (np.isnan(fval) or np.isnan(xmin)) + + if success: + message = ("\nOptimization terminated successfully;\n" + "The returned value satisfies the termination criteria\n" + f"(using xtol = {xtol} )") + else: + if nit >= maxiter: + message = "\nMaximum number of iterations exceeded" + if np.isnan(xmin) or np.isnan(fval): + message = f"{_status_message['nan']}" + + if disp: + _print_success_message_or_warn(not success, message) + + return OptimizeResult(fun=fval, nfev=funcalls, x=xmin, nit=nit, + success=success, message=message) + + +def bracket(func, xa=0.0, xb=1.0, args=(), grow_limit=110.0, maxiter=1000): + """ + Bracket the minimum of a function. + + Given a function and distinct initial points, search in the + downhill direction (as defined by the initial points) and return + three points that bracket the minimum of the function. + + Parameters + ---------- + func : callable f(x,*args) + Objective function to minimize. + xa, xb : float, optional + Initial points. Defaults `xa` to 0.0, and `xb` to 1.0. + A local minimum need not be contained within this interval. + args : tuple, optional + Additional arguments (if present), passed to `func`. + grow_limit : float, optional + Maximum grow limit. Defaults to 110.0 + maxiter : int, optional + Maximum number of iterations to perform. Defaults to 1000. + + Returns + ------- + xa, xb, xc : float + Final points of the bracket. + fa, fb, fc : float + Objective function values at the bracket points. + funcalls : int + Number of function evaluations made. + + Raises + ------ + BracketError + If no valid bracket is found before the algorithm terminates. + See notes for conditions of a valid bracket. + + Notes + ----- + The algorithm attempts to find three strictly ordered points (i.e. + :math:`x_a < x_b < x_c` or :math:`x_c < x_b < x_a`) satisfying + :math:`f(x_b) ≤ f(x_a)` and :math:`f(x_b) ≤ f(x_c)`, where one of the + inequalities must be satistfied strictly and all :math:`x_i` must be + finite. + + Examples + -------- + This function can find a downward convex region of a function: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.optimize import bracket + >>> def f(x): + ... return 10*x**2 + 3*x + 5 + >>> x = np.linspace(-2, 2) + >>> y = f(x) + >>> init_xa, init_xb = 0.1, 1 + >>> xa, xb, xc, fa, fb, fc, funcalls = bracket(f, xa=init_xa, xb=init_xb) + >>> plt.axvline(x=init_xa, color="k", linestyle="--") + >>> plt.axvline(x=init_xb, color="k", linestyle="--") + >>> plt.plot(x, y, "-k") + >>> plt.plot(xa, fa, "bx") + >>> plt.plot(xb, fb, "rx") + >>> plt.plot(xc, fc, "bx") + >>> plt.show() + + Note that both initial points were to the right of the minimum, and the + third point was found in the "downhill" direction: the direction + in which the function appeared to be decreasing (to the left). + The final points are strictly ordered, and the function value + at the middle point is less than the function values at the endpoints; + it follows that a minimum must lie within the bracket. + + """ + _gold = 1.618034 # golden ratio: (1.0+sqrt(5.0))/2.0 + _verysmall_num = 1e-21 + # convert to numpy floats if not already + xa, xb = np.asarray([xa, xb]) + fa = func(*(xa,) + args) + fb = func(*(xb,) + args) + if (fa < fb): # Switch so fa > fb + xa, xb = xb, xa + fa, fb = fb, fa + xc = xb + _gold * (xb - xa) + fc = func(*((xc,) + args)) + funcalls = 3 + iter = 0 + while (fc < fb): + tmp1 = (xb - xa) * (fb - fc) + tmp2 = (xb - xc) * (fb - fa) + val = tmp2 - tmp1 + if np.abs(val) < _verysmall_num: + denom = 2.0 * _verysmall_num + else: + denom = 2.0 * val + w = xb - ((xb - xc) * tmp2 - (xb - xa) * tmp1) / denom + wlim = xb + grow_limit * (xc - xb) + msg = ("No valid bracket was found before the iteration limit was " + "reached. Consider trying different initial points or " + "increasing `maxiter`.") + if iter > maxiter: + raise RuntimeError(msg) + iter += 1 + if (w - xc) * (xb - w) > 0.0: + fw = func(*((w,) + args)) + funcalls += 1 + if (fw < fc): + xa = xb + xb = w + fa = fb + fb = fw + break + elif (fw > fb): + xc = w + fc = fw + break + w = xc + _gold * (xc - xb) + fw = func(*((w,) + args)) + funcalls += 1 + elif (w - wlim)*(wlim - xc) >= 0.0: + w = wlim + fw = func(*((w,) + args)) + funcalls += 1 + elif (w - wlim)*(xc - w) > 0.0: + fw = func(*((w,) + args)) + funcalls += 1 + if (fw < fc): + xb = xc + xc = w + w = xc + _gold * (xc - xb) + fb = fc + fc = fw + fw = func(*((w,) + args)) + funcalls += 1 + else: + w = xc + _gold * (xc - xb) + fw = func(*((w,) + args)) + funcalls += 1 + xa = xb + xb = xc + xc = w + fa = fb + fb = fc + fc = fw + + # three conditions for a valid bracket + cond1 = (fb < fc and fb <= fa) or (fb < fa and fb <= fc) + cond2 = (xa < xb < xc or xc < xb < xa) + cond3 = np.isfinite(xa) and np.isfinite(xb) and np.isfinite(xc) + msg = ("The algorithm terminated without finding a valid bracket. " + "Consider trying different initial points.") + if not (cond1 and cond2 and cond3): + e = BracketError(msg) + e.data = (xa, xb, xc, fa, fb, fc, funcalls) + raise e + + return xa, xb, xc, fa, fb, fc, funcalls + + +class BracketError(RuntimeError): + pass + + +def _recover_from_bracket_error(solver, fun, bracket, args, **options): + # `bracket` was originally written without checking whether the resulting + # bracket is valid. `brent` and `golden` built on top of it without + # checking the returned bracket for validity, and their output can be + # incorrect without warning/error if the original bracket is invalid. + # gh-14858 noticed the problem, and the following is the desired + # behavior: + # - `scipy.optimize.bracket`, `scipy.optimize.brent`, and + # `scipy.optimize.golden` should raise an error if the bracket is + # invalid, as opposed to silently returning garbage + # - `scipy.optimize.minimize_scalar` should return with `success=False` + # and other information + # The changes that would be required to achieve this the traditional + # way (`return`ing all the required information from bracket all the way + # up to `minimizer_scalar`) are extensive and invasive. (See a6aa40d.) + # We can achieve the same thing by raising the error in `bracket`, but + # storing the information needed by `minimize_scalar` in the error object, + # and intercepting it here. + try: + res = solver(fun, bracket, args, **options) + except BracketError as e: + msg = str(e) + xa, xb, xc, fa, fb, fc, funcalls = e.data + xs, fs = [xa, xb, xc], [fa, fb, fc] + if np.any(np.isnan([xs, fs])): + x, fun = np.nan, np.nan + else: + imin = np.argmin(fs) + x, fun = xs[imin], fs[imin] + return OptimizeResult(fun=fun, nfev=funcalls, x=x, + nit=0, success=False, message=msg) + return res + + +def _line_for_search(x0, alpha, lower_bound, upper_bound): + """ + Given a parameter vector ``x0`` with length ``n`` and a direction + vector ``alpha`` with length ``n``, and lower and upper bounds on + each of the ``n`` parameters, what are the bounds on a scalar + ``l`` such that ``lower_bound <= x0 + alpha * l <= upper_bound``. + + + Parameters + ---------- + x0 : np.array. + The vector representing the current location. + Note ``np.shape(x0) == (n,)``. + alpha : np.array. + The vector representing the direction. + Note ``np.shape(alpha) == (n,)``. + lower_bound : np.array. + The lower bounds for each parameter in ``x0``. If the ``i``th + parameter in ``x0`` is unbounded below, then ``lower_bound[i]`` + should be ``-np.inf``. + Note ``np.shape(lower_bound) == (n,)``. + upper_bound : np.array. + The upper bounds for each parameter in ``x0``. If the ``i``th + parameter in ``x0`` is unbounded above, then ``upper_bound[i]`` + should be ``np.inf``. + Note ``np.shape(upper_bound) == (n,)``. + + Returns + ------- + res : tuple ``(lmin, lmax)`` + The bounds for ``l`` such that + ``lower_bound[i] <= x0[i] + alpha[i] * l <= upper_bound[i]`` + for all ``i``. + + """ + # get nonzero indices of alpha so we don't get any zero division errors. + # alpha will not be all zero, since it is called from _linesearch_powell + # where we have a check for this. + nonzero, = alpha.nonzero() + lower_bound, upper_bound = lower_bound[nonzero], upper_bound[nonzero] + x0, alpha = x0[nonzero], alpha[nonzero] + low = (lower_bound - x0) / alpha + high = (upper_bound - x0) / alpha + + # positive and negative indices + pos = alpha > 0 + + lmin_pos = np.where(pos, low, 0) + lmin_neg = np.where(pos, 0, high) + lmax_pos = np.where(pos, high, 0) + lmax_neg = np.where(pos, 0, low) + + lmin = np.max(lmin_pos + lmin_neg) + lmax = np.min(lmax_pos + lmax_neg) + + # if x0 is outside the bounds, then it is possible that there is + # no way to get back in the bounds for the parameters being updated + # with the current direction alpha. + # when this happens, lmax < lmin. + # If this is the case, then we can just return (0, 0) + return (lmin, lmax) if lmax >= lmin else (0, 0) + + +def _linesearch_powell(func, p, xi, tol=1e-3, + lower_bound=None, upper_bound=None, fval=None): + """Line-search algorithm using fminbound. + + Find the minimum of the function ``func(x0 + alpha*direc)``. + + lower_bound : np.array. + The lower bounds for each parameter in ``x0``. If the ``i``th + parameter in ``x0`` is unbounded below, then ``lower_bound[i]`` + should be ``-np.inf``. + Note ``np.shape(lower_bound) == (n,)``. + upper_bound : np.array. + The upper bounds for each parameter in ``x0``. If the ``i``th + parameter in ``x0`` is unbounded above, then ``upper_bound[i]`` + should be ``np.inf``. + Note ``np.shape(upper_bound) == (n,)``. + fval : number. + ``fval`` is equal to ``func(p)``, the idea is just to avoid + recomputing it so we can limit the ``fevals``. + + """ + def myfunc(alpha): + return func(p + alpha*xi) + + # if xi is zero, then don't optimize + if not np.any(xi): + return ((fval, p, xi) if fval is not None else (func(p), p, xi)) + elif lower_bound is None and upper_bound is None: + # non-bounded minimization + res = _recover_from_bracket_error(_minimize_scalar_brent, + myfunc, None, tuple(), xtol=tol) + alpha_min, fret = res.x, res.fun + xi = alpha_min * xi + return squeeze(fret), p + xi, xi + else: + bound = _line_for_search(p, xi, lower_bound, upper_bound) + if np.isneginf(bound[0]) and np.isposinf(bound[1]): + # equivalent to unbounded + return _linesearch_powell(func, p, xi, fval=fval, tol=tol) + elif not np.isneginf(bound[0]) and not np.isposinf(bound[1]): + # we can use a bounded scalar minimization + res = _minimize_scalar_bounded(myfunc, bound, xatol=tol / 100) + xi = res.x * xi + return squeeze(res.fun), p + xi, xi + else: + # only bounded on one side. use the tangent function to convert + # the infinity bound to a finite bound. The new bounded region + # is a subregion of the region bounded by -np.pi/2 and np.pi/2. + bound = np.arctan(bound[0]), np.arctan(bound[1]) + res = _minimize_scalar_bounded( + lambda x: myfunc(np.tan(x)), + bound, + xatol=tol / 100) + xi = np.tan(res.x) * xi + return squeeze(res.fun), p + xi, xi + + +def fmin_powell(func, x0, args=(), xtol=1e-4, ftol=1e-4, maxiter=None, + maxfun=None, full_output=0, disp=1, retall=0, callback=None, + direc=None): + """ + Minimize a function using modified Powell's method. + + This method only uses function values, not derivatives. + + Parameters + ---------- + func : callable f(x,*args) + Objective function to be minimized. + x0 : ndarray + Initial guess. + args : tuple, optional + Extra arguments passed to func. + xtol : float, optional + Line-search error tolerance. + ftol : float, optional + Relative error in ``func(xopt)`` acceptable for convergence. + maxiter : int, optional + Maximum number of iterations to perform. + maxfun : int, optional + Maximum number of function evaluations to make. + full_output : bool, optional + If True, ``fopt``, ``xi``, ``direc``, ``iter``, ``funcalls``, and + ``warnflag`` are returned. + disp : bool, optional + If True, print convergence messages. + retall : bool, optional + If True, return a list of the solution at each iteration. + callback : callable, optional + An optional user-supplied function, called after each + iteration. Called as ``callback(xk)``, where ``xk`` is the + current parameter vector. + direc : ndarray, optional + Initial fitting step and parameter order set as an (N, N) array, where N + is the number of fitting parameters in `x0`. Defaults to step size 1.0 + fitting all parameters simultaneously (``np.eye((N, N))``). To + prevent initial consideration of values in a step or to change initial + step size, set to 0 or desired step size in the Jth position in the Mth + block, where J is the position in `x0` and M is the desired evaluation + step, with steps being evaluated in index order. Step size and ordering + will change freely as minimization proceeds. + + Returns + ------- + xopt : ndarray + Parameter which minimizes `func`. + fopt : number + Value of function at minimum: ``fopt = func(xopt)``. + direc : ndarray + Current direction set. + iter : int + Number of iterations. + funcalls : int + Number of function calls made. + warnflag : int + Integer warning flag: + 1 : Maximum number of function evaluations. + 2 : Maximum number of iterations. + 3 : NaN result encountered. + 4 : The result is out of the provided bounds. + allvecs : list + List of solutions at each iteration. + + See also + -------- + minimize: Interface to unconstrained minimization algorithms for + multivariate functions. See the 'Powell' method in particular. + + Notes + ----- + Uses a modification of Powell's method to find the minimum of + a function of N variables. Powell's method is a conjugate + direction method. + + The algorithm has two loops. The outer loop merely iterates over the inner + loop. The inner loop minimizes over each current direction in the direction + set. At the end of the inner loop, if certain conditions are met, the + direction that gave the largest decrease is dropped and replaced with the + difference between the current estimated x and the estimated x from the + beginning of the inner-loop. + + The technical conditions for replacing the direction of greatest + increase amount to checking that + + 1. No further gain can be made along the direction of greatest increase + from that iteration. + 2. The direction of greatest increase accounted for a large sufficient + fraction of the decrease in the function value from that iteration of + the inner loop. + + References + ---------- + Powell M.J.D. (1964) An efficient method for finding the minimum of a + function of several variables without calculating derivatives, + Computer Journal, 7 (2):155-162. + + Press W., Teukolsky S.A., Vetterling W.T., and Flannery B.P.: + Numerical Recipes (any edition), Cambridge University Press + + Examples + -------- + >>> def f(x): + ... return x**2 + + >>> from scipy import optimize + + >>> minimum = optimize.fmin_powell(f, -1) + Optimization terminated successfully. + Current function value: 0.000000 + Iterations: 2 + Function evaluations: 16 + >>> minimum + array(0.0) + + """ + opts = {'xtol': xtol, + 'ftol': ftol, + 'maxiter': maxiter, + 'maxfev': maxfun, + 'disp': disp, + 'direc': direc, + 'return_all': retall} + + callback = _wrap_callback(callback) + res = _minimize_powell(func, x0, args, callback=callback, **opts) + + if full_output: + retlist = (res['x'], res['fun'], res['direc'], res['nit'], + res['nfev'], res['status']) + if retall: + retlist += (res['allvecs'], ) + return retlist + else: + if retall: + return res['x'], res['allvecs'] + else: + return res['x'] + + +def _minimize_powell(func, x0, args=(), callback=None, bounds=None, + xtol=1e-4, ftol=1e-4, maxiter=None, maxfev=None, + disp=False, direc=None, return_all=False, + **unknown_options): + """ + Minimization of scalar function of one or more variables using the + modified Powell algorithm. + + Parameters + ---------- + fun : callable + The objective function to be minimized. + + ``fun(x, *args) -> float`` + + where ``x`` is a 1-D array with shape (n,) and ``args`` + is a tuple of the fixed parameters needed to completely + specify the function. + x0 : ndarray, shape (n,) + Initial guess. Array of real elements of size (n,), + where ``n`` is the number of independent variables. + args : tuple, optional + Extra arguments passed to the objective function and its + derivatives (`fun`, `jac` and `hess` functions). + method : str or callable, optional + The present documentation is specific to ``method='powell'``, but other + options are available. See documentation for `scipy.optimize.minimize`. + bounds : sequence or `Bounds`, optional + Bounds on decision variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. Sequence of ``(min, max)`` pairs for each element in `x`. None + is used to specify no bound. + + If bounds are not provided, then an unbounded line search will be used. + If bounds are provided and the initial guess is within the bounds, then + every function evaluation throughout the minimization procedure will be + within the bounds. If bounds are provided, the initial guess is outside + the bounds, and `direc` is full rank (or left to default), then some + function evaluations during the first iteration may be outside the + bounds, but every function evaluation after the first iteration will be + within the bounds. If `direc` is not full rank, then some parameters + may not be optimized and the solution is not guaranteed to be within + the bounds. + + options : dict, optional + A dictionary of solver options. All methods accept the following + generic options: + + maxiter : int + Maximum number of iterations to perform. Depending on the + method each iteration may use several function evaluations. + disp : bool + Set to True to print convergence messages. + + See method-specific options for ``method='powell'`` below. + callback : callable, optional + Called after each iteration. The signature is: + + ``callback(xk)`` + + where ``xk`` is the current parameter vector. + + Returns + ------- + res : OptimizeResult + The optimization result represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the optimizer exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. + + Options + ------- + disp : bool + Set to True to print convergence messages. + xtol : float + Relative error in solution `xopt` acceptable for convergence. + ftol : float + Relative error in ``fun(xopt)`` acceptable for convergence. + maxiter, maxfev : int + Maximum allowed number of iterations and function evaluations. + Will default to ``N*1000``, where ``N`` is the number of + variables, if neither `maxiter` or `maxfev` is set. If both + `maxiter` and `maxfev` are set, minimization will stop at the + first reached. + direc : ndarray + Initial set of direction vectors for the Powell method. + return_all : bool, optional + Set to True to return a list of the best solution at each of the + iterations. + """ + _check_unknown_options(unknown_options) + maxfun = maxfev + retall = return_all + + x = asarray(x0).flatten() + if retall: + allvecs = [x] + N = len(x) + # If neither are set, then set both to default + if maxiter is None and maxfun is None: + maxiter = N * 1000 + maxfun = N * 1000 + elif maxiter is None: + # Convert remaining Nones, to np.inf, unless the other is np.inf, in + # which case use the default to avoid unbounded iteration + if maxfun == np.inf: + maxiter = N * 1000 + else: + maxiter = np.inf + elif maxfun is None: + if maxiter == np.inf: + maxfun = N * 1000 + else: + maxfun = np.inf + + # we need to use a mutable object here that we can update in the + # wrapper function + fcalls, func = _wrap_scalar_function_maxfun_validation(func, args, maxfun) + + if direc is None: + direc = eye(N, dtype=float) + else: + direc = asarray(direc, dtype=float) + if np.linalg.matrix_rank(direc) != direc.shape[0]: + warnings.warn("direc input is not full rank, some parameters may " + "not be optimized", + OptimizeWarning, stacklevel=3) + + if bounds is None: + # don't make these arrays of all +/- inf. because + # _linesearch_powell will do an unnecessary check of all the elements. + # just keep them None, _linesearch_powell will not have to check + # all the elements. + lower_bound, upper_bound = None, None + else: + # bounds is standardized in _minimize.py. + lower_bound, upper_bound = bounds.lb, bounds.ub + if np.any(lower_bound > x0) or np.any(x0 > upper_bound): + warnings.warn("Initial guess is not within the specified bounds", + OptimizeWarning, stacklevel=3) + + fval = squeeze(func(x)) + x1 = x.copy() + iter = 0 + while True: + try: + fx = fval + bigind = 0 + delta = 0.0 + for i in range(N): + direc1 = direc[i] + fx2 = fval + fval, x, direc1 = _linesearch_powell(func, x, direc1, + tol=xtol * 100, + lower_bound=lower_bound, + upper_bound=upper_bound, + fval=fval) + if (fx2 - fval) > delta: + delta = fx2 - fval + bigind = i + iter += 1 + if retall: + allvecs.append(x) + intermediate_result = OptimizeResult(x=x, fun=fval) + if _call_callback_maybe_halt(callback, intermediate_result): + break + bnd = ftol * (np.abs(fx) + np.abs(fval)) + 1e-20 + if 2.0 * (fx - fval) <= bnd: + break + if fcalls[0] >= maxfun: + break + if iter >= maxiter: + break + if np.isnan(fx) and np.isnan(fval): + # Ended up in a nan-region: bail out + break + + # Construct the extrapolated point + direc1 = x - x1 + x1 = x.copy() + # make sure that we don't go outside the bounds when extrapolating + if lower_bound is None and upper_bound is None: + lmax = 1 + else: + _, lmax = _line_for_search(x, direc1, lower_bound, upper_bound) + x2 = x + min(lmax, 1) * direc1 + fx2 = squeeze(func(x2)) + + if (fx > fx2): + t = 2.0*(fx + fx2 - 2.0*fval) + temp = (fx - fval - delta) + t *= temp*temp + temp = fx - fx2 + t -= delta*temp*temp + if t < 0.0: + fval, x, direc1 = _linesearch_powell( + func, x, direc1, + tol=xtol * 100, + lower_bound=lower_bound, + upper_bound=upper_bound, + fval=fval + ) + if np.any(direc1): + direc[bigind] = direc[-1] + direc[-1] = direc1 + except _MaxFuncCallError: + break + + warnflag = 0 + msg = _status_message['success'] + # out of bounds is more urgent than exceeding function evals or iters, + # but I don't want to cause inconsistencies by changing the + # established warning flags for maxfev and maxiter, so the out of bounds + # warning flag becomes 3, but is checked for first. + if bounds and (np.any(lower_bound > x) or np.any(x > upper_bound)): + warnflag = 4 + msg = _status_message['out_of_bounds'] + elif fcalls[0] >= maxfun: + warnflag = 1 + msg = _status_message['maxfev'] + elif iter >= maxiter: + warnflag = 2 + msg = _status_message['maxiter'] + elif np.isnan(fval) or np.isnan(x).any(): + warnflag = 3 + msg = _status_message['nan'] + + if disp: + _print_success_message_or_warn(warnflag, msg, RuntimeWarning) + print(" Current function value: %f" % fval) + print(" Iterations: %d" % iter) + print(" Function evaluations: %d" % fcalls[0]) + + result = OptimizeResult(fun=fval, direc=direc, nit=iter, nfev=fcalls[0], + status=warnflag, success=(warnflag == 0), + message=msg, x=x) + if retall: + result['allvecs'] = allvecs + return result + + +def _endprint(x, flag, fval, maxfun, xtol, disp): + if flag == 0: + if disp > 1: + print("\nOptimization terminated successfully;\n" + "The returned value satisfies the termination criteria\n" + "(using xtol = ", xtol, ")") + return + + if flag == 1: + msg = ("\nMaximum number of function evaluations exceeded --- " + "increase maxfun argument.\n") + elif flag == 2: + msg = "\n{}".format(_status_message['nan']) + + _print_success_message_or_warn(flag, msg) + return + + +def brute(func, ranges, args=(), Ns=20, full_output=0, finish=fmin, + disp=False, workers=1): + """Minimize a function over a given range by brute force. + + Uses the "brute force" method, i.e., computes the function's value + at each point of a multidimensional grid of points, to find the global + minimum of the function. + + The function is evaluated everywhere in the range with the datatype of the + first call to the function, as enforced by the ``vectorize`` NumPy + function. The value and type of the function evaluation returned when + ``full_output=True`` are affected in addition by the ``finish`` argument + (see Notes). + + The brute force approach is inefficient because the number of grid points + increases exponentially - the number of grid points to evaluate is + ``Ns ** len(x)``. Consequently, even with coarse grid spacing, even + moderately sized problems can take a long time to run, and/or run into + memory limitations. + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the + form ``f(x, *args)``, where ``x`` is the argument in + the form of a 1-D array and ``args`` is a tuple of any + additional fixed parameters needed to completely specify + the function. + ranges : tuple + Each component of the `ranges` tuple must be either a + "slice object" or a range tuple of the form ``(low, high)``. + The program uses these to create the grid of points on which + the objective function will be computed. See `Note 2` for + more detail. + args : tuple, optional + Any additional fixed parameters needed to completely specify + the function. + Ns : int, optional + Number of grid points along the axes, if not otherwise + specified. See `Note2`. + full_output : bool, optional + If True, return the evaluation grid and the objective function's + values on it. + finish : callable, optional + An optimization function that is called with the result of brute force + minimization as initial guess. `finish` should take `func` and + the initial guess as positional arguments, and take `args` as + keyword arguments. It may additionally take `full_output` + and/or `disp` as keyword arguments. Use None if no "polishing" + function is to be used. See Notes for more details. + disp : bool, optional + Set to True to print convergence messages from the `finish` callable. + workers : int or map-like callable, optional + If `workers` is an int the grid is subdivided into `workers` + sections and evaluated in parallel (uses + `multiprocessing.Pool `). + Supply `-1` to use all cores available to the Process. + Alternatively supply a map-like callable, such as + `multiprocessing.Pool.map` for evaluating the grid in parallel. + This evaluation is carried out as ``workers(func, iterable)``. + Requires that `func` be pickleable. + + .. versionadded:: 1.3.0 + + Returns + ------- + x0 : ndarray + A 1-D array containing the coordinates of a point at which the + objective function had its minimum value. (See `Note 1` for + which point is returned.) + fval : float + Function value at the point `x0`. (Returned when `full_output` is + True.) + grid : tuple + Representation of the evaluation grid. It has the same + length as `x0`. (Returned when `full_output` is True.) + Jout : ndarray + Function values at each point of the evaluation + grid, i.e., ``Jout = func(*grid)``. (Returned + when `full_output` is True.) + + See Also + -------- + basinhopping, differential_evolution + + Notes + ----- + *Note 1*: The program finds the gridpoint at which the lowest value + of the objective function occurs. If `finish` is None, that is the + point returned. When the global minimum occurs within (or not very far + outside) the grid's boundaries, and the grid is fine enough, that + point will be in the neighborhood of the global minimum. + + However, users often employ some other optimization program to + "polish" the gridpoint values, i.e., to seek a more precise + (local) minimum near `brute's` best gridpoint. + The `brute` function's `finish` option provides a convenient way to do + that. Any polishing program used must take `brute's` output as its + initial guess as a positional argument, and take `brute's` input values + for `args` as keyword arguments, otherwise an error will be raised. + It may additionally take `full_output` and/or `disp` as keyword arguments. + + `brute` assumes that the `finish` function returns either an + `OptimizeResult` object or a tuple in the form: + ``(xmin, Jmin, ... , statuscode)``, where ``xmin`` is the minimizing + value of the argument, ``Jmin`` is the minimum value of the objective + function, "..." may be some other returned values (which are not used + by `brute`), and ``statuscode`` is the status code of the `finish` program. + + Note that when `finish` is not None, the values returned are those + of the `finish` program, *not* the gridpoint ones. Consequently, + while `brute` confines its search to the input grid points, + the `finish` program's results usually will not coincide with any + gridpoint, and may fall outside the grid's boundary. Thus, if a + minimum only needs to be found over the provided grid points, make + sure to pass in `finish=None`. + + *Note 2*: The grid of points is a `numpy.mgrid` object. + For `brute` the `ranges` and `Ns` inputs have the following effect. + Each component of the `ranges` tuple can be either a slice object or a + two-tuple giving a range of values, such as (0, 5). If the component is a + slice object, `brute` uses it directly. If the component is a two-tuple + range, `brute` internally converts it to a slice object that interpolates + `Ns` points from its low-value to its high-value, inclusive. + + Examples + -------- + We illustrate the use of `brute` to seek the global minimum of a function + of two variables that is given as the sum of a positive-definite + quadratic and two deep "Gaussian-shaped" craters. Specifically, define + the objective function `f` as the sum of three other functions, + ``f = f1 + f2 + f3``. We suppose each of these has a signature + ``(z, *params)``, where ``z = (x, y)``, and ``params`` and the functions + are as defined below. + + >>> import numpy as np + >>> params = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5) + >>> def f1(z, *params): + ... x, y = z + ... a, b, c, d, e, f, g, h, i, j, k, l, scale = params + ... return (a * x**2 + b * x * y + c * y**2 + d*x + e*y + f) + + >>> def f2(z, *params): + ... x, y = z + ... a, b, c, d, e, f, g, h, i, j, k, l, scale = params + ... return (-g*np.exp(-((x-h)**2 + (y-i)**2) / scale)) + + >>> def f3(z, *params): + ... x, y = z + ... a, b, c, d, e, f, g, h, i, j, k, l, scale = params + ... return (-j*np.exp(-((x-k)**2 + (y-l)**2) / scale)) + + >>> def f(z, *params): + ... return f1(z, *params) + f2(z, *params) + f3(z, *params) + + Thus, the objective function may have local minima near the minimum + of each of the three functions of which it is composed. To + use `fmin` to polish its gridpoint result, we may then continue as + follows: + + >>> rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25)) + >>> from scipy import optimize + >>> resbrute = optimize.brute(f, rranges, args=params, full_output=True, + ... finish=optimize.fmin) + >>> resbrute[0] # global minimum + array([-1.05665192, 1.80834843]) + >>> resbrute[1] # function value at global minimum + -3.4085818767 + + Note that if `finish` had been set to None, we would have gotten the + gridpoint [-1.0 1.75] where the rounded function value is -2.892. + + """ + N = len(ranges) + if N > 40: + raise ValueError("Brute Force not possible with more " + "than 40 variables.") + lrange = list(ranges) + for k in range(N): + if not isinstance(lrange[k], slice): + if len(lrange[k]) < 3: + lrange[k] = tuple(lrange[k]) + (complex(Ns),) + lrange[k] = slice(*lrange[k]) + if (N == 1): + lrange = lrange[0] + + grid = np.mgrid[lrange] + + # obtain an array of parameters that is iterable by a map-like callable + inpt_shape = grid.shape + if (N > 1): + grid = np.reshape(grid, (inpt_shape[0], np.prod(inpt_shape[1:]))).T + + if not np.iterable(args): + args = (args,) + + wrapped_func = _Brute_Wrapper(func, args) + + # iterate over input arrays, possibly in parallel + with MapWrapper(pool=workers) as mapper: + Jout = np.array(list(mapper(wrapped_func, grid))) + if (N == 1): + grid = (grid,) + Jout = np.squeeze(Jout) + elif (N > 1): + Jout = np.reshape(Jout, inpt_shape[1:]) + grid = np.reshape(grid.T, inpt_shape) + + Nshape = shape(Jout) + + indx = argmin(Jout.ravel(), axis=-1) + Nindx = np.empty(N, int) + xmin = np.empty(N, float) + for k in range(N - 1, -1, -1): + thisN = Nshape[k] + Nindx[k] = indx % Nshape[k] + indx = indx // thisN + for k in range(N): + xmin[k] = grid[k][tuple(Nindx)] + + Jmin = Jout[tuple(Nindx)] + if (N == 1): + grid = grid[0] + xmin = xmin[0] + + if callable(finish): + # set up kwargs for `finish` function + finish_args = _getfullargspec(finish).args + finish_kwargs = dict() + if 'full_output' in finish_args: + finish_kwargs['full_output'] = 1 + if 'disp' in finish_args: + finish_kwargs['disp'] = disp + elif 'options' in finish_args: + # pass 'disp' as `options` + # (e.g., if `finish` is `minimize`) + finish_kwargs['options'] = {'disp': disp} + + # run minimizer + res = finish(func, xmin, args=args, **finish_kwargs) + + if isinstance(res, OptimizeResult): + xmin = res.x + Jmin = res.fun + success = res.success + else: + xmin = res[0] + Jmin = res[1] + success = res[-1] == 0 + if not success: + if disp: + warnings.warn("Either final optimization did not succeed or `finish` " + "does not return `statuscode` as its last argument.", + RuntimeWarning, stacklevel=2) + + if full_output: + return xmin, Jmin, grid, Jout + else: + return xmin + + +class _Brute_Wrapper: + """ + Object to wrap user cost function for optimize.brute, allowing picklability + """ + + def __init__(self, f, args): + self.f = f + self.args = [] if args is None else args + + def __call__(self, x): + # flatten needed for one dimensional case. + return self.f(np.asarray(x).flatten(), *self.args) + + +def show_options(solver=None, method=None, disp=True): + """ + Show documentation for additional options of optimization solvers. + + These are method-specific options that can be supplied through the + ``options`` dict. + + Parameters + ---------- + solver : str + Type of optimization solver. One of 'minimize', 'minimize_scalar', + 'root', 'root_scalar', 'linprog', or 'quadratic_assignment'. + method : str, optional + If not given, shows all methods of the specified solver. Otherwise, + show only the options for the specified method. Valid values + corresponds to methods' names of respective solver (e.g., 'BFGS' for + 'minimize'). + disp : bool, optional + Whether to print the result rather than returning it. + + Returns + ------- + text + Either None (for disp=True) or the text string (disp=False) + + Notes + ----- + The solver-specific methods are: + + `scipy.optimize.minimize` + + - :ref:`Nelder-Mead ` + - :ref:`Powell ` + - :ref:`CG ` + - :ref:`BFGS ` + - :ref:`Newton-CG ` + - :ref:`L-BFGS-B ` + - :ref:`TNC ` + - :ref:`COBYLA ` + - :ref:`COBYQA ` + - :ref:`SLSQP ` + - :ref:`dogleg ` + - :ref:`trust-ncg ` + + `scipy.optimize.root` + + - :ref:`hybr ` + - :ref:`lm ` + - :ref:`broyden1 ` + - :ref:`broyden2 ` + - :ref:`anderson ` + - :ref:`linearmixing ` + - :ref:`diagbroyden ` + - :ref:`excitingmixing ` + - :ref:`krylov ` + - :ref:`df-sane ` + + `scipy.optimize.minimize_scalar` + + - :ref:`brent ` + - :ref:`golden ` + - :ref:`bounded ` + + `scipy.optimize.root_scalar` + + - :ref:`bisect ` + - :ref:`brentq ` + - :ref:`brenth ` + - :ref:`ridder ` + - :ref:`toms748 ` + - :ref:`newton ` + - :ref:`secant ` + - :ref:`halley ` + + `scipy.optimize.linprog` + + - :ref:`simplex ` + - :ref:`interior-point ` + - :ref:`revised simplex ` + - :ref:`highs ` + - :ref:`highs-ds ` + - :ref:`highs-ipm ` + + `scipy.optimize.quadratic_assignment` + + - :ref:`faq ` + - :ref:`2opt ` + + Examples + -------- + We can print documentations of a solver in stdout: + + >>> from scipy.optimize import show_options + >>> show_options(solver="minimize") + ... + + Specifying a method is possible: + + >>> show_options(solver="minimize", method="Nelder-Mead") + ... + + We can also get the documentations as a string: + + >>> show_options(solver="minimize", method="Nelder-Mead", disp=False) + Minimization of scalar function of one or more variables using the ... + + """ + import textwrap + + doc_routines = { + 'minimize': ( + ('bfgs', 'scipy.optimize._optimize._minimize_bfgs'), + ('cg', 'scipy.optimize._optimize._minimize_cg'), + ('cobyla', 'scipy.optimize._cobyla_py._minimize_cobyla'), + ('cobyqa', 'scipy.optimize._cobyqa_py._minimize_cobyqa'), + ('dogleg', 'scipy.optimize._trustregion_dogleg._minimize_dogleg'), + ('l-bfgs-b', 'scipy.optimize._lbfgsb_py._minimize_lbfgsb'), + ('nelder-mead', 'scipy.optimize._optimize._minimize_neldermead'), + ('newton-cg', 'scipy.optimize._optimize._minimize_newtoncg'), + ('powell', 'scipy.optimize._optimize._minimize_powell'), + ('slsqp', 'scipy.optimize._slsqp_py._minimize_slsqp'), + ('tnc', 'scipy.optimize._tnc._minimize_tnc'), + ('trust-ncg', + 'scipy.optimize._trustregion_ncg._minimize_trust_ncg'), + ('trust-constr', + 'scipy.optimize._trustregion_constr.' + '_minimize_trustregion_constr'), + ('trust-exact', + 'scipy.optimize._trustregion_exact._minimize_trustregion_exact'), + ('trust-krylov', + 'scipy.optimize._trustregion_krylov._minimize_trust_krylov'), + ), + 'root': ( + ('hybr', 'scipy.optimize._minpack_py._root_hybr'), + ('lm', 'scipy.optimize._root._root_leastsq'), + ('broyden1', 'scipy.optimize._root._root_broyden1_doc'), + ('broyden2', 'scipy.optimize._root._root_broyden2_doc'), + ('anderson', 'scipy.optimize._root._root_anderson_doc'), + ('diagbroyden', 'scipy.optimize._root._root_diagbroyden_doc'), + ('excitingmixing', 'scipy.optimize._root._root_excitingmixing_doc'), + ('linearmixing', 'scipy.optimize._root._root_linearmixing_doc'), + ('krylov', 'scipy.optimize._root._root_krylov_doc'), + ('df-sane', 'scipy.optimize._spectral._root_df_sane'), + ), + 'root_scalar': ( + ('bisect', 'scipy.optimize._root_scalar._root_scalar_bisect_doc'), + ('brentq', 'scipy.optimize._root_scalar._root_scalar_brentq_doc'), + ('brenth', 'scipy.optimize._root_scalar._root_scalar_brenth_doc'), + ('ridder', 'scipy.optimize._root_scalar._root_scalar_ridder_doc'), + ('toms748', 'scipy.optimize._root_scalar._root_scalar_toms748_doc'), + ('secant', 'scipy.optimize._root_scalar._root_scalar_secant_doc'), + ('newton', 'scipy.optimize._root_scalar._root_scalar_newton_doc'), + ('halley', 'scipy.optimize._root_scalar._root_scalar_halley_doc'), + ), + 'linprog': ( + ('simplex', 'scipy.optimize._linprog._linprog_simplex_doc'), + ('interior-point', 'scipy.optimize._linprog._linprog_ip_doc'), + ('revised simplex', 'scipy.optimize._linprog._linprog_rs_doc'), + ('highs-ipm', 'scipy.optimize._linprog._linprog_highs_ipm_doc'), + ('highs-ds', 'scipy.optimize._linprog._linprog_highs_ds_doc'), + ('highs', 'scipy.optimize._linprog._linprog_highs_doc'), + ), + 'quadratic_assignment': ( + ('faq', 'scipy.optimize._qap._quadratic_assignment_faq'), + ('2opt', 'scipy.optimize._qap._quadratic_assignment_2opt'), + ), + 'minimize_scalar': ( + ('brent', 'scipy.optimize._optimize._minimize_scalar_brent'), + ('bounded', 'scipy.optimize._optimize._minimize_scalar_bounded'), + ('golden', 'scipy.optimize._optimize._minimize_scalar_golden'), + ), + } + + if solver is None: + text = ["\n\n\n========\n", "minimize\n", "========\n"] + text.append(show_options('minimize', disp=False)) + text.extend(["\n\n===============\n", "minimize_scalar\n", + "===============\n"]) + text.append(show_options('minimize_scalar', disp=False)) + text.extend(["\n\n\n====\n", "root\n", + "====\n"]) + text.append(show_options('root', disp=False)) + text.extend(['\n\n\n=======\n', 'linprog\n', + '=======\n']) + text.append(show_options('linprog', disp=False)) + text = "".join(text) + else: + solver = solver.lower() + if solver not in doc_routines: + raise ValueError(f'Unknown solver {solver!r}') + + if method is None: + text = [] + for name, _ in doc_routines[solver]: + text.extend(["\n\n" + name, "\n" + "="*len(name) + "\n\n"]) + text.append(show_options(solver, name, disp=False)) + text = "".join(text) + else: + method = method.lower() + methods = dict(doc_routines[solver]) + if method not in methods: + raise ValueError(f"Unknown method {method!r}") + name = methods[method] + + # Import function object + parts = name.split('.') + mod_name = ".".join(parts[:-1]) + __import__(mod_name) + obj = getattr(sys.modules[mod_name], parts[-1]) + + # Get doc + doc = obj.__doc__ + if doc is not None: + text = textwrap.dedent(doc).strip() + else: + text = "" + + if disp: + print(text) + return + else: + return text diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_qap.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_qap.py new file mode 100644 index 0000000000000000000000000000000000000000..094119c0ad6c1e4bba72978390c7273f10ac7fff --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_qap.py @@ -0,0 +1,731 @@ +import numpy as np +import operator +from . import (linear_sum_assignment, OptimizeResult) +from ._optimize import _check_unknown_options + +from scipy._lib._util import check_random_state +import itertools + +QUADRATIC_ASSIGNMENT_METHODS = ['faq', '2opt'] + +def quadratic_assignment(A, B, method="faq", options=None): + r""" + Approximates solution to the quadratic assignment problem and + the graph matching problem. + + Quadratic assignment solves problems of the following form: + + .. math:: + + \min_P & \ {\ \text{trace}(A^T P B P^T)}\\ + \mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\ + + where :math:`\mathcal{P}` is the set of all permutation matrices, + and :math:`A` and :math:`B` are square matrices. + + Graph matching tries to *maximize* the same objective function. + This algorithm can be thought of as finding the alignment of the + nodes of two graphs that minimizes the number of induced edge + disagreements, or, in the case of weighted graphs, the sum of squared + edge weight differences. + + Note that the quadratic assignment problem is NP-hard. The results given + here are approximations and are not guaranteed to be optimal. + + + Parameters + ---------- + A : 2-D array, square + The square matrix :math:`A` in the objective function above. + + B : 2-D array, square + The square matrix :math:`B` in the objective function above. + + method : str in {'faq', '2opt'} (default: 'faq') + The algorithm used to solve the problem. + :ref:`'faq' ` (default) and + :ref:`'2opt' ` are available. + + options : dict, optional + A dictionary of solver options. All solvers support the following: + + maximize : bool (default: False) + Maximizes the objective function if ``True``. + + partial_match : 2-D array of integers, optional (default: None) + Fixes part of the matching. Also known as a "seed" [2]_. + + Each row of `partial_match` specifies a pair of matched nodes: + node ``partial_match[i, 0]`` of `A` is matched to node + ``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``, + where ``m`` is not greater than the number of nodes, :math:`n`. + + rng : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + + For method-specific options, see + :func:`show_options('quadratic_assignment') `. + + Returns + ------- + res : OptimizeResult + `OptimizeResult` containing the following fields. + + col_ind : 1-D array + Column indices corresponding to the best permutation found of the + nodes of `B`. + fun : float + The objective value of the solution. + nit : int + The number of iterations performed during optimization. + + Notes + ----- + The default method :ref:`'faq' ` uses the Fast + Approximate QAP algorithm [1]_; it typically offers the best combination of + speed and accuracy. + Method :ref:`'2opt' ` can be computationally expensive, + but may be a useful alternative, or it can be used to refine the solution + returned by another method. + + References + ---------- + .. [1] J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik, + S.G. Kratzer, E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and + C.E. Priebe, "Fast approximate quadratic programming for graph + matching," PLOS one, vol. 10, no. 4, p. e0121002, 2015, + :doi:`10.1371/journal.pone.0121002` + + .. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski, + C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019): + 203-215, :doi:`10.1016/j.patcog.2018.09.014` + + .. [3] "2-opt," Wikipedia. + https://en.wikipedia.org/wiki/2-opt + + Examples + -------- + >>> import numpy as np + >>> from scipy.optimize import quadratic_assignment + >>> A = np.array([[0, 80, 150, 170], [80, 0, 130, 100], + ... [150, 130, 0, 120], [170, 100, 120, 0]]) + >>> B = np.array([[0, 5, 2, 7], [0, 0, 3, 8], + ... [0, 0, 0, 3], [0, 0, 0, 0]]) + >>> res = quadratic_assignment(A, B) + >>> print(res) + fun: 3260 + col_ind: [0 3 2 1] + nit: 9 + + The see the relationship between the returned ``col_ind`` and ``fun``, + use ``col_ind`` to form the best permutation matrix found, then evaluate + the objective function :math:`f(P) = trace(A^T P B P^T )`. + + >>> perm = res['col_ind'] + >>> P = np.eye(len(A), dtype=int)[perm] + >>> fun = np.trace(A.T @ P @ B @ P.T) + >>> print(fun) + 3260 + + Alternatively, to avoid constructing the permutation matrix explicitly, + directly permute the rows and columns of the distance matrix. + + >>> fun = np.trace(A.T @ B[perm][:, perm]) + >>> print(fun) + 3260 + + Although not guaranteed in general, ``quadratic_assignment`` happens to + have found the globally optimal solution. + + >>> from itertools import permutations + >>> perm_opt, fun_opt = None, np.inf + >>> for perm in permutations([0, 1, 2, 3]): + ... perm = np.array(perm) + ... fun = np.trace(A.T @ B[perm][:, perm]) + ... if fun < fun_opt: + ... fun_opt, perm_opt = fun, perm + >>> print(np.array_equal(perm_opt, res['col_ind'])) + True + + Here is an example for which the default method, + :ref:`'faq' `, does not find the global optimum. + + >>> A = np.array([[0, 5, 8, 6], [5, 0, 5, 1], + ... [8, 5, 0, 2], [6, 1, 2, 0]]) + >>> B = np.array([[0, 1, 8, 4], [1, 0, 5, 2], + ... [8, 5, 0, 5], [4, 2, 5, 0]]) + >>> res = quadratic_assignment(A, B) + >>> print(res) + fun: 178 + col_ind: [1 0 3 2] + nit: 13 + + If accuracy is important, consider using :ref:`'2opt' ` + to refine the solution. + + >>> guess = np.array([np.arange(len(A)), res.col_ind]).T + >>> res = quadratic_assignment(A, B, method="2opt", + ... options = {'partial_guess': guess}) + >>> print(res) + fun: 176 + col_ind: [1 2 3 0] + nit: 17 + + """ + + if options is None: + options = {} + + method = method.lower() + methods = {"faq": _quadratic_assignment_faq, + "2opt": _quadratic_assignment_2opt} + if method not in methods: + raise ValueError(f"method {method} must be in {methods}.") + res = methods[method](A, B, **options) + return res + + +def _calc_score(A, B, perm): + # equivalent to objective function but avoids matmul + return np.sum(A * B[perm][:, perm]) + + +def _common_input_validation(A, B, partial_match): + A = np.atleast_2d(A) + B = np.atleast_2d(B) + + if partial_match is None: + partial_match = np.array([[], []]).T + partial_match = np.atleast_2d(partial_match).astype(int) + + msg = None + if A.shape[0] != A.shape[1]: + msg = "`A` must be square" + elif B.shape[0] != B.shape[1]: + msg = "`B` must be square" + elif A.ndim != 2 or B.ndim != 2: + msg = "`A` and `B` must have exactly two dimensions" + elif A.shape != B.shape: + msg = "`A` and `B` matrices must be of equal size" + elif partial_match.shape[0] > A.shape[0]: + msg = "`partial_match` can have only as many seeds as there are nodes" + elif partial_match.shape[1] != 2: + msg = "`partial_match` must have two columns" + elif partial_match.ndim != 2: + msg = "`partial_match` must have exactly two dimensions" + elif (partial_match < 0).any(): + msg = "`partial_match` must contain only positive indices" + elif (partial_match >= len(A)).any(): + msg = "`partial_match` entries must be less than number of nodes" + elif (not len(set(partial_match[:, 0])) == len(partial_match[:, 0]) or + not len(set(partial_match[:, 1])) == len(partial_match[:, 1])): + msg = "`partial_match` column entries must be unique" + + if msg is not None: + raise ValueError(msg) + + return A, B, partial_match + + +def _quadratic_assignment_faq(A, B, + maximize=False, partial_match=None, rng=None, + P0="barycenter", shuffle_input=False, maxiter=30, + tol=0.03, **unknown_options): + r"""Solve the quadratic assignment problem (approximately). + + This function solves the Quadratic Assignment Problem (QAP) and the + Graph Matching Problem (GMP) using the Fast Approximate QAP Algorithm + (FAQ) [1]_. + + Quadratic assignment solves problems of the following form: + + .. math:: + + \min_P & \ {\ \text{trace}(A^T P B P^T)}\\ + \mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\ + + where :math:`\mathcal{P}` is the set of all permutation matrices, + and :math:`A` and :math:`B` are square matrices. + + Graph matching tries to *maximize* the same objective function. + This algorithm can be thought of as finding the alignment of the + nodes of two graphs that minimizes the number of induced edge + disagreements, or, in the case of weighted graphs, the sum of squared + edge weight differences. + + Note that the quadratic assignment problem is NP-hard. The results given + here are approximations and are not guaranteed to be optimal. + + Parameters + ---------- + A : 2-D array, square + The square matrix :math:`A` in the objective function above. + B : 2-D array, square + The square matrix :math:`B` in the objective function above. + method : str in {'faq', '2opt'} (default: 'faq') + The algorithm used to solve the problem. This is the method-specific + documentation for 'faq'. + :ref:`'2opt' ` is also available. + + Options + ------- + maximize : bool (default: False) + Maximizes the objective function if ``True``. + partial_match : 2-D array of integers, optional (default: None) + Fixes part of the matching. Also known as a "seed" [2]_. + + Each row of `partial_match` specifies a pair of matched nodes: + node ``partial_match[i, 0]`` of `A` is matched to node + ``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``, where + ``m`` is not greater than the number of nodes, :math:`n`. + + rng : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + P0 : 2-D array, "barycenter", or "randomized" (default: "barycenter") + Initial position. Must be a doubly-stochastic matrix [3]_. + + If the initial position is an array, it must be a doubly stochastic + matrix of size :math:`m' \times m'` where :math:`m' = n - m`. + + If ``"barycenter"`` (default), the initial position is the barycenter + of the Birkhoff polytope (the space of doubly stochastic matrices). + This is a :math:`m' \times m'` matrix with all entries equal to + :math:`1 / m'`. + + If ``"randomized"`` the initial search position is + :math:`P_0 = (J + K) / 2`, where :math:`J` is the barycenter and + :math:`K` is a random doubly stochastic matrix. + shuffle_input : bool (default: False) + Set to `True` to resolve degenerate gradients randomly. For + non-degenerate gradients this option has no effect. + maxiter : int, positive (default: 30) + Integer specifying the max number of Frank-Wolfe iterations performed. + tol : float (default: 0.03) + Tolerance for termination. Frank-Wolfe iteration terminates when + :math:`\frac{||P_{i}-P_{i+1}||_F}{\sqrt{m')}} \leq tol`, + where :math:`i` is the iteration number. + + Returns + ------- + res : OptimizeResult + `OptimizeResult` containing the following fields. + + col_ind : 1-D array + Column indices corresponding to the best permutation found of the + nodes of `B`. + fun : float + The objective value of the solution. + nit : int + The number of Frank-Wolfe iterations performed. + + Notes + ----- + The algorithm may be sensitive to the initial permutation matrix (or + search "position") due to the possibility of several local minima + within the feasible region. A barycenter initialization is more likely to + result in a better solution than a single random initialization. However, + calling ``quadratic_assignment`` several times with different random + initializations may result in a better optimum at the cost of longer + total execution time. + + Examples + -------- + As mentioned above, a barycenter initialization often results in a better + solution than a single random initialization. + + >>> from numpy.random import default_rng + >>> rng = default_rng() + >>> n = 15 + >>> A = rng.random((n, n)) + >>> B = rng.random((n, n)) + >>> res = quadratic_assignment(A, B) # FAQ is default method + >>> print(res.fun) + 46.871483385480545 # may vary + + >>> options = {"P0": "randomized"} # use randomized initialization + >>> res = quadratic_assignment(A, B, options=options) + >>> print(res.fun) + 47.224831071310625 # may vary + + However, consider running from several randomized initializations and + keeping the best result. + + >>> res = min([quadratic_assignment(A, B, options=options) + ... for i in range(30)], key=lambda x: x.fun) + >>> print(res.fun) + 46.671852533681516 # may vary + + The '2-opt' method can be used to further refine the results. + + >>> options = {"partial_guess": np.array([np.arange(n), res.col_ind]).T} + >>> res = quadratic_assignment(A, B, method="2opt", options=options) + >>> print(res.fun) + 46.47160735721583 # may vary + + References + ---------- + .. [1] J.T. Vogelstein, J.M. Conroy, V. Lyzinski, L.J. Podrazik, + S.G. Kratzer, E.T. Harley, D.E. Fishkind, R.J. Vogelstein, and + C.E. Priebe, "Fast approximate quadratic programming for graph + matching," PLOS one, vol. 10, no. 4, p. e0121002, 2015, + :doi:`10.1371/journal.pone.0121002` + + .. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski, + C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019): + 203-215, :doi:`10.1016/j.patcog.2018.09.014` + + .. [3] "Doubly stochastic Matrix," Wikipedia. + https://en.wikipedia.org/wiki/Doubly_stochastic_matrix + + """ + + _check_unknown_options(unknown_options) + + maxiter = operator.index(maxiter) + + # ValueError check + A, B, partial_match = _common_input_validation(A, B, partial_match) + + msg = None + if isinstance(P0, str) and P0 not in {'barycenter', 'randomized'}: + msg = "Invalid 'P0' parameter string" + elif maxiter <= 0: + msg = "'maxiter' must be a positive integer" + elif tol <= 0: + msg = "'tol' must be a positive float" + if msg is not None: + raise ValueError(msg) + + rng = check_random_state(rng) + n = len(A) # number of vertices in graphs + n_seeds = len(partial_match) # number of seeds + n_unseed = n - n_seeds + + # [1] Algorithm 1 Line 1 - choose initialization + if not isinstance(P0, str): + P0 = np.atleast_2d(P0) + if P0.shape != (n_unseed, n_unseed): + msg = "`P0` matrix must have shape m' x m', where m'=n-m" + elif ((P0 < 0).any() or not np.allclose(np.sum(P0, axis=0), 1) + or not np.allclose(np.sum(P0, axis=1), 1)): + msg = "`P0` matrix must be doubly stochastic" + if msg is not None: + raise ValueError(msg) + elif P0 == 'barycenter': + P0 = np.ones((n_unseed, n_unseed)) / n_unseed + elif P0 == 'randomized': + J = np.ones((n_unseed, n_unseed)) / n_unseed + # generate a nxn matrix where each entry is a random number [0, 1] + # would use rand, but Generators don't have it + # would use random, but old mtrand.RandomStates don't have it + K = _doubly_stochastic(rng.uniform(size=(n_unseed, n_unseed))) + P0 = (J + K) / 2 + + # check trivial cases + if n == 0 or n_seeds == n: + score = _calc_score(A, B, partial_match[:, 1]) + res = {"col_ind": partial_match[:, 1], "fun": score, "nit": 0} + return OptimizeResult(res) + + obj_func_scalar = 1 + if maximize: + obj_func_scalar = -1 + + nonseed_B = np.setdiff1d(range(n), partial_match[:, 1]) + if shuffle_input: + nonseed_B = rng.permutation(nonseed_B) + + nonseed_A = np.setdiff1d(range(n), partial_match[:, 0]) + perm_A = np.concatenate([partial_match[:, 0], nonseed_A]) + perm_B = np.concatenate([partial_match[:, 1], nonseed_B]) + + # definitions according to Seeded Graph Matching [2]. + A11, A12, A21, A22 = _split_matrix(A[perm_A][:, perm_A], n_seeds) + B11, B12, B21, B22 = _split_matrix(B[perm_B][:, perm_B], n_seeds) + const_sum = A21 @ B21.T + A12.T @ B12 + + P = P0 + # [1] Algorithm 1 Line 2 - loop while stopping criteria not met + for n_iter in range(1, maxiter+1): + # [1] Algorithm 1 Line 3 - compute the gradient of f(P) = -tr(APB^tP^t) + grad_fp = (const_sum + A22 @ P @ B22.T + A22.T @ P @ B22) + # [1] Algorithm 1 Line 4 - get direction Q by solving Eq. 8 + _, cols = linear_sum_assignment(grad_fp, maximize=maximize) + Q = np.eye(n_unseed)[cols] + + # [1] Algorithm 1 Line 5 - compute the step size + # Noting that e.g. trace(Ax) = trace(A)*x, expand and re-collect + # terms as ax**2 + bx + c. c does not affect location of minimum + # and can be ignored. Also, note that trace(A@B) = (A.T*B).sum(); + # apply where possible for efficiency. + R = P - Q + b21 = ((R.T @ A21) * B21).sum() + b12 = ((R.T @ A12.T) * B12.T).sum() + AR22 = A22.T @ R + BR22 = B22 @ R.T + b22a = (AR22 * B22.T[cols]).sum() + b22b = (A22 * BR22[cols]).sum() + a = (AR22.T * BR22).sum() + b = b21 + b12 + b22a + b22b + # critical point of ax^2 + bx + c is at x = -d/(2*e) + # if a * obj_func_scalar > 0, it is a minimum + # if minimum is not in [0, 1], only endpoints need to be considered + if a*obj_func_scalar > 0 and 0 <= -b/(2*a) <= 1: + alpha = -b/(2*a) + else: + alpha = np.argmin([0, (b + a)*obj_func_scalar]) + + # [1] Algorithm 1 Line 6 - Update P + P_i1 = alpha * P + (1 - alpha) * Q + if np.linalg.norm(P - P_i1) / np.sqrt(n_unseed) < tol: + P = P_i1 + break + P = P_i1 + # [1] Algorithm 1 Line 7 - end main loop + + # [1] Algorithm 1 Line 8 - project onto the set of permutation matrices + _, col = linear_sum_assignment(P, maximize=True) + perm = np.concatenate((np.arange(n_seeds), col + n_seeds)) + + unshuffled_perm = np.zeros(n, dtype=int) + unshuffled_perm[perm_A] = perm_B[perm] + + score = _calc_score(A, B, unshuffled_perm) + res = {"col_ind": unshuffled_perm, "fun": score, "nit": n_iter} + return OptimizeResult(res) + + +def _split_matrix(X, n): + # definitions according to Seeded Graph Matching [2]. + upper, lower = X[:n], X[n:] + return upper[:, :n], upper[:, n:], lower[:, :n], lower[:, n:] + + +def _doubly_stochastic(P, tol=1e-3): + # Adapted from @btaba implementation + # https://github.com/btaba/sinkhorn_knopp + # of Sinkhorn-Knopp algorithm + # https://projecteuclid.org/euclid.pjm/1102992505 + + max_iter = 1000 + c = 1 / P.sum(axis=0) + r = 1 / (P @ c) + P_eps = P + + for it in range(max_iter): + if ((np.abs(P_eps.sum(axis=1) - 1) < tol).all() and + (np.abs(P_eps.sum(axis=0) - 1) < tol).all()): + # All column/row sums ~= 1 within threshold + break + + c = 1 / (r @ P) + r = 1 / (P @ c) + P_eps = r[:, None] * P * c + + return P_eps + + +def _quadratic_assignment_2opt(A, B, maximize=False, rng=None, + partial_match=None, + partial_guess=None, + **unknown_options): + r"""Solve the quadratic assignment problem (approximately). + + This function solves the Quadratic Assignment Problem (QAP) and the + Graph Matching Problem (GMP) using the 2-opt algorithm [1]_. + + Quadratic assignment solves problems of the following form: + + .. math:: + + \min_P & \ {\ \text{trace}(A^T P B P^T)}\\ + \mbox{s.t. } & {P \ \epsilon \ \mathcal{P}}\\ + + where :math:`\mathcal{P}` is the set of all permutation matrices, + and :math:`A` and :math:`B` are square matrices. + + Graph matching tries to *maximize* the same objective function. + This algorithm can be thought of as finding the alignment of the + nodes of two graphs that minimizes the number of induced edge + disagreements, or, in the case of weighted graphs, the sum of squared + edge weight differences. + + Note that the quadratic assignment problem is NP-hard. The results given + here are approximations and are not guaranteed to be optimal. + + Parameters + ---------- + A : 2-D array, square + The square matrix :math:`A` in the objective function above. + B : 2-D array, square + The square matrix :math:`B` in the objective function above. + method : str in {'faq', '2opt'} (default: 'faq') + The algorithm used to solve the problem. This is the method-specific + documentation for '2opt'. + :ref:`'faq' ` is also available. + + Options + ------- + maximize : bool (default: False) + Maximizes the objective function if ``True``. + rng : {None, int, `numpy.random.Generator`, + `numpy.random.RandomState`}, optional + + If `seed` is None (or `np.random`), the `numpy.random.RandomState` + singleton is used. + If `seed` is an int, a new ``RandomState`` instance is used, + seeded with `seed`. + If `seed` is already a ``Generator`` or ``RandomState`` instance then + that instance is used. + partial_match : 2-D array of integers, optional (default: None) + Fixes part of the matching. Also known as a "seed" [2]_. + + Each row of `partial_match` specifies a pair of matched nodes: node + ``partial_match[i, 0]`` of `A` is matched to node + ``partial_match[i, 1]`` of `B`. The array has shape ``(m, 2)``, + where ``m`` is not greater than the number of nodes, :math:`n`. + + .. note:: + `partial_match` must be sorted by the first column. + + partial_guess : 2-D array of integers, optional (default: None) + A guess for the matching between the two matrices. Unlike + `partial_match`, `partial_guess` does not fix the indices; they are + still free to be optimized. + + Each row of `partial_guess` specifies a pair of matched nodes: node + ``partial_guess[i, 0]`` of `A` is matched to node + ``partial_guess[i, 1]`` of `B`. The array has shape ``(m, 2)``, + where ``m`` is not greater than the number of nodes, :math:`n`. + + .. note:: + `partial_guess` must be sorted by the first column. + + Returns + ------- + res : OptimizeResult + `OptimizeResult` containing the following fields. + + col_ind : 1-D array + Column indices corresponding to the best permutation found of the + nodes of `B`. + fun : float + The objective value of the solution. + nit : int + The number of iterations performed during optimization. + + Notes + ----- + This is a greedy algorithm that works similarly to bubble sort: beginning + with an initial permutation, it iteratively swaps pairs of indices to + improve the objective function until no such improvements are possible. + + References + ---------- + .. [1] "2-opt," Wikipedia. + https://en.wikipedia.org/wiki/2-opt + + .. [2] D. Fishkind, S. Adali, H. Patsolic, L. Meng, D. Singh, V. Lyzinski, + C. Priebe, "Seeded graph matching", Pattern Recognit. 87 (2019): + 203-215, https://doi.org/10.1016/j.patcog.2018.09.014 + + """ + _check_unknown_options(unknown_options) + rng = check_random_state(rng) + A, B, partial_match = _common_input_validation(A, B, partial_match) + + N = len(A) + # check trivial cases + if N == 0 or partial_match.shape[0] == N: + score = _calc_score(A, B, partial_match[:, 1]) + res = {"col_ind": partial_match[:, 1], "fun": score, "nit": 0} + return OptimizeResult(res) + + if partial_guess is None: + partial_guess = np.array([[], []]).T + partial_guess = np.atleast_2d(partial_guess).astype(int) + + msg = None + if partial_guess.shape[0] > A.shape[0]: + msg = ("`partial_guess` can have only as " + "many entries as there are nodes") + elif partial_guess.shape[1] != 2: + msg = "`partial_guess` must have two columns" + elif partial_guess.ndim != 2: + msg = "`partial_guess` must have exactly two dimensions" + elif (partial_guess < 0).any(): + msg = "`partial_guess` must contain only positive indices" + elif (partial_guess >= len(A)).any(): + msg = "`partial_guess` entries must be less than number of nodes" + elif (not len(set(partial_guess[:, 0])) == len(partial_guess[:, 0]) or + not len(set(partial_guess[:, 1])) == len(partial_guess[:, 1])): + msg = "`partial_guess` column entries must be unique" + if msg is not None: + raise ValueError(msg) + + fixed_rows = None + if partial_match.size or partial_guess.size: + # use partial_match and partial_guess for initial permutation, + # but randomly permute the rest. + guess_rows = np.zeros(N, dtype=bool) + guess_cols = np.zeros(N, dtype=bool) + fixed_rows = np.zeros(N, dtype=bool) + fixed_cols = np.zeros(N, dtype=bool) + perm = np.zeros(N, dtype=int) + + rg, cg = partial_guess.T + guess_rows[rg] = True + guess_cols[cg] = True + perm[guess_rows] = cg + + # match overrides guess + rf, cf = partial_match.T + fixed_rows[rf] = True + fixed_cols[cf] = True + perm[fixed_rows] = cf + + random_rows = ~fixed_rows & ~guess_rows + random_cols = ~fixed_cols & ~guess_cols + perm[random_rows] = rng.permutation(np.arange(N)[random_cols]) + else: + perm = rng.permutation(np.arange(N)) + + best_score = _calc_score(A, B, perm) + + i_free = np.arange(N) + if fixed_rows is not None: + i_free = i_free[~fixed_rows] + + better = operator.gt if maximize else operator.lt + n_iter = 0 + done = False + while not done: + # equivalent to nested for loops i in range(N), j in range(i, N) + for i, j in itertools.combinations_with_replacement(i_free, 2): + n_iter += 1 + perm[i], perm[j] = perm[j], perm[i] + score = _calc_score(A, B, perm) + if better(score, best_score): + best_score = score + break + # faster to swap back than to create a new list every time + perm[i], perm[j] = perm[j], perm[i] + else: # no swaps made + done = True + + res = {"col_ind": perm, "fun": best_score, "nit": n_iter} + return OptimizeResult(res) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_remove_redundancy.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_remove_redundancy.py new file mode 100644 index 0000000000000000000000000000000000000000..cb81ad1696b768d2304b2fc42a80cc9678cbde00 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_remove_redundancy.py @@ -0,0 +1,522 @@ +""" +Routines for removing redundant (linearly dependent) equations from linear +programming equality constraints. +""" +# Author: Matt Haberland + +import numpy as np +from scipy.linalg import svd +from scipy.linalg.interpolative import interp_decomp +import scipy +from scipy.linalg.blas import dtrsm + + +def _row_count(A): + """ + Counts the number of nonzeros in each row of input array A. + Nonzeros are defined as any element with absolute value greater than + tol = 1e-13. This value should probably be an input to the function. + + Parameters + ---------- + A : 2-D array + An array representing a matrix + + Returns + ------- + rowcount : 1-D array + Number of nonzeros in each row of A + + """ + tol = 1e-13 + return np.array((abs(A) > tol).sum(axis=1)).flatten() + + +def _get_densest(A, eligibleRows): + """ + Returns the index of the densest row of A. Ignores rows that are not + eligible for consideration. + + Parameters + ---------- + A : 2-D array + An array representing a matrix + eligibleRows : 1-D logical array + Values indicate whether the corresponding row of A is eligible + to be considered + + Returns + ------- + i_densest : int + Index of the densest row in A eligible for consideration + + """ + rowCounts = _row_count(A) + return np.argmax(rowCounts * eligibleRows) + + +def _remove_zero_rows(A, b): + """ + Eliminates trivial equations from system of equations defined by Ax = b + and identifies trivial infeasibilities + + Parameters + ---------- + A : 2-D array + An array representing the left-hand side of a system of equations + b : 1-D array + An array representing the right-hand side of a system of equations + + Returns + ------- + A : 2-D array + An array representing the left-hand side of a system of equations + b : 1-D array + An array representing the right-hand side of a system of equations + status: int + An integer indicating the status of the removal operation + 0: No infeasibility identified + 2: Trivially infeasible + message : str + A string descriptor of the exit status of the optimization. + + """ + status = 0 + message = "" + i_zero = _row_count(A) == 0 + A = A[np.logical_not(i_zero), :] + if not np.allclose(b[i_zero], 0): + status = 2 + message = "There is a zero row in A_eq with a nonzero corresponding " \ + "entry in b_eq. The problem is infeasible." + b = b[np.logical_not(i_zero)] + return A, b, status, message + + +def bg_update_dense(plu, perm_r, v, j): + LU, p = plu + + vperm = v[perm_r] + u = dtrsm(1, LU, vperm, lower=1, diag=1) + LU[:j+1, j] = u[:j+1] + l = u[j+1:] + piv = LU[j, j] + LU[j+1:, j] += (l/piv) + return LU, p + + +def _remove_redundancy_pivot_dense(A, rhs, true_rank=None): + """ + Eliminates redundant equations from system of equations defined by Ax = b + and identifies infeasibilities. + + Parameters + ---------- + A : 2-D sparse matrix + An matrix representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + + Returns + ------- + A : 2-D sparse matrix + A matrix representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + status: int + An integer indicating the status of the system + 0: No infeasibility identified + 2: Trivially infeasible + message : str + A string descriptor of the exit status of the optimization. + + References + ---------- + .. [2] Andersen, Erling D. "Finding all linearly dependent rows in + large-scale linear programming." Optimization Methods and Software + 6.3 (1995): 219-227. + + """ + tolapiv = 1e-8 + tolprimal = 1e-8 + status = 0 + message = "" + inconsistent = ("There is a linear combination of rows of A_eq that " + "results in zero, suggesting a redundant constraint. " + "However the same linear combination of b_eq is " + "nonzero, suggesting that the constraints conflict " + "and the problem is infeasible.") + A, rhs, status, message = _remove_zero_rows(A, rhs) + + if status != 0: + return A, rhs, status, message + + m, n = A.shape + + v = list(range(m)) # Artificial column indices. + b = list(v) # Basis column indices. + # This is better as a list than a set because column order of basis matrix + # needs to be consistent. + d = [] # Indices of dependent rows + perm_r = None + + A_orig = A + A = np.zeros((m, m + n), order='F') + np.fill_diagonal(A, 1) + A[:, m:] = A_orig + e = np.zeros(m) + + js_candidates = np.arange(m, m+n, dtype=int) # candidate columns for basis + # manual masking was faster than masked array + js_mask = np.ones(js_candidates.shape, dtype=bool) + + # Implements basic algorithm from [2] + # Uses some of the suggested improvements (removing zero rows and + # Bartels-Golub update idea). + # Removing column singletons would be easy, but it is not as important + # because the procedure is performed only on the equality constraint + # matrix from the original problem - not on the canonical form matrix, + # which would have many more column singletons due to slack variables + # from the inequality constraints. + # The thoughts on "crashing" the initial basis are only really useful if + # the matrix is sparse. + + lu = np.eye(m, order='F'), np.arange(m) # initial LU is trivial + perm_r = lu[1] + for i in v: + + e[i] = 1 + if i > 0: + e[i-1] = 0 + + try: # fails for i==0 and any time it gets ill-conditioned + j = b[i-1] + lu = bg_update_dense(lu, perm_r, A[:, j], i-1) + except Exception: + lu = scipy.linalg.lu_factor(A[:, b]) + LU, p = lu + perm_r = list(range(m)) + for i1, i2 in enumerate(p): + perm_r[i1], perm_r[i2] = perm_r[i2], perm_r[i1] + + pi = scipy.linalg.lu_solve(lu, e, trans=1) + + js = js_candidates[js_mask] + batch = 50 + + # This is a tiny bit faster than looping over columns individually, + # like for j in js: if abs(A[:,j].transpose().dot(pi)) > tolapiv: + for j_index in range(0, len(js), batch): + j_indices = js[j_index: min(j_index+batch, len(js))] + + c = abs(A[:, j_indices].transpose().dot(pi)) + if (c > tolapiv).any(): + j = js[j_index + np.argmax(c)] # very independent column + b[i] = j + js_mask[j-m] = False + break + else: + bibar = pi.T.dot(rhs.reshape(-1, 1)) + bnorm = np.linalg.norm(rhs) + if abs(bibar)/(1+bnorm) > tolprimal: # inconsistent + status = 2 + message = inconsistent + return A_orig, rhs, status, message + else: # dependent + d.append(i) + if true_rank is not None and len(d) == m - true_rank: + break # found all redundancies + + keep = set(range(m)) + keep = list(keep - set(d)) + return A_orig[keep, :], rhs[keep], status, message + + +def _remove_redundancy_pivot_sparse(A, rhs): + """ + Eliminates redundant equations from system of equations defined by Ax = b + and identifies infeasibilities. + + Parameters + ---------- + A : 2-D sparse matrix + An matrix representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + + Returns + ------- + A : 2-D sparse matrix + A matrix representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + status: int + An integer indicating the status of the system + 0: No infeasibility identified + 2: Trivially infeasible + message : str + A string descriptor of the exit status of the optimization. + + References + ---------- + .. [2] Andersen, Erling D. "Finding all linearly dependent rows in + large-scale linear programming." Optimization Methods and Software + 6.3 (1995): 219-227. + + """ + + tolapiv = 1e-8 + tolprimal = 1e-8 + status = 0 + message = "" + inconsistent = ("There is a linear combination of rows of A_eq that " + "results in zero, suggesting a redundant constraint. " + "However the same linear combination of b_eq is " + "nonzero, suggesting that the constraints conflict " + "and the problem is infeasible.") + A, rhs, status, message = _remove_zero_rows(A, rhs) + + if status != 0: + return A, rhs, status, message + + m, n = A.shape + + v = list(range(m)) # Artificial column indices. + b = list(v) # Basis column indices. + # This is better as a list than a set because column order of basis matrix + # needs to be consistent. + k = set(range(m, m+n)) # Structural column indices. + d = [] # Indices of dependent rows + + A_orig = A + A = scipy.sparse.hstack((scipy.sparse.eye(m), A)).tocsc() + e = np.zeros(m) + + # Implements basic algorithm from [2] + # Uses only one of the suggested improvements (removing zero rows). + # Removing column singletons would be easy, but it is not as important + # because the procedure is performed only on the equality constraint + # matrix from the original problem - not on the canonical form matrix, + # which would have many more column singletons due to slack variables + # from the inequality constraints. + # The thoughts on "crashing" the initial basis sound useful, but the + # description of the procedure seems to assume a lot of familiarity with + # the subject; it is not very explicit. I already went through enough + # trouble getting the basic algorithm working, so I was not interested in + # trying to decipher this, too. (Overall, the paper is fraught with + # mistakes and ambiguities - which is strange, because the rest of + # Andersen's papers are quite good.) + # I tried and tried and tried to improve performance using the + # Bartels-Golub update. It works, but it's only practical if the LU + # factorization can be specialized as described, and that is not possible + # until the SciPy SuperLU interface permits control over column + # permutation - see issue #7700. + + for i in v: + B = A[:, b] + + e[i] = 1 + if i > 0: + e[i-1] = 0 + + pi = scipy.sparse.linalg.spsolve(B.transpose(), e).reshape(-1, 1) + + js = list(k-set(b)) # not efficient, but this is not the time sink... + + # Due to overhead, it tends to be faster (for problems tested) to + # compute the full matrix-vector product rather than individual + # vector-vector products (with the chance of terminating as soon + # as any are nonzero). For very large matrices, it might be worth + # it to compute, say, 100 or 1000 at a time and stop when a nonzero + # is found. + + c = (np.abs(A[:, js].transpose().dot(pi)) > tolapiv).nonzero()[0] + if len(c) > 0: # independent + j = js[c[0]] + # in a previous commit, the previous line was changed to choose + # index j corresponding with the maximum dot product. + # While this avoided issues with almost + # singular matrices, it slowed the routine in most NETLIB tests. + # I think this is because these columns were denser than the + # first column with nonzero dot product (c[0]). + # It would be nice to have a heuristic that balances sparsity with + # high dot product, but I don't think it's worth the time to + # develop one right now. Bartels-Golub update is a much higher + # priority. + b[i] = j # replace artificial column + else: + bibar = pi.T.dot(rhs.reshape(-1, 1)) + bnorm = np.linalg.norm(rhs) + if abs(bibar)/(1 + bnorm) > tolprimal: + status = 2 + message = inconsistent + return A_orig, rhs, status, message + else: # dependent + d.append(i) + + keep = set(range(m)) + keep = list(keep - set(d)) + return A_orig[keep, :], rhs[keep], status, message + + +def _remove_redundancy_svd(A, b): + """ + Eliminates redundant equations from system of equations defined by Ax = b + and identifies infeasibilities. + + Parameters + ---------- + A : 2-D array + An array representing the left-hand side of a system of equations + b : 1-D array + An array representing the right-hand side of a system of equations + + Returns + ------- + A : 2-D array + An array representing the left-hand side of a system of equations + b : 1-D array + An array representing the right-hand side of a system of equations + status: int + An integer indicating the status of the system + 0: No infeasibility identified + 2: Trivially infeasible + message : str + A string descriptor of the exit status of the optimization. + + References + ---------- + .. [2] Andersen, Erling D. "Finding all linearly dependent rows in + large-scale linear programming." Optimization Methods and Software + 6.3 (1995): 219-227. + + """ + + A, b, status, message = _remove_zero_rows(A, b) + + if status != 0: + return A, b, status, message + + U, s, Vh = svd(A) + eps = np.finfo(float).eps + tol = s.max() * max(A.shape) * eps + + m, n = A.shape + s_min = s[-1] if m <= n else 0 + + # this algorithm is faster than that of [2] when the nullspace is small + # but it could probably be improvement by randomized algorithms and with + # a sparse implementation. + # it relies on repeated singular value decomposition to find linearly + # dependent rows (as identified by columns of U that correspond with zero + # singular values). Unfortunately, only one row can be removed per + # decomposition (I tried otherwise; doing so can cause problems.) + # It would be nice if we could do truncated SVD like sp.sparse.linalg.svds + # but that function is unreliable at finding singular values near zero. + # Finding max eigenvalue L of A A^T, then largest eigenvalue (and + # associated eigenvector) of -A A^T + L I (I is identity) via power + # iteration would also work in theory, but is only efficient if the + # smallest nonzero eigenvalue of A A^T is close to the largest nonzero + # eigenvalue. + + while abs(s_min) < tol: + v = U[:, -1] # TODO: return these so user can eliminate from problem? + # rows need to be represented in significant amount + eligibleRows = np.abs(v) > tol * 10e6 + if not np.any(eligibleRows) or np.any(np.abs(v.dot(A)) > tol): + status = 4 + message = ("Due to numerical issues, redundant equality " + "constraints could not be removed automatically. " + "Try providing your constraint matrices as sparse " + "matrices to activate sparse presolve, try turning " + "off redundancy removal, or try turning off presolve " + "altogether.") + break + if np.any(np.abs(v.dot(b)) > tol * 100): # factor of 100 to fix 10038 and 10349 + status = 2 + message = ("There is a linear combination of rows of A_eq that " + "results in zero, suggesting a redundant constraint. " + "However the same linear combination of b_eq is " + "nonzero, suggesting that the constraints conflict " + "and the problem is infeasible.") + break + + i_remove = _get_densest(A, eligibleRows) + A = np.delete(A, i_remove, axis=0) + b = np.delete(b, i_remove) + U, s, Vh = svd(A) + m, n = A.shape + s_min = s[-1] if m <= n else 0 + + return A, b, status, message + + +def _remove_redundancy_id(A, rhs, rank=None, randomized=True): + """Eliminates redundant equations from a system of equations. + + Eliminates redundant equations from system of equations defined by Ax = b + and identifies infeasibilities. + + Parameters + ---------- + A : 2-D array + An array representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + rank : int, optional + The rank of A + randomized: bool, optional + True for randomized interpolative decomposition + + Returns + ------- + A : 2-D array + An array representing the left-hand side of a system of equations + rhs : 1-D array + An array representing the right-hand side of a system of equations + status: int + An integer indicating the status of the system + 0: No infeasibility identified + 2: Trivially infeasible + message : str + A string descriptor of the exit status of the optimization. + + """ + + status = 0 + message = "" + inconsistent = ("There is a linear combination of rows of A_eq that " + "results in zero, suggesting a redundant constraint. " + "However the same linear combination of b_eq is " + "nonzero, suggesting that the constraints conflict " + "and the problem is infeasible.") + + A, rhs, status, message = _remove_zero_rows(A, rhs) + + if status != 0: + return A, rhs, status, message + + m, n = A.shape + + k = rank + if rank is None: + k = np.linalg.matrix_rank(A) + + idx, proj = interp_decomp(A.T, k, rand=randomized) + + # first k entries in idx are indices of the independent rows + # remaining entries are the indices of the m-k dependent rows + # proj provides a linear combinations of rows of A2 that form the + # remaining m-k (dependent) rows. The same linear combination of entries + # in rhs2 must give the remaining m-k entries. If not, the system is + # inconsistent, and the problem is infeasible. + if not np.allclose(rhs[idx[:k]] @ proj, rhs[idx[k:]]): + status = 2 + message = inconsistent + + # sort indices because the other redundancy removal routines leave rows + # in original order and tests were written with that in mind + idx = sorted(idx[:k]) + A2 = A[idx, :] + rhs2 = rhs[idx] + return A2, rhs2, status, message diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root.py new file mode 100644 index 0000000000000000000000000000000000000000..2847619bb8039af0c3f96ce5b3347a082ad449e2 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root.py @@ -0,0 +1,732 @@ +""" +Unified interfaces to root finding algorithms. + +Functions +--------- +- root : find a root of a vector function. +""" +__all__ = ['root'] + +import numpy as np + +from warnings import warn + +from ._optimize import MemoizeJac, OptimizeResult, _check_unknown_options +from ._minpack_py import _root_hybr, leastsq +from ._spectral import _root_df_sane +from . import _nonlin as nonlin + + +ROOT_METHODS = ['hybr', 'lm', 'broyden1', 'broyden2', 'anderson', + 'linearmixing', 'diagbroyden', 'excitingmixing', 'krylov', + 'df-sane'] + + +def root(fun, x0, args=(), method='hybr', jac=None, tol=None, callback=None, + options=None): + r""" + Find a root of a vector function. + + Parameters + ---------- + fun : callable + A vector function to find a root of. + x0 : ndarray + Initial guess. + args : tuple, optional + Extra arguments passed to the objective function and its Jacobian. + method : str, optional + Type of solver. Should be one of + + - 'hybr' :ref:`(see here) ` + - 'lm' :ref:`(see here) ` + - 'broyden1' :ref:`(see here) ` + - 'broyden2' :ref:`(see here) ` + - 'anderson' :ref:`(see here) ` + - 'linearmixing' :ref:`(see here) ` + - 'diagbroyden' :ref:`(see here) ` + - 'excitingmixing' :ref:`(see here) ` + - 'krylov' :ref:`(see here) ` + - 'df-sane' :ref:`(see here) ` + + jac : bool or callable, optional + If `jac` is a Boolean and is True, `fun` is assumed to return the + value of Jacobian along with the objective function. If False, the + Jacobian will be estimated numerically. + `jac` can also be a callable returning the Jacobian of `fun`. In + this case, it must accept the same arguments as `fun`. + tol : float, optional + Tolerance for termination. For detailed control, use solver-specific + options. + callback : function, optional + Optional callback function. It is called on every iteration as + ``callback(x, f)`` where `x` is the current solution and `f` + the corresponding residual. For all methods but 'hybr' and 'lm'. + options : dict, optional + A dictionary of solver options. E.g., `xtol` or `maxiter`, see + :obj:`show_options()` for details. + + Returns + ------- + sol : OptimizeResult + The solution represented as a ``OptimizeResult`` object. + Important attributes are: ``x`` the solution array, ``success`` a + Boolean flag indicating if the algorithm exited successfully and + ``message`` which describes the cause of the termination. See + `OptimizeResult` for a description of other attributes. + + See also + -------- + show_options : Additional options accepted by the solvers + + Notes + ----- + This section describes the available solvers that can be selected by the + 'method' parameter. The default method is *hybr*. + + Method *hybr* uses a modification of the Powell hybrid method as + implemented in MINPACK [1]_. + + Method *lm* solves the system of nonlinear equations in a least squares + sense using a modification of the Levenberg-Marquardt algorithm as + implemented in MINPACK [1]_. + + Method *df-sane* is a derivative-free spectral method. [3]_ + + Methods *broyden1*, *broyden2*, *anderson*, *linearmixing*, + *diagbroyden*, *excitingmixing*, *krylov* are inexact Newton methods, + with backtracking or full line searches [2]_. Each method corresponds + to a particular Jacobian approximations. + + - Method *broyden1* uses Broyden's first Jacobian approximation, it is + known as Broyden's good method. + - Method *broyden2* uses Broyden's second Jacobian approximation, it + is known as Broyden's bad method. + - Method *anderson* uses (extended) Anderson mixing. + - Method *Krylov* uses Krylov approximation for inverse Jacobian. It + is suitable for large-scale problem. + - Method *diagbroyden* uses diagonal Broyden Jacobian approximation. + - Method *linearmixing* uses a scalar Jacobian approximation. + - Method *excitingmixing* uses a tuned diagonal Jacobian + approximation. + + .. warning:: + + The algorithms implemented for methods *diagbroyden*, + *linearmixing* and *excitingmixing* may be useful for specific + problems, but whether they will work may depend strongly on the + problem. + + .. versionadded:: 0.11.0 + + References + ---------- + .. [1] More, Jorge J., Burton S. Garbow, and Kenneth E. Hillstrom. + 1980. User Guide for MINPACK-1. + .. [2] C. T. Kelley. 1995. Iterative Methods for Linear and Nonlinear + Equations. Society for Industrial and Applied Mathematics. + + .. [3] W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. 75, 1429 (2006). + + Examples + -------- + The following functions define a system of nonlinear equations and its + jacobian. + + >>> import numpy as np + >>> def fun(x): + ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, + ... 0.5 * (x[1] - x[0])**3 + x[1]] + + >>> def jac(x): + ... return np.array([[1 + 1.5 * (x[0] - x[1])**2, + ... -1.5 * (x[0] - x[1])**2], + ... [-1.5 * (x[1] - x[0])**2, + ... 1 + 1.5 * (x[1] - x[0])**2]]) + + A solution can be obtained as follows. + + >>> from scipy import optimize + >>> sol = optimize.root(fun, [0, 0], jac=jac, method='hybr') + >>> sol.x + array([ 0.8411639, 0.1588361]) + + **Large problem** + + Suppose that we needed to solve the following integrodifferential + equation on the square :math:`[0,1]\times[0,1]`: + + .. math:: + + \nabla^2 P = 10 \left(\int_0^1\int_0^1\cosh(P)\,dx\,dy\right)^2 + + with :math:`P(x,1) = 1` and :math:`P=0` elsewhere on the boundary of + the square. + + The solution can be found using the ``method='krylov'`` solver: + + >>> from scipy import optimize + >>> # parameters + >>> nx, ny = 75, 75 + >>> hx, hy = 1./(nx-1), 1./(ny-1) + + >>> P_left, P_right = 0, 0 + >>> P_top, P_bottom = 1, 0 + + >>> def residual(P): + ... d2x = np.zeros_like(P) + ... d2y = np.zeros_like(P) + ... + ... d2x[1:-1] = (P[2:] - 2*P[1:-1] + P[:-2]) / hx/hx + ... d2x[0] = (P[1] - 2*P[0] + P_left)/hx/hx + ... d2x[-1] = (P_right - 2*P[-1] + P[-2])/hx/hx + ... + ... d2y[:,1:-1] = (P[:,2:] - 2*P[:,1:-1] + P[:,:-2])/hy/hy + ... d2y[:,0] = (P[:,1] - 2*P[:,0] + P_bottom)/hy/hy + ... d2y[:,-1] = (P_top - 2*P[:,-1] + P[:,-2])/hy/hy + ... + ... return d2x + d2y - 10*np.cosh(P).mean()**2 + + >>> guess = np.zeros((nx, ny), float) + >>> sol = optimize.root(residual, guess, method='krylov') + >>> print('Residual: %g' % abs(residual(sol.x)).max()) + Residual: 5.7972e-06 # may vary + + >>> import matplotlib.pyplot as plt + >>> x, y = np.mgrid[0:1:(nx*1j), 0:1:(ny*1j)] + >>> plt.pcolormesh(x, y, sol.x, shading='gouraud') + >>> plt.colorbar() + >>> plt.show() + + """ + def _wrapped_fun(*fargs): + """ + Wrapped `func` to track the number of times + the function has been called. + """ + _wrapped_fun.nfev += 1 + return fun(*fargs) + + _wrapped_fun.nfev = 0 + + if not isinstance(args, tuple): + args = (args,) + + meth = method.lower() + if options is None: + options = {} + + if callback is not None and meth in ('hybr', 'lm'): + warn('Method %s does not accept callback.' % method, + RuntimeWarning, stacklevel=2) + + # fun also returns the Jacobian + if not callable(jac) and meth in ('hybr', 'lm'): + if bool(jac): + fun = MemoizeJac(fun) + jac = fun.derivative + else: + jac = None + + # set default tolerances + if tol is not None: + options = dict(options) + if meth in ('hybr', 'lm'): + options.setdefault('xtol', tol) + elif meth in ('df-sane',): + options.setdefault('ftol', tol) + elif meth in ('broyden1', 'broyden2', 'anderson', 'linearmixing', + 'diagbroyden', 'excitingmixing', 'krylov'): + options.setdefault('xtol', tol) + options.setdefault('xatol', np.inf) + options.setdefault('ftol', np.inf) + options.setdefault('fatol', np.inf) + + if meth == 'hybr': + sol = _root_hybr(_wrapped_fun, x0, args=args, jac=jac, **options) + elif meth == 'lm': + sol = _root_leastsq(_wrapped_fun, x0, args=args, jac=jac, **options) + elif meth == 'df-sane': + _warn_jac_unused(jac, method) + sol = _root_df_sane(_wrapped_fun, x0, args=args, callback=callback, + **options) + elif meth in ('broyden1', 'broyden2', 'anderson', 'linearmixing', + 'diagbroyden', 'excitingmixing', 'krylov'): + _warn_jac_unused(jac, method) + sol = _root_nonlin_solve(_wrapped_fun, x0, args=args, jac=jac, + _method=meth, _callback=callback, + **options) + else: + raise ValueError('Unknown solver %s' % method) + + sol.nfev = _wrapped_fun.nfev + return sol + + +def _warn_jac_unused(jac, method): + if jac is not None: + warn(f'Method {method} does not use the jacobian (jac).', + RuntimeWarning, stacklevel=2) + + +def _root_leastsq(fun, x0, args=(), jac=None, + col_deriv=0, xtol=1.49012e-08, ftol=1.49012e-08, + gtol=0.0, maxiter=0, eps=0.0, factor=100, diag=None, + **unknown_options): + """ + Solve for least squares with Levenberg-Marquardt + + Options + ------- + col_deriv : bool + non-zero to specify that the Jacobian function computes derivatives + down the columns (faster, because there is no transpose operation). + ftol : float + Relative error desired in the sum of squares. + xtol : float + Relative error desired in the approximate solution. + gtol : float + Orthogonality desired between the function vector and the columns + of the Jacobian. + maxiter : int + The maximum number of calls to the function. If zero, then + 100*(N+1) is the maximum where N is the number of elements in x0. + eps : float + A suitable step length for the forward-difference approximation of + the Jacobian (for Dfun=None). If `eps` is less than the machine + precision, it is assumed that the relative errors in the functions + are of the order of the machine precision. + factor : float + A parameter determining the initial step bound + (``factor * || diag * x||``). Should be in interval ``(0.1, 100)``. + diag : sequence + N positive entries that serve as a scale factors for the variables. + """ + nfev = 0 + def _wrapped_fun(*fargs): + """ + Wrapped `func` to track the number of times + the function has been called. + """ + nonlocal nfev + nfev += 1 + return fun(*fargs) + + _check_unknown_options(unknown_options) + x, cov_x, info, msg, ier = leastsq(_wrapped_fun, x0, args=args, + Dfun=jac, full_output=True, + col_deriv=col_deriv, xtol=xtol, + ftol=ftol, gtol=gtol, + maxfev=maxiter, epsfcn=eps, + factor=factor, diag=diag) + sol = OptimizeResult(x=x, message=msg, status=ier, + success=ier in (1, 2, 3, 4), cov_x=cov_x, + fun=info.pop('fvec'), method="lm") + sol.update(info) + sol.nfev = nfev + return sol + + +def _root_nonlin_solve(fun, x0, args=(), jac=None, + _callback=None, _method=None, + nit=None, disp=False, maxiter=None, + ftol=None, fatol=None, xtol=None, xatol=None, + tol_norm=None, line_search='armijo', jac_options=None, + **unknown_options): + _check_unknown_options(unknown_options) + + f_tol = fatol + f_rtol = ftol + x_tol = xatol + x_rtol = xtol + verbose = disp + if jac_options is None: + jac_options = dict() + + jacobian = {'broyden1': nonlin.BroydenFirst, + 'broyden2': nonlin.BroydenSecond, + 'anderson': nonlin.Anderson, + 'linearmixing': nonlin.LinearMixing, + 'diagbroyden': nonlin.DiagBroyden, + 'excitingmixing': nonlin.ExcitingMixing, + 'krylov': nonlin.KrylovJacobian + }[_method] + + if args: + if jac is True: + def f(x): + return fun(x, *args)[0] + else: + def f(x): + return fun(x, *args) + else: + f = fun + + x, info = nonlin.nonlin_solve(f, x0, jacobian=jacobian(**jac_options), + iter=nit, verbose=verbose, + maxiter=maxiter, f_tol=f_tol, + f_rtol=f_rtol, x_tol=x_tol, + x_rtol=x_rtol, tol_norm=tol_norm, + line_search=line_search, + callback=_callback, full_output=True, + raise_exception=False) + sol = OptimizeResult(x=x, method=_method) + sol.update(info) + return sol + +def _root_broyden1_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + alpha : float, optional + Initial guess for the Jacobian is (-1/alpha). + reduction_method : str or tuple, optional + Method used in ensuring that the rank of the Broyden + matrix stays low. Can either be a string giving the + name of the method, or a tuple of the form ``(method, + param1, param2, ...)`` that gives the name of the + method and values for additional parameters. + + Methods available: + + - ``restart`` + Drop all matrix columns. Has no + extra parameters. + - ``simple`` + Drop oldest matrix column. Has no + extra parameters. + - ``svd`` + Keep only the most significant SVD + components. + + Extra parameters: + + - ``to_retain`` + Number of SVD components to + retain when rank reduction is done. + Default is ``max_rank - 2``. + max_rank : int, optional + Maximum rank for the Broyden matrix. + Default is infinity (i.e., no rank reduction). + + Examples + -------- + >>> def func(x): + ... return np.cos(x) + x[::-1] - [1, 2, 3, 4] + ... + >>> from scipy import optimize + >>> res = optimize.root(func, [1, 1, 1, 1], method='broyden1', tol=1e-14) + >>> x = res.x + >>> x + array([4.04674914, 3.91158389, 2.71791677, 1.61756251]) + >>> np.cos(x) + x[::-1] + array([1., 2., 3., 4.]) + + """ + pass + +def _root_broyden2_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + alpha : float, optional + Initial guess for the Jacobian is (-1/alpha). + reduction_method : str or tuple, optional + Method used in ensuring that the rank of the Broyden + matrix stays low. Can either be a string giving the + name of the method, or a tuple of the form ``(method, + param1, param2, ...)`` that gives the name of the + method and values for additional parameters. + + Methods available: + + - ``restart`` + Drop all matrix columns. Has no + extra parameters. + - ``simple`` + Drop oldest matrix column. Has no + extra parameters. + - ``svd`` + Keep only the most significant SVD + components. + + Extra parameters: + + - ``to_retain`` + Number of SVD components to + retain when rank reduction is done. + Default is ``max_rank - 2``. + max_rank : int, optional + Maximum rank for the Broyden matrix. + Default is infinity (i.e., no rank reduction). + """ + pass + +def _root_anderson_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + alpha : float, optional + Initial guess for the Jacobian is (-1/alpha). + M : float, optional + Number of previous vectors to retain. Defaults to 5. + w0 : float, optional + Regularization parameter for numerical stability. + Compared to unity, good values of the order of 0.01. + """ + pass + +def _root_linearmixing_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + alpha : float, optional + initial guess for the jacobian is (-1/alpha). + """ + pass + +def _root_diagbroyden_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + alpha : float, optional + initial guess for the jacobian is (-1/alpha). + """ + pass + +def _root_excitingmixing_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + alpha : float, optional + Initial Jacobian approximation is (-1/alpha). + alphamax : float, optional + The entries of the diagonal Jacobian are kept in the range + ``[alpha, alphamax]``. + """ + pass + +def _root_krylov_doc(): + """ + Options + ------- + nit : int, optional + Number of iterations to make. If omitted (default), make as many + as required to meet tolerances. + disp : bool, optional + Print status to stdout on every iteration. + maxiter : int, optional + Maximum number of iterations to make. + ftol : float, optional + Relative tolerance for the residual. If omitted, not used. + fatol : float, optional + Absolute tolerance (in max-norm) for the residual. + If omitted, default is 6e-6. + xtol : float, optional + Relative minimum step size. If omitted, not used. + xatol : float, optional + Absolute minimum step size, as determined from the Jacobian + approximation. If the step size is smaller than this, optimization + is terminated as successful. If omitted, not used. + tol_norm : function(vector) -> scalar, optional + Norm to use in convergence check. Default is the maximum norm. + line_search : {None, 'armijo' (default), 'wolfe'}, optional + Which type of a line search to use to determine the step size in + the direction given by the Jacobian approximation. Defaults to + 'armijo'. + jac_options : dict, optional + Options for the respective Jacobian approximation. + + rdiff : float, optional + Relative step size to use in numerical differentiation. + method : str or callable, optional + Krylov method to use to approximate the Jacobian. Can be a string, + or a function implementing the same interface as the iterative + solvers in `scipy.sparse.linalg`. If a string, needs to be one of: + ``'lgmres'``, ``'gmres'``, ``'bicgstab'``, ``'cgs'``, ``'minres'``, + ``'tfqmr'``. + + The default is `scipy.sparse.linalg.lgmres`. + inner_M : LinearOperator or InverseJacobian + Preconditioner for the inner Krylov iteration. + Note that you can use also inverse Jacobians as (adaptive) + preconditioners. For example, + + >>> jac = BroydenFirst() + >>> kjac = KrylovJacobian(inner_M=jac.inverse). + + If the preconditioner has a method named 'update', it will + be called as ``update(x, f)`` after each nonlinear step, + with ``x`` giving the current point, and ``f`` the current + function value. + inner_tol, inner_maxiter, ... + Parameters to pass on to the "inner" Krylov solver. + See `scipy.sparse.linalg.gmres` for details. + outer_k : int, optional + Size of the subspace kept across LGMRES nonlinear + iterations. + + See `scipy.sparse.linalg.lgmres` for details. + """ + pass diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root_scalar.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root_scalar.py new file mode 100644 index 0000000000000000000000000000000000000000..550098bbe677825b34e19aec29e340143b3522cc --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_root_scalar.py @@ -0,0 +1,525 @@ +""" +Unified interfaces to root finding algorithms for real or complex +scalar functions. + +Functions +--------- +- root : find a root of a scalar function. +""" +import numpy as np + +from . import _zeros_py as optzeros +from ._numdiff import approx_derivative + +__all__ = ['root_scalar'] + +ROOT_SCALAR_METHODS = ['bisect', 'brentq', 'brenth', 'ridder', 'toms748', + 'newton', 'secant', 'halley'] + + +class MemoizeDer: + """Decorator that caches the value and derivative(s) of function each + time it is called. + + This is a simplistic memoizer that calls and caches a single value + of `f(x, *args)`. + It assumes that `args` does not change between invocations. + It supports the use case of a root-finder where `args` is fixed, + `x` changes, and only rarely, if at all, does x assume the same value + more than once.""" + def __init__(self, fun): + self.fun = fun + self.vals = None + self.x = None + self.n_calls = 0 + + def __call__(self, x, *args): + r"""Calculate f or use cached value if available""" + # Derivative may be requested before the function itself, always check + if self.vals is None or x != self.x: + fg = self.fun(x, *args) + self.x = x + self.n_calls += 1 + self.vals = fg[:] + return self.vals[0] + + def fprime(self, x, *args): + r"""Calculate f' or use a cached value if available""" + if self.vals is None or x != self.x: + self(x, *args) + return self.vals[1] + + def fprime2(self, x, *args): + r"""Calculate f'' or use a cached value if available""" + if self.vals is None or x != self.x: + self(x, *args) + return self.vals[2] + + def ncalls(self): + return self.n_calls + + +def root_scalar(f, args=(), method=None, bracket=None, + fprime=None, fprime2=None, + x0=None, x1=None, + xtol=None, rtol=None, maxiter=None, + options=None): + """ + Find a root of a scalar function. + + Parameters + ---------- + f : callable + A function to find a root of. + args : tuple, optional + Extra arguments passed to the objective function and its derivative(s). + method : str, optional + Type of solver. Should be one of + + - 'bisect' :ref:`(see here) ` + - 'brentq' :ref:`(see here) ` + - 'brenth' :ref:`(see here) ` + - 'ridder' :ref:`(see here) ` + - 'toms748' :ref:`(see here) ` + - 'newton' :ref:`(see here) ` + - 'secant' :ref:`(see here) ` + - 'halley' :ref:`(see here) ` + + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + x0 : float, optional + Initial guess. + x1 : float, optional + A second guess. + fprime : bool or callable, optional + If `fprime` is a boolean and is True, `f` is assumed to return the + value of the objective function and of the derivative. + `fprime` can also be a callable returning the derivative of `f`. In + this case, it must accept the same arguments as `f`. + fprime2 : bool or callable, optional + If `fprime2` is a boolean and is True, `f` is assumed to return the + value of the objective function and of the + first and second derivatives. + `fprime2` can also be a callable returning the second derivative of `f`. + In this case, it must accept the same arguments as `f`. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options : dict, optional + A dictionary of solver options. E.g., ``k``, see + :obj:`show_options()` for details. + + Returns + ------- + sol : RootResults + The solution represented as a ``RootResults`` object. + Important attributes are: ``root`` the solution , ``converged`` a + boolean flag indicating if the algorithm exited successfully and + ``flag`` which describes the cause of the termination. See + `RootResults` for a description of other attributes. + + See also + -------- + show_options : Additional options accepted by the solvers + root : Find a root of a vector function. + + Notes + ----- + This section describes the available solvers that can be selected by the + 'method' parameter. + + The default is to use the best method available for the situation + presented. + If a bracket is provided, it may use one of the bracketing methods. + If a derivative and an initial value are specified, it may + select one of the derivative-based methods. + If no method is judged applicable, it will raise an Exception. + + Arguments for each method are as follows (x=required, o=optional). + + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | method | f | args | bracket | x0 | x1 | fprime | fprime2 | xtol | rtol | maxiter | options | + +===============================================+===+======+=========+====+====+========+=========+======+======+=========+=========+ + | :ref:`bisect ` | x | o | x | | | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`brentq ` | x | o | x | | | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`brenth ` | x | o | x | | | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`ridder ` | x | o | x | | | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`toms748 ` | x | o | x | | | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`secant ` | x | o | | x | o | | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`newton ` | x | o | | x | | o | | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + | :ref:`halley ` | x | o | | x | | x | x | o | o | o | o | + +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+ + + Examples + -------- + + Find the root of a simple cubic + + >>> from scipy import optimize + >>> def f(x): + ... return (x**3 - 1) # only one real root at x = 1 + + >>> def fprime(x): + ... return 3*x**2 + + The `brentq` method takes as input a bracket + + >>> sol = optimize.root_scalar(f, bracket=[0, 3], method='brentq') + >>> sol.root, sol.iterations, sol.function_calls + (1.0, 10, 11) + + The `newton` method takes as input a single point and uses the + derivative(s). + + >>> sol = optimize.root_scalar(f, x0=0.2, fprime=fprime, method='newton') + >>> sol.root, sol.iterations, sol.function_calls + (1.0, 11, 22) + + The function can provide the value and derivative(s) in a single call. + + >>> def f_p_pp(x): + ... return (x**3 - 1), 3*x**2, 6*x + + >>> sol = optimize.root_scalar( + ... f_p_pp, x0=0.2, fprime=True, method='newton' + ... ) + >>> sol.root, sol.iterations, sol.function_calls + (1.0, 11, 11) + + >>> sol = optimize.root_scalar( + ... f_p_pp, x0=0.2, fprime=True, fprime2=True, method='halley' + ... ) + >>> sol.root, sol.iterations, sol.function_calls + (1.0, 7, 8) + + + """ # noqa: E501 + if not isinstance(args, tuple): + args = (args,) + + if options is None: + options = {} + + # fun also returns the derivative(s) + is_memoized = False + if fprime2 is not None and not callable(fprime2): + if bool(fprime2): + f = MemoizeDer(f) + is_memoized = True + fprime2 = f.fprime2 + fprime = f.fprime + else: + fprime2 = None + if fprime is not None and not callable(fprime): + if bool(fprime): + f = MemoizeDer(f) + is_memoized = True + fprime = f.fprime + else: + fprime = None + + # respect solver-specific default tolerances - only pass in if actually set + kwargs = {} + for k in ['xtol', 'rtol', 'maxiter']: + v = locals().get(k) + if v is not None: + kwargs[k] = v + + # Set any solver-specific options + if options: + kwargs.update(options) + # Always request full_output from the underlying method as _root_scalar + # always returns a RootResults object + kwargs.update(full_output=True, disp=False) + + # Pick a method if not specified. + # Use the "best" method available for the situation. + if not method: + if bracket: + method = 'brentq' + elif x0 is not None: + if fprime: + if fprime2: + method = 'halley' + else: + method = 'newton' + elif x1 is not None: + method = 'secant' + else: + method = 'newton' + if not method: + raise ValueError('Unable to select a solver as neither bracket ' + 'nor starting point provided.') + + meth = method.lower() + map2underlying = {'halley': 'newton', 'secant': 'newton'} + + try: + methodc = getattr(optzeros, map2underlying.get(meth, meth)) + except AttributeError as e: + raise ValueError('Unknown solver %s' % meth) from e + + if meth in ['bisect', 'ridder', 'brentq', 'brenth', 'toms748']: + if not isinstance(bracket, (list, tuple, np.ndarray)): + raise ValueError('Bracket needed for %s' % method) + + a, b = bracket[:2] + try: + r, sol = methodc(f, a, b, args=args, **kwargs) + except ValueError as e: + # gh-17622 fixed some bugs in low-level solvers by raising an error + # (rather than returning incorrect results) when the callable + # returns a NaN. It did so by wrapping the callable rather than + # modifying compiled code, so the iteration count is not available. + if hasattr(e, "_x"): + sol = optzeros.RootResults(root=e._x, + iterations=np.nan, + function_calls=e._function_calls, + flag=str(e), method=method) + else: + raise + + elif meth in ['secant']: + if x0 is None: + raise ValueError('x0 must not be None for %s' % method) + if 'xtol' in kwargs: + kwargs['tol'] = kwargs.pop('xtol') + r, sol = methodc(f, x0, args=args, fprime=None, fprime2=None, + x1=x1, **kwargs) + elif meth in ['newton']: + if x0 is None: + raise ValueError('x0 must not be None for %s' % method) + if not fprime: + # approximate fprime with finite differences + + def fprime(x, *args): + # `root_scalar` doesn't actually seem to support vectorized + # use of `newton`. In that case, `approx_derivative` will + # always get scalar input. Nonetheless, it always returns an + # array, so we extract the element to produce scalar output. + return approx_derivative(f, x, method='2-point', args=args)[0] + + if 'xtol' in kwargs: + kwargs['tol'] = kwargs.pop('xtol') + r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=None, + **kwargs) + elif meth in ['halley']: + if x0 is None: + raise ValueError('x0 must not be None for %s' % method) + if not fprime: + raise ValueError('fprime must be specified for %s' % method) + if not fprime2: + raise ValueError('fprime2 must be specified for %s' % method) + if 'xtol' in kwargs: + kwargs['tol'] = kwargs.pop('xtol') + r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=fprime2, **kwargs) + else: + raise ValueError('Unknown solver %s' % method) + + if is_memoized: + # Replace the function_calls count with the memoized count. + # Avoids double and triple-counting. + n_calls = f.n_calls + sol.function_calls = n_calls + + return sol + + +def _root_scalar_brentq_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options: dict, optional + Specifies any method-specific options not covered above + + """ + pass + + +def _root_scalar_brenth_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + +def _root_scalar_toms748_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + + +def _root_scalar_secant_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + x0 : float, required + Initial guess. + x1 : float, required + A second guess. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + + +def _root_scalar_newton_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function and its derivative. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + x0 : float, required + Initial guess. + fprime : bool or callable, optional + If `fprime` is a boolean and is True, `f` is assumed to return the + value of derivative along with the objective function. + `fprime` can also be a callable returning the derivative of `f`. In + this case, it must accept the same arguments as `f`. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + + +def _root_scalar_halley_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function and its derivatives. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + x0 : float, required + Initial guess. + fprime : bool or callable, required + If `fprime` is a boolean and is True, `f` is assumed to return the + value of derivative along with the objective function. + `fprime` can also be a callable returning the derivative of `f`. In + this case, it must accept the same arguments as `f`. + fprime2 : bool or callable, required + If `fprime2` is a boolean and is True, `f` is assumed to return the + value of 1st and 2nd derivatives along with the objective function. + `fprime2` can also be a callable returning the 2nd derivative of `f`. + In this case, it must accept the same arguments as `f`. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + + +def _root_scalar_ridder_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass + + +def _root_scalar_bisect_doc(): + r""" + Options + ------- + args : tuple, optional + Extra arguments passed to the objective function. + bracket: A sequence of 2 floats, optional + An interval bracketing a root. `f(x, *args)` must have different + signs at the two endpoints. + xtol : float, optional + Tolerance (absolute) for termination. + rtol : float, optional + Tolerance (relative) for termination. + maxiter : int, optional + Maximum number of iterations. + options: dict, optional + Specifies any method-specific options not covered above. + + """ + pass diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_shgo.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_shgo.py new file mode 100644 index 0000000000000000000000000000000000000000..4dce006dcbcac78513451441e067f027016b6f5b --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_shgo.py @@ -0,0 +1,1598 @@ +"""shgo: The simplicial homology global optimisation algorithm.""" +from collections import namedtuple +import time +import logging +import warnings +import sys + +import numpy as np + +from scipy import spatial +from scipy.optimize import OptimizeResult, minimize, Bounds +from scipy.optimize._optimize import MemoizeJac +from scipy.optimize._constraints import new_bounds_to_old +from scipy.optimize._minimize import standardize_constraints +from scipy._lib._util import _FunctionWrapper + +from scipy.optimize._shgo_lib._complex import Complex + +__all__ = ['shgo'] + + +def shgo( + func, bounds, args=(), constraints=None, n=100, iters=1, callback=None, + minimizer_kwargs=None, options=None, sampling_method='simplicial', *, + workers=1 +): + """ + Finds the global minimum of a function using SHG optimization. + + SHGO stands for "simplicial homology global optimization". + + Parameters + ---------- + func : callable + The objective function to be minimized. Must be in the form + ``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array + and ``args`` is a tuple of any additional fixed parameters needed to + completely specify the function. + bounds : sequence or `Bounds` + Bounds for variables. There are two ways to specify the bounds: + + 1. Instance of `Bounds` class. + 2. Sequence of ``(min, max)`` pairs for each element in `x`. + + args : tuple, optional + Any additional fixed parameters needed to completely specify the + objective function. + constraints : {Constraint, dict} or List of {Constraint, dict}, optional + Constraints definition. Only for COBYLA, COBYQA, SLSQP and trust-constr. + See the tutorial [5]_ for further details on specifying constraints. + + .. note:: + + Only COBYLA, COBYQA, SLSQP, and trust-constr local minimize methods + currently support constraint arguments. If the ``constraints`` + sequence used in the local optimization problem is not defined in + ``minimizer_kwargs`` and a constrained method is used then the + global ``constraints`` will be used. + (Defining a ``constraints`` sequence in ``minimizer_kwargs`` + means that ``constraints`` will not be added so if equality + constraints and so forth need to be added then the inequality + functions in ``constraints`` need to be added to + ``minimizer_kwargs`` too). + COBYLA only supports inequality constraints. + + .. versionchanged:: 1.11.0 + + ``constraints`` accepts `NonlinearConstraint`, `LinearConstraint`. + + n : int, optional + Number of sampling points used in the construction of the simplicial + complex. For the default ``simplicial`` sampling method 2**dim + 1 + sampling points are generated instead of the default `n=100`. For all + other specified values `n` sampling points are generated. For + ``sobol``, ``halton`` and other arbitrary `sampling_methods` `n=100` or + another specified number of sampling points are generated. + iters : int, optional + Number of iterations used in the construction of the simplicial + complex. Default is 1. + callback : callable, optional + Called after each iteration, as ``callback(xk)``, where ``xk`` is the + current parameter vector. + minimizer_kwargs : dict, optional + Extra keyword arguments to be passed to the minimizer + ``scipy.optimize.minimize`` Some important options could be: + + * method : str + The minimization method. If not given, chosen to be one of + BFGS, L-BFGS-B, SLSQP, depending on whether or not the + problem has constraints or bounds. + * args : tuple + Extra arguments passed to the objective function (``func``) and + its derivatives (Jacobian, Hessian). + * options : dict, optional + Note that by default the tolerance is specified as + ``{ftol: 1e-12}`` + + options : dict, optional + A dictionary of solver options. Many of the options specified for the + global routine are also passed to the scipy.optimize.minimize routine. + The options that are also passed to the local routine are marked with + "(L)". + + Stopping criteria, the algorithm will terminate if any of the specified + criteria are met. However, the default algorithm does not require any + to be specified: + + * maxfev : int (L) + Maximum number of function evaluations in the feasible domain. + (Note only methods that support this option will terminate + the routine at precisely exact specified value. Otherwise the + criterion will only terminate during a global iteration) + * f_min + Specify the minimum objective function value, if it is known. + * f_tol : float + Precision goal for the value of f in the stopping + criterion. Note that the global routine will also + terminate if a sampling point in the global routine is + within this tolerance. + * maxiter : int + Maximum number of iterations to perform. + * maxev : int + Maximum number of sampling evaluations to perform (includes + searching in infeasible points). + * maxtime : float + Maximum processing runtime allowed + * minhgrd : int + Minimum homology group rank differential. The homology group of the + objective function is calculated (approximately) during every + iteration. The rank of this group has a one-to-one correspondence + with the number of locally convex subdomains in the objective + function (after adequate sampling points each of these subdomains + contain a unique global minimum). If the difference in the hgr is 0 + between iterations for ``maxhgrd`` specified iterations the + algorithm will terminate. + + Objective function knowledge: + + * symmetry : list or bool + Specify if the objective function contains symmetric variables. + The search space (and therefore performance) is decreased by up to + O(n!) times in the fully symmetric case. If `True` is specified + then all variables will be set symmetric to the first variable. + Default + is set to False. + + E.g. f(x) = (x_1 + x_2 + x_3) + (x_4)**2 + (x_5)**2 + (x_6)**2 + + In this equation x_2 and x_3 are symmetric to x_1, while x_5 and + x_6 are symmetric to x_4, this can be specified to the solver as: + + symmetry = [0, # Variable 1 + 0, # symmetric to variable 1 + 0, # symmetric to variable 1 + 3, # Variable 4 + 3, # symmetric to variable 4 + 3, # symmetric to variable 4 + ] + + * jac : bool or callable, optional + Jacobian (gradient) of objective function. Only for CG, BFGS, + Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg. If ``jac`` is a + boolean and is True, ``fun`` is assumed to return the gradient + along with the objective function. If False, the gradient will be + estimated numerically. ``jac`` can also be a callable returning the + gradient of the objective. In this case, it must accept the same + arguments as ``fun``. (Passed to `scipy.optimize.minimize` + automatically) + + * hess, hessp : callable, optional + Hessian (matrix of second-order derivatives) of objective function + or Hessian of objective function times an arbitrary vector p. + Only for Newton-CG, dogleg, trust-ncg. Only one of ``hessp`` or + ``hess`` needs to be given. If ``hess`` is provided, then + ``hessp`` will be ignored. If neither ``hess`` nor ``hessp`` is + provided, then the Hessian product will be approximated using + finite differences on ``jac``. ``hessp`` must compute the Hessian + times an arbitrary vector. (Passed to `scipy.optimize.minimize` + automatically) + + Algorithm settings: + + * minimize_every_iter : bool + If True then promising global sampling points will be passed to a + local minimization routine every iteration. If True then only the + final minimizer pool will be run. Defaults to True. + * local_iter : int + Only evaluate a few of the best minimizer pool candidates every + iteration. If False all potential points are passed to the local + minimization routine. + * infty_constraints : bool + If True then any sampling points generated which are outside will + the feasible domain will be saved and given an objective function + value of ``inf``. If False then these points will be discarded. + Using this functionality could lead to higher performance with + respect to function evaluations before the global minimum is found, + specifying False will use less memory at the cost of a slight + decrease in performance. Defaults to True. + + Feedback: + + * disp : bool (L) + Set to True to print convergence messages. + + sampling_method : str or function, optional + Current built in sampling method options are ``halton``, ``sobol`` and + ``simplicial``. The default ``simplicial`` provides + the theoretical guarantee of convergence to the global minimum in + finite time. ``halton`` and ``sobol`` method are faster in terms of + sampling point generation at the cost of the loss of + guaranteed convergence. It is more appropriate for most "easier" + problems where the convergence is relatively fast. + User defined sampling functions must accept two arguments of ``n`` + sampling points of dimension ``dim`` per call and output an array of + sampling points with shape `n x dim`. + + workers : int or map-like callable, optional + Sample and run the local serial minimizations in parallel. + Supply -1 to use all available CPU cores, or an int to use + that many Processes (uses `multiprocessing.Pool `). + + Alternatively supply a map-like callable, such as + `multiprocessing.Pool.map` for parallel evaluation. + This evaluation is carried out as ``workers(func, iterable)``. + Requires that `func` be pickleable. + + .. versionadded:: 1.11.0 + + Returns + ------- + res : OptimizeResult + The optimization result represented as a `OptimizeResult` object. + Important attributes are: + ``x`` the solution array corresponding to the global minimum, + ``fun`` the function output at the global solution, + ``xl`` an ordered list of local minima solutions, + ``funl`` the function output at the corresponding local solutions, + ``success`` a Boolean flag indicating if the optimizer exited + successfully, + ``message`` which describes the cause of the termination, + ``nfev`` the total number of objective function evaluations including + the sampling calls, + ``nlfev`` the total number of objective function evaluations + culminating from all local search optimizations, + ``nit`` number of iterations performed by the global routine. + + Notes + ----- + Global optimization using simplicial homology global optimization [1]_. + Appropriate for solving general purpose NLP and blackbox optimization + problems to global optimality (low-dimensional problems). + + In general, the optimization problems are of the form:: + + minimize f(x) subject to + + g_i(x) >= 0, i = 1,...,m + h_j(x) = 0, j = 1,...,p + + where x is a vector of one or more variables. ``f(x)`` is the objective + function ``R^n -> R``, ``g_i(x)`` are the inequality constraints, and + ``h_j(x)`` are the equality constraints. + + Optionally, the lower and upper bounds for each element in x can also be + specified using the `bounds` argument. + + While most of the theoretical advantages of SHGO are only proven for when + ``f(x)`` is a Lipschitz smooth function, the algorithm is also proven to + converge to the global optimum for the more general case where ``f(x)`` is + non-continuous, non-convex and non-smooth, if the default sampling method + is used [1]_. + + The local search method may be specified using the ``minimizer_kwargs`` + parameter which is passed on to ``scipy.optimize.minimize``. By default, + the ``SLSQP`` method is used. In general, it is recommended to use the + ``SLSQP``, ``COBYLA``, or ``COBYQA`` local minimization if inequality + constraints are defined for the problem since the other methods do not use + constraints. + + The ``halton`` and ``sobol`` method points are generated using + `scipy.stats.qmc`. Any other QMC method could be used. + + References + ---------- + .. [1] Endres, SC, Sandrock, C, Focke, WW (2018) "A simplicial homology + algorithm for lipschitz optimisation", Journal of Global + Optimization. + .. [2] Joe, SW and Kuo, FY (2008) "Constructing Sobol' sequences with + better two-dimensional projections", SIAM J. Sci. Comput. 30, + 2635-2654. + .. [3] Hock, W and Schittkowski, K (1981) "Test examples for nonlinear + programming codes", Lecture Notes in Economics and Mathematical + Systems, 187. Springer-Verlag, New York. + http://www.ai7.uni-bayreuth.de/test_problem_coll.pdf + .. [4] Wales, DJ (2015) "Perspective: Insight into reaction coordinates and + dynamics from the potential energy landscape", + Journal of Chemical Physics, 142(13), 2015. + .. [5] https://docs.scipy.org/doc/scipy/tutorial/optimize.html#constrained-minimization-of-multivariate-scalar-functions-minimize + + Examples + -------- + First consider the problem of minimizing the Rosenbrock function, `rosen`: + + >>> from scipy.optimize import rosen, shgo + >>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)] + >>> result = shgo(rosen, bounds) + >>> result.x, result.fun + (array([1., 1., 1., 1., 1.]), 2.920392374190081e-18) + + Note that bounds determine the dimensionality of the objective + function and is therefore a required input, however you can specify + empty bounds using ``None`` or objects like ``np.inf`` which will be + converted to large float numbers. + + >>> bounds = [(None, None), ]*4 + >>> result = shgo(rosen, bounds) + >>> result.x + array([0.99999851, 0.99999704, 0.99999411, 0.9999882 ]) + + Next, we consider the Eggholder function, a problem with several local + minima and one global minimum. We will demonstrate the use of arguments and + the capabilities of `shgo`. + (https://en.wikipedia.org/wiki/Test_functions_for_optimization) + + >>> import numpy as np + >>> def eggholder(x): + ... return (-(x[1] + 47.0) + ... * np.sin(np.sqrt(abs(x[0]/2.0 + (x[1] + 47.0)))) + ... - x[0] * np.sin(np.sqrt(abs(x[0] - (x[1] + 47.0)))) + ... ) + ... + >>> bounds = [(-512, 512), (-512, 512)] + + `shgo` has built-in low discrepancy sampling sequences. First, we will + input 64 initial sampling points of the *Sobol'* sequence: + + >>> result = shgo(eggholder, bounds, n=64, sampling_method='sobol') + >>> result.x, result.fun + (array([512. , 404.23180824]), -959.6406627208397) + + `shgo` also has a return for any other local minima that was found, these + can be called using: + + >>> result.xl + array([[ 512. , 404.23180824], + [ 283.0759062 , -487.12565635], + [-294.66820039, -462.01964031], + [-105.87688911, 423.15323845], + [-242.97926 , 274.38030925], + [-506.25823477, 6.3131022 ], + [-408.71980731, -156.10116949], + [ 150.23207937, 301.31376595], + [ 91.00920901, -391.283763 ], + [ 202.89662724, -269.38043241], + [ 361.66623976, -106.96493868], + [-219.40612786, -244.06020508]]) + + >>> result.funl + array([-959.64066272, -718.16745962, -704.80659592, -565.99778097, + -559.78685655, -557.36868733, -507.87385942, -493.9605115 , + -426.48799655, -421.15571437, -419.31194957, -410.98477763]) + + These results are useful in applications where there are many global minima + and the values of other global minima are desired or where the local minima + can provide insight into the system (for example morphologies + in physical chemistry [4]_). + + If we want to find a larger number of local minima, we can increase the + number of sampling points or the number of iterations. We'll increase the + number of sampling points to 64 and the number of iterations from the + default of 1 to 3. Using ``simplicial`` this would have given us + 64 x 3 = 192 initial sampling points. + + >>> result_2 = shgo(eggholder, + ... bounds, n=64, iters=3, sampling_method='sobol') + >>> len(result.xl), len(result_2.xl) + (12, 23) + + Note the difference between, e.g., ``n=192, iters=1`` and ``n=64, + iters=3``. + In the first case the promising points contained in the minimiser pool + are processed only once. In the latter case it is processed every 64 + sampling points for a total of 3 times. + + To demonstrate solving problems with non-linear constraints consider the + following example from Hock and Schittkowski problem 73 (cattle-feed) + [3]_:: + + minimize: f = 24.55 * x_1 + 26.75 * x_2 + 39 * x_3 + 40.50 * x_4 + + subject to: 2.3 * x_1 + 5.6 * x_2 + 11.1 * x_3 + 1.3 * x_4 - 5 >= 0, + + 12 * x_1 + 11.9 * x_2 + 41.8 * x_3 + 52.1 * x_4 - 21 + -1.645 * sqrt(0.28 * x_1**2 + 0.19 * x_2**2 + + 20.5 * x_3**2 + 0.62 * x_4**2) >= 0, + + x_1 + x_2 + x_3 + x_4 - 1 == 0, + + 1 >= x_i >= 0 for all i + + The approximate answer given in [3]_ is:: + + f([0.6355216, -0.12e-11, 0.3127019, 0.05177655]) = 29.894378 + + >>> def f(x): # (cattle-feed) + ... return 24.55*x[0] + 26.75*x[1] + 39*x[2] + 40.50*x[3] + ... + >>> def g1(x): + ... return 2.3*x[0] + 5.6*x[1] + 11.1*x[2] + 1.3*x[3] - 5 # >=0 + ... + >>> def g2(x): + ... return (12*x[0] + 11.9*x[1] +41.8*x[2] + 52.1*x[3] - 21 + ... - 1.645 * np.sqrt(0.28*x[0]**2 + 0.19*x[1]**2 + ... + 20.5*x[2]**2 + 0.62*x[3]**2) + ... ) # >=0 + ... + >>> def h1(x): + ... return x[0] + x[1] + x[2] + x[3] - 1 # == 0 + ... + >>> cons = ({'type': 'ineq', 'fun': g1}, + ... {'type': 'ineq', 'fun': g2}, + ... {'type': 'eq', 'fun': h1}) + >>> bounds = [(0, 1.0),]*4 + >>> res = shgo(f, bounds, n=150, constraints=cons) + >>> res + message: Optimization terminated successfully. + success: True + fun: 29.894378159142136 + funl: [ 2.989e+01] + x: [ 6.355e-01 1.137e-13 3.127e-01 5.178e-02] # may vary + xl: [[ 6.355e-01 1.137e-13 3.127e-01 5.178e-02]] # may vary + nit: 1 + nfev: 142 # may vary + nlfev: 35 # may vary + nljev: 5 + nlhev: 0 + + >>> g1(res.x), g2(res.x), h1(res.x) + (-5.062616992290714e-14, -2.9594104944408173e-12, 0.0) + + """ + # if necessary, convert bounds class to old bounds + if isinstance(bounds, Bounds): + bounds = new_bounds_to_old(bounds.lb, bounds.ub, len(bounds.lb)) + + # Initiate SHGO class + # use in context manager to make sure that any parallelization + # resources are freed. + with SHGO(func, bounds, args=args, constraints=constraints, n=n, + iters=iters, callback=callback, + minimizer_kwargs=minimizer_kwargs, + options=options, sampling_method=sampling_method, + workers=workers) as shc: + # Run the algorithm, process results and test success + shc.iterate_all() + + if not shc.break_routine: + if shc.disp: + logging.info("Successfully completed construction of complex.") + + # Test post iterations success + if len(shc.LMC.xl_maps) == 0: + # If sampling failed to find pool, return lowest sampled point + # with a warning + shc.find_lowest_vertex() + shc.break_routine = True + shc.fail_routine(mes="Failed to find a feasible minimizer point. " + f"Lowest sampling point = {shc.f_lowest}") + shc.res.fun = shc.f_lowest + shc.res.x = shc.x_lowest + shc.res.nfev = shc.fn + shc.res.tnev = shc.n_sampled + else: + # Test that the optimal solutions do not violate any constraints + pass # TODO + + # Confirm the routine ran successfully + if not shc.break_routine: + shc.res.message = 'Optimization terminated successfully.' + shc.res.success = True + + # Return the final results + return shc.res + + +class SHGO: + def __init__(self, func, bounds, args=(), constraints=None, n=None, + iters=None, callback=None, minimizer_kwargs=None, + options=None, sampling_method='simplicial', workers=1): + from scipy.stats import qmc + # Input checks + methods = ['halton', 'sobol', 'simplicial'] + if isinstance(sampling_method, str) and sampling_method not in methods: + raise ValueError(("Unknown sampling_method specified." + " Valid methods: {}").format(', '.join(methods))) + + # Split obj func if given with Jac + try: + if ((minimizer_kwargs['jac'] is True) and + (not callable(minimizer_kwargs['jac']))): + self.func = MemoizeJac(func) + jac = self.func.derivative + minimizer_kwargs['jac'] = jac + func = self.func # .fun + else: + self.func = func # Normal definition of objective function + except (TypeError, KeyError): + self.func = func # Normal definition of objective function + + # Initiate class + self.func = _FunctionWrapper(func, args) + self.bounds = bounds + self.args = args + self.callback = callback + + # Bounds + abound = np.array(bounds, float) + self.dim = np.shape(abound)[0] # Dimensionality of problem + + # Set none finite values to large floats + infind = ~np.isfinite(abound) + abound[infind[:, 0], 0] = -1e50 + abound[infind[:, 1], 1] = 1e50 + + # Check if bounds are correctly specified + bnderr = abound[:, 0] > abound[:, 1] + if bnderr.any(): + raise ValueError('Error: lb > ub in bounds {}.' + .format(', '.join(str(b) for b in bnderr))) + + self.bounds = abound + + # Constraints + # Process constraint dict sequence: + self.constraints = constraints + if constraints is not None: + self.min_cons = constraints + self.g_cons = [] + self.g_args = [] + + # shgo internals deals with old-style constraints + # self.constraints is used to create Complex, so need + # to be stored internally in old-style. + # `minimize` takes care of normalising these constraints + # for slsqp/cobyla/cobyqa/trust-constr. + self.constraints = standardize_constraints( + constraints, + np.empty(self.dim, float), + 'old' + ) + for cons in self.constraints: + if cons['type'] in ('ineq'): + self.g_cons.append(cons['fun']) + try: + self.g_args.append(cons['args']) + except KeyError: + self.g_args.append(()) + self.g_cons = tuple(self.g_cons) + self.g_args = tuple(self.g_args) + else: + self.g_cons = None + self.g_args = None + + # Define local minimization keyword arguments + # Start with defaults + self.minimizer_kwargs = {'method': 'SLSQP', + 'bounds': self.bounds, + 'options': {}, + 'callback': self.callback + } + if minimizer_kwargs is not None: + # Overwrite with supplied values + self.minimizer_kwargs.update(minimizer_kwargs) + + else: + self.minimizer_kwargs['options'] = {'ftol': 1e-12} + + if ( + self.minimizer_kwargs['method'].lower() in ('slsqp', 'cobyla', + 'cobyqa', + 'trust-constr') + and ( + minimizer_kwargs is not None and + 'constraints' not in minimizer_kwargs and + constraints is not None + ) or + (self.g_cons is not None) + ): + self.minimizer_kwargs['constraints'] = self.min_cons + + # Process options dict + if options is not None: + self.init_options(options) + else: # Default settings: + self.f_min_true = None + self.minimize_every_iter = True + + # Algorithm limits + self.maxiter = None + self.maxfev = None + self.maxev = None + self.maxtime = None + self.f_min_true = None + self.minhgrd = None + + # Objective function knowledge + self.symmetry = None + + # Algorithm functionality + self.infty_cons_sampl = True + self.local_iter = False + + # Feedback + self.disp = False + + # Remove unknown arguments in self.minimizer_kwargs + # Start with arguments all the solvers have in common + self.min_solver_args = ['fun', 'x0', 'args', + 'callback', 'options', 'method'] + # then add the ones unique to specific solvers + solver_args = { + '_custom': ['jac', 'hess', 'hessp', 'bounds', 'constraints'], + 'nelder-mead': [], + 'powell': [], + 'cg': ['jac'], + 'bfgs': ['jac'], + 'newton-cg': ['jac', 'hess', 'hessp'], + 'l-bfgs-b': ['jac', 'bounds'], + 'tnc': ['jac', 'bounds'], + 'cobyla': ['constraints', 'catol'], + 'cobyqa': ['bounds', 'constraints', 'feasibility_tol'], + 'slsqp': ['jac', 'bounds', 'constraints'], + 'dogleg': ['jac', 'hess'], + 'trust-ncg': ['jac', 'hess', 'hessp'], + 'trust-krylov': ['jac', 'hess', 'hessp'], + 'trust-exact': ['jac', 'hess'], + 'trust-constr': ['jac', 'hess', 'hessp', 'constraints'], + } + method = self.minimizer_kwargs['method'] + self.min_solver_args += solver_args[method.lower()] + + # Only retain the known arguments + def _restrict_to_keys(dictionary, goodkeys): + """Remove keys from dictionary if not in goodkeys - inplace""" + existingkeys = set(dictionary) + for key in existingkeys - set(goodkeys): + dictionary.pop(key, None) + + _restrict_to_keys(self.minimizer_kwargs, self.min_solver_args) + _restrict_to_keys(self.minimizer_kwargs['options'], + self.min_solver_args + ['ftol']) + + # Algorithm controls + # Global controls + self.stop_global = False # Used in the stopping_criteria method + self.break_routine = False # Break the algorithm globally + self.iters = iters # Iterations to be ran + self.iters_done = 0 # Iterations completed + self.n = n # Sampling points per iteration + self.nc = 0 # n # Sampling points to sample in current iteration + self.n_prc = 0 # Processed points (used to track Delaunay iters) + self.n_sampled = 0 # To track no. of sampling points already generated + self.fn = 0 # Number of feasible sampling points evaluations performed + self.hgr = 0 # Homology group rank + # Initially attempt to build the triangulation incrementally: + self.qhull_incremental = True + + # Default settings if no sampling criteria. + if (self.n is None) and (self.iters is None) \ + and (sampling_method == 'simplicial'): + self.n = 2 ** self.dim + 1 + self.nc = 0 # self.n + if self.iters is None: + self.iters = 1 + if (self.n is None) and not (sampling_method == 'simplicial'): + self.n = self.n = 100 + self.nc = 0 # self.n + if (self.n == 100) and (sampling_method == 'simplicial'): + self.n = 2 ** self.dim + 1 + + if not ((self.maxiter is None) and (self.maxfev is None) and ( + self.maxev is None) + and (self.minhgrd is None) and (self.f_min_true is None)): + self.iters = None + + # Set complex construction mode based on a provided stopping criteria: + # Initialise sampling Complex and function cache + # Note that sfield_args=() since args are already wrapped in self.func + # using the_FunctionWrapper class. + self.HC = Complex(dim=self.dim, domain=self.bounds, + sfield=self.func, sfield_args=(), + symmetry=self.symmetry, + constraints=self.constraints, + workers=workers) + + # Choose complex constructor + if sampling_method == 'simplicial': + self.iterate_complex = self.iterate_hypercube + self.sampling_method = sampling_method + + elif sampling_method in ['halton', 'sobol'] or \ + not isinstance(sampling_method, str): + self.iterate_complex = self.iterate_delaunay + # Sampling method used + if sampling_method in ['halton', 'sobol']: + if sampling_method == 'sobol': + self.n = int(2 ** np.ceil(np.log2(self.n))) + # self.n #TODO: Should always be self.n, this is + # unacceptable for shgo, check that nfev behaves as + # expected. + self.nc = 0 + self.sampling_method = 'sobol' + self.qmc_engine = qmc.Sobol(d=self.dim, scramble=False, + seed=0) + else: + self.sampling_method = 'halton' + self.qmc_engine = qmc.Halton(d=self.dim, scramble=True, + seed=0) + + def sampling_method(n, d): + return self.qmc_engine.random(n) + + else: + # A user defined sampling method: + self.sampling_method = 'custom' + + self.sampling = self.sampling_custom + self.sampling_function = sampling_method # F(n, d) + + # Local controls + self.stop_l_iter = False # Local minimisation iterations + self.stop_complex_iter = False # Sampling iterations + + # Initiate storage objects used in algorithm classes + self.minimizer_pool = [] + + # Cache of local minimizers mapped + self.LMC = LMapCache() + + # Initialize return object + self.res = OptimizeResult() # scipy.optimize.OptimizeResult object + self.res.nfev = 0 # Includes each sampling point as func evaluation + self.res.nlfev = 0 # Local function evals for all minimisers + self.res.nljev = 0 # Local Jacobian evals for all minimisers + self.res.nlhev = 0 # Local Hessian evals for all minimisers + + # Initiation aids + def init_options(self, options): + """ + Initiates the options. + + Can also be useful to change parameters after class initiation. + + Parameters + ---------- + options : dict + + Returns + ------- + None + + """ + # Update 'options' dict passed to optimize.minimize + # Do this first so we don't mutate `options` below. + self.minimizer_kwargs['options'].update(options) + + # Ensure that 'jac', 'hess', and 'hessp' are passed directly to + # `minimize` as keywords, not as part of its 'options' dictionary. + for opt in ['jac', 'hess', 'hessp']: + if opt in self.minimizer_kwargs['options']: + self.minimizer_kwargs[opt] = ( + self.minimizer_kwargs['options'].pop(opt)) + + # Default settings: + self.minimize_every_iter = options.get('minimize_every_iter', True) + + # Algorithm limits + # Maximum number of iterations to perform. + self.maxiter = options.get('maxiter', None) + # Maximum number of function evaluations in the feasible domain + self.maxfev = options.get('maxfev', None) + # Maximum number of sampling evaluations (includes searching in + # infeasible points + self.maxev = options.get('maxev', None) + # Maximum processing runtime allowed + self.init = time.time() + self.maxtime = options.get('maxtime', None) + if 'f_min' in options: + # Specify the minimum objective function value, if it is known. + self.f_min_true = options['f_min'] + self.f_tol = options.get('f_tol', 1e-4) + else: + self.f_min_true = None + + self.minhgrd = options.get('minhgrd', None) + + # Objective function knowledge + self.symmetry = options.get('symmetry', False) + if self.symmetry: + self.symmetry = [0, ]*len(self.bounds) + else: + self.symmetry = None + # Algorithm functionality + # Only evaluate a few of the best candidates + self.local_iter = options.get('local_iter', False) + self.infty_cons_sampl = options.get('infty_constraints', True) + + # Feedback + self.disp = options.get('disp', False) + + def __enter__(self): + return self + + def __exit__(self, *args): + return self.HC.V._mapwrapper.__exit__(*args) + + # Iteration properties + # Main construction loop: + def iterate_all(self): + """ + Construct for `iters` iterations. + + If uniform sampling is used, every iteration adds 'n' sampling points. + + Iterations if a stopping criteria (e.g., sampling points or + processing time) has been met. + + """ + if self.disp: + logging.info('Splitting first generation') + + while not self.stop_global: + if self.break_routine: + break + # Iterate complex, process minimisers + self.iterate() + self.stopping_criteria() + + # Build minimiser pool + # Final iteration only needed if pools weren't minimised every + # iteration + if not self.minimize_every_iter: + if not self.break_routine: + self.find_minima() + + self.res.nit = self.iters_done # + 1 + self.fn = self.HC.V.nfev + + def find_minima(self): + """ + Construct the minimizer pool, map the minimizers to local minima + and sort the results into a global return object. + """ + if self.disp: + logging.info('Searching for minimizer pool...') + + self.minimizers() + + if len(self.X_min) != 0: + # Minimize the pool of minimizers with local minimization methods + # Note that if Options['local_iter'] is an `int` instead of default + # value False then only that number of candidates will be minimized + self.minimise_pool(self.local_iter) + # Sort results and build the global return object + self.sort_result() + + # Lowest values used to report in case of failures + self.f_lowest = self.res.fun + self.x_lowest = self.res.x + else: + self.find_lowest_vertex() + + if self.disp: + logging.info(f"Minimiser pool = SHGO.X_min = {self.X_min}") + + def find_lowest_vertex(self): + # Find the lowest objective function value on one of + # the vertices of the simplicial complex + self.f_lowest = np.inf + for x in self.HC.V.cache: + if self.HC.V[x].f < self.f_lowest: + if self.disp: + logging.info(f'self.HC.V[x].f = {self.HC.V[x].f}') + self.f_lowest = self.HC.V[x].f + self.x_lowest = self.HC.V[x].x_a + for lmc in self.LMC.cache: + if self.LMC[lmc].f_min < self.f_lowest: + self.f_lowest = self.LMC[lmc].f_min + self.x_lowest = self.LMC[lmc].x_l + + if self.f_lowest == np.inf: # no feasible point + self.f_lowest = None + self.x_lowest = None + + # Stopping criteria functions: + def finite_iterations(self): + mi = min(x for x in [self.iters, self.maxiter] if x is not None) + if self.disp: + logging.info(f'Iterations done = {self.iters_done} / {mi}') + if self.iters is not None: + if self.iters_done >= (self.iters): + self.stop_global = True + + if self.maxiter is not None: # Stop for infeasible sampling + if self.iters_done >= (self.maxiter): + self.stop_global = True + return self.stop_global + + def finite_fev(self): + # Finite function evals in the feasible domain + if self.disp: + logging.info(f'Function evaluations done = {self.fn} / {self.maxfev}') + if self.fn >= self.maxfev: + self.stop_global = True + return self.stop_global + + def finite_ev(self): + # Finite evaluations including infeasible sampling points + if self.disp: + logging.info(f'Sampling evaluations done = {self.n_sampled} ' + f'/ {self.maxev}') + if self.n_sampled >= self.maxev: + self.stop_global = True + + def finite_time(self): + if self.disp: + logging.info(f'Time elapsed = {time.time() - self.init} ' + f'/ {self.maxtime}') + if (time.time() - self.init) >= self.maxtime: + self.stop_global = True + + def finite_precision(self): + """ + Stop the algorithm if the final function value is known + + Specify in options (with ``self.f_min_true = options['f_min']``) + and the tolerance with ``f_tol = options['f_tol']`` + """ + # If no minimizer has been found use the lowest sampling value + self.find_lowest_vertex() + if self.disp: + logging.info(f'Lowest function evaluation = {self.f_lowest}') + logging.info(f'Specified minimum = {self.f_min_true}') + # If no feasible point was return from test + if self.f_lowest is None: + return self.stop_global + + # Function to stop algorithm at specified percentage error: + if self.f_min_true == 0.0: + if self.f_lowest <= self.f_tol: + self.stop_global = True + else: + pe = (self.f_lowest - self.f_min_true) / abs(self.f_min_true) + if self.f_lowest <= self.f_min_true: + self.stop_global = True + # 2if (pe - self.f_tol) <= abs(1.0 / abs(self.f_min_true)): + if abs(pe) >= 2 * self.f_tol: + warnings.warn( + f"A much lower value than expected f* = {self.f_min_true} " + f"was found f_lowest = {self.f_lowest}", + stacklevel=3 + ) + if pe <= self.f_tol: + self.stop_global = True + + return self.stop_global + + def finite_homology_growth(self): + """ + Stop the algorithm if homology group rank did not grow in iteration. + """ + if self.LMC.size == 0: + return # pass on no reason to stop yet. + self.hgrd = self.LMC.size - self.hgr + + self.hgr = self.LMC.size + if self.hgrd <= self.minhgrd: + self.stop_global = True + if self.disp: + logging.info(f'Current homology growth = {self.hgrd} ' + f' (minimum growth = {self.minhgrd})') + return self.stop_global + + def stopping_criteria(self): + """ + Various stopping criteria ran every iteration + + Returns + ------- + stop : bool + """ + if self.maxiter is not None: + self.finite_iterations() + if self.iters is not None: + self.finite_iterations() + if self.maxfev is not None: + self.finite_fev() + if self.maxev is not None: + self.finite_ev() + if self.maxtime is not None: + self.finite_time() + if self.f_min_true is not None: + self.finite_precision() + if self.minhgrd is not None: + self.finite_homology_growth() + return self.stop_global + + def iterate(self): + self.iterate_complex() + + # Build minimizer pool + if self.minimize_every_iter: + if not self.break_routine: + self.find_minima() # Process minimizer pool + + # Algorithm updates + self.iters_done += 1 + + def iterate_hypercube(self): + """ + Iterate a subdivision of the complex + + Note: called with ``self.iterate_complex()`` after class initiation + """ + # Iterate the complex + if self.disp: + logging.info('Constructing and refining simplicial complex graph ' + 'structure') + if self.n is None: + self.HC.refine_all() + self.n_sampled = self.HC.V.size() # nevs counted + else: + self.HC.refine(self.n) + self.n_sampled += self.n + + if self.disp: + logging.info('Triangulation completed, evaluating all constraints ' + 'and objective function values.') + + # Re-add minimisers to complex + if len(self.LMC.xl_maps) > 0: + for xl in self.LMC.cache: + v = self.HC.V[xl] + v_near = v.star() + for v in v.nn: + v_near = v_near.union(v.nn) + # Reconnect vertices to complex + # if self.HC.connect_vertex_non_symm(tuple(self.LMC[xl].x_l), + # near=v_near): + # continue + # else: + # If failure to find in v_near, then search all vertices + # (very expensive operation: + # self.HC.connect_vertex_non_symm(tuple(self.LMC[xl].x_l) + # ) + + # Evaluate all constraints and functions + self.HC.V.process_pools() + if self.disp: + logging.info('Evaluations completed.') + + # feasible sampling points counted by the triangulation.py routines + self.fn = self.HC.V.nfev + return + + def iterate_delaunay(self): + """ + Build a complex of Delaunay triangulated points + + Note: called with ``self.iterate_complex()`` after class initiation + """ + self.nc += self.n + self.sampled_surface(infty_cons_sampl=self.infty_cons_sampl) + + # Add sampled points to a triangulation, construct self.Tri + if self.disp: + logging.info(f'self.n = {self.n}') + logging.info(f'self.nc = {self.nc}') + logging.info('Constructing and refining simplicial complex graph ' + 'structure from sampling points.') + + if self.dim < 2: + self.Ind_sorted = np.argsort(self.C, axis=0) + self.Ind_sorted = self.Ind_sorted.flatten() + tris = [] + for ind, ind_s in enumerate(self.Ind_sorted): + if ind > 0: + tris.append(self.Ind_sorted[ind - 1:ind + 1]) + + tris = np.array(tris) + # Store 1D triangulation: + self.Tri = namedtuple('Tri', ['points', 'simplices'])(self.C, tris) + self.points = {} + else: + if self.C.shape[0] > self.dim + 1: # Ensure a simplex can be built + self.delaunay_triangulation(n_prc=self.n_prc) + self.n_prc = self.C.shape[0] + + if self.disp: + logging.info('Triangulation completed, evaluating all ' + 'constraints and objective function values.') + + if hasattr(self, 'Tri'): + self.HC.vf_to_vv(self.Tri.points, self.Tri.simplices) + + # Process all pools + # Evaluate all constraints and functions + if self.disp: + logging.info('Triangulation completed, evaluating all constraints ' + 'and objective function values.') + + # Evaluate all constraints and functions + self.HC.V.process_pools() + if self.disp: + logging.info('Evaluations completed.') + + # feasible sampling points counted by the triangulation.py routines + self.fn = self.HC.V.nfev + self.n_sampled = self.nc # nevs counted in triangulation + return + + # Hypercube minimizers + def minimizers(self): + """ + Returns the indexes of all minimizers + """ + self.minimizer_pool = [] + # Note: Can implement parallelization here + for x in self.HC.V.cache: + in_LMC = False + if len(self.LMC.xl_maps) > 0: + for xlmi in self.LMC.xl_maps: + if np.all(np.array(x) == np.array(xlmi)): + in_LMC = True + if in_LMC: + continue + + if self.HC.V[x].minimiser(): + if self.disp: + logging.info('=' * 60) + logging.info(f'v.x = {self.HC.V[x].x_a} is minimizer') + logging.info(f'v.f = {self.HC.V[x].f} is minimizer') + logging.info('=' * 30) + + if self.HC.V[x] not in self.minimizer_pool: + self.minimizer_pool.append(self.HC.V[x]) + + if self.disp: + logging.info('Neighbors:') + logging.info('=' * 30) + for vn in self.HC.V[x].nn: + logging.info(f'x = {vn.x} || f = {vn.f}') + + logging.info('=' * 60) + self.minimizer_pool_F = [] + self.X_min = [] + # normalized tuple in the Vertex cache + self.X_min_cache = {} # Cache used in hypercube sampling + + for v in self.minimizer_pool: + self.X_min.append(v.x_a) + self.minimizer_pool_F.append(v.f) + self.X_min_cache[tuple(v.x_a)] = v.x + + self.minimizer_pool_F = np.array(self.minimizer_pool_F) + self.X_min = np.array(self.X_min) + + # TODO: Only do this if global mode + self.sort_min_pool() + + return self.X_min + + # Local minimisation + # Minimiser pool processing + def minimise_pool(self, force_iter=False): + """ + This processing method can optionally minimise only the best candidate + solutions in the minimiser pool + + Parameters + ---------- + force_iter : int + Number of starting minimizers to process (can be specified + globally or locally) + + """ + # Find first local minimum + # NOTE: Since we always minimize this value regardless it is a waste to + # build the topograph first before minimizing + lres_f_min = self.minimize(self.X_min[0], ind=self.minimizer_pool[0]) + + # Trim minimized point from current minimizer set + self.trim_min_pool(0) + + while not self.stop_l_iter: + # Global stopping criteria: + self.stopping_criteria() + + # Note first iteration is outside loop: + if force_iter: + force_iter -= 1 + if force_iter == 0: + self.stop_l_iter = True + break + + if np.shape(self.X_min)[0] == 0: + self.stop_l_iter = True + break + + # Construct topograph from current minimizer set + # (NOTE: This is a very small topograph using only the minizer pool + # , it might be worth using some graph theory tools instead. + self.g_topograph(lres_f_min.x, self.X_min) + + # Find local minimum at the miniser with the greatest Euclidean + # distance from the current solution + ind_xmin_l = self.Z[:, -1] + lres_f_min = self.minimize(self.Ss[-1, :], self.minimizer_pool[-1]) + + # Trim minimised point from current minimizer set + self.trim_min_pool(ind_xmin_l) + + # Reset controls + self.stop_l_iter = False + return + + def sort_min_pool(self): + # Sort to find minimum func value in min_pool + self.ind_f_min = np.argsort(self.minimizer_pool_F) + self.minimizer_pool = np.array(self.minimizer_pool)[self.ind_f_min] + self.minimizer_pool_F = np.array(self.minimizer_pool_F)[ + self.ind_f_min] + return + + def trim_min_pool(self, trim_ind): + self.X_min = np.delete(self.X_min, trim_ind, axis=0) + self.minimizer_pool_F = np.delete(self.minimizer_pool_F, trim_ind) + self.minimizer_pool = np.delete(self.minimizer_pool, trim_ind) + return + + def g_topograph(self, x_min, X_min): + """ + Returns the topographical vector stemming from the specified value + ``x_min`` for the current feasible set ``X_min`` with True boolean + values indicating positive entries and False values indicating + negative entries. + + """ + x_min = np.array([x_min]) + self.Y = spatial.distance.cdist(x_min, X_min, 'euclidean') + # Find sorted indexes of spatial distances: + self.Z = np.argsort(self.Y, axis=-1) + + self.Ss = X_min[self.Z][0] + self.minimizer_pool = self.minimizer_pool[self.Z] + self.minimizer_pool = self.minimizer_pool[0] + return self.Ss + + # Local bound functions + def construct_lcb_simplicial(self, v_min): + """ + Construct locally (approximately) convex bounds + + Parameters + ---------- + v_min : Vertex object + The minimizer vertex + + Returns + ------- + cbounds : list of lists + List of size dimension with length-2 list of bounds for each + dimension. + + """ + cbounds = [[x_b_i[0], x_b_i[1]] for x_b_i in self.bounds] + # Loop over all bounds + for vn in v_min.nn: + for i, x_i in enumerate(vn.x_a): + # Lower bound + if (x_i < v_min.x_a[i]) and (x_i > cbounds[i][0]): + cbounds[i][0] = x_i + + # Upper bound + if (x_i > v_min.x_a[i]) and (x_i < cbounds[i][1]): + cbounds[i][1] = x_i + + if self.disp: + logging.info(f'cbounds found for v_min.x_a = {v_min.x_a}') + logging.info(f'cbounds = {cbounds}') + + return cbounds + + def construct_lcb_delaunay(self, v_min, ind=None): + """ + Construct locally (approximately) convex bounds + + Parameters + ---------- + v_min : Vertex object + The minimizer vertex + + Returns + ------- + cbounds : list of lists + List of size dimension with length-2 list of bounds for each + dimension. + """ + cbounds = [[x_b_i[0], x_b_i[1]] for x_b_i in self.bounds] + + return cbounds + + # Minimize a starting point locally + def minimize(self, x_min, ind=None): + """ + This function is used to calculate the local minima using the specified + sampling point as a starting value. + + Parameters + ---------- + x_min : vector of floats + Current starting point to minimize. + + Returns + ------- + lres : OptimizeResult + The local optimization result represented as a `OptimizeResult` + object. + """ + # Use minima maps if vertex was already run + if self.disp: + logging.info(f'Vertex minimiser maps = {self.LMC.v_maps}') + + if self.LMC[x_min].lres is not None: + logging.info(f'Found self.LMC[x_min].lres = ' + f'{self.LMC[x_min].lres}') + return self.LMC[x_min].lres + + if self.callback is not None: + logging.info(f'Callback for minimizer starting at {x_min}:') + + if self.disp: + logging.info(f'Starting minimization at {x_min}...') + + if self.sampling_method == 'simplicial': + x_min_t = tuple(x_min) + # Find the normalized tuple in the Vertex cache: + x_min_t_norm = self.X_min_cache[tuple(x_min_t)] + x_min_t_norm = tuple(x_min_t_norm) + g_bounds = self.construct_lcb_simplicial(self.HC.V[x_min_t_norm]) + if 'bounds' in self.min_solver_args: + self.minimizer_kwargs['bounds'] = g_bounds + logging.info(self.minimizer_kwargs['bounds']) + + else: + g_bounds = self.construct_lcb_delaunay(x_min, ind=ind) + if 'bounds' in self.min_solver_args: + self.minimizer_kwargs['bounds'] = g_bounds + logging.info(self.minimizer_kwargs['bounds']) + + if self.disp and 'bounds' in self.minimizer_kwargs: + logging.info('bounds in kwarg:') + logging.info(self.minimizer_kwargs['bounds']) + + # Local minimization using scipy.optimize.minimize: + lres = minimize(self.func, x_min, **self.minimizer_kwargs) + + if self.disp: + logging.info(f'lres = {lres}') + + # Local function evals for all minimizers + self.res.nlfev += lres.nfev + if 'njev' in lres: + self.res.nljev += lres.njev + if 'nhev' in lres: + self.res.nlhev += lres.nhev + + try: # Needed because of the brain dead 1x1 NumPy arrays + lres.fun = lres.fun[0] + except (IndexError, TypeError): + lres.fun + + # Append minima maps + self.LMC[x_min] + self.LMC.add_res(x_min, lres, bounds=g_bounds) + + return lres + + # Post local minimization processing + def sort_result(self): + """ + Sort results and build the global return object + """ + # Sort results in local minima cache + results = self.LMC.sort_cache_result() + self.res.xl = results['xl'] + self.res.funl = results['funl'] + self.res.x = results['x'] + self.res.fun = results['fun'] + + # Add local func evals to sampling func evals + # Count the number of feasible vertices and add to local func evals: + self.res.nfev = self.fn + self.res.nlfev + return self.res + + # Algorithm controls + def fail_routine(self, mes=("Failed to converge")): + self.break_routine = True + self.res.success = False + self.X_min = [None] + self.res.message = mes + + def sampled_surface(self, infty_cons_sampl=False): + """ + Sample the function surface. + + There are 2 modes, if ``infty_cons_sampl`` is True then the sampled + points that are generated outside the feasible domain will be + assigned an ``inf`` value in accordance with SHGO rules. + This guarantees convergence and usually requires less objective + function evaluations at the computational costs of more Delaunay + triangulation points. + + If ``infty_cons_sampl`` is False, then the infeasible points are + discarded and only a subspace of the sampled points are used. This + comes at the cost of the loss of guaranteed convergence and usually + requires more objective function evaluations. + """ + # Generate sampling points + if self.disp: + logging.info('Generating sampling points') + self.sampling(self.nc, self.dim) + if len(self.LMC.xl_maps) > 0: + self.C = np.vstack((self.C, np.array(self.LMC.xl_maps))) + if not infty_cons_sampl: + # Find subspace of feasible points + if self.g_cons is not None: + self.sampling_subspace() + + # Sort remaining samples + self.sorted_samples() + + # Find objective function references + self.n_sampled = self.nc + + def sampling_custom(self, n, dim): + """ + Generates uniform sampling points in a hypercube and scales the points + to the bound limits. + """ + # Generate sampling points. + # Generate uniform sample points in [0, 1]^m \subset R^m + if self.n_sampled == 0: + self.C = self.sampling_function(n, dim) + else: + self.C = self.sampling_function(n, dim) + # Distribute over bounds + for i in range(len(self.bounds)): + self.C[:, i] = (self.C[:, i] * + (self.bounds[i][1] - self.bounds[i][0]) + + self.bounds[i][0]) + return self.C + + def sampling_subspace(self): + """Find subspace of feasible points from g_func definition""" + # Subspace of feasible points. + for ind, g in enumerate(self.g_cons): + # C.shape = (Z, dim) where Z is the number of sampling points to + # evaluate and dim is the dimensionality of the problem. + # the constraint function may not be vectorised so have to step + # through each sampling point sequentially. + feasible = np.array( + [np.all(g(x_C, *self.g_args[ind]) >= 0.0) for x_C in self.C], + dtype=bool + ) + self.C = self.C[feasible] + + if self.C.size == 0: + self.res.message = ('No sampling point found within the ' + + 'feasible set. Increasing sampling ' + + 'size.') + # sampling correctly for both 1-D and >1-D cases + if self.disp: + logging.info(self.res.message) + + def sorted_samples(self): # Validated + """Find indexes of the sorted sampling points""" + self.Ind_sorted = np.argsort(self.C, axis=0) + self.Xs = self.C[self.Ind_sorted] + return self.Ind_sorted, self.Xs + + def delaunay_triangulation(self, n_prc=0): + if hasattr(self, 'Tri') and self.qhull_incremental: + # TODO: Uncertain if n_prc needs to add len(self.LMC.xl_maps) + # in self.sampled_surface + self.Tri.add_points(self.C[n_prc:, :]) + else: + try: + self.Tri = spatial.Delaunay(self.C, + incremental=self.qhull_incremental, + ) + except spatial.QhullError: + if str(sys.exc_info()[1])[:6] == 'QH6239': + logging.warning('QH6239 Qhull precision error detected, ' + 'this usually occurs when no bounds are ' + 'specified, Qhull can only run with ' + 'handling cocircular/cospherical points' + ' and in this case incremental mode is ' + 'switched off. The performance of shgo ' + 'will be reduced in this mode.') + self.qhull_incremental = False + self.Tri = spatial.Delaunay(self.C, + incremental= + self.qhull_incremental) + else: + raise + + return self.Tri + + +class LMap: + def __init__(self, v): + self.v = v + self.x_l = None + self.lres = None + self.f_min = None + self.lbounds = [] + + +class LMapCache: + def __init__(self): + self.cache = {} + + # Lists for search queries + self.v_maps = [] + self.xl_maps = [] + self.xl_maps_set = set() + self.f_maps = [] + self.lbound_maps = [] + self.size = 0 + + def __getitem__(self, v): + try: + v = np.ndarray.tolist(v) + except TypeError: + pass + v = tuple(v) + try: + return self.cache[v] + except KeyError: + xval = LMap(v) + self.cache[v] = xval + + return self.cache[v] + + def add_res(self, v, lres, bounds=None): + v = np.ndarray.tolist(v) + v = tuple(v) + self.cache[v].x_l = lres.x + self.cache[v].lres = lres + self.cache[v].f_min = lres.fun + self.cache[v].lbounds = bounds + + # Update cache size + self.size += 1 + + # Cache lists for search queries + self.v_maps.append(v) + self.xl_maps.append(lres.x) + self.xl_maps_set.add(tuple(lres.x)) + self.f_maps.append(lres.fun) + self.lbound_maps.append(bounds) + + def sort_cache_result(self): + """ + Sort results and build the global return object + """ + results = {} + # Sort results and save + self.xl_maps = np.array(self.xl_maps) + self.f_maps = np.array(self.f_maps) + + # Sorted indexes in Func_min + ind_sorted = np.argsort(self.f_maps) + + # Save ordered list of minima + results['xl'] = self.xl_maps[ind_sorted] # Ordered x vals + self.f_maps = np.array(self.f_maps) + results['funl'] = self.f_maps[ind_sorted] + results['funl'] = results['funl'].T + + # Find global of all minimizers + results['x'] = self.xl_maps[ind_sorted[0]] # Save global minima + results['fun'] = self.f_maps[ind_sorted[0]] # Save global fun value + + self.xl_maps = np.ndarray.tolist(self.xl_maps) + self.f_maps = np.ndarray.tolist(self.f_maps) + return results diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..4ce2e585afa3c7b8ad9e88af2ad2a5dcd73d11fc Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp_py.py new file mode 100644 index 0000000000000000000000000000000000000000..b6b78aafdd2c13ac58b392e8c520f6caaa730d3f --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_slsqp_py.py @@ -0,0 +1,510 @@ +""" +This module implements the Sequential Least Squares Programming optimization +algorithm (SLSQP), originally developed by Dieter Kraft. +See http://www.netlib.org/toms/733 + +Functions +--------- +.. autosummary:: + :toctree: generated/ + + approx_jacobian + fmin_slsqp + +""" + +__all__ = ['approx_jacobian', 'fmin_slsqp'] + +import numpy as np +from scipy.optimize._slsqp import slsqp +from numpy import (zeros, array, linalg, append, concatenate, finfo, + sqrt, vstack, isfinite, atleast_1d) +from ._optimize import (OptimizeResult, _check_unknown_options, + _prepare_scalar_function, _clip_x_for_func, + _check_clip_x) +from ._numdiff import approx_derivative +from ._constraints import old_bound_to_new, _arr_to_scalar +from scipy._lib._array_api import atleast_nd, array_namespace + + +__docformat__ = "restructuredtext en" + +_epsilon = sqrt(finfo(float).eps) + + +def approx_jacobian(x, func, epsilon, *args): + """ + Approximate the Jacobian matrix of a callable function. + + Parameters + ---------- + x : array_like + The state vector at which to compute the Jacobian matrix. + func : callable f(x,*args) + The vector-valued function. + epsilon : float + The perturbation used to determine the partial derivatives. + args : sequence + Additional arguments passed to func. + + Returns + ------- + An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length + of the outputs of `func`, and ``lenx`` is the number of elements in + `x`. + + Notes + ----- + The approximation is done using forward differences. + + """ + # approx_derivative returns (m, n) == (lenf, lenx) + jac = approx_derivative(func, x, method='2-point', abs_step=epsilon, + args=args) + # if func returns a scalar jac.shape will be (lenx,). Make sure + # it's at least a 2D array. + return np.atleast_2d(jac) + + +def fmin_slsqp(func, x0, eqcons=(), f_eqcons=None, ieqcons=(), f_ieqcons=None, + bounds=(), fprime=None, fprime_eqcons=None, + fprime_ieqcons=None, args=(), iter=100, acc=1.0E-6, + iprint=1, disp=None, full_output=0, epsilon=_epsilon, + callback=None): + """ + Minimize a function using Sequential Least Squares Programming + + Python interface function for the SLSQP Optimization subroutine + originally implemented by Dieter Kraft. + + Parameters + ---------- + func : callable f(x,*args) + Objective function. Must return a scalar. + x0 : 1-D ndarray of float + Initial guess for the independent variable(s). + eqcons : list, optional + A list of functions of length n such that + eqcons[j](x,*args) == 0.0 in a successfully optimized + problem. + f_eqcons : callable f(x,*args), optional + Returns a 1-D array in which each element must equal 0.0 in a + successfully optimized problem. If f_eqcons is specified, + eqcons is ignored. + ieqcons : list, optional + A list of functions of length n such that + ieqcons[j](x,*args) >= 0.0 in a successfully optimized + problem. + f_ieqcons : callable f(x,*args), optional + Returns a 1-D ndarray in which each element must be greater or + equal to 0.0 in a successfully optimized problem. If + f_ieqcons is specified, ieqcons is ignored. + bounds : list, optional + A list of tuples specifying the lower and upper bound + for each independent variable [(xl0, xu0),(xl1, xu1),...] + Infinite values will be interpreted as large floating values. + fprime : callable `f(x,*args)`, optional + A function that evaluates the partial derivatives of func. + fprime_eqcons : callable `f(x,*args)`, optional + A function of the form `f(x, *args)` that returns the m by n + array of equality constraint normals. If not provided, + the normals will be approximated. The array returned by + fprime_eqcons should be sized as ( len(eqcons), len(x0) ). + fprime_ieqcons : callable `f(x,*args)`, optional + A function of the form `f(x, *args)` that returns the m by n + array of inequality constraint normals. If not provided, + the normals will be approximated. The array returned by + fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ). + args : sequence, optional + Additional arguments passed to func and fprime. + iter : int, optional + The maximum number of iterations. + acc : float, optional + Requested accuracy. + iprint : int, optional + The verbosity of fmin_slsqp : + + * iprint <= 0 : Silent operation + * iprint == 1 : Print summary upon completion (default) + * iprint >= 2 : Print status of each iterate and summary + disp : int, optional + Overrides the iprint interface (preferred). + full_output : bool, optional + If False, return only the minimizer of func (default). + Otherwise, output final objective function and summary + information. + epsilon : float, optional + The step size for finite-difference derivative estimates. + callback : callable, optional + Called after each iteration, as ``callback(x)``, where ``x`` is the + current parameter vector. + + Returns + ------- + out : ndarray of float + The final minimizer of func. + fx : ndarray of float, if full_output is true + The final value of the objective function. + its : int, if full_output is true + The number of iterations. + imode : int, if full_output is true + The exit mode from the optimizer (see below). + smode : string, if full_output is true + Message describing the exit mode from the optimizer. + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'SLSQP' `method` in particular. + + Notes + ----- + Exit modes are defined as follows :: + + -1 : Gradient evaluation required (g & a) + 0 : Optimization terminated successfully + 1 : Function evaluation required (f & c) + 2 : More equality constraints than independent variables + 3 : More than 3*n iterations in LSQ subproblem + 4 : Inequality constraints incompatible + 5 : Singular matrix E in LSQ subproblem + 6 : Singular matrix C in LSQ subproblem + 7 : Rank-deficient equality constraint subproblem HFTI + 8 : Positive directional derivative for linesearch + 9 : Iteration limit reached + + Examples + -------- + Examples are given :ref:`in the tutorial `. + + """ + if disp is not None: + iprint = disp + + opts = {'maxiter': iter, + 'ftol': acc, + 'iprint': iprint, + 'disp': iprint != 0, + 'eps': epsilon, + 'callback': callback} + + # Build the constraints as a tuple of dictionaries + cons = () + # 1. constraints of the 1st kind (eqcons, ieqcons); no Jacobian; take + # the same extra arguments as the objective function. + cons += tuple({'type': 'eq', 'fun': c, 'args': args} for c in eqcons) + cons += tuple({'type': 'ineq', 'fun': c, 'args': args} for c in ieqcons) + # 2. constraints of the 2nd kind (f_eqcons, f_ieqcons) and their Jacobian + # (fprime_eqcons, fprime_ieqcons); also take the same extra arguments + # as the objective function. + if f_eqcons: + cons += ({'type': 'eq', 'fun': f_eqcons, 'jac': fprime_eqcons, + 'args': args}, ) + if f_ieqcons: + cons += ({'type': 'ineq', 'fun': f_ieqcons, 'jac': fprime_ieqcons, + 'args': args}, ) + + res = _minimize_slsqp(func, x0, args, jac=fprime, bounds=bounds, + constraints=cons, **opts) + if full_output: + return res['x'], res['fun'], res['nit'], res['status'], res['message'] + else: + return res['x'] + + +def _minimize_slsqp(func, x0, args=(), jac=None, bounds=None, + constraints=(), + maxiter=100, ftol=1.0E-6, iprint=1, disp=False, + eps=_epsilon, callback=None, finite_diff_rel_step=None, + **unknown_options): + """ + Minimize a scalar function of one or more variables using Sequential + Least Squares Programming (SLSQP). + + Options + ------- + ftol : float + Precision goal for the value of f in the stopping criterion. + eps : float + Step size used for numerical approximation of the Jacobian. + disp : bool + Set to True to print convergence messages. If False, + `verbosity` is ignored and set to 0. + maxiter : int + Maximum number of iterations. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of `jac`. The absolute step + size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, + possibly adjusted to fit into the bounds. For ``method='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + """ + _check_unknown_options(unknown_options) + iter = maxiter - 1 + acc = ftol + epsilon = eps + + if not disp: + iprint = 0 + + # Transform x0 into an array. + xp = array_namespace(x0) + x0 = atleast_nd(x0, ndim=1, xp=xp) + dtype = xp.float64 + if xp.isdtype(x0.dtype, "real floating"): + dtype = x0.dtype + x = xp.reshape(xp.astype(x0, dtype), -1) + + # SLSQP is sent 'old-style' bounds, 'new-style' bounds are required by + # ScalarFunction + if bounds is None or len(bounds) == 0: + new_bounds = (-np.inf, np.inf) + else: + new_bounds = old_bound_to_new(bounds) + + # clip the initial guess to bounds, otherwise ScalarFunction doesn't work + x = np.clip(x, new_bounds[0], new_bounds[1]) + + # Constraints are triaged per type into a dictionary of tuples + if isinstance(constraints, dict): + constraints = (constraints, ) + + cons = {'eq': (), 'ineq': ()} + for ic, con in enumerate(constraints): + # check type + try: + ctype = con['type'].lower() + except KeyError as e: + raise KeyError('Constraint %d has no type defined.' % ic) from e + except TypeError as e: + raise TypeError('Constraints must be defined using a ' + 'dictionary.') from e + except AttributeError as e: + raise TypeError("Constraint's type must be a string.") from e + else: + if ctype not in ['eq', 'ineq']: + raise ValueError("Unknown constraint type '%s'." % con['type']) + + # check function + if 'fun' not in con: + raise ValueError('Constraint %d has no function defined.' % ic) + + # check Jacobian + cjac = con.get('jac') + if cjac is None: + # approximate Jacobian function. The factory function is needed + # to keep a reference to `fun`, see gh-4240. + def cjac_factory(fun): + def cjac(x, *args): + x = _check_clip_x(x, new_bounds) + + if jac in ['2-point', '3-point', 'cs']: + return approx_derivative(fun, x, method=jac, args=args, + rel_step=finite_diff_rel_step, + bounds=new_bounds) + else: + return approx_derivative(fun, x, method='2-point', + abs_step=epsilon, args=args, + bounds=new_bounds) + + return cjac + cjac = cjac_factory(con['fun']) + + # update constraints' dictionary + cons[ctype] += ({'fun': con['fun'], + 'jac': cjac, + 'args': con.get('args', ())}, ) + + exit_modes = {-1: "Gradient evaluation required (g & a)", + 0: "Optimization terminated successfully", + 1: "Function evaluation required (f & c)", + 2: "More equality constraints than independent variables", + 3: "More than 3*n iterations in LSQ subproblem", + 4: "Inequality constraints incompatible", + 5: "Singular matrix E in LSQ subproblem", + 6: "Singular matrix C in LSQ subproblem", + 7: "Rank-deficient equality constraint subproblem HFTI", + 8: "Positive directional derivative for linesearch", + 9: "Iteration limit reached"} + + # Set the parameters that SLSQP will need + # meq, mieq: number of equality and inequality constraints + meq = sum(map(len, [atleast_1d(c['fun'](x, *c['args'])) + for c in cons['eq']])) + mieq = sum(map(len, [atleast_1d(c['fun'](x, *c['args'])) + for c in cons['ineq']])) + # m = The total number of constraints + m = meq + mieq + # la = The number of constraints, or 1 if there are no constraints + la = array([1, m]).max() + # n = The number of independent variables + n = len(x) + + # Define the workspaces for SLSQP + n1 = n + 1 + mineq = m - meq + n1 + n1 + len_w = (3*n1+m)*(n1+1)+(n1-meq+1)*(mineq+2) + 2*mineq+(n1+mineq)*(n1-meq) \ + + 2*meq + n1 + ((n+1)*n)//2 + 2*m + 3*n + 3*n1 + 1 + len_jw = mineq + w = zeros(len_w) + jw = zeros(len_jw) + + # Decompose bounds into xl and xu + if bounds is None or len(bounds) == 0: + xl = np.empty(n, dtype=float) + xu = np.empty(n, dtype=float) + xl.fill(np.nan) + xu.fill(np.nan) + else: + bnds = array([(_arr_to_scalar(l), _arr_to_scalar(u)) + for (l, u) in bounds], float) + if bnds.shape[0] != n: + raise IndexError('SLSQP Error: the length of bounds is not ' + 'compatible with that of x0.') + + with np.errstate(invalid='ignore'): + bnderr = bnds[:, 0] > bnds[:, 1] + + if bnderr.any(): + raise ValueError('SLSQP Error: lb > ub in bounds %s.' % + ', '.join(str(b) for b in bnderr)) + xl, xu = bnds[:, 0], bnds[:, 1] + + # Mark infinite bounds with nans; the Fortran code understands this + infbnd = ~isfinite(bnds) + xl[infbnd[:, 0]] = np.nan + xu[infbnd[:, 1]] = np.nan + + # ScalarFunction provides function and gradient evaluation + sf = _prepare_scalar_function(func, x, jac=jac, args=args, epsilon=eps, + finite_diff_rel_step=finite_diff_rel_step, + bounds=new_bounds) + # gh11403 SLSQP sometimes exceeds bounds by 1 or 2 ULP, make sure this + # doesn't get sent to the func/grad evaluator. + wrapped_fun = _clip_x_for_func(sf.fun, new_bounds) + wrapped_grad = _clip_x_for_func(sf.grad, new_bounds) + + # Initialize the iteration counter and the mode value + mode = array(0, int) + acc = array(acc, float) + majiter = array(iter, int) + majiter_prev = 0 + + # Initialize internal SLSQP state variables + alpha = array(0, float) + f0 = array(0, float) + gs = array(0, float) + h1 = array(0, float) + h2 = array(0, float) + h3 = array(0, float) + h4 = array(0, float) + t = array(0, float) + t0 = array(0, float) + tol = array(0, float) + iexact = array(0, int) + incons = array(0, int) + ireset = array(0, int) + itermx = array(0, int) + line = array(0, int) + n1 = array(0, int) + n2 = array(0, int) + n3 = array(0, int) + + # Print the header if iprint >= 2 + if iprint >= 2: + print("%5s %5s %16s %16s" % ("NIT", "FC", "OBJFUN", "GNORM")) + + # mode is zero on entry, so call objective, constraints and gradients + # there should be no func evaluations here because it's cached from + # ScalarFunction + fx = wrapped_fun(x) + g = append(wrapped_grad(x), 0.0) + c = _eval_constraint(x, cons) + a = _eval_con_normals(x, cons, la, n, m, meq, mieq) + + while 1: + # Call SLSQP + slsqp(m, meq, x, xl, xu, fx, c, g, a, acc, majiter, mode, w, jw, + alpha, f0, gs, h1, h2, h3, h4, t, t0, tol, + iexact, incons, ireset, itermx, line, + n1, n2, n3) + + if mode == 1: # objective and constraint evaluation required + fx = wrapped_fun(x) + c = _eval_constraint(x, cons) + + if mode == -1: # gradient evaluation required + g = append(wrapped_grad(x), 0.0) + a = _eval_con_normals(x, cons, la, n, m, meq, mieq) + + if majiter > majiter_prev: + # call callback if major iteration has incremented + if callback is not None: + callback(np.copy(x)) + + # Print the status of the current iterate if iprint > 2 + if iprint >= 2: + print("%5i %5i % 16.6E % 16.6E" % (majiter, sf.nfev, + fx, linalg.norm(g))) + + # If exit mode is not -1 or 1, slsqp has completed + if abs(mode) != 1: + break + + majiter_prev = int(majiter) + + # Optimization loop complete. Print status if requested + if iprint >= 1: + print(exit_modes[int(mode)] + " (Exit mode " + str(mode) + ')') + print(" Current function value:", fx) + print(" Iterations:", majiter) + print(" Function evaluations:", sf.nfev) + print(" Gradient evaluations:", sf.ngev) + + return OptimizeResult(x=x, fun=fx, jac=g[:-1], nit=int(majiter), + nfev=sf.nfev, njev=sf.ngev, status=int(mode), + message=exit_modes[int(mode)], success=(mode == 0)) + + +def _eval_constraint(x, cons): + # Compute constraints + if cons['eq']: + c_eq = concatenate([atleast_1d(con['fun'](x, *con['args'])) + for con in cons['eq']]) + else: + c_eq = zeros(0) + + if cons['ineq']: + c_ieq = concatenate([atleast_1d(con['fun'](x, *con['args'])) + for con in cons['ineq']]) + else: + c_ieq = zeros(0) + + # Now combine c_eq and c_ieq into a single matrix + c = concatenate((c_eq, c_ieq)) + return c + + +def _eval_con_normals(x, cons, la, n, m, meq, mieq): + # Compute the normals of the constraints + if cons['eq']: + a_eq = vstack([con['jac'](x, *con['args']) + for con in cons['eq']]) + else: # no equality constraint + a_eq = zeros((meq, n)) + + if cons['ineq']: + a_ieq = vstack([con['jac'](x, *con['args']) + for con in cons['ineq']]) + else: # no inequality constraint + a_ieq = zeros((mieq, n)) + + # Now combine a_eq and a_ieq into a single a matrix + if m == 0: # no constraints + a = zeros((la, n)) + else: + a = vstack((a_eq, a_ieq)) + a = concatenate((a, zeros([la, 1])), 1) + + return a diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_spectral.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_spectral.py new file mode 100644 index 0000000000000000000000000000000000000000..5ff5bef0283b2d6b6c018c1c8b98cd46a335d7cb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_spectral.py @@ -0,0 +1,260 @@ +""" +Spectral Algorithm for Nonlinear Equations +""" +import collections + +import numpy as np +from scipy.optimize import OptimizeResult +from scipy.optimize._optimize import _check_unknown_options +from ._linesearch import _nonmonotone_line_search_cruz, _nonmonotone_line_search_cheng + +class _NoConvergence(Exception): + pass + + +def _root_df_sane(func, x0, args=(), ftol=1e-8, fatol=1e-300, maxfev=1000, + fnorm=None, callback=None, disp=False, M=10, eta_strategy=None, + sigma_eps=1e-10, sigma_0=1.0, line_search='cruz', **unknown_options): + r""" + Solve nonlinear equation with the DF-SANE method + + Options + ------- + ftol : float, optional + Relative norm tolerance. + fatol : float, optional + Absolute norm tolerance. + Algorithm terminates when ``||func(x)|| < fatol + ftol ||func(x_0)||``. + fnorm : callable, optional + Norm to use in the convergence check. If None, 2-norm is used. + maxfev : int, optional + Maximum number of function evaluations. + disp : bool, optional + Whether to print convergence process to stdout. + eta_strategy : callable, optional + Choice of the ``eta_k`` parameter, which gives slack for growth + of ``||F||**2``. Called as ``eta_k = eta_strategy(k, x, F)`` with + `k` the iteration number, `x` the current iterate and `F` the current + residual. Should satisfy ``eta_k > 0`` and ``sum(eta, k=0..inf) < inf``. + Default: ``||F||**2 / (1 + k)**2``. + sigma_eps : float, optional + The spectral coefficient is constrained to ``sigma_eps < sigma < 1/sigma_eps``. + Default: 1e-10 + sigma_0 : float, optional + Initial spectral coefficient. + Default: 1.0 + M : int, optional + Number of iterates to include in the nonmonotonic line search. + Default: 10 + line_search : {'cruz', 'cheng'} + Type of line search to employ. 'cruz' is the original one defined in + [Martinez & Raydan. Math. Comp. 75, 1429 (2006)], 'cheng' is + a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)]. + Default: 'cruz' + + References + ---------- + .. [1] "Spectral residual method without gradient information for solving + large-scale nonlinear systems of equations." W. La Cruz, + J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006). + .. [2] W. La Cruz, Opt. Meth. Software, 29, 24 (2014). + .. [3] W. Cheng, D.-H. Li. IMA J. Numer. Anal. **29**, 814 (2009). + + """ + _check_unknown_options(unknown_options) + + if line_search not in ('cheng', 'cruz'): + raise ValueError(f"Invalid value {line_search!r} for 'line_search'") + + nexp = 2 + + if eta_strategy is None: + # Different choice from [1], as their eta is not invariant + # vs. scaling of F. + def eta_strategy(k, x, F): + # Obtain squared 2-norm of the initial residual from the outer scope + return f_0 / (1 + k)**2 + + if fnorm is None: + def fnorm(F): + # Obtain squared 2-norm of the current residual from the outer scope + return f_k**(1.0/nexp) + + def fmerit(F): + return np.linalg.norm(F)**nexp + + nfev = [0] + f, x_k, x_shape, f_k, F_k, is_complex = _wrap_func(func, x0, fmerit, + nfev, maxfev, args) + + k = 0 + f_0 = f_k + sigma_k = sigma_0 + + F_0_norm = fnorm(F_k) + + # For the 'cruz' line search + prev_fs = collections.deque([f_k], M) + + # For the 'cheng' line search + Q = 1.0 + C = f_0 + + converged = False + message = "too many function evaluations required" + + while True: + F_k_norm = fnorm(F_k) + + if disp: + print("iter %d: ||F|| = %g, sigma = %g" % (k, F_k_norm, sigma_k)) + + if callback is not None: + callback(x_k, F_k) + + if F_k_norm < ftol * F_0_norm + fatol: + # Converged! + message = "successful convergence" + converged = True + break + + # Control spectral parameter, from [2] + if abs(sigma_k) > 1/sigma_eps: + sigma_k = 1/sigma_eps * np.sign(sigma_k) + elif abs(sigma_k) < sigma_eps: + sigma_k = sigma_eps + + # Line search direction + d = -sigma_k * F_k + + # Nonmonotone line search + eta = eta_strategy(k, x_k, F_k) + try: + if line_search == 'cruz': + alpha, xp, fp, Fp = _nonmonotone_line_search_cruz(f, x_k, d, prev_fs, + eta=eta) + elif line_search == 'cheng': + alpha, xp, fp, Fp, C, Q = _nonmonotone_line_search_cheng(f, x_k, d, f_k, + C, Q, eta=eta) + except _NoConvergence: + break + + # Update spectral parameter + s_k = xp - x_k + y_k = Fp - F_k + sigma_k = np.vdot(s_k, s_k) / np.vdot(s_k, y_k) + + # Take step + x_k = xp + F_k = Fp + f_k = fp + + # Store function value + if line_search == 'cruz': + prev_fs.append(fp) + + k += 1 + + x = _wrap_result(x_k, is_complex, shape=x_shape) + F = _wrap_result(F_k, is_complex) + + result = OptimizeResult(x=x, success=converged, + message=message, + fun=F, nfev=nfev[0], nit=k, method="df-sane") + + return result + + +def _wrap_func(func, x0, fmerit, nfev_list, maxfev, args=()): + """ + Wrap a function and an initial value so that (i) complex values + are wrapped to reals, and (ii) value for a merit function + fmerit(x, f) is computed at the same time, (iii) iteration count + is maintained and an exception is raised if it is exceeded. + + Parameters + ---------- + func : callable + Function to wrap + x0 : ndarray + Initial value + fmerit : callable + Merit function fmerit(f) for computing merit value from residual. + nfev_list : list + List to store number of evaluations in. Should be [0] in the beginning. + maxfev : int + Maximum number of evaluations before _NoConvergence is raised. + args : tuple + Extra arguments to func + + Returns + ------- + wrap_func : callable + Wrapped function, to be called as + ``F, fp = wrap_func(x0)`` + x0_wrap : ndarray of float + Wrapped initial value; raveled to 1-D and complex + values mapped to reals. + x0_shape : tuple + Shape of the initial value array + f : float + Merit function at F + F : ndarray of float + Residual at x0_wrap + is_complex : bool + Whether complex values were mapped to reals + + """ + x0 = np.asarray(x0) + x0_shape = x0.shape + F = np.asarray(func(x0, *args)).ravel() + is_complex = np.iscomplexobj(x0) or np.iscomplexobj(F) + x0 = x0.ravel() + + nfev_list[0] = 1 + + if is_complex: + def wrap_func(x): + if nfev_list[0] >= maxfev: + raise _NoConvergence() + nfev_list[0] += 1 + z = _real2complex(x).reshape(x0_shape) + v = np.asarray(func(z, *args)).ravel() + F = _complex2real(v) + f = fmerit(F) + return f, F + + x0 = _complex2real(x0) + F = _complex2real(F) + else: + def wrap_func(x): + if nfev_list[0] >= maxfev: + raise _NoConvergence() + nfev_list[0] += 1 + x = x.reshape(x0_shape) + F = np.asarray(func(x, *args)).ravel() + f = fmerit(F) + return f, F + + return wrap_func, x0, x0_shape, fmerit(F), F, is_complex + + +def _wrap_result(result, is_complex, shape=None): + """ + Convert from real to complex and reshape result arrays. + """ + if is_complex: + z = _real2complex(result) + else: + z = result + if shape is not None: + z = z.reshape(shape) + return z + + +def _real2complex(x): + return np.ascontiguousarray(x, dtype=float).view(np.complex128) + + +def _complex2real(z): + return np.ascontiguousarray(z, dtype=complex).view(np.float64) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tnc.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tnc.py new file mode 100644 index 0000000000000000000000000000000000000000..0f0b3be740368eb759d608b541930dbb88ec042b --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tnc.py @@ -0,0 +1,430 @@ +# TNC Python interface +# @(#) $Jeannot: tnc.py,v 1.11 2005/01/28 18:27:31 js Exp $ + +# Copyright (c) 2004-2005, Jean-Sebastien Roy (js@jeannot.org) + +# Permission is hereby granted, free of charge, to any person obtaining a +# copy of this software and associated documentation files (the +# "Software"), to deal in the Software without restriction, including +# without limitation the rights to use, copy, modify, merge, publish, +# distribute, sublicense, and/or sell copies of the Software, and to +# permit persons to whom the Software is furnished to do so, subject to +# the following conditions: + +# The above copyright notice and this permission notice shall be included +# in all copies or substantial portions of the Software. + +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS +# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY +# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, +# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE +# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + +""" +TNC: A Python interface to the TNC non-linear optimizer + +TNC is a non-linear optimizer. To use it, you must provide a function to +minimize. The function must take one argument: the list of coordinates where to +evaluate the function; and it must return either a tuple, whose first element is the +value of the function, and whose second argument is the gradient of the function +(as a list of values); or None, to abort the minimization. +""" + +from scipy.optimize import _moduleTNC as moduleTNC +from ._optimize import (MemoizeJac, OptimizeResult, _check_unknown_options, + _prepare_scalar_function) +from ._constraints import old_bound_to_new +from scipy._lib._array_api import atleast_nd, array_namespace + +from numpy import inf, array, zeros + +__all__ = ['fmin_tnc'] + + +MSG_NONE = 0 # No messages +MSG_ITER = 1 # One line per iteration +MSG_INFO = 2 # Informational messages +MSG_VERS = 4 # Version info +MSG_EXIT = 8 # Exit reasons +MSG_ALL = MSG_ITER + MSG_INFO + MSG_VERS + MSG_EXIT + +MSGS = { + MSG_NONE: "No messages", + MSG_ITER: "One line per iteration", + MSG_INFO: "Informational messages", + MSG_VERS: "Version info", + MSG_EXIT: "Exit reasons", + MSG_ALL: "All messages" +} + +INFEASIBLE = -1 # Infeasible (lower bound > upper bound) +LOCALMINIMUM = 0 # Local minimum reached (|pg| ~= 0) +FCONVERGED = 1 # Converged (|f_n-f_(n-1)| ~= 0) +XCONVERGED = 2 # Converged (|x_n-x_(n-1)| ~= 0) +MAXFUN = 3 # Max. number of function evaluations reached +LSFAIL = 4 # Linear search failed +CONSTANT = 5 # All lower bounds are equal to the upper bounds +NOPROGRESS = 6 # Unable to progress +USERABORT = 7 # User requested end of minimization + +RCSTRINGS = { + INFEASIBLE: "Infeasible (lower bound > upper bound)", + LOCALMINIMUM: "Local minimum reached (|pg| ~= 0)", + FCONVERGED: "Converged (|f_n-f_(n-1)| ~= 0)", + XCONVERGED: "Converged (|x_n-x_(n-1)| ~= 0)", + MAXFUN: "Max. number of function evaluations reached", + LSFAIL: "Linear search failed", + CONSTANT: "All lower bounds are equal to the upper bounds", + NOPROGRESS: "Unable to progress", + USERABORT: "User requested end of minimization" +} + +# Changes to interface made by Travis Oliphant, Apr. 2004 for inclusion in +# SciPy + + +def fmin_tnc(func, x0, fprime=None, args=(), approx_grad=0, + bounds=None, epsilon=1e-8, scale=None, offset=None, + messages=MSG_ALL, maxCGit=-1, maxfun=None, eta=-1, + stepmx=0, accuracy=0, fmin=0, ftol=-1, xtol=-1, pgtol=-1, + rescale=-1, disp=None, callback=None): + """ + Minimize a function with variables subject to bounds, using + gradient information in a truncated Newton algorithm. This + method wraps a C implementation of the algorithm. + + Parameters + ---------- + func : callable ``func(x, *args)`` + Function to minimize. Must do one of: + + 1. Return f and g, where f is the value of the function and g its + gradient (a list of floats). + + 2. Return the function value but supply gradient function + separately as `fprime`. + + 3. Return the function value and set ``approx_grad=True``. + + If the function returns None, the minimization + is aborted. + x0 : array_like + Initial estimate of minimum. + fprime : callable ``fprime(x, *args)``, optional + Gradient of `func`. If None, then either `func` must return the + function value and the gradient (``f,g = func(x, *args)``) + or `approx_grad` must be True. + args : tuple, optional + Arguments to pass to function. + approx_grad : bool, optional + If true, approximate the gradient numerically. + bounds : list, optional + (min, max) pairs for each element in x0, defining the + bounds on that parameter. Use None or +/-inf for one of + min or max when there is no bound in that direction. + epsilon : float, optional + Used if approx_grad is True. The stepsize in a finite + difference approximation for fprime. + scale : array_like, optional + Scaling factors to apply to each variable. If None, the + factors are up-low for interval bounded variables and + 1+|x| for the others. Defaults to None. + offset : array_like, optional + Value to subtract from each variable. If None, the + offsets are (up+low)/2 for interval bounded variables + and x for the others. + messages : int, optional + Bit mask used to select messages display during + minimization values defined in the MSGS dict. Defaults to + MGS_ALL. + disp : int, optional + Integer interface to messages. 0 = no message, 5 = all messages + maxCGit : int, optional + Maximum number of hessian*vector evaluations per main + iteration. If maxCGit == 0, the direction chosen is + -gradient if maxCGit < 0, maxCGit is set to + max(1,min(50,n/2)). Defaults to -1. + maxfun : int, optional + Maximum number of function evaluation. If None, maxfun is + set to max(100, 10*len(x0)). Defaults to None. Note that this function + may violate the limit because of evaluating gradients by numerical + differentiation. + eta : float, optional + Severity of the line search. If < 0 or > 1, set to 0.25. + Defaults to -1. + stepmx : float, optional + Maximum step for the line search. May be increased during + call. If too small, it will be set to 10.0. Defaults to 0. + accuracy : float, optional + Relative precision for finite difference calculations. If + <= machine_precision, set to sqrt(machine_precision). + Defaults to 0. + fmin : float, optional + Minimum function value estimate. Defaults to 0. + ftol : float, optional + Precision goal for the value of f in the stopping criterion. + If ftol < 0.0, ftol is set to 0.0 defaults to -1. + xtol : float, optional + Precision goal for the value of x in the stopping + criterion (after applying x scaling factors). If xtol < + 0.0, xtol is set to sqrt(machine_precision). Defaults to + -1. + pgtol : float, optional + Precision goal for the value of the projected gradient in + the stopping criterion (after applying x scaling factors). + If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy). + Setting it to 0.0 is not recommended. Defaults to -1. + rescale : float, optional + Scaling factor (in log10) used to trigger f value + rescaling. If 0, rescale at each iteration. If a large + value, never rescale. If < 0, rescale is set to 1.3. + callback : callable, optional + Called after each iteration, as callback(xk), where xk is the + current parameter vector. + + Returns + ------- + x : ndarray + The solution. + nfeval : int + The number of function evaluations. + rc : int + Return code, see below + + See also + -------- + minimize: Interface to minimization algorithms for multivariate + functions. See the 'TNC' `method` in particular. + + Notes + ----- + The underlying algorithm is truncated Newton, also called + Newton Conjugate-Gradient. This method differs from + scipy.optimize.fmin_ncg in that + + 1. it wraps a C implementation of the algorithm + 2. it allows each variable to be given an upper and lower bound. + + The algorithm incorporates the bound constraints by determining + the descent direction as in an unconstrained truncated Newton, + but never taking a step-size large enough to leave the space + of feasible x's. The algorithm keeps track of a set of + currently active constraints, and ignores them when computing + the minimum allowable step size. (The x's associated with the + active constraint are kept fixed.) If the maximum allowable + step size is zero then a new constraint is added. At the end + of each iteration one of the constraints may be deemed no + longer active and removed. A constraint is considered + no longer active is if it is currently active + but the gradient for that variable points inward from the + constraint. The specific constraint removed is the one + associated with the variable of largest index whose + constraint is no longer active. + + Return codes are defined as follows:: + + -1 : Infeasible (lower bound > upper bound) + 0 : Local minimum reached (|pg| ~= 0) + 1 : Converged (|f_n-f_(n-1)| ~= 0) + 2 : Converged (|x_n-x_(n-1)| ~= 0) + 3 : Max. number of function evaluations reached + 4 : Linear search failed + 5 : All lower bounds are equal to the upper bounds + 6 : Unable to progress + 7 : User requested end of minimization + + References + ---------- + Wright S., Nocedal J. (2006), 'Numerical Optimization' + + Nash S.G. (1984), "Newton-Type Minimization Via the Lanczos Method", + SIAM Journal of Numerical Analysis 21, pp. 770-778 + + """ + # handle fprime/approx_grad + if approx_grad: + fun = func + jac = None + elif fprime is None: + fun = MemoizeJac(func) + jac = fun.derivative + else: + fun = func + jac = fprime + + if disp is not None: # disp takes precedence over messages + mesg_num = disp + else: + mesg_num = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS, + 4:MSG_EXIT, 5:MSG_ALL}.get(messages, MSG_ALL) + # build options + opts = {'eps': epsilon, + 'scale': scale, + 'offset': offset, + 'mesg_num': mesg_num, + 'maxCGit': maxCGit, + 'maxfun': maxfun, + 'eta': eta, + 'stepmx': stepmx, + 'accuracy': accuracy, + 'minfev': fmin, + 'ftol': ftol, + 'xtol': xtol, + 'gtol': pgtol, + 'rescale': rescale, + 'disp': False} + + res = _minimize_tnc(fun, x0, args, jac, bounds, callback=callback, **opts) + + return res['x'], res['nfev'], res['status'] + + +def _minimize_tnc(fun, x0, args=(), jac=None, bounds=None, + eps=1e-8, scale=None, offset=None, mesg_num=None, + maxCGit=-1, eta=-1, stepmx=0, accuracy=0, + minfev=0, ftol=-1, xtol=-1, gtol=-1, rescale=-1, disp=False, + callback=None, finite_diff_rel_step=None, maxfun=None, + **unknown_options): + """ + Minimize a scalar function of one or more variables using a truncated + Newton (TNC) algorithm. + + Options + ------- + eps : float or ndarray + If `jac is None` the absolute step size used for numerical + approximation of the jacobian via forward differences. + scale : list of floats + Scaling factors to apply to each variable. If None, the + factors are up-low for interval bounded variables and + 1+|x] for the others. Defaults to None. + offset : float + Value to subtract from each variable. If None, the + offsets are (up+low)/2 for interval bounded variables + and x for the others. + disp : bool + Set to True to print convergence messages. + maxCGit : int + Maximum number of hessian*vector evaluations per main + iteration. If maxCGit == 0, the direction chosen is + -gradient if maxCGit < 0, maxCGit is set to + max(1,min(50,n/2)). Defaults to -1. + eta : float + Severity of the line search. If < 0 or > 1, set to 0.25. + Defaults to -1. + stepmx : float + Maximum step for the line search. May be increased during + call. If too small, it will be set to 10.0. Defaults to 0. + accuracy : float + Relative precision for finite difference calculations. If + <= machine_precision, set to sqrt(machine_precision). + Defaults to 0. + minfev : float + Minimum function value estimate. Defaults to 0. + ftol : float + Precision goal for the value of f in the stopping criterion. + If ftol < 0.0, ftol is set to 0.0 defaults to -1. + xtol : float + Precision goal for the value of x in the stopping + criterion (after applying x scaling factors). If xtol < + 0.0, xtol is set to sqrt(machine_precision). Defaults to + -1. + gtol : float + Precision goal for the value of the projected gradient in + the stopping criterion (after applying x scaling factors). + If gtol < 0.0, gtol is set to 1e-2 * sqrt(accuracy). + Setting it to 0.0 is not recommended. Defaults to -1. + rescale : float + Scaling factor (in log10) used to trigger f value + rescaling. If 0, rescale at each iteration. If a large + value, never rescale. If < 0, rescale is set to 1.3. + finite_diff_rel_step : None or array_like, optional + If `jac in ['2-point', '3-point', 'cs']` the relative step size to + use for numerical approximation of the jacobian. The absolute step + size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``, + possibly adjusted to fit into the bounds. For ``method='3-point'`` + the sign of `h` is ignored. If None (default) then step is selected + automatically. + maxfun : int + Maximum number of function evaluations. If None, `maxfun` is + set to max(100, 10*len(x0)). Defaults to None. + """ + _check_unknown_options(unknown_options) + fmin = minfev + pgtol = gtol + + xp = array_namespace(x0) + x0 = atleast_nd(x0, ndim=1, xp=xp) + dtype = xp.float64 + if xp.isdtype(x0.dtype, "real floating"): + dtype = x0.dtype + x0 = xp.reshape(xp.astype(x0, dtype), -1) + + n = len(x0) + + if bounds is None: + bounds = [(None,None)] * n + if len(bounds) != n: + raise ValueError('length of x0 != length of bounds') + new_bounds = old_bound_to_new(bounds) + + if mesg_num is not None: + messages = {0:MSG_NONE, 1:MSG_ITER, 2:MSG_INFO, 3:MSG_VERS, + 4:MSG_EXIT, 5:MSG_ALL}.get(mesg_num, MSG_ALL) + elif disp: + messages = MSG_ALL + else: + messages = MSG_NONE + + sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, epsilon=eps, + finite_diff_rel_step=finite_diff_rel_step, + bounds=new_bounds) + func_and_grad = sf.fun_and_grad + + """ + low, up : the bounds (lists of floats) + if low is None, the lower bounds are removed. + if up is None, the upper bounds are removed. + low and up defaults to None + """ + low = zeros(n) + up = zeros(n) + for i in range(n): + if bounds[i] is None: + l, u = -inf, inf + else: + l,u = bounds[i] + if l is None: + low[i] = -inf + else: + low[i] = l + if u is None: + up[i] = inf + else: + up[i] = u + + if scale is None: + scale = array([]) + + if offset is None: + offset = array([]) + + if maxfun is None: + maxfun = max(100, 10*len(x0)) + + rc, nf, nit, x, funv, jacv = moduleTNC.tnc_minimize( + func_and_grad, x0, low, up, scale, + offset, messages, maxCGit, maxfun, + eta, stepmx, accuracy, fmin, ftol, + xtol, pgtol, rescale, callback + ) + # the TNC documentation states: "On output, x, f and g may be very + # slightly out of sync because of scaling". Therefore re-evaluate + # func_and_grad so they are synced. + funv, jacv = func_and_grad(x) + + return OptimizeResult(x=x, fun=funv, jac=jacv, nfev=sf.nfev, + nit=nit, status=rc, message=RCSTRINGS[rc], + success=(-1 < rc < 3)) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion.py new file mode 100644 index 0000000000000000000000000000000000000000..f2355cf68ac8e1cac7e2688a9b91364ff2b2dcee --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion.py @@ -0,0 +1,304 @@ +"""Trust-region optimization.""" +import math +import warnings + +import numpy as np +import scipy.linalg +from ._optimize import (_check_unknown_options, _status_message, + OptimizeResult, _prepare_scalar_function, + _call_callback_maybe_halt) +from scipy.optimize._hessian_update_strategy import HessianUpdateStrategy +from scipy.optimize._differentiable_functions import FD_METHODS +__all__ = [] + + +def _wrap_function(function, args): + # wraps a minimizer function to count number of evaluations + # and to easily provide an args kwd. + ncalls = [0] + if function is None: + return ncalls, None + + def function_wrapper(x, *wrapper_args): + ncalls[0] += 1 + # A copy of x is sent to the user function (gh13740) + return function(np.copy(x), *(wrapper_args + args)) + + return ncalls, function_wrapper + + +class BaseQuadraticSubproblem: + """ + Base/abstract class defining the quadratic model for trust-region + minimization. Child classes must implement the ``solve`` method. + + Values of the objective function, Jacobian and Hessian (if provided) at + the current iterate ``x`` are evaluated on demand and then stored as + attributes ``fun``, ``jac``, ``hess``. + """ + + def __init__(self, x, fun, jac, hess=None, hessp=None): + self._x = x + self._f = None + self._g = None + self._h = None + self._g_mag = None + self._cauchy_point = None + self._newton_point = None + self._fun = fun + self._jac = jac + self._hess = hess + self._hessp = hessp + + def __call__(self, p): + return self.fun + np.dot(self.jac, p) + 0.5 * np.dot(p, self.hessp(p)) + + @property + def fun(self): + """Value of objective function at current iteration.""" + if self._f is None: + self._f = self._fun(self._x) + return self._f + + @property + def jac(self): + """Value of Jacobian of objective function at current iteration.""" + if self._g is None: + self._g = self._jac(self._x) + return self._g + + @property + def hess(self): + """Value of Hessian of objective function at current iteration.""" + if self._h is None: + self._h = self._hess(self._x) + return self._h + + def hessp(self, p): + if self._hessp is not None: + return self._hessp(self._x, p) + else: + return np.dot(self.hess, p) + + @property + def jac_mag(self): + """Magnitude of jacobian of objective function at current iteration.""" + if self._g_mag is None: + self._g_mag = scipy.linalg.norm(self.jac) + return self._g_mag + + def get_boundaries_intersections(self, z, d, trust_radius): + """ + Solve the scalar quadratic equation ``||z + t d|| == trust_radius``. + This is like a line-sphere intersection. + Return the two values of t, sorted from low to high. + """ + a = np.dot(d, d) + b = 2 * np.dot(z, d) + c = np.dot(z, z) - trust_radius**2 + sqrt_discriminant = math.sqrt(b*b - 4*a*c) + + # The following calculation is mathematically + # equivalent to: + # ta = (-b - sqrt_discriminant) / (2*a) + # tb = (-b + sqrt_discriminant) / (2*a) + # but produce smaller round off errors. + # Look at Matrix Computation p.97 + # for a better justification. + aux = b + math.copysign(sqrt_discriminant, b) + ta = -aux / (2*a) + tb = -2*c / aux + return sorted([ta, tb]) + + def solve(self, trust_radius): + raise NotImplementedError('The solve method should be implemented by ' + 'the child class') + + +def _minimize_trust_region(fun, x0, args=(), jac=None, hess=None, hessp=None, + subproblem=None, initial_trust_radius=1.0, + max_trust_radius=1000.0, eta=0.15, gtol=1e-4, + maxiter=None, disp=False, return_all=False, + callback=None, inexact=True, **unknown_options): + """ + Minimization of scalar function of one or more variables using a + trust-region algorithm. + + Options for the trust-region algorithm are: + initial_trust_radius : float + Initial trust radius. + max_trust_radius : float + Never propose steps that are longer than this value. + eta : float + Trust region related acceptance stringency for proposed steps. + gtol : float + Gradient norm must be less than `gtol` + before successful termination. + maxiter : int + Maximum number of iterations to perform. + disp : bool + If True, print convergence message. + inexact : bool + Accuracy to solve subproblems. If True requires less nonlinear + iterations, but more vector products. Only effective for method + trust-krylov. + + This function is called by the `minimize` function. + It is not supposed to be called directly. + """ + _check_unknown_options(unknown_options) + + if jac is None: + raise ValueError('Jacobian is currently required for trust-region ' + 'methods') + if hess is None and hessp is None: + raise ValueError('Either the Hessian or the Hessian-vector product ' + 'is currently required for trust-region methods') + if subproblem is None: + raise ValueError('A subproblem solving strategy is required for ' + 'trust-region methods') + if not (0 <= eta < 0.25): + raise Exception('invalid acceptance stringency') + if max_trust_radius <= 0: + raise Exception('the max trust radius must be positive') + if initial_trust_radius <= 0: + raise ValueError('the initial trust radius must be positive') + if initial_trust_radius >= max_trust_radius: + raise ValueError('the initial trust radius must be less than the ' + 'max trust radius') + + # force the initial guess into a nice format + x0 = np.asarray(x0).flatten() + + # A ScalarFunction representing the problem. This caches calls to fun, jac, + # hess. + sf = _prepare_scalar_function(fun, x0, jac=jac, hess=hess, args=args) + fun = sf.fun + jac = sf.grad + if callable(hess): + hess = sf.hess + elif callable(hessp): + # this elif statement must come before examining whether hess + # is estimated by FD methods or a HessianUpdateStrategy + pass + elif (hess in FD_METHODS or isinstance(hess, HessianUpdateStrategy)): + # If the Hessian is being estimated by finite differences or a + # Hessian update strategy then ScalarFunction.hess returns a + # LinearOperator or a HessianUpdateStrategy. This enables the + # calculation/creation of a hessp. BUT you only want to do this + # if the user *hasn't* provided a callable(hessp) function. + hess = None + + def hessp(x, p, *args): + return sf.hess(x).dot(p) + else: + raise ValueError('Either the Hessian or the Hessian-vector product ' + 'is currently required for trust-region methods') + + # ScalarFunction doesn't represent hessp + nhessp, hessp = _wrap_function(hessp, args) + + # limit the number of iterations + if maxiter is None: + maxiter = len(x0)*200 + + # init the search status + warnflag = 0 + + # initialize the search + trust_radius = initial_trust_radius + x = x0 + if return_all: + allvecs = [x] + m = subproblem(x, fun, jac, hess, hessp) + k = 0 + + # search for the function min + # do not even start if the gradient is small enough + while m.jac_mag >= gtol: + + # Solve the sub-problem. + # This gives us the proposed step relative to the current position + # and it tells us whether the proposed step + # has reached the trust region boundary or not. + try: + p, hits_boundary = m.solve(trust_radius) + except np.linalg.LinAlgError: + warnflag = 3 + break + + # calculate the predicted value at the proposed point + predicted_value = m(p) + + # define the local approximation at the proposed point + x_proposed = x + p + m_proposed = subproblem(x_proposed, fun, jac, hess, hessp) + + # evaluate the ratio defined in equation (4.4) + actual_reduction = m.fun - m_proposed.fun + predicted_reduction = m.fun - predicted_value + if predicted_reduction <= 0: + warnflag = 2 + break + rho = actual_reduction / predicted_reduction + + # update the trust radius according to the actual/predicted ratio + if rho < 0.25: + trust_radius *= 0.25 + elif rho > 0.75 and hits_boundary: + trust_radius = min(2*trust_radius, max_trust_radius) + + # if the ratio is high enough then accept the proposed step + if rho > eta: + x = x_proposed + m = m_proposed + + # append the best guess, call back, increment the iteration count + if return_all: + allvecs.append(np.copy(x)) + k += 1 + + intermediate_result = OptimizeResult(x=x, fun=m.fun) + if _call_callback_maybe_halt(callback, intermediate_result): + break + + # check if the gradient is small enough to stop + if m.jac_mag < gtol: + warnflag = 0 + break + + # check if we have looked at enough iterations + if k >= maxiter: + warnflag = 1 + break + + # print some stuff if requested + status_messages = ( + _status_message['success'], + _status_message['maxiter'], + 'A bad approximation caused failure to predict improvement.', + 'A linalg error occurred, such as a non-psd Hessian.', + ) + if disp: + if warnflag == 0: + print(status_messages[warnflag]) + else: + warnings.warn(status_messages[warnflag], RuntimeWarning, stacklevel=3) + print(" Current function value: %f" % m.fun) + print(" Iterations: %d" % k) + print(" Function evaluations: %d" % sf.nfev) + print(" Gradient evaluations: %d" % sf.ngev) + print(" Hessian evaluations: %d" % (sf.nhev + nhessp[0])) + + result = OptimizeResult(x=x, success=(warnflag == 0), status=warnflag, + fun=m.fun, jac=m.jac, nfev=sf.nfev, njev=sf.ngev, + nhev=sf.nhev + nhessp[0], nit=k, + message=status_messages[warnflag]) + + if hess is not None: + result['hess'] = m.hess + + if return_all: + result['allvecs'] = allvecs + + return result diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_dogleg.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_dogleg.py new file mode 100644 index 0000000000000000000000000000000000000000..a54abd60c703408d6c87cb5020d6781fdf0213c7 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_dogleg.py @@ -0,0 +1,122 @@ +"""Dog-leg trust-region optimization.""" +import numpy as np +import scipy.linalg +from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem) + +__all__ = [] + + +def _minimize_dogleg(fun, x0, args=(), jac=None, hess=None, + **trust_region_options): + """ + Minimization of scalar function of one or more variables using + the dog-leg trust-region algorithm. + + Options + ------- + initial_trust_radius : float + Initial trust-region radius. + max_trust_radius : float + Maximum value of the trust-region radius. No steps that are longer + than this value will be proposed. + eta : float + Trust region related acceptance stringency for proposed steps. + gtol : float + Gradient norm must be less than `gtol` before successful + termination. + + """ + if jac is None: + raise ValueError('Jacobian is required for dogleg minimization') + if not callable(hess): + raise ValueError('Hessian is required for dogleg minimization') + return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess, + subproblem=DoglegSubproblem, + **trust_region_options) + + +class DoglegSubproblem(BaseQuadraticSubproblem): + """Quadratic subproblem solved by the dogleg method""" + + def cauchy_point(self): + """ + The Cauchy point is minimal along the direction of steepest descent. + """ + if self._cauchy_point is None: + g = self.jac + Bg = self.hessp(g) + self._cauchy_point = -(np.dot(g, g) / np.dot(g, Bg)) * g + return self._cauchy_point + + def newton_point(self): + """ + The Newton point is a global minimum of the approximate function. + """ + if self._newton_point is None: + g = self.jac + B = self.hess + cho_info = scipy.linalg.cho_factor(B) + self._newton_point = -scipy.linalg.cho_solve(cho_info, g) + return self._newton_point + + def solve(self, trust_radius): + """ + Minimize a function using the dog-leg trust-region algorithm. + + This algorithm requires function values and first and second derivatives. + It also performs a costly Hessian decomposition for most iterations, + and the Hessian is required to be positive definite. + + Parameters + ---------- + trust_radius : float + We are allowed to wander only this far away from the origin. + + Returns + ------- + p : ndarray + The proposed step. + hits_boundary : bool + True if the proposed step is on the boundary of the trust region. + + Notes + ----- + The Hessian is required to be positive definite. + + References + ---------- + .. [1] Jorge Nocedal and Stephen Wright, + Numerical Optimization, second edition, + Springer-Verlag, 2006, page 73. + """ + + # Compute the Newton point. + # This is the optimum for the quadratic model function. + # If it is inside the trust radius then return this point. + p_best = self.newton_point() + if scipy.linalg.norm(p_best) < trust_radius: + hits_boundary = False + return p_best, hits_boundary + + # Compute the Cauchy point. + # This is the predicted optimum along the direction of steepest descent. + p_u = self.cauchy_point() + + # If the Cauchy point is outside the trust region, + # then return the point where the path intersects the boundary. + p_u_norm = scipy.linalg.norm(p_u) + if p_u_norm >= trust_radius: + p_boundary = p_u * (trust_radius / p_u_norm) + hits_boundary = True + return p_boundary, hits_boundary + + # Compute the intersection of the trust region boundary + # and the line segment connecting the Cauchy and Newton points. + # This requires solving a quadratic equation. + # ||p_u + t*(p_best - p_u)||**2 == trust_radius**2 + # Solve this for positive time t using the quadratic formula. + _, tb = self.get_boundaries_intersections(p_u, p_best - p_u, + trust_radius) + p_boundary = p_u + tb * (p_best - p_u) + hits_boundary = True + return p_boundary, hits_boundary diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_exact.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_exact.py new file mode 100644 index 0000000000000000000000000000000000000000..21fc3d5609d2b41eb5b5ad840ef464522565054c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_exact.py @@ -0,0 +1,438 @@ +"""Nearly exact trust-region optimization subproblem.""" +import numpy as np +from scipy.linalg import (norm, get_lapack_funcs, solve_triangular, + cho_solve) +from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem) + +__all__ = ['_minimize_trustregion_exact', + 'estimate_smallest_singular_value', + 'singular_leading_submatrix', + 'IterativeSubproblem'] + + +def _minimize_trustregion_exact(fun, x0, args=(), jac=None, hess=None, + **trust_region_options): + """ + Minimization of scalar function of one or more variables using + a nearly exact trust-region algorithm. + + Options + ------- + initial_trust_radius : float + Initial trust-region radius. + max_trust_radius : float + Maximum value of the trust-region radius. No steps that are longer + than this value will be proposed. + eta : float + Trust region related acceptance stringency for proposed steps. + gtol : float + Gradient norm must be less than ``gtol`` before successful + termination. + """ + + if jac is None: + raise ValueError('Jacobian is required for trust region ' + 'exact minimization.') + if not callable(hess): + raise ValueError('Hessian matrix is required for trust region ' + 'exact minimization.') + return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess, + subproblem=IterativeSubproblem, + **trust_region_options) + + +def estimate_smallest_singular_value(U): + """Given upper triangular matrix ``U`` estimate the smallest singular + value and the correspondent right singular vector in O(n**2) operations. + + Parameters + ---------- + U : ndarray + Square upper triangular matrix. + + Returns + ------- + s_min : float + Estimated smallest singular value of the provided matrix. + z_min : ndarray + Estimatied right singular vector. + + Notes + ----- + The procedure is based on [1]_ and is done in two steps. First, it finds + a vector ``e`` with components selected from {+1, -1} such that the + solution ``w`` from the system ``U.T w = e`` is as large as possible. + Next it estimate ``U v = w``. The smallest singular value is close + to ``norm(w)/norm(v)`` and the right singular vector is close + to ``v/norm(v)``. + + The estimation will be better more ill-conditioned is the matrix. + + References + ---------- + .. [1] Cline, A. K., Moler, C. B., Stewart, G. W., Wilkinson, J. H. + An estimate for the condition number of a matrix. 1979. + SIAM Journal on Numerical Analysis, 16(2), 368-375. + """ + + U = np.atleast_2d(U) + m, n = U.shape + + if m != n: + raise ValueError("A square triangular matrix should be provided.") + + # A vector `e` with components selected from {+1, -1} + # is selected so that the solution `w` to the system + # `U.T w = e` is as large as possible. Implementation + # based on algorithm 3.5.1, p. 142, from reference [2] + # adapted for lower triangular matrix. + + p = np.zeros(n) + w = np.empty(n) + + # Implemented according to: Golub, G. H., Van Loan, C. F. (2013). + # "Matrix computations". Forth Edition. JHU press. pp. 140-142. + for k in range(n): + wp = (1-p[k]) / U.T[k, k] + wm = (-1-p[k]) / U.T[k, k] + pp = p[k+1:] + U.T[k+1:, k]*wp + pm = p[k+1:] + U.T[k+1:, k]*wm + + if abs(wp) + norm(pp, 1) >= abs(wm) + norm(pm, 1): + w[k] = wp + p[k+1:] = pp + else: + w[k] = wm + p[k+1:] = pm + + # The system `U v = w` is solved using backward substitution. + v = solve_triangular(U, w) + + v_norm = norm(v) + w_norm = norm(w) + + # Smallest singular value + s_min = w_norm / v_norm + + # Associated vector + z_min = v / v_norm + + return s_min, z_min + + +def gershgorin_bounds(H): + """ + Given a square matrix ``H`` compute upper + and lower bounds for its eigenvalues (Gregoshgorin Bounds). + Defined ref. [1]. + + References + ---------- + .. [1] Conn, A. R., Gould, N. I., & Toint, P. L. + Trust region methods. 2000. Siam. pp. 19. + """ + + H_diag = np.diag(H) + H_diag_abs = np.abs(H_diag) + H_row_sums = np.sum(np.abs(H), axis=1) + lb = np.min(H_diag + H_diag_abs - H_row_sums) + ub = np.max(H_diag - H_diag_abs + H_row_sums) + + return lb, ub + + +def singular_leading_submatrix(A, U, k): + """ + Compute term that makes the leading ``k`` by ``k`` + submatrix from ``A`` singular. + + Parameters + ---------- + A : ndarray + Symmetric matrix that is not positive definite. + U : ndarray + Upper triangular matrix resulting of an incomplete + Cholesky decomposition of matrix ``A``. + k : int + Positive integer such that the leading k by k submatrix from + `A` is the first non-positive definite leading submatrix. + + Returns + ------- + delta : float + Amount that should be added to the element (k, k) of the + leading k by k submatrix of ``A`` to make it singular. + v : ndarray + A vector such that ``v.T B v = 0``. Where B is the matrix A after + ``delta`` is added to its element (k, k). + """ + + # Compute delta + delta = np.sum(U[:k-1, k-1]**2) - A[k-1, k-1] + + n = len(A) + + # Inicialize v + v = np.zeros(n) + v[k-1] = 1 + + # Compute the remaining values of v by solving a triangular system. + if k != 1: + v[:k-1] = solve_triangular(U[:k-1, :k-1], -U[:k-1, k-1]) + + return delta, v + + +class IterativeSubproblem(BaseQuadraticSubproblem): + """Quadratic subproblem solved by nearly exact iterative method. + + Notes + ----- + This subproblem solver was based on [1]_, [2]_ and [3]_, + which implement similar algorithms. The algorithm is basically + that of [1]_ but ideas from [2]_ and [3]_ were also used. + + References + ---------- + .. [1] A.R. Conn, N.I. Gould, and P.L. Toint, "Trust region methods", + Siam, pp. 169-200, 2000. + .. [2] J. Nocedal and S. Wright, "Numerical optimization", + Springer Science & Business Media. pp. 83-91, 2006. + .. [3] J.J. More and D.C. Sorensen, "Computing a trust region step", + SIAM Journal on Scientific and Statistical Computing, vol. 4(3), + pp. 553-572, 1983. + """ + + # UPDATE_COEFF appears in reference [1]_ + # in formula 7.3.14 (p. 190) named as "theta". + # As recommended there it value is fixed in 0.01. + UPDATE_COEFF = 0.01 + + EPS = np.finfo(float).eps + + def __init__(self, x, fun, jac, hess, hessp=None, + k_easy=0.1, k_hard=0.2): + + super().__init__(x, fun, jac, hess) + + # When the trust-region shrinks in two consecutive + # calculations (``tr_radius < previous_tr_radius``) + # the lower bound ``lambda_lb`` may be reused, + # facilitating the convergence. To indicate no + # previous value is known at first ``previous_tr_radius`` + # is set to -1 and ``lambda_lb`` to None. + self.previous_tr_radius = -1 + self.lambda_lb = None + + self.niter = 0 + + # ``k_easy`` and ``k_hard`` are parameters used + # to determine the stop criteria to the iterative + # subproblem solver. Take a look at pp. 194-197 + # from reference _[1] for a more detailed description. + self.k_easy = k_easy + self.k_hard = k_hard + + # Get Lapack function for cholesky decomposition. + # The implemented SciPy wrapper does not return + # the incomplete factorization needed by the method. + self.cholesky, = get_lapack_funcs(('potrf',), (self.hess,)) + + # Get info about Hessian + self.dimension = len(self.hess) + self.hess_gershgorin_lb,\ + self.hess_gershgorin_ub = gershgorin_bounds(self.hess) + self.hess_inf = norm(self.hess, np.inf) + self.hess_fro = norm(self.hess, 'fro') + + # A constant such that for vectors smaller than that + # backward substituition is not reliable. It was stabilished + # based on Golub, G. H., Van Loan, C. F. (2013). + # "Matrix computations". Forth Edition. JHU press., p.165. + self.CLOSE_TO_ZERO = self.dimension * self.EPS * self.hess_inf + + def _initial_values(self, tr_radius): + """Given a trust radius, return a good initial guess for + the damping factor, the lower bound and the upper bound. + The values were chosen accordingly to the guidelines on + section 7.3.8 (p. 192) from [1]_. + """ + + # Upper bound for the damping factor + lambda_ub = max(0, self.jac_mag/tr_radius + min(-self.hess_gershgorin_lb, + self.hess_fro, + self.hess_inf)) + + # Lower bound for the damping factor + lambda_lb = max(0, -min(self.hess.diagonal()), + self.jac_mag/tr_radius - min(self.hess_gershgorin_ub, + self.hess_fro, + self.hess_inf)) + + # Improve bounds with previous info + if tr_radius < self.previous_tr_radius: + lambda_lb = max(self.lambda_lb, lambda_lb) + + # Initial guess for the damping factor + if lambda_lb == 0: + lambda_initial = 0 + else: + lambda_initial = max(np.sqrt(lambda_lb * lambda_ub), + lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb)) + + return lambda_initial, lambda_lb, lambda_ub + + def solve(self, tr_radius): + """Solve quadratic subproblem""" + + lambda_current, lambda_lb, lambda_ub = self._initial_values(tr_radius) + n = self.dimension + hits_boundary = True + already_factorized = False + self.niter = 0 + + while True: + + # Compute Cholesky factorization + if already_factorized: + already_factorized = False + else: + H = self.hess+lambda_current*np.eye(n) + U, info = self.cholesky(H, lower=False, + overwrite_a=False, + clean=True) + + self.niter += 1 + + # Check if factorization succeeded + if info == 0 and self.jac_mag > self.CLOSE_TO_ZERO: + # Successful factorization + + # Solve `U.T U p = s` + p = cho_solve((U, False), -self.jac) + + p_norm = norm(p) + + # Check for interior convergence + if p_norm <= tr_radius and lambda_current == 0: + hits_boundary = False + break + + # Solve `U.T w = p` + w = solve_triangular(U, p, trans='T') + + w_norm = norm(w) + + # Compute Newton step accordingly to + # formula (4.44) p.87 from ref [2]_. + delta_lambda = (p_norm/w_norm)**2 * (p_norm-tr_radius)/tr_radius + lambda_new = lambda_current + delta_lambda + + if p_norm < tr_radius: # Inside boundary + s_min, z_min = estimate_smallest_singular_value(U) + + ta, tb = self.get_boundaries_intersections(p, z_min, + tr_radius) + + # Choose `step_len` with the smallest magnitude. + # The reason for this choice is explained at + # ref [3]_, p. 6 (Immediately before the formula + # for `tau`). + step_len = min([ta, tb], key=abs) + + # Compute the quadratic term (p.T*H*p) + quadratic_term = np.dot(p, np.dot(H, p)) + + # Check stop criteria + relative_error = ((step_len**2 * s_min**2) + / (quadratic_term + lambda_current*tr_radius**2)) + if relative_error <= self.k_hard: + p += step_len * z_min + break + + # Update uncertanty bounds + lambda_ub = lambda_current + lambda_lb = max(lambda_lb, lambda_current - s_min**2) + + # Compute Cholesky factorization + H = self.hess + lambda_new*np.eye(n) + c, info = self.cholesky(H, lower=False, + overwrite_a=False, + clean=True) + + # Check if the factorization have succeeded + # + if info == 0: # Successful factorization + # Update damping factor + lambda_current = lambda_new + already_factorized = True + else: # Unsuccessful factorization + # Update uncertanty bounds + lambda_lb = max(lambda_lb, lambda_new) + + # Update damping factor + lambda_current = max( + np.sqrt(lambda_lb * lambda_ub), + lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb) + ) + + else: # Outside boundary + # Check stop criteria + relative_error = abs(p_norm - tr_radius) / tr_radius + if relative_error <= self.k_easy: + break + + # Update uncertanty bounds + lambda_lb = lambda_current + + # Update damping factor + lambda_current = lambda_new + + elif info == 0 and self.jac_mag <= self.CLOSE_TO_ZERO: + # jac_mag very close to zero + + # Check for interior convergence + if lambda_current == 0: + p = np.zeros(n) + hits_boundary = False + break + + s_min, z_min = estimate_smallest_singular_value(U) + step_len = tr_radius + + # Check stop criteria + if (step_len**2 * s_min**2 + <= self.k_hard * lambda_current * tr_radius**2): + p = step_len * z_min + break + + # Update uncertanty bounds + lambda_ub = lambda_current + lambda_lb = max(lambda_lb, lambda_current - s_min**2) + + # Update damping factor + lambda_current = max( + np.sqrt(lambda_lb * lambda_ub), + lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb) + ) + + else: # Unsuccessful factorization + + # Compute auxiliary terms + delta, v = singular_leading_submatrix(H, U, info) + v_norm = norm(v) + + # Update uncertanty interval + lambda_lb = max(lambda_lb, lambda_current + delta/v_norm**2) + + # Update damping factor + lambda_current = max( + np.sqrt(lambda_lb * lambda_ub), + lambda_lb + self.UPDATE_COEFF*(lambda_ub-lambda_lb) + ) + + self.lambda_lb = lambda_lb + self.lambda_current = lambda_current + self.previous_tr_radius = tr_radius + + return p, hits_boundary diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_krylov.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_krylov.py new file mode 100644 index 0000000000000000000000000000000000000000..54e861ae2de02164966a33c437e5fdb08ba3006c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_krylov.py @@ -0,0 +1,65 @@ +from ._trustregion import (_minimize_trust_region) +from ._trlib import (get_trlib_quadratic_subproblem) + +__all__ = ['_minimize_trust_krylov'] + +def _minimize_trust_krylov(fun, x0, args=(), jac=None, hess=None, hessp=None, + inexact=True, **trust_region_options): + """ + Minimization of a scalar function of one or more variables using + a nearly exact trust-region algorithm that only requires matrix + vector products with the hessian matrix. + + .. versionadded:: 1.0.0 + + Options + ------- + inexact : bool, optional + Accuracy to solve subproblems. If True requires less nonlinear + iterations, but more vector products. + """ + + if jac is None: + raise ValueError('Jacobian is required for trust region ', + 'exact minimization.') + if hess is None and hessp is None: + raise ValueError('Either the Hessian or the Hessian-vector product ' + 'is required for Krylov trust-region minimization') + + # tol_rel specifies the termination tolerance relative to the initial + # gradient norm in the Krylov subspace iteration. + + # - tol_rel_i specifies the tolerance for interior convergence. + # - tol_rel_b specifies the tolerance for boundary convergence. + # in nonlinear programming applications it is not necessary to solve + # the boundary case as exact as the interior case. + + # - setting tol_rel_i=-2 leads to a forcing sequence in the Krylov + # subspace iteration leading to quadratic convergence if eventually + # the trust region stays inactive. + # - setting tol_rel_b=-3 leads to a forcing sequence in the Krylov + # subspace iteration leading to superlinear convergence as long + # as the iterates hit the trust region boundary. + + # For details consult the documentation of trlib_krylov_min + # in _trlib/trlib_krylov.h + # + # Optimality of this choice of parameters among a range of possibilities + # has been tested on the unconstrained subset of the CUTEst library. + + if inexact: + return _minimize_trust_region(fun, x0, args=args, jac=jac, + hess=hess, hessp=hessp, + subproblem=get_trlib_quadratic_subproblem( + tol_rel_i=-2.0, tol_rel_b=-3.0, + disp=trust_region_options.get('disp', False) + ), + **trust_region_options) + else: + return _minimize_trust_region(fun, x0, args=args, jac=jac, + hess=hess, hessp=hessp, + subproblem=get_trlib_quadratic_subproblem( + tol_rel_i=1e-8, tol_rel_b=1e-6, + disp=trust_region_options.get('disp', False) + ), + **trust_region_options) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_ncg.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_ncg.py new file mode 100644 index 0000000000000000000000000000000000000000..fed17ff8b84eaf019c0ad69a03f260ca674477ad --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_trustregion_ncg.py @@ -0,0 +1,126 @@ +"""Newton-CG trust-region optimization.""" +import math + +import numpy as np +import scipy.linalg +from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem) + +__all__ = [] + + +def _minimize_trust_ncg(fun, x0, args=(), jac=None, hess=None, hessp=None, + **trust_region_options): + """ + Minimization of scalar function of one or more variables using + the Newton conjugate gradient trust-region algorithm. + + Options + ------- + initial_trust_radius : float + Initial trust-region radius. + max_trust_radius : float + Maximum value of the trust-region radius. No steps that are longer + than this value will be proposed. + eta : float + Trust region related acceptance stringency for proposed steps. + gtol : float + Gradient norm must be less than `gtol` before successful + termination. + + """ + if jac is None: + raise ValueError('Jacobian is required for Newton-CG trust-region ' + 'minimization') + if hess is None and hessp is None: + raise ValueError('Either the Hessian or the Hessian-vector product ' + 'is required for Newton-CG trust-region minimization') + return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess, + hessp=hessp, subproblem=CGSteihaugSubproblem, + **trust_region_options) + + +class CGSteihaugSubproblem(BaseQuadraticSubproblem): + """Quadratic subproblem solved by a conjugate gradient method""" + def solve(self, trust_radius): + """ + Solve the subproblem using a conjugate gradient method. + + Parameters + ---------- + trust_radius : float + We are allowed to wander only this far away from the origin. + + Returns + ------- + p : ndarray + The proposed step. + hits_boundary : bool + True if the proposed step is on the boundary of the trust region. + + Notes + ----- + This is algorithm (7.2) of Nocedal and Wright 2nd edition. + Only the function that computes the Hessian-vector product is required. + The Hessian itself is not required, and the Hessian does + not need to be positive semidefinite. + """ + + # get the norm of jacobian and define the origin + p_origin = np.zeros_like(self.jac) + + # define a default tolerance + tolerance = min(0.5, math.sqrt(self.jac_mag)) * self.jac_mag + + # Stop the method if the search direction + # is a direction of nonpositive curvature. + if self.jac_mag < tolerance: + hits_boundary = False + return p_origin, hits_boundary + + # init the state for the first iteration + z = p_origin + r = self.jac + d = -r + + # Search for the min of the approximation of the objective function. + while True: + + # do an iteration + Bd = self.hessp(d) + dBd = np.dot(d, Bd) + if dBd <= 0: + # Look at the two boundary points. + # Find both values of t to get the boundary points such that + # ||z + t d|| == trust_radius + # and then choose the one with the predicted min value. + ta, tb = self.get_boundaries_intersections(z, d, trust_radius) + pa = z + ta * d + pb = z + tb * d + if self(pa) < self(pb): + p_boundary = pa + else: + p_boundary = pb + hits_boundary = True + return p_boundary, hits_boundary + r_squared = np.dot(r, r) + alpha = r_squared / dBd + z_next = z + alpha * d + if scipy.linalg.norm(z_next) >= trust_radius: + # Find t >= 0 to get the boundary point such that + # ||z + t d|| == trust_radius + ta, tb = self.get_boundaries_intersections(z, d, trust_radius) + p_boundary = z + tb * d + hits_boundary = True + return p_boundary, hits_boundary + r_next = r + alpha * Bd + r_next_squared = np.dot(r_next, r_next) + if math.sqrt(r_next_squared) < tolerance: + hits_boundary = False + return z_next, hits_boundary + beta_next = r_next_squared / r_squared + d_next = -r_next + beta_next * d + + # update the state for the next iteration + z = z_next + r = r_next + d = d_next diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tstutils.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tstutils.py new file mode 100644 index 0000000000000000000000000000000000000000..f56e835e345d66023efae81114a45ed29269f18d --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_tstutils.py @@ -0,0 +1,972 @@ +r""" +Parameters used in test and benchmark methods. + +Collections of test cases suitable for testing 1-D root-finders + 'original': The original benchmarking functions. + Real-valued functions of real-valued inputs on an interval + with a zero. + f1, .., f3 are continuous and infinitely differentiable + f4 has a left- and right- discontinuity at the root + f5 has a root at 1 replacing a 1st order pole + f6 is randomly positive on one side of the root, + randomly negative on the other. + f4 - f6 are not continuous at the root. + + 'aps': The test problems in the 1995 paper + TOMS "Algorithm 748: Enclosing Zeros of Continuous Functions" + by Alefeld, Potra and Shi. Real-valued functions of + real-valued inputs on an interval with a zero. + Suitable for methods which start with an enclosing interval, and + derivatives up to 2nd order. + + 'complex': Some complex-valued functions of complex-valued inputs. + No enclosing bracket is provided. + Suitable for methods which use one or more starting values, and + derivatives up to 2nd order. + + The test cases are provided as a list of dictionaries. The dictionary + keys will be a subset of: + ["f", "fprime", "fprime2", "args", "bracket", "smoothness", + "a", "b", "x0", "x1", "root", "ID"] +""" + +# Sources: +# [1] Alefeld, G. E. and Potra, F. A. and Shi, Yixun, +# "Algorithm 748: Enclosing Zeros of Continuous Functions", +# ACM Trans. Math. Softw. Volume 221(1995) +# doi = {10.1145/210089.210111}, +# [2] Chandrupatla, Tirupathi R. "A new hybrid quadratic/bisection algorithm +# for finding the zero of a nonlinear function without using derivatives." +# Advances in Engineering Software 28.3 (1997): 145-149. + +from random import random + +import numpy as np + +from scipy.optimize import _zeros_py as cc +from scipy._lib._array_api import array_namespace + +# "description" refers to the original functions +description = """ +f2 is a symmetric parabola, x**2 - 1 +f3 is a quartic polynomial with large hump in interval +f4 is step function with a discontinuity at 1 +f5 is a hyperbola with vertical asymptote at 1 +f6 has random values positive to left of 1, negative to right + +Of course, these are not real problems. They just test how the +'good' solvers behave in bad circumstances where bisection is +really the best. A good solver should not be much worse than +bisection in such circumstance, while being faster for smooth +monotone sorts of functions. +""" + + +def f1(x): + r"""f1 is a quadratic with roots at 0 and 1""" + return x * (x - 1.) + + +def f1_fp(x): + return 2 * x - 1 + + +def f1_fpp(x): + return 2 + + +def f2(x): + r"""f2 is a symmetric parabola, x**2 - 1""" + return x**2 - 1 + + +def f2_fp(x): + return 2 * x + + +def f2_fpp(x): + return 2 + + +def f3(x): + r"""A quartic with roots at 0, 1, 2 and 3""" + return x * (x - 1.) * (x - 2.) * (x - 3.) # x**4 - 6x**3 + 11x**2 - 6x + + +def f3_fp(x): + return 4 * x**3 - 18 * x**2 + 22 * x - 6 + + +def f3_fpp(x): + return 12 * x**2 - 36 * x + 22 + + +def f4(x): + r"""Piecewise linear, left- and right- discontinuous at x=1, the root.""" + if x > 1: + return 1.0 + .1 * x + if x < 1: + return -1.0 + .1 * x + return 0 + + +def f5(x): + r""" + Hyperbola with a pole at x=1, but pole replaced with 0. Not continuous at root. + """ + if x != 1: + return 1.0 / (1. - x) + return 0 + + +# f6(x) returns random value. Without memoization, calling twice with the +# same x returns different values, hence a "random value", not a +# "function with random values" +_f6_cache = {} +def f6(x): + v = _f6_cache.get(x, None) + if v is None: + if x > 1: + v = random() + elif x < 1: + v = -random() + else: + v = 0 + _f6_cache[x] = v + return v + + +# Each Original test case has +# - a function and its two derivatives, +# - additional arguments, +# - a bracket enclosing a root, +# - the order of differentiability (smoothness) on this interval +# - a starting value for methods which don't require a bracket +# - the root (inside the bracket) +# - an Identifier of the test case + +_ORIGINAL_TESTS_KEYS = [ + "f", "fprime", "fprime2", "args", "bracket", "smoothness", "x0", "root", "ID" +] +_ORIGINAL_TESTS = [ + [f1, f1_fp, f1_fpp, (), [0.5, np.sqrt(3)], np.inf, 0.6, 1.0, "original.01.00"], + [f2, f2_fp, f2_fpp, (), [0.5, np.sqrt(3)], np.inf, 0.6, 1.0, "original.02.00"], + [f3, f3_fp, f3_fpp, (), [0.5, np.sqrt(3)], np.inf, 0.6, 1.0, "original.03.00"], + [f4, None, None, (), [0.5, np.sqrt(3)], -1, 0.6, 1.0, "original.04.00"], + [f5, None, None, (), [0.5, np.sqrt(3)], -1, 0.6, 1.0, "original.05.00"], + [f6, None, None, (), [0.5, np.sqrt(3)], -np.inf, 0.6, 1.0, "original.05.00"] +] + +_ORIGINAL_TESTS_DICTS = [ + dict(zip(_ORIGINAL_TESTS_KEYS, testcase)) for testcase in _ORIGINAL_TESTS +] + +# ################## +# "APS" test cases +# Functions and test cases that appear in [1] + + +def aps01_f(x): + r"""Straightforward sum of trigonometric function and polynomial""" + return np.sin(x) - x / 2 + + +def aps01_fp(x): + return np.cos(x) - 1.0 / 2 + + +def aps01_fpp(x): + return -np.sin(x) + + +def aps02_f(x): + r"""poles at x=n**2, 1st and 2nd derivatives at root are also close to 0""" + ii = np.arange(1, 21) + return -2 * np.sum((2 * ii - 5)**2 / (x - ii**2)**3) + + +def aps02_fp(x): + ii = np.arange(1, 21) + return 6 * np.sum((2 * ii - 5)**2 / (x - ii**2)**4) + + +def aps02_fpp(x): + ii = np.arange(1, 21) + return 24 * np.sum((2 * ii - 5)**2 / (x - ii**2)**5) + + +def aps03_f(x, a, b): + r"""Rapidly changing at the root""" + return a * x * np.exp(b * x) + + +def aps03_fp(x, a, b): + return a * (b * x + 1) * np.exp(b * x) + + +def aps03_fpp(x, a, b): + return a * (b * (b * x + 1) + b) * np.exp(b * x) + + +def aps04_f(x, n, a): + r"""Medium-degree polynomial""" + return x**n - a + + +def aps04_fp(x, n, a): + return n * x**(n - 1) + + +def aps04_fpp(x, n, a): + return n * (n - 1) * x**(n - 2) + + +def aps05_f(x): + r"""Simple Trigonometric function""" + return np.sin(x) - 1.0 / 2 + + +def aps05_fp(x): + return np.cos(x) + + +def aps05_fpp(x): + return -np.sin(x) + + +def aps06_f(x, n): + r"""Exponential rapidly changing from -1 to 1 at x=0""" + return 2 * x * np.exp(-n) - 2 * np.exp(-n * x) + 1 + + +def aps06_fp(x, n): + return 2 * np.exp(-n) + 2 * n * np.exp(-n * x) + + +def aps06_fpp(x, n): + return -2 * n * n * np.exp(-n * x) + + +def aps07_f(x, n): + r"""Upside down parabola with parametrizable height""" + return (1 + (1 - n)**2) * x - (1 - n * x)**2 + + +def aps07_fp(x, n): + return (1 + (1 - n)**2) + 2 * n * (1 - n * x) + + +def aps07_fpp(x, n): + return -2 * n * n + + +def aps08_f(x, n): + r"""Degree n polynomial""" + return x * x - (1 - x)**n + + +def aps08_fp(x, n): + return 2 * x + n * (1 - x)**(n - 1) + + +def aps08_fpp(x, n): + return 2 - n * (n - 1) * (1 - x)**(n - 2) + + +def aps09_f(x, n): + r"""Upside down quartic with parametrizable height""" + return (1 + (1 - n)**4) * x - (1 - n * x)**4 + + +def aps09_fp(x, n): + return (1 + (1 - n)**4) + 4 * n * (1 - n * x)**3 + + +def aps09_fpp(x, n): + return -12 * n * (1 - n * x)**2 + + +def aps10_f(x, n): + r"""Exponential plus a polynomial""" + return np.exp(-n * x) * (x - 1) + x**n + + +def aps10_fp(x, n): + return np.exp(-n * x) * (-n * (x - 1) + 1) + n * x**(n - 1) + + +def aps10_fpp(x, n): + return (np.exp(-n * x) * (-n * (-n * (x - 1) + 1) + -n * x) + + n * (n - 1) * x**(n - 2)) + + +def aps11_f(x, n): + r"""Rational function with a zero at x=1/n and a pole at x=0""" + return (n * x - 1) / ((n - 1) * x) + + +def aps11_fp(x, n): + return 1 / (n - 1) / x**2 + + +def aps11_fpp(x, n): + return -2 / (n - 1) / x**3 + + +def aps12_f(x, n): + r"""nth root of x, with a zero at x=n""" + return np.power(x, 1.0 / n) - np.power(n, 1.0 / n) + + +def aps12_fp(x, n): + return np.power(x, (1.0 - n) / n) / n + + +def aps12_fpp(x, n): + return np.power(x, (1.0 - 2 * n) / n) * (1.0 / n) * (1.0 - n) / n + + +_MAX_EXPABLE = np.log(np.finfo(float).max) + + +def aps13_f(x): + r"""Function with *all* derivatives 0 at the root""" + if x == 0: + return 0 + # x2 = 1.0/x**2 + # if x2 > 708: + # return 0 + y = 1 / x**2 + if y > _MAX_EXPABLE: + return 0 + return x / np.exp(y) + + +def aps13_fp(x): + if x == 0: + return 0 + y = 1 / x**2 + if y > _MAX_EXPABLE: + return 0 + return (1 + 2 / x**2) / np.exp(y) + + +def aps13_fpp(x): + if x == 0: + return 0 + y = 1 / x**2 + if y > _MAX_EXPABLE: + return 0 + return 2 * (2 - x**2) / x**5 / np.exp(y) + + +def aps14_f(x, n): + r"""0 for negative x-values, trigonometric+linear for x positive""" + if x <= 0: + return -n / 20.0 + return n / 20.0 * (x / 1.5 + np.sin(x) - 1) + + +def aps14_fp(x, n): + if x <= 0: + return 0 + return n / 20.0 * (1.0 / 1.5 + np.cos(x)) + + +def aps14_fpp(x, n): + if x <= 0: + return 0 + return -n / 20.0 * (np.sin(x)) + + +def aps15_f(x, n): + r"""piecewise linear, constant outside of [0, 0.002/(1+n)]""" + if x < 0: + return -0.859 + if x > 2 * 1e-3 / (1 + n): + return np.e - 1.859 + return np.exp((n + 1) * x / 2 * 1000) - 1.859 + + +def aps15_fp(x, n): + if not 0 <= x <= 2 * 1e-3 / (1 + n): + return np.e - 1.859 + return np.exp((n + 1) * x / 2 * 1000) * (n + 1) / 2 * 1000 + + +def aps15_fpp(x, n): + if not 0 <= x <= 2 * 1e-3 / (1 + n): + return np.e - 1.859 + return np.exp((n + 1) * x / 2 * 1000) * (n + 1) / 2 * 1000 * (n + 1) / 2 * 1000 + + +# Each APS test case has +# - a function and its two derivatives, +# - additional arguments, +# - a bracket enclosing a root, +# - the order of differentiability of the function on this interval +# - a starting value for methods which don't require a bracket +# - the root (inside the bracket) +# - an Identifier of the test case +# +# Algorithm 748 is a bracketing algorithm so a bracketing interval was provided +# in [1] for each test case. Newton and Halley methods need a single +# starting point x0, which was chosen to be near the middle of the interval, +# unless that would have made the problem too easy. + +_APS_TESTS_KEYS = [ + "f", "fprime", "fprime2", "args", "bracket", "smoothness", "x0", "root", "ID" +] +_APS_TESTS = [ + [aps01_f, aps01_fp, aps01_fpp, (), [np.pi / 2, np.pi], np.inf, + 3, 1.89549426703398094e+00, "aps.01.00"], + [aps02_f, aps02_fp, aps02_fpp, (), [1 + 1e-9, 4 - 1e-9], np.inf, + 2, 3.02291534727305677e+00, "aps.02.00"], + [aps02_f, aps02_fp, aps02_fpp, (), [4 + 1e-9, 9 - 1e-9], np.inf, + 5, 6.68375356080807848e+00, "aps.02.01"], + [aps02_f, aps02_fp, aps02_fpp, (), [9 + 1e-9, 16 - 1e-9], np.inf, + 10, 1.12387016550022114e+01, "aps.02.02"], + [aps02_f, aps02_fp, aps02_fpp, (), [16 + 1e-9, 25 - 1e-9], np.inf, + 17, 1.96760000806234103e+01, "aps.02.03"], + [aps02_f, aps02_fp, aps02_fpp, (), [25 + 1e-9, 36 - 1e-9], np.inf, + 26, 2.98282273265047557e+01, "aps.02.04"], + [aps02_f, aps02_fp, aps02_fpp, (), [36 + 1e-9, 49 - 1e-9], np.inf, + 37, 4.19061161952894139e+01, "aps.02.05"], + [aps02_f, aps02_fp, aps02_fpp, (), [49 + 1e-9, 64 - 1e-9], np.inf, + 50, 5.59535958001430913e+01, "aps.02.06"], + [aps02_f, aps02_fp, aps02_fpp, (), [64 + 1e-9, 81 - 1e-9], np.inf, + 65, 7.19856655865877997e+01, "aps.02.07"], + [aps02_f, aps02_fp, aps02_fpp, (), [81 + 1e-9, 100 - 1e-9], np.inf, + 82, 9.00088685391666701e+01, "aps.02.08"], + [aps02_f, aps02_fp, aps02_fpp, (), [100 + 1e-9, 121 - 1e-9], np.inf, + 101, 1.10026532748330197e+02, "aps.02.09"], + [aps03_f, aps03_fp, aps03_fpp, (-40, -1), [-9, 31], np.inf, + -2, 0, "aps.03.00"], + [aps03_f, aps03_fp, aps03_fpp, (-100, -2), [-9, 31], np.inf, + -2, 0, "aps.03.01"], + [aps03_f, aps03_fp, aps03_fpp, (-200, -3), [-9, 31], np.inf, + -2, 0, "aps.03.02"], + [aps04_f, aps04_fp, aps04_fpp, (4, 0.2), [0, 5], np.inf, + 2.5, 6.68740304976422006e-01, "aps.04.00"], + [aps04_f, aps04_fp, aps04_fpp, (6, 0.2), [0, 5], np.inf, + 2.5, 7.64724491331730039e-01, "aps.04.01"], + [aps04_f, aps04_fp, aps04_fpp, (8, 0.2), [0, 5], np.inf, + 2.5, 8.17765433957942545e-01, "aps.04.02"], + [aps04_f, aps04_fp, aps04_fpp, (10, 0.2), [0, 5], np.inf, + 2.5, 8.51339922520784609e-01, "aps.04.03"], + [aps04_f, aps04_fp, aps04_fpp, (12, 0.2), [0, 5], np.inf, + 2.5, 8.74485272221167897e-01, "aps.04.04"], + [aps04_f, aps04_fp, aps04_fpp, (4, 1), [0, 5], np.inf, + 2.5, 1, "aps.04.05"], + [aps04_f, aps04_fp, aps04_fpp, (6, 1), [0, 5], np.inf, + 2.5, 1, "aps.04.06"], + [aps04_f, aps04_fp, aps04_fpp, (8, 1), [0, 5], np.inf, + 2.5, 1, "aps.04.07"], + [aps04_f, aps04_fp, aps04_fpp, (10, 1), [0, 5], np.inf, + 2.5, 1, "aps.04.08"], + [aps04_f, aps04_fp, aps04_fpp, (12, 1), [0, 5], np.inf, + 2.5, 1, "aps.04.09"], + [aps04_f, aps04_fp, aps04_fpp, (8, 1), [-0.95, 4.05], np.inf, + 1.5, 1, "aps.04.10"], + [aps04_f, aps04_fp, aps04_fpp, (10, 1), [-0.95, 4.05], np.inf, + 1.5, 1, "aps.04.11"], + [aps04_f, aps04_fp, aps04_fpp, (12, 1), [-0.95, 4.05], np.inf, + 1.5, 1, 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[-1000, 1e-4], 0, + -2, 4.96030966991445609e-05, "aps.15.04"], + [aps15_f, aps15_fp, aps15_fpp, (25,), [-1000, 1e-4], 0, + -2, 4.76952852876389951e-05, "aps.15.05"], + [aps15_f, aps15_fp, aps15_fpp, (26,), [-1000, 1e-4], 0, + -2, 4.59287932399486662e-05, "aps.15.06"], + [aps15_f, aps15_fp, aps15_fpp, (27,), [-1000, 1e-4], 0, + -2, 4.42884791956647841e-05, "aps.15.07"], + [aps15_f, aps15_fp, aps15_fpp, (28,), [-1000, 1e-4], 0, + -2, 4.27612902578832391e-05, "aps.15.08"], + [aps15_f, aps15_fp, aps15_fpp, (29,), [-1000, 1e-4], 0, + -2, 4.13359139159538030e-05, "aps.15.09"], + [aps15_f, aps15_fp, aps15_fpp, (30,), [-1000, 1e-4], 0, + -2, 4.00024973380198076e-05, "aps.15.10"], + [aps15_f, aps15_fp, aps15_fpp, (31,), [-1000, 1e-4], 0, + -2, 3.87524192962066869e-05, "aps.15.11"], + [aps15_f, aps15_fp, aps15_fpp, (32,), [-1000, 1e-4], 0, + -2, 3.75781035599579910e-05, "aps.15.12"], + [aps15_f, aps15_fp, aps15_fpp, (33,), [-1000, 1e-4], 0, + -2, 3.64728652199592355e-05, "aps.15.13"], + [aps15_f, aps15_fp, aps15_fpp, (34,), [-1000, 1e-4], 0, + -2, 3.54307833565318273e-05, "aps.15.14"], + [aps15_f, aps15_fp, aps15_fpp, (35,), [-1000, 1e-4], 0, + -2, 3.44465949299614980e-05, "aps.15.15"], + [aps15_f, aps15_fp, aps15_fpp, (36,), [-1000, 1e-4], 0, + -2, 3.35156058778003705e-05, "aps.15.16"], + [aps15_f, aps15_fp, aps15_fpp, (37,), [-1000, 1e-4], 0, + -2, 3.26336162494372125e-05, "aps.15.17"], + [aps15_f, aps15_fp, aps15_fpp, (38,), [-1000, 1e-4], 0, + -2, 3.17968568584260013e-05, "aps.15.18"], + [aps15_f, aps15_fp, aps15_fpp, (39,), [-1000, 1e-4], 0, + -2, 3.10019354369653455e-05, "aps.15.19"], + [aps15_f, aps15_fp, aps15_fpp, (40,), [-1000, 1e-4], 0, + -2, 3.02457906702100968e-05, "aps.15.20"], + [aps15_f, aps15_fp, aps15_fpp, (100,), [-1000, 1e-4], 0, + -2, 1.22779942324615231e-05, "aps.15.21"], + [aps15_f, aps15_fp, aps15_fpp, (200,), [-1000, 1e-4], 0, + -2, 6.16953939044086617e-06, "aps.15.22"], + [aps15_f, aps15_fp, aps15_fpp, (300,), [-1000, 1e-4], 0, + -2, 4.11985852982928163e-06, "aps.15.23"], + [aps15_f, aps15_fp, aps15_fpp, (400,), [-1000, 1e-4], 0, + -2, 3.09246238772721682e-06, "aps.15.24"], + [aps15_f, aps15_fp, aps15_fpp, (500,), [-1000, 1e-4], 0, + -2, 2.47520442610501789e-06, "aps.15.25"], + [aps15_f, aps15_fp, aps15_fpp, (600,), [-1000, 1e-4], 0, + -2, 2.06335676785127107e-06, "aps.15.26"], + [aps15_f, aps15_fp, aps15_fpp, (700,), [-1000, 1e-4], 0, + -2, 1.76901200781542651e-06, "aps.15.27"], + [aps15_f, aps15_fp, aps15_fpp, (800,), [-1000, 1e-4], 0, + -2, 1.54816156988591016e-06, "aps.15.28"], + [aps15_f, aps15_fp, aps15_fpp, (900,), [-1000, 1e-4], 0, + -2, 1.37633453660223511e-06, "aps.15.29"], + [aps15_f, aps15_fp, aps15_fpp, (1000,), [-1000, 1e-4], 0, + -2, 1.23883857889971403e-06, "aps.15.30"] +] + +_APS_TESTS_DICTS = [dict(zip(_APS_TESTS_KEYS, testcase)) for testcase in _APS_TESTS] + + +# ################## +# "complex" test cases +# A few simple, complex-valued, functions, defined on the complex plane. + + +def cplx01_f(z, n, a): + r"""z**n-a: Use to find the nth root of a""" + return z**n - a + + +def cplx01_fp(z, n, a): + return n * z**(n - 1) + + +def cplx01_fpp(z, n, a): + return n * (n - 1) * z**(n - 2) + + +def cplx02_f(z, a): + r"""e**z - a: Use to find the log of a""" + return np.exp(z) - a + + +def cplx02_fp(z, a): + return np.exp(z) + + +def cplx02_fpp(z, a): + return np.exp(z) + + +# Each "complex" test case has +# - a function and its two derivatives, +# - additional arguments, +# - the order of differentiability of the function on this interval +# - two starting values x0 and x1 +# - the root +# - an Identifier of the test case +# +# Algorithm 748 is a bracketing algorithm so a bracketing interval was provided +# in [1] for each test case. Newton and Halley need a single starting point +# x0, which was chosen to be near the middle of the interval, unless that +# would make the problem too easy. + + +_COMPLEX_TESTS_KEYS = [ + "f", "fprime", "fprime2", "args", "smoothness", "x0", "x1", "root", "ID" +] +_COMPLEX_TESTS = [ + [cplx01_f, cplx01_fp, cplx01_fpp, (2, -1), np.inf, + (1 + 1j), (0.5 + 0.5j), 1j, "complex.01.00"], + [cplx01_f, cplx01_fp, cplx01_fpp, (3, 1), np.inf, + (-1 + 1j), (-0.5 + 2.0j), (-0.5 + np.sqrt(3) / 2 * 1.0j), + "complex.01.01"], + [cplx01_f, cplx01_fp, cplx01_fpp, (3, -1), np.inf, + 1j, (0.5 + 0.5j), (0.5 + np.sqrt(3) / 2 * 1.0j), + "complex.01.02"], + [cplx01_f, cplx01_fp, cplx01_fpp, (3, 8), np.inf, + 5, 4, 2, "complex.01.03"], + [cplx02_f, cplx02_fp, cplx02_fpp, (-1,), np.inf, + (1 + 2j), (0.5 + 0.5j), np.pi * 1.0j, "complex.02.00"], + [cplx02_f, cplx02_fp, cplx02_fpp, (1j,), np.inf, + (1 + 2j), (0.5 + 0.5j), np.pi * 0.5j, "complex.02.01"], +] + +_COMPLEX_TESTS_DICTS = [ + dict(zip(_COMPLEX_TESTS_KEYS, testcase)) for testcase in _COMPLEX_TESTS +] + + +def _add_a_b(tests): + r"""Add "a" and "b" keys to each test from the "bracket" value""" + for d in tests: + for k, v in zip(['a', 'b'], d.get('bracket', [])): + d[k] = v + + +_add_a_b(_ORIGINAL_TESTS_DICTS) +_add_a_b(_APS_TESTS_DICTS) +_add_a_b(_COMPLEX_TESTS_DICTS) + + +def get_tests(collection='original', smoothness=None): + r"""Return the requested collection of test cases, as an array of dicts with subset-specific keys + + Allowed values of collection: + 'original': The original benchmarking functions. + Real-valued functions of real-valued inputs on an interval with a zero. + f1, .., f3 are continuous and infinitely differentiable + f4 has a single discontinuity at the root + f5 has a root at 1 replacing a 1st order pole + f6 is randomly positive on one side of the root, randomly negative on the other + 'aps': The test problems in the TOMS "Algorithm 748: Enclosing Zeros of Continuous Functions" + paper by Alefeld, Potra and Shi. Real-valued functions of + real-valued inputs on an interval with a zero. + Suitable for methods which start with an enclosing interval, and + derivatives up to 2nd order. + 'complex': Some complex-valued functions of complex-valued inputs. + No enclosing bracket is provided. + Suitable for methods which use one or more starting values, and + derivatives up to 2nd order. + + The dictionary keys will be a subset of + ["f", "fprime", "fprime2", "args", "bracket", "a", b", "smoothness", "x0", "x1", "root", "ID"] + """ # noqa: E501 + collection = collection or "original" + subsets = {"aps": _APS_TESTS_DICTS, + "complex": _COMPLEX_TESTS_DICTS, + "original": _ORIGINAL_TESTS_DICTS, + "chandrupatla": _CHANDRUPATLA_TESTS_DICTS} + tests = subsets.get(collection, []) + if smoothness is not None: + tests = [tc for tc in tests if tc['smoothness'] >= smoothness] + return tests + + +# Backwards compatibility +methods = [cc.bisect, cc.ridder, cc.brenth, cc.brentq] +mstrings = ['cc.bisect', 'cc.ridder', 'cc.brenth', 'cc.brentq'] +functions = [f2, f3, f4, f5, f6] +fstrings = ['f2', 'f3', 'f4', 'f5', 'f6'] + +# ################## +# "Chandrupatla" test cases +# Functions and test cases that appear in [2] + +def fun1(x): + return x**3 - 2*x - 5 +fun1.root = 2.0945514815423265 # additional precision using mpmath.findroot + + +def fun2(x): + return 1 - 1/x**2 +fun2.root = 1 + + +def fun3(x): + return (x-3)**3 +fun3.root = 3 + + +def fun4(x): + return 6*(x-2)**5 +fun4.root = 2 + + +def fun5(x): + return x**9 +fun5.root = 0 + + +def fun6(x): + return x**19 +fun6.root = 0 + + +def fun7(x): + xp = array_namespace(x) + return 0 if xp.abs(x) < 3.8e-4 else x*xp.exp(-x**(-2)) +fun7.root = 0 + + +def fun8(x): + xp = array_namespace(x) + xi = 0.61489 + return -(3062*(1-xi)*xp.exp(-x))/(xi + (1-xi)*xp.exp(-x)) - 1013 + 1628/x +fun8.root = 1.0375360332870405 + + +def fun9(x): + xp = array_namespace(x) + return xp.exp(x) - 2 - 0.01/x**2 + .000002/x**3 +fun9.root = 0.7032048403631358 + +# Each "chandropatla" test case has +# - a function, +# - two starting values x0 and x1 +# - the root +# - the number of function evaluations required by Chandrupatla's algorithm +# - an Identifier of the test case +# +# Chandrupatla's is a bracketing algorithm, so a bracketing interval was +# provided in [2] for each test case. No special support for testing with +# secant/Newton/Halley is provided. + +_CHANDRUPATLA_TESTS_KEYS = ["f", "bracket", "root", "nfeval", "ID"] +_CHANDRUPATLA_TESTS = [ + [fun1, [2, 3], fun1.root, 7], + [fun1, [1, 10], fun1.root, 11], + [fun1, [1, 100], fun1.root, 14], + [fun1, [-1e4, 1e4], fun1.root, 23], + [fun1, [-1e10, 1e10], fun1.root, 43], + [fun2, [0.5, 1.51], fun2.root, 8], + [fun2, [1e-4, 1e4], fun2.root, 22], + [fun2, [1e-6, 1e6], fun2.root, 28], + [fun2, [1e-10, 1e10], fun2.root, 41], + [fun2, [1e-12, 1e12], fun2.root, 48], + [fun3, [0, 5], fun3.root, 21], + [fun3, [-10, 10], fun3.root, 23], + [fun3, [-1e4, 1e4], fun3.root, 36], + [fun3, [-1e6, 1e6], fun3.root, 45], + [fun3, [-1e10, 1e10], fun3.root, 55], + [fun4, [0, 5], fun4.root, 21], + [fun4, [-10, 10], fun4.root, 23], + [fun4, [-1e4, 1e4], fun4.root, 33], + [fun4, [-1e6, 1e6], fun4.root, 43], + [fun4, [-1e10, 1e10], fun4.root, 54], + [fun5, [-1, 4], fun5.root, 21], + [fun5, [-2, 5], fun5.root, 22], + [fun5, [-1, 10], fun5.root, 23], + [fun5, [-5, 50], fun5.root, 25], + [fun5, [-10, 100], fun5.root, 26], + [fun6, [-1., 4.], fun6.root, 21], + [fun6, [-2., 5.], fun6.root, 22], + [fun6, [-1., 10.], fun6.root, 23], + [fun6, [-5., 50.], fun6.root, 25], + [fun6, [-10., 100.], fun6.root, 26], + [fun7, [-1, 4], fun7.root, 8], + [fun7, [-2, 5], fun7.root, 8], + [fun7, [-1, 10], fun7.root, 11], + [fun7, [-5, 50], fun7.root, 18], + [fun7, [-10, 100], fun7.root, 19], + [fun8, [2e-4, 2], fun8.root, 9], + [fun8, [2e-4, 3], fun8.root, 10], + [fun8, [2e-4, 9], fun8.root, 11], + [fun8, [2e-4, 27], fun8.root, 12], + [fun8, [2e-4, 81], fun8.root, 14], + [fun9, [2e-4, 1], fun9.root, 7], + [fun9, [2e-4, 3], fun9.root, 8], + [fun9, [2e-4, 9], fun9.root, 10], + [fun9, [2e-4, 27], fun9.root, 11], + [fun9, [2e-4, 81], fun9.root, 13], +] +_CHANDRUPATLA_TESTS = [test + [f'{test[0].__name__}.{i%5+1}'] + for i, test in enumerate(_CHANDRUPATLA_TESTS)] + +_CHANDRUPATLA_TESTS_DICTS = [dict(zip(_CHANDRUPATLA_TESTS_KEYS, testcase)) + for testcase in _CHANDRUPATLA_TESTS] +_add_a_b(_CHANDRUPATLA_TESTS_DICTS) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros.cpython-310-x86_64-linux-gnu.so b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..7af3971d3d8f44903d9da2be40e4e414cbf6463d Binary files /dev/null and b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros.cpython-310-x86_64-linux-gnu.so differ diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros_py.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros_py.py new file mode 100644 index 0000000000000000000000000000000000000000..986031920d69578c1c7c470b03deae5b3d24c309 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/_zeros_py.py @@ -0,0 +1,1403 @@ +import warnings +from collections import namedtuple +import operator +from . import _zeros +from ._optimize import OptimizeResult +import numpy as np + + +_iter = 100 +_xtol = 2e-12 +_rtol = 4 * np.finfo(float).eps + +__all__ = ['newton', 'bisect', 'ridder', 'brentq', 'brenth', 'toms748', + 'RootResults'] + +# Must agree with CONVERGED, SIGNERR, CONVERR, ... in zeros.h +_ECONVERGED = 0 +_ESIGNERR = -1 # used in _chandrupatla +_ECONVERR = -2 +_EVALUEERR = -3 +_ECALLBACK = -4 +_EINPROGRESS = 1 + +CONVERGED = 'converged' +SIGNERR = 'sign error' +CONVERR = 'convergence error' +VALUEERR = 'value error' +INPROGRESS = 'No error' + + +flag_map = {_ECONVERGED: CONVERGED, _ESIGNERR: SIGNERR, _ECONVERR: CONVERR, + _EVALUEERR: VALUEERR, _EINPROGRESS: INPROGRESS} + + +class RootResults(OptimizeResult): + """Represents the root finding result. + + Attributes + ---------- + root : float + Estimated root location. + iterations : int + Number of iterations needed to find the root. + function_calls : int + Number of times the function was called. + converged : bool + True if the routine converged. + flag : str + Description of the cause of termination. + method : str + Root finding method used. + + """ + + def __init__(self, root, iterations, function_calls, flag, method): + self.root = root + self.iterations = iterations + self.function_calls = function_calls + self.converged = flag == _ECONVERGED + if flag in flag_map: + self.flag = flag_map[flag] + else: + self.flag = flag + self.method = method + + +def results_c(full_output, r, method): + if full_output: + x, funcalls, iterations, flag = r + results = RootResults(root=x, + iterations=iterations, + function_calls=funcalls, + flag=flag, method=method) + return x, results + else: + return r + + +def _results_select(full_output, r, method): + """Select from a tuple of (root, funccalls, iterations, flag)""" + x, funcalls, iterations, flag = r + if full_output: + results = RootResults(root=x, + iterations=iterations, + function_calls=funcalls, + flag=flag, method=method) + return x, results + return x + + +def _wrap_nan_raise(f): + + def f_raise(x, *args): + fx = f(x, *args) + f_raise._function_calls += 1 + if np.isnan(fx): + msg = (f'The function value at x={x} is NaN; ' + 'solver cannot continue.') + err = ValueError(msg) + err._x = x + err._function_calls = f_raise._function_calls + raise err + return fx + + f_raise._function_calls = 0 + return f_raise + + +def newton(func, x0, fprime=None, args=(), tol=1.48e-8, maxiter=50, + fprime2=None, x1=None, rtol=0.0, + full_output=False, disp=True): + """ + Find a root of a real or complex function using the Newton-Raphson + (or secant or Halley's) method. + + Find a root of the scalar-valued function `func` given a nearby scalar + starting point `x0`. + The Newton-Raphson method is used if the derivative `fprime` of `func` + is provided, otherwise the secant method is used. If the second order + derivative `fprime2` of `func` is also provided, then Halley's method is + used. + + If `x0` is a sequence with more than one item, `newton` returns an array: + the roots of the function from each (scalar) starting point in `x0`. + In this case, `func` must be vectorized to return a sequence or array of + the same shape as its first argument. If `fprime` (`fprime2`) is given, + then its return must also have the same shape: each element is the first + (second) derivative of `func` with respect to its only variable evaluated + at each element of its first argument. + + `newton` is for finding roots of a scalar-valued functions of a single + variable. For problems involving several variables, see `root`. + + Parameters + ---------- + func : callable + The function whose root is wanted. It must be a function of a + single variable of the form ``f(x,a,b,c...)``, where ``a,b,c...`` + are extra arguments that can be passed in the `args` parameter. + x0 : float, sequence, or ndarray + An initial estimate of the root that should be somewhere near the + actual root. If not scalar, then `func` must be vectorized and return + a sequence or array of the same shape as its first argument. + fprime : callable, optional + The derivative of the function when available and convenient. If it + is None (default), then the secant method is used. + args : tuple, optional + Extra arguments to be used in the function call. + tol : float, optional + The allowable error of the root's value. If `func` is complex-valued, + a larger `tol` is recommended as both the real and imaginary parts + of `x` contribute to ``|x - x0|``. + maxiter : int, optional + Maximum number of iterations. + fprime2 : callable, optional + The second order derivative of the function when available and + convenient. If it is None (default), then the normal Newton-Raphson + or the secant method is used. If it is not None, then Halley's method + is used. + x1 : float, optional + Another estimate of the root that should be somewhere near the + actual root. Used if `fprime` is not provided. + rtol : float, optional + Tolerance (relative) for termination. + full_output : bool, optional + If `full_output` is False (default), the root is returned. + If True and `x0` is scalar, the return value is ``(x, r)``, where ``x`` + is the root and ``r`` is a `RootResults` object. + If True and `x0` is non-scalar, the return value is ``(x, converged, + zero_der)`` (see Returns section for details). + disp : bool, optional + If True, raise a RuntimeError if the algorithm didn't converge, with + the error message containing the number of iterations and current + function value. Otherwise, the convergence status is recorded in a + `RootResults` return object. + Ignored if `x0` is not scalar. + *Note: this has little to do with displaying, however, + the `disp` keyword cannot be renamed for backwards compatibility.* + + Returns + ------- + root : float, sequence, or ndarray + Estimated location where function is zero. + r : `RootResults`, optional + Present if ``full_output=True`` and `x0` is scalar. + Object containing information about the convergence. In particular, + ``r.converged`` is True if the routine converged. + converged : ndarray of bool, optional + Present if ``full_output=True`` and `x0` is non-scalar. + For vector functions, indicates which elements converged successfully. + zero_der : ndarray of bool, optional + Present if ``full_output=True`` and `x0` is non-scalar. + For vector functions, indicates which elements had a zero derivative. + + See Also + -------- + root_scalar : interface to root solvers for scalar functions + root : interface to root solvers for multi-input, multi-output functions + + Notes + ----- + The convergence rate of the Newton-Raphson method is quadratic, + the Halley method is cubic, and the secant method is + sub-quadratic. This means that if the function is well-behaved + the actual error in the estimated root after the nth iteration + is approximately the square (cube for Halley) of the error + after the (n-1)th step. However, the stopping criterion used + here is the step size and there is no guarantee that a root + has been found. Consequently, the result should be verified. + Safer algorithms are brentq, brenth, ridder, and bisect, + but they all require that the root first be bracketed in an + interval where the function changes sign. The brentq algorithm + is recommended for general use in one dimensional problems + when such an interval has been found. + + When `newton` is used with arrays, it is best suited for the following + types of problems: + + * The initial guesses, `x0`, are all relatively the same distance from + the roots. + * Some or all of the extra arguments, `args`, are also arrays so that a + class of similar problems can be solved together. + * The size of the initial guesses, `x0`, is larger than O(100) elements. + Otherwise, a naive loop may perform as well or better than a vector. + + Examples + -------- + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy import optimize + + >>> def f(x): + ... return (x**3 - 1) # only one real root at x = 1 + + ``fprime`` is not provided, use the secant method: + + >>> root = optimize.newton(f, 1.5) + >>> root + 1.0000000000000016 + >>> root = optimize.newton(f, 1.5, fprime2=lambda x: 6 * x) + >>> root + 1.0000000000000016 + + Only ``fprime`` is provided, use the Newton-Raphson method: + + >>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2) + >>> root + 1.0 + + Both ``fprime2`` and ``fprime`` are provided, use Halley's method: + + >>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2, + ... fprime2=lambda x: 6 * x) + >>> root + 1.0 + + When we want to find roots for a set of related starting values and/or + function parameters, we can provide both of those as an array of inputs: + + >>> f = lambda x, a: x**3 - a + >>> fder = lambda x, a: 3 * x**2 + >>> rng = np.random.default_rng() + >>> x = rng.standard_normal(100) + >>> a = np.arange(-50, 50) + >>> vec_res = optimize.newton(f, x, fprime=fder, args=(a, ), maxiter=200) + + The above is the equivalent of solving for each value in ``(x, a)`` + separately in a for-loop, just faster: + + >>> loop_res = [optimize.newton(f, x0, fprime=fder, args=(a0,), + ... maxiter=200) + ... for x0, a0 in zip(x, a)] + >>> np.allclose(vec_res, loop_res) + True + + Plot the results found for all values of ``a``: + + >>> analytical_result = np.sign(a) * np.abs(a)**(1/3) + >>> fig, ax = plt.subplots() + >>> ax.plot(a, analytical_result, 'o') + >>> ax.plot(a, vec_res, '.') + >>> ax.set_xlabel('$a$') + >>> ax.set_ylabel('$x$ where $f(x, a)=0$') + >>> plt.show() + + """ + if tol <= 0: + raise ValueError("tol too small (%g <= 0)" % tol) + maxiter = operator.index(maxiter) + if maxiter < 1: + raise ValueError("maxiter must be greater than 0") + if np.size(x0) > 1: + return _array_newton(func, x0, fprime, args, tol, maxiter, fprime2, + full_output) + + # Convert to float (don't use float(x0); this works also for complex x0) + # Use np.asarray because we want x0 to be a numpy object, not a Python + # object. e.g. np.complex(1+1j) > 0 is possible, but (1 + 1j) > 0 raises + # a TypeError + x0 = np.asarray(x0)[()] * 1.0 + p0 = x0 + funcalls = 0 + if fprime is not None: + # Newton-Raphson method + method = "newton" + for itr in range(maxiter): + # first evaluate fval + fval = func(p0, *args) + funcalls += 1 + # If fval is 0, a root has been found, then terminate + if fval == 0: + return _results_select( + full_output, (p0, funcalls, itr, _ECONVERGED), method) + fder = fprime(p0, *args) + funcalls += 1 + if fder == 0: + msg = "Derivative was zero." + if disp: + msg += ( + " Failed to converge after %d iterations, value is %s." + % (itr + 1, p0)) + raise RuntimeError(msg) + warnings.warn(msg, RuntimeWarning, stacklevel=2) + return _results_select( + full_output, (p0, funcalls, itr + 1, _ECONVERR), method) + newton_step = fval / fder + if fprime2: + fder2 = fprime2(p0, *args) + funcalls += 1 + method = "halley" + # Halley's method: + # newton_step /= (1.0 - 0.5 * newton_step * fder2 / fder) + # Only do it if denominator stays close enough to 1 + # Rationale: If 1-adj < 0, then Halley sends x in the + # opposite direction to Newton. Doesn't happen if x is close + # enough to root. + adj = newton_step * fder2 / fder / 2 + if np.abs(adj) < 1: + newton_step /= 1.0 - adj + p = p0 - newton_step + if np.isclose(p, p0, rtol=rtol, atol=tol): + return _results_select( + full_output, (p, funcalls, itr + 1, _ECONVERGED), method) + p0 = p + else: + # Secant method + method = "secant" + if x1 is not None: + if x1 == x0: + raise ValueError("x1 and x0 must be different") + p1 = x1 + else: + eps = 1e-4 + p1 = x0 * (1 + eps) + p1 += (eps if p1 >= 0 else -eps) + q0 = func(p0, *args) + funcalls += 1 + q1 = func(p1, *args) + funcalls += 1 + if abs(q1) < abs(q0): + p0, p1, q0, q1 = p1, p0, q1, q0 + for itr in range(maxiter): + if q1 == q0: + if p1 != p0: + msg = "Tolerance of %s reached." % (p1 - p0) + if disp: + msg += ( + " Failed to converge after %d iterations, value is %s." + % (itr + 1, p1)) + raise RuntimeError(msg) + warnings.warn(msg, RuntimeWarning, stacklevel=2) + p = (p1 + p0) / 2.0 + return _results_select( + full_output, (p, funcalls, itr + 1, _ECONVERR), method) + else: + if abs(q1) > abs(q0): + p = (-q0 / q1 * p1 + p0) / (1 - q0 / q1) + else: + p = (-q1 / q0 * p0 + p1) / (1 - q1 / q0) + if np.isclose(p, p1, rtol=rtol, atol=tol): + return _results_select( + full_output, (p, funcalls, itr + 1, _ECONVERGED), method) + p0, q0 = p1, q1 + p1 = p + q1 = func(p1, *args) + funcalls += 1 + + if disp: + msg = ("Failed to converge after %d iterations, value is %s." + % (itr + 1, p)) + raise RuntimeError(msg) + + return _results_select(full_output, (p, funcalls, itr + 1, _ECONVERR), method) + + +def _array_newton(func, x0, fprime, args, tol, maxiter, fprime2, full_output): + """ + A vectorized version of Newton, Halley, and secant methods for arrays. + + Do not use this method directly. This method is called from `newton` + when ``np.size(x0) > 1`` is ``True``. For docstring, see `newton`. + """ + # Explicitly copy `x0` as `p` will be modified inplace, but the + # user's array should not be altered. + p = np.array(x0, copy=True) + + failures = np.ones_like(p, dtype=bool) + nz_der = np.ones_like(failures) + if fprime is not None: + # Newton-Raphson method + for iteration in range(maxiter): + # first evaluate fval + fval = np.asarray(func(p, *args)) + # If all fval are 0, all roots have been found, then terminate + if not fval.any(): + failures = fval.astype(bool) + break + fder = np.asarray(fprime(p, *args)) + nz_der = (fder != 0) + # stop iterating if all derivatives are zero + if not nz_der.any(): + break + # Newton step + dp = fval[nz_der] / fder[nz_der] + if fprime2 is not None: + fder2 = np.asarray(fprime2(p, *args)) + dp = dp / (1.0 - 0.5 * dp * fder2[nz_der] / fder[nz_der]) + # only update nonzero derivatives + p = np.asarray(p, dtype=np.result_type(p, dp, np.float64)) + p[nz_der] -= dp + failures[nz_der] = np.abs(dp) >= tol # items not yet converged + # stop iterating if there aren't any failures, not incl zero der + if not failures[nz_der].any(): + break + else: + # Secant method + dx = np.finfo(float).eps**0.33 + p1 = p * (1 + dx) + np.where(p >= 0, dx, -dx) + q0 = np.asarray(func(p, *args)) + q1 = np.asarray(func(p1, *args)) + active = np.ones_like(p, dtype=bool) + for iteration in range(maxiter): + nz_der = (q1 != q0) + # stop iterating if all derivatives are zero + if not nz_der.any(): + p = (p1 + p) / 2.0 + break + # Secant Step + dp = (q1 * (p1 - p))[nz_der] / (q1 - q0)[nz_der] + # only update nonzero derivatives + p = np.asarray(p, dtype=np.result_type(p, p1, dp, np.float64)) + p[nz_der] = p1[nz_der] - dp + active_zero_der = ~nz_der & active + p[active_zero_der] = (p1 + p)[active_zero_der] / 2.0 + active &= nz_der # don't assign zero derivatives again + failures[nz_der] = np.abs(dp) >= tol # not yet converged + # stop iterating if there aren't any failures, not incl zero der + if not failures[nz_der].any(): + break + p1, p = p, p1 + q0 = q1 + q1 = np.asarray(func(p1, *args)) + + zero_der = ~nz_der & failures # don't include converged with zero-ders + if zero_der.any(): + # Secant warnings + if fprime is None: + nonzero_dp = (p1 != p) + # non-zero dp, but infinite newton step + zero_der_nz_dp = (zero_der & nonzero_dp) + if zero_der_nz_dp.any(): + rms = np.sqrt( + sum((p1[zero_der_nz_dp] - p[zero_der_nz_dp]) ** 2) + ) + warnings.warn(f'RMS of {rms:g} reached', RuntimeWarning, stacklevel=3) + # Newton or Halley warnings + else: + all_or_some = 'all' if zero_der.all() else 'some' + msg = f'{all_or_some:s} derivatives were zero' + warnings.warn(msg, RuntimeWarning, stacklevel=3) + elif failures.any(): + all_or_some = 'all' if failures.all() else 'some' + msg = f'{all_or_some:s} failed to converge after {maxiter:d} iterations' + if failures.all(): + raise RuntimeError(msg) + warnings.warn(msg, RuntimeWarning, stacklevel=3) + + if full_output: + result = namedtuple('result', ('root', 'converged', 'zero_der')) + p = result(p, ~failures, zero_der) + + return p + + +def bisect(f, a, b, args=(), + xtol=_xtol, rtol=_rtol, maxiter=_iter, + full_output=False, disp=True): + """ + Find root of a function within an interval using bisection. + + Basic bisection routine to find a root of the function `f` between the + arguments `a` and `b`. `f(a)` and `f(b)` cannot have the same signs. + Slow but sure. + + Parameters + ---------- + f : function + Python function returning a number. `f` must be continuous, and + f(a) and f(b) must have opposite signs. + a : scalar + One end of the bracketing interval [a,b]. + b : scalar + The other end of the bracketing interval [a,b]. + xtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter must be positive. + rtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter cannot be smaller than its default value of + ``4*np.finfo(float).eps``. + maxiter : int, optional + If convergence is not achieved in `maxiter` iterations, an error is + raised. Must be >= 0. + args : tuple, optional + Containing extra arguments for the function `f`. + `f` is called by ``apply(f, (x)+args)``. + full_output : bool, optional + If `full_output` is False, the root is returned. If `full_output` is + True, the return value is ``(x, r)``, where x is the root, and r is + a `RootResults` object. + disp : bool, optional + If True, raise RuntimeError if the algorithm didn't converge. + Otherwise, the convergence status is recorded in a `RootResults` + return object. + + Returns + ------- + root : float + Root of `f` between `a` and `b`. + r : `RootResults` (present if ``full_output = True``) + Object containing information about the convergence. In particular, + ``r.converged`` is True if the routine converged. + + Examples + -------- + + >>> def f(x): + ... return (x**2 - 1) + + >>> from scipy import optimize + + >>> root = optimize.bisect(f, 0, 2) + >>> root + 1.0 + + >>> root = optimize.bisect(f, -2, 0) + >>> root + -1.0 + + See Also + -------- + brentq, brenth, bisect, newton + fixed_point : scalar fixed-point finder + fsolve : n-dimensional root-finding + + """ + if not isinstance(args, tuple): + args = (args,) + maxiter = operator.index(maxiter) + if xtol <= 0: + raise ValueError("xtol too small (%g <= 0)" % xtol) + if rtol < _rtol: + raise ValueError(f"rtol too small ({rtol:g} < {_rtol:g})") + f = _wrap_nan_raise(f) + r = _zeros._bisect(f, a, b, xtol, rtol, maxiter, args, full_output, disp) + return results_c(full_output, r, "bisect") + + +def ridder(f, a, b, args=(), + xtol=_xtol, rtol=_rtol, maxiter=_iter, + full_output=False, disp=True): + """ + Find a root of a function in an interval using Ridder's method. + + Parameters + ---------- + f : function + Python function returning a number. f must be continuous, and f(a) and + f(b) must have opposite signs. + a : scalar + One end of the bracketing interval [a,b]. + b : scalar + The other end of the bracketing interval [a,b]. + xtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter must be positive. + rtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter cannot be smaller than its default value of + ``4*np.finfo(float).eps``. + maxiter : int, optional + If convergence is not achieved in `maxiter` iterations, an error is + raised. Must be >= 0. + args : tuple, optional + Containing extra arguments for the function `f`. + `f` is called by ``apply(f, (x)+args)``. + full_output : bool, optional + If `full_output` is False, the root is returned. If `full_output` is + True, the return value is ``(x, r)``, where `x` is the root, and `r` is + a `RootResults` object. + disp : bool, optional + If True, raise RuntimeError if the algorithm didn't converge. + Otherwise, the convergence status is recorded in any `RootResults` + return object. + + Returns + ------- + root : float + Root of `f` between `a` and `b`. + r : `RootResults` (present if ``full_output = True``) + Object containing information about the convergence. + In particular, ``r.converged`` is True if the routine converged. + + See Also + -------- + brentq, brenth, bisect, newton : 1-D root-finding + fixed_point : scalar fixed-point finder + + Notes + ----- + Uses [Ridders1979]_ method to find a root of the function `f` between the + arguments `a` and `b`. Ridders' method is faster than bisection, but not + generally as fast as the Brent routines. [Ridders1979]_ provides the + classic description and source of the algorithm. A description can also be + found in any recent edition of Numerical Recipes. + + The routine used here diverges slightly from standard presentations in + order to be a bit more careful of tolerance. + + References + ---------- + .. [Ridders1979] + Ridders, C. F. J. "A New Algorithm for Computing a + Single Root of a Real Continuous Function." + IEEE Trans. Circuits Systems 26, 979-980, 1979. + + Examples + -------- + + >>> def f(x): + ... return (x**2 - 1) + + >>> from scipy import optimize + + >>> root = optimize.ridder(f, 0, 2) + >>> root + 1.0 + + >>> root = optimize.ridder(f, -2, 0) + >>> root + -1.0 + """ + if not isinstance(args, tuple): + args = (args,) + maxiter = operator.index(maxiter) + if xtol <= 0: + raise ValueError("xtol too small (%g <= 0)" % xtol) + if rtol < _rtol: + raise ValueError(f"rtol too small ({rtol:g} < {_rtol:g})") + f = _wrap_nan_raise(f) + r = _zeros._ridder(f, a, b, xtol, rtol, maxiter, args, full_output, disp) + return results_c(full_output, r, "ridder") + + +def brentq(f, a, b, args=(), + xtol=_xtol, rtol=_rtol, maxiter=_iter, + full_output=False, disp=True): + """ + Find a root of a function in a bracketing interval using Brent's method. + + Uses the classic Brent's method to find a root of the function `f` on + the sign changing interval [a , b]. Generally considered the best of the + rootfinding routines here. It is a safe version of the secant method that + uses inverse quadratic extrapolation. Brent's method combines root + bracketing, interval bisection, and inverse quadratic interpolation. It is + sometimes known as the van Wijngaarden-Dekker-Brent method. Brent (1973) + claims convergence is guaranteed for functions computable within [a,b]. + + [Brent1973]_ provides the classic description of the algorithm. Another + description can be found in a recent edition of Numerical Recipes, including + [PressEtal1992]_. A third description is at + http://mathworld.wolfram.com/BrentsMethod.html. It should be easy to + understand the algorithm just by reading our code. Our code diverges a bit + from standard presentations: we choose a different formula for the + extrapolation step. + + Parameters + ---------- + f : function + Python function returning a number. The function :math:`f` + must be continuous, and :math:`f(a)` and :math:`f(b)` must + have opposite signs. + a : scalar + One end of the bracketing interval :math:`[a, b]`. + b : scalar + The other end of the bracketing interval :math:`[a, b]`. + xtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter must be positive. For nice functions, Brent's + method will often satisfy the above condition with ``xtol/2`` + and ``rtol/2``. [Brent1973]_ + rtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter cannot be smaller than its default value of + ``4*np.finfo(float).eps``. For nice functions, Brent's + method will often satisfy the above condition with ``xtol/2`` + and ``rtol/2``. [Brent1973]_ + maxiter : int, optional + If convergence is not achieved in `maxiter` iterations, an error is + raised. Must be >= 0. + args : tuple, optional + Containing extra arguments for the function `f`. + `f` is called by ``apply(f, (x)+args)``. + full_output : bool, optional + If `full_output` is False, the root is returned. If `full_output` is + True, the return value is ``(x, r)``, where `x` is the root, and `r` is + a `RootResults` object. + disp : bool, optional + If True, raise RuntimeError if the algorithm didn't converge. + Otherwise, the convergence status is recorded in any `RootResults` + return object. + + Returns + ------- + root : float + Root of `f` between `a` and `b`. + r : `RootResults` (present if ``full_output = True``) + Object containing information about the convergence. In particular, + ``r.converged`` is True if the routine converged. + + Notes + ----- + `f` must be continuous. f(a) and f(b) must have opposite signs. + + Related functions fall into several classes: + + multivariate local optimizers + `fmin`, `fmin_powell`, `fmin_cg`, `fmin_bfgs`, `fmin_ncg` + nonlinear least squares minimizer + `leastsq` + constrained multivariate optimizers + `fmin_l_bfgs_b`, `fmin_tnc`, `fmin_cobyla` + global optimizers + `basinhopping`, `brute`, `differential_evolution` + local scalar minimizers + `fminbound`, `brent`, `golden`, `bracket` + N-D root-finding + `fsolve` + 1-D root-finding + `brenth`, `ridder`, `bisect`, `newton` + scalar fixed-point finder + `fixed_point` + + References + ---------- + .. [Brent1973] + Brent, R. P., + *Algorithms for Minimization Without Derivatives*. + Englewood Cliffs, NJ: Prentice-Hall, 1973. Ch. 3-4. + + .. [PressEtal1992] + Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. + *Numerical Recipes in FORTRAN: The Art of Scientific Computing*, 2nd ed. + Cambridge, England: Cambridge University Press, pp. 352-355, 1992. + Section 9.3: "Van Wijngaarden-Dekker-Brent Method." + + Examples + -------- + >>> def f(x): + ... return (x**2 - 1) + + >>> from scipy import optimize + + >>> root = optimize.brentq(f, -2, 0) + >>> root + -1.0 + + >>> root = optimize.brentq(f, 0, 2) + >>> root + 1.0 + """ + if not isinstance(args, tuple): + args = (args,) + maxiter = operator.index(maxiter) + if xtol <= 0: + raise ValueError("xtol too small (%g <= 0)" % xtol) + if rtol < _rtol: + raise ValueError(f"rtol too small ({rtol:g} < {_rtol:g})") + f = _wrap_nan_raise(f) + r = _zeros._brentq(f, a, b, xtol, rtol, maxiter, args, full_output, disp) + return results_c(full_output, r, "brentq") + + +def brenth(f, a, b, args=(), + xtol=_xtol, rtol=_rtol, maxiter=_iter, + full_output=False, disp=True): + """Find a root of a function in a bracketing interval using Brent's + method with hyperbolic extrapolation. + + A variation on the classic Brent routine to find a root of the function f + between the arguments a and b that uses hyperbolic extrapolation instead of + inverse quadratic extrapolation. Bus & Dekker (1975) guarantee convergence + for this method, claiming that the upper bound of function evaluations here + is 4 or 5 times that of bisection. + f(a) and f(b) cannot have the same signs. Generally, on a par with the + brent routine, but not as heavily tested. It is a safe version of the + secant method that uses hyperbolic extrapolation. + The version here is by Chuck Harris, and implements Algorithm M of + [BusAndDekker1975]_, where further details (convergence properties, + additional remarks and such) can be found + + Parameters + ---------- + f : function + Python function returning a number. f must be continuous, and f(a) and + f(b) must have opposite signs. + a : scalar + One end of the bracketing interval [a,b]. + b : scalar + The other end of the bracketing interval [a,b]. + xtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter must be positive. As with `brentq`, for nice + functions the method will often satisfy the above condition + with ``xtol/2`` and ``rtol/2``. + rtol : number, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter cannot be smaller than its default value of + ``4*np.finfo(float).eps``. As with `brentq`, for nice functions + the method will often satisfy the above condition with + ``xtol/2`` and ``rtol/2``. + maxiter : int, optional + If convergence is not achieved in `maxiter` iterations, an error is + raised. Must be >= 0. + args : tuple, optional + Containing extra arguments for the function `f`. + `f` is called by ``apply(f, (x)+args)``. + full_output : bool, optional + If `full_output` is False, the root is returned. If `full_output` is + True, the return value is ``(x, r)``, where `x` is the root, and `r` is + a `RootResults` object. + disp : bool, optional + If True, raise RuntimeError if the algorithm didn't converge. + Otherwise, the convergence status is recorded in any `RootResults` + return object. + + Returns + ------- + root : float + Root of `f` between `a` and `b`. + r : `RootResults` (present if ``full_output = True``) + Object containing information about the convergence. In particular, + ``r.converged`` is True if the routine converged. + + See Also + -------- + fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg : multivariate local optimizers + leastsq : nonlinear least squares minimizer + fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers + basinhopping, differential_evolution, brute : global optimizers + fminbound, brent, golden, bracket : local scalar minimizers + fsolve : N-D root-finding + brentq, brenth, ridder, bisect, newton : 1-D root-finding + fixed_point : scalar fixed-point finder + + References + ---------- + .. [BusAndDekker1975] + Bus, J. C. P., Dekker, T. J., + "Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero + of a Function", ACM Transactions on Mathematical Software, Vol. 1, Issue + 4, Dec. 1975, pp. 330-345. Section 3: "Algorithm M". + :doi:`10.1145/355656.355659` + + Examples + -------- + >>> def f(x): + ... return (x**2 - 1) + + >>> from scipy import optimize + + >>> root = optimize.brenth(f, -2, 0) + >>> root + -1.0 + + >>> root = optimize.brenth(f, 0, 2) + >>> root + 1.0 + + """ + if not isinstance(args, tuple): + args = (args,) + maxiter = operator.index(maxiter) + if xtol <= 0: + raise ValueError("xtol too small (%g <= 0)" % xtol) + if rtol < _rtol: + raise ValueError(f"rtol too small ({rtol:g} < {_rtol:g})") + f = _wrap_nan_raise(f) + r = _zeros._brenth(f, a, b, xtol, rtol, maxiter, args, full_output, disp) + return results_c(full_output, r, "brenth") + + +################################ +# TOMS "Algorithm 748: Enclosing Zeros of Continuous Functions", by +# Alefeld, G. E. and Potra, F. A. and Shi, Yixun, +# See [1] + + +def _notclose(fs, rtol=_rtol, atol=_xtol): + # Ensure not None, not 0, all finite, and not very close to each other + notclosefvals = ( + all(fs) and all(np.isfinite(fs)) and + not any(any(np.isclose(_f, fs[i + 1:], rtol=rtol, atol=atol)) + for i, _f in enumerate(fs[:-1]))) + return notclosefvals + + +def _secant(xvals, fvals): + """Perform a secant step, taking a little care""" + # Secant has many "mathematically" equivalent formulations + # x2 = x0 - (x1 - x0)/(f1 - f0) * f0 + # = x1 - (x1 - x0)/(f1 - f0) * f1 + # = (-x1 * f0 + x0 * f1) / (f1 - f0) + # = (-f0 / f1 * x1 + x0) / (1 - f0 / f1) + # = (-f1 / f0 * x0 + x1) / (1 - f1 / f0) + x0, x1 = xvals[:2] + f0, f1 = fvals[:2] + if f0 == f1: + return np.nan + if np.abs(f1) > np.abs(f0): + x2 = (-f0 / f1 * x1 + x0) / (1 - f0 / f1) + else: + x2 = (-f1 / f0 * x0 + x1) / (1 - f1 / f0) + return x2 + + +def _update_bracket(ab, fab, c, fc): + """Update a bracket given (c, fc), return the discarded endpoints.""" + fa, fb = fab + idx = (0 if np.sign(fa) * np.sign(fc) > 0 else 1) + rx, rfx = ab[idx], fab[idx] + fab[idx] = fc + ab[idx] = c + return rx, rfx + + +def _compute_divided_differences(xvals, fvals, N=None, full=True, + forward=True): + """Return a matrix of divided differences for the xvals, fvals pairs + + DD[i, j] = f[x_{i-j}, ..., x_i] for 0 <= j <= i + + If full is False, just return the main diagonal(or last row): + f[a], f[a, b] and f[a, b, c]. + If forward is False, return f[c], f[b, c], f[a, b, c].""" + if full: + if forward: + xvals = np.asarray(xvals) + else: + xvals = np.array(xvals)[::-1] + M = len(xvals) + N = M if N is None else min(N, M) + DD = np.zeros([M, N]) + DD[:, 0] = fvals[:] + for i in range(1, N): + DD[i:, i] = (np.diff(DD[i - 1:, i - 1]) / + (xvals[i:] - xvals[:M - i])) + return DD + + xvals = np.asarray(xvals) + dd = np.array(fvals) + row = np.array(fvals) + idx2Use = (0 if forward else -1) + dd[0] = fvals[idx2Use] + for i in range(1, len(xvals)): + denom = xvals[i:i + len(row) - 1] - xvals[:len(row) - 1] + row = np.diff(row)[:] / denom + dd[i] = row[idx2Use] + return dd + + +def _interpolated_poly(xvals, fvals, x): + """Compute p(x) for the polynomial passing through the specified locations. + + Use Neville's algorithm to compute p(x) where p is the minimal degree + polynomial passing through the points xvals, fvals""" + xvals = np.asarray(xvals) + N = len(xvals) + Q = np.zeros([N, N]) + D = np.zeros([N, N]) + Q[:, 0] = fvals[:] + D[:, 0] = fvals[:] + for k in range(1, N): + alpha = D[k:, k - 1] - Q[k - 1:N - 1, k - 1] + diffik = xvals[0:N - k] - xvals[k:N] + Q[k:, k] = (xvals[k:] - x) / diffik * alpha + D[k:, k] = (xvals[:N - k] - x) / diffik * alpha + # Expect Q[-1, 1:] to be small relative to Q[-1, 0] as x approaches a root + return np.sum(Q[-1, 1:]) + Q[-1, 0] + + +def _inverse_poly_zero(a, b, c, d, fa, fb, fc, fd): + """Inverse cubic interpolation f-values -> x-values + + Given four points (fa, a), (fb, b), (fc, c), (fd, d) with + fa, fb, fc, fd all distinct, find poly IP(y) through the 4 points + and compute x=IP(0). + """ + return _interpolated_poly([fa, fb, fc, fd], [a, b, c, d], 0) + + +def _newton_quadratic(ab, fab, d, fd, k): + """Apply Newton-Raphson like steps, using divided differences to approximate f' + + ab is a real interval [a, b] containing a root, + fab holds the real values of f(a), f(b) + d is a real number outside [ab, b] + k is the number of steps to apply + """ + a, b = ab + fa, fb = fab + _, B, A = _compute_divided_differences([a, b, d], [fa, fb, fd], + forward=True, full=False) + + # _P is the quadratic polynomial through the 3 points + def _P(x): + # Horner evaluation of fa + B * (x - a) + A * (x - a) * (x - b) + return (A * (x - b) + B) * (x - a) + fa + + if A == 0: + r = a - fa / B + else: + r = (a if np.sign(A) * np.sign(fa) > 0 else b) + # Apply k Newton-Raphson steps to _P(x), starting from x=r + for i in range(k): + r1 = r - _P(r) / (B + A * (2 * r - a - b)) + if not (ab[0] < r1 < ab[1]): + if (ab[0] < r < ab[1]): + return r + r = sum(ab) / 2.0 + break + r = r1 + + return r + + +class TOMS748Solver: + """Solve f(x, *args) == 0 using Algorithm748 of Alefeld, Potro & Shi. + """ + _MU = 0.5 + _K_MIN = 1 + _K_MAX = 100 # A very high value for real usage. Expect 1, 2, maybe 3. + + def __init__(self): + self.f = None + self.args = None + self.function_calls = 0 + self.iterations = 0 + self.k = 2 + # ab=[a,b] is a global interval containing a root + self.ab = [np.nan, np.nan] + # fab is function values at a, b + self.fab = [np.nan, np.nan] + self.d = None + self.fd = None + self.e = None + self.fe = None + self.disp = False + self.xtol = _xtol + self.rtol = _rtol + self.maxiter = _iter + + def configure(self, xtol, rtol, maxiter, disp, k): + self.disp = disp + self.xtol = xtol + self.rtol = rtol + self.maxiter = maxiter + # Silently replace a low value of k with 1 + self.k = max(k, self._K_MIN) + # Noisily replace a high value of k with self._K_MAX + if self.k > self._K_MAX: + msg = "toms748: Overriding k: ->%d" % self._K_MAX + warnings.warn(msg, RuntimeWarning, stacklevel=3) + self.k = self._K_MAX + + def _callf(self, x, error=True): + """Call the user-supplied function, update book-keeping""" + fx = self.f(x, *self.args) + self.function_calls += 1 + if not np.isfinite(fx) and error: + raise ValueError(f"Invalid function value: f({x:f}) -> {fx} ") + return fx + + def get_result(self, x, flag=_ECONVERGED): + r"""Package the result and statistics into a tuple.""" + return (x, self.function_calls, self.iterations, flag) + + def _update_bracket(self, c, fc): + return _update_bracket(self.ab, self.fab, c, fc) + + def start(self, f, a, b, args=()): + r"""Prepare for the iterations.""" + self.function_calls = 0 + self.iterations = 0 + + self.f = f + self.args = args + self.ab[:] = [a, b] + if not np.isfinite(a) or np.imag(a) != 0: + raise ValueError("Invalid x value: %s " % (a)) + if not np.isfinite(b) or np.imag(b) != 0: + raise ValueError("Invalid x value: %s " % (b)) + + fa = self._callf(a) + if not np.isfinite(fa) or np.imag(fa) != 0: + raise ValueError(f"Invalid function value: f({a:f}) -> {fa} ") + if fa == 0: + return _ECONVERGED, a + fb = self._callf(b) + if not np.isfinite(fb) or np.imag(fb) != 0: + raise ValueError(f"Invalid function value: f({b:f}) -> {fb} ") + if fb == 0: + return _ECONVERGED, b + + if np.sign(fb) * np.sign(fa) > 0: + raise ValueError("f(a) and f(b) must have different signs, but " + f"f({a:e})={fa:e}, f({b:e})={fb:e} ") + self.fab[:] = [fa, fb] + + return _EINPROGRESS, sum(self.ab) / 2.0 + + def get_status(self): + """Determine the current status.""" + a, b = self.ab[:2] + if np.isclose(a, b, rtol=self.rtol, atol=self.xtol): + return _ECONVERGED, sum(self.ab) / 2.0 + if self.iterations >= self.maxiter: + return _ECONVERR, sum(self.ab) / 2.0 + return _EINPROGRESS, sum(self.ab) / 2.0 + + def iterate(self): + """Perform one step in the algorithm. + + Implements Algorithm 4.1(k=1) or 4.2(k=2) in [APS1995] + """ + self.iterations += 1 + eps = np.finfo(float).eps + d, fd, e, fe = self.d, self.fd, self.e, self.fe + ab_width = self.ab[1] - self.ab[0] # Need the start width below + c = None + + for nsteps in range(2, self.k+2): + # If the f-values are sufficiently separated, perform an inverse + # polynomial interpolation step. Otherwise, nsteps repeats of + # an approximate Newton-Raphson step. + if _notclose(self.fab + [fd, fe], rtol=0, atol=32*eps): + c0 = _inverse_poly_zero(self.ab[0], self.ab[1], d, e, + self.fab[0], self.fab[1], fd, fe) + if self.ab[0] < c0 < self.ab[1]: + c = c0 + if c is None: + c = _newton_quadratic(self.ab, self.fab, d, fd, nsteps) + + fc = self._callf(c) + if fc == 0: + return _ECONVERGED, c + + # re-bracket + e, fe = d, fd + d, fd = self._update_bracket(c, fc) + + # u is the endpoint with the smallest f-value + uix = (0 if np.abs(self.fab[0]) < np.abs(self.fab[1]) else 1) + u, fu = self.ab[uix], self.fab[uix] + + _, A = _compute_divided_differences(self.ab, self.fab, + forward=(uix == 0), full=False) + c = u - 2 * fu / A + if np.abs(c - u) > 0.5 * (self.ab[1] - self.ab[0]): + c = sum(self.ab) / 2.0 + else: + if np.isclose(c, u, rtol=eps, atol=0): + # c didn't change (much). + # Either because the f-values at the endpoints have vastly + # differing magnitudes, or because the root is very close to + # that endpoint + frs = np.frexp(self.fab)[1] + if frs[uix] < frs[1 - uix] - 50: # Differ by more than 2**50 + c = (31 * self.ab[uix] + self.ab[1 - uix]) / 32 + else: + # Make a bigger adjustment, about the + # size of the requested tolerance. + mm = (1 if uix == 0 else -1) + adj = mm * np.abs(c) * self.rtol + mm * self.xtol + c = u + adj + if not self.ab[0] < c < self.ab[1]: + c = sum(self.ab) / 2.0 + + fc = self._callf(c) + if fc == 0: + return _ECONVERGED, c + + e, fe = d, fd + d, fd = self._update_bracket(c, fc) + + # If the width of the new interval did not decrease enough, bisect + if self.ab[1] - self.ab[0] > self._MU * ab_width: + e, fe = d, fd + z = sum(self.ab) / 2.0 + fz = self._callf(z) + if fz == 0: + return _ECONVERGED, z + d, fd = self._update_bracket(z, fz) + + # Record d and e for next iteration + self.d, self.fd = d, fd + self.e, self.fe = e, fe + + status, xn = self.get_status() + return status, xn + + def solve(self, f, a, b, args=(), + xtol=_xtol, rtol=_rtol, k=2, maxiter=_iter, disp=True): + r"""Solve f(x) = 0 given an interval containing a root.""" + self.configure(xtol=xtol, rtol=rtol, maxiter=maxiter, disp=disp, k=k) + status, xn = self.start(f, a, b, args) + if status == _ECONVERGED: + return self.get_result(xn) + + # The first step only has two x-values. + c = _secant(self.ab, self.fab) + if not self.ab[0] < c < self.ab[1]: + c = sum(self.ab) / 2.0 + fc = self._callf(c) + if fc == 0: + return self.get_result(c) + + self.d, self.fd = self._update_bracket(c, fc) + self.e, self.fe = None, None + self.iterations += 1 + + while True: + status, xn = self.iterate() + if status == _ECONVERGED: + return self.get_result(xn) + if status == _ECONVERR: + fmt = "Failed to converge after %d iterations, bracket is %s" + if disp: + msg = fmt % (self.iterations + 1, self.ab) + raise RuntimeError(msg) + return self.get_result(xn, _ECONVERR) + + +def toms748(f, a, b, args=(), k=1, + xtol=_xtol, rtol=_rtol, maxiter=_iter, + full_output=False, disp=True): + """ + Find a root using TOMS Algorithm 748 method. + + Implements the Algorithm 748 method of Alefeld, Potro and Shi to find a + root of the function `f` on the interval `[a , b]`, where `f(a)` and + `f(b)` must have opposite signs. + + It uses a mixture of inverse cubic interpolation and + "Newton-quadratic" steps. [APS1995]. + + Parameters + ---------- + f : function + Python function returning a scalar. The function :math:`f` + must be continuous, and :math:`f(a)` and :math:`f(b)` + have opposite signs. + a : scalar, + lower boundary of the search interval + b : scalar, + upper boundary of the search interval + args : tuple, optional + containing extra arguments for the function `f`. + `f` is called by ``f(x, *args)``. + k : int, optional + The number of Newton quadratic steps to perform each + iteration. ``k>=1``. + xtol : scalar, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The + parameter must be positive. + rtol : scalar, optional + The computed root ``x0`` will satisfy ``np.allclose(x, x0, + atol=xtol, rtol=rtol)``, where ``x`` is the exact root. + maxiter : int, optional + If convergence is not achieved in `maxiter` iterations, an error is + raised. Must be >= 0. + full_output : bool, optional + If `full_output` is False, the root is returned. If `full_output` is + True, the return value is ``(x, r)``, where `x` is the root, and `r` is + a `RootResults` object. + disp : bool, optional + If True, raise RuntimeError if the algorithm didn't converge. + Otherwise, the convergence status is recorded in the `RootResults` + return object. + + Returns + ------- + root : float + Approximate root of `f` + r : `RootResults` (present if ``full_output = True``) + Object containing information about the convergence. In particular, + ``r.converged`` is True if the routine converged. + + See Also + -------- + brentq, brenth, ridder, bisect, newton + fsolve : find roots in N dimensions. + + Notes + ----- + `f` must be continuous. + Algorithm 748 with ``k=2`` is asymptotically the most efficient + algorithm known for finding roots of a four times continuously + differentiable function. + In contrast with Brent's algorithm, which may only decrease the length of + the enclosing bracket on the last step, Algorithm 748 decreases it each + iteration with the same asymptotic efficiency as it finds the root. + + For easy statement of efficiency indices, assume that `f` has 4 + continuouous deriviatives. + For ``k=1``, the convergence order is at least 2.7, and with about + asymptotically 2 function evaluations per iteration, the efficiency + index is approximately 1.65. + For ``k=2``, the order is about 4.6 with asymptotically 3 function + evaluations per iteration, and the efficiency index 1.66. + For higher values of `k`, the efficiency index approaches + the kth root of ``(3k-2)``, hence ``k=1`` or ``k=2`` are + usually appropriate. + + References + ---------- + .. [APS1995] + Alefeld, G. E. and Potra, F. A. and Shi, Yixun, + *Algorithm 748: Enclosing Zeros of Continuous Functions*, + ACM Trans. Math. Softw. Volume 221(1995) + doi = {10.1145/210089.210111} + + Examples + -------- + >>> def f(x): + ... return (x**3 - 1) # only one real root at x = 1 + + >>> from scipy import optimize + >>> root, results = optimize.toms748(f, 0, 2, full_output=True) + >>> root + 1.0 + >>> results + converged: True + flag: converged + function_calls: 11 + iterations: 5 + root: 1.0 + method: toms748 + """ + if xtol <= 0: + raise ValueError("xtol too small (%g <= 0)" % xtol) + if rtol < _rtol / 4: + raise ValueError(f"rtol too small ({rtol:g} < {_rtol/4:g})") + maxiter = operator.index(maxiter) + if maxiter < 1: + raise ValueError("maxiter must be greater than 0") + if not np.isfinite(a): + raise ValueError("a is not finite %s" % a) + if not np.isfinite(b): + raise ValueError("b is not finite %s" % b) + if a >= b: + raise ValueError(f"a and b are not an interval [{a}, {b}]") + if not k >= 1: + raise ValueError("k too small (%s < 1)" % k) + + if not isinstance(args, tuple): + args = (args,) + f = _wrap_nan_raise(f) + solver = TOMS748Solver() + result = solver.solve(f, a, b, args=args, k=k, xtol=xtol, rtol=rtol, + maxiter=maxiter, disp=disp) + x, function_calls, iterations, flag = result + return _results_select(full_output, (x, function_calls, iterations, flag), + "toms748") diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cobyla.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cobyla.py new file mode 100644 index 0000000000000000000000000000000000000000..87d111d8fc1634e54d3766a3f1c58abd37ac58cb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cobyla.py @@ -0,0 +1,19 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'OptimizeResult', + 'fmin_cobyla', +] + +def __dir__(): + return __all__ + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="cobyla", + private_modules=["_cobyla_py"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cython_optimize.pxd b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cython_optimize.pxd new file mode 100644 index 0000000000000000000000000000000000000000..d35f8da68b34d3a587f3a99326770d8550a2135c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/cython_optimize.pxd @@ -0,0 +1,11 @@ +# Public Cython API declarations +# +# See doc/source/dev/contributor/public_cython_api.rst for guidelines + + +# The following cimport statement provides legacy ABI +# support. Changing it causes an ABI forward-compatibility break +# (gh-11793), so we currently leave it as is (no further cimport +# statements should be used in this file). +from scipy.optimize.cython_optimize._zeros cimport ( + brentq, brenth, ridder, bisect, zeros_full_output) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/lbfgsb.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/lbfgsb.py new file mode 100644 index 0000000000000000000000000000000000000000..866407cabb3decf0ff72239e6fd372f69f7550c0 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/lbfgsb.py @@ -0,0 +1,23 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'LbfgsInvHessProduct', + 'OptimizeResult', + 'fmin_l_bfgs_b', + 'zeros', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="lbfgsb", + private_modules=["_lbfgsb_py"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/linesearch.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/linesearch.py new file mode 100644 index 0000000000000000000000000000000000000000..cb34b25092da34991c868683da3d6a894d1a7f80 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/linesearch.py @@ -0,0 +1,18 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = ["line_search"] # noqa: F822 + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="linesearch", + private_modules=["_linesearch"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack.py new file mode 100644 index 0000000000000000000000000000000000000000..29fddef537361d8508e6343d23b2c3c7d6d12ec6 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack.py @@ -0,0 +1,27 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'OptimizeResult', + 'OptimizeWarning', + 'curve_fit', + 'fixed_point', + 'fsolve', + 'least_squares', + 'leastsq', + 'zeros', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="minpack", + private_modules=["_minpack_py"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack2.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack2.py new file mode 100644 index 0000000000000000000000000000000000000000..cdb3503e0e1e4c886c89bfb62e6a2efc3ba54549 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/minpack2.py @@ -0,0 +1,17 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + +__all__: list[str] = [] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="minpack2", + private_modules=["_minpack2"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/moduleTNC.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/moduleTNC.py new file mode 100644 index 0000000000000000000000000000000000000000..3fc5884ed5c39437b7681395419d641443a1fdb8 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/moduleTNC.py @@ -0,0 +1,19 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="moduleTNC", + private_modules=["_moduleTNC"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/nonlin.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/nonlin.py new file mode 100644 index 0000000000000000000000000000000000000000..20b490b40ef790a2943d539790b45fc378df2c76 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/nonlin.py @@ -0,0 +1,29 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'BroydenFirst', + 'InverseJacobian', + 'KrylovJacobian', + 'anderson', + 'broyden1', + 'broyden2', + 'diagbroyden', + 'excitingmixing', + 'linearmixing', + 'newton_krylov', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="nonlin", + private_modules=["_nonlin"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/optimize.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/optimize.py new file mode 100644 index 0000000000000000000000000000000000000000..4db770e5f6e921906c916f2650003d92f5507791 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/optimize.py @@ -0,0 +1,40 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'OptimizeResult', + 'OptimizeWarning', + 'approx_fprime', + 'bracket', + 'brent', + 'brute', + 'check_grad', + 'fmin', + 'fmin_bfgs', + 'fmin_cg', + 'fmin_ncg', + 'fmin_powell', + 'fminbound', + 'golden', + 'line_search', + 'rosen', + 'rosen_der', + 'rosen_hess', + 'rosen_hess_prod', + 'show_options', + 'zeros', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="optimize", + private_modules=["_optimize"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/slsqp.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/slsqp.py new file mode 100644 index 0000000000000000000000000000000000000000..c2b77d2eb447527cd91e92907e06ad53dd1ad3d8 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/slsqp.py @@ -0,0 +1,23 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'OptimizeResult', + 'fmin_slsqp', + 'slsqp', + 'zeros', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="slsqp", + private_modules=["_slsqp_py"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_cobyqa.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_cobyqa.py new file mode 100644 index 0000000000000000000000000000000000000000..a77cca135849d015dfa1be25d6b1752b731776c5 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_cobyqa.py @@ -0,0 +1,246 @@ +import numpy as np +import pytest +from numpy.testing import assert_allclose, assert_equal + +from scipy.optimize import ( + Bounds, + LinearConstraint, + NonlinearConstraint, + OptimizeResult, + minimize, +) + + +class TestCOBYQA: + + def setup_method(self): + self.x0 = [4.95, 0.66] + self.options = {'maxfev': 100} + + @staticmethod + def fun(x, c=1.0): + return x[0]**2 + c * abs(x[1])**3 + + @staticmethod + def con(x): + return x[0]**2 + x[1]**2 - 25.0 + + def test_minimize_simple(self): + class Callback: + def __init__(self): + self.n_calls = 0 + + def __call__(self, x): + assert isinstance(x, np.ndarray) + self.n_calls += 1 + + class CallbackNewSyntax: + def __init__(self): + self.n_calls = 0 + + def __call__(self, intermediate_result): + assert isinstance(intermediate_result, OptimizeResult) + self.n_calls += 1 + + callback = Callback() + callback_new_syntax = CallbackNewSyntax() + + # Minimize with method='cobyqa'. + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + callback=callback, + options=self.options, + ) + sol_new = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + callback=callback_new_syntax, + options=self.options, + ) + solution = [np.sqrt(25.0 - 4.0 / 9.0), 2.0 / 3.0] + assert_allclose(sol.x, solution, atol=1e-4) + assert sol.success, sol.message + assert sol.maxcv < 1e-8, sol + assert sol.nfev <= 100, sol + assert sol.fun < self.fun(solution) + 1e-3, sol + assert sol.nfev == callback.n_calls, \ + "Callback is not called exactly once for every function eval." + assert_equal(sol.x, sol_new.x) + assert sol_new.success, sol_new.message + assert sol.fun == sol_new.fun + assert sol.maxcv == sol_new.maxcv + assert sol.nfev == sol_new.nfev + assert sol.nit == sol_new.nit + assert sol_new.nfev == callback_new_syntax.n_calls, \ + "Callback is not called exactly once for every function eval." + + def test_minimize_bounds(self): + def fun_check_bounds(x): + assert np.all(bounds.lb <= x) and np.all(x <= bounds.ub) + return self.fun(x) + + # Case where the bounds are not active at the solution. + bounds = Bounds([4.5, 0.6], [5.0, 0.7]) + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + sol = minimize( + fun_check_bounds, + self.x0, + method='cobyqa', + bounds=bounds, + constraints=constraints, + options=self.options, + ) + solution = [np.sqrt(25.0 - 4.0 / 9.0), 2.0 / 3.0] + assert_allclose(sol.x, solution, atol=1e-4) + assert sol.success, sol.message + assert sol.maxcv < 1e-8, sol + assert np.all(bounds.lb <= sol.x) and np.all(sol.x <= bounds.ub), sol + assert sol.nfev <= 100, sol + assert sol.fun < self.fun(solution) + 1e-3, sol + + # Case where the bounds are active at the solution. + bounds = Bounds([5.0, 0.6], [5.5, 0.65]) + sol = minimize( + fun_check_bounds, + self.x0, + method='cobyqa', + bounds=bounds, + constraints=constraints, + options=self.options, + ) + assert not sol.success, sol.message + assert sol.maxcv > 0.35, sol + assert np.all(bounds.lb <= sol.x) and np.all(sol.x <= bounds.ub), sol + assert sol.nfev <= 100, sol + + def test_minimize_linear_constraints(self): + constraints = LinearConstraint([1.0, 1.0], 1.0, 1.0) + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + options=self.options, + ) + solution = [(4 - np.sqrt(7)) / 3, (np.sqrt(7) - 1) / 3] + assert_allclose(sol.x, solution, atol=1e-4) + assert sol.success, sol.message + assert sol.maxcv < 1e-8, sol + assert sol.nfev <= 100, sol + assert sol.fun < self.fun(solution) + 1e-3, sol + + def test_minimize_args(self): + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + sol = minimize( + self.fun, + self.x0, + args=(2.0,), + method='cobyqa', + constraints=constraints, + options=self.options, + ) + solution = [np.sqrt(25.0 - 4.0 / 36.0), 2.0 / 6.0] + assert_allclose(sol.x, solution, atol=1e-4) + assert sol.success, sol.message + assert sol.maxcv < 1e-8, sol + assert sol.nfev <= 100, sol + assert sol.fun < self.fun(solution, 2.0) + 1e-3, sol + + def test_minimize_array(self): + def fun_array(x, dim): + f = np.array(self.fun(x)) + return np.reshape(f, (1,) * dim) + + # The argument fun can return an array with a single element. + bounds = Bounds([4.5, 0.6], [5.0, 0.7]) + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + bounds=bounds, + constraints=constraints, + options=self.options, + ) + for dim in [0, 1, 2]: + sol_array = minimize( + fun_array, + self.x0, + args=(dim,), + method='cobyqa', + bounds=bounds, + constraints=constraints, + options=self.options, + ) + assert_equal(sol.x, sol_array.x) + assert sol_array.success, sol_array.message + assert sol.fun == sol_array.fun + assert sol.maxcv == sol_array.maxcv + assert sol.nfev == sol_array.nfev + assert sol.nit == sol_array.nit + + # The argument fun cannot return an array with more than one element. + with pytest.raises(TypeError): + minimize( + lambda x: np.array([self.fun(x), self.fun(x)]), + self.x0, + method='cobyqa', + bounds=bounds, + constraints=constraints, + options=self.options, + ) + + def test_minimize_maxfev(self): + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + options = {'maxfev': 2} + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + options=options, + ) + assert not sol.success, sol.message + assert sol.nfev <= 2, sol + + def test_minimize_maxiter(self): + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + options = {'maxiter': 2} + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + options=options, + ) + assert not sol.success, sol.message + assert sol.nit <= 2, sol + + def test_minimize_f_target(self): + constraints = NonlinearConstraint(self.con, 0.0, 0.0) + sol_ref = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + options=self.options, + ) + options = dict(self.options) + options['f_target'] = sol_ref.fun + sol = minimize( + self.fun, + self.x0, + method='cobyqa', + constraints=constraints, + options=options, + ) + assert sol.success, sol.message + assert sol.maxcv < 1e-8, sol + assert sol.nfev <= sol_ref.nfev, sol + assert sol.fun <= sol_ref.fun, sol diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_constraint_conversion.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_constraint_conversion.py new file mode 100644 index 0000000000000000000000000000000000000000..df5ab6dee478742ba7fef2eaaa503fe6781b83a8 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_constraint_conversion.py @@ -0,0 +1,278 @@ +""" +Unit test for constraint conversion +""" + +import numpy as np +from numpy.testing import (assert_array_almost_equal, + assert_allclose, assert_warns, suppress_warnings) +import pytest +from scipy.optimize import (NonlinearConstraint, LinearConstraint, + OptimizeWarning, minimize, BFGS) +from .test_minimize_constrained import (Maratos, HyperbolicIneq, Rosenbrock, + IneqRosenbrock, EqIneqRosenbrock, + BoundedRosenbrock, Elec) + + +class TestOldToNew: + x0 = (2, 0) + bnds = ((0, None), (0, None)) + method = "trust-constr" + + def test_constraint_dictionary_1(self): + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + cons = ({'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2}, + {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6}, + {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2}) + + with suppress_warnings() as sup: + sup.filter(UserWarning, "delta_grad == 0.0") + res = minimize(fun, self.x0, method=self.method, + bounds=self.bnds, constraints=cons) + assert_allclose(res.x, [1.4, 1.7], rtol=1e-4) + assert_allclose(res.fun, 0.8, rtol=1e-4) + + def test_constraint_dictionary_2(self): + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + cons = {'type': 'eq', + 'fun': lambda x, p1, p2: p1*x[0] - p2*x[1], + 'args': (1, 1.1), + 'jac': lambda x, p1, p2: np.array([[p1, -p2]])} + with suppress_warnings() as sup: + sup.filter(UserWarning, "delta_grad == 0.0") + res = minimize(fun, self.x0, method=self.method, + bounds=self.bnds, constraints=cons) + assert_allclose(res.x, [1.7918552, 1.62895927]) + assert_allclose(res.fun, 1.3857466063348418) + + def test_constraint_dictionary_3(self): + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + cons = [{'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2}, + NonlinearConstraint(lambda x: x[0] - x[1], 0, 0)] + + with suppress_warnings() as sup: + sup.filter(UserWarning, "delta_grad == 0.0") + res = minimize(fun, self.x0, method=self.method, + bounds=self.bnds, constraints=cons) + assert_allclose(res.x, [1.75, 1.75], rtol=1e-4) + assert_allclose(res.fun, 1.125, rtol=1e-4) + + +class TestNewToOld: + + def test_multiple_constraint_objects(self): + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2 + x0 = [2, 0, 1] + coni = [] # only inequality constraints (can use cobyla) + methods = ["slsqp", "cobyla", "cobyqa", "trust-constr"] + + # mixed old and new + coni.append([{'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2}, + NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)]) + + coni.append([LinearConstraint([1, -2, 0], -2, np.inf), + NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)]) + + coni.append([NonlinearConstraint(lambda x: x[0] - 2 * x[1] + 2, 0, np.inf), + NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)]) + + for con in coni: + funs = {} + for method in methods: + with suppress_warnings() as sup: + sup.filter(UserWarning) + result = minimize(fun, x0, method=method, constraints=con) + funs[method] = result.fun + assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-4) + assert_allclose(funs['cobyla'], funs['trust-constr'], rtol=1e-4) + assert_allclose(funs['cobyqa'], funs['trust-constr'], rtol=1e-4) + + @pytest.mark.fail_slow(10) + def test_individual_constraint_objects(self): + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2 + x0 = [2, 0, 1] + + cone = [] # with equality constraints (can't use cobyla) + coni = [] # only inequality constraints (can use cobyla) + methods = ["slsqp", "cobyla", "cobyqa", "trust-constr"] + + # nonstandard data types for constraint equality bounds + cone.append(NonlinearConstraint(lambda x: x[0] - x[1], 1, 1)) + cone.append(NonlinearConstraint(lambda x: x[0] - x[1], [1.21], [1.21])) + cone.append(NonlinearConstraint(lambda x: x[0] - x[1], + 1.21, np.array([1.21]))) + + # multiple equalities + cone.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + 1.21, 1.21)) # two same equalities + cone.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [1.21, 1.4], [1.21, 1.4])) # two different equalities + cone.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [1.21, 1.21], 1.21)) # equality specified two ways + cone.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [1.21, -np.inf], [1.21, np.inf])) # equality + unbounded + + # nonstandard data types for constraint inequality bounds + coni.append(NonlinearConstraint(lambda x: x[0] - x[1], 1.21, np.inf)) + coni.append(NonlinearConstraint(lambda x: x[0] - x[1], [1.21], np.inf)) + coni.append(NonlinearConstraint(lambda x: x[0] - x[1], + 1.21, np.array([np.inf]))) + coni.append(NonlinearConstraint(lambda x: x[0] - x[1], -np.inf, -3)) + coni.append(NonlinearConstraint(lambda x: x[0] - x[1], + np.array(-np.inf), -3)) + + # multiple inequalities/equalities + coni.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + 1.21, np.inf)) # two same inequalities + cone.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [1.21, -np.inf], [1.21, 1.4])) # mixed equality/inequality + coni.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [1.1, .8], [1.2, 1.4])) # bounded above and below + coni.append(NonlinearConstraint( + lambda x: [x[0] - x[1], x[1] - x[2]], + [-1.2, -1.4], [-1.1, -.8])) # - bounded above and below + + # quick check of LinearConstraint class (very little new code to test) + cone.append(LinearConstraint([1, -1, 0], 1.21, 1.21)) + cone.append(LinearConstraint([[1, -1, 0], [0, 1, -1]], 1.21, 1.21)) + cone.append(LinearConstraint([[1, -1, 0], [0, 1, -1]], + [1.21, -np.inf], [1.21, 1.4])) + + for con in coni: + funs = {} + for method in methods: + with suppress_warnings() as sup: + sup.filter(UserWarning) + result = minimize(fun, x0, method=method, constraints=con) + funs[method] = result.fun + assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-3) + assert_allclose(funs['cobyla'], funs['trust-constr'], rtol=1e-3) + assert_allclose(funs['cobyqa'], funs['trust-constr'], rtol=1e-3) + + for con in cone: + funs = {} + for method in [method for method in methods if method != 'cobyla']: + with suppress_warnings() as sup: + sup.filter(UserWarning) + result = minimize(fun, x0, method=method, constraints=con) + funs[method] = result.fun + assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-3) + assert_allclose(funs['cobyqa'], funs['trust-constr'], rtol=1e-3) + + +class TestNewToOldSLSQP: + method = 'slsqp' + elec = Elec(n_electrons=2) + elec.x_opt = np.array([-0.58438468, 0.58438466, 0.73597047, + -0.73597044, 0.34180668, -0.34180667]) + brock = BoundedRosenbrock() + brock.x_opt = [0, 0] + list_of_problems = [Maratos(), + HyperbolicIneq(), + Rosenbrock(), + IneqRosenbrock(), + EqIneqRosenbrock(), + elec, + brock + ] + + def test_list_of_problems(self): + + for prob in self.list_of_problems: + + with suppress_warnings() as sup: + sup.filter(UserWarning) + result = minimize(prob.fun, prob.x0, + method=self.method, + bounds=prob.bounds, + constraints=prob.constr) + + assert_array_almost_equal(result.x, prob.x_opt, decimal=3) + + def test_warn_mixed_constraints(self): + # warns about inefficiency of mixed equality/inequality constraints + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2 + cons = NonlinearConstraint(lambda x: [x[0]**2 - x[1], x[1] - x[2]], + [1.1, .8], [1.1, 1.4]) + bnds = ((0, None), (0, None), (0, None)) + with suppress_warnings() as sup: + sup.filter(UserWarning, "delta_grad == 0.0") + assert_warns(OptimizeWarning, minimize, fun, (2, 0, 1), + method=self.method, bounds=bnds, constraints=cons) + + def test_warn_ignored_options(self): + # warns about constraint options being ignored + def fun(x): + return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 + (x[2] - 0.75) ** 2 + x0 = (2, 0, 1) + + if self.method == "slsqp": + bnds = ((0, None), (0, None), (0, None)) + else: + bnds = None + + cons = NonlinearConstraint(lambda x: x[0], 2, np.inf) + res = minimize(fun, x0, method=self.method, + bounds=bnds, constraints=cons) + # no warnings without constraint options + assert_allclose(res.fun, 1) + + cons = LinearConstraint([1, 0, 0], 2, np.inf) + res = minimize(fun, x0, method=self.method, + bounds=bnds, constraints=cons) + # no warnings without constraint options + assert_allclose(res.fun, 1) + + cons = [] + cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf, + keep_feasible=True)) + cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf, + hess=BFGS())) + cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf, + finite_diff_jac_sparsity=42)) + cons.append(NonlinearConstraint(lambda x: x[0]**2, 2, np.inf, + finite_diff_rel_step=42)) + cons.append(LinearConstraint([1, 0, 0], 2, np.inf, + keep_feasible=True)) + for con in cons: + assert_warns(OptimizeWarning, minimize, fun, x0, + method=self.method, bounds=bnds, constraints=cons) + + +class TestNewToOldCobyla: + method = 'cobyla' + + list_of_problems = [ + Elec(n_electrons=2), + Elec(n_electrons=4), + ] + + @pytest.mark.slow + def test_list_of_problems(self): + + for prob in self.list_of_problems: + + with suppress_warnings() as sup: + sup.filter(UserWarning) + truth = minimize(prob.fun, prob.x0, + method='trust-constr', + bounds=prob.bounds, + constraints=prob.constr) + result = minimize(prob.fun, prob.x0, + method=self.method, + bounds=prob.bounds, + constraints=prob.constr) + + assert_allclose(result.fun, truth.fun, rtol=1e-3) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_linesearch.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_linesearch.py new file mode 100644 index 0000000000000000000000000000000000000000..f5ae5cc6f4d4065de7a33dab79edb44d550bfeeb --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_linesearch.py @@ -0,0 +1,314 @@ +""" +Tests for line search routines +""" +from numpy.testing import (assert_equal, assert_array_almost_equal, + assert_array_almost_equal_nulp, assert_warns, + suppress_warnings) +import scipy.optimize._linesearch as ls +from scipy.optimize._linesearch import LineSearchWarning +import numpy as np + + +def assert_wolfe(s, phi, derphi, c1=1e-4, c2=0.9, err_msg=""): + """ + Check that strong Wolfe conditions apply + """ + phi1 = phi(s) + phi0 = phi(0) + derphi0 = derphi(0) + derphi1 = derphi(s) + msg = (f"s = {s}; phi(0) = {phi0}; phi(s) = {phi1}; phi'(0) = {derphi0};" + f" phi'(s) = {derphi1}; {err_msg}") + + assert phi1 <= phi0 + c1*s*derphi0, "Wolfe 1 failed: " + msg + assert abs(derphi1) <= abs(c2*derphi0), "Wolfe 2 failed: " + msg + + +def assert_armijo(s, phi, c1=1e-4, err_msg=""): + """ + Check that Armijo condition applies + """ + phi1 = phi(s) + phi0 = phi(0) + msg = f"s = {s}; phi(0) = {phi0}; phi(s) = {phi1}; {err_msg}" + assert phi1 <= (1 - c1*s)*phi0, msg + + +def assert_line_wolfe(x, p, s, f, fprime, **kw): + assert_wolfe(s, phi=lambda sp: f(x + p*sp), + derphi=lambda sp: np.dot(fprime(x + p*sp), p), **kw) + + +def assert_line_armijo(x, p, s, f, **kw): + assert_armijo(s, phi=lambda sp: f(x + p*sp), **kw) + + +def assert_fp_equal(x, y, err_msg="", nulp=50): + """Assert two arrays are equal, up to some floating-point rounding error""" + try: + assert_array_almost_equal_nulp(x, y, nulp) + except AssertionError as e: + raise AssertionError(f"{e}\n{err_msg}") from e + + +class TestLineSearch: + # -- scalar functions; must have dphi(0.) < 0 + def _scalar_func_1(self, s): # skip name check + self.fcount += 1 + p = -s - s**3 + s**4 + dp = -1 - 3*s**2 + 4*s**3 + return p, dp + + def _scalar_func_2(self, s): # skip name check + self.fcount += 1 + p = np.exp(-4*s) + s**2 + dp = -4*np.exp(-4*s) + 2*s + return p, dp + + def _scalar_func_3(self, s): # skip name check + self.fcount += 1 + p = -np.sin(10*s) + dp = -10*np.cos(10*s) + return p, dp + + # -- n-d functions + + def _line_func_1(self, x): # skip name check + self.fcount += 1 + f = np.dot(x, x) + df = 2*x + return f, df + + def _line_func_2(self, x): # skip name check + self.fcount += 1 + f = np.dot(x, np.dot(self.A, x)) + 1 + df = np.dot(self.A + self.A.T, x) + return f, df + + # -- + + def setup_method(self): + self.scalar_funcs = [] + self.line_funcs = [] + self.N = 20 + self.fcount = 0 + + def bind_index(func, idx): + # Remember Python's closure semantics! + return lambda *a, **kw: func(*a, **kw)[idx] + + for name in sorted(dir(self)): + if name.startswith('_scalar_func_'): + value = getattr(self, name) + self.scalar_funcs.append( + (name, bind_index(value, 0), bind_index(value, 1))) + elif name.startswith('_line_func_'): + value = getattr(self, name) + self.line_funcs.append( + (name, bind_index(value, 0), bind_index(value, 1))) + + np.random.seed(1234) + self.A = np.random.randn(self.N, self.N) + + def scalar_iter(self): + for name, phi, derphi in self.scalar_funcs: + for old_phi0 in np.random.randn(3): + yield name, phi, derphi, old_phi0 + + def line_iter(self): + for name, f, fprime in self.line_funcs: + k = 0 + while k < 9: + x = np.random.randn(self.N) + p = np.random.randn(self.N) + if np.dot(p, fprime(x)) >= 0: + # always pick a descent direction + continue + k += 1 + old_fv = float(np.random.randn()) + yield name, f, fprime, x, p, old_fv + + # -- Generic scalar searches + + def test_scalar_search_wolfe1(self): + c = 0 + for name, phi, derphi, old_phi0 in self.scalar_iter(): + c += 1 + s, phi1, phi0 = ls.scalar_search_wolfe1(phi, derphi, phi(0), + old_phi0, derphi(0)) + assert_fp_equal(phi0, phi(0), name) + assert_fp_equal(phi1, phi(s), name) + assert_wolfe(s, phi, derphi, err_msg=name) + + assert c > 3 # check that the iterator really works... + + def test_scalar_search_wolfe2(self): + for name, phi, derphi, old_phi0 in self.scalar_iter(): + s, phi1, phi0, derphi1 = ls.scalar_search_wolfe2( + phi, derphi, phi(0), old_phi0, derphi(0)) + assert_fp_equal(phi0, phi(0), name) + assert_fp_equal(phi1, phi(s), name) + if derphi1 is not None: + assert_fp_equal(derphi1, derphi(s), name) + assert_wolfe(s, phi, derphi, err_msg=f"{name} {old_phi0:g}") + + def test_scalar_search_wolfe2_with_low_amax(self): + def phi(alpha): + return (alpha - 5) ** 2 + + def derphi(alpha): + return 2 * (alpha - 5) + + alpha_star, _, _, derphi_star = ls.scalar_search_wolfe2(phi, derphi, amax=0.001) + assert alpha_star is None # Not converged + assert derphi_star is None # Not converged + + def test_scalar_search_wolfe2_regression(self): + # Regression test for gh-12157 + # This phi has its minimum at alpha=4/3 ~ 1.333. + def phi(alpha): + if alpha < 1: + return - 3*np.pi/2 * (alpha - 1) + else: + return np.cos(3*np.pi/2 * alpha - np.pi) + + def derphi(alpha): + if alpha < 1: + return - 3*np.pi/2 + else: + return - 3*np.pi/2 * np.sin(3*np.pi/2 * alpha - np.pi) + + s, _, _, _ = ls.scalar_search_wolfe2(phi, derphi) + # Without the fix in gh-13073, the scalar_search_wolfe2 + # returned s=2.0 instead. + assert s < 1.5 + + def test_scalar_search_armijo(self): + for name, phi, derphi, old_phi0 in self.scalar_iter(): + s, phi1 = ls.scalar_search_armijo(phi, phi(0), derphi(0)) + assert_fp_equal(phi1, phi(s), name) + assert_armijo(s, phi, err_msg=f"{name} {old_phi0:g}") + + # -- Generic line searches + + def test_line_search_wolfe1(self): + c = 0 + smax = 100 + for name, f, fprime, x, p, old_f in self.line_iter(): + f0 = f(x) + g0 = fprime(x) + self.fcount = 0 + s, fc, gc, fv, ofv, gv = ls.line_search_wolfe1(f, fprime, x, p, + g0, f0, old_f, + amax=smax) + assert_equal(self.fcount, fc+gc) + assert_fp_equal(ofv, f(x)) + if s is None: + continue + assert_fp_equal(fv, f(x + s*p)) + assert_array_almost_equal(gv, fprime(x + s*p), decimal=14) + if s < smax: + c += 1 + assert_line_wolfe(x, p, s, f, fprime, err_msg=name) + + assert c > 3 # check that the iterator really works... + + def test_line_search_wolfe2(self): + c = 0 + smax = 512 + for name, f, fprime, x, p, old_f in self.line_iter(): + f0 = f(x) + g0 = fprime(x) + self.fcount = 0 + with suppress_warnings() as sup: + sup.filter(LineSearchWarning, + "The line search algorithm could not find a solution") + sup.filter(LineSearchWarning, + "The line search algorithm did not converge") + s, fc, gc, fv, ofv, gv = ls.line_search_wolfe2(f, fprime, x, p, + g0, f0, old_f, + amax=smax) + assert_equal(self.fcount, fc+gc) + assert_fp_equal(ofv, f(x)) + assert_fp_equal(fv, f(x + s*p)) + if gv is not None: + assert_array_almost_equal(gv, fprime(x + s*p), decimal=14) + if s < smax: + c += 1 + assert_line_wolfe(x, p, s, f, fprime, err_msg=name) + assert c > 3 # check that the iterator really works... + + def test_line_search_wolfe2_bounds(self): + # See gh-7475 + + # For this f and p, starting at a point on axis 0, the strong Wolfe + # condition 2 is met if and only if the step length s satisfies + # |x + s| <= c2 * |x| + def f(x): + return np.dot(x, x) + def fp(x): + return 2 * x + p = np.array([1, 0]) + + # Smallest s satisfying strong Wolfe conditions for these arguments is 30 + x = -60 * p + c2 = 0.5 + + s, _, _, _, _, _ = ls.line_search_wolfe2(f, fp, x, p, amax=30, c2=c2) + assert_line_wolfe(x, p, s, f, fp) + + s, _, _, _, _, _ = assert_warns(LineSearchWarning, + ls.line_search_wolfe2, f, fp, x, p, + amax=29, c2=c2) + assert s is None + + # s=30 will only be tried on the 6th iteration, so this won't converge + assert_warns(LineSearchWarning, ls.line_search_wolfe2, f, fp, x, p, + c2=c2, maxiter=5) + + def test_line_search_armijo(self): + c = 0 + for name, f, fprime, x, p, old_f in self.line_iter(): + f0 = f(x) + g0 = fprime(x) + self.fcount = 0 + s, fc, fv = ls.line_search_armijo(f, x, p, g0, f0) + c += 1 + assert_equal(self.fcount, fc) + assert_fp_equal(fv, f(x + s*p)) + assert_line_armijo(x, p, s, f, err_msg=name) + assert c >= 9 + + # -- More specific tests + + def test_armijo_terminate_1(self): + # Armijo should evaluate the function only once if the trial step + # is already suitable + count = [0] + + def phi(s): + count[0] += 1 + return -s + 0.01*s**2 + s, phi1 = ls.scalar_search_armijo(phi, phi(0), -1, alpha0=1) + assert_equal(s, 1) + assert_equal(count[0], 2) + assert_armijo(s, phi) + + def test_wolfe_terminate(self): + # wolfe1 and wolfe2 should also evaluate the function only a few + # times if the trial step is already suitable + + def phi(s): + count[0] += 1 + return -s + 0.05*s**2 + + def derphi(s): + count[0] += 1 + return -1 + 0.05*2*s + + for func in [ls.scalar_search_wolfe1, ls.scalar_search_wolfe2]: + count = [0] + r = func(phi, derphi, phi(0), None, derphi(0)) + assert r[0] is not None, (r, func) + assert count[0] <= 2 + 2, (count, func) + assert_wolfe(r[0], phi, derphi, err_msg=str(func)) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_lsq_common.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_lsq_common.py new file mode 100644 index 0000000000000000000000000000000000000000..650deedce88b6babd8a3f2b62a5839f1a6cb966c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_lsq_common.py @@ -0,0 +1,297 @@ +from numpy.testing import assert_, assert_allclose, assert_equal +from pytest import raises as assert_raises +import numpy as np + +from scipy.optimize._lsq.common import ( + step_size_to_bound, find_active_constraints, make_strictly_feasible, + CL_scaling_vector, intersect_trust_region, build_quadratic_1d, + minimize_quadratic_1d, evaluate_quadratic, reflective_transformation, + left_multiplied_operator, right_multiplied_operator) + + +class TestBounds: + def test_step_size_to_bounds(self): + lb = np.array([-1.0, 2.5, 10.0]) + ub = np.array([1.0, 5.0, 100.0]) + x = np.array([0.0, 2.5, 12.0]) + + s = np.array([0.1, 0.0, 0.0]) + step, hits = step_size_to_bound(x, s, lb, ub) + assert_equal(step, 10) + assert_equal(hits, [1, 0, 0]) + + s = np.array([0.01, 0.05, -1.0]) + step, hits = step_size_to_bound(x, s, lb, ub) + assert_equal(step, 2) + assert_equal(hits, [0, 0, -1]) + + s = np.array([10.0, -0.0001, 100.0]) + step, hits = step_size_to_bound(x, s, lb, ub) + assert_equal(step, np.array(-0)) + assert_equal(hits, [0, -1, 0]) + + s = np.array([1.0, 0.5, -2.0]) + step, hits = step_size_to_bound(x, s, lb, ub) + assert_equal(step, 1.0) + assert_equal(hits, [1, 0, -1]) + + s = np.zeros(3) + step, hits = step_size_to_bound(x, s, lb, ub) + assert_equal(step, np.inf) + assert_equal(hits, [0, 0, 0]) + + def test_find_active_constraints(self): + lb = np.array([0.0, -10.0, 1.0]) + ub = np.array([1.0, 0.0, 100.0]) + + x = np.array([0.5, -5.0, 2.0]) + active = find_active_constraints(x, lb, ub) + assert_equal(active, [0, 0, 0]) + + x = np.array([0.0, 0.0, 10.0]) + active = find_active_constraints(x, lb, ub) + assert_equal(active, [-1, 1, 0]) + + active = find_active_constraints(x, lb, ub, rtol=0) + assert_equal(active, [-1, 1, 0]) + + x = np.array([1e-9, -1e-8, 100 - 1e-9]) + active = find_active_constraints(x, lb, ub) + assert_equal(active, [0, 0, 1]) + + active = find_active_constraints(x, lb, ub, rtol=1.5e-9) + assert_equal(active, [-1, 0, 1]) + + lb = np.array([1.0, -np.inf, -np.inf]) + ub = np.array([np.inf, 10.0, np.inf]) + + x = np.ones(3) + active = find_active_constraints(x, lb, ub) + assert_equal(active, [-1, 0, 0]) + + # Handles out-of-bound cases. + x = np.array([0.0, 11.0, 0.0]) + active = find_active_constraints(x, lb, ub) + assert_equal(active, [-1, 1, 0]) + + active = find_active_constraints(x, lb, ub, rtol=0) + assert_equal(active, [-1, 1, 0]) + + def test_make_strictly_feasible(self): + lb = np.array([-0.5, -0.8, 2.0]) + ub = np.array([0.8, 1.0, 3.0]) + + x = np.array([-0.5, 0.0, 2 + 1e-10]) + + x_new = make_strictly_feasible(x, lb, ub, rstep=0) + assert_(x_new[0] > -0.5) + assert_equal(x_new[1:], x[1:]) + + x_new = make_strictly_feasible(x, lb, ub, rstep=1e-4) + assert_equal(x_new, [-0.5 + 1e-4, 0.0, 2 * (1 + 1e-4)]) + + x = np.array([-0.5, -1, 3.1]) + x_new = make_strictly_feasible(x, lb, ub) + assert_(np.all((x_new >= lb) & (x_new <= ub))) + + x_new = make_strictly_feasible(x, lb, ub, rstep=0) + assert_(np.all((x_new >= lb) & (x_new <= ub))) + + lb = np.array([-1, 100.0]) + ub = np.array([1, 100.0 + 1e-10]) + x = np.array([0, 100.0]) + x_new = make_strictly_feasible(x, lb, ub, rstep=1e-8) + assert_equal(x_new, [0, 100.0 + 0.5e-10]) + + def test_scaling_vector(self): + lb = np.array([-np.inf, -5.0, 1.0, -np.inf]) + ub = np.array([1.0, np.inf, 10.0, np.inf]) + x = np.array([0.5, 2.0, 5.0, 0.0]) + g = np.array([1.0, 0.1, -10.0, 0.0]) + v, dv = CL_scaling_vector(x, g, lb, ub) + assert_equal(v, [1.0, 7.0, 5.0, 1.0]) + assert_equal(dv, [0.0, 1.0, -1.0, 0.0]) + + +class TestQuadraticFunction: + def setup_method(self): + self.J = np.array([ + [0.1, 0.2], + [-1.0, 1.0], + [0.5, 0.2]]) + self.g = np.array([0.8, -2.0]) + self.diag = np.array([1.0, 2.0]) + + def test_build_quadratic_1d(self): + s = np.zeros(2) + a, b = build_quadratic_1d(self.J, self.g, s) + assert_equal(a, 0) + assert_equal(b, 0) + + a, b = build_quadratic_1d(self.J, self.g, s, diag=self.diag) + assert_equal(a, 0) + assert_equal(b, 0) + + s = np.array([1.0, -1.0]) + a, b = build_quadratic_1d(self.J, self.g, s) + assert_equal(a, 2.05) + assert_equal(b, 2.8) + + a, b = build_quadratic_1d(self.J, self.g, s, diag=self.diag) + assert_equal(a, 3.55) + assert_equal(b, 2.8) + + s0 = np.array([0.5, 0.5]) + a, b, c = build_quadratic_1d(self.J, self.g, s, diag=self.diag, s0=s0) + assert_equal(a, 3.55) + assert_allclose(b, 2.39) + assert_allclose(c, -0.1525) + + def test_minimize_quadratic_1d(self): + a = 5 + b = -1 + + t, y = minimize_quadratic_1d(a, b, 1, 2) + assert_equal(t, 1) + assert_allclose(y, a * t**2 + b * t, rtol=1e-15) + + t, y = minimize_quadratic_1d(a, b, -2, -1) + assert_equal(t, -1) + assert_allclose(y, a * t**2 + b * t, rtol=1e-15) + + t, y = minimize_quadratic_1d(a, b, -1, 1) + assert_equal(t, 0.1) + assert_allclose(y, a * t**2 + b * t, rtol=1e-15) + + c = 10 + t, y = minimize_quadratic_1d(a, b, -1, 1, c=c) + assert_equal(t, 0.1) + assert_allclose(y, a * t**2 + b * t + c, rtol=1e-15) + + t, y = minimize_quadratic_1d(a, b, -np.inf, np.inf, c=c) + assert_equal(t, 0.1) + assert_allclose(y, a * t ** 2 + b * t + c, rtol=1e-15) + + t, y = minimize_quadratic_1d(a, b, 0, np.inf, c=c) + assert_equal(t, 0.1) + assert_allclose(y, a * t ** 2 + b * t + c, rtol=1e-15) + + t, y = minimize_quadratic_1d(a, b, -np.inf, 0, c=c) + assert_equal(t, 0) + assert_allclose(y, a * t ** 2 + b * t + c, rtol=1e-15) + + a = -1 + b = 0.2 + t, y = minimize_quadratic_1d(a, b, -np.inf, np.inf) + assert_equal(y, -np.inf) + + t, y = minimize_quadratic_1d(a, b, 0, np.inf) + assert_equal(t, np.inf) + assert_equal(y, -np.inf) + + t, y = minimize_quadratic_1d(a, b, -np.inf, 0) + assert_equal(t, -np.inf) + assert_equal(y, -np.inf) + + def test_evaluate_quadratic(self): + s = np.array([1.0, -1.0]) + + value = evaluate_quadratic(self.J, self.g, s) + assert_equal(value, 4.85) + + value = evaluate_quadratic(self.J, self.g, s, diag=self.diag) + assert_equal(value, 6.35) + + s = np.array([[1.0, -1.0], + [1.0, 1.0], + [0.0, 0.0]]) + + values = evaluate_quadratic(self.J, self.g, s) + assert_allclose(values, [4.85, -0.91, 0.0]) + + values = evaluate_quadratic(self.J, self.g, s, diag=self.diag) + assert_allclose(values, [6.35, 0.59, 0.0]) + + +class TestTrustRegion: + def test_intersect(self): + Delta = 1.0 + + x = np.zeros(3) + s = np.array([1.0, 0.0, 0.0]) + t_neg, t_pos = intersect_trust_region(x, s, Delta) + assert_equal(t_neg, -1) + assert_equal(t_pos, 1) + + s = np.array([-1.0, 1.0, -1.0]) + t_neg, t_pos = intersect_trust_region(x, s, Delta) + assert_allclose(t_neg, -3**-0.5) + assert_allclose(t_pos, 3**-0.5) + + x = np.array([0.5, -0.5, 0]) + s = np.array([0, 0, 1.0]) + t_neg, t_pos = intersect_trust_region(x, s, Delta) + assert_allclose(t_neg, -2**-0.5) + assert_allclose(t_pos, 2**-0.5) + + x = np.ones(3) + assert_raises(ValueError, intersect_trust_region, x, s, Delta) + + x = np.zeros(3) + s = np.zeros(3) + assert_raises(ValueError, intersect_trust_region, x, s, Delta) + + +def test_reflective_transformation(): + lb = np.array([-1, -2], dtype=float) + ub = np.array([5, 3], dtype=float) + + y = np.array([0, 0]) + x, g = reflective_transformation(y, lb, ub) + assert_equal(x, y) + assert_equal(g, np.ones(2)) + + y = np.array([-4, 4], dtype=float) + + x, g = reflective_transformation(y, lb, np.array([np.inf, np.inf])) + assert_equal(x, [2, 4]) + assert_equal(g, [-1, 1]) + + x, g = reflective_transformation(y, np.array([-np.inf, -np.inf]), ub) + assert_equal(x, [-4, 2]) + assert_equal(g, [1, -1]) + + x, g = reflective_transformation(y, lb, ub) + assert_equal(x, [2, 2]) + assert_equal(g, [-1, -1]) + + lb = np.array([-np.inf, -2]) + ub = np.array([5, np.inf]) + y = np.array([10, 10], dtype=float) + x, g = reflective_transformation(y, lb, ub) + assert_equal(x, [0, 10]) + assert_equal(g, [-1, 1]) + + +def test_linear_operators(): + A = np.arange(6).reshape((3, 2)) + + d_left = np.array([-1, 2, 5]) + DA = np.diag(d_left).dot(A) + J_left = left_multiplied_operator(A, d_left) + + d_right = np.array([5, 10]) + AD = A.dot(np.diag(d_right)) + J_right = right_multiplied_operator(A, d_right) + + x = np.array([-2, 3]) + X = -2 * np.arange(2, 8).reshape((2, 3)) + xt = np.array([0, -2, 15]) + + assert_allclose(DA.dot(x), J_left.matvec(x)) + assert_allclose(DA.dot(X), J_left.matmat(X)) + assert_allclose(DA.T.dot(xt), J_left.rmatvec(xt)) + + assert_allclose(AD.dot(x), J_right.matvec(x)) + assert_allclose(AD.dot(X), J_right.matmat(X)) + assert_allclose(AD.T.dot(xt), J_right.rmatvec(xt)) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_milp.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_milp.py new file mode 100644 index 0000000000000000000000000000000000000000..0970a15a8bccc3deb7bc67f7b62763947c1b237c --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tests/test_milp.py @@ -0,0 +1,385 @@ +""" +Unit test for Mixed Integer Linear Programming +""" +import re + +import numpy as np +from numpy.testing import assert_allclose, assert_array_equal +import pytest + +from .test_linprog import magic_square +from scipy.optimize import milp, Bounds, LinearConstraint +from scipy import sparse + + +def test_milp_iv(): + + message = "`c` must be a dense array" + with pytest.raises(ValueError, match=message): + milp(sparse.coo_array([0, 0])) + + message = "`c` must be a one-dimensional array of finite numbers with" + with pytest.raises(ValueError, match=message): + milp(np.zeros((3, 4))) + with pytest.raises(ValueError, match=message): + milp([]) + with pytest.raises(ValueError, match=message): + milp(None) + + message = "`bounds` must be convertible into an instance of..." + with pytest.raises(ValueError, match=message): + milp(1, bounds=10) + + message = "`constraints` (or each element within `constraints`) must be" + with pytest.raises(ValueError, match=re.escape(message)): + milp(1, constraints=10) + with pytest.raises(ValueError, match=re.escape(message)): + milp(np.zeros(3), constraints=([[1, 2, 3]], [2, 3], [2, 3])) + with pytest.raises(ValueError, match=re.escape(message)): + milp(np.zeros(2), constraints=([[1, 2]], [2], sparse.coo_array([2]))) + + message = "The shape of `A` must be (len(b_l), len(c))." + with pytest.raises(ValueError, match=re.escape(message)): + milp(np.zeros(3), constraints=([[1, 2]], [2], [2])) + + message = "`integrality` must be a dense array" + with pytest.raises(ValueError, match=message): + milp([1, 2], integrality=sparse.coo_array([1, 2])) + + message = ("`integrality` must contain integers 0-3 and be broadcastable " + "to `c.shape`.") + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], integrality=[1, 2]) + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], integrality=[1, 5, 3]) + + message = "Lower and upper bounds must be dense arrays." + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2], sparse.coo_array([3, 4]))) + + message = "`lb`, `ub`, and `keep_feasible` must be broadcastable." + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2], [3, 4, 5])) + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2, 3], [4, 5])) + + message = "`bounds.lb` and `bounds.ub` must contain reals and..." + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2], [3, 4])) + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2, 3], ["3+4", 4, 5])) + with pytest.raises(ValueError, match=message): + milp([1, 2, 3], bounds=([1, 2, 3], [set(), 4, 5])) + + +@pytest.mark.xfail(run=False, + reason="Needs to be fixed in `_highs_wrapper`") +def test_milp_options(capsys): + # run=False now because of gh-16347 + message = "Unrecognized options detected: {'ekki'}..." + options = {'ekki': True} + with pytest.warns(RuntimeWarning, match=message): + milp(1, options=options) + + A, b, c, numbers, M = magic_square(3) + options = {"disp": True, "presolve": False, "time_limit": 0.05} + res = milp(c=c, constraints=(A, b, b), bounds=(0, 1), integrality=1, + options=options) + + captured = capsys.readouterr() + assert "Presolve is switched off" in captured.out + assert "Time Limit Reached" in captured.out + assert not res.success + + +def test_result(): + A, b, c, numbers, M = magic_square(3) + res = milp(c=c, constraints=(A, b, b), bounds=(0, 1), integrality=1) + assert res.status == 0 + assert res.success + msg = "Optimization terminated successfully. (HiGHS Status 7:" + assert res.message.startswith(msg) + assert isinstance(res.x, np.ndarray) + assert isinstance(res.fun, float) + assert isinstance(res.mip_node_count, int) + assert isinstance(res.mip_dual_bound, float) + assert isinstance(res.mip_gap, float) + + A, b, c, numbers, M = magic_square(6) + res = milp(c=c*0, constraints=(A, b, b), bounds=(0, 1), integrality=1, + options={'time_limit': 0.05}) + assert res.status == 1 + assert not res.success + msg = "Time limit reached. (HiGHS Status 13:" + assert res.message.startswith(msg) + assert (res.fun is res.mip_dual_bound is res.mip_gap + is res.mip_node_count is res.x is None) + + res = milp(1, bounds=(1, -1)) + assert res.status == 2 + assert not res.success + msg = "The problem is infeasible. (HiGHS Status 8:" + assert res.message.startswith(msg) + assert (res.fun is res.mip_dual_bound is res.mip_gap + is res.mip_node_count is res.x is None) + + res = milp(-1) + assert res.status == 3 + assert not res.success + msg = "The problem is unbounded. (HiGHS Status 10:" + assert res.message.startswith(msg) + assert (res.fun is res.mip_dual_bound is res.mip_gap + is res.mip_node_count is res.x is None) + + +def test_milp_optional_args(): + # check that arguments other than `c` are indeed optional + res = milp(1) + assert res.fun == 0 + assert_array_equal(res.x, [0]) + + +def test_milp_1(): + # solve magic square problem + n = 3 + A, b, c, numbers, M = magic_square(n) + A = sparse.csc_array(A) # confirm that sparse arrays are accepted + res = milp(c=c*0, constraints=(A, b, b), bounds=(0, 1), integrality=1) + + # check that solution is a magic square + x = np.round(res.x) + s = (numbers.flatten() * x).reshape(n**2, n, n) + square = np.sum(s, axis=0) + np.testing.assert_allclose(square.sum(axis=0), M) + np.testing.assert_allclose(square.sum(axis=1), M) + np.testing.assert_allclose(np.diag(square).sum(), M) + np.testing.assert_allclose(np.diag(square[:, ::-1]).sum(), M) + + +def test_milp_2(): + # solve MIP with inequality constraints and all integer constraints + # source: slide 5, + # https://www.cs.upc.edu/~erodri/webpage/cps/theory/lp/milp/slides.pdf + # also check that `milp` accepts all valid ways of specifying constraints + c = -np.ones(2) + A = [[-2, 2], [-8, 10]] + b_l = [1, -np.inf] + b_u = [np.inf, 13] + linear_constraint = LinearConstraint(A, b_l, b_u) + + # solve original problem + res1 = milp(c=c, constraints=(A, b_l, b_u), integrality=True) + res2 = milp(c=c, constraints=linear_constraint, integrality=True) + res3 = milp(c=c, constraints=[(A, b_l, b_u)], integrality=True) + res4 = milp(c=c, constraints=[linear_constraint], integrality=True) + res5 = milp(c=c, integrality=True, + constraints=[(A[:1], b_l[:1], b_u[:1]), + (A[1:], b_l[1:], b_u[1:])]) + res6 = milp(c=c, integrality=True, + constraints=[LinearConstraint(A[:1], b_l[:1], b_u[:1]), + LinearConstraint(A[1:], b_l[1:], b_u[1:])]) + res7 = milp(c=c, integrality=True, + constraints=[(A[:1], b_l[:1], b_u[:1]), + LinearConstraint(A[1:], b_l[1:], b_u[1:])]) + xs = np.array([res1.x, res2.x, res3.x, res4.x, res5.x, res6.x, res7.x]) + funs = np.array([res1.fun, res2.fun, res3.fun, + res4.fun, res5.fun, res6.fun, res7.fun]) + np.testing.assert_allclose(xs, np.broadcast_to([1, 2], xs.shape)) + np.testing.assert_allclose(funs, -3) + + # solve relaxed problem + res = milp(c=c, constraints=(A, b_l, b_u)) + np.testing.assert_allclose(res.x, [4, 4.5]) + np.testing.assert_allclose(res.fun, -8.5) + + +def test_milp_3(): + # solve MIP with inequality constraints and all integer constraints + # source: https://en.wikipedia.org/wiki/Integer_programming#Example + c = [0, -1] + A = [[-1, 1], [3, 2], [2, 3]] + b_u = [1, 12, 12] + b_l = np.full_like(b_u, -np.inf, dtype=np.float64) + constraints = LinearConstraint(A, b_l, b_u) + + integrality = np.ones_like(c) + + # solve original problem + res = milp(c=c, constraints=constraints, integrality=integrality) + assert_allclose(res.fun, -2) + # two optimal solutions possible, just need one of them + assert np.allclose(res.x, [1, 2]) or np.allclose(res.x, [2, 2]) + + # solve relaxed problem + res = milp(c=c, constraints=constraints) + assert_allclose(res.fun, -2.8) + assert_allclose(res.x, [1.8, 2.8]) + + +def test_milp_4(): + # solve MIP with inequality constraints and only one integer constraint + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + c = [8, 1] + integrality = [0, 1] + A = [[1, 2], [-4, -1], [2, 1]] + b_l = [-14, -np.inf, -np.inf] + b_u = [np.inf, -33, 20] + constraints = LinearConstraint(A, b_l, b_u) + bounds = Bounds(-np.inf, np.inf) + + res = milp(c, integrality=integrality, bounds=bounds, + constraints=constraints) + assert_allclose(res.fun, 59) + assert_allclose(res.x, [6.5, 7]) + + +def test_milp_5(): + # solve MIP with inequality and equality constraints + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + c = [-3, -2, -1] + integrality = [0, 0, 1] + lb = [0, 0, 0] + ub = [np.inf, np.inf, 1] + bounds = Bounds(lb, ub) + A = [[1, 1, 1], [4, 2, 1]] + b_l = [-np.inf, 12] + b_u = [7, 12] + constraints = LinearConstraint(A, b_l, b_u) + + res = milp(c, integrality=integrality, bounds=bounds, + constraints=constraints) + # there are multiple solutions + assert_allclose(res.fun, -12) + + +@pytest.mark.slow +@pytest.mark.timeout(120) # prerelease_deps_coverage_64bit_blas job +def test_milp_6(): + # solve a larger MIP with only equality constraints + # source: https://www.mathworks.com/help/optim/ug/intlinprog.html + integrality = 1 + A_eq = np.array([[22, 13, 26, 33, 21, 3, 14, 26], + [39, 16, 22, 28, 26, 30, 23, 24], + [18, 14, 29, 27, 30, 38, 26, 26], + [41, 26, 28, 36, 18, 38, 16, 26]]) + b_eq = np.array([7872, 10466, 11322, 12058]) + c = np.array([2, 10, 13, 17, 7, 5, 7, 3]) + + res = milp(c=c, constraints=(A_eq, b_eq, b_eq), integrality=integrality) + + np.testing.assert_allclose(res.fun, 1854) + + +def test_infeasible_prob_16609(): + # Ensure presolve does not mark trivially infeasible problems + # as Optimal -- see gh-16609 + c = [1.0, 0.0] + integrality = [0, 1] + + lb = [0, -np.inf] + ub = [np.inf, np.inf] + bounds = Bounds(lb, ub) + + A_eq = [[0.0, 1.0]] + b_eq = [0.5] + constraints = LinearConstraint(A_eq, b_eq, b_eq) + + res = milp(c, integrality=integrality, bounds=bounds, + constraints=constraints) + np.testing.assert_equal(res.status, 2) + + +_msg_time = "Time limit reached. (HiGHS Status 13:" +_msg_iter = "Iteration limit reached. (HiGHS Status 14:" + + +@pytest.mark.skipif(np.intp(0).itemsize < 8, + reason="Unhandled 32-bit GCC FP bug") +@pytest.mark.slow +@pytest.mark.parametrize(["options", "msg"], [({"time_limit": 0.1}, _msg_time), + ({"node_limit": 1}, _msg_iter)]) +def test_milp_timeout_16545(options, msg): + # Ensure solution is not thrown away if MILP solver times out + # -- see gh-16545 + rng = np.random.default_rng(5123833489170494244) + A = rng.integers(0, 5, size=(100, 100)) + b_lb = np.full(100, fill_value=-np.inf) + b_ub = np.full(100, fill_value=25) + constraints = LinearConstraint(A, b_lb, b_ub) + variable_lb = np.zeros(100) + variable_ub = np.ones(100) + variable_bounds = Bounds(variable_lb, variable_ub) + integrality = np.ones(100) + c_vector = -np.ones(100) + res = milp( + c_vector, + integrality=integrality, + bounds=variable_bounds, + constraints=constraints, + options=options, + ) + + assert res.message.startswith(msg) + assert res["x"] is not None + + # ensure solution is feasible + x = res["x"] + tol = 1e-8 # sometimes needed due to finite numerical precision + assert np.all(b_lb - tol <= A @ x) and np.all(A @ x <= b_ub + tol) + assert np.all(variable_lb - tol <= x) and np.all(x <= variable_ub + tol) + assert np.allclose(x, np.round(x)) + + +def test_three_constraints_16878(): + # `milp` failed when exactly three constraints were passed + # Ensure that this is no longer the case. + rng = np.random.default_rng(5123833489170494244) + A = rng.integers(0, 5, size=(6, 6)) + bl = np.full(6, fill_value=-np.inf) + bu = np.full(6, fill_value=10) + constraints = [LinearConstraint(A[:2], bl[:2], bu[:2]), + LinearConstraint(A[2:4], bl[2:4], bu[2:4]), + LinearConstraint(A[4:], bl[4:], bu[4:])] + constraints2 = [(A[:2], bl[:2], bu[:2]), + (A[2:4], bl[2:4], bu[2:4]), + (A[4:], bl[4:], bu[4:])] + lb = np.zeros(6) + ub = np.ones(6) + variable_bounds = Bounds(lb, ub) + c = -np.ones(6) + res1 = milp(c, bounds=variable_bounds, constraints=constraints) + res2 = milp(c, bounds=variable_bounds, constraints=constraints2) + ref = milp(c, bounds=variable_bounds, constraints=(A, bl, bu)) + assert res1.success and res2.success + assert_allclose(res1.x, ref.x) + assert_allclose(res2.x, ref.x) + + +@pytest.mark.xslow +def test_mip_rel_gap_passdown(): + # Solve problem with decreasing mip_gap to make sure mip_rel_gap decreases + # Adapted from test_linprog::TestLinprogHiGHSMIP::test_mip_rel_gap_passdown + # MIP taken from test_mip_6 above + A_eq = np.array([[22, 13, 26, 33, 21, 3, 14, 26], + [39, 16, 22, 28, 26, 30, 23, 24], + [18, 14, 29, 27, 30, 38, 26, 26], + [41, 26, 28, 36, 18, 38, 16, 26]]) + b_eq = np.array([7872, 10466, 11322, 12058]) + c = np.array([2, 10, 13, 17, 7, 5, 7, 3]) + + mip_rel_gaps = [0.25, 0.01, 0.001] + sol_mip_gaps = [] + for mip_rel_gap in mip_rel_gaps: + res = milp(c=c, bounds=(0, np.inf), constraints=(A_eq, b_eq, b_eq), + integrality=True, options={"mip_rel_gap": mip_rel_gap}) + # assert that the solution actually has mip_gap lower than the + # required mip_rel_gap supplied + assert res.mip_gap <= mip_rel_gap + # check that `res.mip_gap` is as defined in the documentation + assert res.mip_gap == (res.fun - res.mip_dual_bound)/res.fun + sol_mip_gaps.append(res.mip_gap) + + # make sure that the mip_rel_gap parameter is actually doing something + # check that differences between solution gaps are declining + # monotonically with the mip_rel_gap parameter. + assert np.all(np.diff(sol_mip_gaps) < 0) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tnc.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tnc.py new file mode 100644 index 0000000000000000000000000000000000000000..e0f66058bbcc501eb1303eb3075cb55705b93192 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/tnc.py @@ -0,0 +1,22 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'OptimizeResult', + 'fmin_tnc', + 'zeros', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="tnc", + private_modules=["_tnc"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/zeros.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/zeros.py new file mode 100644 index 0000000000000000000000000000000000000000..907d49d37fc1e7476e81a25dbbc0d3910cbbe004 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/optimize/zeros.py @@ -0,0 +1,26 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.optimize` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'RootResults', + 'bisect', + 'brenth', + 'brentq', + 'newton', + 'ridder', + 'toms748', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="optimize", module="zeros", + private_modules=["_zeros_py"], all=__all__, + attribute=name) diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/special.pxd b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/special.pxd new file mode 100644 index 0000000000000000000000000000000000000000..1daa9fb379572aac4bc9b6d74330a18c5c52bf79 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/special.pxd @@ -0,0 +1 @@ +from scipy.special cimport cython_special diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/version.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/version.py new file mode 100644 index 0000000000000000000000000000000000000000..067ba51c8ddea9d278f9c18e62d1bca6c96a2695 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/scipy/version.py @@ -0,0 +1,12 @@ +# THIS FILE IS GENERATED DURING THE SCIPY BUILD +# See tools/version_utils.py for details + +short_version = '1.14.1' +version = '1.14.1' +full_version = '1.14.1' +git_revision = '92d2a85' +commit_count = '1441' +release = True + +if not release: + version = full_version diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/setuptools-59.6.0.virtualenv b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/setuptools-59.6.0.virtualenv new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/threadpoolctl.py b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/threadpoolctl.py new file mode 100644 index 0000000000000000000000000000000000000000..2a72d1b57e1d764d73052583d3c5a8e8b7697eae --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/lib/python3.10/site-packages/threadpoolctl.py @@ -0,0 +1,1280 @@ +"""threadpoolctl + +This module provides utilities to introspect native libraries that relies on +thread pools (notably BLAS and OpenMP implementations) and dynamically set the +maximal number of threads they can use. +""" + +# License: BSD 3-Clause + +# The code to introspect dynamically loaded libraries on POSIX systems is +# adapted from code by Intel developer @anton-malakhov available at +# https://github.com/IntelPython/smp (Copyright (c) 2017, Intel Corporation) +# and also published under the BSD 3-Clause license +import os +import re +import sys +import ctypes +import itertools +import textwrap +from typing import final +import warnings +from ctypes.util import find_library +from abc import ABC, abstractmethod +from functools import lru_cache +from contextlib import ContextDecorator + +__version__ = "3.5.0" +__all__ = [ + "threadpool_limits", + "threadpool_info", + "ThreadpoolController", + "LibController", + "register", +] + + +# One can get runtime errors or even segfaults due to multiple OpenMP libraries +# loaded simultaneously which can happen easily in Python when importing and +# using compiled extensions built with different compilers and therefore +# different OpenMP runtimes in the same program. In particular libiomp (used by +# Intel ICC) and libomp used by clang/llvm tend to crash. This can happen for +# instance when calling BLAS inside a prange. Setting the following environment +# variable allows multiple OpenMP libraries to be loaded. It should not degrade +# performances since we manually take care of potential over-subscription +# performance issues, in sections of the code where nested OpenMP loops can +# happen, by dynamically reconfiguring the inner OpenMP runtime to temporarily +# disable it while under the scope of the outer OpenMP parallel section. +os.environ.setdefault("KMP_DUPLICATE_LIB_OK", "True") + +# Structure to cast the info on dynamically loaded library. See +# https://linux.die.net/man/3/dl_iterate_phdr for more details. +_SYSTEM_UINT = ctypes.c_uint64 if sys.maxsize > 2**32 else ctypes.c_uint32 +_SYSTEM_UINT_HALF = ctypes.c_uint32 if sys.maxsize > 2**32 else ctypes.c_uint16 + + +class _dl_phdr_info(ctypes.Structure): + _fields_ = [ + ("dlpi_addr", _SYSTEM_UINT), # Base address of object + ("dlpi_name", ctypes.c_char_p), # path to the library + ("dlpi_phdr", ctypes.c_void_p), # pointer on dlpi_headers + ("dlpi_phnum", _SYSTEM_UINT_HALF), # number of elements in dlpi_phdr + ] + + +# The RTLD_NOLOAD flag for loading shared libraries is not defined on Windows. +try: + _RTLD_NOLOAD = os.RTLD_NOLOAD +except AttributeError: + _RTLD_NOLOAD = ctypes.DEFAULT_MODE + + +class LibController(ABC): + """Abstract base class for the individual library controllers + + A library controller must expose the following class attributes: + - user_api : str + Usually the name of the library or generic specification the library + implements, e.g. "blas" is a specification with different implementations. + - internal_api : str + Usually the name of the library or concrete implementation of some + specification, e.g. "openblas" is an implementation of the "blas" + specification. + - filename_prefixes : tuple + Possible prefixes of the shared library's filename that allow to + identify the library. e.g. "libopenblas" for libopenblas.so. + + and implement the following methods: `get_num_threads`, `set_num_threads` and + `get_version`. + + Threadpoolctl loops through all the loaded shared libraries and tries to match + the filename of each library with the `filename_prefixes`. If a match is found, a + controller is instantiated and a handler to the library is stored in the `dynlib` + attribute as a `ctypes.CDLL` object. It can be used to access the necessary symbols + of the shared library to implement the above methods. + + The following information will be exposed in the info dictionary: + - user_api : standardized API, if any, or a copy of internal_api. + - internal_api : implementation-specific API. + - num_threads : the current thread limit. + - prefix : prefix of the shared library's filename. + - filepath : path to the loaded shared library. + - version : version of the library (if available). + + In addition, each library controller may expose internal API specific entries. They + must be set as attributes in the `set_additional_attributes` method. + """ + + @final + def __init__(self, *, filepath=None, prefix=None, parent=None): + """This is not meant to be overriden by subclasses.""" + self.parent = parent + self.prefix = prefix + self.filepath = filepath + self.dynlib = ctypes.CDLL(filepath, mode=_RTLD_NOLOAD) + self._symbol_prefix, self._symbol_suffix = self._find_affixes() + self.version = self.get_version() + self.set_additional_attributes() + + def info(self): + """Return relevant info wrapped in a dict""" + hidden_attrs = ("dynlib", "parent", "_symbol_prefix", "_symbol_suffix") + return { + "user_api": self.user_api, + "internal_api": self.internal_api, + "num_threads": self.num_threads, + **{k: v for k, v in vars(self).items() if k not in hidden_attrs}, + } + + def set_additional_attributes(self): + """Set additional attributes meant to be exposed in the info dict""" + + @property + def num_threads(self): + """Exposes the current thread limit as a dynamic property + + This is not meant to be used or overriden by subclasses. + """ + return self.get_num_threads() + + @abstractmethod + def get_num_threads(self): + """Return the maximum number of threads available to use""" + + @abstractmethod + def set_num_threads(self, num_threads): + """Set the maximum number of threads to use""" + + @abstractmethod + def get_version(self): + """Return the version of the shared library""" + + def _find_affixes(self): + """Return the affixes for the symbols of the shared library""" + return "", "" + + def _get_symbol(self, name): + """Return the symbol of the shared library accounding for the affixes""" + return getattr( + self.dynlib, f"{self._symbol_prefix}{name}{self._symbol_suffix}", None + ) + + +class OpenBLASController(LibController): + """Controller class for OpenBLAS""" + + user_api = "blas" + internal_api = "openblas" + filename_prefixes = ("libopenblas", "libblas", "libscipy_openblas") + + _symbol_prefixes = ("", "scipy_") + _symbol_suffixes = ("", "64_", "_64") + + # All variations of "openblas_get_num_threads", accounting for the affixes + check_symbols = tuple( + f"{prefix}openblas_get_num_threads{suffix}" + for prefix, suffix in itertools.product(_symbol_prefixes, _symbol_suffixes) + ) + + def _find_affixes(self): + for prefix, suffix in itertools.product( + self._symbol_prefixes, self._symbol_suffixes + ): + if hasattr(self.dynlib, f"{prefix}openblas_get_num_threads{suffix}"): + return prefix, suffix + + def set_additional_attributes(self): + self.threading_layer = self._get_threading_layer() + self.architecture = self._get_architecture() + + def get_num_threads(self): + get_num_threads_func = self._get_symbol("openblas_get_num_threads") + if get_num_threads_func is not None: + return get_num_threads_func() + return None + + def set_num_threads(self, num_threads): + set_num_threads_func = self._get_symbol("openblas_set_num_threads") + if set_num_threads_func is not None: + return set_num_threads_func(num_threads) + return None + + def get_version(self): + # None means OpenBLAS is not loaded or version < 0.3.4, since OpenBLAS + # did not expose its version before that. + get_version_func = self._get_symbol("openblas_get_config") + if get_version_func is not None: + get_version_func.restype = ctypes.c_char_p + config = get_version_func().split() + if config[0] == b"OpenBLAS": + return config[1].decode("utf-8") + return None + return None + + def _get_threading_layer(self): + """Return the threading layer of OpenBLAS""" + get_threading_layer_func = self._get_symbol("openblas_get_parallel") + if get_threading_layer_func is not None: + threading_layer = get_threading_layer_func() + if threading_layer == 2: + return "openmp" + elif threading_layer == 1: + return "pthreads" + return "disabled" + return "unknown" + + def _get_architecture(self): + """Return the architecture detected by OpenBLAS""" + get_architecture_func = self._get_symbol("openblas_get_corename") + if get_architecture_func is not None: + get_architecture_func.restype = ctypes.c_char_p + return get_architecture_func().decode("utf-8") + return None + + +class BLISController(LibController): + """Controller class for BLIS""" + + user_api = "blas" + internal_api = "blis" + filename_prefixes = ("libblis", "libblas") + check_symbols = ( + "bli_thread_get_num_threads", + "bli_thread_set_num_threads", + "bli_info_get_version_str", + "bli_info_get_enable_openmp", + "bli_info_get_enable_pthreads", + "bli_arch_query_id", + "bli_arch_string", + ) + + def set_additional_attributes(self): + self.threading_layer = self._get_threading_layer() + self.architecture = self._get_architecture() + + def get_num_threads(self): + get_func = getattr(self.dynlib, "bli_thread_get_num_threads", lambda: None) + num_threads = get_func() + # by default BLIS is single-threaded and get_num_threads + # returns -1. We map it to 1 for consistency with other libraries. + return 1 if num_threads == -1 else num_threads + + def set_num_threads(self, num_threads): + set_func = getattr( + self.dynlib, "bli_thread_set_num_threads", lambda num_threads: None + ) + return set_func(num_threads) + + def get_version(self): + get_version_ = getattr(self.dynlib, "bli_info_get_version_str", None) + if get_version_ is None: + return None + + get_version_.restype = ctypes.c_char_p + return get_version_().decode("utf-8") + + def _get_threading_layer(self): + """Return the threading layer of BLIS""" + if getattr(self.dynlib, "bli_info_get_enable_openmp", lambda: False)(): + return "openmp" + elif getattr(self.dynlib, "bli_info_get_enable_pthreads", lambda: False)(): + return "pthreads" + return "disabled" + + def _get_architecture(self): + """Return the architecture detected by BLIS""" + bli_arch_query_id = getattr(self.dynlib, "bli_arch_query_id", None) + bli_arch_string = getattr(self.dynlib, "bli_arch_string", None) + if bli_arch_query_id is None or bli_arch_string is None: + return None + + # the true restype should be BLIS' arch_t (enum) but int should work + # for us: + bli_arch_query_id.restype = ctypes.c_int + bli_arch_string.restype = ctypes.c_char_p + return bli_arch_string(bli_arch_query_id()).decode("utf-8") + + +class FlexiBLASController(LibController): + """Controller class for FlexiBLAS""" + + user_api = "blas" + internal_api = "flexiblas" + filename_prefixes = ("libflexiblas",) + check_symbols = ( + "flexiblas_get_num_threads", + "flexiblas_set_num_threads", + "flexiblas_get_version", + "flexiblas_list", + "flexiblas_list_loaded", + "flexiblas_current_backend", + ) + + @property + def loaded_backends(self): + return self._get_backend_list(loaded=True) + + @property + def current_backend(self): + return self._get_current_backend() + + def info(self): + """Return relevant info wrapped in a dict""" + # We override the info method because the loaded and current backends + # are dynamic properties + exposed_attrs = super().info() + exposed_attrs["loaded_backends"] = self.loaded_backends + exposed_attrs["current_backend"] = self.current_backend + + return exposed_attrs + + def set_additional_attributes(self): + self.available_backends = self._get_backend_list(loaded=False) + + def get_num_threads(self): + get_func = getattr(self.dynlib, "flexiblas_get_num_threads", lambda: None) + num_threads = get_func() + # by default BLIS is single-threaded and get_num_threads + # returns -1. We map it to 1 for consistency with other libraries. + return 1 if num_threads == -1 else num_threads + + def set_num_threads(self, num_threads): + set_func = getattr( + self.dynlib, "flexiblas_set_num_threads", lambda num_threads: None + ) + return set_func(num_threads) + + def get_version(self): + get_version_ = getattr(self.dynlib, "flexiblas_get_version", None) + if get_version_ is None: + return None + + major = ctypes.c_int() + minor = ctypes.c_int() + patch = ctypes.c_int() + get_version_(ctypes.byref(major), ctypes.byref(minor), ctypes.byref(patch)) + return f"{major.value}.{minor.value}.{patch.value}" + + def _get_backend_list(self, loaded=False): + """Return the list of available backends for FlexiBLAS. + + If loaded is False, return the list of available backends from the FlexiBLAS + configuration. If loaded is True, return the list of actually loaded backends. + """ + func_name = f"flexiblas_list{'_loaded' if loaded else ''}" + get_backend_list_ = getattr(self.dynlib, func_name, None) + if get_backend_list_ is None: + return None + + n_backends = get_backend_list_(None, 0, 0) + + backends = [] + for i in range(n_backends): + backend_name = ctypes.create_string_buffer(1024) + get_backend_list_(backend_name, 1024, i) + if backend_name.value.decode("utf-8") != "__FALLBACK__": + # We don't know when to expect __FALLBACK__ but it is not a real + # backend and does not show up when running flexiblas list. + backends.append(backend_name.value.decode("utf-8")) + return backends + + def _get_current_backend(self): + """Return the backend of FlexiBLAS""" + get_backend_ = getattr(self.dynlib, "flexiblas_current_backend", None) + if get_backend_ is None: + return None + + backend = ctypes.create_string_buffer(1024) + get_backend_(backend, ctypes.sizeof(backend)) + return backend.value.decode("utf-8") + + def switch_backend(self, backend): + """Switch the backend of FlexiBLAS + + Parameters + ---------- + backend : str + The name or the path to the shared library of the backend to switch to. If + the backend is not already loaded, it will be loaded first. + """ + if backend not in self.loaded_backends: + if backend in self.available_backends: + load_func = getattr(self.dynlib, "flexiblas_load_backend", lambda _: -1) + else: # assume backend is a path to a shared library + load_func = getattr( + self.dynlib, "flexiblas_load_backend_library", lambda _: -1 + ) + res = load_func(str(backend).encode("utf-8")) + if res == -1: + raise RuntimeError( + f"Failed to load backend {backend!r}. It must either be the name of" + " a backend available in the FlexiBLAS configuration " + f"{self.available_backends} or the path to a valid shared library." + ) + + # Trigger a new search of loaded shared libraries since loading a new + # backend caused a dlopen. + self.parent._load_libraries() + + switch_func = getattr(self.dynlib, "flexiblas_switch", lambda _: -1) + idx = self.loaded_backends.index(backend) + res = switch_func(idx) + if res == -1: + raise RuntimeError(f"Failed to switch to backend {backend!r}.") + + +class MKLController(LibController): + """Controller class for MKL""" + + user_api = "blas" + internal_api = "mkl" + filename_prefixes = ("libmkl_rt", "mkl_rt", "libblas") + check_symbols = ( + "MKL_Get_Max_Threads", + "MKL_Set_Num_Threads", + "MKL_Get_Version_String", + "MKL_Set_Threading_Layer", + ) + + def set_additional_attributes(self): + self.threading_layer = self._get_threading_layer() + + def get_num_threads(self): + get_func = getattr(self.dynlib, "MKL_Get_Max_Threads", lambda: None) + return get_func() + + def set_num_threads(self, num_threads): + set_func = getattr(self.dynlib, "MKL_Set_Num_Threads", lambda num_threads: None) + return set_func(num_threads) + + def get_version(self): + if not hasattr(self.dynlib, "MKL_Get_Version_String"): + return None + + res = ctypes.create_string_buffer(200) + self.dynlib.MKL_Get_Version_String(res, 200) + + version = res.value.decode("utf-8") + group = re.search(r"Version ([^ ]+) ", version) + if group is not None: + version = group.groups()[0] + return version.strip() + + def _get_threading_layer(self): + """Return the threading layer of MKL""" + # The function mkl_set_threading_layer returns the current threading + # layer. Calling it with an invalid threading layer allows us to safely + # get the threading layer + set_threading_layer = getattr( + self.dynlib, "MKL_Set_Threading_Layer", lambda layer: -1 + ) + layer_map = { + 0: "intel", + 1: "sequential", + 2: "pgi", + 3: "gnu", + 4: "tbb", + -1: "not specified", + } + return layer_map[set_threading_layer(-1)] + + +class OpenMPController(LibController): + """Controller class for OpenMP""" + + user_api = "openmp" + internal_api = "openmp" + filename_prefixes = ("libiomp", "libgomp", "libomp", "vcomp") + check_symbols = ( + "omp_get_max_threads", + "omp_get_num_threads", + ) + + def get_num_threads(self): + get_func = getattr(self.dynlib, "omp_get_max_threads", lambda: None) + return get_func() + + def set_num_threads(self, num_threads): + set_func = getattr(self.dynlib, "omp_set_num_threads", lambda num_threads: None) + return set_func(num_threads) + + def get_version(self): + # There is no way to get the version number programmatically in OpenMP. + return None + + +# Controllers for the libraries that we'll look for in the loaded libraries. +# Third party libraries can register their own controllers. +_ALL_CONTROLLERS = [ + OpenBLASController, + BLISController, + MKLController, + OpenMPController, + FlexiBLASController, +] + +# Helpers for the doc and test names +_ALL_USER_APIS = list(set(lib.user_api for lib in _ALL_CONTROLLERS)) +_ALL_INTERNAL_APIS = [lib.internal_api for lib in _ALL_CONTROLLERS] +_ALL_PREFIXES = list( + set(prefix for lib in _ALL_CONTROLLERS for prefix in lib.filename_prefixes) +) +_ALL_BLAS_LIBRARIES = [ + lib.internal_api for lib in _ALL_CONTROLLERS if lib.user_api == "blas" +] +_ALL_OPENMP_LIBRARIES = OpenMPController.filename_prefixes + + +def register(controller): + """Register a new controller""" + _ALL_CONTROLLERS.append(controller) + _ALL_USER_APIS.append(controller.user_api) + _ALL_INTERNAL_APIS.append(controller.internal_api) + _ALL_PREFIXES.extend(controller.filename_prefixes) + + +def _format_docstring(*args, **kwargs): + def decorator(o): + if o.__doc__ is not None: + o.__doc__ = o.__doc__.format(*args, **kwargs) + return o + + return decorator + + +@lru_cache(maxsize=10000) +def _realpath(filepath): + """Small caching wrapper around os.path.realpath to limit system calls""" + return os.path.realpath(filepath) + + +@_format_docstring(USER_APIS=list(_ALL_USER_APIS), INTERNAL_APIS=_ALL_INTERNAL_APIS) +def threadpool_info(): + """Return the maximal number of threads for each detected library. + + Return a list with all the supported libraries that have been found. Each + library is represented by a dict with the following information: + + - "user_api" : user API. Possible values are {USER_APIS}. + - "internal_api": internal API. Possible values are {INTERNAL_APIS}. + - "prefix" : filename prefix of the specific implementation. + - "filepath": path to the loaded library. + - "version": version of the library (if available). + - "num_threads": the current thread limit. + + In addition, each library may contain internal_api specific entries. + """ + return ThreadpoolController().info() + + +class _ThreadpoolLimiter: + """The guts of ThreadpoolController.limit + + Refer to the docstring of ThreadpoolController.limit for more details. + + It will only act on the library controllers held by the provided `controller`. + Using the default constructor sets the limits right away such that it can be used as + a callable. Setting the limits can be delayed by using the `wrap` class method such + that it can be used as a decorator. + """ + + def __init__(self, controller, *, limits=None, user_api=None): + self._controller = controller + self._limits, self._user_api, self._prefixes = self._check_params( + limits, user_api + ) + self._original_info = self._controller.info() + self._set_threadpool_limits() + + def __enter__(self): + return self + + def __exit__(self, type, value, traceback): + self.restore_original_limits() + + @classmethod + def wrap(cls, controller, *, limits=None, user_api=None): + """Return an instance of this class that can be used as a decorator""" + return _ThreadpoolLimiterDecorator( + controller=controller, limits=limits, user_api=user_api + ) + + def restore_original_limits(self): + """Set the limits back to their original values""" + for lib_controller, original_info in zip( + self._controller.lib_controllers, self._original_info + ): + lib_controller.set_num_threads(original_info["num_threads"]) + + # Alias of `restore_original_limits` for backward compatibility + unregister = restore_original_limits + + def get_original_num_threads(self): + """Original num_threads from before calling threadpool_limits + + Return a dict `{user_api: num_threads}`. + """ + num_threads = {} + warning_apis = [] + + for user_api in self._user_api: + limits = [ + lib_info["num_threads"] + for lib_info in self._original_info + if lib_info["user_api"] == user_api + ] + limits = set(limits) + n_limits = len(limits) + + if n_limits == 1: + limit = limits.pop() + elif n_limits == 0: + limit = None + else: + limit = min(limits) + warning_apis.append(user_api) + + num_threads[user_api] = limit + + if warning_apis: + warnings.warn( + "Multiple value possible for following user apis: " + + ", ".join(warning_apis) + + ". Returning the minimum." + ) + + return num_threads + + def _check_params(self, limits, user_api): + """Suitable values for the _limits, _user_api and _prefixes attributes""" + + if isinstance(limits, str) and limits == "sequential_blas_under_openmp": + ( + limits, + user_api, + ) = self._controller._get_params_for_sequential_blas_under_openmp().values() + + if limits is None or isinstance(limits, int): + if user_api is None: + user_api = _ALL_USER_APIS + elif user_api in _ALL_USER_APIS: + user_api = [user_api] + else: + raise ValueError( + f"user_api must be either in {_ALL_USER_APIS} or None. Got " + f"{user_api} instead." + ) + + if limits is not None: + limits = {api: limits for api in user_api} + prefixes = [] + else: + if isinstance(limits, list): + # This should be a list of dicts of library info, for + # compatibility with the result from threadpool_info. + limits = { + lib_info["prefix"]: lib_info["num_threads"] for lib_info in limits + } + elif isinstance(limits, ThreadpoolController): + # To set the limits from the library controllers of a + # ThreadpoolController object. + limits = { + lib_controller.prefix: lib_controller.num_threads + for lib_controller in limits.lib_controllers + } + + if not isinstance(limits, dict): + raise TypeError( + "limits must either be an int, a list, a dict, or " + f"'sequential_blas_under_openmp'. Got {type(limits)} instead" + ) + + # With a dictionary, can set both specific limit for given + # libraries and global limit for user_api. Fetch each separately. + prefixes = [prefix for prefix in limits if prefix in _ALL_PREFIXES] + user_api = [api for api in limits if api in _ALL_USER_APIS] + + return limits, user_api, prefixes + + def _set_threadpool_limits(self): + """Change the maximal number of threads in selected thread pools. + + Return a list with all the supported libraries that have been found + matching `self._prefixes` and `self._user_api`. + """ + if self._limits is None: + return + + for lib_controller in self._controller.lib_controllers: + # self._limits is a dict {key: num_threads} where key is either + # a prefix or a user_api. If a library matches both, the limit + # corresponding to the prefix is chosen. + if lib_controller.prefix in self._limits: + num_threads = self._limits[lib_controller.prefix] + elif lib_controller.user_api in self._limits: + num_threads = self._limits[lib_controller.user_api] + else: + continue + + if num_threads is not None: + lib_controller.set_num_threads(num_threads) + + +class _ThreadpoolLimiterDecorator(_ThreadpoolLimiter, ContextDecorator): + """Same as _ThreadpoolLimiter but to be used as a decorator""" + + def __init__(self, controller, *, limits=None, user_api=None): + self._limits, self._user_api, self._prefixes = self._check_params( + limits, user_api + ) + self._controller = controller + + def __enter__(self): + # we need to set the limits here and not in the __init__ because we want the + # limits to be set when calling the decorated function, not when creating the + # decorator. + self._original_info = self._controller.info() + self._set_threadpool_limits() + return self + + +@_format_docstring( + USER_APIS=", ".join(f'"{api}"' for api in _ALL_USER_APIS), + BLAS_LIBS=", ".join(_ALL_BLAS_LIBRARIES), + OPENMP_LIBS=", ".join(_ALL_OPENMP_LIBRARIES), +) +class threadpool_limits(_ThreadpoolLimiter): + """Change the maximal number of threads that can be used in thread pools. + + This object can be used either as a callable (the construction of this object + limits the number of threads), as a context manager in a `with` block to + automatically restore the original state of the controlled libraries when exiting + the block, or as a decorator through its `wrap` method. + + Set the maximal number of threads that can be used in thread pools used in + the supported libraries to `limit`. This function works for libraries that + are already loaded in the interpreter and can be changed dynamically. + + This effect is global and impacts the whole Python process. There is no thread level + isolation as these libraries do not offer thread-local APIs to configure the number + of threads to use in nested parallel calls. + + Parameters + ---------- + limits : int, dict, 'sequential_blas_under_openmp' or None (default=None) + The maximal number of threads that can be used in thread pools + + - If int, sets the maximum number of threads to `limits` for each + library selected by `user_api`. + + - If it is a dictionary `{{key: max_threads}}`, this function sets a + custom maximum number of threads for each `key` which can be either a + `user_api` or a `prefix` for a specific library. + + - If 'sequential_blas_under_openmp', it will chose the appropriate `limits` + and `user_api` parameters for the specific use case of sequential BLAS + calls within an OpenMP parallel region. The `user_api` parameter is + ignored. + + - If None, this function does not do anything. + + user_api : {USER_APIS} or None (default=None) + APIs of libraries to limit. Used only if `limits` is an int. + + - If "blas", it will only limit BLAS supported libraries ({BLAS_LIBS}). + + - If "openmp", it will only limit OpenMP supported libraries + ({OPENMP_LIBS}). Note that it can affect the number of threads used + by the BLAS libraries if they rely on OpenMP. + + - If None, this function will apply to all supported libraries. + """ + + def __init__(self, limits=None, user_api=None): + super().__init__(ThreadpoolController(), limits=limits, user_api=user_api) + + @classmethod + def wrap(cls, limits=None, user_api=None): + return super().wrap(ThreadpoolController(), limits=limits, user_api=user_api) + + +class ThreadpoolController: + """Collection of LibController objects for all loaded supported libraries + + Attributes + ---------- + lib_controllers : list of `LibController` objects + The list of library controllers of all loaded supported libraries. + """ + + # Cache for libc under POSIX and a few system libraries under Windows. + # We use a class level cache instead of an instance level cache because + # it's very unlikely that a shared library will be unloaded and reloaded + # during the lifetime of a program. + _system_libraries = dict() + + def __init__(self): + self.lib_controllers = [] + self._load_libraries() + self._warn_if_incompatible_openmp() + + @classmethod + def _from_controllers(cls, lib_controllers): + new_controller = cls.__new__(cls) + new_controller.lib_controllers = lib_controllers + return new_controller + + def info(self): + """Return lib_controllers info as a list of dicts""" + return [lib_controller.info() for lib_controller in self.lib_controllers] + + def select(self, **kwargs): + """Return a ThreadpoolController containing a subset of its current + library controllers + + It will select all libraries matching at least one pair (key, value) from kwargs + where key is an entry of the library info dict (like "user_api", "internal_api", + "prefix", ...) and value is the value or a list of acceptable values for that + entry. + + For instance, `ThreadpoolController().select(internal_api=["blis", "openblas"])` + will select all library controllers whose internal_api is either "blis" or + "openblas". + """ + for key, vals in kwargs.items(): + kwargs[key] = [vals] if not isinstance(vals, list) else vals + + lib_controllers = [ + lib_controller + for lib_controller in self.lib_controllers + if any( + getattr(lib_controller, key, None) in vals + for key, vals in kwargs.items() + ) + ] + + return ThreadpoolController._from_controllers(lib_controllers) + + def _get_params_for_sequential_blas_under_openmp(self): + """Return appropriate params to use for a sequential BLAS call in an OpenMP loop + + This function takes into account the unexpected behavior of OpenBLAS with the + OpenMP threading layer. + """ + if self.select( + internal_api="openblas", threading_layer="openmp" + ).lib_controllers: + return {"limits": None, "user_api": None} + return {"limits": 1, "user_api": "blas"} + + @_format_docstring( + USER_APIS=", ".join('"{}"'.format(api) for api in _ALL_USER_APIS), + BLAS_LIBS=", ".join(_ALL_BLAS_LIBRARIES), + OPENMP_LIBS=", ".join(_ALL_OPENMP_LIBRARIES), + ) + def limit(self, *, limits=None, user_api=None): + """Change the maximal number of threads that can be used in thread pools. + + This function returns an object that can be used either as a callable (the + construction of this object limits the number of threads) or as a context + manager, in a `with` block to automatically restore the original state of the + controlled libraries when exiting the block. + + Set the maximal number of threads that can be used in thread pools used in + the supported libraries to `limits`. This function works for libraries that + are already loaded in the interpreter and can be changed dynamically. + + This effect is global and impacts the whole Python process. There is no thread + level isolation as these libraries do not offer thread-local APIs to configure + the number of threads to use in nested parallel calls. + + Parameters + ---------- + limits : int, dict, 'sequential_blas_under_openmp' or None (default=None) + The maximal number of threads that can be used in thread pools + + - If int, sets the maximum number of threads to `limits` for each + library selected by `user_api`. + + - If it is a dictionary `{{key: max_threads}}`, this function sets a + custom maximum number of threads for each `key` which can be either a + `user_api` or a `prefix` for a specific library. + + - If 'sequential_blas_under_openmp', it will chose the appropriate `limits` + and `user_api` parameters for the specific use case of sequential BLAS + calls within an OpenMP parallel region. The `user_api` parameter is + ignored. + + - If None, this function does not do anything. + + user_api : {USER_APIS} or None (default=None) + APIs of libraries to limit. Used only if `limits` is an int. + + - If "blas", it will only limit BLAS supported libraries ({BLAS_LIBS}). + + - If "openmp", it will only limit OpenMP supported libraries + ({OPENMP_LIBS}). Note that it can affect the number of threads used + by the BLAS libraries if they rely on OpenMP. + + - If None, this function will apply to all supported libraries. + """ + return _ThreadpoolLimiter(self, limits=limits, user_api=user_api) + + @_format_docstring( + USER_APIS=", ".join('"{}"'.format(api) for api in _ALL_USER_APIS), + BLAS_LIBS=", ".join(_ALL_BLAS_LIBRARIES), + OPENMP_LIBS=", ".join(_ALL_OPENMP_LIBRARIES), + ) + def wrap(self, *, limits=None, user_api=None): + """Change the maximal number of threads that can be used in thread pools. + + This function returns an object that can be used as a decorator. + + Set the maximal number of threads that can be used in thread pools used in + the supported libraries to `limits`. This function works for libraries that + are already loaded in the interpreter and can be changed dynamically. + + Parameters + ---------- + limits : int, dict or None (default=None) + The maximal number of threads that can be used in thread pools + + - If int, sets the maximum number of threads to `limits` for each + library selected by `user_api`. + + - If it is a dictionary `{{key: max_threads}}`, this function sets a + custom maximum number of threads for each `key` which can be either a + `user_api` or a `prefix` for a specific library. + + - If None, this function does not do anything. + + user_api : {USER_APIS} or None (default=None) + APIs of libraries to limit. Used only if `limits` is an int. + + - If "blas", it will only limit BLAS supported libraries ({BLAS_LIBS}). + + - If "openmp", it will only limit OpenMP supported libraries + ({OPENMP_LIBS}). Note that it can affect the number of threads used + by the BLAS libraries if they rely on OpenMP. + + - If None, this function will apply to all supported libraries. + """ + return _ThreadpoolLimiter.wrap(self, limits=limits, user_api=user_api) + + def __len__(self): + return len(self.lib_controllers) + + def _load_libraries(self): + """Loop through loaded shared libraries and store the supported ones""" + if sys.platform == "darwin": + self._find_libraries_with_dyld() + elif sys.platform == "win32": + self._find_libraries_with_enum_process_module_ex() + elif "pyodide" in sys.modules: + self._find_libraries_pyodide() + else: + self._find_libraries_with_dl_iterate_phdr() + + def _find_libraries_with_dl_iterate_phdr(self): + """Loop through loaded libraries and return binders on supported ones + + This function is expected to work on POSIX system only. + This code is adapted from code by Intel developer @anton-malakhov + available at https://github.com/IntelPython/smp + + Copyright (c) 2017, Intel Corporation published under the BSD 3-Clause + license + """ + libc = self._get_libc() + if not hasattr(libc, "dl_iterate_phdr"): # pragma: no cover + warnings.warn( + "Could not find dl_iterate_phdr in the C standard library.", + RuntimeWarning, + ) + return [] + + # Callback function for `dl_iterate_phdr` which is called for every + # library loaded in the current process until it returns 1. + def match_library_callback(info, size, data): + # Get the path of the current library + filepath = info.contents.dlpi_name + if filepath: + filepath = filepath.decode("utf-8") + + # Store the library controller if it is supported and selected + self._make_controller_from_path(filepath) + return 0 + + c_func_signature = ctypes.CFUNCTYPE( + ctypes.c_int, # Return type + ctypes.POINTER(_dl_phdr_info), + ctypes.c_size_t, + ctypes.c_char_p, + ) + c_match_library_callback = c_func_signature(match_library_callback) + + data = ctypes.c_char_p(b"") + libc.dl_iterate_phdr(c_match_library_callback, data) + + def _find_libraries_with_dyld(self): + """Loop through loaded libraries and return binders on supported ones + + This function is expected to work on OSX system only + """ + libc = self._get_libc() + if not hasattr(libc, "_dyld_image_count"): # pragma: no cover + warnings.warn( + "Could not find _dyld_image_count in the C standard library.", + RuntimeWarning, + ) + return [] + + n_dyld = libc._dyld_image_count() + libc._dyld_get_image_name.restype = ctypes.c_char_p + + for i in range(n_dyld): + filepath = ctypes.string_at(libc._dyld_get_image_name(i)) + filepath = filepath.decode("utf-8") + + # Store the library controller if it is supported and selected + self._make_controller_from_path(filepath) + + def _find_libraries_with_enum_process_module_ex(self): + """Loop through loaded libraries and return binders on supported ones + + This function is expected to work on windows system only. + This code is adapted from code by Philipp Hagemeister @phihag available + at https://stackoverflow.com/questions/17474574 + """ + from ctypes.wintypes import DWORD, HMODULE, MAX_PATH + + PROCESS_QUERY_INFORMATION = 0x0400 + PROCESS_VM_READ = 0x0010 + + LIST_LIBRARIES_ALL = 0x03 + + ps_api = self._get_windll("Psapi") + kernel_32 = self._get_windll("kernel32") + + h_process = kernel_32.OpenProcess( + PROCESS_QUERY_INFORMATION | PROCESS_VM_READ, False, os.getpid() + ) + if not h_process: # pragma: no cover + raise OSError(f"Could not open PID {os.getpid()}") + + try: + buf_count = 256 + needed = DWORD() + # Grow the buffer until it becomes large enough to hold all the + # module headers + while True: + buf = (HMODULE * buf_count)() + buf_size = ctypes.sizeof(buf) + if not ps_api.EnumProcessModulesEx( + h_process, + ctypes.byref(buf), + buf_size, + ctypes.byref(needed), + LIST_LIBRARIES_ALL, + ): + raise OSError("EnumProcessModulesEx failed") + if buf_size >= needed.value: + break + buf_count = needed.value // (buf_size // buf_count) + + count = needed.value // (buf_size // buf_count) + h_modules = map(HMODULE, buf[:count]) + + # Loop through all the module headers and get the library path + buf = ctypes.create_unicode_buffer(MAX_PATH) + n_size = DWORD() + for h_module in h_modules: + # Get the path of the current module + if not ps_api.GetModuleFileNameExW( + h_process, h_module, ctypes.byref(buf), ctypes.byref(n_size) + ): + raise OSError("GetModuleFileNameEx failed") + filepath = buf.value + + # Store the library controller if it is supported and selected + self._make_controller_from_path(filepath) + finally: + kernel_32.CloseHandle(h_process) + + def _find_libraries_pyodide(self): + """Pyodide specific implementation for finding loaded libraries. + + Adapted from suggestion in https://github.com/joblib/threadpoolctl/pull/169#issuecomment-1946696449. + + One day, we may have a simpler solution. libc dl_iterate_phdr needs to + be implemented in Emscripten and exposed in Pyodide, see + https://github.com/emscripten-core/emscripten/issues/21354 for more + details. + """ + try: + from pyodide_js._module import LDSO + except ImportError: + warnings.warn( + "Unable to import LDSO from pyodide_js._module. This should never " + "happen." + ) + return + + for filepath in LDSO.loadedLibsByName.as_object_map(): + # Some libraries are duplicated by Pyodide and do not exist in the + # filesystem, so we first check for the existence of the file. For + # more details, see + # https://github.com/joblib/threadpoolctl/pull/169#issuecomment-1947946728 + if os.path.exists(filepath): + self._make_controller_from_path(filepath) + + def _make_controller_from_path(self, filepath): + """Store a library controller if it is supported and selected""" + # Required to resolve symlinks + filepath = _realpath(filepath) + # `lower` required to take account of OpenMP dll case on Windows + # (vcomp, VCOMP, Vcomp, ...) + filename = os.path.basename(filepath).lower() + + # Loop through supported libraries to find if this filename corresponds + # to a supported one. + for controller_class in _ALL_CONTROLLERS: + # check if filename matches a supported prefix + prefix = self._check_prefix(filename, controller_class.filename_prefixes) + + # filename does not match any of the prefixes of the candidate + # library. move to next library. + if prefix is None: + continue + + # workaround for BLAS libraries packaged by conda-forge on windows, which + # are all renamed "libblas.dll". We thus have to check to which BLAS + # implementation it actually corresponds looking for implementation + # specific symbols. + if prefix == "libblas": + if filename.endswith(".dll"): + libblas = ctypes.CDLL(filepath, _RTLD_NOLOAD) + if not any( + hasattr(libblas, func) + for func in controller_class.check_symbols + ): + continue + else: + # We ignore libblas on other platforms than windows because there + # might be a libblas dso comming with openblas for instance that + # can't be used to instantiate a pertinent LibController (many + # symbols are missing) and would create confusion by making a + # duplicate entry in threadpool_info. + continue + + # filename matches a prefix. Now we check if the library has the symbols we + # are looking for. If none of the symbols exists, it's very likely not the + # expected library (e.g. a library having a common prefix with one of the + # our supported libraries). Otherwise, create and store the library + # controller. + lib_controller = controller_class( + filepath=filepath, prefix=prefix, parent=self + ) + + if filepath in (lib.filepath for lib in self.lib_controllers): + # We already have a controller for this library. + continue + + if not hasattr(controller_class, "check_symbols") or any( + hasattr(lib_controller.dynlib, func) + for func in controller_class.check_symbols + ): + self.lib_controllers.append(lib_controller) + + def _check_prefix(self, library_basename, filename_prefixes): + """Return the prefix library_basename starts with + + Return None if none matches. + """ + for prefix in filename_prefixes: + if library_basename.startswith(prefix): + return prefix + return None + + def _warn_if_incompatible_openmp(self): + """Raise a warning if llvm-OpenMP and intel-OpenMP are both loaded""" + prefixes = [lib_controller.prefix for lib_controller in self.lib_controllers] + msg = textwrap.dedent( + """ + Found Intel OpenMP ('libiomp') and LLVM OpenMP ('libomp') loaded at + the same time. Both libraries are known to be incompatible and this + can cause random crashes or deadlocks on Linux when loaded in the + same Python program. + Using threadpoolctl may cause crashes or deadlocks. For more + information and possible workarounds, please see + https://github.com/joblib/threadpoolctl/blob/master/multiple_openmp.md + """ + ) + if "libomp" in prefixes and "libiomp" in prefixes: + warnings.warn(msg, RuntimeWarning) + + @classmethod + def _get_libc(cls): + """Load the lib-C for unix systems.""" + libc = cls._system_libraries.get("libc") + if libc is None: + # Remark: If libc is statically linked or if Python is linked against an + # alternative implementation of libc like musl, find_library will return + # None and CDLL will load the main program itself which should contain the + # libc symbols. We still name it libc for convenience. + # If the main program does not contain the libc symbols, it's ok because + # we check their presence later anyway. + libc = ctypes.CDLL(find_library("c"), mode=_RTLD_NOLOAD) + cls._system_libraries["libc"] = libc + return libc + + @classmethod + def _get_windll(cls, dll_name): + """Load a windows DLL""" + dll = cls._system_libraries.get(dll_name) + if dll is None: + dll = ctypes.WinDLL(f"{dll_name}.dll") + cls._system_libraries[dll_name] = dll + return dll + + +def _main(): + """Commandline interface to display thread-pool information and exit.""" + import argparse + import importlib + import json + import sys + + parser = argparse.ArgumentParser( + usage="python -m threadpoolctl -i numpy scipy.linalg xgboost", + description="Display thread-pool information and exit.", + ) + parser.add_argument( + "-i", + "--import", + dest="modules", + nargs="*", + default=(), + help="Python modules to import before introspecting thread-pools.", + ) + 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this.new_model({model_name:l.model_name,model_module:l.model_module,model_module_version:l.model_module_version,model_id:e,comm:t},l.state);else{const t=await this.get_model(e),o=await t.constructor._deserialize_state(l.state,this);t.set_state(o)}}catch(e){console.error(e)}})))}async _loadFromKernelModels(){const e=await this._get_comm_info(),t=await Promise.all(Object.keys(e).map((async e=>{if(this.has_model(e))return;const t=await this._create_comm(this.comm_target_name,e);let o="";const r=new n.PromiseDelegate;return t.on_msg((e=>{if(e.parent_header.msg_id===o&&"comm_msg"===e.header.msg_type&&"update"===e.content.data.method){const o=e.content.data,n=o.buffer_paths||[],l=e.buffers||[];(0,s.put_buffers)(o.state,n,l),r.resolve({comm:t,msg:e})}})),o=t.send({method:"request_state"},this.callbacks(void 0)),r.promise})));await Promise.all(t.map((async e=>{if(!e)return;const t=e.msg.content;await this.new_model({model_name:t.data.state._model_name,model_module:t.data.state._model_module,model_module_version:t.data.state._model_module_version,comm:e.comm},t.data.state)})))}async _make_model(e,t={}){const o=e.model_id,n=this.loadModelClass(e.model_name,e.model_module,e.model_module_version);let r;const l=(e,t)=>new(s.createErrorWidgetModel(e,t));try{r=await n}catch(e){const t="Could not instantiate widget";return console.error(t),l(e,t)}if(!r){const t="Could not instantiate widget";return console.error(t),l(new Error(`Cannot find model module ${e.model_module}@${e.model_module_version}, ${e.model_name}`),t)}let a;try{const s=await r._deserialize_state(t,this);a=new r(s,{widget_manager:this,model_id:o,comm:e.comm})}catch(t){console.error(t),a=l(t,`Model class '${e.model_name}' from module '${e.model_module}' is loaded but can not be instantiated`)}return a.name=e.model_name,a.module=e.model_module,a}clear_state(){return(0,s.resolvePromisesDict)(this._models).then((e=>{Object.keys(e).forEach((t=>e[t].close())),this._models=Object.create(null)}))}get_state(e={}){const t=Object.keys(this._models).map((e=>this._models[e]));return Promise.all(t).then((t=>b(t,e)))}set_state(e){if(!(e.version_major&&e.version_major<=2))throw"Unsupported widget state format";const t=e.state;return this._get_comm_info().then((e=>Promise.all(Object.keys(t).map((o=>{const n={base64:d,hex:i},r=t[o],l=r.state;if(r.buffers){const e=r.buffers.map((e=>e.path)),t=r.buffers.map((e=>new DataView(n[e.encoding](e.data))));(0,s.put_buffers)(r.state,e,t)}if(this.has_model(o))return this.get_model(o).then((e=>e.constructor._deserialize_state(l||{},this).then((t=>(e.set_state(t),e)))));const a={model_id:o,model_name:r.model_name,model_module:r.model_module,model_module_version:r.model_module_version};return Object.prototype.hasOwnProperty.call(e,"model_id")?this._create_comm(this.comm_target_name,o).then((e=>(a.comm=e,this.new_model(a)))):this.new_model(a,l)})))))}disconnect(){Object.keys(this._models).forEach((e=>{this._models[e].then((e=>{e.comm_live=!1}))}))}resolveUrl(e){return Promise.resolve(e)}inline_sanitize(e){const t=function(e){const t=[];let o,s=null,n=null,r=null,l=0;/`/.test(e)?(e=e.replace(/~/g,"~T").replace(/(^|[^\\])(`+)([^\n]*?[^`\n])\2(?!`)/gm,(e=>e.replace(/\$/g,"~D"))),o=e=>e.replace(/~([TD])/g,((e,t)=>"T"===t?"~":"$"))):o=e=>e;let a=e.replace(/\r\n?/g,"\n").split(_);for(let e=1,i=a.length;e{let o=n[t];return"\\\\("===o.substr(0,3)&&"\\\\)"===o.substr(o.length-3)?o="\\("+o.substring(3,o.length-3)+"\\)":"\\\\["===o.substr(0,3)&&"\\\\]"===o.substr(o.length-3)&&(o="\\["+o.substring(3,o.length-3)+"\\]"),o}))}async loadModelClass(e,t,o){try{const s=this.loadClass(e,t,o);return await s,s}catch(o){console.error(o);const n=`Failed to load model class '${e}' from module '${t}'`;return s.createErrorWidgetModel(o,n)}}async loadViewClass(e,t,o){try{const s=this.loadClass(e,t,o);return await s,s}catch(o){console.error(o);const n=`Failed to load view class '${e}' from module '${t}'`;return s.createErrorWidgetView(o,n)}}filterExistingModelState(e){let t=e.state;return t=Object.keys(t).filter((e=>!this.has_model(e))).reduce(((e,o)=>(e[o]=t[o],e)),{}),Object.assign(Object.assign({},e),{state:t})}}function b(e,t={}){const o={};return e.forEach((e=>{const n=e.model_id,r=(0,s.remove_buffers)(e.serialize(e.get_state(t.drop_defaults))),l=r.buffers.map(((e,t)=>({data:m(e),path:r.buffer_paths[t],encoding:"base64"})));o[n]={model_name:e.name,model_module:e.module,model_module_version:e.get("_model_module_version"),state:r.state},l.length>0&&(o[n].buffers=l)})),{version_major:2,version_minor:0,state:o}}},3215:()=>{},8892:()=>{},5324:()=>{},8645:()=>{},588:()=>{}}]); \ No newline at end of file diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/420.23ab95819c045f6c36bc.js b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/420.23ab95819c045f6c36bc.js new file mode 100644 index 0000000000000000000000000000000000000000..0c2d7a62ca88d2776109906ed6acc44401b8cdca --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/420.23ab95819c045f6c36bc.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunk_jupyter_widgets_jupyterlab_manager=self.webpackChunk_jupyter_widgets_jupyterlab_manager||[]).push([[420],{4420:(e,t,u)=>{u.r(t),u.d(t,{OUTPUT_WIDGET_VERSION:()=>_,OutputModel:()=>d,OutputView:()=>l});var s=u(7401);const _="1.0.0";class d extends s.DOMWidgetModel{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"OutputModel",_view_name:"OutputView",_model_module:"@jupyter-widgets/output",_view_module:"@jupyter-widgets/output",_model_module_version:_,_view_module_version:_})}}class l extends s.DOMWidgetView{}}}]); \ No newline at end of file diff --git a/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/446.f8696ce72124c78273da.js b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/446.f8696ce72124c78273da.js new file mode 100644 index 0000000000000000000000000000000000000000..5a288c678db50af65f89bfc31e982e71be08fe47 --- /dev/null +++ b/emissary-ml/llm-scripts/fine-tuning/llama3/venv/share/jupyter/labextensions/@jupyter-widgets/jupyterlab-manager/static/446.f8696ce72124c78273da.js @@ -0,0 +1 @@ +"use strict";(self.webpackChunk_jupyter_widgets_jupyterlab_manager=self.webpackChunk_jupyter_widgets_jupyterlab_manager||[]).push([[446,701],{1556:(e,n,t)=>{t.d(n,{A:()=>d});var i=t(4786),r=t.n(i),o=t(9451),a=t.n(o)()(r());a.push([e.id,"/* Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n */\n\n.jupyter-widgets-disconnected::before {\n content: '\\f127'; /* chain-broken */\n display: inline-block;\n font: normal normal 900 14px/1 'Font Awesome 5 Free', 'FontAwesome';\n text-rendering: auto;\n -webkit-font-smoothing: antialiased;\n -moz-osx-font-smoothing: grayscale;\n color: #d9534f;\n padding: 3px;\n align-self: flex-start;\n}\n\n.jupyter-widgets-error-widget {\n display: flex;\n flex-direction: column;\n justify-content: center;\n height: 100%;\n border: solid 1px red;\n margin: 0 auto;\n}\n\n.jupyter-widgets-error-widget.icon-error {\n min-width: var(--jp-widgets-inline-width-short);\n}\n.jupyter-widgets-error-widget.text-error {\n min-width: calc(2 * var(--jp-widgets-inline-width));\n min-height: calc(3 * var(--jp-widgets-inline-height));\n}\n\n.jupyter-widgets-error-widget p {\n text-align: center;\n}\n\n.jupyter-widgets-error-widget.text-error pre::first-line {\n font-weight: bold;\n}\n",""]);const d=a},1451:(e,n,t)=>{t.d(n,{A:()=>d});var i=t(4786),r=t.n(i),o=t(9451),a=t.n(o)()(r());a.push([e.id,"/* This file has code derived from Lumino CSS files, as noted below. The license for this Lumino code is:\n\nCopyright (c) 2019 Project Jupyter Contributors\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n3. Neither the name of the copyright holder nor the names of its\n contributors may be used to endorse or promote products derived from\n this software without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n\n\nCopyright (c) 2014-2017, PhosphorJS Contributors\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n* Redistributions of source code must retain the above copyright notice, this\n list of conditions and the following disclaimer.\n\n* Redistributions in binary form must reproduce the above copyright notice,\n this list of conditions and the following disclaimer in the documentation\n and/or other materials provided with the distribution.\n\n* Neither the name of the copyright holder nor the names of its\n contributors may be used to endorse or promote products derived from\n this software without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n*/\n\n/*\n * The following section is derived from https://github.com/jupyterlab/lumino/blob/23b9d075ebc5b73ab148b6ebfc20af97f85714c4/packages/widgets/style/tabbar.css \n * We've scoped the rules so that they are consistent with exactly our code.\n */\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar {\n display: flex;\n -webkit-user-select: none;\n -moz-user-select: none;\n -ms-user-select: none;\n user-select: none;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar[data-orientation='horizontal'], /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar[data-orientation='horizontal'], /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar[data-orientation='horizontal'] {\n flex-direction: row;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar[data-orientation='vertical'], /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar[data-orientation='vertical'], /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar[data-orientation='vertical'] {\n flex-direction: column;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar > .p-TabBar-content, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar > .p-TabBar-content, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar > .lm-TabBar-content {\n margin: 0;\n padding: 0;\n display: flex;\n flex: 1 1 auto;\n list-style-type: none;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar[data-orientation='horizontal']\n > .p-TabBar-content,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n> .p-TabBar[data-orientation='horizontal']\n> .p-TabBar-content,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar[data-orientation='horizontal']\n > .lm-TabBar-content {\n flex-direction: row;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar[data-orientation='vertical']\n > .p-TabBar-content,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n> .p-TabBar[data-orientation='vertical']\n> .p-TabBar-content,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar[data-orientation='vertical']\n > .lm-TabBar-content {\n flex-direction: column;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab {\n display: flex;\n flex-direction: row;\n box-sizing: border-box;\n overflow: hidden;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabIcon, /* */\n/* */ .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabCloseIcon, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabIcon, /* */\n/* */ .jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabCloseIcon, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabIcon,\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabCloseIcon {\n flex: 0 0 auto;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabLabel, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabLabel, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabLabel {\n flex: 1 1 auto;\n overflow: hidden;\n white-space: nowrap;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-hidden, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab.p-mod-hidden, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab.lm-mod-hidden {\n display: none !important;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar.p-mod-dragging .p-TabBar-tab, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar.p-mod-dragging .p-TabBar-tab, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar.lm-mod-dragging .lm-TabBar-tab {\n position: relative;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar.p-mod-dragging[data-orientation='horizontal']\n .p-TabBar-tab,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .p-TabBar.p-mod-dragging[data-orientation='horizontal']\n .p-TabBar-tab,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar.lm-mod-dragging[data-orientation='horizontal']\n .lm-TabBar-tab {\n left: 0;\n transition: left 150ms ease;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar.p-mod-dragging[data-orientation='vertical']\n .p-TabBar-tab,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n> .p-TabBar.p-mod-dragging[data-orientation='vertical']\n.p-TabBar-tab,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar.lm-mod-dragging[data-orientation='vertical']\n .lm-TabBar-tab {\n top: 0;\n transition: top 150ms ease;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar.p-mod-dragging\n .p-TabBar-tab.p-mod-dragging,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n> .p-TabBar.p-mod-dragging\n.p-TabBar-tab.p-mod-dragging,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar.lm-mod-dragging\n .lm-TabBar-tab.lm-mod-dragging {\n transition: none;\n}\n\n/* End tabbar.css */\n",""]);const d=a},9013:(e,n,t)=>{t.d(n,{A:()=>d});var i=t(4786),r=t.n(i),o=t(9451),a=t.n(o)()(r());a.push([e.id,'/*\n\nThe nouislider.css file is autogenerated from nouislider.less, which imports and wraps the nouislider/src/nouislider.less styles.\n\nMIT License\n\nCopyright (c) 2019 Léon Gersen\n\nPermission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.\n*/\n/* The .widget-slider class is deprecated */\n.widget-slider,\n.jupyter-widget-slider {\n /* Functional styling;\n * These styles are required for noUiSlider to function.\n * You don\'t need to change these rules to apply your design.\n */\n /* Wrapper for all connect elements.\n */\n /* Offset direction\n */\n /* Give origins 0 height/width so they don\'t interfere with clicking the\n * connect elements.\n */\n /* Slider size and handle placement;\n */\n /* Styling;\n * Giving the connect element a border radius causes issues with using transform: scale\n */\n /* Handles and cursors;\n */\n /* Handle stripes;\n */\n /* Disabled state;\n */\n /* Base;\n *\n */\n /* Values;\n *\n */\n /* Markings;\n *\n */\n /* Horizontal layout;\n *\n */\n /* Vertical layout;\n *\n */\n /* Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n */\n /* Custom CSS for nouislider */\n}\n.widget-slider .noUi-target,\n.jupyter-widget-slider .noUi-target,\n.widget-slider .noUi-target *,\n.jupyter-widget-slider .noUi-target * {\n -webkit-touch-callout: none;\n -webkit-tap-highlight-color: rgba(0, 0, 0, 0);\n -webkit-user-select: none;\n -ms-touch-action: none;\n touch-action: none;\n -ms-user-select: none;\n -moz-user-select: none;\n user-select: none;\n -moz-box-sizing: border-box;\n box-sizing: border-box;\n}\n.widget-slider .noUi-target,\n.jupyter-widget-slider .noUi-target {\n position: relative;\n}\n.widget-slider .noUi-base,\n.jupyter-widget-slider .noUi-base,\n.widget-slider .noUi-connects,\n.jupyter-widget-slider .noUi-connects {\n width: 100%;\n height: 100%;\n position: relative;\n z-index: 1;\n}\n.widget-slider .noUi-connects,\n.jupyter-widget-slider .noUi-connects {\n overflow: hidden;\n z-index: 0;\n}\n.widget-slider .noUi-connect,\n.jupyter-widget-slider .noUi-connect,\n.widget-slider .noUi-origin,\n.jupyter-widget-slider .noUi-origin {\n will-change: transform;\n position: absolute;\n z-index: 1;\n top: 0;\n right: 0;\n -ms-transform-origin: 0 0;\n -webkit-transform-origin: 0 0;\n -webkit-transform-style: preserve-3d;\n transform-origin: 0 0;\n transform-style: flat;\n}\n.widget-slider .noUi-connect,\n.jupyter-widget-slider .noUi-connect {\n height: 100%;\n width: 100%;\n}\n.widget-slider .noUi-origin,\n.jupyter-widget-slider .noUi-origin {\n height: 10%;\n width: 10%;\n}\n.widget-slider .noUi-txt-dir-rtl.noUi-horizontal .noUi-origin,\n.jupyter-widget-slider .noUi-txt-dir-rtl.noUi-horizontal .noUi-origin {\n left: 0;\n right: auto;\n}\n.widget-slider .noUi-vertical .noUi-origin,\n.jupyter-widget-slider .noUi-vertical .noUi-origin {\n width: 0;\n}\n.widget-slider .noUi-horizontal .noUi-origin,\n.jupyter-widget-slider .noUi-horizontal .noUi-origin {\n height: 0;\n}\n.widget-slider .noUi-handle,\n.jupyter-widget-slider .noUi-handle {\n -webkit-backface-visibility: hidden;\n backface-visibility: hidden;\n position: absolute;\n}\n.widget-slider .noUi-touch-area,\n.jupyter-widget-slider .noUi-touch-area {\n height: 100%;\n width: 100%;\n}\n.widget-slider .noUi-state-tap .noUi-connect,\n.jupyter-widget-slider .noUi-state-tap .noUi-connect,\n.widget-slider .noUi-state-tap .noUi-origin,\n.jupyter-widget-slider .noUi-state-tap .noUi-origin {\n -webkit-transition: transform 0.3s;\n transition: transform 0.3s;\n}\n.widget-slider .noUi-state-drag *,\n.jupyter-widget-slider .noUi-state-drag * {\n cursor: inherit !important;\n}\n.widget-slider .noUi-horizontal,\n.jupyter-widget-slider .noUi-horizontal {\n height: 18px;\n}\n.widget-slider .noUi-horizontal .noUi-handle,\n.jupyter-widget-slider .noUi-horizontal .noUi-handle {\n width: 34px;\n height: 28px;\n right: -17px;\n top: -6px;\n}\n.widget-slider .noUi-vertical,\n.jupyter-widget-slider .noUi-vertical {\n width: 18px;\n}\n.widget-slider .noUi-vertical .noUi-handle,\n.jupyter-widget-slider .noUi-vertical .noUi-handle {\n width: 28px;\n height: 34px;\n right: -6px;\n top: -17px;\n}\n.widget-slider .noUi-txt-dir-rtl.noUi-horizontal .noUi-handle,\n.jupyter-widget-slider .noUi-txt-dir-rtl.noUi-horizontal .noUi-handle {\n left: -17px;\n right: auto;\n}\n.widget-slider .noUi-target,\n.jupyter-widget-slider .noUi-target {\n background: #FAFAFA;\n border-radius: 4px;\n border: 1px solid #D3D3D3;\n box-shadow: inset 0 1px 1px #F0F0F0, 0 3px 6px -5px #BBB;\n}\n.widget-slider .noUi-connects,\n.jupyter-widget-slider .noUi-connects {\n border-radius: 3px;\n}\n.widget-slider .noUi-connect,\n.jupyter-widget-slider .noUi-connect {\n background: #3FB8AF;\n}\n.widget-slider .noUi-draggable,\n.jupyter-widget-slider .noUi-draggable {\n cursor: ew-resize;\n}\n.widget-slider .noUi-vertical .noUi-draggable,\n.jupyter-widget-slider .noUi-vertical .noUi-draggable {\n cursor: ns-resize;\n}\n.widget-slider .noUi-handle,\n.jupyter-widget-slider .noUi-handle {\n border: 1px solid #D9D9D9;\n border-radius: 3px;\n background: #FFF;\n cursor: default;\n box-shadow: inset 0 0 1px #FFF, inset 0 1px 7px #EBEBEB, 0 3px 6px -3px #BBB;\n}\n.widget-slider .noUi-active,\n.jupyter-widget-slider .noUi-active {\n box-shadow: inset 0 0 1px #FFF, inset 0 1px 7px #DDD, 0 3px 6px -3px #BBB;\n}\n.widget-slider .noUi-handle:before,\n.jupyter-widget-slider .noUi-handle:before,\n.widget-slider .noUi-handle:after,\n.jupyter-widget-slider .noUi-handle:after {\n content: "";\n display: block;\n position: absolute;\n height: 14px;\n width: 1px;\n background: #E8E7E6;\n left: 14px;\n top: 6px;\n}\n.widget-slider .noUi-handle:after,\n.jupyter-widget-slider .noUi-handle:after {\n left: 17px;\n}\n.widget-slider .noUi-vertical .noUi-handle:before,\n.jupyter-widget-slider .noUi-vertical .noUi-handle:before,\n.widget-slider .noUi-vertical .noUi-handle:after,\n.jupyter-widget-slider .noUi-vertical .noUi-handle:after {\n width: 14px;\n height: 1px;\n left: 6px;\n top: 14px;\n}\n.widget-slider .noUi-vertical .noUi-handle:after,\n.jupyter-widget-slider .noUi-vertical .noUi-handle:after {\n top: 17px;\n}\n.widget-slider [disabled] .noUi-connect,\n.jupyter-widget-slider [disabled] .noUi-connect {\n background: #B8B8B8;\n}\n.widget-slider [disabled].noUi-target,\n.jupyter-widget-slider [disabled].noUi-target,\n.widget-slider [disabled].noUi-handle,\n.jupyter-widget-slider [disabled].noUi-handle,\n.widget-slider [disabled] .noUi-handle,\n.jupyter-widget-slider [disabled] .noUi-handle {\n cursor: not-allowed;\n}\n.widget-slider .noUi-pips,\n.jupyter-widget-slider .noUi-pips,\n.widget-slider .noUi-pips *,\n.jupyter-widget-slider .noUi-pips * {\n -moz-box-sizing: border-box;\n box-sizing: border-box;\n}\n.widget-slider .noUi-pips,\n.jupyter-widget-slider .noUi-pips {\n position: absolute;\n color: #999;\n}\n.widget-slider .noUi-value,\n.jupyter-widget-slider .noUi-value {\n position: absolute;\n white-space: nowrap;\n text-align: center;\n}\n.widget-slider .noUi-value-sub,\n.jupyter-widget-slider .noUi-value-sub {\n color: #ccc;\n font-size: 10px;\n}\n.widget-slider .noUi-marker,\n.jupyter-widget-slider .noUi-marker {\n position: absolute;\n background: #CCC;\n}\n.widget-slider .noUi-marker-sub,\n.jupyter-widget-slider .noUi-marker-sub {\n background: #AAA;\n}\n.widget-slider .noUi-marker-large,\n.jupyter-widget-slider .noUi-marker-large {\n background: #AAA;\n}\n.widget-slider .noUi-pips-horizontal,\n.jupyter-widget-slider .noUi-pips-horizontal {\n padding: 10px 0;\n height: 80px;\n top: 100%;\n left: 0;\n width: 100%;\n}\n.widget-slider .noUi-value-horizontal,\n.jupyter-widget-slider .noUi-value-horizontal {\n -webkit-transform: translate(-50%, 50%);\n transform: translate(-50%, 50%);\n}\n.noUi-rtl .widget-slider .noUi-value-horizontal,\n.noUi-rtl .jupyter-widget-slider .noUi-value-horizontal {\n -webkit-transform: translate(50%, 50%);\n transform: translate(50%, 50%);\n}\n.widget-slider .noUi-marker-horizontal.noUi-marker,\n.jupyter-widget-slider .noUi-marker-horizontal.noUi-marker {\n margin-left: -1px;\n width: 2px;\n height: 5px;\n}\n.widget-slider .noUi-marker-horizontal.noUi-marker-sub,\n.jupyter-widget-slider .noUi-marker-horizontal.noUi-marker-sub {\n height: 10px;\n}\n.widget-slider .noUi-marker-horizontal.noUi-marker-large,\n.jupyter-widget-slider .noUi-marker-horizontal.noUi-marker-large {\n height: 15px;\n}\n.widget-slider .noUi-pips-vertical,\n.jupyter-widget-slider .noUi-pips-vertical {\n padding: 0 10px;\n height: 100%;\n top: 0;\n left: 100%;\n}\n.widget-slider .noUi-value-vertical,\n.jupyter-widget-slider .noUi-value-vertical {\n -webkit-transform: translate(0, -50%);\n transform: translate(0, -50%);\n padding-left: 25px;\n}\n.noUi-rtl .widget-slider .noUi-value-vertical,\n.noUi-rtl .jupyter-widget-slider .noUi-value-vertical {\n -webkit-transform: translate(0, 50%);\n transform: translate(0, 50%);\n}\n.widget-slider .noUi-marker-vertical.noUi-marker,\n.jupyter-widget-slider .noUi-marker-vertical.noUi-marker {\n width: 5px;\n height: 2px;\n margin-top: -1px;\n}\n.widget-slider .noUi-marker-vertical.noUi-marker-sub,\n.jupyter-widget-slider .noUi-marker-vertical.noUi-marker-sub {\n width: 10px;\n}\n.widget-slider .noUi-marker-vertical.noUi-marker-large,\n.jupyter-widget-slider .noUi-marker-vertical.noUi-marker-large {\n width: 15px;\n}\n.widget-slider .noUi-tooltip,\n.jupyter-widget-slider .noUi-tooltip {\n display: block;\n position: absolute;\n border: 1px solid #D9D9D9;\n border-radius: 3px;\n background: #fff;\n color: #000;\n padding: 5px;\n text-align: center;\n white-space: nowrap;\n}\n.widget-slider .noUi-horizontal .noUi-tooltip,\n.jupyter-widget-slider .noUi-horizontal .noUi-tooltip {\n -webkit-transform: translate(-50%, 0);\n transform: translate(-50%, 0);\n left: 50%;\n bottom: 120%;\n}\n.widget-slider .noUi-vertical .noUi-tooltip,\n.jupyter-widget-slider .noUi-vertical .noUi-tooltip {\n -webkit-transform: translate(0, -50%);\n transform: translate(0, -50%);\n top: 50%;\n right: 120%;\n}\n.widget-slider .noUi-horizontal .noUi-origin > .noUi-tooltip,\n.jupyter-widget-slider .noUi-horizontal .noUi-origin > .noUi-tooltip {\n -webkit-transform: translate(50%, 0);\n transform: translate(50%, 0);\n left: auto;\n bottom: 10px;\n}\n.widget-slider .noUi-vertical .noUi-origin > .noUi-tooltip,\n.jupyter-widget-slider .noUi-vertical .noUi-origin > .noUi-tooltip {\n -webkit-transform: translate(0, -18px);\n transform: translate(0, -18px);\n top: auto;\n right: 28px;\n}\n.widget-slider .noUi-connect,\n.jupyter-widget-slider .noUi-connect {\n background: #2196f3;\n}\n.widget-slider .noUi-horizontal,\n.jupyter-widget-slider .noUi-horizontal {\n height: var(--jp-widgets-slider-track-thickness);\n}\n.widget-slider .noUi-vertical,\n.jupyter-widget-slider .noUi-vertical {\n width: var(--jp-widgets-slider-track-thickness);\n height: 100%;\n}\n.widget-slider .noUi-horizontal .noUi-handle,\n.jupyter-widget-slider .noUi-horizontal .noUi-handle {\n width: var(--jp-widgets-slider-handle-size);\n height: var(--jp-widgets-slider-handle-size);\n border-radius: 50%;\n top: calc((var(--jp-widgets-slider-track-thickness) - var(--jp-widgets-slider-handle-size)) / 2);\n right: calc(var(--jp-widgets-slider-handle-size) / -2);\n}\n.widget-slider .noUi-vertical .noUi-handle,\n.jupyter-widget-slider .noUi-vertical .noUi-handle {\n height: var(--jp-widgets-slider-handle-size);\n width: var(--jp-widgets-slider-handle-size);\n border-radius: 50%;\n right: calc((var(--jp-widgets-slider-handle-size) - var(--jp-widgets-slider-track-thickness)) / -2);\n top: calc(var(--jp-widgets-slider-handle-size) / -2);\n}\n.widget-slider .noUi-handle:after,\n.jupyter-widget-slider .noUi-handle:after {\n content: none;\n}\n.widget-slider .noUi-handle:before,\n.jupyter-widget-slider .noUi-handle:before {\n content: none;\n}\n.widget-slider .noUi-target,\n.jupyter-widget-slider .noUi-target {\n background: #fafafa;\n border-radius: 4px;\n border: 1px;\n /* box-shadow: inset 0 1px 1px #F0F0F0, 0 3px 6px -5px #BBB; */\n}\n.widget-slider .ui-slider,\n.jupyter-widget-slider .ui-slider {\n border: var(--jp-widgets-slider-border-width) solid var(--jp-layout-color3);\n background: var(--jp-layout-color3);\n box-sizing: border-box;\n position: relative;\n border-radius: 0px;\n}\n.widget-slider .noUi-handle,\n.jupyter-widget-slider .noUi-handle {\n width: var(--jp-widgets-slider-handle-size);\n border: 1px solid #d9d9d9;\n border-radius: 3px;\n background: #fff;\n cursor: default;\n box-shadow: none;\n outline: none;\n}\n.widget-slider .noUi-target:not([disabled]) .noUi-handle:hover,\n.jupyter-widget-slider .noUi-target:not([disabled]) .noUi-handle:hover,\n.widget-slider .noUi-target:not([disabled]) .noUi-handle:focus,\n.jupyter-widget-slider .noUi-target:not([disabled]) .noUi-handle:focus {\n background-color: var(--jp-widgets-slider-active-handle-color);\n border: var(--jp-widgets-slider-border-width) solid var(--jp-widgets-slider-active-handle-color);\n}\n.widget-slider [disabled].noUi-target,\n.jupyter-widget-slider [disabled].noUi-target {\n opacity: 0.35;\n}\n.widget-slider .noUi-connects,\n.jupyter-widget-slider .noUi-connects {\n overflow: visible;\n z-index: 0;\n background: var(--jp-layout-color3);\n}\n.widget-slider .noUi-vertical .noUi-connect,\n.jupyter-widget-slider .noUi-vertical .noUi-connect {\n width: calc(100% + 2px);\n right: -1px;\n}\n.widget-slider .noUi-horizontal .noUi-connect,\n.jupyter-widget-slider .noUi-horizontal .noUi-connect {\n height: calc(100% + 2px);\n top: -1px;\n}\n',""]);const d=a},7654:(e,n,t)=>{t.d(n,{A:()=>w});var i=t(4786),r=t.n(i),o=t(9451),a=t.n(o),d=t(1451),s=t(9013),l=t(7298),g=t.n(l),p=new URL(t(2426),t.b),c=a()(r());c.i(d.A),c.i(s.A);var u=g()(p);c.push([e.id,`/* Copyright (c) Jupyter Development Team.\n * Distributed under the terms of the Modified BSD License.\n */\n\n/*\n * We assume that the CSS variables in\n * https://github.com/jupyterlab/jupyterlab/blob/master/src/default-theme/variables.css\n * have been defined.\n */\n\n:root {\n --jp-widgets-color: var(--jp-content-font-color1);\n --jp-widgets-label-color: var(--jp-widgets-color);\n --jp-widgets-readout-color: var(--jp-widgets-color);\n --jp-widgets-font-size: var(--jp-ui-font-size1);\n --jp-widgets-margin: 2px;\n --jp-widgets-inline-height: 28px;\n --jp-widgets-inline-width: 300px;\n --jp-widgets-inline-width-short: calc(\n var(--jp-widgets-inline-width) / 2 - var(--jp-widgets-margin)\n );\n --jp-widgets-inline-width-tiny: calc(\n var(--jp-widgets-inline-width-short) / 2 - var(--jp-widgets-margin)\n );\n --jp-widgets-inline-margin: 4px; /* margin between inline elements */\n --jp-widgets-inline-label-width: 80px;\n --jp-widgets-border-width: var(--jp-border-width);\n --jp-widgets-vertical-height: 200px;\n --jp-widgets-horizontal-tab-height: 24px;\n --jp-widgets-horizontal-tab-width: 144px;\n --jp-widgets-horizontal-tab-top-border: 2px;\n --jp-widgets-progress-thickness: 20px;\n --jp-widgets-container-padding: 15px;\n --jp-widgets-input-padding: 4px;\n --jp-widgets-radio-item-height-adjustment: 8px;\n --jp-widgets-radio-item-height: calc(\n var(--jp-widgets-inline-height) -\n var(--jp-widgets-radio-item-height-adjustment)\n );\n --jp-widgets-slider-track-thickness: 4px;\n --jp-widgets-slider-border-width: var(--jp-widgets-border-width);\n --jp-widgets-slider-handle-size: 16px;\n --jp-widgets-slider-handle-border-color: var(--jp-border-color1);\n --jp-widgets-slider-handle-background-color: var(--jp-layout-color1);\n --jp-widgets-slider-active-handle-color: var(--jp-brand-color1);\n --jp-widgets-menu-item-height: 24px;\n --jp-widgets-dropdown-arrow: url(${u});\n --jp-widgets-input-color: var(--jp-ui-font-color1);\n --jp-widgets-input-background-color: var(--jp-layout-color1);\n --jp-widgets-input-border-color: var(--jp-border-color1);\n --jp-widgets-input-focus-border-color: var(--jp-brand-color2);\n --jp-widgets-input-border-width: var(--jp-widgets-border-width);\n --jp-widgets-disabled-opacity: 0.6;\n\n /* From Material Design Lite */\n --md-shadow-key-umbra-opacity: 0.2;\n --md-shadow-key-penumbra-opacity: 0.14;\n --md-shadow-ambient-shadow-opacity: 0.12;\n}\n\n.jupyter-widgets {\n margin: var(--jp-widgets-margin);\n box-sizing: border-box;\n color: var(--jp-widgets-color);\n overflow: visible;\n}\n\n.jp-Output-result > .jupyter-widgets {\n margin-left: 0;\n margin-right: 0;\n}\n\n/* vbox and hbox */\n\n/* */\n.widget-inline-hbox, /* */\n .jupyter-widget-inline-hbox {\n /* Horizontal widgets */\n box-sizing: border-box;\n display: flex;\n flex-direction: row;\n align-items: baseline;\n}\n\n/* */\n.widget-inline-vbox, /* */\n .jupyter-widget-inline-vbox {\n /* Vertical Widgets */\n box-sizing: border-box;\n display: flex;\n flex-direction: column;\n align-items: center;\n}\n\n/* */\n.widget-box, /* */\n.jupyter-widget-box {\n box-sizing: border-box;\n display: flex;\n margin: 0;\n overflow: auto;\n}\n\n/* */\n.widget-gridbox, /* */\n.jupyter-widget-gridbox {\n box-sizing: border-box;\n display: grid;\n margin: 0;\n overflow: auto;\n}\n\n/* */\n.widget-hbox, /* */\n.jupyter-widget-hbox {\n flex-direction: row;\n}\n\n/* */\n.widget-vbox, /* */\n.jupyter-widget-vbox {\n flex-direction: column;\n}\n\n/* General Tags Styling */\n\n.jupyter-widget-tagsinput {\n display: flex;\n flex-direction: row;\n flex-wrap: wrap;\n align-items: center;\n overflow: auto;\n\n cursor: text;\n}\n\n.jupyter-widget-tag {\n padding-left: 10px;\n padding-right: 10px;\n padding-top: 0px;\n padding-bottom: 0px;\n display: inline-block;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n text-align: center;\n font-size: var(--jp-widgets-font-size);\n\n height: calc(var(--jp-widgets-inline-height) - 2px);\n border: 0px solid;\n line-height: calc(var(--jp-widgets-inline-height) - 2px);\n box-shadow: none;\n\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color2);\n border-color: var(--jp-border-color2);\n border: none;\n user-select: none;\n\n cursor: grab;\n transition: margin-left 200ms;\n margin: 1px 1px 1px 1px;\n}\n\n.jupyter-widget-tag.mod-active {\n /* MD Lite 4dp shadow */\n box-shadow: 0 4px 5px 0 rgba(0, 0, 0, var(--md-shadow-key-penumbra-opacity)),\n 0 1px 10px 0 rgba(0, 0, 0, var(--md-shadow-ambient-shadow-opacity)),\n 0 2px 4px -1px rgba(0, 0, 0, var(--md-shadow-key-umbra-opacity));\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color3);\n}\n\n.jupyter-widget-colortag {\n color: var(--jp-inverse-ui-font-color1);\n}\n\n.jupyter-widget-colortag.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n}\n\n.jupyter-widget-taginput {\n color: var(--jp-ui-font-color0);\n background-color: var(--jp-layout-color0);\n\n cursor: text;\n text-align: left;\n}\n\n.jupyter-widget-taginput:focus {\n outline: none;\n}\n\n.jupyter-widget-tag-close {\n margin-left: var(--jp-widgets-inline-margin);\n padding: 2px 0px 2px 2px;\n}\n\n.jupyter-widget-tag-close:hover {\n cursor: pointer;\n}\n\n/* Tag "Primary" Styling */\n\n.jupyter-widget-tag.mod-primary {\n color: var(--jp-inverse-ui-font-color1);\n background-color: var(--jp-brand-color1);\n}\n\n.jupyter-widget-tag.mod-primary.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n background-color: var(--jp-brand-color0);\n}\n\n/* Tag "Success" Styling */\n\n.jupyter-widget-tag.mod-success {\n color: var(--jp-inverse-ui-font-color1);\n background-color: var(--jp-success-color1);\n}\n\n.jupyter-widget-tag.mod-success.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n background-color: var(--jp-success-color0);\n}\n\n/* Tag "Info" Styling */\n\n.jupyter-widget-tag.mod-info {\n color: var(--jp-inverse-ui-font-color1);\n background-color: var(--jp-info-color1);\n}\n\n.jupyter-widget-tag.mod-info.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n background-color: var(--jp-info-color0);\n}\n\n/* Tag "Warning" Styling */\n\n.jupyter-widget-tag.mod-warning {\n color: var(--jp-inverse-ui-font-color1);\n background-color: var(--jp-warn-color1);\n}\n\n.jupyter-widget-tag.mod-warning.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n background-color: var(--jp-warn-color0);\n}\n\n/* Tag "Danger" Styling */\n\n.jupyter-widget-tag.mod-danger {\n color: var(--jp-inverse-ui-font-color1);\n background-color: var(--jp-error-color1);\n}\n\n.jupyter-widget-tag.mod-danger.mod-active {\n color: var(--jp-inverse-ui-font-color0);\n background-color: var(--jp-error-color0);\n}\n\n/* General Button Styling */\n\n.jupyter-button {\n padding-left: 10px;\n padding-right: 10px;\n padding-top: 0px;\n padding-bottom: 0px;\n display: inline-block;\n white-space: nowrap;\n overflow: hidden;\n text-overflow: ellipsis;\n text-align: center;\n font-size: var(--jp-widgets-font-size);\n cursor: pointer;\n\n height: var(--jp-widgets-inline-height);\n border: 0px solid;\n line-height: var(--jp-widgets-inline-height);\n box-shadow: none;\n\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color2);\n border-color: var(--jp-border-color2);\n border: none;\n user-select: none;\n}\n\n.jupyter-button i.fa {\n margin-right: var(--jp-widgets-inline-margin);\n pointer-events: none;\n}\n\n.jupyter-button:empty:before {\n content: '\\200b'; /* zero-width space */\n}\n\n.jupyter-widgets.jupyter-button:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n.jupyter-button i.fa.center {\n margin-right: 0;\n}\n\n.jupyter-button:hover:enabled,\n.jupyter-button:focus:enabled {\n /* MD Lite 2dp shadow */\n box-shadow: 0 2px 2px 0 rgba(0, 0, 0, var(--md-shadow-key-penumbra-opacity)),\n 0 3px 1px -2px rgba(0, 0, 0, var(--md-shadow-key-umbra-opacity)),\n 0 1px 5px 0 rgba(0, 0, 0, var(--md-shadow-ambient-shadow-opacity));\n}\n\n.jupyter-button:active,\n.jupyter-button.mod-active {\n /* MD Lite 4dp shadow */\n box-shadow: 0 4px 5px 0 rgba(0, 0, 0, var(--md-shadow-key-penumbra-opacity)),\n 0 1px 10px 0 rgba(0, 0, 0, var(--md-shadow-ambient-shadow-opacity)),\n 0 2px 4px -1px rgba(0, 0, 0, var(--md-shadow-key-umbra-opacity));\n color: var(--jp-ui-font-color1);\n background-color: var(--jp-layout-color3);\n}\n\n.jupyter-button:focus:enabled {\n outline: 1px solid var(--jp-widgets-input-focus-border-color);\n}\n\n/* Button "Primary" Styling */\n\n.jupyter-button.mod-primary {\n color: var(--jp-ui-inverse-font-color1);\n background-color: var(--jp-brand-color1);\n}\n\n.jupyter-button.mod-primary.mod-active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-brand-color0);\n}\n\n.jupyter-button.mod-primary:active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-brand-color0);\n}\n\n/* Button "Success" Styling */\n\n.jupyter-button.mod-success {\n color: var(--jp-ui-inverse-font-color1);\n background-color: var(--jp-success-color1);\n}\n\n.jupyter-button.mod-success.mod-active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-success-color0);\n}\n\n.jupyter-button.mod-success:active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-success-color0);\n}\n\n/* Button "Info" Styling */\n\n.jupyter-button.mod-info {\n color: var(--jp-ui-inverse-font-color1);\n background-color: var(--jp-info-color1);\n}\n\n.jupyter-button.mod-info.mod-active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-info-color0);\n}\n\n.jupyter-button.mod-info:active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-info-color0);\n}\n\n/* Button "Warning" Styling */\n\n.jupyter-button.mod-warning {\n color: var(--jp-ui-inverse-font-color1);\n background-color: var(--jp-warn-color1);\n}\n\n.jupyter-button.mod-warning.mod-active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-warn-color0);\n}\n\n.jupyter-button.mod-warning:active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-warn-color0);\n}\n\n/* Button "Danger" Styling */\n\n.jupyter-button.mod-danger {\n color: var(--jp-ui-inverse-font-color1);\n background-color: var(--jp-error-color1);\n}\n\n.jupyter-button.mod-danger.mod-active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-error-color0);\n}\n\n.jupyter-button.mod-danger:active {\n color: var(--jp-ui-inverse-font-color0);\n background-color: var(--jp-error-color0);\n}\n\n/* Widget Button, Widget Toggle Button, Widget Upload */\n\n/* */\n.widget-button, /* */\n/* */ .widget-toggle-button, /* */\n/* */ .widget-upload, /* */\n.jupyter-widget-button,\n.jupyter-widget-toggle-button,\n.jupyter-widget-upload {\n width: var(--jp-widgets-inline-width-short);\n}\n\n/* Widget Label Styling */\n\n/* Override Bootstrap label css */\n.jupyter-widgets label {\n margin-bottom: initial;\n}\n\n/* */\n.widget-label-basic, /* */\n.jupyter-widget-label-basic {\n /* Basic Label */\n color: var(--jp-widgets-label-color);\n font-size: var(--jp-widgets-font-size);\n overflow: hidden;\n text-overflow: ellipsis;\n white-space: nowrap;\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-label, /* */\n.jupyter-widget-label {\n /* Label */\n color: var(--jp-widgets-label-color);\n font-size: var(--jp-widgets-font-size);\n overflow: hidden;\n text-overflow: ellipsis;\n white-space: nowrap;\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-inline-hbox .widget-label, /* */\n.jupyter-widget-inline-hbox .jupyter-widget-label {\n /* Horizontal Widget Label */\n color: var(--jp-widgets-label-color);\n text-align: right;\n margin-right: calc(var(--jp-widgets-inline-margin) * 2);\n width: var(--jp-widgets-inline-label-width);\n flex-shrink: 0;\n}\n\n/* */\n.widget-inline-vbox .widget-label, /* */\n.jupyter-widget-inline-vbox .jupyter-widget-label {\n /* Vertical Widget Label */\n color: var(--jp-widgets-label-color);\n text-align: center;\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* Widget Readout Styling */\n\n/* */\n.widget-readout, /* */\n.jupyter-widget-readout {\n color: var(--jp-widgets-readout-color);\n font-size: var(--jp-widgets-font-size);\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n overflow: hidden;\n white-space: nowrap;\n text-align: center;\n}\n\n/* */\n.widget-readout.overflow, /* */\n.jupyter-widget-readout.overflow {\n /* Overflowing Readout */\n\n /* From Material Design Lite\n shadow-key-umbra-opacity: 0.2;\n shadow-key-penumbra-opacity: 0.14;\n shadow-ambient-shadow-opacity: 0.12;\n */\n -webkit-box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.2),\n 0 3px 1px -2px rgba(0, 0, 0, 0.14), 0 1px 5px 0 rgba(0, 0, 0, 0.12);\n\n -moz-box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.2),\n 0 3px 1px -2px rgba(0, 0, 0, 0.14), 0 1px 5px 0 rgba(0, 0, 0, 0.12);\n\n box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.2), 0 3px 1px -2px rgba(0, 0, 0, 0.14),\n 0 1px 5px 0 rgba(0, 0, 0, 0.12);\n}\n\n/* */\n.widget-inline-hbox .widget-readout, /* */\n.jupyter-widget-inline-hbox .jupyter-widget-readout {\n /* Horizontal Readout */\n text-align: center;\n max-width: var(--jp-widgets-inline-width-short);\n min-width: var(--jp-widgets-inline-width-tiny);\n margin-left: var(--jp-widgets-inline-margin);\n}\n\n/* */\n.widget-inline-vbox .widget-readout, /* */\n.jupyter-widget-inline-vbox .jupyter-widget-readout {\n /* Vertical Readout */\n margin-top: var(--jp-widgets-inline-margin);\n /* as wide as the widget */\n width: inherit;\n}\n\n/* Widget Checkbox Styling */\n\n/* */\n.widget-checkbox, /* */\n.jupyter-widget-checkbox {\n width: var(--jp-widgets-inline-width);\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-checkbox input[type='checkbox'], /* */\n.jupyter-widget-checkbox input[type='checkbox'] {\n margin: 0px calc(var(--jp-widgets-inline-margin) * 2) 0px 0px;\n line-height: var(--jp-widgets-inline-height);\n font-size: large;\n flex-grow: 1;\n flex-shrink: 0;\n align-self: center;\n}\n\n/* Widget Valid Styling */\n\n/* */\n.widget-valid, /* */\n.jupyter-widget-valid {\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n width: var(--jp-widgets-inline-width-short);\n font-size: var(--jp-widgets-font-size);\n}\n\n/* */\n.widget-valid i, /* */\n.jupyter-widget-valid i {\n line-height: var(--jp-widgets-inline-height);\n margin-right: var(--jp-widgets-inline-margin);\n margin-left: var(--jp-widgets-inline-margin);\n}\n\n/* */\n.widget-valid.mod-valid i, /* */\n.jupyter-widget-valid.mod-valid i {\n color: green;\n}\n\n/* */\n.widget-valid.mod-invalid i, /* */\n.jupyter-widget-valid.mod-invalid i {\n color: red;\n}\n\n/* */\n.widget-valid.mod-valid .widget-valid-readout, /* */\n.jupyter-widget-valid.mod-valid .jupyter-widget-valid-readout {\n display: none;\n}\n\n/* Widget Text and TextArea Styling */\n\n/* */\n.widget-textarea, /* */\n/* */ .widget-text, /* */\n.jupyter-widget-textarea,\n.jupyter-widget-text {\n width: var(--jp-widgets-inline-width);\n}\n\n/* */\n.widget-text input[type='text'], /* */\n/* */ .widget-text input[type='number'], /* */\n/* */ .widget-text input[type='password'], /* */\n.jupyter-widget-text input[type='text'],\n.jupyter-widget-text input[type='number'],\n.jupyter-widget-text input[type='password'] {\n height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-text input[type='text']:disabled, /* */\n/* */ .widget-text input[type='number']:disabled, /* */\n/* */ .widget-text input[type='password']:disabled, /* */\n/* */ .widget-textarea textarea:disabled, /* */\n.jupyter-widget-text input[type='text']:disabled,\n.jupyter-widget-text input[type='number']:disabled,\n.jupyter-widget-text input[type='password']:disabled,\n.jupyter-widget-textarea textarea:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* */\n.widget-text input[type='text'], /* */\n/* */ .widget-text input[type='number'], /* */\n/* */ .widget-text input[type='password'], /* */\n/* */ .widget-textarea textarea, /* */\n.jupyter-widget-text input[type='text'],\n.jupyter-widget-text input[type='number'],\n.jupyter-widget-text input[type='password'],\n.jupyter-widget-textarea textarea {\n box-sizing: border-box;\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n background-color: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n font-size: var(--jp-widgets-font-size);\n flex-grow: 1;\n min-width: 0; /* This makes it possible for the flexbox to shrink this input */\n flex-shrink: 1;\n outline: none !important;\n}\n\n/* */\n.widget-text input[type='text'], /* */\n/* */ .widget-text input[type='password'], /* */\n/* */ .widget-textarea textarea, /* */\n.jupyter-widget-text input[type='text'],\n.jupyter-widget-text input[type='password'],\n.jupyter-widget-textarea textarea {\n padding: var(--jp-widgets-input-padding)\n calc(var(--jp-widgets-input-padding) * 2);\n}\n\n/* */\n.widget-text input[type='number'], /* */\n.jupyter-widget-text input[type='number'] {\n padding: var(--jp-widgets-input-padding) 0 var(--jp-widgets-input-padding)\n calc(var(--jp-widgets-input-padding) * 2);\n}\n\n/* */\n.widget-textarea textarea, /* */\n.jupyter-widget-textarea textarea {\n height: inherit;\n width: inherit;\n}\n\n/* */\n.widget-text input:focus, /* */\n/* */ .widget-textarea textarea:focus, /* */\n.jupyter-widget-text input:focus,\n.jupyter-widget-textarea textarea:focus {\n border-color: var(--jp-widgets-input-focus-border-color);\n}\n\n/* Horizontal Slider */\n/* */\n.widget-hslider, /* */\n.jupyter-widget-hslider {\n width: var(--jp-widgets-inline-width);\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n\n /* Override the align-items baseline. This way, the description and readout\n still seem to align their baseline properly, and we don't have to have\n align-self: stretch in the .slider-container. */\n align-items: center;\n}\n\n/* */\n.widgets-slider .slider-container, /* */\n.jupyter-widgets-slider .slider-container {\n overflow: visible;\n}\n\n/* */\n.widget-hslider .slider-container, /* */\n.jupyter-widget-hslider .slider-container {\n margin-left: calc(\n var(--jp-widgets-slider-handle-size) / 2 - 2 *\n var(--jp-widgets-slider-border-width)\n );\n margin-right: calc(\n var(--jp-widgets-slider-handle-size) / 2 - 2 *\n var(--jp-widgets-slider-border-width)\n );\n flex: 1 1 var(--jp-widgets-inline-width-short);\n}\n\n/* Vertical Slider */\n\n/* */\n.widget-vbox .widget-label, /* */\n.jupyter-widget-vbox .jupyter-widget-label {\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-vslider, /* */\n.jupyter-widget-vslider {\n /* Vertical Slider */\n height: var(--jp-widgets-vertical-height);\n width: var(--jp-widgets-inline-width-tiny);\n}\n\n/* */\n.widget-vslider .slider-container, /* */\n.jupyter-widget-vslider .slider-container {\n flex: 1 1 var(--jp-widgets-inline-width-short);\n margin-left: auto;\n margin-right: auto;\n margin-bottom: calc(\n var(--jp-widgets-slider-handle-size) / 2 - 2 *\n var(--jp-widgets-slider-border-width)\n );\n margin-top: calc(\n var(--jp-widgets-slider-handle-size) / 2 - 2 *\n var(--jp-widgets-slider-border-width)\n );\n display: flex;\n flex-direction: column;\n}\n\n/* Widget Progress Styling */\n\n.progress-bar {\n -webkit-transition: none;\n -moz-transition: none;\n -ms-transition: none;\n -o-transition: none;\n transition: none;\n}\n\n.progress-bar {\n height: var(--jp-widgets-inline-height);\n}\n\n.progress-bar {\n background-color: var(--jp-brand-color1);\n}\n\n.progress-bar-success {\n background-color: var(--jp-success-color1);\n}\n\n.progress-bar-info {\n background-color: var(--jp-info-color1);\n}\n\n.progress-bar-warning {\n background-color: var(--jp-warn-color1);\n}\n\n.progress-bar-danger {\n background-color: var(--jp-error-color1);\n}\n\n.progress {\n background-color: var(--jp-layout-color2);\n border: none;\n box-shadow: none;\n}\n\n/* Horisontal Progress */\n\n/* */\n.widget-hprogress, /* */\n.jupyter-widget-hprogress {\n /* Progress Bar */\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n width: var(--jp-widgets-inline-width);\n align-items: center;\n}\n\n/* */\n.widget-hprogress .progress, /* */\n.jupyter-widget-hprogress .progress {\n flex-grow: 1;\n margin-top: var(--jp-widgets-input-padding);\n margin-bottom: var(--jp-widgets-input-padding);\n align-self: stretch;\n /* Override bootstrap style */\n height: initial;\n}\n\n/* Vertical Progress */\n\n/* */\n.widget-vprogress, /* */\n.jupyter-widget-vprogress {\n height: var(--jp-widgets-vertical-height);\n width: var(--jp-widgets-inline-width-tiny);\n}\n\n/* */\n.widget-vprogress .progress, /* */\n.jupyter-widget-vprogress .progress {\n flex-grow: 1;\n width: var(--jp-widgets-progress-thickness);\n margin-left: auto;\n margin-right: auto;\n margin-bottom: 0;\n}\n\n/* Select Widget Styling */\n\n/* */\n.widget-dropdown, /* */\n.jupyter-widget-dropdown {\n height: var(--jp-widgets-inline-height);\n width: var(--jp-widgets-inline-width);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-dropdown > select, /* */\n.jupyter-widget-dropdown > select {\n padding-right: 20px;\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n border-radius: 0;\n height: inherit;\n flex: 1 1 var(--jp-widgets-inline-width-short);\n min-width: 0; /* This makes it possible for the flexbox to shrink this input */\n box-sizing: border-box;\n outline: none !important;\n box-shadow: none;\n background-color: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n font-size: var(--jp-widgets-font-size);\n vertical-align: top;\n padding-left: calc(var(--jp-widgets-input-padding) * 2);\n appearance: none;\n -webkit-appearance: none;\n -moz-appearance: none;\n background-repeat: no-repeat;\n background-size: 20px;\n background-position: right center;\n background-image: var(--jp-widgets-dropdown-arrow);\n}\n/* */\n.widget-dropdown > select:focus, /* */\n.jupyter-widget-dropdown > select:focus {\n border-color: var(--jp-widgets-input-focus-border-color);\n}\n\n/* */\n.widget-dropdown > select:disabled, /* */\n.jupyter-widget-dropdown > select:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* To disable the dotted border in Firefox around select controls.\n See http://stackoverflow.com/a/18853002 */\n/* */\n.widget-dropdown > select:-moz-focusring, /* */\n.jupyter-widget-dropdown > select:-moz-focusring {\n color: transparent;\n text-shadow: 0 0 0 #000;\n}\n\n/* Select and SelectMultiple */\n\n/* */\n.widget-select, /* */\n.jupyter-widget-select {\n width: var(--jp-widgets-inline-width);\n line-height: var(--jp-widgets-inline-height);\n\n /* Because Firefox defines the baseline of a select as the bottom of the\n control, we align the entire control to the top and add padding to the\n select to get an approximate first line baseline alignment. */\n align-items: flex-start;\n}\n\n/* */\n.widget-select > select, /* */\n.jupyter-widget-select > select {\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n background-color: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n font-size: var(--jp-widgets-font-size);\n flex: 1 1 var(--jp-widgets-inline-width-short);\n outline: none !important;\n overflow: auto;\n height: inherit;\n\n /* Because Firefox defines the baseline of a select as the bottom of the\n control, we align the entire control to the top and add padding to the\n select to get an approximate first line baseline alignment. */\n padding-top: 5px;\n}\n\n/* */\n.widget-select > select:focus, /* */\n.jupyter-widget-select > select:focus {\n border-color: var(--jp-widgets-input-focus-border-color);\n}\n\n.wiget-select > select > option,\n.jupyter-wiget-select > select > option {\n padding-left: var(--jp-widgets-input-padding);\n line-height: var(--jp-widgets-inline-height);\n /* line-height doesn't work on some browsers for select options */\n padding-top: calc(\n var(--jp-widgets-inline-height) - var(--jp-widgets-font-size) / 2\n );\n padding-bottom: calc(\n var(--jp-widgets-inline-height) - var(--jp-widgets-font-size) / 2\n );\n}\n\n/* Toggle Buttons Styling */\n\n/* */\n.widget-toggle-buttons, /* */\n.jupyter-widget-toggle-buttons {\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-toggle-buttons .widget-toggle-button, /* */\n.jupyter-widget-toggle-buttons .jupyter-widget-toggle-button {\n margin-left: var(--jp-widgets-margin);\n margin-right: var(--jp-widgets-margin);\n}\n\n/* */\n.widget-toggle-buttons .jupyter-button:disabled, /* */\n.jupyter-widget-toggle-buttons .jupyter-button:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* Radio Buttons Styling */\n\n/* */\n.widget-radio, /* */\n.jupyter-widget-radio {\n width: var(--jp-widgets-inline-width);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-radio-box, /* */\n.jupyter-widget-radio-box {\n display: flex;\n flex-direction: column;\n align-items: stretch;\n box-sizing: border-box;\n flex-grow: 1;\n margin-bottom: var(--jp-widgets-radio-item-height-adjustment);\n}\n\n/* */\n.widget-radio-box-vertical, /* */\n.jupyter-widget-radio-box-vertical {\n flex-direction: column;\n}\n\n/* */\n.widget-radio-box-horizontal, /* */\n.jupyter-widget-radio-box-horizontal {\n flex-direction: row;\n}\n\n/* */\n.widget-radio-box label, /* */\n.jupyter-widget-radio-box label {\n height: var(--jp-widgets-radio-item-height);\n line-height: var(--jp-widgets-radio-item-height);\n font-size: var(--jp-widgets-font-size);\n}\n\n.widget-radio-box-horizontal label,\n.jupyter-widget-radio-box-horizontal label {\n margin: 0 calc(var(--jp-widgets-input-padding) * 2) 0 0;\n}\n\n/* */\n.widget-radio-box input, /* */\n.jupyter-widget-radio-box input {\n height: var(--jp-widgets-radio-item-height);\n line-height: var(--jp-widgets-radio-item-height);\n margin: 0 calc(var(--jp-widgets-input-padding) * 2) 0 1px;\n float: left;\n}\n\n/* Color Picker Styling */\n\n/* */\n.widget-colorpicker, /* */\n.jupyter-widget-colorpicker {\n width: var(--jp-widgets-inline-width);\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-colorpicker > .widget-colorpicker-input, /* */\n.jupyter-widget-colorpicker > .jupyter-widget-colorpicker-input {\n flex-grow: 1;\n flex-shrink: 1;\n min-width: var(--jp-widgets-inline-width-tiny);\n}\n\n/* */\n.widget-colorpicker input[type='color'], /* */\n.jupyter-widget-colorpicker input[type='color'] {\n width: var(--jp-widgets-inline-height);\n height: var(--jp-widgets-inline-height);\n padding: 0 2px; /* make the color square actually square on Chrome on OS X */\n background: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n border-left: none;\n flex-grow: 0;\n flex-shrink: 0;\n box-sizing: border-box;\n align-self: stretch;\n outline: none !important;\n}\n\n/* */\n.widget-colorpicker.concise input[type='color'], /* */\n.jupyter-widget-colorpicker.concise input[type='color'] {\n border-left: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n}\n\n/* */\n.widget-colorpicker input[type='color']:focus, /* */\n/* */ .widget-colorpicker input[type='text']:focus, /* */\n.jupyter-widget-colorpicker input[type='color']:focus,\n.jupyter-widget-colorpicker input[type='text']:focus {\n border-color: var(--jp-widgets-input-focus-border-color);\n}\n\n/* */\n.widget-colorpicker input[type='text'], /* */\n.jupyter-widget-colorpicker input[type='text'] {\n flex-grow: 1;\n outline: none !important;\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n background: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n font-size: var(--jp-widgets-font-size);\n padding: var(--jp-widgets-input-padding)\n calc(var(--jp-widgets-input-padding) * 2);\n min-width: 0; /* This makes it possible for the flexbox to shrink this input */\n flex-shrink: 1;\n box-sizing: border-box;\n}\n\n/* */\n.widget-colorpicker input[type='text']:disabled, /* */\n.jupyter-widget-colorpicker input[type='text']:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* Date Picker Styling */\n\n/* */\n.widget-datepicker, /* */\n.jupyter-widget-datepicker {\n width: var(--jp-widgets-inline-width);\n height: var(--jp-widgets-inline-height);\n line-height: var(--jp-widgets-inline-height);\n}\n\n/* */\n.widget-datepicker input[type='date'], /* */\n.jupyter-widget-datepicker input[type='date'] {\n flex-grow: 1;\n flex-shrink: 1;\n min-width: 0; /* This makes it possible for the flexbox to shrink this input */\n outline: none !important;\n height: var(--jp-widgets-inline-height);\n border: var(--jp-widgets-input-border-width) solid\n var(--jp-widgets-input-border-color);\n background-color: var(--jp-widgets-input-background-color);\n color: var(--jp-widgets-input-color);\n font-size: var(--jp-widgets-font-size);\n padding: var(--jp-widgets-input-padding)\n calc(var(--jp-widgets-input-padding) * 2);\n box-sizing: border-box;\n}\n\n/* */\n.widget-datepicker input[type='date']:focus, /* */\n.jupyter-widget-datepicker input[type='date']:focus {\n border-color: var(--jp-widgets-input-focus-border-color);\n}\n\n/* */\n.widget-datepicker input[type='date']:invalid, /* */\n.jupyter-widget-datepicker input[type='date']:invalid {\n border-color: var(--jp-warn-color1);\n}\n\n/* */\n.widget-datepicker input[type='date']:disabled, /* */\n.jupyter-widget-datepicker input[type='date']:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* Play Widget */\n\n/* */\n.widget-play, /* */\n.jupyter-widget-play {\n width: var(--jp-widgets-inline-width-short);\n display: flex;\n align-items: stretch;\n}\n\n/* */\n.widget-play .jupyter-button, /* */\n.jupyter-widget-play .jupyter-button {\n flex-grow: 1;\n height: auto;\n}\n\n/* */\n.widget-play .jupyter-button:disabled, /* */\n.jupyter-widget-play .jupyter-button:disabled {\n opacity: var(--jp-widgets-disabled-opacity);\n}\n\n/* Tab Widget */\n\n/* */\n.jupyter-widgets.widget-tab, /* */\n.jupyter-widgets.jupyter-widget-tab {\n display: flex;\n flex-direction: column;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar {\n /* Necessary so that a tab can be shifted down to overlay the border of the box below. */\n overflow-x: visible;\n overflow-y: visible;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar > .p-TabBar-content, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar > .p-TabBar-content, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar > .lm-TabBar-content {\n /* Make sure that the tab grows from bottom up */\n align-items: flex-end;\n min-width: 0;\n min-height: 0;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .widget-tab-contents, /* */\n.jupyter-widgets.jupyter-widget-tab > .widget-tab-contents {\n width: 100%;\n box-sizing: border-box;\n margin: 0;\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n border: var(--jp-border-width) solid var(--jp-border-color1);\n padding: var(--jp-widgets-container-padding);\n flex-grow: 1;\n overflow: auto;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar {\n font: var(--jp-widgets-font-size) Helvetica, Arial, sans-serif;\n min-height: calc(\n var(--jp-widgets-horizontal-tab-height) + var(--jp-border-width)\n );\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab {\n flex: 0 1 var(--jp-widgets-horizontal-tab-width);\n min-width: 35px;\n min-height: calc(\n var(--jp-widgets-horizontal-tab-height) + var(--jp-border-width)\n );\n line-height: var(--jp-widgets-horizontal-tab-height);\n margin-left: calc(-1 * var(--jp-border-width));\n padding: 0px 10px;\n background: var(--jp-layout-color2);\n color: var(--jp-ui-font-color2);\n border: var(--jp-border-width) solid var(--jp-border-color1);\n border-bottom: none;\n position: relative;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab.lm-mod-current {\n color: var(--jp-ui-font-color0);\n /* We want the background to match the tab content background */\n background: var(--jp-layout-color1);\n min-height: calc(\n var(--jp-widgets-horizontal-tab-height) + 2 * var(--jp-border-width)\n );\n transform: translateY(var(--jp-border-width));\n overflow: visible;\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current:before, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current:before, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab.lm-mod-current:before {\n position: absolute;\n top: calc(-1 * var(--jp-border-width));\n left: calc(-1 * var(--jp-border-width));\n content: '';\n height: var(--jp-widgets-horizontal-tab-top-border);\n width: calc(100% + 2 * var(--jp-border-width));\n background: var(--jp-brand-color1);\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab:first-child, /* */\n/* */.jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tab:first-child, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tab:first-child {\n margin-left: 0;\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar\n .p-TabBar-tab:hover:not(.p-mod-current),\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .p-TabBar\n .p-TabBar-tab:hover:not(.p-mod-current),\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar\n .lm-TabBar-tab:hover:not(.lm-mod-current) {\n background: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n}\n\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar\n .p-mod-closable\n > .p-TabBar-tabCloseIcon,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-tab\n> .p-TabBar\n.p-mod-closable\n> .p-TabBar-tabCloseIcon,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar\n .lm-mod-closable\n > .lm-TabBar-tabCloseIcon {\n margin-left: 4px;\n}\n\n/* This font-awesome strategy may not work across FA4 and FA5, but we don't\nactually support closable tabs, so it really doesn't matter */\n/* */\n.jupyter-widgets.widget-tab\n > .p-TabBar\n .p-mod-closable\n > .p-TabBar-tabCloseIcon:before,\n/* */\n/* */\n.jupyter-widgets.jupyter-widget-widget-tab\n> .p-TabBar\n.p-mod-closable\n> .p-TabBar-tabCloseIcon:before,\n/* */\n.jupyter-widgets.jupyter-widget-tab\n > .lm-TabBar\n .lm-mod-closable\n > .lm-TabBar-tabCloseIcon:before {\n font-family: FontAwesome;\n content: '\\f00d'; /* close */\n}\n\n/* */\n.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabIcon, /* */\n/* */ .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabLabel, /* */\n/* */ .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabCloseIcon, /* */\n/* */ .jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabIcon, /* */\n/* */ .jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabLabel, /* */\n/* */ .jupyter-widgets.jupyter-widget-tab > .p-TabBar .p-TabBar-tabCloseIcon, /* */\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabIcon,\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabLabel,\n.jupyter-widgets.jupyter-widget-tab > .lm-TabBar .lm-TabBar-tabCloseIcon {\n line-height: var(--jp-widgets-horizontal-tab-height);\n}\n\n/* Accordion Widget */\n\n.jupyter-widget-Collapse {\n display: flex;\n flex-direction: column;\n align-items: stretch;\n}\n\n.jupyter-widget-Collapse-header {\n padding: var(--jp-widgets-input-padding);\n cursor: pointer;\n color: var(--jp-ui-font-color2);\n background-color: var(--jp-layout-color2);\n border: var(--jp-widgets-border-width) solid var(--jp-border-color1);\n padding: calc(var(--jp-widgets-container-padding) * 2 / 3)\n var(--jp-widgets-container-padding);\n font-weight: bold;\n}\n\n.jupyter-widget-Collapse-header:hover {\n background-color: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n}\n\n.jupyter-widget-Collapse-open > .jupyter-widget-Collapse-header {\n background-color: var(--jp-layout-color1);\n color: var(--jp-ui-font-color0);\n cursor: default;\n border-bottom: none;\n}\n\n.jupyter-widget-Collapse-contents {\n padding: var(--jp-widgets-container-padding);\n background-color: var(--jp-layout-color1);\n color: var(--jp-ui-font-color1);\n border-left: var(--jp-widgets-border-width) solid var(--jp-border-color1);\n border-right: var(--jp-widgets-border-width) solid var(--jp-border-color1);\n border-bottom: var(--jp-widgets-border-width) solid var(--jp-border-color1);\n overflow: auto;\n}\n\n.jupyter-widget-Accordion {\n display: flex;\n flex-direction: column;\n align-items: stretch;\n}\n\n.jupyter-widget-Accordion .jupyter-widget-Collapse {\n margin-bottom: 0;\n}\n\n.jupyter-widget-Accordion .jupyter-widget-Collapse + .jupyter-widget-Collapse {\n margin-top: 4px;\n}\n\n/* HTML widget */\n\n/* */\n.widget-html, /* */\n/* */ .widget-htmlmath, /* */\n.jupyter-widget-html,\n.jupyter-widget-htmlmath {\n font-size: var(--jp-widgets-font-size);\n}\n\n/* */\n.widget-html > .widget-html-content, /* */\n/* */.widget-htmlmath > .widget-html-content, /* */\n.jupyter-widget-html > .jupyter-widget-html-content,\n.jupyter-widget-htmlmath > .jupyter-widget-html-content {\n /* Fill out the area in the HTML widget */\n align-self: stretch;\n flex-grow: 1;\n flex-shrink: 1;\n /* Makes sure the baseline is still aligned with other elements */\n line-height: var(--jp-widgets-inline-height);\n /* Make it possible to have absolutely-positioned elements in the html */\n position: relative;\n}\n\n/* Image widget */\n\n/* */\n.widget-image, /* */\n.jupyter-widget-image {\n max-width: 100%;\n height: auto;\n}\n`,""]);const w=c},9451:e=>{e.exports=function(e){var n=[];return n.toString=function(){return this.map((function(n){var t="",i=void 0!==n[5];return n[4]&&(t+="@supports 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This probably means that the value for the 'insert' parameter is invalid.");i.appendChild(t)}},4999:e=>{e.exports=function(e){var n=document.createElement("style");return e.setAttributes(n,e.attributes),e.insert(n,e.options),n}},9443:(e,n,t)=>{e.exports=function(e){var n=t.nc;n&&e.setAttribute("nonce",n)}},376:e=>{e.exports=function(e){if("undefined"==typeof document)return{update:function(){},remove:function(){}};var n=e.insertStyleElement(e);return{update:function(t){!function(e,n,t){var i="";t.supports&&(i+="@supports (".concat(t.supports,") {")),t.media&&(i+="@media ".concat(t.media," {"));var r=void 0!==t.layer;r&&(i+="@layer".concat(t.layer.length>0?" ".concat(t.layer):""," {")),i+=t.css,r&&(i+="}"),t.media&&(i+="}"),t.supports&&(i+="}");var o=t.sourceMap;o&&"undefined"!=typeof btoa&&(i+="\n/*# sourceMappingURL=data:application/json;base64,".concat(btoa(unescape(encodeURIComponent(JSON.stringify(o))))," */")),n.styleTagTransform(i,e,n.options)}(n,e,t)},remove:function(){!function(e){if(null===e.parentNode)return!1;e.parentNode.removeChild(e)}(n)}}}},9252:e=>{e.exports=function(e,n){if(n.styleSheet)n.styleSheet.cssText=e;else{for(;n.firstChild;)n.removeChild(n.firstChild);n.appendChild(document.createTextNode(e))}}},8701:(e,n,t)=>{t.d(n,{A:()=>i});const i="2.0.0"},1446:(e,n,t)=>{t.r(n),t.d(n,{KernelWidgetManager:()=>T,LabWidgetManager:()=>v,WidgetManager:()=>f,WidgetRenderer:()=>w,default:()=>ce,output:()=>i,registerWidgetManager:()=>te});var i={};t.r(i),t.d(i,{OUTPUT_WIDGET_VERSION:()=>P,OutputModel:()=>U,OutputView:()=>k});var r=t(8612),o=t(1378),a=t(4970),d=t(9895),s=t(1113),l=t(632),g=t(4053),p=t(9012),c=t(7262),u=t(5256);class w extends u.Panel{constructor(e,n){super(),this._manager=new c.PromiseDelegate,this._rerenderMimeModel=null,this.mimeType=e.mimeType,n&&(this.manager=n)}set manager(e){e.restored.connect(this._rerender,this),this._manager.resolve(e)}async renderModel(e){const n=e.data[this.mimeType];this.node.textContent="Loading widget...";const t=await this._manager.promise;if(""===n.model_id)return this.hide(),Promise.resolve();let i,r;try{i=await t.get_model(n.model_id)}catch(n){return t.restoredStatus?(this.node.textContent="Error displaying widget: model not found",this.addClass("jupyter-widgets"),void console.error(n)):void(this._rerenderMimeModel=e)}this._rerenderMimeModel=null;try{const e=await t.create_view(i);r=e.luminoWidget||e.pWidget}catch(e){return this.node.textContent="Error displaying widget",this.addClass("jupyter-widgets"),void console.error(e)}this.node.textContent="",this.addWidget(r),r.disposed.connect((()=>{this.hide(),n.model_id=""}))}dispose(){this.isDisposed||(this._manager=null,super.dispose())}_rerender(){this._rerenderMimeModel&&(this.node.textContent="",this.removeClass("jupyter-widgets"),this.renderModel(this._rerenderMimeModel))}}var h=t(7401),E=t(8875),b=t(4602),j=t(4585);class y{constructor(){this._cache=Object.create(null)}set(e,n,t){if(e in this._cache||(this._cache[e]=Object.create(null)),n in this._cache[e])throw`Version ${n} of key ${e} already registered.`;this._cache[e][n]=t}get(e,n){if(e in this._cache){const t=this._cache[e],i=(0,j.maxSatisfying)(Object.keys(t),n);if(null!==i)return t[i]}}getAllVersions(e){if(e in this._cache)return this._cache[e]}}const m="application/vnd.jupyter.widget-view+json",D="application/vnd.jupyter.widget-state+json";class v extends E.ManagerBase{constructor(e){super(),this._handleCommOpen=async(e,n)=>{const t=new h.shims.services.Comm(e);await 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e=this.model.get("description");0===e.length?this.label.style.display="none":(this.model.get("description_allow_html")?this.label.innerHTML=this.model.widget_manager.inline_sanitize(e):this.label.textContent=e,this.typeset(this.label),this.label.style.display="")}updateTooltip(){this.label&&(this.label.title=this.model.get("tooltip"))}}class u extends r{}class c extends h{}class p extends i.WidgetModel{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"CoreWidgetModel",_view_module:"@jupyter-widgets/controls",_model_module:"@jupyter-widgets/controls",_view_module_version:n.A,_model_module_version:n.A})}}class g extends i.DOMWidgetModel{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"CoreDOMWidgetModel",_view_module:"@jupyter-widgets/controls",_model_module:"@jupyter-widgets/controls",_view_module_version:n.A,_model_module_version:n.A})}}class m extends r{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"CoreDescriptionModel",_view_module:"@jupyter-widgets/controls",_model_module:"@jupyter-widgets/controls",_view_module_version:n.A,_model_module_version:n.A})}}class _ extends p{defaults(){return Object.assign(Object.assign({},super.defaults()),{target:void 0,source:void 0,_model_name:"DirectionalLinkModel"})}initialize(e,t){super.initialize(e,t),this.on("change",this.updateBindings,this),this.updateBindings()}updateValue(e,t,s,i){if(!this._updating){this._updating=!0;try{s&&(s.set(i,e.get(t)),s.save_changes())}finally{this._updating=!1}}}updateBindings(){this.cleanup(),[this.sourceModel,this.sourceAttr]=this.get("source")||[null,null],[this.targetModel,this.targetAttr]=this.get("target")||[null,null],this.sourceModel&&(this.listenTo(this.sourceModel,"change:"+this.sourceAttr,(()=>{this.updateValue(this.sourceModel,this.sourceAttr,this.targetModel,this.targetAttr)})),this.updateValue(this.sourceModel,this.sourceAttr,this.targetModel,this.targetAttr),this.listenToOnce(this.sourceModel,"destroy",this.cleanup)),this.targetModel&&this.listenToOnce(this.targetModel,"destroy",this.cleanup)}cleanup(){this.sourceModel&&(this.stopListening(this.sourceModel,"change:"+this.sourceAttr,void 0),this.stopListening(this.sourceModel,"destroy",void 0)),this.targetModel&&this.stopListening(this.targetModel,"destroy",void 0)}}_.serializers=Object.assign(Object.assign({},p.serializers),{target:{deserialize:i.unpack_models},source:{deserialize:i.unpack_models}});class b extends _{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"LinkModel"})}updateBindings(){super.updateBindings(),this.targetModel&&this.listenTo(this.targetModel,"change:"+this.targetAttr,(()=>{this.updateValue(this.targetModel,this.targetAttr,this.sourceModel,this.sourceAttr)}))}cleanup(){super.cleanup(),this.targetModel&&this.stopListening(this.targetModel,"change:"+this.targetAttr,void 0)}}class v extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"CheckboxStyleModel"})}}v.styleProperties=Object.assign(Object.assign({},o.styleProperties),{background:{selector:"",attribute:"background",default:null}});class x extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ToggleButtonStyleModel"})}}x.styleProperties=Object.assign(Object.assign({},o.styleProperties),{font_family:{selector:"",attribute:"font-family",default:""},font_size:{selector:"",attribute:"font-size",default:""},font_style:{selector:"",attribute:"font-style",default:""},font_variant:{selector:"",attribute:"font-variant",default:""},font_weight:{selector:"",attribute:"font-weight",default:""},text_color:{selector:"",attribute:"color",default:""},text_decoration:{selector:"",attribute:"text-decoration",default:""}});class f extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:!1,disabled:!1,_model_name:"BoolModel"})}}class w extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{indent:!0,style:null,_view_name:"CheckboxView",_model_name:"CheckboxModel"})}}class y extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-checkbox"),this.label.innerHTML="​",this.checkboxLabel=document.createElement("label"),this.checkboxLabel.classList.add("widget-label-basic"),this.el.appendChild(this.checkboxLabel),this.checkbox=document.createElement("input"),this.checkbox.setAttribute("type","checkbox"),this.checkboxLabel.appendChild(this.checkbox),this.descriptionSpan=document.createElement("span"),this.checkboxLabel.appendChild(this.descriptionSpan),this.listenTo(this.model,"change:indent",this.updateIndent),this.listenTo(this.model,"change:tabbable",this.updateTabindex),this.update(),this.updateDescription(),this.updateIndent(),this.updateTabindex(),this.updateTooltip()}updateDescription(){if(null==this.checkboxLabel)return;const e=this.model.get("description");this.model.get("description_allow_html")?this.descriptionSpan.innerHTML=this.model.widget_manager.inline_sanitize(e):this.descriptionSpan.textContent=e,this.typeset(this.descriptionSpan),this.descriptionSpan.title=e,this.checkbox.title=e}updateIndent(){const e=this.model.get("indent");this.label.style.display=e?"":"none"}updateTabindex(){if(!this.checkbox)return;const e=this.model.get("tabbable");!0===e?this.checkbox.setAttribute("tabIndex","0"):!1===e?this.checkbox.setAttribute("tabIndex","-1"):null===e&&this.checkbox.removeAttribute("tabIndex")}updateTooltip(){if(!this.checkbox)return;const e=this.model.get("tooltip");e?0===this.model.get("description").length&&this.checkbox.setAttribute("title",e):this.checkbox.removeAttribute("title")}events(){return{'click input[type="checkbox"]':"_handle_click"}}_handle_click(){const e=this.model.get("value");this.model.set("value",!e,{updated_view:this}),this.touch()}update(e){return this.checkbox.checked=this.model.get("value"),void 0!==e&&e.updated_view==this||(this.checkbox.disabled=this.model.get("disabled")),super.update()}handle_message(e){"focus"==e.do?this.checkbox.focus():"blur"==e.do&&this.checkbox.blur()}}class C extends f{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"ToggleButtonView",_model_name:"ToggleButtonModel",tooltip:"",icon:"",button_style:"",style:null})}}class M extends i.DOMWidgetView{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("jupyter-button"),this.el.classList.add("widget-toggle-button"),this.listenTo(this.model,"change:button_style",this.update_button_style),this.listenTo(this.model,"change:tabbable",this.updateTabindex),this.set_button_style(),this.update()}update_button_style(){this.update_mapped_classes(M.class_map,"button_style")}set_button_style(){this.set_mapped_classes(M.class_map,"button_style")}update(e){if(this.model.get("value")?this.el.classList.add("mod-active"):this.el.classList.remove("mod-active"),void 0===e||e.updated_view!==this){this.el.disabled=this.model.get("disabled"),this.el.setAttribute("tabbable",this.model.get("tabbable")),this.el.setAttribute("title",this.model.get("tooltip"));const e=this.model.get("description"),t=this.model.get("icon");if(0===e.trim().length&&0===t.trim().length)this.el.innerHTML=" ";else{if(this.el.textContent="",t.trim().length){const e=document.createElement("i");this.el.appendChild(e),e.classList.add("fa"),e.classList.add("fa-"+t)}this.el.appendChild(document.createTextNode(e))}}return this.updateTabindex(),super.update()}events(){return{click:"_handle_click"}}_handle_click(e){e.preventDefault();const t=this.model.get("value");this.model.set("value",!t,{updated_view:this}),this.touch()}preinitialize(){this.tagName="button"}}M.class_map={primary:["mod-primary"],success:["mod-success"],info:["mod-info"],warning:["mod-warning"],danger:["mod-danger"]};class j extends f{defaults(){return Object.assign(Object.assign({},super.defaults()),{readout:"Invalid",_view_name:"ValidView",_model_name:"ValidModel"})}}class T extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-valid"),this.el.classList.add("widget-inline-hbox"),this.icon=document.createElement("i"),this.icon.classList.add("fa","fa-fw"),this.el.appendChild(this.icon),this.readout=document.createElement("span"),this.readout.classList.add("widget-valid-readout"),this.readout.classList.add("widget-readout"),this.el.appendChild(this.readout),this.update()}update(){this.el.classList.remove("mod-valid"),this.el.classList.remove("mod-invalid"),this.icon.classList.remove("fa-check"),this.icon.classList.remove("fa-times"),this.readout.textContent=this.model.get("readout"),this.model.get("value")?(this.el.classList.add("mod-valid"),this.icon.classList.add("fa-check")):(this.el.classList.add("mod-invalid"),this.icon.classList.add("fa-times"))}}class S extends i.StyleModel{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ButtonStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}S.styleProperties={button_color:{selector:"",attribute:"background-color",default:null},font_family:{selector:"",attribute:"font-family",default:""},font_size:{selector:"",attribute:"font-size",default:""},font_style:{selector:"",attribute:"font-style",default:""},font_variant:{selector:"",attribute:"font-variant",default:""},font_weight:{selector:"",attribute:"font-weight",default:""},text_color:{selector:"",attribute:"color",default:""},text_decoration:{selector:"",attribute:"text-decoration",default:""}};class O extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{description:"",tooltip:"",disabled:!1,icon:"",button_style:"",_view_name:"ButtonView",_model_name:"ButtonModel",style:null})}}class k extends i.DOMWidgetView{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("jupyter-button"),this.el.classList.add("widget-button"),this.listenTo(this.model,"change:button_style",this.update_button_style),this.listenTo(this.model,"change:tabbable",this.updateTabindex),this.set_button_style(),this.update()}update(){this.el.disabled=this.model.get("disabled"),this.updateTabindex();const e=this.model.get("tooltip"),t=this.model.get("description"),s=this.model.get("icon");if(this.el.setAttribute("title",null!=e?e:t),t.length||s.length){if(this.el.textContent="",s.length){const e=document.createElement("i");e.classList.add("fa"),e.classList.add(...s.split(/[\s]+/).filter(Boolean).map((e=>`fa-${e}`))),0===t.length&&e.classList.add("center"),this.el.appendChild(e)}this.el.appendChild(document.createTextNode(t))}return super.update()}update_button_style(){this.update_mapped_classes(k.class_map,"button_style")}set_button_style(){this.set_mapped_classes(k.class_map,"button_style")}events(){return{click:"_handle_click"}}_handle_click(e){e.preventDefault(),this.send({event:"click"})}preinitialize(){this.tagName="button"}}k.class_map={primary:["mod-primary"],success:["mod-success"],info:["mod-info"],warning:["mod-warning"],danger:["mod-danger"]};var L=s(4053),V=s(6230),I=s(5256),A=s(8596),W=s.n(A);class E extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"BoxView",_model_name:"BoxModel",children:[],box_style:""})}}E.serializers=Object.assign(Object.assign({},g.serializers),{children:{deserialize:i.unpack_models}});class B extends E{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"HBoxView",_model_name:"HBoxModel"})}}class z extends E{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"VBoxView",_model_name:"VBoxModel"})}}class D extends i.DOMWidgetView{_createElement(e){return this.luminoWidget=new i.JupyterLuminoPanelWidget({view:this}),this.luminoWidget.node}_setElement(e){if(this.el||e!==this.luminoWidget.node)throw new Error("Cannot reset the DOM element.");this.el=this.luminoWidget.node,this.$el=W()(this.luminoWidget.node)}initialize(e){super.initialize(e),this.children_views=new i.ViewList(this.add_child_model,null,this),this.listenTo(this.model,"change:children",this.update_children),this.listenTo(this.model,"change:box_style",this.update_box_style),this.luminoWidget.addClass("jupyter-widgets"),this.luminoWidget.addClass("widget-container"),this.luminoWidget.addClass("widget-box")}render(){super.render(),this.update_children(),this.set_box_style()}update_children(){var e;null===(e=this.children_views)||void 0===e||e.update(this.model.get("children")).then((e=>{e.forEach((e=>{V.MessageLoop.postMessage(e.luminoWidget,I.Widget.ResizeMessage.UnknownSize)}))}))}update_box_style(){this.update_mapped_classes(D.class_map,"box_style")}set_box_style(){this.set_mapped_classes(D.class_map,"box_style")}add_child_model(e){const t=new I.Widget;return this.luminoWidget.addWidget(t),this.create_child_view(e).then((e=>{const s=L.ArrayExt.firstIndexOf(this.luminoWidget.widgets,t);return this.luminoWidget.insertWidget(s,e.luminoWidget),t.dispose(),e})).catch((0,i.reject)("Could not add child view to box",!0))}remove(){this.children_views=null,super.remove()}}D.class_map={success:["alert","alert-success"],info:["alert","alert-info"],warning:["alert","alert-warning"],danger:["alert","alert-danger"]};class P extends D{initialize(e){super.initialize(e),this.luminoWidget.addClass("widget-hbox")}}class U extends D{initialize(e){super.initialize(e),this.luminoWidget.addClass("widget-vbox")}}class F extends D{initialize(e){super.initialize(e),this.luminoWidget.addClass("widget-gridbox"),this.luminoWidget.removeClass("widget-box")}}class R extends E{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"GridBoxView",_model_name:"GridBoxModel"})}}class $ extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ImageModel",_view_name:"ImageView",format:"png",width:"",height:"",value:new DataView(new ArrayBuffer(0))})}}$.serializers=Object.assign(Object.assign({},g.serializers),{value:{serialize:e=>new DataView(e.buffer.slice(0))}});class N extends i.DOMWidgetView{render(){super.render(),this.luminoWidget.addClass("jupyter-widgets"),this.luminoWidget.addClass("widget-image"),this.update()}update(){let e;const t=this.model.get("format"),s=this.model.get("value");if("url"!==t){const t=new Blob([s],{type:`image/${this.model.get("format")}`});e=URL.createObjectURL(t)}else e=new TextDecoder("utf-8").decode(s.buffer);const i=this.el.src;this.el.src=e,i&&URL.revokeObjectURL(i);const a=this.model.get("width");void 0!==a&&a.length>0?this.el.setAttribute("width",a):this.el.removeAttribute("width");const l=this.model.get("height");return void 0!==l&&l.length>0?this.el.setAttribute("height",l):this.el.removeAttribute("height"),super.update()}remove(){this.el.src&&URL.revokeObjectURL(this.el.src),super.remove()}preinitialize(){this.tagName="img"}}class H extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"VideoModel",_view_name:"VideoView",format:"mp4",width:"",height:"",autoplay:!0,loop:!0,controls:!0,value:new DataView(new ArrayBuffer(0))})}}H.serializers=Object.assign(Object.assign({},g.serializers),{value:{serialize:e=>new DataView(e.buffer.slice(0))}});class K extends i.DOMWidgetView{render(){super.render(),this.luminoWidget.addClass("jupyter-widgets"),this.luminoWidget.addClass("widget-image"),this.update()}update(){let e;const t=this.model.get("format"),s=this.model.get("value");if("url"!==t){const t=new Blob([s],{type:`video/${this.model.get("format")}`});e=URL.createObjectURL(t)}else e=new TextDecoder("utf-8").decode(s.buffer);const i=this.el.src;this.el.src=e,i&&URL.revokeObjectURL(i);const a=this.model.get("width");void 0!==a&&a.length>0?this.el.setAttribute("width",a):this.el.removeAttribute("width");const l=this.model.get("height");return void 0!==l&&l.length>0?this.el.setAttribute("height",l):this.el.removeAttribute("height"),this.el.loop=this.model.get("loop"),this.el.autoplay=this.model.get("autoplay"),this.el.controls=this.model.get("controls"),super.update()}remove(){this.el.src&&URL.revokeObjectURL(this.el.src),super.remove()}preinitialize(){this.tagName="video"}}class q extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"AudioModel",_view_name:"AudioView",format:"mp3",autoplay:!0,loop:!0,controls:!0,value:new DataView(new ArrayBuffer(0))})}}q.serializers=Object.assign(Object.assign({},g.serializers),{value:{serialize:e=>new DataView(e.buffer.slice(0))}});class G extends i.DOMWidgetView{render(){super.render(),this.luminoWidget.addClass("jupyter-widgets"),this.update()}update(){let e;const t=this.model.get("format"),s=this.model.get("value");if("url"!==t){const t=new Blob([s],{type:`audio/${this.model.get("format")}`});e=URL.createObjectURL(t)}else e=new TextDecoder("utf-8").decode(s.buffer);const i=this.el.src;return this.el.src=e,i&&URL.revokeObjectURL(i),this.el.loop=this.model.get("loop"),this.el.autoplay=this.model.get("autoplay"),this.el.controls=this.model.get("controls"),super.update()}remove(){this.el.src&&URL.revokeObjectURL(this.el.src),super.remove()}preinitialize(){this.tagName="audio"}}const J={aliceblue:"#f0f8ff",antiquewhite:"#faebd7",aqua:"#00ffff",aquamarine:"#7fffd4",azure:"#f0ffff",beige:"#f5f5dc",bisque:"#ffe4c4",black:"#000000",blanchedalmond:"#ffebcd",blue:"#0000ff",blueviolet:"#8a2be2",brown:"#a52a2a",burlywood:"#deb887",cadetblue:"#5f9ea0",chartreuse:"#7fff00",chocolate:"#d2691e",coral:"#ff7f50",cornflowerblue:"#6495ed",cornsilk:"#fff8dc",crimson:"#dc143c",cyan:"#00ffff",darkblue:"#00008b",darkcyan:"#008b8b",darkgoldenrod:"#b8860b",darkgray:"#a9a9a9",darkgrey:"#a9a9a9",darkgreen:"#006400",darkkhaki:"#bdb76b",darkmagenta:"#8b008b",darkolivegreen:"#556b2f",darkorange:"#ff8c00",darkorchid:"#9932cc",darkred:"#8b0000",darksalmon:"#e9967a",darkseagreen:"#8fbc8f",darkslateblue:"#483d8b",darkslategray:"#2f4f4f",darkslategrey:"#2f4f4f",darkturquoise:"#00ced1",darkviolet:"#9400d3",deeppink:"#ff1493",deepskyblue:"#00bfff",dimgray:"#696969",dimgrey:"#696969",dodgerblue:"#1e90ff",firebrick:"#b22222",floralwhite:"#fffaf0",forestgreen:"#228b22",fuchsia:"#ff00ff",gainsboro:"#dcdcdc",ghostwhite:"#f8f8ff",gold:"#ffd700",goldenrod:"#daa520",gray:"#808080",grey:"#808080",green:"#008000",greenyellow:"#adff2f",honeydew:"#f0fff0",hotpink:"#ff69b4",indianred:"#cd5c5c",indigo:"#4b0082",ivory:"#fffff0",khaki:"#f0e68c",lavender:"#e6e6fa",lavenderblush:"#fff0f5",lawngreen:"#7cfc00",lemonchiffon:"#fffacd",lightblue:"#add8e6",lightcoral:"#f08080",lightcyan:"#e0ffff",lightgoldenrodyellow:"#fafad2",lightgreen:"#90ee90",lightgray:"#d3d3d3",lightgrey:"#d3d3d3",lightpink:"#ffb6c1",lightsalmon:"#ffa07a",lightseagreen:"#20b2aa",lightskyblue:"#87cefa",lightslategray:"#778899",lightslategrey:"#778899",lightsteelblue:"#b0c4de",lightyellow:"#ffffe0",lime:"#00ff00",limegreen:"#32cd32",linen:"#faf0e6",magenta:"#ff00ff",maroon:"#800000",mediumaquamarine:"#66cdaa",mediumblue:"#0000cd",mediumorchid:"#ba55d3",mediumpurple:"#9370db",mediumseagreen:"#3cb371",mediumslateblue:"#7b68ee",mediumspringgreen:"#00fa9a",mediumturquoise:"#48d1cc",mediumvioletred:"#c71585",midnightblue:"#191970",mintcream:"#f5fffa",mistyrose:"#ffe4e1",moccasin:"#ffe4b5",navajowhite:"#ffdead",navy:"#000080",oldlace:"#fdf5e6",olive:"#808000",olivedrab:"#6b8e23",orange:"#ffa500",orangered:"#ff4500",orchid:"#da70d6",palegoldenrod:"#eee8aa",palegreen:"#98fb98",paleturquoise:"#afeeee",palevioletred:"#db7093",papayawhip:"#ffefd5",peachpuff:"#ffdab9",peru:"#cd853f",pink:"#ffc0cb",plum:"#dda0dd",powderblue:"#b0e0e6",purple:"#800080",red:"#ff0000",rosybrown:"#bc8f8f",royalblue:"#4169e1",saddlebrown:"#8b4513",salmon:"#fa8072",sandybrown:"#f4a460",seagreen:"#2e8b57",seashell:"#fff5ee",sienna:"#a0522d",silver:"#c0c0c0",skyblue:"#87ceeb",slateblue:"#6a5acd",slategray:"#708090",slategrey:"#708090",snow:"#fffafa",springgreen:"#00ff7f",steelblue:"#4682b4",tan:"#d2b48c",teal:"#008080",thistle:"#d8bfd8",tomato:"#ff6347",turquoise:"#40e0d0",violet:"#ee82ee",wheat:"#f5deb3",white:"#ffffff",whitesmoke:"#f5f5f5",yellow:"#ffff00",yellowgreen:"#9acd32"};class Y extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:"black",concise:!1,_model_name:"ColorPickerModel",_view_name:"ColorPickerView"})}}class Q extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-colorpicker"),this._color_container=document.createElement("div"),this._color_container.className="widget-inline-hbox widget-colorpicker-input",this.el.appendChild(this._color_container),this._textbox=document.createElement("input"),this._textbox.setAttribute("type","text"),this._textbox.id=this.label.htmlFor=(0,i.uuid)(),this._color_container.appendChild(this._textbox),this._textbox.value=this.model.get("value"),this._colorpicker=document.createElement("input"),this._colorpicker.setAttribute("type","color"),this._color_container.appendChild(this._colorpicker),this.listenTo(this.model,"change:value",this._update_value),this.listenTo(this.model,"change:concise",this._update_concise),this._update_concise(),this._update_value(),this.update()}update(e){if(void 0===e||e.updated_view!=this){const e=this.model.get("disabled");this._textbox.disabled=e,this._colorpicker.disabled=e}return super.update()}events(){return this._picker_change,this._text_change,{'change [type="color"]':"_picker_change",'change [type="text"]':"_text_change"}}_update_value(){const e=this.model.get("value");var t,s;this._colorpicker.value=J[(t=e).toLowerCase()]||(7===(s=t).length?s:"#"+s.charAt(1)+s.charAt(1)+s.charAt(2)+s.charAt(2)+s.charAt(3)+s.charAt(3)),this._textbox.value=e}_update_concise(){this.model.get("concise")?(this.el.classList.add("concise"),this._textbox.style.display="none"):(this.el.classList.remove("concise"),this._textbox.style.display="")}_picker_change(){this.model.set("value",this._colorpicker.value),this.touch()}_text_change(){const e=this._validate_color(this._textbox.value,this.model.get("value"));this.model.set("value",e),this.touch()}_validate_color(e,t){return e.match(/#[a-fA-F0-9]{3}(?:[a-fA-F0-9]{3})?$/)||J[e.toLowerCase()]?e:t}}function X(e){return null===e?null:{year:e.getUTCFullYear(),month:e.getUTCMonth(),date:e.getUTCDate()}}function Z(e){if(null===e)return null;{const t=new Date;return t.setUTCFullYear(e.year,e.month,e.date),t.setUTCHours(0,0,0,0),t}}class ee extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:null,_model_name:"DatePickerModel",_view_name:"DatePickerView"})}}ee.serializers=Object.assign(Object.assign({},m.serializers),{value:{serialize:X,deserialize:Z}});class te extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-datepicker"),this._datepicker=document.createElement("input"),this._datepicker.setAttribute("type","date"),this._datepicker.id=this.label.htmlFor=(0,i.uuid)(),this.el.appendChild(this._datepicker),this.listenTo(this.model,"change:value",this._update_value),this._update_value(),this.update()}update(e){return void 0!==e&&e.updated_view===this||(this._datepicker.disabled=this.model.get("disabled")),super.update()}events(){return this._picker_change,this._picker_focusout,{'change [type="date"]':"_picker_change",'focusout [type="date"]':"_picker_focusout"}}_update_value(){const e=this.model.get("value");this._datepicker.valueAsDate=e}_picker_change(){this._datepicker.validity.badInput||(this.model.set("value",this._datepicker.valueAsDate),this.touch())}_picker_focusout(){this._datepicker.validity.badInput&&(this.model.set("value",null),this.touch())}}const se=/(\d\d):(\d\d)(:(\d\d)(.(\d{1,3})\d*)?)?/;function ie(e){if(null===e)return null;{const t=se.exec(e);return null===t?null:{hours:Math.min(23,parseInt(t[1],10)),minutes:Math.min(59,parseInt(t[2],10)),seconds:t[4]?Math.min(59,parseInt(t[4],10)):0,milliseconds:t[6]?parseInt(t[6],10):0}}}function ae(e){if(null===e)return null;{const t=[`${e.hours.toString().padStart(2,"0")}:${e.minutes.toString().padStart(2,"0")}`];return(e.seconds>0||e.milliseconds>0)&&(t.push(`:${e.seconds.toString().padStart(2,"0")}`),e.milliseconds>0&&t.push(`.${e.milliseconds.toString().padStart(3,"0")}`)),t.join("")}}const le={serialize:ie,deserialize:ae};class de extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:de.model_name,_view_name:de.view_name,value:null,disabled:!1,min:null,max:null,step:60})}}de.serializers=Object.assign(Object.assign({},m.serializers),{value:le,min:le,max:le}),de.model_name="TimeModel",de.view_name="TimeView";class ne extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-timepicker"),this._timepicker=document.createElement("input"),this._timepicker.setAttribute("type","time"),this._timepicker.id=this.label.htmlFor=(0,i.uuid)(),this.el.appendChild(this._timepicker),this.listenTo(this.model,"change:value",this._update_value),this.listenTo(this.model,"change",this.update2),this._update_value(),this.update2()}update2(e,t){return void 0!==t&&t.updated_view===this||(this._timepicker.disabled=this.model.get("disabled"),this._timepicker.min=this.model.get("min"),this._timepicker.max=this.model.get("max"),this._timepicker.step=this.model.get("step")),super.update()}events(){return this._picker_change,this._picker_focusout,{'change [type="time"]':"_picker_change",'focusout [type="time"]':"_picker_focusout"}}_update_value(e,t,s){void 0!==s&&s.updated_view===this||(this._timepicker.value=this.model.get("value"))}_picker_change(){this._timepicker.validity.badInput||(this.model.set("value",this._timepicker.value,{updated_view:this}),this.touch())}_picker_focusout(){this._timepicker.validity.badInput&&(this.model.set("value",null,{updated_view:this}),this.touch())}}function oe(e){return null===e?null:{year:e.getUTCFullYear(),month:e.getUTCMonth(),date:e.getUTCDate(),hours:e.getUTCHours(),minutes:e.getUTCMinutes(),seconds:e.getUTCSeconds(),milliseconds:e.getUTCMilliseconds()}}function re(e){if(null===e)return null;{const t=new Date;return t.setUTCFullYear(e.year,e.month,e.date),t.setUTCHours(e.hours,e.minutes,e.seconds,e.milliseconds),t}}const he={serialize:oe,deserialize:re};class ue extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"DatetimeModel",_view_name:"DatetimeView",value:null,disabled:!1,min:null,max:null})}}ue.serializers=Object.assign(Object.assign({},m.serializers),{value:he,min:he,max:he});class ce extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-datetimepicker");const e=document.createElement("input");e.type="datetime-local","text"===e.type?(this._datepicker=document.createElement("input"),this._datepicker.setAttribute("type","date"),this._datepicker.id=this.label.htmlFor=(0,i.uuid)(),this._timepicker=document.createElement("input"),this._timepicker.setAttribute("type","time"),this._timepicker.id=(0,i.uuid)(),this.el.appendChild(this._datepicker),this.el.appendChild(this._timepicker)):(this._datetimepicker=e,this._datetimepicker.id=this.label.htmlFor=(0,i.uuid)(),this.el.appendChild(this._datetimepicker)),this.listenTo(this.model,"change:value",this._update_value),this.listenTo(this.model,"change",this.update2),this._update_value(),this.update2()}update2(e,t){if(void 0===t||t.updated_view!==this){const e=this.model.get("min"),t=this.model.get("max");this._datetimepicker?(this._datetimepicker.disabled=this.model.get("disabled"),this._datetimepicker.min=pe.dt_as_dt_string(e),this._datetimepicker.max=pe.dt_as_dt_string(t)):(this._datepicker.disabled=this.model.get("disabled"),this._datepicker.min=pe.dt_as_date_string(e),this._datepicker.max=pe.dt_as_date_string(t),this._timepicker.disabled=this.model.get("disabled"))}}events(){return this._picker_change,this._picker_focusout,{'change [type="date"]':"_picker_change",'change [type="time"]':"_picker_change",'change [type="datetime-local"]':"_picker_change",'focusout [type="date"]':"_picker_focusout",'focusout [type="datetime-local"]':"_picker_focusout",'focusout [type="time"]':"_picker_focusout"}}_update_value(e,t,s){if(void 0===s||s.updated_view!==this){const e=this.model.get("value");this._datetimepicker?this._datetimepicker.value=pe.dt_as_dt_string(e):(this._datepicker.valueAsDate=e,this._timepicker.value=pe.dt_as_time_string(e))}}_picker_change(){if(this._datetimepicker){if(!this._datetimepicker.validity.badInput){const e=this._datetimepicker.value;let t=e?new Date(e):null;t&&isNaN(t.valueOf())&&(t=null),this.model.set("value",t,{updated_view:this}),this.touch()}}else if(!this._datepicker.validity.badInput&&!this._timepicker.validity.badInput){const e=this._datepicker.valueAsDate,t=ie(this._timepicker.value);null!==e&&null!==t&&e.setHours(t.hours,t.minutes,t.seconds,t.milliseconds),this.model.set("value",null!==t&&e,{updated_view:this}),this.touch()}}_picker_focusout(){[this._datetimepicker,this._datepicker,this._timepicker].some((e=>e&&e.validity.badInput))&&(this.model.set("value",null),this.touch())}}var pe;function ge(e){return null===e?null:{year:e.getFullYear(),month:e.getMonth(),date:e.getDate(),hours:e.getHours(),minutes:e.getMinutes(),seconds:e.getSeconds(),milliseconds:e.getMilliseconds()}}function me(e){if(null===e)return null;{const t=new Date;return t.setFullYear(e.year,e.month,e.date),t.setHours(e.hours,e.minutes,e.seconds,e.milliseconds),t}}!function(e){function t(e){if(null===e)return"";const t=[];return t.push(`${e.getFullYear().toString().padStart(4,"0")}`),t.push(`-${(e.getMonth()+1).toString().padStart(2,"0")}`),t.push(`-${e.getDate().toString().padStart(2,"0")}`),t.push(`T${e.getHours().toString().padStart(2,"0")}`),t.push(`:${e.getMinutes().toString().padStart(2,"0")}`),(e.getSeconds()>0||e.getMilliseconds()>0)&&(t.push(`:${e.getSeconds().toString().padStart(2,"0")}`),e.getMilliseconds()>0&&t.push(`.${e.getMilliseconds().toString().padStart(3,"0")}`)),t.join("")}e.dt_as_dt_string=t,e.dt_as_date_string=function(e){return e?t(e).split("T",2)[0]:""},e.dt_as_time_string=function(e){return e?t(e).split("T",2)[1]:""}}(pe||(pe={}));const _e={serialize:ge,deserialize:me};class be extends ue{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"NaiveDatetimeModel"})}}be.serializers=Object.assign(Object.assign({},m.serializers),{value:_e,min:_e,max:_e});var ve=s(7102),xe=s(5715),fe=s.n(xe);class we extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"IntModel",value:0})}}class ye extends we{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"BoundedIntModel",max:100,min:0})}}class Ce extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"SliderStyleModel"})}}Ce.styleProperties=Object.assign(Object.assign({},o.styleProperties),{handle_color:{selector:".noUi-handle",attribute:"background-color",default:null}});class Me extends ye{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"IntSliderModel",_view_name:"IntSliderView",step:1,orientation:"horizontal",readout:!0,readout_format:"d",continuous_update:!0,style:null,disabled:!1})}initialize(e,t){super.initialize(e,t),this.on("change:readout_format",this.update_readout_format,this),this.update_readout_format()}update_readout_format(){this.readout_formatter=(0,ve.GP)(this.get("readout_format"))}}class je extends Me{}class Te extends h{constructor(){super(...arguments),this._parse_value=parseInt}render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-slider"),this.el.classList.add("widget-hslider"),this.$slider=document.createElement("div"),this.$slider.classList.add("slider"),this.slider_container=document.createElement("div"),this.slider_container.classList.add("slider-container"),this.slider_container.appendChild(this.$slider),this.el.appendChild(this.slider_container),this.readout=document.createElement("div"),this.el.appendChild(this.readout),this.readout.classList.add("widget-readout"),this.readout.contentEditable="true",this.readout.style.display="none",this.createSlider(),this.model.on("change:orientation",this.regenSlider,this),this.model.on("change:max",this.updateSliderOptions,this),this.model.on("change:min",this.updateSliderOptions,this),this.model.on("change:step",this.updateSliderOptions,this),this.model.on("change:value",this.updateSliderValue,this),this.update()}update(e){return void 0!==e&&e.updated_view===this||(this.model.get("disabled")?(this.readout.contentEditable="false",this.$slider.setAttribute("disabled",!0)):(this.readout.contentEditable="true",this.$slider.removeAttribute("disabled")),"vertical"===this.model.get("orientation")?(this.el.classList.remove("widget-hslider"),this.el.classList.add("widget-vslider"),this.el.classList.remove("widget-inline-hbox"),this.el.classList.add("widget-inline-vbox")):(this.el.classList.remove("widget-vslider"),this.el.classList.add("widget-hslider"),this.el.classList.remove("widget-inline-vbox"),this.el.classList.add("widget-inline-hbox")),this.model.get("readout")?(this.readout.style.display="",this.displayed.then((()=>{this.readout_overflow()?this.readout.classList.add("overflow"):this.readout.classList.remove("overflow")}))):this.readout.style.display="none"),super.update()}readout_overflow(){return this.readout.scrollWidth>this.readout.clientWidth}events(){return{"blur [contentEditable=true]":"handleTextChange","keydown [contentEditable=true]":"handleKeyDown"}}handleKeyDown(e){13===e.keyCode&&(e.preventDefault(),this.handleTextChange())}createSlider(){const e=this.model.get("orientation"),t=this.model.get("behavior");fe().create(this.$slider,{start:this.model.get("value"),connect:!0,behaviour:t,range:{min:this.model.get("min"),max:this.model.get("max")},step:this.model.get("step"),animate:!1,orientation:e,direction:"horizontal"===e?"ltr":"rtl",format:{from:e=>Number(e),to:e=>this._validate_slide_value(e)}}),this.$slider.noUiSlider.on("update",((e,t)=>{this.handleSliderUpdateEvent(e,t)})),this.$slider.noUiSlider.on("change",((e,t)=>{this.handleSliderChangeEvent(e,t)}))}regenSlider(e){this.$slider.noUiSlider.destroy(),this.createSlider()}_validate_slide_value(e){return Math.round(e)}}class Se extends Te{constructor(){super(...arguments),this._range_regex=/^\s*([+-]?\d+)\s*[-:–]\s*([+-]?\d+)/}update(e){super.update(e);const t=this.model.get("value");this.readout.textContent=this.valueToString(t),this.model.get("value")!==t&&(this.model.set("value",t,{updated_view:this}),this.touch())}valueToString(e){const t=this.model.readout_formatter;return e.map((function(e){return t(e)})).join(" – ")}stringToValue(e){if(null===e)return null;const t=this._range_regex.exec(e);return t?[this._parse_value(t[1]),this._parse_value(t[2])]:null}handleTextChange(){let e=this.stringToValue(this.readout.textContent);const t=this.model.get("min"),s=this.model.get("max");null===e||isNaN(e[0])||isNaN(e[1])||e[0]>e[1]?this.readout.textContent=this.valueToString(this.model.get("value")):(e=[Math.max(Math.min(e[0],s),t),Math.max(Math.min(e[1],s),t)],e[0]!==this.model.get("value")[0]||e[1]!==this.model.get("value")[1]?(this.readout.textContent=this.valueToString(e),this.model.set("value",e),this.touch()):this.readout.textContent=this.valueToString(this.model.get("value")))}handleSliderChangeEvent(e,t){const s=e.map(this._validate_slide_value);this.readout.textContent=this.valueToString(s),this.handleSliderChanged(e,t)}handleSliderUpdateEvent(e,t){const s=e.map(this._validate_slide_value);this.readout.textContent=this.valueToString(s),this.model.get("continuous_update")&&this.handleSliderChanged(e,t)}handleSliderChanged(e,t){const s=e.map(this._validate_slide_value);this.model.set("value",s,{updated_view:this}),this.touch()}updateSliderOptions(e){this.$slider.noUiSlider.updateOptions({start:this.model.get("value"),range:{min:this.model.get("min"),max:this.model.get("max")},step:this.model.get("step")})}updateSliderValue(e,t,s){if(s.updated_view===this)return;const i=this.$slider.noUiSlider.get(),a=this.model.get("value");i[0]===a[0]&&i[1]===a[1]||this.$slider.noUiSlider.set(a)}}class Oe extends Te{update(e){super.update(e);const t=this.model.get("min"),s=this.model.get("max");let i=this.model.get("value");i>s?i=s:i=1){const e=s.substr(1);s=s[0]+e.replace(/[+-]/g,"")}t.value!==s&&(e.preventDefault(),t.value=s)}handleChanging(e){const t=e.target.value.trim();""===t||["-","-.",".","+.","+"].indexOf(t)>=0||this.model.get("continuous_update")&&this.handleChanged(e)}handleChanged(e){const t=e.target;let s=this._parse_value(t.value);if(isNaN(s))t.value=this.model.get("value");else{let e=s;void 0!==this.model.get("max")&&(e=Math.min(this.model.get("max"),e)),void 0!==this.model.get("min")&&(e=Math.max(this.model.get("min"),e)),e!==s&&(t.value=e,s=e),s!==this.model.get("value")&&(this.model.set("value",s,{updated_view:this}),this.touch())}}}class Ie extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ProgressStyleModel"})}}Ie.styleProperties=Object.assign(Object.assign({},o.styleProperties),{bar_color:{selector:".progress-bar",attribute:"background-color",default:null}});class Ae extends ye{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"IntProgressModel",_view_name:"ProgressView",orientation:"horizontal",bar_style:"",style:null})}}class We extends h{initialize(e){super.initialize(e),this.listenTo(this.model,"change:bar_style",this.update_bar_style),this.luminoWidget.addClass("jupyter-widgets")}render(){super.render();const e="horizontal"===this.model.get("orientation")?"widget-hprogress":"widget-vprogress";this.el.classList.add(e),this.progress=document.createElement("div"),this.progress.classList.add("progress"),this.progress.style.position="relative",this.el.appendChild(this.progress),this.bar=document.createElement("div"),this.bar.classList.add("progress-bar"),this.bar.style.position="absolute",this.bar.style.bottom="0px",this.bar.style.left="0px",this.progress.appendChild(this.bar),this.update(),this.set_bar_style()}update(){const e=this.model.get("value"),t=this.model.get("max"),s=this.model.get("min"),i=100*(e-s)/(t-s);return"horizontal"===this.model.get("orientation")?(this.el.classList.remove("widget-inline-vbox"),this.el.classList.remove("widget-vprogress"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-hprogress"),this.bar.style.width=i+"%",this.bar.style.height="100%"):(this.el.classList.remove("widget-inline-hbox"),this.el.classList.remove("widget-hprogress"),this.el.classList.add("widget-inline-vbox"),this.el.classList.add("widget-vprogress"),this.bar.style.width="100%",this.bar.style.height=i+"%"),super.update()}update_bar_style(){this.update_mapped_classes(We.class_map,"bar_style",this.bar)}set_bar_style(){this.set_mapped_classes(We.class_map,"bar_style",this.bar)}}We.class_map={success:["progress-bar-success"],info:["progress-bar-info"],warning:["progress-bar-warning"],danger:["progress-bar-danger"]};class Ee extends ye{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"PlayModel",_view_name:"PlayView",repeat:!1,playing:!1,show_repeat:!0,interval:100,step:1,disabled:!1})}initialize(e,t){super.initialize(e,t)}loop(){if(!this.get("playing"))return;const e=this.get("value")+this.get("step");e<=this.get("max")?(this.set("value",e),this.schedule_next()):this.get("repeat")?(this.set("value",this.get("min")),this.schedule_next()):this.pause(),this.save_changes()}schedule_next(){this._timerId=window.setTimeout(this.loop.bind(this),this.get("interval"))}stop(){this.pause(),this.set("value",this.get("min")),this.save_changes()}pause(){window.clearTimeout(this._timerId),this._timerId=void 0,this.set("playing",!1),this.save_changes()}animate(){void 0===this._timerId&&(this.get("value")===this.get("max")?(this.set("value",this.get("min")),this.schedule_next(),this.save_changes()):this.loop(),this.save_changes())}play(){this.set("playing",!this.get("playing")),this.save_changes()}repeat(){this.set("repeat",!this.get("repeat")),this.save_changes()}}class Be extends i.DOMWidgetView{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox"),this.el.classList.add("widget-play"),this.playPauseButton=document.createElement("button"),this.stopButton=document.createElement("button"),this.repeatButton=document.createElement("button"),this.playPauseButton.className="jupyter-button",this.stopButton.className="jupyter-button",this.repeatButton.className="jupyter-button",this.el.appendChild(this.playPauseButton),this.el.appendChild(this.stopButton),this.el.appendChild(this.repeatButton);const e=document.createElement("i");e.className="fa fa-play",this.playPauseButton.appendChild(e);const t=document.createElement("i");t.className="fa fa-stop",this.stopButton.appendChild(t);const s=document.createElement("i");s.className="fa fa-retweet",this.repeatButton.appendChild(s),this.playPauseButton.onclick=this.model.play.bind(this.model),this.stopButton.onclick=this.model.stop.bind(this.model),this.repeatButton.onclick=this.model.repeat.bind(this.model),this.listenTo(this.model,"change:playing",this.onPlayingChanged),this.listenTo(this.model,"change:repeat",this.updateRepeat),this.listenTo(this.model,"change:show_repeat",this.updateRepeat),this.updatePlaying(),this.updateRepeat(),this.update()}update(){const e=this.model.get("disabled");this.playPauseButton.disabled=e,this.stopButton.disabled=e,this.repeatButton.disabled=e,this.updatePlaying()}onPlayingChanged(){this.updatePlaying();const e=this.model.previous("playing"),t=this.model.get("playing");!e&&t?this.model.animate():this.model.pause()}updatePlaying(){const e=this.model.get("playing");this.playPauseButton.getElementsByTagName("i")[0].className=e?"fa fa-pause":"fa fa-play"}updateRepeat(){const e=this.model.get("repeat");this.repeatButton.style.display=this.model.get("show_repeat")?this.playPauseButton.style.display:"none",e?this.repeatButton.classList.add("mod-active"):this.repeatButton.classList.remove("mod-active")}}class ze extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"FloatModel",value:0})}}class De extends ze{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"BoundedFloatModel",max:100,min:0})}}class Pe extends De{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"FloatSliderModel",_view_name:"FloatSliderView",step:1,orientation:"horizontal",_range:!1,readout:!0,readout_format:".2f",slider_color:null,continuous_update:!0,disabled:!1})}initialize(e,t){super.initialize(e,t),this.on("change:readout_format",this.update_readout_format,this),this.update_readout_format()}update_readout_format(){this.readout_formatter=(0,ve.GP)(this.get("readout_format"))}}class Ue extends De{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"FloatLogSliderModel",_view_name:"FloatLogSliderView",step:.1,orientation:"horizontal",_range:!1,readout:!0,readout_format:".3g",slider_color:null,continuous_update:!0,disabled:!1,base:10,value:1,min:0,max:4})}initialize(e,t){super.initialize(e,t),this.on("change:readout_format",this.update_readout_format,this),this.update_readout_format()}update_readout_format(){this.readout_formatter=(0,ve.GP)(this.get("readout_format"))}}class Fe extends Pe{}class Re extends Oe{constructor(){super(...arguments),this._parse_value=parseFloat}_validate_slide_value(e){return e}}class $e extends Te{constructor(){super(...arguments),this._parse_value=parseFloat}update(e){super.update(e);const t=this.model.get("value");this.readout.textContent=this.valueToString(t)}logCalc(e){const t=this.model.get("min"),s=this.model.get("max"),i=this.model.get("base");let a=Math.log(e)/Math.log(i);return a>s?a=s:aNumber(e),to:e=>e}}),this.$slider.noUiSlider.on("update",((e,t)=>{this.handleSliderUpdateEvent(e,t)})),this.$slider.noUiSlider.on("change",((e,t)=>{this.handleSliderChangeEvent(e,t)}))}valueToString(e){return(0,this.model.readout_formatter)(e)}stringToValue(e){return null===e?NaN:this._parse_value(e)}handleTextChange(){let e=this.stringToValue(this.readout.textContent);const t=this.model.get("min"),s=this.model.get("max"),i=this.model.get("base");isNaN(e)?this.readout.textContent=this.valueToString(this.model.get("value")):(e=Math.max(Math.min(e,Math.pow(i,s)),Math.pow(i,t)),e!==this.model.get("value")?(this.readout.textContent=this.valueToString(e),this.model.set("value",e),this.touch()):this.readout.textContent=this.valueToString(this.model.get("value")))}handleSliderUpdateEvent(e,t){const s=this.model.get("base"),i=Math.pow(s,this._validate_slide_value(e[0]));this.readout.textContent=this.valueToString(i),this.model.get("continuous_update")&&this.handleSliderChanged(e,t)}handleSliderChangeEvent(e,t){const s=this.model.get("base"),i=Math.pow(s,this._validate_slide_value(e[0]));this.readout.textContent=this.valueToString(i),this.handleSliderChanged(e,t)}handleSliderChanged(e,t){if(this._updating_slider)return;const s=this.model.get("base"),i=Math.pow(s,this._validate_slide_value(e[0]));this.model.set("value",i,{updated_view:this}),this.touch()}updateSliderValue(e,t,s){if(s.updated_view===this)return;const i=this.logCalc(this.model.get("value"));this.$slider.noUiSlider.set(i)}updateSliderOptions(e){this.$slider.noUiSlider.updateOptions({start:this.logCalc(this.model.get("value")),range:{min:this.model.get("min"),max:this.model.get("max")},step:this.model.get("step")})}_validate_slide_value(e){return e}}class Ne extends Se{constructor(){super(...arguments),this._parse_value=parseFloat,this._range_regex=/^\s*([+-]?(?:\d*\.?\d+|\d+\.)(?:[eE][-:]?\d+)?)\s*[-:–]\s*([+-]?(?:\d*\.?\d+|\d+\.)(?:[eE][+-]?\d+)?)/}_validate_slide_value(e){return e}}class He extends ze{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"FloatTextModel",_view_name:"FloatTextView",disabled:!1,continuous_update:!1})}}class Ke extends De{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"BoundedFloatTextModel",_view_name:"FloatTextView",disabled:!1,continuous_update:!1,step:.1})}}class qe extends Ve{constructor(){super(...arguments),this._parse_value=parseFloat,this._default_step="any"}handleKeypress(e){e.stopPropagation()}handleKeyUp(e){}}class Ge extends De{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"FloatProgressModel",_view_name:"ProgressView",orientation:"horizontal",bar_style:"",style:null})}}class Je extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ControllerButtonModel",_view_name:"ControllerButtonView",value:0,pressed:!1})}}class Ye extends i.DOMWidgetView{render(){this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-controller-button"),this.el.style.width="fit-content",this.support=document.createElement("div"),this.support.style.position="relative",this.support.style.margin="1px",this.support.style.width="16px",this.support.style.height="16px",this.support.style.border="1px solid black",this.support.style.background="lightgray",this.el.appendChild(this.support),this.bar=document.createElement("div"),this.bar.style.position="absolute",this.bar.style.width="100%",this.bar.style.bottom="0px",this.bar.style.background="gray",this.support.appendChild(this.bar),this.update(),this.label=document.createElement("div"),this.label.textContent=this.model.get("description"),this.label.style.textAlign="center",this.el.appendChild(this.label)}update(){this.bar.style.height=100*this.model.get("value")+"%"}}class Qe extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ControllerAxisModel",_view_name:"ControllerAxisView",value:0})}}class Xe extends i.DOMWidgetView{render(){this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-controller-axis"),this.el.style.width="16px",this.el.style.padding="4px",this.support=document.createElement("div"),this.support.style.position="relative",this.support.style.margin="1px",this.support.style.width="4px",this.support.style.height="64px",this.support.style.border="1px solid black",this.support.style.background="lightgray",this.bullet=document.createElement("div"),this.bullet.style.position="absolute",this.bullet.style.margin="-3px",this.bullet.style.boxSizing="unset",this.bullet.style.width="10px",this.bullet.style.height="10px",this.bullet.style.background="gray",this.label=document.createElement("div"),this.label.textContent=this.model.get("description"),this.label.style.textAlign="center",this.support.appendChild(this.bullet),this.el.appendChild(this.support),this.el.appendChild(this.label),this.update()}update(){this.bullet.style.top=50*(this.model.get("value")+1)+"%"}}class Ze extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"ControllerModel",_view_name:"ControllerView",index:0,name:"",mapping:"",connected:!1,timestamp:0,buttons:[],axes:[]})}initialize(e,t){super.initialize(e,t),void 0===navigator.getGamepads?(this.readout="This browser does not support gamepads.",console.error(this.readout)):(this.readout="Connect gamepad and press any button.",this.get("connected")?this.update_loop():this.wait_loop())}wait_loop(){const e=this.get("index"),t=navigator.getGamepads()[e];t?this.setup(t).then((e=>{this.set(e),this.save_changes(),window.requestAnimationFrame(this.update_loop.bind(this))})):window.requestAnimationFrame(this.wait_loop.bind(this))}setup(e){return this.set({name:e.id,mapping:e.mapping,connected:e.connected,timestamp:e.timestamp}),i.resolvePromisesDict({buttons:Promise.all(e.buttons.map(((e,t)=>this._create_button_model(t)))),axes:Promise.all(e.axes.map(((e,t)=>this._create_axis_model(t))))})}update_loop(){const e=this.get("index"),t=this.get("name"),s=navigator.getGamepads()[e];s&&e===s.index&&t===s.id?(this.set({timestamp:s.timestamp,connected:s.connected}),this.save_changes(),this.get("buttons").forEach((function(e,t){e.set({value:s.buttons[t].value,pressed:s.buttons[t].pressed}),e.save_changes()})),this.get("axes").forEach((function(e,t){e.set("value",s.axes[t]),e.save_changes()})),window.requestAnimationFrame(this.update_loop.bind(this))):this.reset_gamepad()}reset_gamepad(){this.get("buttons").forEach((function(e){e.close()})),this.get("axes").forEach((function(e){e.close()})),this.set({name:"",mapping:"",connected:!1,timestamp:0,buttons:[],axes:[]}),this.save_changes(),window.requestAnimationFrame(this.wait_loop.bind(this))}_create_button_model(e){return this.widget_manager.new_widget({model_name:"ControllerButtonModel",model_module:"@jupyter-widgets/controls",model_module_version:this.get("_model_module_version"),view_name:"ControllerButtonView",view_module:"@jupyter-widgets/controls",view_module_version:this.get("_view_module_version")}).then((function(t){return t.set("description",e),t}))}_create_axis_model(e){return this.widget_manager.new_widget({model_name:"ControllerAxisModel",model_module:"@jupyter-widgets/controls",model_module_version:this.get("_model_module_version"),view_name:"ControllerAxisView",view_module:"@jupyter-widgets/controls",view_module_version:this.get("_view_module_version")}).then((function(t){return t.set("description",e),t}))}}Ze.serializers=Object.assign(Object.assign({},g.serializers),{buttons:{deserialize:i.unpack_models},axes:{deserialize:i.unpack_models}});class et extends i.DOMWidgetView{_createElement(e){return this.luminoWidget=new i.JupyterLuminoPanelWidget({view:this}),this.luminoWidget.node}_setElement(e){if(this.el||e!==this.luminoWidget.node)throw new Error("Cannot reset the DOM element.");this.el=this.luminoWidget.node,this.$el=W()(this.luminoWidget.node)}initialize(e){super.initialize(e),this.button_views=new i.ViewList(this.add_button,null,this),this.listenTo(this.model,"change:buttons",((e,t)=>{this.button_views.update(t)})),this.axis_views=new i.ViewList(this.add_axis,null,this),this.listenTo(this.model,"change:axes",((e,t)=>{this.axis_views.update(t)})),this.listenTo(this.model,"change:name",this.update_label)}render(){this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-controller"),this.label=document.createElement("div"),this.el.appendChild(this.label),this.axis_box=new I.Panel,this.axis_box.node.style.display="flex",this.luminoWidget.addWidget(this.axis_box),this.button_box=new I.Panel,this.button_box.node.style.display="flex",this.luminoWidget.addWidget(this.button_box),this.button_views.update(this.model.get("buttons")),this.axis_views.update(this.model.get("axes")),this.update_label()}update_label(){this.label.textContent=this.model.get("name")||this.model.readout}add_button(e){const t=new I.Widget;return this.button_box.addWidget(t),this.create_child_view(e).then((e=>{const s=L.ArrayExt.firstIndexOf(this.button_box.widgets,t);return this.button_box.insertWidget(s,e.luminoWidget),t.dispose(),e})).catch((0,i.reject)("Could not add child button view to controller",!0))}add_axis(e){const t=new I.Widget;return this.axis_box.addWidget(t),this.create_child_view(e).then((e=>{const s=L.ArrayExt.firstIndexOf(this.axis_box.widgets,t);return this.axis_box.insertWidget(s,e.luminoWidget),t.dispose(),e})).catch((0,i.reject)("Could not add child axis view to controller",!0))}remove(){super.remove(),this.button_views.remove(),this.axis_views.remove()}}class tt extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"SelectionModel",index:"",_options_labels:[],disabled:!1})}}class st extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox")}update(){super.update(),this.listbox&&(this.listbox.disabled=this.model.get("disabled")),this.updateTabindex(),this.updateTooltip()}updateTabindex(){if(!this.listbox)return;const e=this.model.get("tabbable");!0===e?this.listbox.setAttribute("tabIndex","0"):!1===e?this.listbox.setAttribute("tabIndex","-1"):null===e&&this.listbox.removeAttribute("tabIndex")}updateTooltip(){if(!this.listbox)return;const e=this.model.get("tooltip");e?0===this.model.get("description").length&&this.listbox.setAttribute("title",e):this.listbox.removeAttribute("title")}}class it extends tt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"DropdownModel",_view_name:"DropdownView",button_style:""})}}class at extends st{render(){super.render(),this.el.classList.add("widget-dropdown"),this.listbox=document.createElement("select"),this.listbox.id=this.label.htmlFor=(0,i.uuid)(),this.el.appendChild(this.listbox),this._updateOptions(),this.update()}update(e){(null==e?void 0:e.updated_view)!==this&&this.model.hasChanged("_options_labels")&&this._updateOptions();const t=this.model.get("index");return this.listbox.selectedIndex=null===t?-1:t,super.update()}_updateOptions(){this.listbox.textContent="";const e=this.model.get("_options_labels");for(let t=0;te.value));let i=t.length!==s.length;if(!i)for(let e=0,a=t.length;e{const s=document.createElement("label");s.textContent=e,this.container.appendChild(s);const i=document.createElement("input");i.setAttribute("type","radio"),i.value=t.toString(),i.setAttribute("data-value",encodeURIComponent(e)),s.appendChild(i)}))),t.forEach(((e,t)=>{const s='input[data-value="'+encodeURIComponent(e)+'"]',i=this.container.querySelectorAll(s);if(i.length>0){const e=i[0];e.checked=this.model.get("index")===t,e.disabled=this.model.get("disabled")}})),setTimeout(this.adjustPadding,0,this),super.update(e)}adjustPadding(e){const t=window.getComputedStyle(e.el),s=parseInt(t.marginTop,10)+parseInt(t.marginBottom,10),i=e.label.offsetHeight+s,a=window.getComputedStyle(e.container),l=parseInt(a.marginBottom,10),d=(e.el.offsetHeight+s-l)%i,n=0===d?0:i-d;e.container.style.marginBottom=n+"px"}events(){return{'click input[type="radio"]':"_handle_click"}}_handle_click(e){const t=e.target;this.model.set("index",parseInt(t.value,10),{updated_view:this}),this.touch()}handle_message(e){if("focus"==e.do)this.container.firstElementChild.focus();else if("blur"==e.do)for(let e=0;ee.value));let h=!1;for(let e=0,a=t.length;e{let i;i=0!==e.trim().length||s[t]&&0!==s[t].trim().length?l(e):" ";const o=document.createElement("i"),r=document.createElement("button");s[t]&&(o.className="fa fa-"+s[t]),r.setAttribute("type","button"),r.className="widget-toggle-button jupyter-button",a&&r.classList.add(a),r.innerHTML=i,r.setAttribute("data-value",encodeURIComponent(e)),r.setAttribute("value",t.toString()),r.appendChild(o),r.disabled=n,d[t]&&r.setAttribute("title",d[t]),this.update_style_traits(r),this.buttongroup.appendChild(r)}))),t.forEach(((e,t)=>{const s='[data-value="'+encodeURIComponent(e)+'"]',i=this.buttongroup.querySelector(s);this.model.get("index")===t?i.classList.add("mod-active"):i.classList.remove("mod-active")})),this.stylePromise.then((function(e){e&&e.style()})),super.update(e)}update_style_traits(e){for(const t in this._css_state)if(Object.prototype.hasOwnProperty.call(this._css_state,"name"))if("margin"===t)this.buttongroup.style[t]=this._css_state[t];else if("width"!==t)if(e)e.style[t]=this._css_state[t];else{const e=this.buttongroup.querySelectorAll("button");e.length&&(e[0].style[t]=this._css_state[t])}}update_button_style(){const e=this.buttongroup.querySelectorAll("button");for(let t=0;tNumber(e),to:e=>Math.round(e)}}),this.$slider.noUiSlider.on("update",((e,t)=>{this.handleSliderUpdateEvent(e,t)})),this.$slider.noUiSlider.on("change",((e,t)=>{this.handleSliderChangeEvent(e,t)}))}events(){return{slide:"handleSliderChange",slidestop:"handleSliderChanged"}}updateSelection(){const e=this.model.get("index");this.updateReadout(e)}updateReadout(e){const t=this.model.get("_options_labels")[e];this.readout.textContent=t}handleSliderUpdateEvent(e,t){const s=e[0];this.updateReadout(s),this.model.get("continuous_update")&&this.handleSliderChanged(e,t)}handleSliderChangeEvent(e,t){const s=e[0];this.updateReadout(s),this.handleSliderChanged(e,t)}handleSliderChanged(e,t){const s=e[0];this.updateReadout(s),this.model.set("index",s,{updated_view:this}),this.touch()}updateSliderOptions(e){const t=this.model.get("_options_labels").length-1;this.$slider.noUiSlider.updateOptions({start:this.model.get("index"),range:{min:0,max:t},step:1})}updateSliderValue(e,t,s){if(s.updated_view===this)return;const i=this.$slider.noUiSlider.get(),a=this.model.get("index");i!==a&&this.$slider.noUiSlider.set(a)}}class gt extends tt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"MultipleSelectionModel"})}}class mt extends gt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"SelectMultipleModel",_view_name:"SelectMultipleView",rows:null})}}class _t extends dt{initialize(e){super.initialize(e),this.listbox.multiple=!0}render(){super.render(),this.el.classList.add("widget-select-multiple")}updateSelection(){const e=this.model.get("index")||[],t=this.listbox.options;this.listbox.selectedIndex=-1,e.forEach((e=>{t[e].selected=!0}))}_handle_change(){const e=Array.prototype.map.call(this.listbox.selectedOptions||[],(function(e){return e.index}));this.model.set("index",e,{updated_view:this}),this.touch()}}class bt extends gt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"SelectionSliderModel",_view_name:"SelectionSliderView",orientation:"horizontal",readout:!0,continuous_update:!0})}}class vt extends pt{render(){super.render()}updateSelection(e){e=e||this.model.get("index"),this.updateReadout(e)}updateReadout(e){const t=this.model.get("_options_labels"),s=t[e[0]],i=t[e[1]];this.readout.textContent=`${s}-${i}`}handleSliderUpdateEvent(e,t){const s=e.map(Math.trunc);this.updateReadout(s),this.model.get("continuous_update")&&this.handleSliderChanged(e,t)}handleSliderChanged(e,t){const s=e.map(Math.round);this.updateReadout(s),this.model.set("index",s.slice(),{updated_view:this}),this.touch()}updateSliderValue(e,t,s){if(s.updated_view===this)return;const i=this.$slider.noUiSlider.get().map(Math.round),a=this.model.get("index").map(Math.round);i[0]===a[0]&&i[1]===a[1]||this.$slider.noUiSlider.set(a)}}var xt=s(4602),ft=s(6209);class wt extends I.Panel{constructor(){super(...arguments),this._widgetRemoved=new xt.Signal(this)}get widgetRemoved(){return this._widgetRemoved}onChildRemoved(e){this._widgetRemoved.emit(e.child)}}class yt extends I.Widget{constructor(e={}){super(),this._currentChanged=new xt.Signal(this),this.addClass("jupyter-widget-TabPanel"),this.tabBar=new I.TabBar(e),this.tabBar.addClass("jupyter-widget-TabPanel-tabBar"),this.tabContents=new wt,this.tabContents.addClass("jupyter-widget-TabPanel-tabContents"),this.tabBar.tabMoved.connect(this._onTabMoved,this),this.tabBar.currentChanged.connect(this._onCurrentChanged,this),this.tabBar.tabCloseRequested.connect(this._onTabCloseRequested,this),this.tabBar.tabActivateRequested.connect(this._onTabActivateRequested,this),this.tabContents.widgetRemoved.connect(this._onWidgetRemoved,this);const t=new I.PanelLayout;t.addWidget(this.tabBar),t.addWidget(this.tabContents),this.layout=t}get currentChanged(){return this._currentChanged}get currentIndex(){const e=this.tabBar.currentIndex;return-1===e?null:e}set currentIndex(e){this.tabBar.currentIndex=null===e?-1:e}get currentWidget(){const e=this.tabBar.currentTitle;return e?e.owner:null}set currentWidget(e){this.tabBar.currentTitle=e?e.title:null}get tabsMovable(){return this.tabBar.tabsMovable}set tabsMovable(e){this.tabBar.tabsMovable=e}get widgets(){return this.tabContents.widgets}addWidget(e){this.insertWidget(this.widgets.length,e)}insertWidget(e,t){t!==this.currentWidget&&t.hide(),this.tabContents.insertWidget(e,t),this.tabBar.insertTab(e,t.title)}_onCurrentChanged(e,t){const{previousIndex:s,previousTitle:i,currentIndex:a,currentTitle:l}=t,d=i?i.owner:null,n=l?l.owner:null;d&&d.hide(),n&&n.show(),this._currentChanged.emit({previousIndex:s,previousWidget:d,currentIndex:a,currentWidget:n}),(ft.Platform.IS_EDGE||ft.Platform.IS_IE)&&V.MessageLoop.flush()}_onTabActivateRequested(e,t){t.title.owner.activate()}_onTabCloseRequested(e,t){t.title.owner.close()}_onTabMoved(e,t){this.tabContents.insertWidget(t.toIndex,t.title.owner)}_onWidgetRemoved(e,t){this.tabBar.removeTab(t.title)}}class Ct{constructor(e,t={}){this._array=null,this._value=null,this._previousValue=null,this._selectionChanged=new xt.Signal(this),this._array=e,this._insertBehavior=t.insertBehavior||"select-item-if-needed",this._removeBehavior=t.removeBehavior||"select-item-after"}get selectionChanged(){return this._selectionChanged}adjustSelectionForSet(e){const t=this.index,s=this.value;if(e!==t)return;this._updateSelectedValue();const i=this.value;this._previousValue=null,s!==i&&this._selectionChanged.emit({previousIndex:t,previousValue:s,currentIndex:t,currentValue:i})}get value(){return this._value}set value(e){null===e||null===this._array?this.index=null:this.index=L.ArrayExt.firstIndexOf(this._array,e)}get index(){return this._index}set index(e){let t;if(null!==e&&null!==this._array?(t=Math.floor(e),(t<0||t>=this._array.length)&&(t=null)):t=null,this._index===t)return;const s=this._index,i=this._value;this._index=t,this._updateSelectedValue(),this._previousValue=i,this._selectionChanged.emit({previousIndex:s,previousValue:i,currentIndex:t,currentValue:this._value})}get insertBehavior(){return this._insertBehavior}set insertBehavior(e){this._insertBehavior=e}get removeBehavior(){return this._removeBehavior}set removeBehavior(e){this._removeBehavior=e}adjustSelectionForInsert(e,t){const s=this._value,i=this._index,a=this._insertBehavior;if("select-item"===a||"select-item-if-needed"===a&&null===i)return this._index=e,this._value=t,this._previousValue=s,void this._selectionChanged.emit({previousIndex:i,previousValue:s,currentIndex:e,currentValue:t});null!==i&&i>=e&&this._index++}clearSelection(){const e=this._index,t=this._value;this._index=null,this._value=null,this._previousValue=null,null!==e&&this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this._value})}adjustSelectionForRemove(e,t){if(null===this._index)return;const s=this._index,i=this._removeBehavior;if(s===e){if(!this._array||0===this._array.length)return this._index=null,this._value=null,this._previousValue=null,void this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this._value});if("select-item-after"===i)return this._index=Math.min(e,this._array.length-1),this._updateSelectedValue(),this._previousValue=null,void this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this._value});if("select-item-before"===i)return this._index=Math.max(0,e-1),this._updateSelectedValue(),this._previousValue=null,void this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this._value});if("select-previous-item"===i)return this._previousValue?this.value=this._previousValue:(this._index=Math.min(e,this._array.length-1),this._updateSelectedValue()),this._previousValue=null,void this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this.value});this._index=null,this._value=null,this._previousValue=null,this._selectionChanged.emit({previousIndex:e,previousValue:t,currentIndex:this._index,currentValue:this._value})}else s>e&&this._index--}_updateSelectedValue(){const e=this._index;this._value=null!==e&&this._array?this._array[e]:null}}const Mt="jupyter-widget-Collapse-open";class jt extends I.Widget{constructor(e){super(e),this._collapseChanged=new xt.Signal(this),this.addClass("jupyter-widget-Collapse"),this._header=new I.Widget,this._header.addClass("jupyter-widget-Collapse-header"),this._header.node.addEventListener("click",this);const t=document.createElement("i");t.classList.add("fa","fa-fw","fa-caret-right"),this._header.node.appendChild(t),this._header.node.appendChild(document.createElement("span")),this._content=new I.Panel,this._content.addClass("jupyter-widget-Collapse-contents");const s=new I.PanelLayout;this.layout=s,s.addWidget(this._header),s.addWidget(this._content),e.widget&&(this.widget=e.widget),this.collapsed=!1}dispose(){this.isDisposed||(super.dispose(),this._header=null,this._widget=null,this._content=null)}get widget(){return this._widget}set widget(e){const t=this._widget;t&&(t.disposed.disconnect(this._onChildDisposed,this),t.title.changed.disconnect(this._onTitleChanged,this),t.parent=null),this._widget=e,e.disposed.connect(this._onChildDisposed,this),e.title.changed.connect(this._onTitleChanged,this),this._onTitleChanged(e.title),this._content.addWidget(e)}get collapsed(){return this._collapsed}set collapsed(e){e!==this._collapsed&&(e?this._collapse():this._uncollapse())}toggle(){this.collapsed=!this.collapsed}get collapseChanged(){return this._collapseChanged}_collapse(){this._collapsed=!0,this._content&&this._content.hide(),this.removeClass(Mt),this._header.node.children[0].classList.add("fa-caret-right"),this._header.node.children[0].classList.remove("fa-caret-down"),this._collapseChanged.emit(void 0)}_uncollapse(){this._collapsed=!1,this._content&&this._content.show(),this.addClass(Mt),this._header.node.children[0].classList.add("fa-caret-down"),this._header.node.children[0].classList.remove("fa-caret-right"),this._collapseChanged.emit(void 0)}handleEvent(e){"click"===e.type&&this._evtClick(e)}_evtClick(e){this.toggle()}_onTitleChanged(e){this._header.node.children[1].textContent=this._widget.title.label}_onChildDisposed(e){this.dispose()}}const Tt="jupyter-widget-Accordion-child-active";class St extends I.Panel{constructor(e){super(e),this._selection=new Ct(this.widgets),this._selection.selectionChanged.connect(this._onSelectionChanged,this),this.addClass("jupyter-widget-Accordion")}get collapseWidgets(){return this.layout.widgets}get selection(){return this._selection}indexOf(e){return L.ArrayExt.findFirstIndex(this.collapseWidgets,(t=>t.widget===e))}addWidget(e){const t=this._wrapWidget(e);return t.collapsed=!0,super.addWidget(t),this._selection.adjustSelectionForInsert(this.widgets.length-1,t),t}insertWidget(e,t){const s=this._wrapWidget(t);s.collapsed=!0,super.insertWidget(e,s),this._selection.adjustSelectionForInsert(e,s)}removeWidget(e){const t=this.indexOf(e);if(t>=0){const s=this.collapseWidgets[t];e.parent=null,s.dispose(),this._selection.adjustSelectionForRemove(t,null)}}_wrapWidget(e){const t=new jt({widget:e});return t.addClass("jupyter-widget-Accordion-child"),t.collapseChanged.connect(this._onCollapseChange,this),t}_onCollapseChange(e){e.collapsed?this._selection.value===e&&e.collapsed&&(this._selection.value=null):this._selection.value=e}_onSelectionChanged(e,t){const s=t.previousValue,i=t.currentValue;s&&(s.collapsed=!0,s.removeClass(Tt)),i&&(i.collapsed=!1,i.addClass(Tt))}}class Ot extends E{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"SelectionContainerModel",selected_index:null,titles:[]})}}class kt extends Ot{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"AccordionModel",_view_name:"AccordionView"})}}class Lt extends St{constructor(e){const t=e.view;delete e.view,super(e),this._view=t}processMessage(e){var t;super.processMessage(e),null===(t=this._view)||void 0===t||t.processLuminoMessage(e)}dispose(){this.isDisposed||(super.dispose(),this._view.remove(),this._view=null)}}class Vt extends i.DOMWidgetView{_createElement(e){return this.luminoWidget=new Lt({view:this}),this.luminoWidget.node}_setElement(e){if(this.el||e!==this.luminoWidget.node)throw new Error("Cannot reset the DOM element.");this.el=this.luminoWidget.node,this.$el=W()(this.luminoWidget.node)}initialize(e){super.initialize(e),this.children_views=new i.ViewList(this.add_child_view,this.remove_child_view,this),this.listenTo(this.model,"change:children",(()=>this.updateChildren())),this.listenTo(this.model,"change:selected_index",(()=>this.update_selected_index())),this.listenTo(this.model,"change:titles",(()=>this.update_titles()))}render(){var e;super.render();const t=this.luminoWidget;t.addClass("jupyter-widgets"),t.addClass("widget-accordion"),t.addClass("widget-container"),t.selection.selectionChanged.connect((e=>{this.updatingChildren||(this.model.set("selected_index",t.selection.index),this.touch())})),null===(e=this.children_views)||void 0===e||e.update(this.model.get("children")),this.update_titles(),this.update_selected_index()}updateChildren(){var e;this.updatingChildren=!0,this.luminoWidget.selection.index=null,null===(e=this.children_views)||void 0===e||e.update(this.model.get("children")),this.update_selected_index(),this.updatingChildren=!1}update_titles(){const e=this.luminoWidget.collapseWidgets,t=this.model.get("titles");for(let s=0;s{const t=e.luminoWidget;return t.title.label=a.title.label,s.collapseWidgets[s.indexOf(a)].widget=t,a.dispose(),e})).catch((0,i.reject)("Could not add child view to box",!0))}remove(){this.children_views=null,super.remove()}}class It extends Ot{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"TabModel",_view_name:"TabView"})}}class At extends yt{constructor(e){const t=e.view;delete e.view,super(e),this._view=t,V.MessageLoop.installMessageHook(this.tabContents,((e,t)=>(this._view.processLuminoMessage(t),!0)))}dispose(){this.isDisposed||(super.dispose(),this._view.remove(),this._view=null)}}class Wt extends i.DOMWidgetView{constructor(){super(...arguments),this.updatingTabs=!1}_createElement(e){return this.luminoWidget=new At({view:this}),this.luminoWidget.node}_setElement(e){if(this.el||e!==this.luminoWidget.node)throw new Error("Cannot reset the DOM element.");this.el=this.luminoWidget.node,this.$el=W()(this.luminoWidget.node)}initialize(e){super.initialize(e),this.childrenViews=new i.ViewList(this.addChildView,(e=>{e.remove()}),this),this.listenTo(this.model,"change:children",(()=>this.updateTabs())),this.listenTo(this.model,"change:titles",(()=>this.updateTitles()))}render(){super.render();const e=this.luminoWidget;e.addClass("jupyter-widgets"),e.addClass("widget-container"),e.addClass("jupyter-widget-tab"),e.addClass("widget-tab"),e.tabsMovable=!0,e.tabBar.insertBehavior="none",e.tabBar.currentChanged.connect(this._onTabChanged,this),e.tabBar.tabMoved.connect(this._onTabMoved,this),e.tabBar.addClass("widget-tab-bar"),e.tabContents.addClass("widget-tab-contents"),e.tabBar.tabsMovable=!1,this.updateTabs(),this.update()}updateTabs(){var e;this.updatingTabs=!0,this.luminoWidget.currentIndex=null,null===(e=this.childrenViews)||void 0===e||e.update(this.model.get("children")),this.luminoWidget.currentIndex=this.model.get("selected_index"),this.updatingTabs=!1}addChildView(e,t){const s=this.model.get("titles")[t]||"",a=this.luminoWidget,l=new I.Widget;return l.title.label=s,a.addWidget(l),this.create_child_view(e).then((e=>{const t=e.luminoWidget;t.title.label=l.title.label,t.title.closable=!1;const s=L.ArrayExt.firstIndexOf(a.widgets,l);return a.insertWidget(s+1,t),l.dispose(),e})).catch((0,i.reject)("Could not add child view to box",!0))}update(){return this.updateSelectedIndex(),super.update()}updateTitles(){const e=this.model.get("titles")||[];(0,L.each)(this.luminoWidget.widgets,((t,s)=>{t.title.label=e[s]||""}))}updateSelectedIndex(){this.luminoWidget.currentIndex=this.model.get("selected_index")}remove(){this.childrenViews=null,super.remove()}_onTabChanged(e,t){if(!this.updatingTabs){const e=t.currentIndex;this.model.set("selected_index",-1===e?null:e),this.touch()}}_onTabMoved(e,t){const s=this.model.get("children").slice();L.ArrayExt.move(s,t.fromIndex,t.toIndex),this.model.set("children",s),this.touch()}}class Et extends Ot{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"StackModel",_view_name:"StackView"})}}class Bt extends D{initialize(e){super.initialize(e),this.listenTo(this.model,"change:selected_index",this.update_children)}update_children(){var e;let t;t=null===this.model.get("selected_index")?[]:[this.model.get("children")[this.model.get("selected_index")]],null===(e=this.children_views)||void 0===e||e.update(t).then((e=>{e.forEach((e=>{V.MessageLoop.postMessage(e.luminoWidget,I.Widget.ResizeMessage.UnknownSize)}))}))}}var zt=s(8996);function Dt(e){for(;e.firstChild;)e.removeChild(e.firstChild)}class Pt{constructor(e,t,s){this.start=e,this.dx=t,this.max=s}isSelected(e){let t,s;return this.dx>=0?(t=this.start,s=this.start+this.dx):(t=this.start+this.dx,s=this.start),t<=e&&ethis.max&&(this.dx=this.max-this.start),this.start+this.dx<0&&(this.dx=-this.start)}}class Ut extends g{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:[],placeholder:"​",allowed_tags:null,allow_duplicates:!0})}}class Ft extends i.DOMWidgetView{constructor(){super(...arguments),this.hoveredTag=null,this.hoveredTagIndex=null}render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("jupyter-widget-tagsinput"),this.taginputWrapper=document.createElement("div"),this.model.get("value").length?this.taginputWrapper.style.display="none":this.taginputWrapper.style.display="inline-block",this.datalistID=(0,i.uuid)(),this.taginput=document.createElement("input"),this.taginput.classList.add("jupyter-widget-tag"),this.taginput.classList.add("jupyter-widget-taginput"),this.taginput.setAttribute("list",this.datalistID),this.taginput.setAttribute("type","text"),this.autocompleteList=document.createElement("datalist"),this.autocompleteList.id=this.datalistID,this.updateAutocomplete(),this.model.on("change:allowed_tags",this.updateAutocomplete.bind(this)),this.updatePlaceholder(),this.model.on("change:placeholder",this.updatePlaceholder.bind(this)),this.taginputWrapper.classList.add("widget-text"),this.taginputWrapper.appendChild(this.taginput),this.taginputWrapper.appendChild(this.autocompleteList),this.el.onclick=this.focus.bind(this),this.el.ondrop=e=>{const t=null==this.hoveredTagIndex?this.tags.length:this.hoveredTagIndex;return this.ondrop(e,t)},this.el.ondragover=this.ondragover.bind(this),this.taginput.onchange=this.handleValueAdded.bind(this),this.taginput.oninput=this.resizeInput.bind(this),this.taginput.onkeydown=this.handleKeyEvent.bind(this),this.taginput.onblur=this.loseFocus.bind(this),this.resizeInput(),this.inputIndex=this.model.get("value").length,this.selection=null,this.preventLoosingFocus=!1,this.update()}update(){this.preventLoosingFocus=!0,Dt(this.el),this.tags=[];const e=this.model.get("value");this.inputIndex=e.length;for(const t in e){const s=parseInt(t),i=this.createTag(e[s],s,null!=this.selection&&this.selection.isSelected(s));i.draggable=!0,i.ondragstart=((e,t)=>s=>{this.ondragstart(s,e,t,this.model.model_id)})(s,e[s]),i.ondrop=(e=>t=>{this.ondrop(t,e)})(s),i.ondragover=this.ondragover.bind(this),i.ondragenter=(e=>t=>{this.ondragenter(t,e)})(s),i.ondragend=this.ondragend.bind(this),this.tags.push(i),this.el.appendChild(i)}return this.el.insertBefore(this.taginputWrapper,this.el.children[this.inputIndex]),this.model.get("value").length?this.taginputWrapper.style.display="none":this.taginputWrapper.style.display="inline-block",this.preventLoosingFocus=!1,super.update()}updateAutocomplete(){Dt(this.autocompleteList);const e=this.model.get("allowed_tags");for(const t of e){const e=document.createElement("option");e.value=t,this.autocompleteList.appendChild(e)}}updatePlaceholder(){this.taginput.placeholder=this.model.get("placeholder"),this.resizeInput()}updateTags(){const e=this.model.get("value");for(const t in this.tags){const s=parseInt(t);this.updateTag(this.tags[s],e[s],s,null!=this.selection&&this.selection.isSelected(s))}}handleValueAdded(e){const t=this.taginput.value.replace(/^\s+|\s+$/g,""),s=this.inputIndex;""!=t&&(this.inputIndex++,this.addTag(s,t)&&(this.taginput.value="",this.resizeInput(),this.focus()))}addTag(e,t){const s=this.model.get("value");let i;try{i=this.validateValue(t)}catch(e){return!1}const a=this.model.get("allowed_tags");if(a.length&&!a.includes(i))return!1;if(!this.model.get("allow_duplicates")&&s.includes(i))return!1;this.selection=null;const l=[...s];return l.splice(e,0,i),this.model.set("value",l),this.model.save_changes(),!0}resizeInput(){let e;e=0!=this.taginput.value.length?this.taginput.value:this.model.get("placeholder");const t=e.length+1;this.taginput.setAttribute("size",String(t))}handleKeyEvent(e){const t=this.model.get("value").length;if(this.taginput.value.length)return;const s=this.inputIndex;switch(e.key){case"ArrowLeft":e.ctrlKey&&e.shiftKey&&this.select(s,-s),!e.ctrlKey&&e.shiftKey&&this.select(s,-1),e.ctrlKey?this.inputIndex=0:this.inputIndex--;break;case"ArrowRight":e.ctrlKey&&e.shiftKey&&this.select(s,t-s),!e.ctrlKey&&e.shiftKey&&this.select(s,1),e.ctrlKey?this.inputIndex=t:this.inputIndex++;break;case"Backspace":this.selection?this.removeSelectedTags():this.removeTag(this.inputIndex-1);break;case"Delete":this.selection?this.removeSelectedTags():this.removeTag(this.inputIndex);break;default:return}var i,a;e.shiftKey||(this.selection=null),this.inputIndex=(i=this.inputIndex,a=t,Math.min(Math.max(i,0),a)),this.update(),this.focus()}ondragstart(e,t,s,i){null!=e.dataTransfer&&(e.dataTransfer.setData("index",String(t)),e.dataTransfer.setData("tagValue",String(s)),e.dataTransfer.setData("origin",i))}ondrop(e,t){if(null==e.dataTransfer)return;e.preventDefault(),e.stopPropagation();const s=e.dataTransfer.getData("tagValue"),i=parseInt(e.dataTransfer.getData("index")),a=e.dataTransfer.getData("origin")==this.model.model_id;if(!isNaN(i)){if(a){const e=[...this.model.get("value")];return i=0;t--)null!=this.selection&&this.selection.isSelected(t)&&(e.splice(t,1),t()=>{this.removeTag(e),this.loseFocus()})(t),i}getTagText(e){return e}updateTag(e,t,s,i){i?e.classList.add("mod-active"):e.classList.remove("mod-active")}}$t.class_map={primary:"mod-primary",success:"mod-success",info:"mod-info",warning:"mod-warning",danger:"mod-danger"};class Nt extends Ut{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:[],_view_name:"ColorsInputView",_model_name:"ColorsInputModel"})}}class Ht extends Ft{createTag(e,t,s){const i=document.createElement("div"),a=e,l=zt.Ay(e).darker().toString();i.classList.add("jupyter-widget-tag"),i.classList.add("jupyter-widget-colortag"),s?(i.classList.add("mod-active"),i.style.backgroundColor=l):i.style.backgroundColor=a;const d=document.createElement("i");return d.classList.add("fa"),d.classList.add("fa-times"),d.classList.add("jupyter-widget-tag-close"),i.appendChild(d),d.onmousedown=(e=>()=>{this.removeTag(e),this.loseFocus()})(t),i}updateTag(e,t,s,i){const a=t,l=zt.Ay(t).darker().toString();i?(e.classList.add("mod-active"),e.style.backgroundColor=l):(e.classList.remove("mod-active"),e.style.backgroundColor=a)}validateValue(e){if(null==zt.Ay(e))throw e+" is not a valid Color";return e}}class Kt extends Rt{defaults(){return Object.assign(Object.assign({},super.defaults()),{min:null,max:null})}}class qt extends $t{render(){this.model.on("change:format",(()=>{this.formatter=ve.GP(this.model.get("format")),this.update()})),this.formatter=ve.GP(this.model.get("format")),super.render()}getTagText(e){return this.formatter(this.parseNumber(e))}validateValue(e){const t=this.parseNumber(e),s=this.model.get("min"),i=this.model.get("max");if(isNaN(t)||null!=s&&ti)throw e+" is not a valid number, it should be in the range ["+s+", "+i+"]";return t}}class Gt extends Kt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"FloatsInputView",_model_name:"FloatsInputModel",format:".1f"})}}class Jt extends qt{parseNumber(e){return parseFloat(e)}}class Yt extends Kt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"IntsInputView",_model_name:"IntsInputModel",format:"d"})}}class Qt extends qt{parseNumber(e){const t=parseInt(e);if(t!=parseFloat(e))throw e+" should be an integer";return t}}class Xt extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"StringStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}Xt.styleProperties=Object.assign(Object.assign({},o.styleProperties),{background:{selector:"",attribute:"background",default:null},font_size:{selector:"",attribute:"font-size",default:""},text_color:{selector:"",attribute:"color",default:""}});class Zt extends Xt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"HTMLStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}Zt.styleProperties=Object.assign({},Xt.styleProperties);class es extends Xt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"HTMLMathStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}es.styleProperties=Object.assign({},Xt.styleProperties);class ts extends Xt{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"LabelStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}ts.styleProperties=Object.assign(Object.assign({},Xt.styleProperties),{font_family:{selector:"",attribute:"font-family",default:""},font_style:{selector:"",attribute:"font-style",default:""},font_variant:{selector:"",attribute:"font-variant",default:""},font_weight:{selector:"",attribute:"font-weight",default:""},text_decoration:{selector:"",attribute:"text-decoration",default:""}});class ss extends o{defaults(){return Object.assign(Object.assign({},super.defaults()),{_model_name:"TextStyleModel",_model_module:"@jupyter-widgets/controls",_model_module_version:n.A})}}ss.styleProperties=Object.assign(Object.assign({},o.styleProperties),{background:{selector:".widget-input",attribute:"background",default:null},font_size:{selector:".widget-input",attribute:"font-size",default:""},text_color:{selector:".widget-input",attribute:"color",default:""}});class is extends m{defaults(){return Object.assign(Object.assign({},super.defaults()),{value:"",disabled:!1,placeholder:"​",_model_name:"StringModel"})}}class as extends h{render(){super.render(),this.el.classList.add("jupyter-widgets"),this.el.classList.add("widget-inline-hbox")}}class ls extends is{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"HTMLView",_model_name:"HTMLModel"})}}class ds extends as{render(){super.render(),this.el.classList.add("widget-html"),this.content=document.createElement("div"),this.content.classList.add("widget-html-content"),this.el.appendChild(this.content),this.update()}update(){return this.content.innerHTML=this.model.get("value"),super.update()}handle_message(e){"focus"===e.do?this.content.focus():"blur"===e.do&&this.content.blur()}}class ns extends is{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"HTMLMathView",_model_name:"HTMLMathModel"})}}class os extends as{render(){super.render(),this.el.classList.add("widget-htmlmath"),this.content=document.createElement("div"),this.content.classList.add("widget-htmlmath-content"),this.el.appendChild(this.content),this.update()}update(){return this.content.innerHTML=this.model.get("value"),this.typeset(this.content),super.update()}handle_message(e){"focus"===e.do?this.content.focus():"blur"===e.do&&this.content.blur()}}class rs extends is{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"LabelView",_model_name:"LabelModel"})}}class hs extends as{render(){super.render(),this.el.classList.add("widget-label"),this.update()}update(){return this.typeset(this.el,this.model.get("value")),super.update()}}class us extends is{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"TextareaView",_model_name:"TextareaModel",rows:null,continuous_update:!0})}}class cs extends as{render(){super.render(),this.el.classList.add("widget-textarea"),this.textbox=document.createElement("textarea"),this.textbox.setAttribute("rows","5"),this.textbox.id=this.label.htmlFor=(0,i.uuid)(),this.textbox.classList.add("widget-input"),this.el.appendChild(this.textbox),this.update(),this.listenTo(this.model,"change:placeholder",((e,t,s)=>{this.update_placeholder(t)})),this.update_placeholder(),this.updateTooltip()}update_placeholder(e){const t=e||this.model.get("placeholder");this.textbox.setAttribute("placeholder",t.toString())}update(e){if(void 0===e||e.updated_view!==this){this.textbox.value=this.model.get("value");let e=this.model.get("rows");null===e&&(e=""),this.textbox.setAttribute("rows",e),this.textbox.disabled=this.model.get("disabled")}return this.updateTabindex(),this.updateTooltip(),super.update()}updateTabindex(){if(!this.textbox)return;const e=this.model.get("tabbable");!0===e?this.textbox.setAttribute("tabIndex","0"):!1===e?this.textbox.setAttribute("tabIndex","-1"):null===e&&this.textbox.removeAttribute("tabIndex")}updateTooltip(){if(!this.textbox)return;const e=this.model.get("tooltip");e?0===this.model.get("description").length&&this.textbox.setAttribute("title",e):this.textbox.removeAttribute("title")}events(){return{"keydown textarea":"handleKeyDown","keypress textarea":"handleKeypress","input textarea":"handleChanging","change textarea":"handleChanged"}}handleKeyDown(e){e.stopPropagation()}handleKeypress(e){e.stopPropagation()}handleChanging(e){this.model.get("continuous_update")&&this.handleChanged(e)}handleChanged(e){const t=e.target;this.model.set("value",t.value,{updated_view:this}),this.touch()}handle_message(e){"focus"===e.do?this.textbox.focus():"blur"===e.do&&this.textbox.blur()}}class ps extends is{defaults(){return Object.assign(Object.assign({},super.defaults()),{_view_name:"TextView",_model_name:"TextModel",continuous_update:!0})}}class gs extends 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