Spaces:
Paused
Paused
File size: 60,822 Bytes
dc2106c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 |
"""
Functions that ignore NaN.
Functions
---------
- `nanmin` -- minimum non-NaN value
- `nanmax` -- maximum non-NaN value
- `nanargmin` -- index of minimum non-NaN value
- `nanargmax` -- index of maximum non-NaN value
- `nansum` -- sum of non-NaN values
- `nanprod` -- product of non-NaN values
- `nancumsum` -- cumulative sum of non-NaN values
- `nancumprod` -- cumulative product of non-NaN values
- `nanmean` -- mean of non-NaN values
- `nanvar` -- variance of non-NaN values
- `nanstd` -- standard deviation of non-NaN values
- `nanmedian` -- median of non-NaN values
- `nanquantile` -- qth quantile of non-NaN values
- `nanpercentile` -- qth percentile of non-NaN values
"""
import functools
import warnings
import numpy as np
from numpy.lib import function_base
from numpy.core import overrides
array_function_dispatch = functools.partial(
overrides.array_function_dispatch, module='numpy')
__all__ = [
'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
'nanmedian', 'nanpercentile', 'nanvar', 'nanstd', 'nanprod',
'nancumsum', 'nancumprod', 'nanquantile'
]
def _nan_mask(a, out=None):
"""
Parameters
----------
a : array-like
Input array with at least 1 dimension.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output and will prevent the allocation of a new array.
Returns
-------
y : bool ndarray or True
A bool array where ``np.nan`` positions are marked with ``False``
and other positions are marked with ``True``. If the type of ``a``
is such that it can't possibly contain ``np.nan``, returns ``True``.
"""
# we assume that a is an array for this private function
if a.dtype.kind not in 'fc':
return True
y = np.isnan(a, out=out)
y = np.invert(y, out=y)
return y
def _replace_nan(a, val):
"""
If `a` is of inexact type, make a copy of `a`, replace NaNs with
the `val` value, and return the copy together with a boolean mask
marking the locations where NaNs were present. If `a` is not of
inexact type, do nothing and return `a` together with a mask of None.
Note that scalars will end up as array scalars, which is important
for using the result as the value of the out argument in some
operations.
Parameters
----------
a : array-like
Input array.
val : float
NaN values are set to val before doing the operation.
Returns
-------
y : ndarray
If `a` is of inexact type, return a copy of `a` with the NaNs
replaced by the fill value, otherwise return `a`.
mask: {bool, None}
If `a` is of inexact type, return a boolean mask marking locations of
NaNs, otherwise return None.
"""
a = np.asanyarray(a)
if a.dtype == np.object_:
# object arrays do not support `isnan` (gh-9009), so make a guess
mask = np.not_equal(a, a, dtype=bool)
elif issubclass(a.dtype.type, np.inexact):
mask = np.isnan(a)
else:
mask = None
if mask is not None:
a = np.array(a, subok=True, copy=True)
np.copyto(a, val, where=mask)
return a, mask
def _copyto(a, val, mask):
"""
Replace values in `a` with NaN where `mask` is True. This differs from
copyto in that it will deal with the case where `a` is a numpy scalar.
Parameters
----------
a : ndarray or numpy scalar
Array or numpy scalar some of whose values are to be replaced
by val.
val : numpy scalar
Value used a replacement.
mask : ndarray, scalar
Boolean array. Where True the corresponding element of `a` is
replaced by `val`. Broadcasts.
Returns
-------
res : ndarray, scalar
Array with elements replaced or scalar `val`.
"""
if isinstance(a, np.ndarray):
np.copyto(a, val, where=mask, casting='unsafe')
else:
a = a.dtype.type(val)
return a
def _remove_nan_1d(arr1d, overwrite_input=False):
"""
Equivalent to arr1d[~arr1d.isnan()], but in a different order
Presumably faster as it incurs fewer copies
Parameters
----------
arr1d : ndarray
Array to remove nans from
overwrite_input : bool
True if `arr1d` can be modified in place
Returns
-------
res : ndarray
Array with nan elements removed
overwrite_input : bool
True if `res` can be modified in place, given the constraint on the
input
"""
c = np.isnan(arr1d)
s = np.nonzero(c)[0]
if s.size == arr1d.size:
warnings.warn("All-NaN slice encountered", RuntimeWarning,
stacklevel=5)
return arr1d[:0], True
elif s.size == 0:
return arr1d, overwrite_input
else:
if not overwrite_input:
arr1d = arr1d.copy()
# select non-nans at end of array
enonan = arr1d[-s.size:][~c[-s.size:]]
# fill nans in beginning of array with non-nans of end
arr1d[s[:enonan.size]] = enonan
return arr1d[:-s.size], True
def _divide_by_count(a, b, out=None):
"""
Compute a/b ignoring invalid results. If `a` is an array the division
is done in place. If `a` is a scalar, then its type is preserved in the
output. If out is None, then then a is used instead so that the
division is in place. Note that this is only called with `a` an inexact
type.
Parameters
----------
a : {ndarray, numpy scalar}
Numerator. Expected to be of inexact type but not checked.
b : {ndarray, numpy scalar}
Denominator.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary.
Returns
-------
ret : {ndarray, numpy scalar}
The return value is a/b. If `a` was an ndarray the division is done
in place. If `a` is a numpy scalar, the division preserves its type.
"""
with np.errstate(invalid='ignore', divide='ignore'):
if isinstance(a, np.ndarray):
if out is None:
return np.divide(a, b, out=a, casting='unsafe')
else:
return np.divide(a, b, out=out, casting='unsafe')
else:
if out is None:
return a.dtype.type(a / b)
else:
# This is questionable, but currently a numpy scalar can
# be output to a zero dimensional array.
return np.divide(a, b, out=out, casting='unsafe')
def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanmin_dispatcher)
def nanmin(a, axis=None, out=None, keepdims=np._NoValue):
"""
Return minimum of an array or minimum along an axis, ignoring any NaNs.
When all-NaN slices are encountered a ``RuntimeWarning`` is raised and
Nan is returned for that slice.
Parameters
----------
a : array_like
Array containing numbers whose minimum is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the minimum is computed. The default is to compute
the minimum of the flattened array.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
:ref:`ufuncs-output-type` for more details.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If the value is anything but the default, then
`keepdims` will be passed through to the `min` method
of sub-classes of `ndarray`. If the sub-classes methods
does not implement `keepdims` any exceptions will be raised.
.. versionadded:: 1.8.0
Returns
-------
nanmin : ndarray
An array with the same shape as `a`, with the specified axis
removed. If `a` is a 0-d array, or if axis is None, an ndarray
scalar is returned. The same dtype as `a` is returned.
See Also
--------
nanmax :
The maximum value of an array along a given axis, ignoring any NaNs.
amin :
The minimum value of an array along a given axis, propagating any NaNs.
fmin :
Element-wise minimum of two arrays, ignoring any NaNs.
minimum :
Element-wise minimum of two arrays, propagating any NaNs.
isnan :
Shows which elements are Not a Number (NaN).
isfinite:
Shows which elements are neither NaN nor infinity.
amax, fmax, maximum
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Positive infinity is treated as a very large number and negative
infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.min.
Examples
--------
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nanmin(a)
1.0
>>> np.nanmin(a, axis=0)
array([1., 2.])
>>> np.nanmin(a, axis=1)
array([1., 3.])
When positive infinity and negative infinity are present:
>>> np.nanmin([1, 2, np.nan, np.inf])
1.0
>>> np.nanmin([1, 2, np.nan, np.NINF])
-inf
"""
kwargs = {}
if keepdims is not np._NoValue:
kwargs['keepdims'] = keepdims
if type(a) is np.ndarray and a.dtype != np.object_:
# Fast, but not safe for subclasses of ndarray, or object arrays,
# which do not implement isnan (gh-9009), or fmin correctly (gh-8975)
res = np.fmin.reduce(a, axis=axis, out=out, **kwargs)
if np.isnan(res).any():
warnings.warn("All-NaN slice encountered", RuntimeWarning,
stacklevel=3)
else:
# Slow, but safe for subclasses of ndarray
a, mask = _replace_nan(a, +np.inf)
res = np.amin(a, axis=axis, out=out, **kwargs)
if mask is None:
return res
# Check for all-NaN axis
mask = np.all(mask, axis=axis, **kwargs)
if np.any(mask):
res = _copyto(res, np.nan, mask)
warnings.warn("All-NaN axis encountered", RuntimeWarning,
stacklevel=3)
return res
def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanmax_dispatcher)
def nanmax(a, axis=None, out=None, keepdims=np._NoValue):
"""
Return the maximum of an array or maximum along an axis, ignoring any
NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is
raised and NaN is returned for that slice.
Parameters
----------
a : array_like
Array containing numbers whose maximum is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the maximum is computed. The default is to compute
the maximum of the flattened array.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
:ref:`ufuncs-output-type` for more details.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If the value is anything but the default, then
`keepdims` will be passed through to the `max` method
of sub-classes of `ndarray`. If the sub-classes methods
does not implement `keepdims` any exceptions will be raised.
.. versionadded:: 1.8.0
Returns
-------
nanmax : ndarray
An array with the same shape as `a`, with the specified axis removed.
If `a` is a 0-d array, or if axis is None, an ndarray scalar is
returned. The same dtype as `a` is returned.
See Also
--------
nanmin :
The minimum value of an array along a given axis, ignoring any NaNs.
amax :
The maximum value of an array along a given axis, propagating any NaNs.
fmax :
Element-wise maximum of two arrays, ignoring any NaNs.
maximum :
Element-wise maximum of two arrays, propagating any NaNs.
isnan :
Shows which elements are Not a Number (NaN).
isfinite:
Shows which elements are neither NaN nor infinity.
amin, fmin, minimum
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
Positive infinity is treated as a very large number and negative
infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.max.
Examples
--------
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nanmax(a)
3.0
>>> np.nanmax(a, axis=0)
array([3., 2.])
>>> np.nanmax(a, axis=1)
array([2., 3.])
When positive infinity and negative infinity are present:
>>> np.nanmax([1, 2, np.nan, np.NINF])
2.0
>>> np.nanmax([1, 2, np.nan, np.inf])
inf
"""
kwargs = {}
if keepdims is not np._NoValue:
kwargs['keepdims'] = keepdims
if type(a) is np.ndarray and a.dtype != np.object_:
# Fast, but not safe for subclasses of ndarray, or object arrays,
# which do not implement isnan (gh-9009), or fmax correctly (gh-8975)
res = np.fmax.reduce(a, axis=axis, out=out, **kwargs)
if np.isnan(res).any():
warnings.warn("All-NaN slice encountered", RuntimeWarning,
stacklevel=3)
else:
# Slow, but safe for subclasses of ndarray
a, mask = _replace_nan(a, -np.inf)
res = np.amax(a, axis=axis, out=out, **kwargs)
if mask is None:
return res
# Check for all-NaN axis
mask = np.all(mask, axis=axis, **kwargs)
if np.any(mask):
res = _copyto(res, np.nan, mask)
warnings.warn("All-NaN axis encountered", RuntimeWarning,
stacklevel=3)
return res
def _nanargmin_dispatcher(a, axis=None):
return (a,)
@array_function_dispatch(_nanargmin_dispatcher)
def nanargmin(a, axis=None):
"""
Return the indices of the minimum values in the specified axis ignoring
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results
cannot be trusted if a slice contains only NaNs and Infs.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
Returns
-------
index_array : ndarray
An array of indices or a single index value.
See Also
--------
argmin, nanargmax
Examples
--------
>>> a = np.array([[np.nan, 4], [2, 3]])
>>> np.argmin(a)
0
>>> np.nanargmin(a)
2
>>> np.nanargmin(a, axis=0)
array([1, 1])
>>> np.nanargmin(a, axis=1)
array([1, 0])
"""
a, mask = _replace_nan(a, np.inf)
res = np.argmin(a, axis=axis)
if mask is not None:
mask = np.all(mask, axis=axis)
if np.any(mask):
raise ValueError("All-NaN slice encountered")
return res
def _nanargmax_dispatcher(a, axis=None):
return (a,)
@array_function_dispatch(_nanargmax_dispatcher)
def nanargmax(a, axis=None):
"""
Return the indices of the maximum values in the specified axis ignoring
NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the
results cannot be trusted if a slice contains only NaNs and -Infs.
Parameters
----------
a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
Returns
-------
index_array : ndarray
An array of indices or a single index value.
See Also
--------
argmax, nanargmin
Examples
--------
>>> a = np.array([[np.nan, 4], [2, 3]])
>>> np.argmax(a)
0
>>> np.nanargmax(a)
1
>>> np.nanargmax(a, axis=0)
array([1, 0])
>>> np.nanargmax(a, axis=1)
array([1, 1])
"""
a, mask = _replace_nan(a, -np.inf)
res = np.argmax(a, axis=axis)
if mask is not None:
mask = np.all(mask, axis=axis)
if np.any(mask):
raise ValueError("All-NaN slice encountered")
return res
def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nansum_dispatcher)
def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
"""
Return the sum of array elements over a given axis treating Not a
Numbers (NaNs) as zero.
In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or
empty. In later versions zero is returned.
Parameters
----------
a : array_like
Array containing numbers whose sum is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the sum is computed. The default is to compute the
sum of the flattened array.
dtype : data-type, optional
The type of the returned array and of the accumulator in which the
elements are summed. By default, the dtype of `a` is used. An
exception is when `a` has an integer type with less precision than
the platform (u)intp. In that case, the default will be either
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
bits. For inexact inputs, dtype must be inexact.
.. versionadded:: 1.8.0
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``. If provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
:ref:`ufuncs-output-type` for more details. The casting of NaN to integer
can yield unexpected results.
.. versionadded:: 1.8.0
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If the value is anything but the default, then
`keepdims` will be passed through to the `mean` or `sum` methods
of sub-classes of `ndarray`. If the sub-classes methods
does not implement `keepdims` any exceptions will be raised.
.. versionadded:: 1.8.0
Returns
-------
nansum : ndarray.
A new array holding the result is returned unless `out` is
specified, in which it is returned. The result has the same
size as `a`, and the same shape as `a` if `axis` is not None
or `a` is a 1-d array.
See Also
--------
numpy.sum : Sum across array propagating NaNs.
isnan : Show which elements are NaN.
isfinite : Show which elements are not NaN or +/-inf.
Notes
-----
If both positive and negative infinity are present, the sum will be Not
A Number (NaN).
Examples
--------
>>> np.nansum(1)
1
>>> np.nansum([1])
1
>>> np.nansum([1, np.nan])
1.0
>>> a = np.array([[1, 1], [1, np.nan]])
>>> np.nansum(a)
3.0
>>> np.nansum(a, axis=0)
array([2., 1.])
>>> np.nansum([1, np.nan, np.inf])
inf
>>> np.nansum([1, np.nan, np.NINF])
-inf
>>> from numpy.testing import suppress_warnings
>>> with suppress_warnings() as sup:
... sup.filter(RuntimeWarning)
... np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
nan
"""
a, mask = _replace_nan(a, 0)
return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanprod_dispatcher)
def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
"""
Return the product of array elements over a given axis treating Not a
Numbers (NaNs) as ones.
One is returned for slices that are all-NaN or empty.
.. versionadded:: 1.10.0
Parameters
----------
a : array_like
Array containing numbers whose product is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the product is computed. The default is to compute
the product of the flattened array.
dtype : data-type, optional
The type of the returned array and of the accumulator in which the
elements are summed. By default, the dtype of `a` is used. An
exception is when `a` has an integer type with less precision than
the platform (u)intp. In that case, the default will be either
(u)int32 or (u)int64 depending on whether the platform is 32 or 64
bits. For inexact inputs, dtype must be inexact.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``. If provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
:ref:`ufuncs-output-type` for more details. The casting of NaN to integer
can yield unexpected results.
keepdims : bool, optional
If True, the axes which are reduced are left in the result as
dimensions with size one. With this option, the result will
broadcast correctly against the original `arr`.
Returns
-------
nanprod : ndarray
A new array holding the result is returned unless `out` is
specified, in which case it is returned.
See Also
--------
numpy.prod : Product across array propagating NaNs.
isnan : Show which elements are NaN.
Examples
--------
>>> np.nanprod(1)
1
>>> np.nanprod([1])
1
>>> np.nanprod([1, np.nan])
1.0
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nanprod(a)
6.0
>>> np.nanprod(a, axis=0)
array([3., 2.])
"""
a, mask = _replace_nan(a, 1)
return np.prod(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):
return (a, out)
@array_function_dispatch(_nancumsum_dispatcher)
def nancumsum(a, axis=None, dtype=None, out=None):
"""
Return the cumulative sum of array elements over a given axis treating Not a
Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are
encountered and leading NaNs are replaced by zeros.
Zeros are returned for slices that are all-NaN or empty.
.. versionadded:: 1.12.0
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative sum is computed. The default
(None) is to compute the cumsum over the flattened array.
dtype : dtype, optional
Type of the returned array and of the accumulator in which the
elements are summed. If `dtype` is not specified, it defaults
to the dtype of `a`, unless `a` has an integer dtype with a
precision less than that of the default platform integer. In
that case, the default platform integer is used.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type will be cast if necessary. See :ref:`ufuncs-output-type` for
more details.
Returns
-------
nancumsum : ndarray.
A new array holding the result is returned unless `out` is
specified, in which it is returned. The result has the same
size as `a`, and the same shape as `a` if `axis` is not None
or `a` is a 1-d array.
See Also
--------
numpy.cumsum : Cumulative sum across array propagating NaNs.
isnan : Show which elements are NaN.
Examples
--------
>>> np.nancumsum(1)
array([1])
>>> np.nancumsum([1])
array([1])
>>> np.nancumsum([1, np.nan])
array([1., 1.])
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nancumsum(a)
array([1., 3., 6., 6.])
>>> np.nancumsum(a, axis=0)
array([[1., 2.],
[4., 2.]])
>>> np.nancumsum(a, axis=1)
array([[1., 3.],
[3., 3.]])
"""
a, mask = _replace_nan(a, 0)
return np.cumsum(a, axis=axis, dtype=dtype, out=out)
def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):
return (a, out)
@array_function_dispatch(_nancumprod_dispatcher)
def nancumprod(a, axis=None, dtype=None, out=None):
"""
Return the cumulative product of array elements over a given axis treating Not a
Numbers (NaNs) as one. The cumulative product does not change when NaNs are
encountered and leading NaNs are replaced by ones.
Ones are returned for slices that are all-NaN or empty.
.. versionadded:: 1.12.0
Parameters
----------
a : array_like
Input array.
axis : int, optional
Axis along which the cumulative product is computed. By default
the input is flattened.
dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which
the elements are multiplied. If *dtype* is not specified, it
defaults to the dtype of `a`, unless `a` has an integer dtype with
a precision less than that of the default platform integer. In
that case, the default platform integer is used instead.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output
but the type of the resulting values will be cast if necessary.
Returns
-------
nancumprod : ndarray
A new array holding the result is returned unless `out` is
specified, in which case it is returned.
See Also
--------
numpy.cumprod : Cumulative product across array propagating NaNs.
isnan : Show which elements are NaN.
Examples
--------
>>> np.nancumprod(1)
array([1])
>>> np.nancumprod([1])
array([1])
>>> np.nancumprod([1, np.nan])
array([1., 1.])
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nancumprod(a)
array([1., 2., 6., 6.])
>>> np.nancumprod(a, axis=0)
array([[1., 2.],
[3., 2.]])
>>> np.nancumprod(a, axis=1)
array([[1., 2.],
[3., 3.]])
"""
a, mask = _replace_nan(a, 1)
return np.cumprod(a, axis=axis, dtype=dtype, out=out)
def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanmean_dispatcher)
def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue):
"""
Compute the arithmetic mean along the specified axis, ignoring NaNs.
Returns the average of the array elements. The average is taken over
the flattened array by default, otherwise over the specified axis.
`float64` intermediate and return values are used for integer inputs.
For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Array containing numbers whose mean is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the means are computed. The default is to compute
the mean of the flattened array.
dtype : data-type, optional
Type to use in computing the mean. For integer inputs, the default
is `float64`; for inexact inputs, it is the same as the input
dtype.
out : ndarray, optional
Alternate output array in which to place the result. The default
is ``None``; if provided, it must have the same shape as the
expected output, but the type will be cast if necessary. See
:ref:`ufuncs-output-type` for more details.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If the value is anything but the default, then
`keepdims` will be passed through to the `mean` or `sum` methods
of sub-classes of `ndarray`. If the sub-classes methods
does not implement `keepdims` any exceptions will be raised.
Returns
-------
m : ndarray, see dtype parameter above
If `out=None`, returns a new array containing the mean values,
otherwise a reference to the output array is returned. Nan is
returned for slices that contain only NaNs.
See Also
--------
average : Weighted average
mean : Arithmetic mean taken while not ignoring NaNs
var, nanvar
Notes
-----
The arithmetic mean is the sum of the non-NaN elements along the axis
divided by the number of non-NaN elements.
Note that for floating-point input, the mean is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32`. Specifying a
higher-precision accumulator using the `dtype` keyword can alleviate
this issue.
Examples
--------
>>> a = np.array([[1, np.nan], [3, 4]])
>>> np.nanmean(a)
2.6666666666666665
>>> np.nanmean(a, axis=0)
array([2., 4.])
>>> np.nanmean(a, axis=1)
array([1., 3.5]) # may vary
"""
arr, mask = _replace_nan(a, 0)
if mask is None:
return np.mean(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
if dtype is not None:
dtype = np.dtype(dtype)
if dtype is not None and not issubclass(dtype.type, np.inexact):
raise TypeError("If a is inexact, then dtype must be inexact")
if out is not None and not issubclass(out.dtype.type, np.inexact):
raise TypeError("If a is inexact, then out must be inexact")
cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=keepdims)
tot = np.sum(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
avg = _divide_by_count(tot, cnt, out=out)
isbad = (cnt == 0)
if isbad.any():
warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=3)
# NaN is the only possible bad value, so no further
# action is needed to handle bad results.
return avg
def _nanmedian1d(arr1d, overwrite_input=False):
"""
Private function for rank 1 arrays. Compute the median ignoring NaNs.
See nanmedian for parameter usage
"""
arr1d_parsed, overwrite_input = _remove_nan_1d(
arr1d, overwrite_input=overwrite_input,
)
if arr1d_parsed.size == 0:
# Ensure that a nan-esque scalar of the appropiate type (and unit)
# is returned for `timedelta64` and `complexfloating`
return arr1d[-1]
return np.median(arr1d_parsed, overwrite_input=overwrite_input)
def _nanmedian(a, axis=None, out=None, overwrite_input=False):
"""
Private function that doesn't support extended axis or keepdims.
These methods are extended to this function using _ureduce
See nanmedian for parameter usage
"""
if axis is None or a.ndim == 1:
part = a.ravel()
if out is None:
return _nanmedian1d(part, overwrite_input)
else:
out[...] = _nanmedian1d(part, overwrite_input)
return out
else:
# for small medians use sort + indexing which is still faster than
# apply_along_axis
# benchmarked with shuffled (50, 50, x) containing a few NaN
if a.shape[axis] < 600:
return _nanmedian_small(a, axis, out, overwrite_input)
result = np.apply_along_axis(_nanmedian1d, axis, a, overwrite_input)
if out is not None:
out[...] = result
return result
def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):
"""
sort + indexing median, faster for small medians along multiple
dimensions due to the high overhead of apply_along_axis
see nanmedian for parameter usage
"""
a = np.ma.masked_array(a, np.isnan(a))
m = np.ma.median(a, axis=axis, overwrite_input=overwrite_input)
for i in range(np.count_nonzero(m.mask.ravel())):
warnings.warn("All-NaN slice encountered", RuntimeWarning,
stacklevel=4)
fill_value = np.timedelta64("NaT") if m.dtype.kind == "m" else np.nan
if out is not None:
out[...] = m.filled(fill_value)
return out
return m.filled(fill_value)
def _nanmedian_dispatcher(
a, axis=None, out=None, overwrite_input=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanmedian_dispatcher)
def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):
"""
Compute the median along the specified axis, while ignoring NaNs.
Returns the median of the array elements.
.. versionadded:: 1.9.0
Parameters
----------
a : array_like
Input array or object that can be converted to an array.
axis : {int, sequence of int, None}, optional
Axis or axes along which the medians are computed. The default
is to compute the median along a flattened version of the array.
A sequence of axes is supported since version 1.9.0.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow use of memory of input array `a` for
calculations. The input array will be modified by the call to
`median`. This will save memory when you do not need to preserve
the contents of the input array. Treat the input as undefined,
but it will probably be fully or partially sorted. Default is
False. If `overwrite_input` is ``True`` and `a` is not already an
`ndarray`, an error will be raised.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If this is anything but the default value it will be passed
through (in the special case of an empty array) to the
`mean` function of the underlying array. If the array is
a sub-class and `mean` does not have the kwarg `keepdims` this
will raise a RuntimeError.
Returns
-------
median : ndarray
A new array holding the result. If the input contains integers
or floats smaller than ``float64``, then the output data-type is
``np.float64``. Otherwise, the data-type of the output is the
same as that of the input. If `out` is specified, that array is
returned instead.
See Also
--------
mean, median, percentile
Notes
-----
Given a vector ``V`` of length ``N``, the median of ``V`` is the
middle value of a sorted copy of ``V``, ``V_sorted`` - i.e.,
``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two
middle values of ``V_sorted`` when ``N`` is even.
Examples
--------
>>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
>>> a[0, 1] = np.nan
>>> a
array([[10., nan, 4.],
[ 3., 2., 1.]])
>>> np.median(a)
nan
>>> np.nanmedian(a)
3.0
>>> np.nanmedian(a, axis=0)
array([6.5, 2. , 2.5])
>>> np.median(a, axis=1)
array([nan, 2.])
>>> b = a.copy()
>>> np.nanmedian(b, axis=1, overwrite_input=True)
array([7., 2.])
>>> assert not np.all(a==b)
>>> b = a.copy()
>>> np.nanmedian(b, axis=None, overwrite_input=True)
3.0
>>> assert not np.all(a==b)
"""
a = np.asanyarray(a)
# apply_along_axis in _nanmedian doesn't handle empty arrays well,
# so deal them upfront
if a.size == 0:
return np.nanmean(a, axis, out=out, keepdims=keepdims)
r, k = function_base._ureduce(a, func=_nanmedian, axis=axis, out=out,
overwrite_input=overwrite_input)
if keepdims and keepdims is not np._NoValue:
return r.reshape(k)
else:
return r
def _nanpercentile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
interpolation=None, keepdims=None):
return (a, q, out)
@array_function_dispatch(_nanpercentile_dispatcher)
def nanpercentile(a, q, axis=None, out=None, overwrite_input=False,
interpolation='linear', keepdims=np._NoValue):
"""
Compute the qth percentile of the data along the specified axis,
while ignoring nan values.
Returns the qth percentile(s) of the array elements.
.. versionadded:: 1.9.0
Parameters
----------
a : array_like
Input array or object that can be converted to an array, containing
nan values to be ignored.
q : array_like of float
Percentile or sequence of percentiles to compute, which must be between
0 and 100 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the percentiles are computed. The
default is to compute the percentile(s) along a flattened
version of the array.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow the input array `a` to be modified by intermediate
calculations, to save memory. In this case, the contents of the input
`a` after this function completes is undefined.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to
use when the desired percentile lies between two data points
``i < j``:
* 'linear': ``i + (j - i) * fraction``, where ``fraction``
is the fractional part of the index surrounded by ``i``
and ``j``.
* 'lower': ``i``.
* 'higher': ``j``.
* 'nearest': ``i`` or ``j``, whichever is nearest.
* 'midpoint': ``(i + j) / 2``.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in
the result as dimensions with size one. With this option, the
result will broadcast correctly against the original array `a`.
If this is anything but the default value it will be passed
through (in the special case of an empty array) to the
`mean` function of the underlying array. If the array is
a sub-class and `mean` does not have the kwarg `keepdims` this
will raise a RuntimeError.
Returns
-------
percentile : scalar or ndarray
If `q` is a single percentile and `axis=None`, then the result
is a scalar. If multiple percentiles are given, first axis of
the result corresponds to the percentiles. The other axes are
the axes that remain after the reduction of `a`. If the input
contains integers or floats smaller than ``float64``, the output
data-type is ``float64``. Otherwise, the output data-type is the
same as that of the input. If `out` is specified, that array is
returned instead.
See Also
--------
nanmean
nanmedian : equivalent to ``nanpercentile(..., 50)``
percentile, median, mean
nanquantile : equivalent to nanpercentile, but with q in the range [0, 1].
Notes
-----
Given a vector ``V`` of length ``N``, the ``q``-th percentile of
``V`` is the value ``q/100`` of the way from the minimum to the
maximum in a sorted copy of ``V``. The values and distances of
the two nearest neighbors as well as the `interpolation` parameter
will determine the percentile if the normalized ranking does not
match the location of ``q`` exactly. This function is the same as
the median if ``q=50``, the same as the minimum if ``q=0`` and the
same as the maximum if ``q=100``.
Examples
--------
>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
>>> a[0][1] = np.nan
>>> a
array([[10., nan, 4.],
[ 3., 2., 1.]])
>>> np.percentile(a, 50)
nan
>>> np.nanpercentile(a, 50)
3.0
>>> np.nanpercentile(a, 50, axis=0)
array([6.5, 2. , 2.5])
>>> np.nanpercentile(a, 50, axis=1, keepdims=True)
array([[7.],
[2.]])
>>> m = np.nanpercentile(a, 50, axis=0)
>>> out = np.zeros_like(m)
>>> np.nanpercentile(a, 50, axis=0, out=out)
array([6.5, 2. , 2.5])
>>> m
array([6.5, 2. , 2.5])
>>> b = a.copy()
>>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
array([7., 2.])
>>> assert not np.all(a==b)
"""
a = np.asanyarray(a)
q = np.true_divide(q, 100.0) # handles the asarray for us too
if not function_base._quantile_is_valid(q):
raise ValueError("Percentiles must be in the range [0, 100]")
return _nanquantile_unchecked(
a, q, axis, out, overwrite_input, interpolation, keepdims)
def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
interpolation=None, keepdims=None):
return (a, q, out)
@array_function_dispatch(_nanquantile_dispatcher)
def nanquantile(a, q, axis=None, out=None, overwrite_input=False,
interpolation='linear', keepdims=np._NoValue):
"""
Compute the qth quantile of the data along the specified axis,
while ignoring nan values.
Returns the qth quantile(s) of the array elements.
.. versionadded:: 1.15.0
Parameters
----------
a : array_like
Input array or object that can be converted to an array, containing
nan values to be ignored
q : array_like of float
Quantile or sequence of quantiles to compute, which must be between
0 and 1 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the quantiles are computed. The
default is to compute the quantile(s) along a flattened
version of the array.
out : ndarray, optional
Alternative output array in which to place the result. It must
have the same shape and buffer length as the expected output,
but the type (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow the input array `a` to be modified by intermediate
calculations, to save memory. In this case, the contents of the input
`a` after this function completes is undefined.
interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
This optional parameter specifies the interpolation method to
use when the desired quantile lies between two data points
``i < j``:
* linear: ``i + (j - i) * fraction``, where ``fraction``
is the fractional part of the index surrounded by ``i``
and ``j``.
* lower: ``i``.
* higher: ``j``.
* nearest: ``i`` or ``j``, whichever is nearest.
* midpoint: ``(i + j) / 2``.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left in
the result as dimensions with size one. With this option, the
result will broadcast correctly against the original array `a`.
If this is anything but the default value it will be passed
through (in the special case of an empty array) to the
`mean` function of the underlying array. If the array is
a sub-class and `mean` does not have the kwarg `keepdims` this
will raise a RuntimeError.
Returns
-------
quantile : scalar or ndarray
If `q` is a single percentile and `axis=None`, then the result
is a scalar. If multiple quantiles are given, first axis of
the result corresponds to the quantiles. The other axes are
the axes that remain after the reduction of `a`. If the input
contains integers or floats smaller than ``float64``, the output
data-type is ``float64``. Otherwise, the output data-type is the
same as that of the input. If `out` is specified, that array is
returned instead.
See Also
--------
quantile
nanmean, nanmedian
nanmedian : equivalent to ``nanquantile(..., 0.5)``
nanpercentile : same as nanquantile, but with q in the range [0, 100].
Examples
--------
>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
>>> a[0][1] = np.nan
>>> a
array([[10., nan, 4.],
[ 3., 2., 1.]])
>>> np.quantile(a, 0.5)
nan
>>> np.nanquantile(a, 0.5)
3.0
>>> np.nanquantile(a, 0.5, axis=0)
array([6.5, 2. , 2.5])
>>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
array([[7.],
[2.]])
>>> m = np.nanquantile(a, 0.5, axis=0)
>>> out = np.zeros_like(m)
>>> np.nanquantile(a, 0.5, axis=0, out=out)
array([6.5, 2. , 2.5])
>>> m
array([6.5, 2. , 2.5])
>>> b = a.copy()
>>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
array([7., 2.])
>>> assert not np.all(a==b)
"""
a = np.asanyarray(a)
q = np.asanyarray(q)
if not function_base._quantile_is_valid(q):
raise ValueError("Quantiles must be in the range [0, 1]")
return _nanquantile_unchecked(
a, q, axis, out, overwrite_input, interpolation, keepdims)
def _nanquantile_unchecked(a, q, axis=None, out=None, overwrite_input=False,
interpolation='linear', keepdims=np._NoValue):
"""Assumes that q is in [0, 1], and is an ndarray"""
# apply_along_axis in _nanpercentile doesn't handle empty arrays well,
# so deal them upfront
if a.size == 0:
return np.nanmean(a, axis, out=out, keepdims=keepdims)
r, k = function_base._ureduce(
a, func=_nanquantile_ureduce_func, q=q, axis=axis, out=out,
overwrite_input=overwrite_input, interpolation=interpolation
)
if keepdims and keepdims is not np._NoValue:
return r.reshape(q.shape + k)
else:
return r
def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False,
interpolation='linear'):
"""
Private function that doesn't support extended axis or keepdims.
These methods are extended to this function using _ureduce
See nanpercentile for parameter usage
"""
if axis is None or a.ndim == 1:
part = a.ravel()
result = _nanquantile_1d(part, q, overwrite_input, interpolation)
else:
result = np.apply_along_axis(_nanquantile_1d, axis, a, q,
overwrite_input, interpolation)
# apply_along_axis fills in collapsed axis with results.
# Move that axis to the beginning to match percentile's
# convention.
if q.ndim != 0:
result = np.moveaxis(result, axis, 0)
if out is not None:
out[...] = result
return result
def _nanquantile_1d(arr1d, q, overwrite_input=False, interpolation='linear'):
"""
Private function for rank 1 arrays. Compute quantile ignoring NaNs.
See nanpercentile for parameter usage
"""
arr1d, overwrite_input = _remove_nan_1d(arr1d,
overwrite_input=overwrite_input)
if arr1d.size == 0:
return np.full(q.shape, np.nan)[()] # convert to scalar
return function_base._quantile_unchecked(
arr1d, q, overwrite_input=overwrite_input, interpolation=interpolation)
def _nanvar_dispatcher(
a, axis=None, dtype=None, out=None, ddof=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanvar_dispatcher)
def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
"""
Compute the variance along the specified axis, while ignoring NaNs.
Returns the variance of the array elements, a measure of the spread of
a distribution. The variance is computed for the flattened array by
default, otherwise over the specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Array containing numbers whose variance is desired. If `a` is not an
array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the variance is computed. The default is to compute
the variance of the flattened array.
dtype : data-type, optional
Type to use in computing the variance. For arrays of integer type
the default is `float64`; for arrays of float types it is the same as
the array type.
out : ndarray, optional
Alternate output array in which to place the result. It must have
the same shape as the expected output, but the type is cast if
necessary.
ddof : int, optional
"Delta Degrees of Freedom": the divisor used in the calculation is
``N - ddof``, where ``N`` represents the number of non-NaN
elements. By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
Returns
-------
variance : ndarray, see dtype parameter above
If `out` is None, return a new array containing the variance,
otherwise return a reference to the output array. If ddof is >= the
number of non-NaN elements in a slice or the slice contains only
NaNs, then the result for that slice is NaN.
See Also
--------
std : Standard deviation
mean : Average
var : Variance while not ignoring NaNs
nanstd, nanmean
:ref:`ufuncs-output-type`
Notes
-----
The variance is the average of the squared deviations from the mean,
i.e., ``var = mean(abs(x - x.mean())**2)``.
The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.
If, however, `ddof` is specified, the divisor ``N - ddof`` is used
instead. In standard statistical practice, ``ddof=1`` provides an
unbiased estimator of the variance of a hypothetical infinite
population. ``ddof=0`` provides a maximum likelihood estimate of the
variance for normally distributed variables.
Note that for complex numbers, the absolute value is taken before
squaring, so that the result is always real and nonnegative.
For floating-point input, the variance is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for `float32` (see example
below). Specifying a higher-accuracy accumulator using the ``dtype``
keyword can alleviate this issue.
For this function to work on sub-classes of ndarray, they must define
`sum` with the kwarg `keepdims`
Examples
--------
>>> a = np.array([[1, np.nan], [3, 4]])
>>> np.nanvar(a)
1.5555555555555554
>>> np.nanvar(a, axis=0)
array([1., 0.])
>>> np.nanvar(a, axis=1)
array([0., 0.25]) # may vary
"""
arr, mask = _replace_nan(a, 0)
if mask is None:
return np.var(arr, axis=axis, dtype=dtype, out=out, ddof=ddof,
keepdims=keepdims)
if dtype is not None:
dtype = np.dtype(dtype)
if dtype is not None and not issubclass(dtype.type, np.inexact):
raise TypeError("If a is inexact, then dtype must be inexact")
if out is not None and not issubclass(out.dtype.type, np.inexact):
raise TypeError("If a is inexact, then out must be inexact")
# Compute mean
if type(arr) is np.matrix:
_keepdims = np._NoValue
else:
_keepdims = True
# we need to special case matrix for reverse compatibility
# in order for this to work, these sums need to be called with
# keepdims=True, however matrix now raises an error in this case, but
# the reason that it drops the keepdims kwarg is to force keepdims=True
# so this used to work by serendipity.
cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=_keepdims)
avg = np.sum(arr, axis=axis, dtype=dtype, keepdims=_keepdims)
avg = _divide_by_count(avg, cnt)
# Compute squared deviation from mean.
np.subtract(arr, avg, out=arr, casting='unsafe')
arr = _copyto(arr, 0, mask)
if issubclass(arr.dtype.type, np.complexfloating):
sqr = np.multiply(arr, arr.conj(), out=arr).real
else:
sqr = np.multiply(arr, arr, out=arr)
# Compute variance.
var = np.sum(sqr, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
if var.ndim < cnt.ndim:
# Subclasses of ndarray may ignore keepdims, so check here.
cnt = cnt.squeeze(axis)
dof = cnt - ddof
var = _divide_by_count(var, dof)
isbad = (dof <= 0)
if np.any(isbad):
warnings.warn("Degrees of freedom <= 0 for slice.", RuntimeWarning,
stacklevel=3)
# NaN, inf, or negative numbers are all possible bad
# values, so explicitly replace them with NaN.
var = _copyto(var, np.nan, isbad)
return var
def _nanstd_dispatcher(
a, axis=None, dtype=None, out=None, ddof=None, keepdims=None):
return (a, out)
@array_function_dispatch(_nanstd_dispatcher)
def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue):
"""
Compute the standard deviation along the specified axis, while
ignoring NaNs.
Returns the standard deviation, a measure of the spread of a
distribution, of the non-NaN array elements. The standard deviation is
computed for the flattened array by default, otherwise over the
specified axis.
For all-NaN slices or slices with zero degrees of freedom, NaN is
returned and a `RuntimeWarning` is raised.
.. versionadded:: 1.8.0
Parameters
----------
a : array_like
Calculate the standard deviation of the non-NaN values.
axis : {int, tuple of int, None}, optional
Axis or axes along which the standard deviation is computed. The default is
to compute the standard deviation of the flattened array.
dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of
integer type the default is float64, for arrays of float types it
is the same as the array type.
out : ndarray, optional
Alternative output array in which to place the result. It must have
the same shape as the expected output but the type (of the
calculated values) will be cast if necessary.
ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations
is ``N - ddof``, where ``N`` represents the number of non-NaN
elements. By default `ddof` is zero.
keepdims : bool, optional
If this is set to True, the axes which are reduced are left
in the result as dimensions with size one. With this option,
the result will broadcast correctly against the original `a`.
If this value is anything but the default it is passed through
as-is to the relevant functions of the sub-classes. If these
functions do not have a `keepdims` kwarg, a RuntimeError will
be raised.
Returns
-------
standard_deviation : ndarray, see dtype parameter above.
If `out` is None, return a new array containing the standard
deviation, otherwise return a reference to the output array. If
ddof is >= the number of non-NaN elements in a slice or the slice
contains only NaNs, then the result for that slice is NaN.
See Also
--------
var, mean, std
nanvar, nanmean
:ref:`ufuncs-output-type`
Notes
-----
The standard deviation is the square root of the average of the squared
deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.
The average squared deviation is normally calculated as
``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is
specified, the divisor ``N - ddof`` is used instead. In standard
statistical practice, ``ddof=1`` provides an unbiased estimator of the
variance of the infinite population. ``ddof=0`` provides a maximum
likelihood estimate of the variance for normally distributed variables.
The standard deviation computed in this function is the square root of
the estimated variance, so even with ``ddof=1``, it will not be an
unbiased estimate of the standard deviation per se.
Note that, for complex numbers, `std` takes the absolute value before
squaring, so that the result is always real and nonnegative.
For floating-point input, the *std* is computed using the same
precision the input has. Depending on the input data, this can cause
the results to be inaccurate, especially for float32 (see example
below). Specifying a higher-accuracy accumulator using the `dtype`
keyword can alleviate this issue.
Examples
--------
>>> a = np.array([[1, np.nan], [3, 4]])
>>> np.nanstd(a)
1.247219128924647
>>> np.nanstd(a, axis=0)
array([1., 0.])
>>> np.nanstd(a, axis=1)
array([0., 0.5]) # may vary
"""
var = nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
keepdims=keepdims)
if isinstance(var, np.ndarray):
std = np.sqrt(var, out=var)
else:
std = var.dtype.type(np.sqrt(var))
return std
|