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https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node190.html	[ "", null, "", null, "", null, "Next: One-Dimensional Compressible Inviscid Flow Up: Equilibrium of Compressible Fluids Previous: Eddington Solar Model\n\n# Exercises\n\n1. Prove that the fraction of the whole mass of an isothermal atmosphere that lies between the ground and a horizontal plane of height", null, "is", null, "Evaluate this fraction for", null, ",", null, ",", null, ", respectively.\n\n2. If the absolute temperature in the atmosphere diminishes upwards according to the law", null, "where", null, "is a constant, show that the pressure varies as", null, "3. If the absolute temperature in the atmosphere diminishes upward according to the law", null, "where", null, "is a constant, show that the pressure varies as", null, "4. Show that if the absolute temperature,", null, ", in the atmosphere is any given function of the altitude,", null, ", then the vertical distribution of pressure in the atmosphere is given by", null, "5. Show that if the Earth were surrounded by an atmosphere of uniform temperature then the pressure a distance", null, "from the Earth's center would be", null, "where", null, "is the Earth's radius.\n\n6. Show that if the whole of space were occupied by air at the uniform temperature", null, "then the densities at the surfaces of the various planets would be proportional to the corresponding values of", null, "where", null, "is the radius of the planet, and", null, "its surface gravitational acceleration.\n\n7. Prove that in an atmosphere arranged in horizontal strata the work (per unit mass) required to interchange two thin strata of equal mass without disturbance of the remaining strata is", null, "where the suffixes refer to the initial states of the two strata. Hence, show that for stability the ratio", null, "must increase upwards.\n8. A spherically symmetric star is such that", null, "is the mass contained within radius", null, ". Show that the star's total gravitational potential energy can be written in the following three alternative forms:", null, "Here,", null, "is the total mass,", null, "the radius,", null, "the gravitational potential per unit mass (defined such that", null, "as", null, "),", null, "the pressure, and", null, ".\n\n9. Suppose that the pressure and density inside a spherically symmetric star are related according to the polytropic gas law,", null, "where", null, "is termed the polytropic index. Let", null, ", where", null, "is the central mass density. Demonstrate that", null, "satisfies the Lane-Emden equation", null, "where", null, ", and", null, "Show that the physical solution to the Lane-Emden equation, which is such that", null, "and", null, ", for some", null, ", is", null, "for", null, ",", null, "for", null, ", and", null, "for", null, ". Determine the ratio of the central density to the mean density in all three cases. Finally, demonstrate that, in the general case, the total gravitational potential energy can be written", null, "where", null, "is the total mass, and", null, "the radius.\n10. A spherically symmetric star of radius", null, "has a mass density of the form", null, "Show that the central mass density is four times the mean density. Demonstrate that the central pressure is", null, "where", null, "is the mass of the star. Finally, show that the total gravitational potential energy of the star can be written", null, "", null, "", null, "", null, "Next: One-Dimensional Compressible Inviscid Flow Up: Equilibrium of Compressible Fluids Previous: Eddington Solar Model\nRichard Fitzpatrick 2016-03-31" ]	[ null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/next.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/up.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/prev.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img17.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img5256.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img5134.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img5257.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img5258.png", null, "https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/img5259.png", null, 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https://www.symscape.com/node/1655	[ "# Time Variant Flow Setup\n\nI am trying to set up a time variant flow at a face but it is not clear to me how set up the values in the parentheses. For example, I am using units of minutes and feet. I want to set up the flow to be zero for 15 seconds then have a vertical flow rate of 250 ft/min after 15 seconds.\n\nAre the units that are used in this field the same as my IP units?\n\nHow do I structure the input?\n\nKen\n\n### Run a transient simulation with fixed inlet flow rate?\n\nThe units are SI for tabulated data, so the vector has to be m/s. From the Tooltip the description of the format is:\n\nTime dependent vector. E.g., table ( (0.5 (5 0 0)) (1 (10 0 0)) ) - (time, (vector))\n\nThis type of boundary condition is not intended to act as a valve (i.e., off/on). The idea is that the flow rate varies with time, without being zero. Instead can you start the simulation with 250 ft/min (i.e., at 15s) as an inlet flow rate and then run the simulation in transient mode?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9027731,"math_prob":0.94519687,"size":999,"snap":"2022-40-2023-06","text_gpt3_token_len":262,"char_repetition_ratio":0.10954774,"word_repetition_ratio":0.0,"special_character_ratio":0.2842843,"punctuation_ratio":0.11965812,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.958467,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-29T19:57:45Z\",\"WARC-Record-ID\":\"<urn:uuid:66e03a8d-6442-4b76-9e9c-5aedc81619c6>\",\"Content-Length\":\"17306\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de915e25-12eb-4e7b-9709-bb87d73393f9>\",\"WARC-Concurrent-To\":\"<urn:uuid:c6ea242f-7460-4e7d-ab75-6ae62ae07d31>\",\"WARC-IP-Address\":\"66.39.59.248\",\"WARC-Target-URI\":\"https://www.symscape.com/node/1655\",\"WARC-Payload-Digest\":\"sha1:WPVPDKQ3BBYA33VDPG3TUPFIP7NRENNT\",\"WARC-Block-Digest\":\"sha1:S7TDLXET2D7W2P7D37H2CRRU32T4VC2H\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499758.83_warc_CC-MAIN-20230129180008-20230129210008-00444.warc.gz\"}"}
http://iconicmath.com/introduction/	[ "# Introduction", null, "This section includes six pages of introductory discussion. The Image of a road sign shows the way.\n\n## Section Contents\n\nThe The Iconic Math Site page is an introduction to the site and to iconic math.\n\nThe Technical Introduction presents the formal techniques of iconic math, how pictures can behave mathematically.\n\nIconic Principles lists several principles of iconic math, with little discussion and no examples.\n\nVarieties introduces some of the textual, pictorial, and physical languages that can be used to express mathematical concepts.\n\nMath Education suggests ways in which math education in US schools might be improved.\n\nEducational Theory discusses the educational research that supports a change to iconic math." ]	[ null, "http://iconicmath.com/wordpress/wp-content/mymedia/featureimage-introduction300x300-41346_186x186.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85680616,"math_prob":0.56651616,"size":716,"snap":"2023-14-2023-23","text_gpt3_token_len":129,"char_repetition_ratio":0.13623595,"word_repetition_ratio":0.0,"special_character_ratio":0.16759777,"punctuation_ratio":0.09917355,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9668981,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-27T10:07:27Z\",\"WARC-Record-ID\":\"<urn:uuid:4138a310-d3e3-4143-a9c1-6e1ac5317c3e>\",\"Content-Length\":\"23922\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:14080103-25d9-48f9-82d2-03a5ae3b6fc0>\",\"WARC-Concurrent-To\":\"<urn:uuid:2bdbeae0-9334-4e53-9652-db800ad52ca9>\",\"WARC-IP-Address\":\"192.145.232.221\",\"WARC-Target-URI\":\"http://iconicmath.com/introduction/\",\"WARC-Payload-Digest\":\"sha1:RCSBQL2T7XK3OVITNWEKM6QEMIQXB5GD\",\"WARC-Block-Digest\":\"sha1:X4FDGYOHU3L7GU2XCPOXUFGNMLXTBZDE\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948620.60_warc_CC-MAIN-20230327092225-20230327122225-00165.warc.gz\"}"}
https://www.dataunitconverter.com/byte-per-minute-to-zebibit-per-hour	[ "# Byte/Minute to Zibit/Hour Calculator - Convert Bytes Per Minute to Zebibits Per Hour", null, "## Conversion History (Last 6)\n\nInput Bytes Per Minute - and press Enter\nByte/Minute\n\nSec\nMin\nHr\nDay\nSec\nMin\nHr\nDay\n\n## Byte/Minute to Zibit/Hour - Conversion Formula and Steps\n\nByte and Zebibit are units of digital information used to measure storage capacity and data transfer rate. Byte is one of the very basic digital unit where as Zebibit is a binary unit. One Byte is equal to 8 bits. One Zebibit is equal to 1024^7 bits. There are 147,573,952,589,676,412,928 Bytes in one Zebibit. - view the difference between both units", null, "Source Data UnitTarget Data Unit\nByte (B)\nEqual to 8 bits\n(Basic Unit)\nZebibit (Zibit)\nEqual to 1024^7 bits\n(Binary Unit)\n\nThe formula of converting the Bytes Per Minute to Zebibits Per Hour is represented as follows :\n\nZibit/Hour = Byte/Minute x 8 / 10247 x 60\n\nNow let us apply the above formula and, write down the steps to convert from Bytes Per Minute (B/Minute) to Zebibits Per Hour (Zibit/Hour). This way, we can try to simplify and reduce to an easy to apply formula.\n\nFORMULA\n\nZebibits Per Hour = Bytes Per Minute x 8 / 10247 x 60\n\nSTEP 1\n\nZebibits Per Hour = Bytes Per Minute x 8 / (1024x1024x1024x1024x1024x1024x1024) x 60\n\nSTEP 2\n\nZebibits Per Hour = Bytes Per Minute x 8 / 1180591620717411303424 x 60\n\nSTEP 3\n\nZebibits Per Hour = Bytes Per Minute x 0.0000000000000000000067762635780344027125 x 60\n\nExample : If we apply the above Formula and steps, conversion from 10 Byte/Minute to Zibit/Hour, will be processed as below.\n\n1. = 10 x 8 / 10247 x 60\n2. = 10 x 8 / (1024x1024x1024x1024x1024x1024x1024) x 60\n3. = 10 x 8 / 1180591620717411303424 x 60\n4. = 10 x 0.0000000000000000000067762635780344027125 x 60\n5. = 0.0000000000000000040657581468206416275\n6. i.e. 10 Byte/Minute is equal to 0.0000000000000000040657581468206416275 Zibit/Hour.\n\n(Result rounded off to 40 decimal positions.)\n\nYou can use above formula and steps to convert Bytes Per Minute to Zebibits Per Hour using any of the programming language such as Java, Python or Powershell.\n\n#### Definition : Byte\n\nA Byte is a unit of digital information that typically consists of 8 bits and can represent a wide range of values such as characters, binary data and it is widely used in the digital world to measure the data size and data transfer speed.\n\n#### Definition : Zebibit\n\nA Zebibit (Zib or Zibit) is a unit of digital information that is equal to 1,180,591,620,717,411,303,424 bits and is defined by the International Electro technical Commission(IEC). The prefix \"zebi\" is derived from the binary number system and it is used to distinguish it from the decimal-based \"zettabit\" (Zb). It is widely used in the field of computing as it more accurately represents the amount of data storage and data transfer in computer systems.\n\n### Excel Formula to convert from Byte/Minute to Zibit/Hour\n\nApply the formula as shown below to convert from Bytes Per Minute to Zebibits Per Hour.\n\nABC\n1Bytes Per Minute (B/Minute)Zebibits Per Hour (Zibit/Hour)\n21=A2 * 0.0000000000000000000067762635780344027125 * 60\n3\n\nDownload - Excel Template for Bytes Per Minute to Zebibits Per Hour Conversion\n\nIf you want to perform bulk conversion locally in your system, then download and make use of above Excel template.\n\n### Python Code for Byte/Minute to Zibit/Hour Conversion\n\nYou can use below code to convert any value in Bytes Per Minute to Zebibits Per Hour in Python.\n\nbytesPerMinute = int(input(\"Enter Bytes Per Minute: \"))\nzebibitsPerHour = bytesPerMinute * 8 / (1024102410241024102410241024) * 60\nprint(\"{} Bytes Per Minute = {} Zebibits Per Hour\".format(bytesPerMinute,zebibitsPerHour))\n\nThe first line of code will prompt the user to enter the Bytes Per Minute as an input. The value of Zebibits Per Hour is calculated on the next line, and the code in third line will display the result." ]	[ null, "https://www.dataunitconverter.com/images/certificate_precise.png", null, "https://www.dataunitconverter.com/showimage.php/Bytes Per Minute_to_Zebibits Per Hour_Dataunitconverter.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.759362,"math_prob":0.96358156,"size":4123,"snap":"2023-14-2023-23","text_gpt3_token_len":1190,"char_repetition_ratio":0.20854576,"word_repetition_ratio":0.15453194,"special_character_ratio":0.31845742,"punctuation_ratio":0.07806191,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9907423,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-30T10:42:33Z\",\"WARC-Record-ID\":\"<urn:uuid:d65bf971-da27-46b5-a795-46c150a2ef24>\",\"Content-Length\":\"75569\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:98d55577-7407-46f2-a9a8-c107d1a7eaf4>\",\"WARC-Concurrent-To\":\"<urn:uuid:6b130774-4458-4bc4-84b5-9d56038d70d5>\",\"WARC-IP-Address\":\"64.227.22.174\",\"WARC-Target-URI\":\"https://www.dataunitconverter.com/byte-per-minute-to-zebibit-per-hour\",\"WARC-Payload-Digest\":\"sha1:YOKBRZDQGGHC6GCXMRAU23TQYBSSCWSC\",\"WARC-Block-Digest\":\"sha1:ZAHQACO4QGBGIRACRXTGGSTTNYSXXZOL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296949181.44_warc_CC-MAIN-20230330101355-20230330131355-00419.warc.gz\"}"}
https://answers.everydaycalculation.com/add-fractions/36-30-plus-50-56	[ "Solutions by everydaycalculation.com\n\n1st number: 1 6/30, 2nd number: 50/56\n\n36/30 + 50/56 is 293/140.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 30 and 56 is 840\n2. For the 1st fraction, since 30 × 28 = 840,\n36/30 = 36 × 28/30 × 28 = 1008/840\n3. Likewise, for the 2nd fraction, since 56 × 15 = 840,\n50/56 = 50 × 15/56 × 15 = 750/840\n1008/840 + 750/840 = 1008 + 750/840 = 1758/840\n5. 1758/840 simplified gives 293/140\n6. So, 36/30 + 50/56 = 293/140\nIn mixed form: 213/140\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.80191624,"math_prob":0.9985362,"size":728,"snap":"2020-10-2020-16","text_gpt3_token_len":287,"char_repetition_ratio":0.13674033,"word_repetition_ratio":0.0,"special_character_ratio":0.53846157,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99686176,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-24T09:59:05Z\",\"WARC-Record-ID\":\"<urn:uuid:dd3442c3-3135-4f37-a565-33b019a934ea>\",\"Content-Length\":\"7369\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3553e76d-9a2b-4e53-bd4b-c95f3cb0fedc>\",\"WARC-Concurrent-To\":\"<urn:uuid:56635e5e-4a23-4fde-b288-ac559714af63>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/add-fractions/36-30-plus-50-56\",\"WARC-Payload-Digest\":\"sha1:BRMDP5S2B4HR6CXMYKY4AGNKDTSEQH2S\",\"WARC-Block-Digest\":\"sha1:UMZSHXMFYHE5UVL743HULKCCXQX52JF2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145910.53_warc_CC-MAIN-20200224071540-20200224101540-00173.warc.gz\"}"}
https://www.tutorialkart.com/cpp/cpp-vector-clear/	[ "## C++ Vector clear() function\n\nclear() function removes all the elements from a vector.\n\n### Syntax\n\nThe syntax of clear() function is\n\n`void clear();`\n\n### Example\n\nIn the following C++ program, we initialise a vector `names` with three elements, and then erase all the elements from this vector using clear() function.\n\nC++ Program\n\n```#include <iostream>\n#include <vector>\nusing namespace std;\n\nint main() {\nvector<string> names{ \"apple\", \"banana\", \"cherry\" };\nnames.clear();\ncout << \"Size of Vector : \" << names.size() << endl;\n}```\n\nOutput\n\n```Size of Vector : 0\nProgram ended with exit code: 0```\n\nAfter clear(), all the elements are removed, and hence the size of the resulting vector is 0.\n\n### Conclusion\n\nIn this C++ Tutorial, we learned the syntax of clear() function, and how to use this clear() function to remove all the elements from given vector." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6364401,"math_prob":0.88147706,"size":818,"snap":"2022-27-2022-33","text_gpt3_token_len":192,"char_repetition_ratio":0.18304668,"word_repetition_ratio":0.0,"special_character_ratio":0.2628362,"punctuation_ratio":0.14569536,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9565199,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-05T07:01:12Z\",\"WARC-Record-ID\":\"<urn:uuid:2d5cbd81-bba4-4a69-9b1d-4780e4142a76>\",\"Content-Length\":\"36747\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:068ba191-dd6b-4597-94e1-20451b162813>\",\"WARC-Concurrent-To\":\"<urn:uuid:adf5ca09-0de8-4084-bb90-d551c963c051>\",\"WARC-IP-Address\":\"18.67.65.96\",\"WARC-Target-URI\":\"https://www.tutorialkart.com/cpp/cpp-vector-clear/\",\"WARC-Payload-Digest\":\"sha1:DOLZZIKZV2N23QU3X2LYWGV37VPIHUX2\",\"WARC-Block-Digest\":\"sha1:32ACYFLI7H6LDNIOIWFJQNPUETD2ODT7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104514861.81_warc_CC-MAIN-20220705053147-20220705083147-00503.warc.gz\"}"}
https://discuss.codechef.com/t/doubt-0-1-graph-hackerrank-hack-the-interview-vi/73739	[ "", null, "# Doubt - 0-1 Graph (Hackerrank Hack the Interview VI)\n\nThe problem is here. All the test cases are available if you solve the problem (you might not be able to access that link). The official editorial is here.\nMy solution gets WA in three of fourteen tests.\n\nMy logic is:\nEach graph can be transformed to a tree which will have the same solution. This tree is constructed such that each vertex > parent of this vertex.\nInitially, the tree is linear ie 1 <- 2 <- 3 <- … <- n. Then, go through the edges of the graph. For each edge (a, b) where a < b, set tree[b] = min(tree[b], a). Then, we traverse the array in reverse manner reducing values to make it a non-decreasing array. But the values are not distances, they are parent vertices. The last loop calculates the sum of distances.\n\n``` void solve() { ll n, nf_edges; scan(n);scan(nf_edges); vector<ll> tree(n + 1); for (ll i = 1; i <= n; ++i) { tree[i] = i - 1; } //print_container(tree); ll one, two, large, small; while (nf_edges --) { scan(one); scan(two); large = max(one, two); small = min(one, two); tree[large] = min(tree[large], small); } //print_container(tree); for (ll i = n, level = n; i > 1; i--) { if (level > tree[i]) { level = tree[i]; } else { tree[i] = level; } } //print_container(tree); ll summ = 0; for (ll i = 2, mul = 0; i <= n; ++i) { if (tree[i - 1] != tree[i]) { mul++; } summ += mul; } pnl(summ); } ```\n\nI’d like an explanation for why this approach is incorrect or a small test case for which my approach fails.\n\nDoubt has been resolved. It turns out the editorial was incorrect.\n\nHello,\n\nI am Darshan, I manage content on HackerRank. We would like to apologize for the issues in this challenge in our latest contest.\n\nFor the complete correctness of the challenge, our author’s greedy solution does not suffice, as indicated correctly by you.\n\nWe benchmark our challenges through multiple coders, and with this specific challenge, a corner case was not discovered by us which resulted in providing an incorrect challenge.\n\nWe are carefully evaluating our internal practices in order to avoid such issues in the future.\n\nThe Greedy Solution provided as part of the Problem Setters solution missed on this key test case, we will be updating the solution here soon.\n\nWe are really sorry for the inconvenience caused and as a result, we have decided to not consider this challenge in the contest to calibrate the results and will update the leaderboard accordingly. We are working on making our problems more robust every day. Your feedback is much appreciated and will help us improve our challenge quality.\n\nHope to see you again in future contests! Thank you.\n\n1 Like" ]	[ null, "https://s3.amazonaws.com/discourseproduction/original/3X/7/f/7ffd6e5e45912aba9f6a1a33447d6baae049de81.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8120419,"math_prob":0.9348919,"size":1428,"snap":"2020-34-2020-40","text_gpt3_token_len":409,"char_repetition_ratio":0.09199438,"word_repetition_ratio":0.0074074073,"special_character_ratio":0.3382353,"punctuation_ratio":0.1826923,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9842676,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T08:45:28Z\",\"WARC-Record-ID\":\"<urn:uuid:4e397b59-6221-4066-85c1-b1838acdd376>\",\"Content-Length\":\"19142\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a02daf29-784f-4ff4-9532-cd75a5b10185>\",\"WARC-Concurrent-To\":\"<urn:uuid:d23b4fdf-e3d5-4c6d-bdad-ebf2aa6274ca>\",\"WARC-IP-Address\":\"18.213.158.143\",\"WARC-Target-URI\":\"https://discuss.codechef.com/t/doubt-0-1-graph-hackerrank-hack-the-interview-vi/73739\",\"WARC-Payload-Digest\":\"sha1:FA2MT6MCWWDQ3THZDVG4YOUCD7NYD5QU\",\"WARC-Block-Digest\":\"sha1:XQ42D6P6TUVJKXGCEWJ4VN73OU6H2DDA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400196999.30_warc_CC-MAIN-20200920062737-20200920092737-00725.warc.gz\"}"}
https://www.mathworks.com/matlabcentral/profile/authors/9766874-fw?s_tid=answers_ctrb	[ "Community Profile", null, "# FW\n\n23 total contributions since 2017\n\n•", null, "View details...\n\nContributions in\nView by\n\nQuestion\n\nHow to convert or extract arrays from a structure?\nIn continuous wavelet analysis, when we export the coefficients into the workspace, the data is exported as a structure (1x1 str...\n\n21 days ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nIntegration via trapezoidal rule in various sections of the same array\nIf the signal S consists of several peaks as a function of time, is there a way to assign integration limits for the trapezoidal...\n\n25 days ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nGenerating Approximations from \"appcoef\" in Wavelet Toolbox\nI have a question regarding the MATLAB example for \"1-D approximation coefficients\" https://www.mathworks.com/help/wavelet/ref/a...\n\n25 days ago \| 0 answers \| 0\n\n### 0\n\nQuestion\n\nHow to replace complex numbers in a column vector with 0.000+0.000i ?\nImage we obtain a fft of a signal and we wish to remove certain frequencies from the signal. I want to fill in zeros after remov...\n\n29 days ago \| 2 answers \| 0\n\n### 2\n\nQuestion\n\nFinding several local maximum values in a given range and corresponding indices\nIf we have a dataset \"y\" which consists of a sum of 5 gaussian peaks as function of time t, there will be 5 local maximum value...\n\n2 months ago \| 2 answers \| 0\n\n### 2\n\nQuestion\n\nHow to locate the index of the maximum value in a given range\nSuppose we have two vectors t= [ 1 2 3 4 5 6 7 8 9 10 11]; % time values y = [1 2 3 4 5 7 5 4 3 2 1]; % a dependent variable...\n\n2 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nHow to implement a formula involving several elements of the same vector?\nSuppose we have two row vectors Time = [ 1 2 3 4 5 6 7 8 9 10]; width= [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0]; % width of p...\n\n2 months ago \| 2 answers \| 0\n\n### 2\n\nQuestion\n\nHow to add non-numerical axis values in 3D scatter plots?\nI am using a 3D scatter plot option. Can the x-axis values be labeled as \"1:1, 2:1, 5:1, 8:1, 10:1\" as peak area ratios? Current...\n\n2 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nIf we have an Excel file, and instead of selecting a range of columns, I would like to select certain columns. The following syn...\n\n2 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nLabeling the columns in an array\nIf we import a .csv or Excel file using readtable, and then convert the table to an array as the following: Data=table2array(re...\n\n4 months ago \| 1 answer \| 1\n\n### 1\n\nQuestion\n\nCorrect choice of one sided frequency axis after fft\nThere are a lot of queries on fft frequency. I guess the following point not discussed anywhere explicitly (at least at one plac...\n\n4 months ago \| 0 answers \| 0\n\n### 0\n\nQuestion\n\nHow to replace numbers in a column vector after certain elements?\nHow should we proceed if we have a column vector X with 1000 elements, and we wish to replace all the values after a certain row...\n\n4 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nfftshift with even and odd number of data points (scaling the positive and negative frequency axis)\nIf we wish to draw double sided frequency axis, i.e., positive and negative frequencies with odd and even number of data points ...\n\n6 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nHow to add labels to an array or table (after conversion from an array)\nI have an array of 2000 x 4 data points. I would like to add labels to the columns only. For example, Column 1 should be 'time/m...\n\n6 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nAssigning indexes in an array and finding max values in a selected range\nIf we have X = time series data and signal in a 8000x 2 array (Matlab 2017b). The first column is time and the second column is ...\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nFrequency scale in fft after zero filling (odd/even number of data)\nProduct: Matlab 2017b If we have data set \"A\" which consists of time versus light absorbance.There is another set of data \"B\"....\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nHow to combine sections from Workspace into a new vector?\nI have Matlab 2017b. 1) If we have two vectors A and B, in the workspace (1000x1), each of same dimension. How can one combine...\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nCreating Timetables: Error Message in SampleRate\nHello, I am trying to use a suggested function to generate a timetable with a sampling frequency of 200 Hz. tt = timetable(rand...\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nDoing averages in blocks for downsampling time series data\nOne way to downsample is to do averaging in blocks. I had asked a question here \"I would like to downsample data simulated at 20...\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nCommand for filling in zeros as powers of 2 for FT\nIf we two sets of signals (A and B) of unequal length, I am using zero padding first to make the length of B equal to A by using...\n\n7 months ago \| 1 answer \| 0\n\n### 1\n\nQuestion\n\nHow to treat a given column in a sheet from Workspace as a variable?\nI am generating exponentially modified Gaussians (EMGs) from a simulation and wish to do FT on a selected sheet in the Workspace...\n\n7 months ago \| 0 answers \| 0\n\n### 0\n\nQuestion\n\nHow to read two Excel files and assign columns as variables in MATLAB?\nHello, I am using MATLAB 2017b. I have two Excel.xlsx files, call them A and B, containing time vs. instrument signals under two...\n\n7 months ago \| 1 answer \| 0" ]	[ null, "https://www.mathworks.com/responsive_image/150/0/0/0/0/cache/matlabcentral/profiles/9766874_1522134132468_DEF.jpg", null, "https://www.mathworks.com/matlabcentral/profile/badges/Thankful_5.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.67685074,"math_prob":0.8664882,"size":851,"snap":"2019-43-2019-47","text_gpt3_token_len":298,"char_repetition_ratio":0.24439198,"word_repetition_ratio":0.8719212,"special_character_ratio":0.38190365,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9865817,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-15T18:08:46Z\",\"WARC-Record-ID\":\"<urn:uuid:9803a547-292c-48bc-aca6-d55e0c27ac80>\",\"Content-Length\":\"117295\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bbf9917e-a4ff-4d65-9d8c-1331669ccf30>\",\"WARC-Concurrent-To\":\"<urn:uuid:0ae89a15-a094-4351-bd4d-ff11de04a600>\",\"WARC-IP-Address\":\"23.50.112.17\",\"WARC-Target-URI\":\"https://www.mathworks.com/matlabcentral/profile/authors/9766874-fw?s_tid=answers_ctrb\",\"WARC-Payload-Digest\":\"sha1:MOVYI3MTQKL6S7C7TV3ZEOQTHD26W7SX\",\"WARC-Block-Digest\":\"sha1:N4QXOCOC2EZD6ZFAD4DMXBIZJTS7WLXJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668699.77_warc_CC-MAIN-20191115171915-20191115195915-00416.warc.gz\"}"}
https://www.colorhexa.com/0d0da5	[ "# #0d0da5 Color Information\n\nIn a RGB color space, hex #0d0da5 is composed of 5.1% red, 5.1% green and 64.7% blue. Whereas in a CMYK color space, it is composed of 92.1% cyan, 92.1% magenta, 0% yellow and 35.3% black. It has a hue angle of 240 degrees, a saturation of 85.4% and a lightness of 34.9%. #0d0da5 color hex could be obtained by blending #1a1aff with #00004b. Closest websafe color is: #000099.\n\n• R 5\n• G 5\n• B 65\nRGB color chart\n• C 92\n• M 92\n• Y 0\n• K 35\nCMYK color chart\n\n#0d0da5 color description : Dark blue.\n\n# #0d0da5 Color Conversion\n\nThe hexadecimal color #0d0da5 has RGB values of R:13, G:13, B:165 and CMYK values of C:0.92, M:0.92, Y:0, K:0.35. Its decimal value is 855461.\n\nHex triplet RGB Decimal 0d0da5 `#0d0da5` 13, 13, 165 `rgb(13,13,165)` 5.1, 5.1, 64.7 `rgb(5.1%,5.1%,64.7%)` 92, 92, 0, 35 240°, 85.4, 34.9 `hsl(240,85.4%,34.9%)` 240°, 92.1, 64.7 000099 `#000099`\nCIE-LAB 20.399, 53.686, -75.306 7.1, 3.089, 35.817 0.154, 0.067, 3.089 20.399, 92.483, 305.485 20.399, -5.655, -78.367 17.577, 41.344, -108.514 00001101, 00001101, 10100101\n\n# Color Schemes with #0d0da5\n\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #a5a50d\n``#a5a50d` `rgb(165,165,13)``\nComplementary Color\n• #0d59a5\n``#0d59a5` `rgb(13,89,165)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #590da5\n``#590da5` `rgb(89,13,165)``\nAnalogous Color\n• #59a50d\n``#59a50d` `rgb(89,165,13)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #a5590d\n``#a5590d` `rgb(165,89,13)``\nSplit Complementary Color\n• #0da50d\n``#0da50d` `rgb(13,165,13)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #a50d0d\n``#a50d0d` `rgb(165,13,13)``\n• #0da5a5\n``#0da5a5` `rgb(13,165,165)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #a50d0d\n``#a50d0d` `rgb(165,13,13)``\n• #a5a50d\n``#a5a50d` `rgb(165,165,13)``\n• #07075e\n``#07075e` `rgb(7,7,94)``\n• #090976\n``#090976` `rgb(9,9,118)``\n• #0b0b8d\n``#0b0b8d` `rgb(11,11,141)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #0f0fbd\n``#0f0fbd` `rgb(15,15,189)``\n• #1111d4\n``#1111d4` `rgb(17,17,212)``\n• #1313ec\n``#1313ec` `rgb(19,19,236)``\nMonochromatic Color\n\n# Alternatives to #0d0da5\n\nBelow, you can see some colors close to #0d0da5. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #0d33a5\n``#0d33a5` `rgb(13,51,165)``\n• #0d26a5\n``#0d26a5` `rgb(13,38,165)``\n• #0d1aa5\n``#0d1aa5` `rgb(13,26,165)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #1a0da5\n``#1a0da5` `rgb(26,13,165)``\n• #260da5\n``#260da5` `rgb(38,13,165)``\n• #330da5\n``#330da5` `rgb(51,13,165)``\nSimilar Colors\n\n# #0d0da5 Preview\n\nThis text has a font color of #0d0da5.\n\n``<span style=\"color:#0d0da5;\">Text here</span>``\n#0d0da5 background color\n\nThis paragraph has a background color of #0d0da5.\n\n``<p style=\"background-color:#0d0da5;\">Content here</p>``\n#0d0da5 border color\n\nThis element has a border color of #0d0da5.\n\n``<div style=\"border:1px solid #0d0da5;\">Content here</div>``\nCSS codes\n``.text {color:#0d0da5;}``\n``.background {background-color:#0d0da5;}``\n``.border {border:1px solid #0d0da5;}``\n\n# Shades and Tints of #0d0da5\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000001 is the darkest color, while #eeeefe is the lightest one.\n\n• #000001\n``#000001` `rgb(0,0,1)``\n• #020214\n``#020214` `rgb(2,2,20)``\n• #030326\n``#030326` `rgb(3,3,38)``\n• #040438\n``#040438` `rgb(4,4,56)``\n• #06064a\n``#06064a` `rgb(6,6,74)``\n• #07075c\n``#07075c` `rgb(7,7,92)``\n• #09096e\n``#09096e` `rgb(9,9,110)``\n• #0a0a81\n``#0a0a81` `rgb(10,10,129)``\n• #0c0c93\n``#0c0c93` `rgb(12,12,147)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #0e0eb7\n``#0e0eb7` `rgb(14,14,183)``\n• #1010c9\n``#1010c9` `rgb(16,16,201)``\n• #1111dc\n``#1111dc` `rgb(17,17,220)``\n• #1414ec\n``#1414ec` `rgb(20,20,236)``\n• #2626ee\n``#2626ee` `rgb(38,38,238)``\n• #3838ef\n``#3838ef` `rgb(56,56,239)``\n• #4b4bf1\n``#4b4bf1` `rgb(75,75,241)``\n• #5d5df2\n``#5d5df2` `rgb(93,93,242)``\n• #6f6ff4\n``#6f6ff4` `rgb(111,111,244)``\n• #8181f5\n``#8181f5` `rgb(129,129,245)``\n• #9393f7\n``#9393f7` `rgb(147,147,247)``\n• #a5a5f8\n``#a5a5f8` `rgb(165,165,248)``\n• #b8b8f9\n``#b8b8f9` `rgb(184,184,249)``\n• #cacafb\n``#cacafb` `rgb(202,202,251)``\n• #dcdcfc\n``#dcdcfc` `rgb(220,220,252)``\n• #eeeefe\n``#eeeefe` `rgb(238,238,254)``\nTint Color Variation\n\n# Tones of #0d0da5\n\nA tone is produced by adding gray to any pure hue. In this case, #58585a is the less saturated color, while #0606ac is the most saturated one.\n\n• #58585a\n``#58585a` `rgb(88,88,90)``\n• #515161\n``#515161` `rgb(81,81,97)``\n• #4b4b67\n``#4b4b67` `rgb(75,75,103)``\n• #44446e\n``#44446e` `rgb(68,68,110)``\n• #3d3d75\n``#3d3d75` `rgb(61,61,117)``\n• #36367c\n``#36367c` `rgb(54,54,124)``\n• #2f2f83\n``#2f2f83` `rgb(47,47,131)``\n• #28288a\n``#28288a` `rgb(40,40,138)``\n• #222290\n``#222290` `rgb(34,34,144)``\n• #1b1b97\n``#1b1b97` `rgb(27,27,151)``\n• #14149e\n``#14149e` `rgb(20,20,158)``\n• #0d0da5\n``#0d0da5` `rgb(13,13,165)``\n• #0606ac\n``#0606ac` `rgb(6,6,172)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #0d0da5 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.514837,"math_prob":0.76977783,"size":3649,"snap":"2020-10-2020-16","text_gpt3_token_len":1679,"char_repetition_ratio":0.124279834,"word_repetition_ratio":0.011111111,"special_character_ratio":0.5522061,"punctuation_ratio":0.23575419,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9835783,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-25T15:40:43Z\",\"WARC-Record-ID\":\"<urn:uuid:cc9bcd39-d247-4946-a01d-51a8da3182e1>\",\"Content-Length\":\"36222\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9b9b66c6-bf67-4c1d-a5fd-358270188b4d>\",\"WARC-Concurrent-To\":\"<urn:uuid:6523284e-3f9b-43bf-8c30-7e1a117f200d>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/0d0da5\",\"WARC-Payload-Digest\":\"sha1:R2W6KEVK6MPNJ5IS3YO36VQHP7UIPM3V\",\"WARC-Block-Digest\":\"sha1:E7DWT565M22WJNPKUY3PQIZBD6QL6JX5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146123.78_warc_CC-MAIN-20200225141345-20200225171345-00150.warc.gz\"}"}
https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/	[ "", null, "# Analysis of Lattice Vibrations in Two Dimensions\n\nInitializing live version", null, "Requires a Wolfram Notebook System\n\nInteract on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.\n\nAt first glance, the hexagonal and square lattices appear to have the same symmetry as their unit cells (a simple hexagon or square), but closer examination reveals more rotational and reflectional symmetries, not to mention a countably infinite number of translations. Of course, a real crystal lattice deviates from perfect symmetry as it interacts with photons in energy transfer that results in the creation of discrete vibrational states.\n\n[more]\n\nSimple restoring force models of linear crystals can be extended to planar crystals by considering angles as well as edges. Resolving the eigenvalues and eigenvectors of a Hessian matrix can help to understand how superpositions of vibrational modes relate to possibly observable spectra. Only some of the computable values will be observed in the laboratory. The best predictions of observable transitions also consider the symmetry of the vibrational modes, as determined by their equivalency class.\n\n[less]\n\nContributed by: Brad Klee (August 2012)\nOpen content licensed under CC BY-NC-SA\n\n## Snapshots", null, "", null, "", null, "## Details\n\nSnapshot 1, Energy Summation Unit: As a tile in the lattice deforms according to the propagation of a wavefunction away from the equilibrium configuration, the potential energy of the entire tiling increases because of the deformed edges and angles. Each contribution to the increase in potential energy is shown as a highlighted edge or highlighted vertex, and the magnitude of the highlighted region indicates the contribution of that deformation to the total potential energy.\n\nSnapshot 2, Hessian Matrix: An array plot of the Hessian matrix shows the magnitude of the second derivative of the potential energy, which is computed using a central difference method and two perturbations for each atom. The eigenvectors and eigenvalues of this matrix are the normal modes and their corresponding vibrational frequencies. The Hessian matrix, given by", null, ", has the units of a force constant.\n\nSnapshot 3, Block Diagonal Transformation: The perturbation basis elements transform into one another according to the operations of dihedral symmetry, for both square and hexagonal lattices. The Hessian matrix computed from these perturbations does not change under conjugation by any transformation of the dihedral group, that is,", null, ". Thus,", null, "can be reduced to block diagonal form using a transformation", null, "derived from the irreducible representations of the dihedral group. Eigenvectors computed from the block-diagonalized matrix can all be real even if eigenvectors computed from the untransformed matrix are complex.\n\nSnapshot 4, Energy Level Diagram: This plot shows energy levels for each selected wavefunction. The left-hand side of each level is labeled by some number linearly proportional to a frequency, computed from the square root of an eigenvalue of the Hessian matrix", null, ". Indices on the right-hand side correspond to symmetries of the vibrational modes, which can be determined using sets of simple linear functionals.\n\nThe construction of the Hessian matrix is adapted from . Each angular dimension resists deformation with a factor of", null, ", and each linear dimension resists deformation with a factor of", null, ". The total energy of a lattice acted upon by periodic deformations is infinite and thus incalculable. However, an adequately apportioned fraction of the total energy can be computed by summing the energy from each tile multiplied by the population percentage of that tile. Care must be taken not to count edges twice.\n\nIn this notebook, the energy computation is correct for the square lattice and for the A hexagonal lattice but not for the B hexagonal lattice. The A hexagonal lattice contains only three species of tiles, while the B hexagonal lattice contains 24 species of tiles. A correct computation for the B hexagonal lattice in 12 dimensions could be accomplished by changing the energy function to sum over the six edges and six angles of all 24 species, with the appropriate prefactors according to relative population and overlap of edges. Each basis pattern has a unique spectrum and perturbation periodicity. It is unknown how many basis patterns exist, and the existence or absence of a basis pattern containing 720 tiles is unproven but not excluded.\n\nBlock diagonalization is performed by considering the irreducible representations of the appropriate dihedral group. Block membership determines an important equivalency class for eigenvectors, related to selection rules and transition probabilities. A classification system based on annihilators and orthogonal to block membership has been used to number the degeneracies.\n\nThis Demonstration should not be considered physical, but systems of springs and masses can give insight for problems where restoring forces hold atoms in a specific geometric pattern while some energy excitations attempt to move them, thus creating phonons.\n\nThanks to Janette Dunn for providing educational resources regarding representation-derived bases.\n\nReference\n\n D. E. Weeks and W. G. Harter, \"Rotation-Vibration Spectra of Icosahedral Molecules. II. Icosahedral Symmetry, Vibrational Eigenfrequencies, and Normal Modes of Buckminsterfullerene,\" Journal of Chemical Physics, 90(9), 1989 pp. 4744–4771. doi: 10.1063/1.456571." ]	[ null, "https://demonstrations.wolfram.com/app-files/assets/img/header-spikey2x.png", null, "https://demonstrations.wolfram.com/img/demonstrations-branding.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/popup_1.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/popup_2.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/popup_3.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc820539275665914492.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc5304669557957932141.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc2955030523413163512.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc3573654321628649414.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc2955030523413163512.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc2690338444961109510.png", null, "https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/img/desc2324787273901706116.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8934413,"math_prob":0.920009,"size":5436,"snap":"2023-14-2023-23","text_gpt3_token_len":1081,"char_repetition_ratio":0.12628865,"word_repetition_ratio":0.00982801,"special_character_ratio":0.17954378,"punctuation_ratio":0.095185995,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9900091,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"im_url_duplicate_count":[null,null,null,null,null,4,null,4,null,4,null,4,null,4,null,8,null,4,null,8,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-01T19:53:59Z\",\"WARC-Record-ID\":\"<urn:uuid:9ecea6ed-9a12-4492-bbc8-b133b8639ff6>\",\"Content-Length\":\"120907\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:970bce23-3d88-410f-8e66-7d923fbd9293>\",\"WARC-Concurrent-To\":\"<urn:uuid:69c35ef6-de58-493a-aac1-dc61035047c6>\",\"WARC-IP-Address\":\"140.177.205.90\",\"WARC-Target-URI\":\"https://demonstrations.wolfram.com/AnalysisOfLatticeVibrationsInTwoDimensions/\",\"WARC-Payload-Digest\":\"sha1:HSM4ZHZTGCVIN6V2SWBXLKRPWISD3VVH\",\"WARC-Block-Digest\":\"sha1:QGZFARFP3OLNVMQNV4AOTUSYE2UJELNL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950247.65_warc_CC-MAIN-20230401191131-20230401221131-00053.warc.gz\"}"}
http://momentumclubs.org/define-gravitational-field.html	[ "# Define gravitational field. Gravitational fields 2019-01-08\n\nDefine gravitational field Rating: 5,3/10 172 reviews\n\n## Gravitational fields", null, "A gravitational field is the force field that exists in the space around every mass or group of masses. Modern field theories of force contain this principle by requiring every entity that is acted upon by a field to be also a source of the field. What do the field lines look like for this two mass case? One possible class of black holes very large stars that have used up all of their so that they are no longer held up by and have collapsed into black holes less-massive stars may collapse into. Search gravitational field and thousands of other words in English definition and synonym dictionary from Reverso. Just as gravitational field strength is used to place a value on the gravitational force that would be experienced by a mass at any point in a gravitational field, the concept of gravitational potential is used to give a value for the potential energy.\n\nNext\n\n## Gravitational force dictionary definition", null, "I just put this section in so you can see that this result can be derived by the straightforward, but quite challenging, method of adding the individual gravitational attractions from all the bits making up the spherical shell. To find the gravitational field at the point P , we just add the contributions from all the rings in the stack. By symmetry, the field at P must point along the x -axis, so all we have to do is compute the strength of the x -component of the gravitational force from one mass, and double it. The , and thus the acceleration of a small body in the space around the massive object, is the negative of the gravitational potential. The Principle of Superposition The fact that the total gravitational field is just given by adding the two vectors together is called the Principle of Superposition.\n\nNext\n\n## Gravitational field", null, "For simple mechanics problems, a convenient zero point would be at the floor of the laboratory or at the surface of a table. If the force were to be removed, the object would fall back down to the ground and the gravitational potential energy would be transferred to kinetic energy of the falling object. Arrows and field lines that represent gravitational field The gravitational field varies slightly at the earth's surface. In other words, the two bodies interact with one another's gravitational field. We all know instinctively that a heavy weight raised above someone's head represents a potentially dangerous situation. This is a thousand times less than the size of an atomic nucleus! This makes all values of the gravitational potential energy negative. The field still exists at all the places where we did not measure it.\n\nNext\n\n## Gravitational field", null, "Definitions in physics are operational, i. Gravitational Field for Two Masses The next simplest case is two equal masses. This experimental support for his general theory of relativity garnered him instant worldwide acclaim. Advanced Engineering Mathematics 2nd ed. A gravitational field is a type of force field and is analogous to electric and magnetic fields for electrically charged particles and magnets, respectively. For a satellite to move from an orbit where the potential is — 4. To move to a higher or lower orbit the satellite must gain or lose energy.\n\nNext\n\n## newtonian gravity", null, "Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction. Why define a new name and new units for the same old quantity? An experiment by the American physicist Lloyd Kreuzer established to within 1 part in 20,000 that different materials produce gravitational fields with a strength the same as that of gravitational fields acting upon them. The pump becomes a generator driven by the gravitational potential energy of the water in the upper reservoir. Field Strength at a Point Equidistant from the Two Masses It is not difficult to find an exact expression for the gravitational field strength from the two equal masses at an equidistant point P. This is clearly not a problem for a one kilogram mass in discussing planetary and solar gravity. By moving the test mass to various positions,we can make a map showing the gravitational field at any point in space. An important fact about all fields of force is that when there is more than one source or sink , the fields add according to the rules of vector addition.\n\nNext\n\n## Gravitational Field: Definition & Formula", null, "We place the zero point of gravitational potential energy at a distance r r r of infinity. The gravitational field vector, gg, at any location in space is found by placing a test mass mtmt at that point. Assume the system has an overall energy efficiency of 80%. Diagram of torsion balance set up When we talk about the gravitational force acting on an object, we can come up with an equation in a couple of different ways using the universal law of gravitation and Newton's Second Law of Motion. Gravitational field strength is a vector quantity: its direction is towards the object that causes the field. If the body has a mass of 1 unit, then the potential energy to be assigned to that body is equal to the gravitational potential.\n\nNext\n\n## gravitational field definition", null, "A point mass is one that has a radial field, like that of the Earth. It says that in general, gravitational force magnitude depends on the source mass, test mass and their separation. Our article on includes some example problems that are solved through an understanding of how gravitational potential energy is converted to other forms. Sketch them in the neighborhood of the origin. As a consequence, the gravitational potential satisfies.\n\nNext\n\n## newtonian gravity", null, "Geologists and prospectors of oil and minerals make precise measurements of the earth's gravitational field to predict what may be beneath the surface. At this point, we could simply fall into Pluto, but then all our gravitational potential energy would be transferred to , and we would crash into Pluto's surface. The radius of the Earth is about 6. The most subtle point about all this is that the gravitational field tells us about what forces would be exerted on a test mass by Earth, Sun, Moon, and the rest of the universe, if we inserted a test mass at the point in question. The potential is half the square of the. In a second scheme an is set up with freely suspended reflectors at the ends of long paths that are at right angles to each other. Classical Dynamics of particles and systems 4th ed.\n\nNext" ]	[ null, "https://engineersfield.com/wp-content/uploads/2017/10/4.8.jpg", null, "https://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Electric_Field_Lines.svg/1200px-Electric_Field_Lines.svg.png", null, "https://imgv2-1-f.scribdassets.com/img/document/161073850/original/5c4fc82d32/1532231915", null, "https://image.slidesharecdn.com/a2gravitationalfield-101010222922-phpapp02/95/a2-gravitational-field-kyuem-physics-16-728.jpg", null, "https://study.com/cimages/multimages/16/arrows_lines.png", null, "https://s3mn.mnimgs.com/img/shared/content_ck_images/ana_qa_image_57e9f09607e73.jpeg", null, "https://www.researchgate.net/profile/Carl_Bender/publication/2093636/figure/fig1/AS:394689871138831@1471112806971/Configuration-of-a-simple-pendulum-of-mass-m-in-a-uniform-gravitational-field-of-strength.png", null, "http://www.milutinmarjanov.com/wp-content/uploads/2014/10/fig-01.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9361081,"math_prob":0.9467046,"size":6265,"snap":"2021-04-2021-17","text_gpt3_token_len":1220,"char_repetition_ratio":0.18990576,"word_repetition_ratio":0.0055658626,"special_character_ratio":0.19074222,"punctuation_ratio":0.07534247,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9867017,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,4,null,2,null,2,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-19T17:40:51Z\",\"WARC-Record-ID\":\"<urn:uuid:c31b9fc8-38ec-4429-9c5e-50adc7b45185>\",\"Content-Length\":\"10893\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8515ac09-8e58-4824-8d4e-a5a259615218>\",\"WARC-Concurrent-To\":\"<urn:uuid:60a15118-fd27-4c6e-a8ea-3620861b8f79>\",\"WARC-IP-Address\":\"52.216.145.242\",\"WARC-Target-URI\":\"http://momentumclubs.org/define-gravitational-field.html\",\"WARC-Payload-Digest\":\"sha1:3AJZP4H5CZVCLYVTDO63MQNAJREX6DSQ\",\"WARC-Block-Digest\":\"sha1:BJWHPHYWAUZ543XSVUZWFYW5HNQDSTST\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703519600.31_warc_CC-MAIN-20210119170058-20210119200058-00228.warc.gz\"}"}
https://arxiv.org/abs/1601.01493	[ "Full-text links:\n\nmath.CO\n\n# Title:A note on induced Ramsey numbers\n\nAbstract: The induced Ramsey number $r_{\\mathrm{ind}}(F)$ of a $k$-uniform hypergraph $F$ is the smallest natural number $n$ for which there exists a $k$-uniform hypergraph $G$ on $n$ vertices such that every two-coloring of the edges of $G$ contains an induced monochromatic copy of $F$. We study this function, showing that $r_{\\mathrm{ind}}(F)$ is bounded above by a reasonable power of $r(F)$. In particular, our result implies that $r_{\\mathrm{ind}}(F) \\leq 2^{2^{ct}}$ for any $3$-uniform hypergraph $F$ with $t$ vertices, mirroring the best known bound for the usual Ramsey number. The proof relies on an application of the hypergraph container method.\n Comments: Dedicated to the memory of Jirka Matoušek, 10 pages, second version addresses changes arising from the referee reports Subjects: Combinatorics (math.CO) Journal reference: A Journey Through Discrete Mathematics (A Tribute to Ji\\v{r}\\'i Matou\\v{s}ek), Springer, 2017, 357-366 DOI: 10.1007/978-3-319-44479-6_13 Cite as: arXiv:1601.01493 [math.CO] (or arXiv:1601.01493v2 [math.CO] for this version)\n\n## Submission history\n\nFrom: Mathias Schacht [view email]\n[v1] Thu, 7 Jan 2016 11:37:21 UTC (10 KB)\n[v2] Fri, 24 Jun 2016 09:48:07 UTC (11 KB)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7626173,"math_prob":0.95191926,"size":1000,"snap":"2019-35-2019-39","text_gpt3_token_len":299,"char_repetition_ratio":0.10040161,"word_repetition_ratio":0.0,"special_character_ratio":0.304,"punctuation_ratio":0.103626944,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99179775,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-21T14:24:13Z\",\"WARC-Record-ID\":\"<urn:uuid:d684725a-4cc0-46f0-a420-59ba55622519>\",\"Content-Length\":\"18348\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:692a3ee9-ab85-484e-b760-51f26628d351>\",\"WARC-Concurrent-To\":\"<urn:uuid:f368b695-2339-45fc-bebf-286f92840891>\",\"WARC-IP-Address\":\"128.84.21.199\",\"WARC-Target-URI\":\"https://arxiv.org/abs/1601.01493\",\"WARC-Payload-Digest\":\"sha1:HU4SWFERRYX6GAWTUO6BIYHMHSJBHF7E\",\"WARC-Block-Digest\":\"sha1:MBKSEQFB7IJGC67QQDWPFRA2I4SQI2YN\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027316021.66_warc_CC-MAIN-20190821131745-20190821153745-00487.warc.gz\"}"}
https://www.arxiv-vanity.com/papers/1210.3637/	[ "# A Gottesman-Knill theorem for all finite Abelian groups\n\nJuan Bermejo-Vega1, Maarten Van den Nest2\n\nMax-Planck-Institut für Quantenoptik,\nHans-Kopfermann-Straße 1, 85748 Garching, Germany.\n11\n22\n###### Abstract\n\nQuantum normalizer circuits were recently introduced as generalizations of Clifford circuits. A normalizer circuit over a finite Abelian group is composed of the quantum Fourier transform (QFT) over together with gates which compute quadratic functions and automorphisms. In [VDNest_12_QFTs] it was shown that every normalizer circuit can be simulated efficiently classically. This result provides a nontrivial example of a family of quantum circuits that cannot yield exponential speed-ups in spite of usage of the QFT—the latter being a central quantum algorithmic primitive. Here we extend the aforementioned result in several ways. Most importantly, we show that normalizer circuits supplemented with intermediate measurements can also be simulated efficiently classically, even when the computation proceeds adaptively. This yields a generalization of the Gottesman-Knill theorem, valid for qubits, to arbitrary . Moreover our simulations are twofold i.e. we show how to classically efficiently sample the measurement probability distributions as well as compute the amplitudes of the state vector. Finally we develop a generalization of the stabilizer formalism relative to arbitrary finite Abelian groups. For example we characterize how to update stabilizers under generalized Pauli measurements and provide a normal form of he amplitudes of generalized stabilizer states using quadratic functions and subgroup cosets.\n\n## 1 Introduction\n\nInvestigating the power of restricted families of quantum circuits is one of the most fruitful approaches to understand the fundamental question How does the power of quantum computers compare to classical ones? A celebrated result in this respect is the Gottesman-Knill theorem, which states that any quantum circuit built out of Clifford gates (Hadamards, CNOTs, -phase gates) and Pauli measurements can be efficiently simulated on a classical computer [Gottesman_PhD_Thesis, gottesman_knill, nielsen_chuang]. Thus, a quantum computer that works exclusively with these operations cannot achieve exponential quantum speed-ups.\n\nThe Gottesman-Knill theorem illustrates how subtle the frontier between classical and quantum computational power can be. For example, even though Clifford circuits can be simulated efficiently classically, replacing the -phase gates by a -phase gate immediately yields a quantum universal gate set [Boykin_etal_99_Clifford_pifourth_is_universal_OPEN, Boykin_etal_00_Clifford_pifourth_is_universal_ELSEVIER]. Another interesting feature is that, even though the computing power of Clifford circuits is not stronger than classical computation, their behavior is genuinely quantum. They can be used, for instance, to prepare highly entangled states (such as cluster states [raussen_briegel_01_Cluster_State, nest06Entanglement_in_Graph_States, raussen_briegel_onewayQC]), or to perform quantum teleportation [gottesman_knill]. Yet in spite of the high degrees on entanglement which may be involved, the evolution of Clifford circuits can be tracked efficiently using a Heisenberg picture: i.e. by employing the stabilizer formalism used in quantum error correction.\n\nIn this work we study the computational power of normalizer circuits. These circuits were introduced in [VDNest_12_QFTs] by one of us, as a class of quantum computations generalizing the Clifford circuits, as well as standard extensions of the latter to qudits [Gottesman98Fault_Tolerant_QC_HigherDimensions, dehaene_demoor_hostens]. A normalizer circuit over a finite Abelian group is a quantum circuit comprising unitary gates that implement the quantum Fourier transform (QFT) over , quadratic functions of the group and automorphisms. If is chosen to be (i.e. the group of -bit strings with addition modulo 2), normalizer circuits precisely coincide with the unitary Clifford circuits (i.e. those composed of CNOT, and phase gates). In [VDNest_12_QFTs] it was shown that arbitrary normalizer circuits (acting on computational basis states and followed by computational basis measurements) can be simulated classically efficiently.\n\nAn interesting feature of the normalizer circuit formalism is the presence of QFTs over any finite Abelian group. Of particular interest is the group , since its corresponding QFT is the “standard” quantum Fourier transform [nielsen_chuang]; the latter lies at the core of several famous quantum algorithms, such as factoring and computing discrete logarithms [Shor]. More generally, QFTs over Abelian groups are central ingredients of quantum algorithms to find hidden subgroups of Abelian groups [lomont_HSP_review, childs_lecture_8, childs_vandam_10_qu_algorithms_algebraic_problems]. In contrast with the role of QFTs in quantum speed-ups, the normalizer circuit formalism provides a nontrivial example of a family of quantum computations that cannot yield exponential speed-ups, in spite of usage of the QFT.\n\nHere we further extend the classical simulation results of [VDNest_12_QFTs]. We do so by considering normalizer circuits where intermediate measurements are allowed at arbitrary times in the computation—whereas in [VDNest_12_QFTs] only terminal measurements were considered. More precisely we define adaptive normalizer circuits over to comprise the following three fundamental ingredients:\n\n• Normalizer gates over , i.e. QFTs, automorphism gates, quadratic phase gates.\n\n• Measurements of generalized Pauli operators over at arbitrary times in the computation.\n\n• Adaptiveness: the choice of normalizer gate at any time may depend (in a polynomial-time computable way) on the outcomes obtained in all previous measurement rounds.\n\nIf is chosen to be , the corresponding class of adaptive normalizer circuits precisely corresponds to the class of adaptive Clifford circuits allowed in the original Gottesman-Knill theorem.\n\nThis paper contains several results, summarized as follows:\n\n• A Gottesman-Knill theorem for all finite Abelian groups (Theorem LABEL:thm_main). Given any Abelian group , every poly-size adaptive normalizer circuit over , acting on any standard basis input, can be efficiently simulated by a classical computer. That is, we show that the conditional probability distribution arising at each measurement (given the outcomes of previous measurements) can be sampled efficiently classically.\n\n• A stabilizer formalism for finite Abelian groups. Generalizing the well-known stabilizer formalism for qubits, we develop a stabilizer formalism for arbitrary Abelian groups. This framework is a key ingredient to efficiently track the evolution of quantum states under normalizer circuits. In particular, our results are:\n\n• We provide an analytic formula, as well as an efficient algorithm, to compute the dimension of any stabilizer code over an Abelian group (Theorem 3).\n\n• We provide an analytic formula, as well as an efficient algorithm, to compute the update of any stabilizer group under Pauli measurements over arbitrary Abelian groups (Theorem LABEL:thm_Measurement_Update_rules).\n\n• A normal form for stabilizer states (Theorem LABEL:thm_Normal_form_of_an_stabilizer_state). We give an analytical formula to characterize the amplitudes of stabilizer states over Abelian groups and show how to compute these amplitudes efficiently. It follows that all stabilizer states over Abelian groups belong to the class of Computationally Tractable (CT) states, introduced in [nest_weak_simulations]. The interest of this property is that all CT states can be simulated classically in various contexts well beyond the setting of the present work—cf. [nest_weak_simulations] for a discussion.\n\nAn important technical difference (and difficulty) compared to the original Gottesman-Knill theorem is that in the context of arbitrary finite Abelian groups (such as ) arithmetic is generally over large integers. This is in contrast to where arithmetic is simply over i.e. modulo 2. The difference is in fact twofold:\n\nFirst, is a field. As a result, it is possible to describe the “standard” stabilizer formalism for qubits with vector space techniques over . In this context methods like Gaussian elimination have straightforward analogues, which can be exploited in the design of classical algorithms. The field property is, however, no longer present in the context of general Abelian groups. This complicates both the analytical theory and algorithmic aspects due to, e.g., the presence of zero divisors.\n\nSecond, in arithmetic is with small numbers (namely 0s and 1s), whereas in general finite Abelian groups arithmetic is with large integers. This is e.g. the case with . Of course, one must beware that a variety of computational problems over the integers may in the worst case be intractable: consider e.g. the factoring problem or computing discrete logarithms. One of the main challenges in our scenario is to show that the “integer arithmetic” used in our classical simulation algorithms can be carried out efficiently. For this purpose, a significant technical portion of our work is dedicated to solving systems of linear equations modulo a finite Abelian group, defined as follows: given a pair of finite Abelian groups and (both of which are given as a direct product of cyclic groups), and a homomorphism between them, we look at systems of the form where and . We present polynomial-time deterministic classical algorithms for counting and finding solutions of these systems. These efficient algorithms lie at the core of our classical simulations of normalizer circuits.\n\nFinally we remark that, beyond the scope of classical simulations, the mathematical tools we develop could also have unexplored applications for quantum error correction viz. quantum stabilizer codes over general finite Abelian groups.\n\n#### Relation to previous work.\n\nIn [VDNest_12_QFTs] it was proven that one can sample classically efficiently the output distribution of any non-adaptive normalizer circuit followed by a terminal measurement in the standard basis. Our work extends on this result in various ways, as outlined above in I-II-III. Main differences are the fact that here we consider adaptive normalizer circuits, and two different types of simulations: sampling output distributions and computation of amplitudes.\n\nRestricting to groups of the form where is constant, our work recovers previous results regarding classical simulations of Clifford circuits for qudits. Previous to our work, the case when is a prime number was well-understood: if , the ability to sample classically efficiently follows from the Gottesman-Knill theorem [Gottesman_PhD_Thesis, gottesman_knill], whereas the computation of amplitudes from [dehaene_demoor_coefficients]; for prime values of larger than 2, techniques given in [Gottesman98Fault_Tolerant_QC_HigherDimensions] yield efficient sampling simulations of adaptive Clifford circuits. Last, in the case when is an arbitrary constant, some investigations have led to efficient simulations of Clifford circuits: first, techniques given in [dehaene_demoor_hostens] can be used to simulate non-adaptive Clifford circuits followed by a terminal standard basis measurement (sampling or computation of relative phases); second, ref. [deBeaudrap12_linearised_stabiliser_formalism] extended the last sampling result to simulate terminal Pauli measurements and, in addition, a subclass of adaptive Clifford operations: the latter can be transformed into equivalent non-adaptive circuits using the principle of deferred measurement. To the best of our knowledge, however, our study seems to be the first that has provided efficient classical simulations of arbitrary adaptive Clifford circuits for qudits when is an arbitrary constant integer.\n\nFinally, our work also connects to previous studies on the simulatibility of Abelian quantum Fourier transforms (QFTs), such as [aharonov_AQFT, yoran_short_QFT, brown_QFT]. The relation between normalizer circuits to those works was discussed in [VDNest_12_QFTs] and we refer to this source.\n\n## 2 Preliminaries on finite Abelian groups\n\nThis section is reserved for the main group-theoretical notions used in this work. Let be the additive group of integers modulo . Then\n\n G=Zd1×⋯×Zdm (1)\n\ndenotes a finite Abelian group, the elements of which are -tuples of the form with . Addition of two group elements is component-wise modulo . Every finite Abelian group can be expressed as a product of the type (1) via isomorphism, yet computing this decomposition is regarded as a hard computational problem [cheung_mosca_01_decomp_abelian_groups]; throughout this paper, a product decomposition (1) of is always explicitly given. The cardinality of is denoted by , and fulfills . For every ranging from 1 to , denotes the group element which has in its -th component and zeroes elsewhere, where in slot represents the neutral element in . Remark that for every so that the elements generate .\n\n### 2.1 Characters\n\nLet . The function is defined as\n\n χg(h)=exp(2{p}{i}m∑i=1g(i)h(i)di) (2)\n\nfor all , . Every function is a character of , i.e., it is a homomorphism from into the nonzero complex numbers . This means that\n\n χg(h+h′)=χg(h)χ(h′) (3)\n\nfor every . Note further that and . The set of all characters of forms a group, called the character group or dual group, which is isomorphic to .\n\n### 2.2 Orthogonal subgroups\n\nThe character functions give rise to a set-theoretical duality, sometimes called orthogonality of Abelian subgroups (although it differs from the usual orthogonality of vector spaces). Given a subgroup of the finite Abelian group , its orthogonal subgroup is defined as\n\n H⊥={g∈G:χh(g)=1,for allh∈H}. (4)\n\nNote that is indeed a subgroup of . The main properties of are summarized below.\n\n###### Lemma 1 (Orthogonal subgroup).\n\nConsider a finite Abelian group as in (1) and let and be two arbitrary subgroups. Then the following statements hold:\n\n• if and only if\n\n• (a-b) are well-known, see e.g. [lomont_HSP_review]. (c) is proved straightforwardly by applying definitions. We prove (d). Since is contained in both and if follows that and . Therefore . We show , which implies the reversed inclusion. This comes from the fact that implies and , or equivalently, and .\n\n### 2.3 Quadratic functions\n\nA function from to the nonzero complex numbers is called bilinear if for every one has\n\n B(g+h,x)=B(g,x)B(h,x)andB(x,g+h)=B(x,g)B(x,h). (5)\n\nA function from to the nonzero complex numbers is called quadratic if there exists a bilinear function such that for every one has\n\n ξ(g+h)=ξ(g)ξ(h)B(g,h). (6)\n\nAlthough it is not obvious from the above definition, the number turns out to be a complex phase for every and for every quadratic function. More precisely, one has for every [VDNest_12_QFTs]. It is easily verified that the product of two quadratic functions is again a quadratic function. Also the complex conjugate of any quadratic function is again quadratic. Using these properties one can show that the set of quadratic functions forms an (Abelian) group.\n\nWe give some examples of quadratic functions (see also ref.[VDNest_12_QFTs]). First we consider . Letting be an matrix with entries in and letting , the following functions are quadratic:\n\n ξA:x→(−1)xTAx and ξa:x→{i}aTx (7)\n\nwhere and is computed over (i.e. modulo 2). Note that the exponent in is polynomial of degree 2 in , whereas the exponent in has degree 1. To prove that these functions are quadratic in the sense used in this work, we note that\n\n ξA(x+y) = ξA(x)ξA(y)(−1)xT(A+AT)y (8) ξa(x+y) = ξ(x)ξ(y)(−1)q(x,y) with q(x,y)=(aTx)(aTy) (9)\n\nIdentity (9) can be proved by distinguishing between the 4 cases . The above identities can be used to show that and are quadratic.\n\nConsidering a single cyclic group , examples of quadratic functions are\n\n z→ωbz2+cz and z→γbz(z+d);ω:={e}2{p}{i}/d, γ:=ω1/2. (10)\n\nWe refer to [VDNest_12_QFTs] for a proof.\n\n### 2.4 Homo-, iso- and auto- morphisms\n\nGiven two finite Abelian groups and , a group homomorphism from to is a map that fulfills for every (in other words, is linear). An isomorphism from to is an invertible group homomorphism. An automorphism of is an isomorphism of the form , i.e. from the group onto itself. The set of all automorphisms of forms a group, called the automorphism group.\n\nThroughout this work, group homomorphisms between Abelian groups are to be described in terms of matrix representations, which are defined as follows:\n\n###### Definition 1 (Matrix representation).\n\nGiven a homomorphism between groups and , an integer matrix is said to be a matrix representation of if its columns are elements of , and if it holds that\n\n A(h)=Ah(modG),for every h∈H. (11)\n\nConversely, an integer matrix is said to define a group homomorphism from to if its columns are elements of and the operation is a group homomorphism.\n\nIn (11) we introduced some conventions, that we will use: first, the element is seen as a column of integer numbers onto which acts via matrix multiplication; second, (mod ) indicates that multiplications and sums involved in the calculation of are performed within , taking remainders when necessary.\n\nThe main properties of matrix representations are now summarized.\n\n###### Proposition 1.\n\nEvery group homomorphism has a matrix representation. Moreover, an matrix with columns defines a homomorphism iff its columns fulfill the equations\n\n ciai=0(modG),for every i. (12)\n• First, given , we show that , where , is a matrix representation. Since every decomposes as , it follows, using linearity of , that\n\n A(h)=A(∑h(i)ei)=∑h(i)A(ei)=Ah(modG). (13)\n\nThe right implication of the iff comes readily from\n\n ciai=ciAei=A(ciei)=A(0)=0(modG) (14)\n\nFor the converse, we let act on , and without taking remainders; we obtain\n\n Ag+Ah=∑[g(i)+h(i)]ai,A(g+h)=∑(g+h)(i)ai. (15)\n\nRecalling associativity of and , the latter expression shows that defines a function from to , and, thus, is a function from to . Last, it holds for every that for some integers , since (by definition of the group ) is the remainder obtained when is divided by ( would be the quotient). It follows, subtracting modularly, that for every , ; and, due to, defines a linear map.\n\n### 2.5 Computational group theory\n\nComputational aspects of finite Abelian groups are now discussed; our discourse focuses on a selected catalog of computational problems relevant to this work and efficient classical algorithms to solve them. Since this section concerns only classical computational complexity, we will tend to omit the epithet classical all the way throughout it.\n\nTo start with, we introduce some basic notions of computer arithmetic. From now on, the size of an integer is the number of bits in its binary expansion. Remark that every group (1) satisfies the inequalities and , for every . It follows thence readily that is , and that one needs at most a polylog amount of memory to store an element (in terms of bits).\n\nWe discuss now how to perform some basic operations efficiently within any finite Abelian group (1). First, given two integers and of size at most , common arithmetic operations can be computed in poly time with elementary algorithms: such as their sum, product, the quotient of divided by , and the remainder [brent_zimmerman10CompArithmetic]. Therefore, given , the sum can be obtained in polylog time by computing the remainders . Similarly, given an integer , the element can be obtained in polylog time by computing the remainders mod .\n\nIn connection with the previous section, it follows from the former properties that matrix representations can be stored using only a polynomial amount of memory, and, moreover, that given the matrix representation we can efficiently compute . Specifically, given a matrix representation of the homomorphism , we need polylog space to store its columns as tuples of integers, and polylog time to compute the function .\n\nPeriodically, and at crucial stages of this investigation, some more advanced algebraic computational problems are bound to arise. The following lemma compiles a list of group theoretical problems that will be relevant to us and can be solved efficiently by classical computers.\n\n###### Lemma 2 (Algorithms for finite Abelian groups).\n\nGiven , , two subgroups of , and , , polynomial-size generating-sets of them, there exist efficient classical algorithms to solve the following problems deterministically.\n\n• Decide whether belongs to ; if so, find integers such that .\n\n• Count the number of elements of .\n\n• Find a generating-set of the intersection .\n\n• Find a generating-set of .\n\n• Given the equations , find elements such that all solutions of the system can be written as linear combinations of the form .\n\nThe proof of the lemma is divided in two parts which are fully detailed i.o. in appendices LABEL:Appendix:_Algorithms_for_Finite_Abelian_Groups and LABEL:Appendix:_System_of_linear_congruences_modulo_Abelian_group. The rest of this section describes the high-level structure of the proof.\n\nIn short, appendix LABEL:Appendix:_Algorithms_for_Finite_Abelian_Groups contains a proof of the following statement.\n\n###### Lemma 3.\n\nProblems (a-e) in lemma 2 are polynomial-time reducible to either counting or finding solutions of systems of equations of the form ; where is a group homomorphism between two (canonically-decomposed) finite Abelian groups, and , to which , respectively belong; given that a matrix representation of is provided.\n\nMind that, since is a linear map, the set of solutions of such a system is either empty or a coset with the structure\n\n Xsol=x0+kerA. (16)\n\nBy finding solutions we refer to the action of finding one particular solution of the system and a (polynomially-large) generating set of .\n\nTo provide an example, we prove now lemma 3 for the problems (d-e) in lemma 2; for the rest of cases, we refer to the appendices.\n\n#### Example: (d,e)th cases of lemma 2.\n\nFirst of all, remark that problem (d) reduces to (e) by setting all to be —this yields the system (4), whose solutions are the elements of the orthogonal subgroup. Thence, it will be enough to prove the (e)th case. Moreover, since the equations can be fulfilled for some only if all are th-roots of the unit, this systems can only have solutions if all are even numbers. As we can determine it efficiently whether these numbers are even, we assume from now on that it is the case.\n\nNow define a tuple of integers coefficient-wise as ; use the later to re-write . Also, denote by the group generated by the elements . By letting multiply numerators and denominators of all fractions in (2), the system of complex exponentials can be turned into an equivalent system of congruences . Finally, by defining a matrix with coefficients the system can be written as\n\n Ωg=b(modG), (17)\n\nwhere belongs to , being the number of generators , and we look for solutions inside . Moreover, the coefficients of fulfill ; hence, condition (12) is met and defines a homomorphism.\n\nFinally, can be computed in using aforementioned algorithms to multiply and divide integers. It is now routine to check, using the concepts developed thus far, that both and are ; as a result, the inputsize of the new problem, as well as the memory needed to store and , are all .\n\nA remark Note that the group homomorphism fulfills . Therefore, if we substitute with in the procedure above, given generators of , we would obtain an integer matrix that defines a second group homomorphism such that\n\n ϖ(g)=Ω′(g)(modG)andkerϖ=H′⊥=H. (18)\n\nAs a result, our algorithm to compute generators of leads also to an efficient method to construct, given any subgroup of , a homomorphism whose kernel is . This fact will be used later in the text, in section LABEL:section_Gottesman-Knill_theorem.\n\nThe final ingredient to complete the proof of lemma 2 is the following theorem.\n\n###### Theorem 1 (Systems of linear equations over finite Abelian groups).\n\nGiven any element of the group and any matrix which defines a group homomorphism from to , consider the system of equations . Then, there exist classical algorithms to solve the following list of problems in polylog time.\n\n1. Decide whether the system admits a solution.\n\n2. Count the number of different solutions of the system.\n\n3. Find such that all solutions of the system are linear combinations of the form .\n\nThe main ideas underlying the proof of theorem 1 are as follows: first, we show how to reduce in polynomial-time to an equivalent system of linear congruences modulo , where is suitably upper-bounded; second, we apply fast algorithms to compute Smith normal forms to tackle the latter problem [storjohann10_phd_thesis]. For details, we refer to appendix LABEL:Appendix:_System_of_linear_congruences_modulo_Abelian_group.\n\n## 3 Pauli and Clifford operators and normalizer circuits over Abelian groups\n\nHere we extend the notion of Pauli and Clifford operators for qubits [nielsen_chuang] and qudits [Knill96non-binaryunitary, Gottesman98Fault_Tolerant_QC_HigherDimensions] to all finite Abelian groups. Throughout this section we follow the definitions of [VDNest_12_QFTs]. Let be a finite Abelian group as in (1). Then is naturally associated to a -dimensional Hilbert space with a basis labeled by group elements\n\n (19)\n\nThis basis is henceforth called the standard basis. Introduce the following operators acting on :\n\n X(g):=∑h∈G\|h+g⟩⟨h\|,Z(g):=∑h∈Gχg(h)\|h⟩⟨h\|, (20)\n\nwhere . Since acts as a permutation on the standard basis, this operator is unitary. Since , the operator is unitary as well. With these definitions, a Pauli operator over (hereafter often simply denoted Pauli operator) is a unitary operator of the form\n\n σ(a,g,h):=γaZ(g)X(h), (21)\n\nwhere is a primitive root of unity and . The triple describing the Pauli operator is called the label of . It is important to remark that the label constitutes an efficient description of comprising bits. Owing to, from now on we will specify Pauli operators in terms of their labels; the latter will represent the standard encoding of these operators.\n\nNote that every Pauli operator factorizes as a tensor product relative to the tensor decomposition of i.e. can be written as where acts on . This property can be verified straightforwardly by applying (20) and the definition (2) of the characters of .\n\nBasic manipulations of Pauli operators can be carried out transparently by translating them into transformations of their labels: we review now some of these rules. First, the Pauli matrices (20) obey the following commutation rules:\n\n X(g)X(h) =X(g+h)=X(h)X(g) Z(g)Z(h) =Z(g+h)=Z(h)Z(g) (22) Z(g)X(h) =χg(h)X(h)Z(g).\n\nCombinations of these rules straightforwardly lead to the next two propositions.\n\n###### Proposition 2 (Products and powers of Pauli operators [VDNest_12_QFTs]).\n\nConsider Pauli operators and and a positive integer . Then , and are also Pauli operators, the labels of which can be computed in polylog time on input of and the labels of and . Moreover, .\n\n###### Proposition 3 (Commutativity).\n\nConsider two Pauli operators and . Then the following statements are equivalent:\n\n• and commute;\n\n• ;\n\n• and are orthogonal elements of i.e. .\n\nProposition 2 implies that the set of all Pauli operators over forms a (finite) group, called the Pauli group (over ).\n\nA unitary operator on is called a Clifford operator (over ) if maps the Pauli group onto itself under the conjugation map . It is easy to see that the set of all Clifford operators forms a group, called the Clifford group . Formally speaking, the Clifford group is the normalizer of the Pauli group in the full unitary group acting on . Next we define three basic classes of unitary operators on which are known to belong to the Clifford group [VDNest_12_QFTs].\n\n• Quantum Fourier transforms. The quantum Fourier transform (QFT) over is the following unitary operator on :\n\n Fi=1√di∑ωxyi\|x⟩⟨y\|;ωi=exp(2{p}{i}/di) (23)\n\nwhere the sum is over all . The QFT over the entire group is given by , which acts on the entire space . Any operator obtained by replacing a subset of operators in this tensor product by identity operators is called a partial QFT.\n\n• Automorphism gates. Given an automorphism of , the associated automorphism gate maps .\n\n• Quadratic phase gates. Given a quadratic function on , the quadratic phase gate is the diagonal operator mapping . Since is a complex phase for every , every quadratic phase gate is a (diagonal) unitary operator.\n\nA unitary operator which is either a (partial) quantum Fourier transform or its inverse, an automorphism gate or a quadratic phase gate is generally referred to as a normalizer gate. A quantum circuit composed entirely of normalizer gates is called a normalizer circuit over . The size of a normalizer circuit is the number of normalizer gates of which it consists.\n\nIn this paper we will be interested in classical simulations of normalizer circuits. To make meaningful statements about classical simulations one has to specify which classical descriptions of normalizer circuits are considered to be available. This is discussed next. First, a partial quantum Fourier transform is described by the set of systems on which it acts nontrivially. Second, an automorphism gate is described by the matrix representation of the associated automorphism. Third, let be an arbitrary quadratic function. Since , there exists such that for every . It was shown in [VDNest_12_QFTs] that the integers and comprise an efficient description of and, thus, of the associated quadratic phase gate. Henceforth we will assume that all normalizer gates are specified in terms of the descriptions given above, which will be called their standard encodings. Each standard encoding comprises polylog bits.\n\nIt is known that every normalizer gate belongs to the Clifford group:\n\n###### Theorem 2 (Normalizer gates are Clifford [VDNest_12_QFTs]).\n\nEvery normalizer gate is a Clifford operator. Furthermore let be a normalizer gate specified in terms of its standard classical encoding as above, and let be a Pauli operator specified in terms of its label. Then the label of can be computed in polylog time.\n\nFor any group of the form , the entire Clifford group is known to be generated (up to global phase factors) by normalizer gates [dehaene_demoor_hostens] (see also section 4). More strongly, every Clifford group element can be written as a product of at most polylog such operators. We conjecture that this feature holds true for Clifford operators over arbitrary :\n\n###### Conjecture 1.\n\nLet be an arbitrary finite Abelian group. Up to a global phase, every Clifford operator over can be written as a product of polylog normalizer gates.\n\nFinally we point out that both automorphism gates and quadratic phase gates have a distinguished role within the Clifford group, characterized as follows:\n\n###### Proposition 4.\n\nUp to a global phase, every Clifford operator which acts on the standard basis as a permutation has the form for some and some automorphism gate . Every diagonal Clifford operator is, up to a global phase, a quadratic phase gate.\n\n• The first statement was proved in [VDNest_12_QFTs]. We prove the second statement. Let be a diagonal unitary operator (so that for all ) in the Clifford group. Without loss of generality we may set which can always be ensured by choosing a suitable (irrelevant) overall phase. Then for every , sends to a Pauli operator under conjugation. This implies that there exists a complex phase and group elements such that\n\n DX(h)D†=γ(h)X(f1(h))Z(f2(h)). (24)\n\nSince is diagonal, it is easy to verify that we must have for every . Now consider an arbitrary . Then\n\n DX(h)D†\|g⟩ = ¯¯¯ξ(g)ξ(g+h)\|g+h⟩; (25) γ(h)X(h)Z(f2(h))\|g⟩ = γ(h)χg(f2(h))\|g+h⟩. (26)\n\nCondition (24) implies that (25) is identical to (26) for every . Choosing and using that and for every it follows that . We thus find that\n\n ξ(g+h)=ξ(g)ξ(h)χg(f2(h)). (27)\n\nThe function is manifestly linear in , since . Furthermore by definition is symmetric in and . Thus is also linear in .\n\n## 4 Examples\n\nHere we give examples of Pauli and Clifford operations. We illustrate in particular how the definitions of the preceding section generalize existing notions of Pauli and Clifford operators for qubits and qudits.\n\n### 4.1 G=Zm2\n\nIn this case the standard definition of -qubit Pauli operators is recovered. To see this, first note that we have i.e. the Hilbert space is a system of qubits. Let and denote the standard Pauli matrices and let be an -bit string. Then, applying definition (20) one finds that\n\n X(g)=σg(1)x⊗⋯⊗σg(m)x,Z(g)=σg(1)z⊗⋯⊗σg(m)z. (28)\n\nHere is an -bit string: i.e. . In short, is a tensor product of -matrices and identities, and is a tensor product of -matrices and identities. Therefore, every Pauli operator (20) has the form where each is a single-qubit operator of the form for some . This recovers the usual notion of a Pauli operator on qubits [nielsen_chuang].\n\nIt was shown in [VDNest_12_QFTs] that the CNOT gate and the CZ gate (acting between any two qubits), the Hadamard gate and the Phase gate diag (acting on any single qubit) are examples of normalizer gates for . Note that these gates are the standard building blocks of the well known class of Clifford circuits for qubits. In fact, the entire Clifford group for qubits is generated by this elementary gate set [nielsen_chuang].\n\n### 4.2 G=Zmd\n\nIn this case the Hilbert space is a system of -level systems (qudits) and Pauli operators have the form , where each is a single-qudit operator of the form for some . Here and are the usual generalizations of and , respectively [Knill96non-binaryunitary, Gottesman98Fault_Tolerant_QC_HigherDimensions]. These operators act on a single -level system as follows:\n\n Xd=∑\|x+1⟩⟨x\| and Zd=∑{e}2{p}{i}x/d\|x⟩⟨x\| (29)\n\nwhere the sums run over all . Examples of normalizer gates over are generalizations of the CNOT, CZ, Hadamard and Phase gates to qudits, as follows:\n\n SUMd = ∑\|x,x+y⟩⟨x,y\|; (30) CZd = ∑ωxyd\|x,y⟩⟨x,y\|;ωd:=%e2{p}{i}/d (31) Fd = 1√d∑{e}2{p}{i}xy/d\|x⟩⟨y\|; (32) Sd = ∑ξx(x+d)d\|x⟩⟨x\|;ξd:={e}{p}{i}/d. (33)\n\nHere and rum over all elements in . To show that SUM is a normalizer gate, note that is indeed an automorphism of . The gates and are quadratic phase gates; see section 11 of ref.[VDNest_12_QFTs]. In addition, the “multiplication gate” is also a normalizer gate, for every which is coprime to . Indeed, for such the map is known to be an automorphism of . It is known that the entire Clifford group for qubits (for arbitrary ) is generated by the gates SUM, , and [dehaene_demoor_hostens].\n\n### 4.3 G=Z2m\n\nOne can also consider to be a single cyclic group, such as . In this case, is a -dimensional Hilbert space with standard basis . Comparing with the previous examples, the important difference with e.g. is that the structure of does not naturally induce a factorization of the Hilbert space into single-qubit systems. As a consequence, normalizer gates over act globally on , in contrast with the previous examples.\n\nExamples of normalizer gates are now given by , and , following the definitions of the previous example with . Note that is the “standard” QFT used in e.g Shor’s algorithm and the phase estimation quantum algorithm.\n\n## 5 Abelian Stabilizer Formalism\n\nIn this section we develop further the stabilizer formalism for finite Abelian groups as started in [VDNest_12_QFTs]. We provide new analytic and algorithmic tools to describe them and analyze their properties. Throughout this section we consider an arbitrary Abelian group of the form .\n\n### 5.1 Stabilizer states and codes\n\nLet be a subgroup of the Pauli group . Then is said to be a stabilizer group (over ) if there exists a non-zero vector which is invariant under all elements in i.e. for every . The linear subspace is called the stabilizer code associated with . If is one-dimensional, its unique element (up to a multiplicative constant) is called the stabilizer state associated with . In this work we will mainly be interested in stabilizer states. Occasionally, however, it will be useful to consider the general setting of stabilizer codes (cf. e.g. theorem 3).\n\nNote that every stabilizer group is Abelian. To see this, consider a state which is invariant under the action of all elements in and consider two arbitrary . Then (22) implies that there exists a complex phase such that . It follows that , where we have used that . We thus find that so that (i.e. and commute).\n\nConversely, not every Abelian subgroup of the Pauli group is a stabilizer group. A simple counterexample is the group where is the identity operator acting on .\n\nThe support of a stabilizer code is the set of all for which has a nonzero overlap with i.e. there exists such that . The support of a stabilizer state is simply the set of all for which .\n\n### 5.2 Label groups\n\nLet be a stabilizer group over . The diagonal subgroup is the subgroup of formed by its diagonal operators i.e. it consists of all operators in of the form . Second, we introduce two subgroups and of called the label groups of :\n\n H ={h∈G:there exists γaZ(g)X(h)∈S}, (34) D ={g∈G:there exists γaZ(g)∈D}, (35)\n\nUsing (22) it is straightforward to verify that is indeed a subgroup of . To prove that is a subgroup as well, one argues as follows. Let be a Pauli operator with label . We call the “-component” and the “-component” of . Denote the -component formally by . Then is the image of under the map . The commutation relations (22) yield\n\n φ(στ)=φ(σ)+φ(τ) for all σ,τ∈S. (36)\n\nThis implies that is a homomorphism from to . It follows that is a subgroup of .\n\n###### Proposition 5 (Label groups).\n\nLet be a stabilizer group and assume that the labels of polylog generators of are given as an input. Then the label groups of have the following properties:\n\n1. ;\n\n2. Generating sets of , can be efficiently computed classically;\n\n3. The labels of a generating set of can be efficiently computed classically.\n\n• Property (i) is a straightforward consequence of the commutation relations given in proposition 3 and the definition of orthogonal subgroup (4). To show property (ii), recall that the map defined above is a homomorphism from to with Im. Suppose that is generated by . Then is generated by : this yields an efficient method to compute generators of . To prove the second statement of (ii) as well as (iii) requires more work. The argument is a direct generalization of the proof of lemma 9 in [VDNest_12_QFTs] and the reader is referred to this work.\n\n### 5.3 Certificates\n\nThe main purpose of this section is to provide a criterion to verify when a stabilizer group gives rise to a one-dimensional stabilizer code i.e. a stabilizer state. This is accomplished in corollary 1. To arrive at this statement we first analyze how the the dimension of a general stabilizer code is related the structure of its stabilizer group.\n\n###### Theorem 3 (Structure Test).\n\nLet be a stabilizer group with stabilizer code . Then there exists such that\n\n (i) supp(V)=g0+D⊥,(ii) dim(V)=\|D⊥\|\|H\|, (37)\n\nwhere , are the label subgroups of . Furthermore, there exist efficient classical algorithms to compute a representative of the support, a generating set of and the dimension .\n\nBefore proving theorem 3, we note that combining property (ii) together with proposition 5(i) immediately yield:\n\n###### Corollary 1 (Uniqueness Test).\n\nLet be a stabilizer group with stabilizer code . Then is one-dimensional if and only if and are dual orthogonal subgroups: .\n\nTheorem 3(ii) also leads to an alternative formula for the dimension of a stabilizer code:\n\n###### Corollary 2.\n\nThe dimension of equals .\n\n• Consider the map as in section 5.2, which is a group homomorphism with image . Furthermore the kernel of is precisely the diagonal subgroup of . Since it follows that . Finally we claim that and are isomorphic groups so that . To prove this, consider the map that sends to . Using (22) it follows that this map is a homomorphism; furthermore, it is a surjective one by definition of , and thus . The kernel of is the set of all having the form . But the only operator in proportional to the identity is the identity itself, since otherwise cannot have a common eigenstate. This shows that the kernel of is trivial, so that and are isomorphic, as claimed. The resulting identity together with (recall lemma 1) and theorem 3(ii) proves the result.\n\nThe result in corollary 2 is well known for stabilizer codes over qubits [Gottesman_PhD_Thesis, nielsen_chuang] (i.e. where so that ) and qudits (where ) [Gottesman_PhD_Thesis, gheorghiu11Qudit_Stabilisers].\n\nWe now prove theorem 3 using techniques developed in [nest_MMS] where the properties of so-called M-spaces were studied. We briefly recall basic concepts and results.\n\nA unitary operator acting on is said to be monomial if it can be written as a product where is diagonal and is a permutation matrix. A subspace of is called an M-space if there exists a group of monomial unitary operators such that iff for every . The group is called a stabilizer group of . If is one-dimensional, its unique (up to a multiplicative factor) element is called an M-state. The support of is defined analogously to the support of a stabilizer code i.e. it is the set of all such that has a nontrivial overlap with . With this terminology, every stabilizer code is an instance of an M-space and every stabilizer state is an M-state. To see this, note that every Pauli operator is a monomial unitary operator. Indeed, can be written as a product where is diagonal and is a permutation matrix.\n\nWe introduce some further terminology. Let be an arbitrary monomial stabilizer group. For every , let be the subset of consisting of all satisfying i.e. acts trivially on , up to an overall phase. This subset is easily seen to be a subgroup of . Also, we define the orbit of as:\n\n Og={h:∃U∈G s.t. U\|g⟩∝\|h⟩} (38)\n\nIn the following result the support of any M-space is characterized in terms of the orbits and the subgroups .\n\n###### Theorem 4 (Support of M-space [nest_MMS]).\n\nConsider an M-space with monomial stabilizer group . Then the following statements hold:\n\n• There exist orbits such that and\n\n (39)\n• Consider and an arbitrary set of generators of . Then supp() if and only if for every .\n\nUsing this result, we can now prove theorem 3.\n\n• [of theorem 3] We apply theorem 4 to the Pauli stabilizer group . In this case, the group and the orbit fulfill\n\n Og=g+H,Sg=D. (40)\n\nTo demonstrate the first identity in (40), we use (20) which implies for every . To show the second identity, first note that for every diagonal operator , showing that . Conversely, if has label then . Since the state is an eigenvector of ; this can only be true if , showing that .\n\nUsing proposition 5, we can efficiently compute the labels of a generating set of , where for some and . Owing to theorem 4(ii), any belongs to the support of if and only if for every . Equivalently, satisfies\n\n γaiχgi(g)=1for alli=1,…,r. (41)\n\nThis system of equations is of the type considered in section 2.5 (cf. lemma 3 and the example after it) and can, therefore, be transformed into an equivalent linear system over groups: . The elements generate the label group , and thus the homomorphism defined by satisfies . Since the system is linear, its solutions form a coset of the form , for some particular solution . This shows statement (i).\n\nFurther, we combine (i) with theorem 4(i) to get a short proof of (ii): the equation\n\n supp(V)=Og1∪⋯∪Ogd=(g1+H)∪⋯∪(gd+H)=g0+D⊥\n\nimplies, computing the cardinalities of the sets involved, that .\n\nFinally, the ability to compute and to find generators of efficiently classically follows applying theorem 1 to a linear system described by a matrix that defines a homomorphism from to , with . Furthermore, we can compute directly using formula (ii) together with proposition 5 and the algorithms of lemma 2.\n\n## 6 Pauli measurements in the stabilizer formalism\n\n### 6.1 Definition\n\nAssociated with every Pauli operator as in (21) we will consider a quantum measurement in the eigenbasis of . Consider the spectral decomposition where are the distinct eigenvalues of and is the projector on the eigenspace associated with eigenvalue . Given a state" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91066915,"math_prob":0.9719547,"size":42400,"snap":"2021-04-2021-17","text_gpt3_token_len":9219,"char_repetition_ratio":0.14862251,"word_repetition_ratio":0.04342086,"special_character_ratio":0.20556603,"punctuation_ratio":0.11341577,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9972527,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-14T08:48:16Z\",\"WARC-Record-ID\":\"<urn:uuid:a4aa6a59-45fb-4a47-8cfe-e3fe9929f651>\",\"Content-Length\":\"1049654\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6f453d03-4f81-4623-b418-f3a679378234>\",\"WARC-Concurrent-To\":\"<urn:uuid:f526796d-8152-4abe-9716-f74ea3b0fa05>\",\"WARC-IP-Address\":\"172.67.158.169\",\"WARC-Target-URI\":\"https://www.arxiv-vanity.com/papers/1210.3637/\",\"WARC-Payload-Digest\":\"sha1:LHCTFUGYPVHZUO2BSJHCZM3A7H7RIZCT\",\"WARC-Block-Digest\":\"sha1:V435ZPBHPRFKQPDRNWKKEZNE7X7347RI\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038077336.28_warc_CC-MAIN-20210414064832-20210414094832-00273.warc.gz\"}"}
https://search.r-project.org/CRAN/refmans/asbio/html/ci.impt.html	[ "ci.impt {asbio} R Documentation\n\n## Confidence interval for the product of two proportions\n\n### Description\n\nProvides one and two-tailed confidence intervals for the true product of two proportions.\n\n### Usage\n\n\nci.impt(y1, n1, y2 = NULL, n2 = NULL, avail.known = FALSE, pi.2 = NULL,\nconf = .95, x100 = TRUE, alternative = \"two.sided\", bonf = TRUE, wald = FALSE)\n\n\n### Arguments\n\n y1 The number of successes associated with the first proportion. n1 The number of trials associated with the first proportion. y2 The number of successes associated with the second proportion. Not used if avail.known = TRUE. n2 The number of trials associated with the first proportion. Not used if avail.known = TRUE. avail.known Logical. Are the proportions π_{2i} known? If avail.known = TRUE these proportions should specified in the pi.2 argument. pi.2 Proportions for π_{2i}. Required if avail.known = TRUE. conf Confidence level, i.e., 1 - α. x100 Logical. If true, estimate is multiplied by 100. alternative One of \"two.sided\", \"less\", \"greater\". Allows lower, upper, and two-tailed confidence intervals. If alternative = \"two.sided\" (the default), then a conventional two-sided confidence interval is given. The specifications alternative = \"less\" and alternative = \"greater\" provide lower and upper tailed CIs, respectively. bonf Logical. If bonf = TRUE, and the number of requested intervals is greater than one, then Bonferroni-adjusted intervals are returned. wald Logical. If avail.known = TRUE one can apply one of two standard error estimators. The default is a delta-derived estimator. If wald = TRUE is specified a modified Wald standard error estimator is used.\n\n### Details\n\nLet Y_1 and Y_2 be multinomial random variables with parameters n_1, π_{1i} and n_2, π_{2i}, respectively; where i = 1,2,…, r. Under delta derivation, the log of the products of π_{1i} and π_{2i} (or the log of a product of π_{1i} and π_{2i} and a constant) is asymptotically normal with mean log(π_{1i} \\times π_{2i}) and variance (1 - π_{1i})/π_{1i}n_1 + (1 - π_{2i})/ π_{2i}n_2. Thus, an asymptotic (1 - α)100 percent confidence interval for π_{1i} \\times π_{2i} is given by:\n\n\\hat{π}_{1i} \\times \\hat{π}_{2i} \\times \\exp(\\pm z_{1-(α/2)}\\hat{σ}_i)\n\nwhere: \\hat{σ}^2_i = \\frac{(1 - \\hat{π}_{1i})}{\\hat{π}_{1i}n_1} + \\frac{(1 - \\hat{π}_{2i})}{\\hat{π}_{2i}n_2} and z_{1-(α/2)} is the standard normal inverse CDF at probability 1 - α.\n\n### Value\n\nReturns a list of class = \"ci\". Printed results are the parameter estimate and confidence bounds.\n\n### Note\n\nMethod will perform poorly given unbalanced sample sizes.\n\nKen Aho\n\n### References\n\nAho, K., and Bowyer, T. 2015. Confidence intervals for a product of proportions: Implications for importance values. Ecosphere 6(11): 1-7.\n\nci.prat, ci.p\nci.impt(30,40, 25,40)" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7313202,"math_prob":0.992323,"size":1897,"snap":"2021-43-2021-49","text_gpt3_token_len":644,"char_repetition_ratio":0.124669835,"word_repetition_ratio":0.08143322,"special_character_ratio":0.36531365,"punctuation_ratio":0.16421568,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9985868,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T18:50:55Z\",\"WARC-Record-ID\":\"<urn:uuid:e6f75779-df8b-49a6-912d-47793324d334>\",\"Content-Length\":\"5464\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e73efe2a-8061-44a0-a6f8-d7afb9e3c417>\",\"WARC-Concurrent-To\":\"<urn:uuid:8c617b5e-4467-4bb9-960a-05750bd00bd1>\",\"WARC-IP-Address\":\"137.208.57.46\",\"WARC-Target-URI\":\"https://search.r-project.org/CRAN/refmans/asbio/html/ci.impt.html\",\"WARC-Payload-Digest\":\"sha1:J4BIB4Y7G4UP27TCDMGW7WCFIKPC4FWU\",\"WARC-Block-Digest\":\"sha1:YOCRIPNUQMEF35BZ6N2ZOSP3723FRD63\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964360881.12_warc_CC-MAIN-20211201173718-20211201203718-00175.warc.gz\"}"}
https://support.bitmain.com/hc/en-us/community/posts/900001552946-Antminer-s19-pro-power-consumption-for-a-month	[ "1 comment\n\n•", null, "3250W = 3.25kw/h (3.250.11€= 0.3575€/h)\n\nso running it 24h/day = 3.2524= 78kw/h (780.11€= 8.58€/day)\n\nso running it a week 7 days a week= 787=546kw/h (5460.11€= 60.06€/week)\n\nso running it a month 30 days a month = 7830 = 2340kw/h (23400.11€= 257.4€/month)\n\nSo running it a year 365 days a year = 78365= 28470kw/h (28470*0.11€=3131.70€/year)\n\nif your kw/h price is like ours 0.11€ then your" ]	[ null, "https://secure.gravatar.com/avatar/26b355a234117f8defc8e2e01a254700", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8456754,"math_prob":0.9735314,"size":765,"snap":"2022-27-2022-33","text_gpt3_token_len":278,"char_repetition_ratio":0.13797635,"word_repetition_ratio":0.0,"special_character_ratio":0.42745098,"punctuation_ratio":0.10695187,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98093915,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-14T10:34:18Z\",\"WARC-Record-ID\":\"<urn:uuid:54b75b5d-dd18-43bc-b4bb-4334cbdd3124>\",\"Content-Length\":\"25274\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5190b7d5-c34b-4126-8447-832d8ea60335>\",\"WARC-Concurrent-To\":\"<urn:uuid:2e01b44f-9dc9-452d-98de-b76544ac5a90>\",\"WARC-IP-Address\":\"104.18.248.37\",\"WARC-Target-URI\":\"https://support.bitmain.com/hc/en-us/community/posts/900001552946-Antminer-s19-pro-power-consumption-for-a-month\",\"WARC-Payload-Digest\":\"sha1:YB67TPTGZN2D5LTCDSUT6QIZSJWBZGN2\",\"WARC-Block-Digest\":\"sha1:GAEP77DBFAVYIMG6LLKGWMOKQHCAU22C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572021.17_warc_CC-MAIN-20220814083156-20220814113156-00477.warc.gz\"}"}
http://ezphysics.org/dokuwiki-2010-11-07a/doku.php?id=network_protocol	[ "# EZPhysics Network Protocol\n\nEZPhysics provides a network interface for sending and receiving data from the ODE simulation. This is done through predefined packets. This page lists what these packages contain and in what order (has determined in EZNetwork class, at EZPhysicsNetwork.cpp).\n\nAn EZPhysics Network Message has the following format:\n\n## Send Packets\n\nSend Packets refers to the packets sent from EZPhysics, which contain the latest simulation's data.\n\n#### EZNETWORK_SEND_COLLISION 01\n\nUsually sent in pairs, refers to the point of contact between two Body's.\n\n1. Float X of the contact point\n2. Float Y of the contact point\n3. Float Z of the contact point\n4. Float depth (penetration of the collision)\n\n#### EZNETWORK_SEND_LIMB 02\n\nA Body's output.\n\n1. Float X of the position vector\n2. Float Y of the position vector\n3. Float Z of the position vector\n4. Float W of the rotation quaternion\n5. Float X of the rotation quaternion\n6. Float Y of the rotation quaternion\n7. Float Z of the rotation quaternion\n8. Float X of the force vector\n9. Float Y of the force vector\n10. Float Z of the force vector\n11. Float X of the torque vector\n12. Float Y of the torque vector\n13. Float Z of the torque vector\n14. Float Unused\n15. Float X of the linear velocity vector\n16. Float Y of the linear velocity vector\n17. Float Z of the linear velocity vector\n18. Float X of the angular velocity vector\n19. Float Y of the angular velocity vector\n20. Float Z of the angular velocity vector\n21. Float Unused\n\n#### EZNETWORK_SEND_JOINTAXIS 03\n\nRefers to each of the possibly several axis of a Joint.\n\n1. Float displacement value of the axis (Relevant for the Slider Joint)\n2. Float angular velocity at the axis\n\n#### EZNETWORK_SEND_JOINTFEEDBACK 04\n\nThe feedback can be used by the user, so that it is known how much force an individual joint exerts.\n\n1. Float X of the force vector of body 1\n2. Float Y of the force vector of body 1\n3. Float Z of the force vector of body 1\n4. Float X of the torque vector of body 1\n5. Float Y of the torque vector of body 1\n6. Float Z of the torque vector of body 1\n7. Float X of the force vector of body 2\n8. Float Y of the force vector of body 2\n9. Float Z of the force vector of body 2\n10. Float X of the torque vector of body 2\n11. Float Y of the torque vector of body 2\n12. Float Z of the torque vector of body 2\n\n#### EZNETWORK_SEND_TIMESTAMP 05\n\nCan be used to determine the current time of simulation.\n\n1. Long ODE step number (since the beginning of the simulation)\n2. Float ODE step size\n\nReceive Packets refers to the packets received in EZPhysics, which contain the control commands to apply in the simulation.\n\n#### EZNETWORK_RECV_RESET 01\n\nCommands the simulation to restart.\n\n#### EZNETWORK_RECV_AXIS_FORCE 02\n\nRepresents a raw torque applied in an axis.\n\n1. Float torque value to apply to the axis 1 of a Joint\n2. Float torque value to apply to the axis 2 of a Joint (May be invalid)\n3. Float torque value to apply to the axis 3 of a Joint (May be invalid)\n\n#### EZNETWORK_RECV_AXIS_MOTOR 03\n\nProvides a common servo motor interface, target velocity and maximum torque.\n\n1. Float target velocity to apply on axis 1 of a Joint\n2. Float maximum torque imposed on axis 1 of a Joint\n3. Float target velocity to apply on axis 2 of a Joint (May be invalid)\n4. Float maximum torque imposed on axis 2 of a Joint (May be invalid)\n5. Float target velocity to apply on axis 3 of a Joint (May be invalid)\n6. Float maximum torque imposed on axis 3 of a Joint (May be invalid)", null, "" ]	[ null, "http://ezphysics.org/dokuwiki-2010-11-07a/lib/exe/indexer.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8222936,"math_prob":0.9551236,"size":3105,"snap":"2023-40-2023-50","text_gpt3_token_len":737,"char_repetition_ratio":0.25282168,"word_repetition_ratio":0.5008183,"special_character_ratio":0.2347826,"punctuation_ratio":0.03577513,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99284935,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T21:47:26Z\",\"WARC-Record-ID\":\"<urn:uuid:d1a0602d-59db-42e4-b86b-df2529a09ef9>\",\"Content-Length\":\"17146\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:937ed468-4f61-48f9-92ad-d23b2d8761ec>\",\"WARC-Concurrent-To\":\"<urn:uuid:35fdf516-4c22-4431-81b9-6ca1942b7c44>\",\"WARC-IP-Address\":\"176.58.105.123\",\"WARC-Target-URI\":\"http://ezphysics.org/dokuwiki-2010-11-07a/doku.php?id=network_protocol\",\"WARC-Payload-Digest\":\"sha1:5RYZWVRQBLFXSLZSL3AWPLP43KPJSWY2\",\"WARC-Block-Digest\":\"sha1:ZHCFSVMBQ5SJCNU7RC44KMLDNBXO5CPL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100972.58_warc_CC-MAIN-20231209202131-20231209232131-00321.warc.gz\"}"}
https://zbmath.org/0763.46028	[ "## A Parseval equation and a generalized finite Hankel transformation.(English)Zbl 0763.46028\n\nFor $$\\mu\\geq-{1\\over 2}$$ a space $$S_ \\mu$$ of certain $$C^ \\infty$$- functions on $$]0,1]$$ and a sequence space $$L_ \\mu$$ are introduced. If $$J_ \\mu$$ denotes the Bessel function of first kind and order $$\\mu$$ and if $$(\\lambda_ n)_{n\\in\\mathbb{N}_ 0}$$ denotes the positive roots of $$J_ \\mu$$ (arranged increasingly) then the finite Hankel transform $(h_ \\mu^* f)(n):=2J_{\\mu+1}^{-2}(\\lambda_ n) \\int_ 0^ 1 J_ \\mu(\\lambda_ n x)f(x)dx, \\quad f\\in S_ \\mu, \\quad \\mu\\in\\mathbb{N}_ 0,$ is shown to be an isomorphism between $$S_ \\mu$$ and $$L_ \\mu$$. Then the generalized finite Hankel transform $$h_ \\mu': S_ \\mu'\\to L_ \\mu'$$ is defined as the adjoint of $$(h_ \\mu^*)^{-1}$$ and it is shown that it extends a previous definition given in the literature.\n\n### MSC:\n\n 46F12 Integral transforms in distribution spaces 44A15 Special integral transforms (Legendre, Hilbert, etc.)\nFull Text:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6522857,"math_prob":1.0000001,"size":1342,"snap":"2023-14-2023-23","text_gpt3_token_len":463,"char_repetition_ratio":0.12032885,"word_repetition_ratio":0.03076923,"special_character_ratio":0.36214605,"punctuation_ratio":0.16845877,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000026,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-28T18:11:51Z\",\"WARC-Record-ID\":\"<urn:uuid:e1c6599f-315d-4855-b090-17a8ec17f905>\",\"Content-Length\":\"51458\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36212907-3555-4d88-b24f-9025ecdc72b6>\",\"WARC-Concurrent-To\":\"<urn:uuid:7ea70b79-02f7-4703-893a-babb3bb8cf66>\",\"WARC-IP-Address\":\"141.66.194.2\",\"WARC-Target-URI\":\"https://zbmath.org/0763.46028\",\"WARC-Payload-Digest\":\"sha1:U2KEENCB7Q2NR24AWCR34LY22PMHP2RH\",\"WARC-Block-Digest\":\"sha1:RIYLKCK2Z3VB2WE2CT3ZPE7N7OOLVY3W\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948868.90_warc_CC-MAIN-20230328170730-20230328200730-00771.warc.gz\"}"}
http://onlinecalc.sdsu.edu/the_limiting_contraction_ratio_revisited.html	[ "", null, "The Limiting Contraction RatioRevisited Nicole R. Nuccitelli and Victor M. Ponce April 2014\n\n ABSTRACT Henderson's formulations of the energy-based and momentum-based limiting contraction ratios are reviewed (Henderson 1966). Henderson's explicit energy-based equation is found to be correct, however, his implicit momentum-based equation is found to be incorrect. A new explicit momentum-based equation is derived, rendering the implicit formulation unnecessary. An online calculator enables the calculation of the limiting contraction ratio for both energy and momentum formulations.\n\n1. THE LIMITING CONTRACTION RATIO\n\nThe limiting contraction ratio σ is the ratio of contraction width bc to upstream channel width b1 (σ = bc /b1), or, alternatively, downstream channel width b3 (σ = bc /b3), that produces critical flow at the contraction in a rectangular channel. The ratio has an upper limit σ = 1 when the upstream or downstream flow is critical.\n\nAccording to Henderson (1966), the ratio σ may be calculated in two ways: (1) using an energy balance between the upstream and critical contraction sections, or (2) using a momentum balance between the critical contraction and downstream sections. Henderson has argued that the momentum balance is more likely to be correct because it does not depend on an assumption of energy conservation. However, Henderson's implicit formulation of the momentum-based limiting contraction ratio appears to be incorrect. These propositions are now substantiated.\n\n2. ENERGY-BASED EQUATION FOR LIMITING CONTRACTION RATIO\n\nThe energy-based equation is derived by equating the specific energy at the upstream flow section (Section 1) with the specific energy at critical flow at the contraction (Section 2, or Section c) (Fig. 1):\n\n E1 = E2 = Ec (1)\n\nThe specific energy of the upstream flow is:\n\n v12 E1 = y1 + _______ 2 g (2)\n\nThe Froude number at the upstream section is defined as follows:\n\n v12 F12 = _______ g y1 (3)\n\nThus, Eq. 2 reduces to:\n\n F12 E1 = y1 [ 1 + ______ ] 2 (4)\n\nBy definition, the critical depth is:\n\n F12 yc = (2/3) E1 = (2/3) y1 [ 1 + ______ ] 2 (5)\n\nThus:\n\n yc F12 _____ = (2/3) [ 1 + ______ ] y1 2 (6)\n\nOr, alternatively:\n\n yc _____ = (1/3) [ 2 + F12 ] y1 (7)\n\nFrom continuity:\n\n v1 y1 b1 = vc yc bc (8)\n\nThe limiting contraction ratio σ is:\n\n bc v1 y1 σ = _______ = ________ b1 vc yc (9)\n\nOr:\n\n v1 σ = _____________ vc (yc /y1 ) (10)\n\nOr:\n\n v1 σ = ___________________ (g yc)1/2 (yc /y1 ) (11)\n\nOr:\n\n v1 σ = ______________________ (g y1)1/2 (yc /y1 )3/2 (12)\n\nReplacing Eq. 3 in Eq. 12:\n\n F1 σ = ______________ (yc /y1 )3/2 (13)\n\nReplacing Eq. 7 in Eq. 13:\n\n F1 σ = ________________________ (1/3)3/2 (2 + F12) 3/2 (14)\n\nSimplifying Eq. 14:\n\n 33/2 F1 σ = _________________ (2 + F12) 3/2 (15)\n\nEquation 15 is the energy-based limiting contraction ratio.\n\nSquaring Eq. 15:\n\n 33 F12 σ2 = ________________ (2 + F12) 3 (16)\n\nEquation 16 is the same as that presented by Henderson for the limiting contraction ratio (op. cit., Eq. 7-35, p. 267).", null, "Fig. 1 Definition sketch.\n\n3. MOMENTUM-BASED EQUATION FOR LIMITING CONTRACTION RATIO\n\nThe momentum-based equation is derived by equating the specific force at critical flow at the contraction (Section 2, or Section c) with the specific force at the downstream flow section (Section 3).\n\n M3 = M2 = Mc (17)\n\nThe specific force at the downstream flow section is:\n\n q32 y32 M3 = _______ + _______ g y3 2 (18)\n\nReplacing the discharge Q:\n\n Q2 y32 M3 = ___________ + ______ g y3 b32 2 (19)\n\nFrom continuity:\n\n Q = v3 y3 b3 = vc yc bc (20)\n\nThus:\n\n v32 y32 y32 M3 = __________ + ______ g y3 2 (21)\n\nThe Froude number at the downstream section is defined as follows:\n\n v32 F32 = _______ g y3 (22)\n\nThus, Eq. 21 reduces to:\n\n 1 M3 = y32 ( ____ + F32 ) 2 (23)\n\nThe specific force at the contraction is:\n\n qc2 yc2 Mc = _______ + _______ g yc 2 (24)\n\nReplacing the discharge Q:\n\n Q2 yc2 Mc = ___________ + ______ g yc bc2 2 (25)\n\nFrom continuity:\n\n v32 y32 b32 yc2 Mc = _______________ + ______ g yc bc2 2 (26)\n\nOr:\n\n v32 y33 b32 yc2 Mc = _______________ + ______ g yc bc2 y3 2 (27)\n\nReplacing Eq. 22 in Eq. 27:\n\n F32 y33 yc2 Mc = ___________ + ______ σ2 yc 2 (28)\n\nBy definition, the critical depth is:\n\n q2 yc = ( ____ ) 1/3 g (29)\n\nOr:\n\n Q2 yc = ( ________ ) 1/3 bc2g (30)\n\nFrom continuity:\n\n v32 y32 b32 yc = ( _____________ ) 1/3 bc2g (31)\n\nOr:\n\n v32 y33 b32 yc = ( _____________ ) 1/3 bc2g y3 (32)\n\nReplacing Eq. 22 in Eq. 32:\n\n F32 y33 yc = ( _________ ) 1/3 σ2 (33)\n\nReplacing Eq. 33 in Eq. 28:\n\n F32 y32 σ2/3 F32 y33 Mc = ______________ + (1/2) ( _________ )2/3 σ2 F32/3 σ2 (34)\n\nReducing terms:\n\n F34/3 Mc = (3/2) ( ________ ) y32 σ4/3 (35)\n\nEquating Eqs. 23 and 35:\n\n 1 F34/3 ( ___ + F32 ) = (3/2) ( ________ ) 2 σ4/3 (36)\n\nReducing:\n\n 33/4 F3 σ = _____________________ ( 1 + 2 F32 ) 3/4 (37)\n\nEquation 37 is the explicit formulation of the momentum-based limiting contraction ratio.\n\n4. IMPLICIT MOMENTUM-BASED FORMULATION\n\nTo derive an implicit formulation, Eq. 36 is expressed as follows:\n\n 3 F34/3 σ4/3 = _______________ 1 + 2 F32 (38)\n\nOr:\n\n (3/σ) F34/3 σ1/3 = _______________ 1 + 2 F32 (39)\n\nReducing:\n\n (3/σ)3 F34 σ = _________________ (1 + 2 F32)3 (40)\n\nEquation 40 differs slightly from Henderson's Eq. 7-36, page 267, repeated here:\n\n (2 + 1/σ)3 F34 σ = __________________ (1 + 2 F32)3 (41)\n\nThus, Henderson's implicit equation for the momentum-based limiting contraction ratio (Eq. 41) appears to be incorrect.\n\n5. SUMMARY\n\nTwo explicit equations for the limiting contraction ratio, the first based on an energy balance, and the second based on a momentum balance, are derived following Henderson (1966). An implicit equation based on momentum balance is also derived, to parallel Henderson's treatment.\n\nThe explicit energy-based equation, which is shown to be same as Henderson's, is:\n\n 33/2 F1 σ = _________________ (2 + F12) 3/2 (15)\n\nThe explicit momentum-based equation, not presented by Henderson, is:\n\n 33/4 F3 σ = __________________ (1 + 2 F32) 3/4 (37)\n\nNote the great resemblance between Eq. 15 (energy-based) and Eq. 37 (momentum-based).\n\nThe implicit momentum-based equation derived here (Eq. 40) differs slightly from that of Henderson (Eq. 41), suggesting that the latter is incorrect.\n\nThe online calculator ONLINE_LIMITING_CONTRACTION calculates the energy-based and momentum-based limiting contraction ratios for a pair of Froude numbers F1 and F3. Additionally, the online calculator ONLINE_LIMITING_CONTRACTION_SET calculates the set of energy-based and momentum-based limiting contraction ratios for a given range of Froude numbers and Froude number interval.\n\nREFERENCES\n\nHenderson, F. M., 1966. Open channel flow. MacMillan Publishing Co., Inc., New York." ]	[ null, "http://onlinecalc.sdsu.edu/the_limiting_contraction_ratio_revisited_01_400.jpg", null, "http://onlinecalc.sdsu.edu/the_limiting_contraction_ratio_revisited_01_600.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7919302,"math_prob":0.9934593,"size":6509,"snap":"2019-13-2019-22","text_gpt3_token_len":2065,"char_repetition_ratio":0.19861645,"word_repetition_ratio":0.11968777,"special_character_ratio":0.4209556,"punctuation_ratio":0.11497976,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99497634,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-20T06:52:43Z\",\"WARC-Record-ID\":\"<urn:uuid:413fc847-8f10-44ba-958c-35ca2ce61e9a>\",\"Content-Length\":\"36815\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0daf21e2-c1de-4065-a41a-205aadb82769>\",\"WARC-Concurrent-To\":\"<urn:uuid:ce24b976-8497-4d0b-a3a5-1fd45300c08c>\",\"WARC-IP-Address\":\"130.191.35.138\",\"WARC-Target-URI\":\"http://onlinecalc.sdsu.edu/the_limiting_contraction_ratio_revisited.html\",\"WARC-Payload-Digest\":\"sha1:N5ZZ4RAFLLF6OSGWEE5QY3WFQDHOTONI\",\"WARC-Block-Digest\":\"sha1:Q37VZPG4ZHBTWEOFFVVRH6Y2WKDGEREH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202303.66_warc_CC-MAIN-20190320064940-20190320090940-00554.warc.gz\"}"}
https://kmmiles.com/327689-km-in-miles	[ "kmmiles.com\n\nSearch\n\n# 327689 km in miles\n\n## Result\n\n327689 km equals 203494.869 miles\n\nYou can also convert 327689 km to mph.\n\n## Conversion formula\n\nMultiply the amount of km by the conversion factor to get the result in miles:\n\n327689 km × 0.621 = 203494.869 mi\n\n## How to convert 327689 km to miles?\n\nThe conversion factor from km to miles is 0.621, which means that 1 km is equal to 0.621 miles:\n\n1 km = 0.621 mi\n\nTo convert 327689 km into miles we have to multiply 327689 by the conversion factor in order to get the amount from km to miles. We can also form a proportion to calculate the result:\n\n1 km → 0.621 mi\n\n327689 km → L(mi)\n\nSolve the above proportion to obtain the length L in miles:\n\nL(mi) = 327689 km × 0.621 mi\n\nL(mi) = 203494.869 mi\n\nThe final result is:\n\n327689 km → 203494.869 mi\n\nWe conclude that 327689 km is equivalent to 203494.869 miles:\n\n327689 km = 203494.869 miles\n\n## Result approximation\n\nFor practical purposes we can round our final result to an approximate numerical value. In this case three hundred twenty-seven thousand six hundred eighty-nine km is approximately two hundred three thousand four hundred ninety-four point eight six nine miles:\n\n327689 km ≅ 203494.869 miles\n\n## Conversion table\n\nFor quick reference purposes, below is the kilometers to miles conversion table:\n\nkilometers (km) miles (mi)\n327690 km 203495.49 miles\n327691 km 203496.111 miles\n327692 km 203496.732 miles\n327693 km 203497.353 miles\n327694 km 203497.974 miles\n327695 km 203498.595 miles\n327696 km 203499.216 miles\n327697 km 203499.837 miles\n327698 km 203500.458 miles\n327699 km 203501.079 miles\n\n## Units definitions\n\nThe units involved in this conversion are kilometers and miles. This is how they are defined:\n\n### Kilometers\n\nThe kilometer (symbol: km) is a unit of length in the metric system, equal to 1000m (also written as 1E+3m). It is commonly used officially for expressing distances between geographical places on land in most of the world.\n\n### Miles\n\nA mile is a most popular measurement unit of length, equal to most commonly 5,280 feet (1,760 yards, or about 1,609 meters). The mile of 5,280 feet is called land mile or the statute mile to distinguish it from the nautical mile (1,852 meters, about 6,076.1 feet). Use of the mile as a unit of measurement is now largely confined to the United Kingdom, the United States, and Canada." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.82136345,"math_prob":0.9350833,"size":2335,"snap":"2023-40-2023-50","text_gpt3_token_len":647,"char_repetition_ratio":0.17245817,"word_repetition_ratio":0.0,"special_character_ratio":0.3665953,"punctuation_ratio":0.12240664,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97920114,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T15:35:20Z\",\"WARC-Record-ID\":\"<urn:uuid:1dad222d-93bf-4353-a2f5-d67b84f7b52f>\",\"Content-Length\":\"17873\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:db7e5726-c8d6-43c2-8eaf-78d60acfec39>\",\"WARC-Concurrent-To\":\"<urn:uuid:48265296-b333-4076-ab61-d1b0d92dd212>\",\"WARC-IP-Address\":\"104.21.6.102\",\"WARC-Target-URI\":\"https://kmmiles.com/327689-km-in-miles\",\"WARC-Payload-Digest\":\"sha1:SQ7KQ2TPEZ6RKS3RBXVNF7PZPISXFJD6\",\"WARC-Block-Digest\":\"sha1:H5ZIRJ4MV7XPPJG57NH4AZQJCJXAQ6TL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511000.99_warc_CC-MAIN-20231002132844-20231002162844-00707.warc.gz\"}"}
http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/eley1.html	[ "", null, "", null, "", null, "SEARCH HOME", null, "Math Central Quandaries & Queries", null, "", null, "Question from ELEY, a parent: WHAT IS THE HEIGHT OF A TRIANGLE IF THE AREA IS 32.4 AND A BASE OF 6.75? PLEASE GIVE ME THE ORDER OF OPERATION TO SOLVE THIS PROBLEM.", null, "Eley,\n\nThe area of a triangle is one-half the base times the height. You have an area of 32.4 square units and a base of 6.75 units. If the height is h units then\n\n32.4 = 1/2 × 6.75 × h.\n\nSolve for h.\n\nPenny\n\nFor a triangle\n\nArea = base x height /2\n\nPut in numbers: say we had area 100 and base 20\n\n100 = 20 x height / 2\n\nNow isolate the unknown on one side by doing the same thing to both sides. For instance, to get rid of the \"/2\" you can multiply both sides by 2 and the equations remains valid:\n\n100 x 2 = 20 x height\n200 = 20 x height\n200/20 = height\n10 = height\n\nGood Hunting!\n-RD", null, "", null, "", null, "", null, "", null, "Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences." ]	[ null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/search.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/pixels/transparent.gif", null, "http://mathcentral.uregina.ca/lid/images/qqsponsors.gif", null, "http://mathcentral.uregina.ca/lid/images/mciconnotext.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89404106,"math_prob":0.9867477,"size":626,"snap":"2020-24-2020-29","text_gpt3_token_len":169,"char_repetition_ratio":0.12379421,"word_repetition_ratio":0.0,"special_character_ratio":0.29392973,"punctuation_ratio":0.08759124,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99729097,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-08T05:41:37Z\",\"WARC-Record-ID\":\"<urn:uuid:d1eda487-6add-46a6-a7cf-effbb8718980>\",\"Content-Length\":\"7467\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:94d9d12a-bfd5-420e-b408-f84f432e0153>\",\"WARC-Concurrent-To\":\"<urn:uuid:aa278de3-69d3-4447-ba13-8e9a4f6ea49e>\",\"WARC-IP-Address\":\"142.3.156.43\",\"WARC-Target-URI\":\"http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/eley1.html\",\"WARC-Payload-Digest\":\"sha1:YUNHF6BOYCH6JNKIID4EYVNIXPRLSDQV\",\"WARC-Block-Digest\":\"sha1:LHXECS2CA7TB3RC7RPO6RGN33UAJCBIR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655896374.33_warc_CC-MAIN-20200708031342-20200708061342-00575.warc.gz\"}"}
http://www.pfindia.com/mbaforums/viewtopic.php?f=16&t=29	[ "", null, "## Doubts of Number Theory Sheet 2\n\nIn this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.\n\n### Doubts of Number Theory Sheet 2\n\nDear All,\n\nPleas post your doubts of number theory sheet 3 on this thread.\n\nPosts: 228\nJoined: Wed Feb 13, 2013 5:51 am\n\n### Re: Doubts of Number Theory Sheet 2\n\nQ23\n\n301 = 743,\n\nso 300 ≡ -1 (mod 7)\n\nThen 300^3000 - 1 ≡ (-1)^3000 - 1 ≡ 1 - 1 ≡ 0 (mod 7)\n\nSo 7 divides 300^3000 - 1\n\n297 = 2711,\n\nso 300 ≡ 3 (mod 11)\n\nThen,\n300^3000 - 1 ≡ 3^3000 - 1 ≡ (3^5)^600 - 1 (mod 11)\n\nBut 3^5 = 243 = 2211 + 1\nso 3^5 ≡ 1 (mod 11)\n\nThen\n300^3000 - 1 ≡ (3^5)^600 - 1 ≡ 1^600 - 1 ≡ 0 (mod 11)\n\nSo 11 divides 300^3000 - 1\n\nFinally, 299 = 2313,\n\nso 300 ≡ 1 (mod 13)\n\nThen\n300^3000 - 1 ≡ 1^3000 - 1 ≡ 0 (mod 13)\n\nSo 13 divides 300^3000 - 1\n\nSince 7, 11, 13 are all prime, it follows that their product, 1001 divides 300^3000 - 1\n\nPosts: 228\nJoined: Wed Feb 13, 2013 5:51 am\n\n### Re: Doubts of Number Theory Sheet 2\n\nYou are right - for both these questions it is better to approach from the options.\n\nPosts: 228\nJoined: Wed Feb 13, 2013 5:51 am\n\n### Re: Doubts of Number Theory Sheet 2\n\nKindly solve question number 16 and 23 in the practice questions. Are we to proceed by options in both the questions or is there a shorter way out?\ngaurav1399\n\nPosts: 48\nJoined: Wed Feb 27, 2013 7:49 am\n\nReturn to QA - Class Sheets -Phase 1\n\n### Who is online\n\nUsers browsing this forum: No registered users and 1 guest", null, "" ]	[ null, "http://www.pfindia.com/images/header_text.png", null, "http://www.pfindia.com/mbaforums/cron.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.52487445,"math_prob":0.9624842,"size":576,"snap":"2019-13-2019-22","text_gpt3_token_len":318,"char_repetition_ratio":0.27097902,"word_repetition_ratio":0.07092199,"special_character_ratio":0.7152778,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9580767,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-24T05:11:25Z\",\"WARC-Record-ID\":\"<urn:uuid:ff49fc26-f575-415f-a672-3a1314ea6716>\",\"Content-Length\":\"27913\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13cd70c2-22a1-43b2-8690-57364f28bce6>\",\"WARC-Concurrent-To\":\"<urn:uuid:5ca67206-4d9e-4a4c-9144-e26793c9e8b0>\",\"WARC-IP-Address\":\"103.251.24.23\",\"WARC-Target-URI\":\"http://www.pfindia.com/mbaforums/viewtopic.php?f=16&t=29\",\"WARC-Payload-Digest\":\"sha1:7XDPJUCFS7TXBKZJL3M6HAT2P7NI4NCR\",\"WARC-Block-Digest\":\"sha1:CKFIR7CGE4CJFNFLVQOU4MU7WCFTWOX4\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912203326.34_warc_CC-MAIN-20190324043400-20190324065400-00235.warc.gz\"}"}
https://www.87994.com/read/d69d2ab400aac7a1cf5a7f764e0b162ad53fb1e1.html	[ "# 高中数学第二章基本初等函数(Ⅰ)2.2.1对数与对数运算第一课时对数课件新人教A版必修1_图文\n\n2.2 对数函数 2.2.1 对数与对数运算\n\n1.理解对数的概念,掌握对数的基本性质. 2.掌握指数式与对数式的互化,能应用对数的定义和性质解方程.\n\n【情境导学】导入某种细胞分裂时,由1个分裂成2个,2个分裂成4个…依此类推,那么1 个这样的细胞分裂x次得到细胞个数N是多少?分裂多少次得到细胞个数为8 个,16个呢? 解:1个细胞分裂x次得到细胞个数N=2x,因为23=8,24=16,所以N=8时,x=3; N=16时,x=4,即细胞分裂3次,4次分别得到细胞个数为8个,16个.\n\n1.对数的概念\n\n.\n\n2.常用对数与自然对数\n\n(1)常用对数:通常我们将以10 为底的对数叫做常用对数,记作lg N\n\n.\n\n(2)自然对数:以e为底的对数称为自然对数,记作 ln N\n\n.\n\n3.对数loga N(a>0,且a≠1)具有下列简单性质 (1) 负数和零没有对数,即N > 0;\n\n(2)1的对数为零\n\n,即loga1= 0\n\n;\n\n(3)底数的对数等于 1\n\n,即logaa= 1\n\n;\n\n(4) aloga N =\n\nN\n\n.\n\n【拓展延伸】 1.指数式与对数式的互化 (1)对数式logaN=x是由指数式ax=N而来的,两式底数相同,对数式中的真数N 就是指数式中的幂的值N,而对数值x是指数式中的幂指数.对数式与指数式的关系如图.\n(2)由于正数的任何次幂都是正数,即ax>0(a>0),故N=ax>0.因此logaN只有在a>0,且a≠1,N>0时才有意义. 在规定了a>0,a≠1,N>0后,logaN的值便随着a,N的确定而唯一确定了.根据这一规定,我们知道并不是每一个指数式都能直接改写成对数式.如(-2)2=4, 不能写成log-24=2,只有a>0,a≠1,N>0时,才有ax=N?x=logaN.\n\n2.对数运算性质的证明\n(1)对数的运算性质的证明\n\n1.(对数概念)下列选项中,可以求对数的是( C )\n\n(A)0\n\n(B)-5\n\n(C)π\n\n(D)-x2\n\n2.(指对互化)若b=a2(a>0且a≠1),则有( D )\n\n(A)log2b=a (B)log2a=b (C)logba=2 (D)logab=2 3.(对数概念)在对数式logx-1(3-x)中,实数x的取值范围应该是( D ) (A)(1,3) (B)(1,2)∪(2,+∞)\n\n(C)(3,+∞) (D)(1,2)∪(2,3)\n\n4.(性质)log2 0181+log2 0182 018=\n\n.\n\n5.(性质)log33+ 3log3 2 =\n\n.\n\n(2)( 1 )m=5.73; 3\n\n(2) log1 5.73 =m.\n3\n\n(3)ln 10=2.303; (4)lg 0.01=-2.\n\n(1)log216=4;(2)lo g 1 27=-3;\n3\n\n(3)lo g x=6;(4)43=64; 3\n\n(5)3-2= 1 ;(6)( 1 )-2=16.\n\n9\n\n4\n\n(3)( 3 )6=x.(4)log464=3.\n\n(5)log3\n\n1 9\n\n=-2.(6)lo g 1\n4\n\n16=-2.\n\n【备用例 1】求下列各式 x 的取值范围. (1)log(x-1)(x+2);\n\n(2)log(x+3)(x+3).\n\n?x ?? x\n\n? ?\n\n3 3\n\n? ?\n\n0, 1,\n\n3 (3)lg 100=x;(4)-ln e2=x.\n\n? ? 解:(1)x=\n\n?\n\n? 64\n\n?2 3\n\n=\n\n43\n\n?2 3\n\n=4-2=\n\n1\n\n.\n\n16\n\n1\n\n1\n\n1\n\n1\n\n? ? ? ? (2)x6=8,所以 x= x6 6 = 86 = 23 6 = 2 2 = 2 .\n\n(3)10x=100=102,于是x=2.\n\n(4)由-ln e2=x,得-x=ln e2,即e-x=e2.\n\n【备用例 2】求下列各式中的 x 的值: (1) log?2x2?1? (3x2+2x-1)=1;\n\n(2)log2[log3(log4x)]=0.\n\n【例 3】求下列各式的值:\n(1) 2log2 3 + 3log3 2 ;\n\n(2)\n\n22?\n\nlog\n\n2\n\n1 3\n\n;\n\n(2)原式=22×\n\n2log\n\n2\n\n1 3\n\n=4×\n\n1\n\n=\n\n4\n\n.……………………6\n\n33\n\n(3)101+lg 2; (4)e-1+ln 3.\n\n(4)原式=e-1×eln 3= 1 ×3= 3 .………………………12 分\n\ne\n\ne\n\n3-1:计算:(1)log927;(2) log4 3\n\n81;(3) log 3 54\n\n625.\n\nx\n(2)设 x= log4 3 81,则( 4 3 )x=81, 3 4 =34,所以 x=16.\n\n(3)令 x= log 3 54\n\n625,所以( 3 54\n\n)x=625,\n\n4x\n53\n\n=54,所以\n\nx=3.\n\n?x2 ? 3x ? x ? 3,\n\n? ?\n\nx\n\n2\n\n?\n\n3x\n\n?\n\n0,\n\n??x ? 3 ? 0，且x ? 3 ? 1,\n\n(A)2或-4 (B)-4\n\n(C)2\n\n(D)-2或4\n\n...Ⅰ2.2.1对数与对数运算第一课时对数课件新人教A版必....ppt\n\n2019秋高中数学第二章基本初等函数2.2.1对数与对数运算....ppt\n2019秋高中数学第二章基本初等函数2.2.1对数与对数运算(第1课时)对数课件新人教A版必修1 - 数学必修① 人教A版第二章基本初等函数(Ⅰ) 2.2 对数函数...\n...Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必....doc\n\n...Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必....doc\n\n...复习第二章基本初等函数(Ⅰ)2.2.1对数与对数运算(第....ppt\n2019高考数学总复习第二章基本初等函数(Ⅰ)2.2.1对数与对数运算(第一课时)课件新人教A版必修 - 2.2 对数函数 2.2.1 对数对数运算问题情境请大家...\n...Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必....doc\n\n...函数Ⅰ2.2.1对数与对数运算第1课时课件新人教A版必....ppt\n\n...复习第二章基本初等函数(Ⅰ)2.2.1对数与对数运算(第....ppt\n2019高考数学总复习第二章基本初等函数(Ⅰ)2.2.1对数与对数运算(第一课时)课件新人教A版必修1 - 2.2 对数函数 2.2.1 对数对数运算问题情境请大家...\n\n...Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必....doc\n2019学年高中数学第二章基本初等函数Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必修1_六年级语文_语文_小学教育_教育专区。2019 ...\n...Ⅰ2-2-1对数与对数运算第一课时对数练习新人教A版必....doc\n\n2018-2019学年高中数学第二章基本初等函数(Ⅰ)2-2-1对....doc\n2018-2019学年高中数学第二章基本初等函数(Ⅰ)2-2-1对数与对数运算第一课时对数练习新人教A版必修1 - this course will help y ou gain the ide...\n\n...Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必....doc\n2019学年高中数学第二章基本初等函数Ⅰ2.2.1对数与对数运算第一课时对数练习新人教A版必修1_数学_高中教育_教育专区。2019 第一课时对数【选题明细表】 ...\n...2019学年高中数学第二章基本初等函数(Ⅰ)2.2.1对数与对数运算....ppt\n2018_2019学年高中数学第二章基本初等函数(Ⅰ)2.2.1对数与对数运算课件新人教A版必修1 - 2.2.1 对数对数运算复习 (1)aras ? ar?s ?a ? 0, r, ..." ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.674917,"math_prob":0.99928766,"size":4143,"snap":"2019-43-2019-47","text_gpt3_token_len":3530,"char_repetition_ratio":0.072239675,"word_repetition_ratio":0.0,"special_character_ratio":0.53898144,"punctuation_ratio":0.25365496,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95113546,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-12T08:01:07Z\",\"WARC-Record-ID\":\"<urn:uuid:73c5154d-7f4e-42ee-a1f6-b89b134bf620>\",\"Content-Length\":\"29182\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:218df258-f403-495a-8ef9-5d92a8123a31>\",\"WARC-Concurrent-To\":\"<urn:uuid:74f3a2c6-1f94-4523-a373-f110a3d6e5b7>\",\"WARC-IP-Address\":\"27.124.42.168\",\"WARC-Target-URI\":\"https://www.87994.com/read/d69d2ab400aac7a1cf5a7f764e0b162ad53fb1e1.html\",\"WARC-Payload-Digest\":\"sha1:MF5Q6AA5H55LVNR4KRWLI4QC7ZDI7KKA\",\"WARC-Block-Digest\":\"sha1:IUOHS75YZWZU65YXP7M657LDIZTIBGZH\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496664808.68_warc_CC-MAIN-20191112074214-20191112102214-00057.warc.gz\"}"}
http://feursteinfeurstein.com/idaho-wildflowers-bbyjbhf/what-is-convex-hull-in-image-processing-420ed6	[ "8:23 Uncategorized\n\n# what is convex hull in image processing\n\nParticle Measurements. Director: Wei Wang, Leonard Kleinrock Professor of Computer Science opencv image-processing convex-hull convex-hull-algorithms contour-detection hand-gesture-recognition Updated Aug 31, 2018; Python; ermel272 / convex-hull-animations Star 1 Code Issues Pull requests Animating the computation of convex hulls in two dimensions. 4428 kb/s. Read a grayscale image into the workspace. 3034. Example Of Convex Hull In Image Processing [Most popular] 1700 kb/s. In this work, we derive some new convex hull properties and then propose a fast algorithm based on these new properties to extract convex hull of the object in binary image. 6448 kb/s. Note that this computation can be very slow. Convert it into a binary image and calculate the union binary convex hull. ... finding the convex hull of particles, and more. Users can define thresholds prior to executing or the plugin will assume a dark background and auto threshold the stack using the IsoData method and the stack histogram. An example would be a 4-pixel rectangle with the pixels coordinates ((1,1), (1,2), (2,1), (2,2)). algorithm - daa - convex hull in image processing . An approximate convex hull can be computed using thickening with the structuring elements shown in Figure 1. Abstract. With these lines we … Develop methods (region filling, thinning, thickening, and pruning) that are frequently used in … 3D is another issue though. In this post we will talk about convex hulls which have a broad range of applications in mathematics, computer science and surely image processing / computer vision. Convex hull is widely used in computer graphic, image processing, CAD/CAM and pattern recognition. In this tutorial you will learn how to: Use the OpenCV function cv::convexHull; Theory Next page. This entry was posted in Image Processing and tagged Convex Hull opencv, convexity defects, convexity defects opencv, cv2.convexityDefects(), draw convexity defects, image processing, opencv python, what are convexity defects on 9 Nov 2020 by kang & atul. Toggle Main Navigation ... Use convhull to compute the convex hull of the (x,y) pairs from step 1. Convex Hull • A region A is convex if a straight line joining any two points in A falls within A. How can I do it? A group of UCLA faculty members are working on high-performance analysis of big data. • A convex hull, H, of a set S is the smallest convex set containing S. • The set difference H-S is called the convex … Otherwise, counter-clockwise. chapter 3 answers for drivers ed 2954. Finally, calculate the objects convex hull and display all the images in one figure window. Contours in image processing. Collision avoidance: Avoid collisions with other objects by defining the convex hull of the objects. This is exactly where the role of convex hulls comes to play. Convex hulls have been utilized in various applications (Duda and Hart, 1973; Rosenfeld and … A good overview of the algorithm is … Convex Hull of set S is the smallest convex set A that contains S ... Thinning is an image-processing operation in which binary valued image regions are reduced to lines The problems with this approach is that pixels are considered to have an area of 1 when calculating the region area, but are treated as points in convex hull calculation, causing disparity. Convex hull contains the same 4 … Prev Tutorial: Finding contours in your image. In mathematics the convex hull (sometimes also called the convex envelope) of a set of points X in the Euclidean plane or Euclidean space is the smallest convex… Example Of Convex Hull In Image Processing \| added by request. points: any contour or Input 2D point set whose convex hull we want to find. More formally, we can describe it as the smallest convex polygon which encloses a set of points such that each point in the set lies within the polygon or on its perimeter. Hello friends, in this video we will discuss convex hull in image processing Hope you like the video then do LIKE, SUBSCRIBE and SHARE the videos. The convex hull or convex envelope or convex closure of a set X points in the Euclidean plane or in a Euclidean space is the smallest convex set that contains X. The algorithm takes O(n log h) time, where h is the number of vertices of the output (the convex hull). I have a 3D array of data which shows one concave figure. Image Processing (imgproc module) Contours in OpenCV; Convex Hull . The convex hull is a good option for concavity detection, but it has drawbacks because it is not specific: it cannot give hints about the scale of concavities. returnPoints: If True (default) then returns the coordinates of the hull points. The first algorithm is applicable when the points are distinct, as in the pattern classification problem or the image processing problem in which the pattern is not connected. convex hull Chan's Algorithm to find Convex Hull. Example Of Convex Hull In Image Processing \| updated. Description: HullAndCircle is a plugin for ImageJ used for finding the convex hull and bounding circle of patterns in binary digital images. In computational geometry, Chan's algorithm, named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set P of n points, in 2- or 3-dimensional space. It … Download Hull_And_Circle.jar to the plugins folder, or subfolder, restart ImageJ, and there well be a new Plugins/Shape Analysis/Hull And Circle command. Today I want to tell a little image processing algorithm story related to my post last week about the new bwconvhull function in the Image Processing Toolbox. Otherwise, returns the indices of contour points corresponding to the hull points. Convex Hull¶ The convex hull of a binary image is the set of pixels included in the smallest convex polygon that surround all white pixels in the input. I want to find all points which don't belong to the figure, but are inside the convex hull. Intuitively, it approximates a shape of complex objects with a simpler convex shape. A 2D convex hull already has a node which works very nicely (I’ve implemented in an example workflow here) and it’s possible to generate some points with connected component analysis after the binary hull image is generated. We can draw imaginary lines between these pixels (or better, points). In this work, we derive some new convex hull properties and then propose a fast algorithm based on these new properties to extract convex hull of the object in binary image. Convex hull is widely used in computer graphic, image processing, CAD/CAM and pattern recognition. It is exactly here that, the role of convex hulls comes to play. clockwise: If it is True, the output convex hull is oriented clockwise. The Convex Hull is the line completely enclosing a set of points in a plane so that there are no concavities in the line. Note Remember we have to pass returnPoints = False while finding convex hull, in … The demands of image processing related systems are robustness, high recognition rates, capability to handle incomplete digital information, and magnanimous flexibility in capturing shape of an object in an image. In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X.. Introduction In image processing and pattern recognition, it has been shown that computing a convex hull of a given set of points in a digitized image is a useful operation. Any deviation of the object from this hull can be considered as convexity defect.We can visualize it using an image. The convex hull is the fundamental geometric structure that has many applications in various scientific areas, including computer graphics, robotics, computer vision, image processing, and many others. On the left in this slide, you see an example. Image Processing and Recognition: The demands of image processing are robustness, high recognition rate, and flexibility in capturing the shape of an object in an image. Goal . Suggestions. Most image processing is performed in the spatial domain. We draw a line joining start point and end point, then draw a circle at the farthest point. The objective of this paper is twofold. Next Tutorial: Creating Bounding boxes and circles for contours. Find the largest convex black area in an image (4) I have an image of which this is a small cut-out: As you can see it are white pixels on a black background. 10472. This plugin calculates the 3D shape descriptors Solidity3d & Convexity3d based upon a convex hull constructed from an 8-bit or 16-bit grayscale image stack. Search results. However, you may want to process an image in the frequency domain to remove unwanted frequency information before you analyze and process the image as you normally would. Image Processing; Written by. Two efficient algorithms for obtaining the convex hull of n points in the plane are proposed and their theoretical analyses presented. convex hull and solidity: convex hull is minimum convex area that encompasses all the points in set T. 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https://hilbert.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2011&oldid=3089	[ "Algebraic Geometry Seminar Fall 2011\n\nThe seminar meets on Fridays at 2:25 pm in Van Vleck B215.\n\nThe schedule for the previous semester is here.\n\nFall 2011\n\ndate speaker title host(s)\nSep. 23 Yifeng Liu (Columbia) Enhanced Grothendieck's operations and base change theorem for\n\nsheaves on Artin stacks\n\nTonghai Yang\nSep. 30 Matthew Ballard (UW-Madison) You got your Hodge Conjecture in my matrix factorizations (local)\nOct. 7 Zhiwei Yun (MIT) Cohomology of Hilbert schemes of singular curves Shamgar Gurevich\nOct. 14 Javier Fernández de Bobadilla (Instituto de Ciencias Matematicas, Madrid) Nash problem for surfaces L. Maxim\nOct. 21 Andrei Caldararu (UW-Madison) The Hodge theorem as a derived self-intersection (local)\nNov. 11 John Francis (Northwestern) Integral transforms and Drinfeld centers in derived algebraic geometry Andrei Caldararu\nNov. 18 Sukhendu Mehrotra (Madison) Moduli spaces of sheaves on K3 surfaces and generalized deformations (local)\nDec. 2 Shamgar Gurevich (Madison) Canonical Hilbert Space: Why? How? and its Categorification\nDec. 9 Sean Paul (Madison) Semistable pairs and quasi-closed orbits\n\nSpring 2012\n\ndate speaker title host(s)\nMarch 16 Weizhe Zheng (Columbia) TBD Tonghai Yang\nMarch 23 Ryan Grady (Notre Dame) Twisted differential operators as observables in QFT. Caldararu\nMay 4 Mark Andrea de Cataldo (Stony Brook) TBA Maxim\n\nAbstracts\n\nTBA\n\nMatthew Ballard\n\nYou got your Hodge Conjecture in my matrix factorizations\n\nAbstract: I will describe how to prove some new cases of Hodge conjecture using the following tools: categories of graded matrix factorizations, the homotopy category of dg-categories, Orlov's Calabi-Yau/Landau-Ginzburg correspondence, Kuznetsov's relationship between the derived categories of a certain K3 surface and the Fermat cubic fourfold, and Hochschild homology. This is joint work with David Favero (Wien) and Ludmil Katzarkov (Miami/Wien).\n\nZhiwei Yun\n\nCohomology of Hilbert schemes of singular curves\n\nAbstract: For a smooth curve, the Hilbert schemes are just symmetric powers of the curve, and their cohomology is easily computed by the H^1 of the curve. This is known as Macdonald's formula. In joint work with Davesh Maulik, we generalize this formula to curves with planar singularities (which was conjectured by L.Migliorini). In the singular case, the compactified Jacobian will play an important role in the formula, and we make use of Ngo's technique in his celebrated proof of the fundamental lemma.\n\nNash problem for surfaces\n\nThe space of arcs through the singular set of an algebraic variety has a infinite dimensional scheme structure. In the late sixties Nash proved that it has finitely many irreducible components. He defined a natural mapping from this set of irreducible components to the set of essential divisors of a resolution of singularities. Roughly speaking the set of essential divisors is the set of irreducible components of the exceptional divisor of a resolution whose birational transform is an irreducible component of the exceptional divisor of any other resolution.\n\nNash proved that this mapping is injective and proposed to study its bijectivity. In 2003 S. Ishii and J. Kollar gave a counterexample to the surjectivity in dimension at least 4. Recently, in a joint work with M. Pe Pereira, the speaker has settled the bijectivity for surfaces. In this talk I will explain the proof.\n\nAndrei Caldararu\n\nThe Hodge theorem as a derived self-intersection\n\nThe Hodge theorem is one of the most important results in complex geometry. It asserts that for a complex projective variety X the topological invariants H^*(X, C) can be refined to new ones that reflect the complex structure. The traditional statement and proof of the Hodge theorem are analytic. Given the multiple applications of the Hodge theorem in algebraic geometry, for many years it has been a major challenge to eliminate this analytic aspect and to obtain a purely algebraic proof of the Hodge theorem. An algebraic formulation of the Hodge theorem has been known since Grothendieck's work in the early 1970's. However, the first purely algebraic (and very surprising) proof was obtained only in 1991 by Deligne and Illusie, using methods involving reduction to characteristic p. In my talk I shall try to explain their ideas, and how recent developments in the field of derived algebraic geometry make their proof more geometric.\n\nJohn Francis\n\nIntegral transforms and Drinfeld centers in derived algebraic geometry\n\nFor a finite group G, conjugation invariant vector bundles on G have a universal property with respect to Rep(G): they form its Drinfeld center. Joint work with David Ben-Zvi and David Nadler generalizes this result, extending work of Hinich, in the setting of derived algebraic geometry. We describe a generalization of the Drinfeld center for a monoidal stable infinity category as a Hochschild cohomology category. For quasi-coherent sheaves on a perfect stack X, we prove that its center is equivalent to sheaves on the derived loop space LX. The structure of this category of sheaves defines an extended 2-dimensional topological quantum field theory.\n\nSukhendu Mehrotra\n\nModuli spaces of sheaves on K3 surfaces and generalized deformations\n\nIt is a result of Mukai that connected components of the moduli space of stable sheaves on a K3 surface X are holomorphic symplectic varities. As any such component Y deforms in a 21 dimensional family, while the moduli space of K3 surfaces is 20 dimensional, the general deformation $\\hat{Y}$ of Y will not be be a moduli space of sheaves on a K3. This talk presents an attempt to associate to such a $\\hat{Y}$ a \"non-commutative K3 surface\" $\\hat{X}$ for which the modular description carries over. This joint work with Eyal Markman." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.889106,"math_prob":0.81984496,"size":5879,"snap":"2022-05-2022-21","text_gpt3_token_len":1443,"char_repetition_ratio":0.0973617,"word_repetition_ratio":0.04217536,"special_character_ratio":0.20343596,"punctuation_ratio":0.0770751,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96475554,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-29T01:54:16Z\",\"WARC-Record-ID\":\"<urn:uuid:914ee8b2-4c29-4c8b-ad13-efd04b1dd547>\",\"Content-Length\":\"24801\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f8eee855-de60-45bb-8097-9f03d42dd877>\",\"WARC-Concurrent-To\":\"<urn:uuid:401cd75d-b8a0-4e33-8c8e-8e9744e31a7a>\",\"WARC-IP-Address\":\"144.92.166.29\",\"WARC-Target-URI\":\"https://hilbert.math.wisc.edu/wiki/index.php?title=Algebraic_Geometry_Seminar_Fall_2011&oldid=3089\",\"WARC-Payload-Digest\":\"sha1:Q2YOH6TZEO7TFU2RSDHTQCVQLZCXWXB4\",\"WARC-Block-Digest\":\"sha1:UIL7EHLAGFCBNFJAJWM2O5V62YI2DK2K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320299894.32_warc_CC-MAIN-20220129002459-20220129032459-00689.warc.gz\"}"}
http://blog.jvbaopeng.com/blog/234.html	[ "``` /无极限分类，返回树形数组结构/\nStatic Public function unlimitedForLayer (\\$cate, \\$pid = 0, \\$name = 'son')\n{\n\\$arr = [];\nforeach (\\$cate as \\$v) {\nif (\\$v['pid'] == \\$pid) {\n\\$v[\\$name] = self::unlimitedForLayer(\\$cate, \\$v['id'],\\$name);\nif(count(\\$v[\\$name])==0){\n\\$v[\\$name] =null;\n}\n\\$arr[] = \\$v;\n}\n}\nreturn \\$arr;\n}```\n\n```if(count(\\$v[\\$name])==0){\n\\$v[\\$name] =null;\n}```\n\n```/无极限分类，返回树形数组结构\n@param array \\$cate 数据库查出来的分类数组\n@param int \\$pid 父分类id\n@param string \\$name 子数组键名\n*/\nStatic Public function unlimitedForLayer (\\$cate, \\$pid = 0, \\$name = 'son')\n{\n\\$arr = [];\nforeach (\\$cate as \\$k=>\\$v) {\nif (\\$v['pid'] == \\$pid) {\nunset(\\$cate[\\$k]);\n\\$v[\\$name] = self::unlimitedForLayer(\\$cate, \\$v['id'],\\$name);\nif(count(\\$v[\\$name])==0){\n\\$v[\\$name] =null;\n}\n\\$arr[] = \\$v;\n}\n}\nreturn \\$arr;\n}```\n\n• 友情链接" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.7036706,"math_prob":0.9944106,"size":1059,"snap":"2019-51-2020-05","text_gpt3_token_len":613,"char_repetition_ratio":0.13080569,"word_repetition_ratio":0.49541286,"special_character_ratio":0.3437205,"punctuation_ratio":0.14906833,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9977994,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-27T08:35:40Z\",\"WARC-Record-ID\":\"<urn:uuid:fad072c1-1b86-407c-8f93-a7c4c542f7f9>\",\"Content-Length\":\"21793\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:03ac3028-35bd-4702-91a4-5dede185d768>\",\"WARC-Concurrent-To\":\"<urn:uuid:7f24bce0-583d-4105-a634-af374cd2babf>\",\"WARC-IP-Address\":\"139.196.93.6\",\"WARC-Target-URI\":\"http://blog.jvbaopeng.com/blog/234.html\",\"WARC-Payload-Digest\":\"sha1:SG6A7BK5BP5TF33Q5F6HLSNHDU4T7642\",\"WARC-Block-Digest\":\"sha1:B3Z5TRYMXOJERBR3ARAWHUPLMBK4TWR7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251696046.73_warc_CC-MAIN-20200127081933-20200127111933-00510.warc.gz\"}"}
https://www.dovov.com/pythonvariables-2.html	[ "# Python嵌套函数中的局部variables\n\n``from functools import partial class Cage(object): def __init__(self, animal): self.animal = animal def gotimes(do_the_petting): do_the_petting() def get_petters(): for animal in ['cow', 'dog', 'cat']: cage = Cage(animal) def pet_function(): print \"Mary pets the \" + cage.animal + \".\" yield (animal, partial(gotimes, pet_function)) funs = list(get_petters()) for name, f in funs: print name + \":\", f()` `\n\n` `cow: Mary pets the cat. dog: Mary pets the cat. cat: Mary pets the cat.` `\n\n• 部分函数示例，使用`functools.partial()`\n\n` `from functools import partial def pet_function(cage=None): print \"Mary pets the \" + cage.animal + \".\" yield (animal, partial(gotimes, partial(pet_function, cage=cage)))` `\n• 创build一个新的作用域示例：\n\n` `def scoped_cage(cage=None): def pet_function(): print \"Mary pets the \" + cage.animal + \".\" return pet_function yield (animal, partial(gotimes, scoped_cage(cage)))` `\n• 将variables绑定为关键字参数的默认值：\n\n` `def pet_function(cage=cage): print \"Mary pets the \" + cage.animal + \".\" yield (animal, partial(gotimes, pet_function))` `\n\n` `funs = list(get_petters())` `\n\n` `for name, f in get_petters(): print name + \":\", f()` `\n\n` `cow: Mary pets the cow. dog: Mary pets the dog. cat: Mary pets the cat.` `\n\n` `for i in range(2): pass print i is 1` `" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.77087855,"math_prob":0.97879153,"size":2287,"snap":"2022-05-2022-21","text_gpt3_token_len":1173,"char_repetition_ratio":0.15549715,"word_repetition_ratio":0.17030568,"special_character_ratio":0.23742895,"punctuation_ratio":0.17445482,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98262376,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-21T03:31:00Z\",\"WARC-Record-ID\":\"<urn:uuid:cc804139-e5a2-4cf5-80e7-24dd59c5d303>\",\"Content-Length\":\"22317\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5b258c22-0d38-48a0-85d2-62744c7d47bf>\",\"WARC-Concurrent-To\":\"<urn:uuid:c189b927-9111-4c0b-9dce-66c00b0f7a9a>\",\"WARC-IP-Address\":\"174.138.186.11\",\"WARC-Target-URI\":\"https://www.dovov.com/pythonvariables-2.html\",\"WARC-Payload-Digest\":\"sha1:GFIJSEZJPAAWCORYAG3Q46OFJNSWHQ6V\",\"WARC-Block-Digest\":\"sha1:R6GIFSNMKFFHIIM4SE5DQ5T35FAD7DWW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662534773.36_warc_CC-MAIN-20220521014358-20220521044358-00106.warc.gz\"}"}
http://fweb.wallawalla.edu/class-wiki/index.php?title=Energy_in_a_signal&diff=2554	[ "# Difference between revisions of \"Energy in a signal\"\n\n### Definition of Energy\n\nEnergy is the ability or potential for something to create change. Scientifically energy is defined as total work done by a force. Work can be mathematically calculated as the line integral of force per infinatesimal unit distance,", null, "$W = \\int \\mathbf{F} \\cdot \\mathrm{d}\\mathbf{s}$\n\nPower represents a change in energy.", null, "$P(t) = \\frac{dW}{dt}$\n\nThis means we can also write energy as", null, "$W = \\int_{-\\infty}^{\\infty} P(t)\\,dt$\n\n### Energy of a Signal\n\nFrom circuit analysis we know that the power generated by voltage source is,", null, "$P(t) = {\\mathbf{V}^2(t) \\over R}$\n\nAssuming that R is 1 then the total energy is just,", null, "$W = \\int_{-\\infty}^\\infty \|\\mathbf{V}\|^2(t) \\mathrm{d}\\mathbf{t}$\n\nThis page is far from complete please feel free to pick up where it has been left off." ]	[ null, "http://fweb.wallawalla.edu/class-wiki/upload/math/5/c/0/5c0b23edaa456374ec84f71596681871.png ", null, "http://fweb.wallawalla.edu/class-wiki/upload/math/a/e/6/ae6514132432b6bff48c27d668c9c2d1.png ", null, "http://fweb.wallawalla.edu/class-wiki/upload/math/3/b/7/3b75bafbbda9d1202cba4ae195227b39.png ", null, "http://fweb.wallawalla.edu/class-wiki/upload/math/7/d/b/7dba69f823326f13dbfdb0954a3d8bc8.png ", null, "http://fweb.wallawalla.edu/class-wiki/upload/math/8/e/9/8e91b65f91f595ba1654b08d36035937.png ", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8756983,"math_prob":0.9995555,"size":1156,"snap":"2019-51-2020-05","text_gpt3_token_len":322,"char_repetition_ratio":0.11892361,"word_repetition_ratio":0.24102564,"special_character_ratio":0.2932526,"punctuation_ratio":0.08597285,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99991167,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,5,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T09:51:16Z\",\"WARC-Record-ID\":\"<urn:uuid:49000b6e-e1d3-40d8-afd3-4e9d6c46293d>\",\"Content-Length\":\"57038\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:11cf7a5d-3153-469f-9094-c01cc15c639b>\",\"WARC-Concurrent-To\":\"<urn:uuid:2f53bd4b-8f3d-4e85-8074-e6bf96a5d6aa>\",\"WARC-IP-Address\":\"192.147.172.36\",\"WARC-Target-URI\":\"http://fweb.wallawalla.edu/class-wiki/index.php?title=Energy_in_a_signal&diff=2554\",\"WARC-Payload-Digest\":\"sha1:DAOK44H4XPACRBLQY6RX43F7XBJHTGGM\",\"WARC-Block-Digest\":\"sha1:BFCEICQQZO7R4YHZEDDZ2QZGQTJ2XNQV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251778168.77_warc_CC-MAIN-20200128091916-20200128121916-00071.warc.gz\"}"}
http://mathonline.wikidot.com/the-dimension-of-the-null-space-and-range-examples-1	[ "The Dimension of The Null Space and Range Examples 1\n\nThe Dimension of The Null Space and Range Examples 1\n\nRecall from The Dimension of The Null Space and Range page that if $T$ is a linear map from $V \\to W$ and $V$ is finite-dimensional then we have the following formula relating the dimension of $V$ to the dimension of the the null space of $T$ and the dimension of the range of $T$:\n\n(1)\n\\begin{align} \\quad \\mathrm{dim} (V) = \\mathrm{dim} (\\mathrm{null}(T)) + \\mathrm{dim} (\\mathrm{range} (T)) \\end{align}\n\nWe will now look at some examples applying this formula.\n\nExample 1\n\nLet $U$, $V$, and $W$ be finite-dimensional vector spaces, and suppose that $S \\in \\mathcal L (V, W)$ and $T \\in \\mathcal L (U, V)$. Let $ST \\in \\mathcal L (U, W)$. Show that $\\mathrm{dim} (\\mathrm{null} (ST)) ≤ \\mathrm{dim} ( \\mathrm{null} (S)) + \\mathrm{dim} ( \\mathrm{null} (T))$.\n\nUsing the dimension formula above we have that:\n\n(2)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (ST)) = \\mathrm{dim} (U) - \\mathrm{dim} (\\mathrm{range} (ST)) \\end{align}\n\nSince $\\mathrm{dim} (U) = \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T))$ we can substitute this into the equation above to get that:\n\n(3)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (ST)) = \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T)) - \\mathrm{dim} (\\mathrm{range} (ST)) \\end{align}\n\nNow notice that $\\mathrm{dim} (\\mathrm{range}(T)) ≤ \\mathrm{dim} (V)$ and so:\n\n(4)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (ST)) ≤ \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (V) - \\mathrm{dim} (\\mathrm{range} (ST)) \\end{align}\n\nSince $\\mathrm{dim} (V) = \\mathrm{dim} (\\mathrm{null} (S)) + \\mathrm{dim} (\\mathrm{range} (S))$, we can substitute this into the equation above to get:\n\n(5)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (ST)) ≤ \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{null} (S)) + \\mathrm{dim} (\\mathrm{range} (S)) - \\mathrm{dim} (\\mathrm{range} (ST)) \\end{align}\n\nNote that $\\mathrm{dim} (\\mathrm{range} (S)) - \\mathrm{dim} (\\mathrm{range} (ST)) ≤ 0$ though since $S$ maps elements $v \\in V$ to elements $S(v) \\in W$, and $ST$ maps elements $T(u) \\in V$ to elements $S(T(u)) \\in W$ and so $\\mathrm{range} S \\subseteq \\mathrm{range} (ST)$ which implies that $\\mathrm{dim} ( \\mathrm{range} (S)) ≤ \\mathrm{dim} ( \\mathrm{range} (ST))$, so:\n\n(6)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (ST)) ≤ \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{null} (S)) \\end{align}\n\nExample 2\n\nLet $V$ be a finite-dimensional vector space. Suppose that $V = \\mathrm{null}(T) + \\mathrm{range}(T)$. Prove that $\\mathrm{null} (T) \\cap \\mathrm{range} (T) = \\{ 0 \\}$.\n\nIf we apply the dimension formula given above, we have that:\n\n(7)\n\\begin{align} \\quad \\mathrm{dim} (V) = \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T)) \\end{align}\n\nFurthermore, from The Dimension of a Sum of Subspaces we have that:\n\n(8)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (T) + \\mathrm{range}(T)) = \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T)) - \\mathrm{dim} (\\mathrm{null} (T) \\cap \\mathrm{range} (T)) \\end{align}\n\nSince $V = \\mathrm{null} (T) + \\mathrm{range} (T)$, this implies that the two equations above are equal, and so:\n\n(9)\n\\begin{align} \\quad \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T)) = \\mathrm{dim} (\\mathrm{null} (T)) + \\mathrm{dim} (\\mathrm{range} (T)) - \\mathrm{dim} (\\mathrm{null} (T) \\cap \\mathrm{range} (T)) \\end{align}\n\nThe equation above implies that $\\mathrm{dim} (\\mathrm{null} (T) \\cap \\mathrm{range} (T)) = 0$, so $\\mathrm{null} (T) \\cap \\mathrm{range} (T) = \\{ 0 \\}$." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.599076,"math_prob":1.0000077,"size":2114,"snap":"2019-43-2019-47","text_gpt3_token_len":696,"char_repetition_ratio":0.24312796,"word_repetition_ratio":0.084084086,"special_character_ratio":0.34011352,"punctuation_ratio":0.07730673,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000085,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-14T20:43:33Z\",\"WARC-Record-ID\":\"<urn:uuid:41bfd781-93dd-45db-b6b2-b71d56921bde>\",\"Content-Length\":\"19335\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2a3243f7-ed76-46b2-9c9c-cd1931528d87>\",\"WARC-Concurrent-To\":\"<urn:uuid:9660475d-1025-4db2-aee4-e3b5d814cea0>\",\"WARC-IP-Address\":\"107.20.139.176\",\"WARC-Target-URI\":\"http://mathonline.wikidot.com/the-dimension-of-the-null-space-and-range-examples-1\",\"WARC-Payload-Digest\":\"sha1:7GDJWLXLZMOY4FMELMYHCVHFZFEOL3GP\",\"WARC-Block-Digest\":\"sha1:XF75VMHBVZWNFZC7X7YUGHTXYOVKLCAH\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986655310.17_warc_CC-MAIN-20191014200522-20191014224022-00118.warc.gz\"}"}
https://vmlc.tamu.edu/Virtual-Math-Learning-Center/Courses/Calculus-I/Inverse-Trigonometric-Functions-only	[ "", null, "#", null, "## Section 1.5 - Inverse Trigonometric Functions\n\nSection Details:\n• Definitions and properties of inverse sine, cosine, and tangent\n• Evaluating inverse trigonometric functions\n• Evaluating compositions of trigonometric and inverse trigonometric functions\n\n## Inverse Trigonometric Functions: MATH 171 Problems 4-6\n\nProperties of inverse trig functions and the derivative of arctangent\n\n## Inverse Trigonometric Functions: MATH 151 Problems 9-12\n\nProperties and derivatives of inverse trigonometric functions" ]	[ null, "https://vmlc.tamu.edu/App_Themes/TAMU/images/top-small.png", null, "https://vmlc.tamu.edu/MLC/media/mainmedia/Home/Logos/VMLC_black.svg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6829065,"math_prob":0.9230602,"size":384,"snap":"2023-40-2023-50","text_gpt3_token_len":75,"char_repetition_ratio":0.20263158,"word_repetition_ratio":0.0,"special_character_ratio":0.15104167,"punctuation_ratio":0.08,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9811979,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T19:43:16Z\",\"WARC-Record-ID\":\"<urn:uuid:01a0cdc0-de87-4f8d-9d24-de2d9e30bd39>\",\"Content-Length\":\"41387\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a32b285c-d8f1-4ab9-b1ac-3507b05f6836>\",\"WARC-Concurrent-To\":\"<urn:uuid:06dfa01e-b35d-420a-82d1-a63f9782f776>\",\"WARC-IP-Address\":\"128.194.14.43\",\"WARC-Target-URI\":\"https://vmlc.tamu.edu/Virtual-Math-Learning-Center/Courses/Calculus-I/Inverse-Trigonometric-Functions-only\",\"WARC-Payload-Digest\":\"sha1:3XIUOZ7HX4AU6N3AXXK6K24NRQCJHKIB\",\"WARC-Block-Digest\":\"sha1:SO7KNIU7Y2CBKF4NGQCVPKAGB6FIGO4O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510924.74_warc_CC-MAIN-20231001173415-20231001203415-00498.warc.gz\"}"}
https://www.puzzles-world.com/2019/05/apples-oranges-and-mangoes-puzzles.html	[ "# Apples Oranges and Mangoes Puzzles", null, "## Apples Oranges and Mangoes Puzzles", null, "A fruit basket contains only Apples, Oranges and Mangoes.\nAll of the fruits are Apples except four of them,\nall of the fruits are Oranges except five of them, and\nall of the fruits are Mangoes except seven of them.\n\nHow many fruits are there in the basket in all ?\n\nThere are 8 fruits in the basket\n\nExplanation :\n1) A + O + M = X (Let say X is total fruits)\n\nA + 4 = X\nO + 5 = X\nM + 7 = X\n\nso\n2) A + O + M + 16 = 3X\n\nnow substituting 1 in 2, we get,\nX + 16 = 3X => 2X = 16\nHence X = 8" ]	[ null, "https://2.bp.blogspot.com/-oN6WuEm11Z8/UxBnEvrgVII/AAAAAAAAC1o/t8GCn3kuOls/s1600/advertisement.png", null, "https://2.bp.blogspot.com/-s0MvDx-N_v0/XNUMjy5C7VI/AAAAAAAAErs/ZqRcdSvHugYTbtkXMf9Tlx5i9W7nIIWjwCLcBGAs/s1600/Apples%2BOranges%2BMangoes%2BPuzzle.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.88744193,"math_prob":0.99661934,"size":535,"snap":"2020-45-2020-50","text_gpt3_token_len":178,"char_repetition_ratio":0.16195858,"word_repetition_ratio":0.032258064,"special_character_ratio":0.33084112,"punctuation_ratio":0.07692308,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9732895,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-30T07:56:03Z\",\"WARC-Record-ID\":\"<urn:uuid:bfdc8f55-b595-4143-9b10-547deba13782>\",\"Content-Length\":\"53172\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:031aa019-bdc2-4680-945d-b3880445ed63>\",\"WARC-Concurrent-To\":\"<urn:uuid:577c9380-6e2f-4e3c-aaa0-c9f6fae69d1b>\",\"WARC-IP-Address\":\"172.217.7.243\",\"WARC-Target-URI\":\"https://www.puzzles-world.com/2019/05/apples-oranges-and-mangoes-puzzles.html\",\"WARC-Payload-Digest\":\"sha1:X263XVZYOADPCD5XBY3CZIVGR6XBKBXG\",\"WARC-Block-Digest\":\"sha1:PVBC4Z2JI2FTSYYMXQ7H7MZ5U3LPEWOZ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141211510.56_warc_CC-MAIN-20201130065516-20201130095516-00473.warc.gz\"}"}
https://blog.kdamball.com/2014/01/15/javascript-and-floating-points-arithmetics/	[ "JavaScript and Floating Points Arithmetics\n\nWe (i.e. anyone who has played with JavaScript) all have heard something about how floating points are tricky and borderline impossible to deal with. While this is not exclusive to JS, it is worth knowing a thing or two behind the limitations of dealing with floating numbers.\n\nLet’s start with a well known example:\n\nvar a = 0.1 + 0.2;\na === 0.3; // false\nconsole.log(a); //0.30000000000000004\n\nThe only way to deal with this is to use the toFixed() property from the Number object or to convert everything into integers, perform the calculations then convert everything back into decimals. Both methods are not guaranteed to produce the correct result, especially when dealing with complex calculations with various floating point variables.\n\nI found out the best way to understand floating point problems is to use the decimal system most humans are so used to. Try expressing 1/3 in a decimal system in the best way possible. There is literally no way to express it to its precision. There are hacks, like 0.333... repeating, but these are all ways that confirm our lack of expressing 1/3 in decimal. Something similar is happening with JavaScript and floating points.\n\nAnyone who has taken an intro class in Calculus will be familiar with the Zeno’s paradox. To summarize it, 1 + 1/2 + 1/4 + 1/8 + .... will always approach 2 but never be equal to 2. This is because we are always halving our distance from 2. That is exactly what is going on when JavaScript tries to express some floating points.\n\nConsider this Binary code:\n\nIntegers:\nBinary: 1 => Decimal: 1\nBinary: 10 => Decimal: 2\nBinary: 1101 => Decimal: 13\n\nFloating points:\nBinary: 0.1 => Decimal: 0.5\nBinary: 0.0101 => Decimal: 0.3125\nBinary: 0.00011001 => Decimal: 0.09765625\nBinary: 0.00011001100110011 => Decimal: 0.09999847412109375\n\nAs you can see from above, the binary value is getting closer and close to 0.1 (in Decimal) but never actually equals it. It is a shortcoming of expressing certain floating points in binary; in the same way we can never fully express certain floating points (e.g: 1/3) in decimal. You can try this with pretty much any base system (try expressing 0.1 (decimal) in Base 3).\n\nTo answer our original issue (i.e. 0.1 + 0.2), calculations are usually transformed into binary, evaluated then converted back into decimal. With its 32-bit limitation, the expression is limited to only 32 floating points. It then becomes:\n\n0.00011001100110011001100110011001 //approx. of 0.1\n+\n0.00110011001100110011001100110011 //approx. of 0.2\n__________________________________\n\n0.01001100110011001100110011001100 //the actual result in binary to be converted into decimal\n\nWant to try something even more fun?\n\nfor(var i = 0, x= 0; i<10;i++){\nx += 0.1; //increment x by 0.1 ten times\n}\n\nconsole.log(x); //0.9999999999999999\n\nPS: I should emphasize that this isn’t something that is unique to JavaScript. Most languages by default have this issue. I just used JavaScript because it’s the most comfortable/easy language to express the idea." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86778736,"math_prob":0.9799995,"size":3006,"snap":"2019-43-2019-47","text_gpt3_token_len":769,"char_repetition_ratio":0.16155896,"word_repetition_ratio":0.0,"special_character_ratio":0.3223553,"punctuation_ratio":0.16747968,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9689546,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-21T07:58:43Z\",\"WARC-Record-ID\":\"<urn:uuid:baa00219-7c94-4f7f-8ce3-2d2151670dae>\",\"Content-Length\":\"63244\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e484c025-116a-4d91-b82b-837795370b9c>\",\"WARC-Concurrent-To\":\"<urn:uuid:26f57a22-5e8a-481f-808b-36226e5fa21b>\",\"WARC-IP-Address\":\"192.0.78.13\",\"WARC-Target-URI\":\"https://blog.kdamball.com/2014/01/15/javascript-and-floating-points-arithmetics/\",\"WARC-Payload-Digest\":\"sha1:7A4T6X7NINHBC5SEL3RN6DIPHDMVH63A\",\"WARC-Block-Digest\":\"sha1:LHTL2YMIRDPUSBQTX4R4OCDDZAE524GW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987763641.74_warc_CC-MAIN-20191021070341-20191021093841-00416.warc.gz\"}"}
https://scribesoftimbuktu.com/solve-for-z-z9213/	[ "# Solve for z (z+9)^2=13", null, "Take the square root of each side of the equation to set up the solution for\nRemove the perfect root factor under the radical to solve for .\nThe complete solution is the result of both the positive and negative portions of the solution.\nFirst, use the positive value of the to find the first solution.\nSubtract from both sides of the equation.\nNext, use the negative value of the to find the second solution.\nSubtract from both sides of the equation.\nThe complete solution is the result of both the positive and negative portions of the solution.\nThe result can be shown in multiple forms.\nExact Form:\nDecimal Form:\nSolve for z (z+9)^2=13\n\n### Solving MATH problems\n\nWe can solve all math problems. Get help on the web or with our math app\n\nScroll to top" ]	[ null, "https://scribesoftimbuktu.com/wp-content/uploads/ask60.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8609981,"math_prob":0.99554276,"size":638,"snap":"2022-40-2023-06","text_gpt3_token_len":136,"char_repetition_ratio":0.18769716,"word_repetition_ratio":0.3272727,"special_character_ratio":0.21003135,"punctuation_ratio":0.09375,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99942315,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T19:58:47Z\",\"WARC-Record-ID\":\"<urn:uuid:eae538ae-8ec0-48f4-85af-4c1b31e98c9e>\",\"Content-Length\":\"73221\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5520cb64-d817-4e36-ae0d-f541e317ae65>\",\"WARC-Concurrent-To\":\"<urn:uuid:cf30021e-dbf2-4427-903c-e3766995b0bb>\",\"WARC-IP-Address\":\"107.167.10.237\",\"WARC-Target-URI\":\"https://scribesoftimbuktu.com/solve-for-z-z9213/\",\"WARC-Payload-Digest\":\"sha1:2CUBORZ45ITY3OEDTHVAQGHTXFPGSPDK\",\"WARC-Block-Digest\":\"sha1:V6CHUJ5YJEVDEM76LERE2NYO4TV4JLDM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337855.83_warc_CC-MAIN-20221006191305-20221006221305-00362.warc.gz\"}"}
https://myhomeworkhelp.com/cpm-org-homework-help-embrace-the-fear-of-financial-mathematic-homework-for-achieving-higher-grades/	[ "# CPM Org Homework Help: Embrace the Fear of Financial Mathematic Homework for Achieving Higher Grades\n\nâ€˜Try to achieve those things that you are afraid of.â€™\n\nFinancial Mathematic is a terror for many students as this subject consists of complex calculations, graphs, reasoning, etc. Mostly, they are scared of solving those sums given by their teachers in homework. If you continue skipping the problems, time will come when you will not understand any concept and lose interest gradually. Proper methods of calculation will help you in achieving higher grades. I so wish that there was cpm org homework help to guide me with the financial calculations in my academic years, my marks would have been better!\n\nSkills one must acquire for completing homework on financial mathematic:\n\nTo completeall complicated sums of financial math with ease, you must possess or acquire few skills. Students need to have skills of strategic and analytical thinking. Calculating maturity value, simple interest, loan payment is not a matter of joke. Hours of practice will help you in solving the complex calculations of financial mathematic with ease. Homework on financial math will seem easier only if you are careful about the calculations.\n\nTo some, financial mathematic seem to be simple and interesting as it creates an abstract and technical branch of math. Besides this, it is also about measuring theoretic probability and learning how to apply these theories in day-to-day life.But for some students like me, homework on financial mathematics is one of the toughest topics in academic life. Have a brief look at the problems faced by students while dealing with homework on financial mathematic.\n\nProblems that most students face on financial mathematic homework:\n\n1. Studying Finance is all about balance sheets and financial concepts. But, many students lag behind as they do not have a proper understanding these complicatedconcepts of finance. So, homework becomes a matter of headache for such students. You may pursue assistance from cpm org homework help for getting a clear idea.\n2. Being a student of Finance, one of the basic problems faced by me was understanding the application of formulas related to statistical analysis, randomness and also probability.\n3. Many are there who face difficulty in calculating and understanding nominal interest and discount, force of interest, discounting, annuities, perpetuities, etc.\n4. Such calculations require proper guidance. But, the basic problem that affects many students while doing homework is they do not get the assistance needed to clear up the concepts.\n\nÂ\n\nHow cpm org homework help can solve your financial mathematic problems?\n\nHave a look at few unique aspects of this system of learning, so that you score higher grades with ease.\n\n• Gives crystal clear idea of financial symbols-\n\nCpm org homework help efficiently assists students to learn one of the most important keys of Financial Mathematics. Now, you might be wondering what the key is. Well, itâ€™s all about understanding the formulas and before that acquiring proper knowledge of all the financial variables and symbols. Unless and until youget a clear idea of what each financial symbol represent, you will not gain interest to learn more.\n\nFor example, N= number of periods, g= rate of growth, B= balance, PV= present value, FV= future value, T= terminal period, rE= effective interest rate, CF= cash flow, PMT= periodic payment. This educational program teaches the students where, how and why to use such symbols.\n\n• Guides in your flexible time\n\nSuppose, the total strength of your class is 40.It is quite natural that students will face problems and come up with queries. Now, is it possible for a teacher to clear up all single queries within a period of 40-45 minutes? Of course, not!Due to this reason, students think of taking extra assistance after school hours. Even that is tiring as there are many other subjects you need to study.\n\nA highly essential facet of this educational system is that they assist students according to their own convenient time. You can just come up with your queries and explanation is provided at that very moment.\n\n• Encourages joint or group study\n\nThe curriculum of cpm org homework help is planned in such a format where students get to solve financial mathematical problem sums jointly. Thus, students discuss the techniques before solving the sums on their own. By doing so, they come up with different procedures to solve a particular problem.\n\nImagine yourself in a situation where you are instructed to complete a difficult sum on financial math. Will you be able to struggle with it for an hour or more without the support of other fellow friends who are sailing in the same boat as you? Hence, this particular curriculum focuses in theunified system of studying.\n\n• Specialized E- books\n\nDo you want to know another interesting aspect of this educational program? You will be very excited to know that they prefer using specialized E- books other than general books on financial mathematics. Descriptive ideas are provided for better explanation of calculating loan payments, interest rate, etc. The concepts of Finance which students may find difficult to understand is simplified by the facility of video tutorials.\n\nThus, if you ever face with a specific sum, you can take help from those tutorials for understanding the procedure step-by-step. Once, you are aware of the steps it will be easier for you to solve the sum, no matter how difficult it is. This system of helping students with their financial math homework is highly co- operative.\n\n• Easier techniques\n\nThe most common problem faced by students is to memorize all the formula sheets required for solving financial math sums. Formulas of simple interest like I=Prt, S= P+I, S= P(1+rt) are very simple. But, rememberingformulas for calculating ordinary simple annuity, ordinary general annuity requires a lot of practice and time.\n\nThis educational program assists students to learn better and upgraded techniques of learning such complex formulas. With advanced and systematic procedures, solving difficult sums and spreadsheets become very easy.\n\nHomework on financial math becomes quite interesting when learning and solving is through technology. Impressive way of completing your homework, isnâ€™t it? Even you can opt for it!\n\nEmbracing new technologies and techniques is a part of human nature especially if it makes life easier than before. So, cpm org homework help is a good option for students who are looking for the guidance of an educational system that will help them in their financial mathematic homework.\n\n## Submit Homework", null, "### Customer Reviews\n\nRatings based on 510 customer reviews.\n\n## What Are the Career Options You Get Studying Applied Mathematics?\n\nDo numbers fascinate you? Is solving complex mathematical problems an easy task for you? Are you interested in making...\n\n## Number Theory is Super Easy but Only If You Work with Mathematics Being a Smarty\n\nMathematics is all about the numbers and their equations which are to be solved with the correct method and a small...\n\n## How to Make Your Mathematics Life in College a Fun One?\n\nCollege life is the life that every school student looks forward to. Think about it, you are independent to attend the...", null, "" ]	[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2026%2026'%3E%3C/svg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%200%200'%3E%3C/svg%3E", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9568018,"math_prob":0.8269157,"size":6537,"snap":"2021-43-2021-49","text_gpt3_token_len":1277,"char_repetition_ratio":0.13883361,"word_repetition_ratio":0.0018993352,"special_character_ratio":0.18800673,"punctuation_ratio":0.10135135,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97604334,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-22T03:42:31Z\",\"WARC-Record-ID\":\"<urn:uuid:ee23077d-3c01-45eb-9721-5c4e27cd8634>\",\"Content-Length\":\"348314\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4dd26ba7-f6bb-4c92-bff3-e02c83df18c9>\",\"WARC-Concurrent-To\":\"<urn:uuid:97663ec2-cd15-40e4-b754-e2b6643f7a46>\",\"WARC-IP-Address\":\"192.124.249.107\",\"WARC-Target-URI\":\"https://myhomeworkhelp.com/cpm-org-homework-help-embrace-the-fear-of-financial-mathematic-homework-for-achieving-higher-grades/\",\"WARC-Payload-Digest\":\"sha1:AWE7DUKTJBP2657O5CPJVCXT4ERJ6TGN\",\"WARC-Block-Digest\":\"sha1:FHKDNBLZP6XXFVTUMJJVE4M4DLRSAFOS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585450.39_warc_CC-MAIN-20211022021705-20211022051705-00516.warc.gz\"}"}
http://www.lvliang.gov.cn/llxxgk/zfxxgk/xxgkml/szfwj/202109/t20210917_1558601.html	[ "• ###### 政民互动", null, "关闭\n 索引号：111423LL00100/2021-01138 发文字号：吕政发〔2021〕13号发布日期：2021年09月07日发文机关：吕梁市人民政府关键字：标　　题：关于收回吕梁市商贸储运公司国有建设用地使用权的决定主题分类：土地成文日期：2021年09月07日\n\n为实施《吕梁市中心城区货源街片区老旧小区改造工作方案》，依照《中华人民共和国土地管理法》《土地储备管理办法》和《吕梁市规划区土地储备实施办法》的规定，作出如下决定：\n\n一、无偿收回你单位位于离石区货源街98号的国有建设用地使用权，面积为3668.45平方米。宗地四至为：东邻居民住宅、南邻市商务局家属院、西至小路、北至货源街。宗地坐标如下：\n\nX1=4153811.3150， Y1=37511960.959；\n\nX2=4153805.4430， Y2=37511976.490；\n\nX3=4153801.8910， Y3=37511994.006；\n\nX4=4153793.0100， Y4=37512019.830；\n\nX5=4153788.3090， Y5=37512018.246；\n\nX6=4153781.2840， Y6=37512018.496；\n\nX7=4153743.5190， Y7=37512019.839；\n\nX8=4153743.2120， Y8=37512011.584；\n\nX9=4153741.5760， Y9=37511967.698；\n\nX10=4153741.2000， Y10=37511957.614；\n\nX11=4153753.9320， Y11=37511957.540；\n\nX12=4153782.5600， Y12=37511957.848；\n\nX13=4153782.5610， Y13=37511957.711；\n\nX14=4153785.8570， Y14=37511957.730；\n\nX15=4153787.0220， Y15=37511957.804；\n\nX16=4153790.9060， Y16=37511958.291；\n\nX1=4153811.3150， Y1=37511960.959。\n\n二、收回的国有建设用地由市土地储备中心储备管理，具体位置以《土地勘测定界技术报告书》编号：RX-(SC2021-003）号为准。\n\n三、请你单位尽快到原土地登记机关办理国有建设用地的使用权注销登记。\n\n2021年9月7日\n\n（此件公开发布）\n\n解读说明：此件不属于政策性文件，不作解读。\n\n咨询电话：市规自局　土地储备中心　8296746", null, "晋公网安备 14110002000102号" ]	[ null, "http://www.lvliang.gov.cn/llxxgk/images/close.png", null, "http://www.lvliang.gov.cn/llxxgk/images/jinghui.png", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.86238563,"math_prob":0.8282643,"size":1297,"snap":"2022-27-2022-33","text_gpt3_token_len":1043,"char_repetition_ratio":0.14617169,"word_repetition_ratio":0.0,"special_character_ratio":0.5959908,"punctuation_ratio":0.15283842,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98782885,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-15T07:38:20Z\",\"WARC-Record-ID\":\"<urn:uuid:6a77819f-ae86-46f2-8de6-e3f9a16fc384>\",\"Content-Length\":\"45901\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1aa7e01c-4b25-4a62-8478-a1f757e26a71>\",\"WARC-Concurrent-To\":\"<urn:uuid:9445aeee-87ad-4f30-a97c-8a8d1e324d2d>\",\"WARC-IP-Address\":\"124.165.206.5\",\"WARC-Target-URI\":\"http://www.lvliang.gov.cn/llxxgk/zfxxgk/xxgkml/szfwj/202109/t20210917_1558601.html\",\"WARC-Payload-Digest\":\"sha1:ANXM3NFXL2HO4D5X5QABE7ZHA7LAXA5I\",\"WARC-Block-Digest\":\"sha1:QC3JHNGWISVC73JNKP7R43AQ4WQFWUD2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572161.46_warc_CC-MAIN-20220815054743-20220815084743-00285.warc.gz\"}"}
https://codereview.stackexchange.com/questions/120369/printing-binary-trees	[ "Printing binary trees\n\nAfter writing this answer, I was inspired to try to design a more elegant solution to the problem of printing binary trees. And what better tool with which to seek elegance than Clojure?\n\nOverall design\n\nThe solution I ended up with involved creating, merging, and printing what I'm going to call sparse strings. A sparse string is simply a map from row/column pairs to substrings. These substrings must not contain newlines or overlap with each other.\n\nSo for instance, this multiline string\n\n baz\nfoo\nbar\nqux\n\n\ncould be represented by this sparse string:\n\n{[3 -2] \"foo\"\n[4 -7] \"bar\"\n[2 -6] \"baz\"\n[5 7] \"qux\"}\n\n\nA few things to note:\n\n1. Empty space is simply filled by regular spaces and newlines\n2. The first coordinate is the row, the second coordinate is the column\n3. The first row and column need not necessarily be zero\n\nThe problem of printing a binary tree then reduces to creating sparse strings from its left and right subtrees (as well as one for its value, which will go at the top), then shifting and merging those sparse strings together.\n\nThe only extra requirement when using sparse strings to represent trees is that the root (or the center of the root, if the root is wider than 1 character) must be at [0 0]. Consider the tree below:\n\n 4\n/ \\\n2 5\n/ \\\n1 3\n\n\nThe in-memory representation of this would be\n\n{:value 4\n:left {:value 2\n:left {:value 1}\n:right {:value 3}}\n:right {:value 5}}\n\n\nTextually, the tree would be represented as\n\n{[0 0] \"4\"\n[2 -2] \"2\"\n[4 -4] \"1\"\n[3 -3] \"/\"\n[4 0] \"1\"\n[3 -1] \"\\\\\"\n[1 -1] \"/\"\n[2 2] \"5\"\n[1 1] \"\\\\\"}\n\n\nI'll refer to this as a tree string. This way, when I combine multiple tree strings to create a bigger tree string, I can safely use [0 0] as an anchor point from which to shift subtrees.\n\nCode\n\n(defn end-col\n\"Returns one plus the maximum column occupied by the sparse string entry x.\"\n[x]\n(let [[[_ col] s] x]\n(+ col (count s))))\n\n(defn min-corner\n\"Returns a vector of the minimum non-empty row and column in sparse-string.\"\n[sparse-string]\n(mapv #(apply min (map % (keys sparse-string)))\n[first second]))\n\n(defn max-corner\n\"Returns a vector of one plus the maximum non-empty row and column in\nsparse-string.\"\n[sparse-string]\n(mapv #(apply max (map % sparse-string))\n[(comp inc first key) end-col]))\n\n(defn fill\n\"Returns a string of newlines and spaces to fill the gap between entries x and\ny in a sparse string whose minimum corner is corner.\"\n[corner x y]\n(let [[_ min-col] corner\n[[prev-row _] _] x\n[[next-row next-col] _] y]\n(apply str (concat (repeat (- next-row prev-row) \\newline)\n(repeat (- next-col\n(if (== prev-row next-row)\n(end-col x)\nmin-col))\n\\space)))))\n\n(defn sparse-str\n\"Converts sparse-string to a string.\"\n[sparse-string]\n(let [corner (min-corner sparse-string)]\n(->> sparse-string\n(sort-by key)\n(cons [corner \"\"])\n(partition 2 1)\n(map (fn [[x y]] (str (fill corner x y) (val y))))\n(apply str))))\n\n(defn shift\n\"Creates and returns a sparse string by adding offset to the position of each\nentry in sparse-string.\"\n[offset sparse-string]\n(into {} (map (fn [[pos s]]\n[(mapv + pos offset) s])\nsparse-string)))\n\n(defn vert-gap\n\"Returns the minimum vertical gap that can be used in combining the left and\nright tree strings.\"\n[left right]\n(if (and left right)\n(max 1 (quot (- (second (max-corner left))\n(second (min-corner right)))\n2))\n1))\n\n(def directions {:left - :right +})\n\n(defn diagonal\n\"Returns a diagonal sparse string with the top end located at corner.\"\n[direction corner length character]\n(let [[first-row first-col] corner]\n(into {} (map (fn [n]\n[[(+ first-row n)\n((directions direction) first-col n)]\n(str character)])\n(range length)))))\n\n(defn leg\n\"Returns a sparse string from shifting tree-string according to direction,\nvert-gap, and value-height, merged with a diagonal strut.\"\n[direction tree-string vert-gap value-height]\n(merge (shift [(+ value-height vert-gap)\n((directions direction) (inc vert-gap))]\ntree-string)\n(diagonal direction\n[value-height ((directions direction) 1)]\nvert-gap\n({:left \\/ :right \\\\} direction))))\n\n(defn assemble\n\"Assembles a complete tree string from the tree strings of a value, left\nsubtree, and right subtree.\"\n[value left right]\n(if (or left right)\n(let [[value-height _] (max-corner value)\nvert-gap (vert-gap left right)]\n(merge value\n(when left\n(leg :left left vert-gap value-height))\n(when right\n(leg :right right vert-gap value-height))))\nvalue))\n\n(defn tree-string\n\"Creates and returns a tree string from node.\"\n[node]\n(let [{:keys [value left right]} node\ns (str value)]\n(apply assemble\n{[0 (- (quot (count s) 2))] s}\n(map #(when % (tree-string %))\n[left right]))))\n\n\nImplementation notes\n\nWhen printing a sparse string, one first needs to find the minimum occupied row and column in the sparse string. This naturally leads to the end-col, min-corner, and max-corner functions for calculating bounding boxes for sparse strings.\n\nNow, how does one print a sparse string? This problem basically boils down to printing the whitespace to fill the gaps between sparse string entries. Once that's accomplished, the actual sparse-str implementation is quite straightforward.\n\nAlso, since I'm going to be combining sparse strings in addition to just creating and printing them, I'll need a function to shift the reference point of an existing sparse string.\n\nAll we need now is a way to convert from that logical representation of the tree to the textual one, which is the task of the tree-string function.\n\nAs you can see, the better part of the work is done in that assemble function. The first thing we need to do is decide how long we're going to make the struts that connect the left and right subtrees. To simplify things, we'll just always make them the same length, which means that the length of the struts, calculated by vert-gap, will equal to the final distance between the bottom of the value tree string and the tops of the left and right tree strings.\n\nAnd of course, we'll need the diagonal function to create the struts themselves.\n\nNow that we have all the rest of the pieces, it's just a matter of assembleing them together. The leg function is just a helper that combines diagonal and shift together into something that can then be merged with the root.\n\nExample\n\nIn case you'd like to test this code yourself, here's a function for generating a random binary tree:\n\n(defn rand-tree\n[weight depth]\n(into {:value (int (Math/pow 2 (rand (dec Integer/SIZE))))}\n(map #(when (and (pos? depth) (< (rand) weight))\n[% (rand-tree weight (dec depth))])\n[:left :right])))\n\n\nSo this...\n\n(println (sparse-str (tree-string (rand-tree 3/4 3))))\n\n\n... will print something like this:\n\n 1369616891\n/ \\\n/ \\\n/ \\\n/ \\\n/ \\\n238883 2\n/ \\ /\n/ \\ 9\n/ \\ / \\\n/ \\ 1 2222\n2949729 6\n/ /\n1836 5299294\n\n• Why are 2's kids on a different level than those of 238883? – Josh Mar 29 '17 at 14:07\n• @Josh Because my code recursively builds the left and right subtrees into tree strings separately and then combines them into a tree string for the whole tree, so in that example the right subtree doesn't know the length of the struts in the left subtree because it doesn't know that the left subtree exists at all. – Sam Estep Mar 29 '17 at 16:37\n• But why are the struts different lengths there?? – Josh Mar 30 '17 at 6:54\n• @Josh Because you can't fit 2949729 and 6 on the same line with struts of length 1 using the centering function #(- (quot (count %) 2)) that you can find in tree-string. – Sam Estep Mar 30 '17 at 11:27\n• @Josh In any case, if you think that my code can be improved, by all means please post an answer! That's why I posted it in this question in the first place. – Sam Estep Mar 30 '17 at 22:27\n\nFirst of all, in my opinion, both the algorithm is nice and interesting, and the code is really well-written, broken down into easily understandable functions! Well done!\n\nThe only addition that I can make are corner-cases (and their possible fixes) for some of the helper functions. However, please note, that from the main entry point, I did not find any way to trigger these corner cases, so, from a user perspective, the program works well even without the changes below.\n\nCorner case # 1\n\n(min-corner {})\n(sparse-str {})\n\n\nBoth throw an exception, due to min in min-corner being called with zero arguments.\n\nI suggest the following change, in order to handle this case:\n\n(defn min-corner\n\"Returns a vector of the minimum non-empty row and column in sparse-string.\"\n[sparse-string]\n(mapv #(apply min (let [args (map % (keys sparse-string))] (if (empty? args) [0 0] args)))\n; (mapv #(apply min (map % (keys sparse-string)))\n[first second]))\n\n\nI.e., call min with a default value (in this case [0 0]), if the arguments are empty.\n\nCorner case #2\n\n(max-corner {})\n\n\nSimilar issue, like for min-corner, similar solution:\n\n(defn max-corner\n\"Returns a vector of one plus the maximum non-empty row and column in\nsparse-string.\"\n[sparse-string]\n(mapv #(apply max (let [args (map % sparse-string)] (if (empty? args) [0 0] args)))\n; (mapv #(apply max (map % sparse-string))\n[(comp inc first key) end-col]))\n\n\nCorner case #3\n\n(sparse-str {[0 0] \"aa\" [0 1] \"b\"})\n\n\nThis will return aab. However, b is misplaced here, because it should be at position [0 1], and it is, instead, at position [0 2]. To be honest, I don't really know what would be the best solution here. I can imagine the following:\n\n1. Leave it as it is: all output is shown, some of it might be on the wrong place.\n2. Overwrite the the end of the first string with the second one (i.e. \"ab\").\n3. Overwrite the beginning of the second string with the first one (in this case: \"aa\").\n4. Throw an exception.\n\nAgain, starting from the main entry point, it is not possible to trigger this situation, because the user does not provide any positions. However, in case the helper functions were to be reused in a library, this is a question that should be addressed.\n\nCorner case #4\n\n(vert-gap {[0 0] \"a\"} {[4 10] \"a\"})\n\n\nIn case the right element has a bigger second coordinate than the left one, the result is always 1. I'm not sure if this is by design, but if not, then I'd suggest to make sure, that vertical gap is calculated correctly also in such cases, by taking the absolute value of the difference, instead of the difference itself:\n\n(defn vert-gap\n\"Returns the minimum vertical gap that can be used in combining the left and\nright tree strings.\"\n[left right]\n(if (and left right)\n(max 1 (quot (Math/abs (- (second (max-corner left))\n(second (min-corner right)))\n) 2))\n1))\n\n\nCorner case # 5\n\n(diagonal :left [0 0] -2 \\a)\n\n\nWith the current implementation, this will return an empty result: {}. Now, with the semantics that the name of the parameter length implies, this should be correct (maybe an exception could be thrown, but that is only detail). However, wouldn't it be nice, if the signum of length could control the direction, in which the first coordinate grows? Something like this:\n\n(defn diagonal\n\"Returns a diagonal sparse string with the top end located at corner.\"\n[direction corner length character]\n(let [[first-row first-col] corner\n_length (Math/abs length)\nop (if (< length 0) - +)]\n(into {} (map (fn [n]\n[[(op first-row n)\n((directions direction) first-col n)]\n(str character)])\n(range _length)))))\n\n\nIn this way, the result of the above example will be: {[0 0] \"a\", [-1 -1] \"a\"}. Of course, it might be worth considering to rename the length parameter, e.g. to horizontal-displacement or something similar.\n\nP.S.:\n\nI setup a github repo for the above mentioned changes, and their corresponding test cases (along other tests):\n\n• Thanks for the awesome write-up! For Corner case #1 and Corner case #2, I think that it would be better for sparse-str to handle the case where its argument is empty (and just return \"\") and for min-corner and max-corner to specify in their docstring that their argument must be nonempty, similar to how it is part of the contract of min and max that they be passed a nonzero number of arguments. – Sam Estep Aug 11 '17 at 19:14\n• For Corner case #3, I definitely agree that the current behavior is undesirable; the \"dimensions\" of the returned string should not depend on whether an overlap is present. Out of the possible solutions you present, I think the second one (overwrite the the end of the first string with the second one) is the best. – Sam Estep Aug 11 '17 at 19:14\n• For Corner case #4, that's an interesting behavior, and on the one hand your solution might be desirable for robustness purposes, but on the other hand, in my definition of \"tree string\", I specified that the root must be present at [0 0], so {[4 10] \"a\"} does not qualify as a tree string, and vert-gap specifies that both of its arguments are tree strings. – Sam Estep Aug 11 '17 at 19:14\n• For Corner case #5, I like your idea of adding semantics to the signum of length! Do you think that could possibly remove the need for the direction and character parameters as well? – Sam Estep Aug 11 '17 at 19:14\n• @SamEstep: re #5: I don't think that we can pack those infos into length, because the signum of length is now the vertical direction, while direction is the horizontal one. Unless length is converted to some kind of structure, but that will still need all three pieces of information IMHO. – Attilio Aug 12 '17 at 11:54" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7888824,"math_prob":0.9394857,"size":6837,"snap":"2019-26-2019-30","text_gpt3_token_len":1765,"char_repetition_ratio":0.15293428,"word_repetition_ratio":0.017436791,"special_character_ratio":0.29003948,"punctuation_ratio":0.07753164,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9827796,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-15T23:48:44Z\",\"WARC-Record-ID\":\"<urn:uuid:bee02f86-eb0a-4723-bf5a-e9267419abba>\",\"Content-Length\":\"160075\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8177ccdc-1b2b-4893-b50c-f1298d02d57b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d05b942e-85e1-4ff3-8071-ab5332709f0b>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://codereview.stackexchange.com/questions/120369/printing-binary-trees\",\"WARC-Payload-Digest\":\"sha1:WKBBVFXAO2TTWOQS62AR3IES7HEQROFJ\",\"WARC-Block-Digest\":\"sha1:67H3BTEMODRIMEE4V4RXQXJVXCH52GR4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627997501.61_warc_CC-MAIN-20190615222657-20190616004657-00405.warc.gz\"}"}
https://www.netket.org/docs/_generated/samplers/netket.sampler.MetropolisPtSampler.html	[ "# netket.sampler.MetropolisPtSampler¶\n\nclass netket.sampler.MetropolisPtSampler(args, __skip_preprocess=False, kwargs)[source]\n\nBases: netket.sampler.metropolis.MetropolisSampler\n\nMetropolis-Hastings with Parallel Tempering sampler.\n\nThis sampler samples an Hilbert space, producing samples off a specific dtype. The samples are generated according to a transition rule that must be specified.\n\n__init__(args, __skip_preprocess=False, kwargs)\n\nMetropolisSampler is a generic Metropolis-Hastings sampler using a transition rule to perform moves in the Markov Chain. The transition kernel is used to generate a proposed state $$s^\\prime$$, starting from the current state $$s$$. The move is accepted with probability\n\n$A(s\\rightarrow s^\\prime) = \\mathrm{min}\\left (1,\\frac{P(s^\\prime)}{P(s)} F(e^{L(s,s^\\prime)})\\right),$\n\nwhere the probability being sampled from is $$P(s)=\|M(s)\|^p. Here ::math::$$ is a user-provided function (the machine), $$p$$ is also user-provided with default value $$p=2$$, and $$L(s,s^\\prime)$$ is a suitable correcting factor computed by the transition kernel.\n\nParameters\n• hilbert – The hilbert space to sample\n\n• rule – A MetropolisRule to generate random transitions from a given state as well as uniform random states.\n\n• n_chains – The number of Markov Chain to be run in parallel on a single process.\n\n• n_sweeps – The number of exchanges that compose a single sweep. If None, sweep_size is equal to the number of degrees of freedom being sampled (the size of the input vector s to the machine).\n\n• n_chains – The number of batches of the states to sample (default = 8)\n\n• machine_pow – The power to which the machine should be exponentiated to generate the pdf (default = 2).\n\n• dtype – The dtype of the statees sampled (default = np.float32).\n\nAttributes\nis_exact\n\nReturns True if the sampler is exact.\n\nThe sampler is exact if all the samples are exactly distributed according to the chosen power of the variational state, and there is no correlation among them.\n\nReturn type\n\nbool\n\nmachine_pow: int = 2\n\nExponent of the pdf sampled.\n\nn_batches\nn_chains\n\nThe total number of chains across all MPI ranks.\n\nIf you are not using MPI, this is equal to n_chains_per_rank\n\nReturn type\n\nint\n\nn_chains_per_rank: int = None\n\nNumber of independent chains on every MPI rank.\n\nn_replicas: int = 32\n\nThe number of replicas\n\nn_sweeps: int = None\n\nNumber of sweeps for each step along the chain. Defaults to number of sites in hilbert space.\n\nreset_chains: bool = False\n\nIf True resets the chain state when reset is called (every new sampling).\n\nrule: MetropolisRule = None\n\nThe metropolis transition rule.\n\nMethods\ninit_state(machine, parameters, seed=None)\n\nCreates the structure holding the state of the sampler.\n\nIf you want reproducible samples, you should specify seed, otherwise the state will be initialised randomly.\n\nIf running across several MPI processes, all sampler_states are guaranteed to be in a different (but deterministic) state. This is achieved by first reducing (summing) the seed provided to every MPI rank, then generating n_rank seeds starting from the reduced one, and every rank is initialized with one of those seeds.\n\nThe resulting state is guaranteed to be a frozen python dataclass (in particular, a flax’s dataclass), and it can be serialized using Flax serialization methods.\n\nParameters\nReturn type\n\nSamplerState\n\nReturns\n\nThe structure holding the state of the sampler. In general you should not expect it to be in a valid state, and should reset it before use.\n\nlog_pdf(model)\n\nReturns a closure with the log_pdf function encoded by this sampler.\n\nNote: the result is returned as an HashablePartial so that the closure does not trigger recompilation.\n\nParameters\n\nmodel (Union[Callable, Module]) – The machine, or apply_fun\n\nReturn type\n\nCallable\n\nReturns\n\nthe log probability density function\n\nreplace(updates)\n\nReturns a new object replacing the specified fields with new values.\n\nreset(machine, parameters, state=None)\n\nResets the state of the sampler. To be used every time the parameters are changed.\n\nParameters\nReturn type\n\nSamplerState\n\nReturns\n\nA valid sampler state.\n\nsample(machine, parameters, *, state=None, chain_length=1)\n\nSamples chain_length elements along the chains.\n\nParameters\nReturns\n\nThe next batch of samples. state: The new state of the sampler\n\nReturn type\n\nσ\n\nsample_next(machine, parameters, state=None)\n\nSamples the next state in the markov chain.\n\nParameters\nReturns\n\nThe new state of the sampler σ: The next batch of samples.\n\nReturn type\n\nstate" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.72722185,"math_prob":0.97623414,"size":5337,"snap":"2021-31-2021-39","text_gpt3_token_len":1277,"char_repetition_ratio":0.15750985,"word_repetition_ratio":0.14765906,"special_character_ratio":0.23121604,"punctuation_ratio":0.12406417,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98902553,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-05T15:16:12Z\",\"WARC-Record-ID\":\"<urn:uuid:fb8b265e-a1ed-44f7-98d3-bc5678d138b5>\",\"Content-Length\":\"64256\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b7f449e7-9b1c-44de-b07f-41a45fd91d59>\",\"WARC-Concurrent-To\":\"<urn:uuid:98c7e5d8-72f0-41e1-a822-b7c726ddbde8>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://www.netket.org/docs/_generated/samplers/netket.sampler.MetropolisPtSampler.html\",\"WARC-Payload-Digest\":\"sha1:C2H6VOKGV56J6ZNR46GKRVZMO2LGA5MX\",\"WARC-Block-Digest\":\"sha1:RVCN56JBGUCOQ752J7XAC5TRTGUQ6LYZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046155925.8_warc_CC-MAIN-20210805130514-20210805160514-00678.warc.gz\"}"}
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"白条鸭供应商\|采购实惠的白条鸭就找中元食品\n\n品牌:中元,,\n\n出厂地:凤山县(凤城镇)\n\n报价：面议\n\n青州中元食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：白条鸭,鸭副产品,鸭胗,鸭舌,鸭心\n\n•", null, "广西锦香食品公司-可靠的腊味供应厂家-香肠代理\n\n品牌:张记锦香,锦香,\n\n出厂地:富川瑶族自治县(富阳镇)\n\n报价：面议\n\n广西浦北锦香食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：广式月饼,广西月饼团购定制,广西月饼厂家,广西月饼团购批发,广西月饼品牌\n\n•", null, "鹅肥肝生产-春冠食品供应划算的鹅肥肝\n\n品牌:春冠,,\n\n出厂地:凤山县(凤城镇)\n\n报价：面议\n\n山东春冠食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：鹅肝厂家,鹅肥肝厂家,法国鹅肥肝,白条鹅加工,鹅副产品\n\n•", null, "山东清真酱牛肉_淄博酱牛肉批发供应\n\n品牌:金岭马荣,马荣,\n\n出厂地:凤山县(凤城镇)\n\n报价：面议\n\n淄博金岭马荣清真食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：淄博酱牛肉,淄博牛肉干,金岭酱牛肉,酱牛肉厂家,山东酱牛肉厂家\n\n•", null, "哪里有鹅肝-山东热门鹅肝厂家\n\n品牌:春冠,,\n\n出厂地:凤山县(凤城镇)\n\n报价：面议\n\n山东春冠食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：鹅肝厂家,鹅肥肝厂家,法国鹅肥肝,白条鹅加工,鹅副产品\n\n•", null, "即食牛蹄筋\|山东物超所值的牛蹄筋供应\n\n品牌:伊增,夯牛,金岭\n\n出厂地:凤山县(凤城镇)\n\n报价：面议\n\n山东伊增清真食品k8凯发\n\n黄金会员：", null, "经营模式：生产型\n\n主营：清真牛肉食品加盟,清真食品代加工,牛肉酱加工厂,牛肉干加工厂,清真牛肉礼盒批发\n\n• 没有找到合适的供应商？您可以发布采购信息\n\n没有找到满足要求的供应商？您可以搜索肉制品批发肉制品公司肉制品厂\n\n### 最新入驻厂家\n\n相关产品:\n鸭翅厂家土猪批发天然的淡菜山东正宗牛肉干白条鸭供应商香肠代理鹅肥肝生产山东清真酱牛肉哪里有鹅肝即食牛蹄筋" ]	[ null, "http://image-ali.bianjiyi.com/1/2016/0805/15/57a43d3f2d677.jpg", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2017/0605/11/5934cb9be2965.jpg", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2018/0412/15/5acf0f065cb96.JPG", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2016/0606/11/5754f5246ed07.jpg", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2016/0805/15/57a43b4d1ad49.jpg", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2018/0505/13/15254965782896.jpg", null, "http://www.qincai.com/Public/Images/ForeApps/grade2.png", null, "http://image-ali.bianjiyi.com/1/2016/0415/12/571072f06cf49.jpg", null, 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http://perplexus.info/show.php?pid=8114&cid=57676	[ "", null, "All about flooble \| fun stuff \| Get a free chatterbox \| Free JavaScript \| Avatars", null, "", null, "perplexus dot info", null, "", null, "Purely prime (Posted on 2013-02-19)", null, "Twenty-one prime numbers are in arithmetic sequence with difference d. Prove that d is divisible by 9699690.\n\n No Solution Yet Submitted by Danish Ahmed Khan Rating: 5.0000 (1 votes)", null, "Comments: ( Back to comment list \| You must be logged in to post comments.)", null, "Primes Comment 3 of 3 \|", null, "Let p1, p2, ..., p21 be the prime numbers. Then, p1+d=p2, p2+d=p3, ..., p20+d=p21. Take any prime p<10. If d is not divisible by p, then at least 2 of the prime numbers are divisible by p. Since p is the only prime divisible by p, that is impossible. Therefore, d is divisible by p. Then, d is divisible by 2357=210. Take any prime 10<p<20. If d is not divisible by p, then at least 1 of the prime numbers is divisible by p. Since p is the only prime divisible by p, pn=p for some n. Since d is divisible by 210, p2>210, ..., p21>210. Since p<20, p2>p, ..., p21>p. Therefore, p1=p. Then, p1+pd is one of the primes. That is impossible. Therefore, d is divisible by p. Then, d is divisible by 235711131719=9699690.\n\n Posted by Math Man on 2016-09-05 21:00:42", null, "Please log in:\n\n Search: Search body:\nForums (0)" ]	[ null, "http://perplexus.info/images/flooble.gif", null, "http://perplexus.info/images/dot.gif", null, "http://perplexus.info/images/dot.gif", null, "http://perplexus.info/images/dot.gif", null, "http://perplexus.info/images/dot.gif", null, "http://perplexus.info/images/perplexus/diff/2.gif", null, "http://perplexus.info/images/dot_black.gif", null, "http://perplexus.info/images/perplexus/icons/solution.gif", null, "http://perplexus.info/images/perplexus/icons/down.gif", null, "http://perplexus.info/images/dot.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.91094,"math_prob":0.9849972,"size":878,"snap":"2019-35-2019-39","text_gpt3_token_len":286,"char_repetition_ratio":0.23684211,"word_repetition_ratio":0.29299363,"special_character_ratio":0.38268793,"punctuation_ratio":0.22857143,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9949024,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-21T08:45:03Z\",\"WARC-Record-ID\":\"<urn:uuid:17861ad2-af13-4048-8f04-3fa2591c2925>\",\"Content-Length\":\"12550\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:11635697-d6bb-4e12-a643-73917f2c519a>\",\"WARC-Concurrent-To\":\"<urn:uuid:4731ebff-6a8a-4d5b-830f-ec9405a97f8d>\",\"WARC-IP-Address\":\"216.67.228.67\",\"WARC-Target-URI\":\"http://perplexus.info/show.php?pid=8114&cid=57676\",\"WARC-Payload-Digest\":\"sha1:6R6SMJHPBVZLJUUUO6VCJILRHDLLZD5D\",\"WARC-Block-Digest\":\"sha1:6K46O4B2NHTJUC3L6UFASJBT36FQ6QBU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514574377.11_warc_CC-MAIN-20190921084226-20190921110226-00344.warc.gz\"}"}
https://cemxpu.burgerfi8518.site/matrix-multiplication-using-mapreduce-github.html	[ "## Matrix multiplication using mapreduce github\n\nmatrix multiplication using mapreduce github Kublanovskaya, J. Examples of Lambda are given below. • Standard http://jwbuurlage. MapReduce. Francis) 1964: Sinkhorn (Richard Sinkhorn) 1965: Golub-Reinsch SVD (Gene Golub) 1969: Sparse matrix ordering (Elizabeth Cuthill, James McKee) 1969: Strassen matrix multiplication (Volker Strassen) The implementation for the multiplication gate with input scalars x and y and output scalar z is class MultiplyGate ( object ): def forward ( x , y ): z = x * y self . combineAlli(x1;:::;xn) : combine all the results from combine2() for node i. g. g. 3. I just want to code a matrix multiplication problem in MapReduce using python for very large sparse matrix. An AggBinaryOp hop can be compiled into the following physical operators. h. This relates mostly to (a) matrix multiplication deficiencies, and (b) handling parallelism. Test naive algorithm locally. Basic Matrix Multiplication Operators. May 15, 2013 · Does anyone need MapReduce?122• I tried to do book recommendations withlinear algebra• Basically, doing matrix multiplication toproduce the full user/item matrix withblanks filled in• My Mac wound up freezing• 185,973 books x 77,805 users =14,469,629,265– assuming 2 bytes per float = 28 GB of RAM• So it doesn’t necessarily take that much tohave some use for MapReduce of the loss J ( i) ( θ) of the i th window vector with respect to the matrix x of window vectors is given by. I built a jar file using the code below. Jun 21, 2020 · MapReduce Program – Finding The Average Age of Male and Female Died in Titanic Disaster; MapReduce – Understanding With Real-Life Example; How to find top-N records using MapReduce; How to Execute WordCount Program in MapReduce using Cloudera Distribution Hadoop(CDH) Matrix Multiplication With 1 MapReduce Step; MapReduce – Combiners 1. element 3 in matrix A is called A21 i. 15 minute read. Introductory example is calculation of Fibonacci numbers where F(N) (problem of size N) is calculated as sum of F(N - 2) and F(N - 1) (problems of size N - 2 and N - 1). KEY: block num (a_block, b_block) VALUE: [(row, col, value), ,( )]//numbers in the block // implement matrix multiplication of the blocks locally res = 0 for i = row of ele in this a block: for k = col of ele in this b block: for j = 0 to n-1: res += A[i][j] * B[j][k] Test. Aug 17, 2018 · Besides matrix-vector and matrix-matrix calculations, relational-algebra operations fit well into the MapReduce style of computing. deeplearn-rs - deeplearn-rs provides simple networks that use matrix multiplication, addition, and ReLU under the MIT license. This file contains the implementation of reducer. Specifically, use test your implementation on the following graphs, 1. Table 2 summarizes the core operations of important ML algorithms. com&nbs 15 Dec 2014 in this area (Hadoop, Map-Reduce and Spark) work exercises. Rawashdeh , M. From the implementation point of view, Before the MapReduce model, MPI was the main tool used to process big data. 2166 II. Certain common operations, like broadcast or matrix multiplication, do know how to deal with array wrappers by using the Adapt. ein\"ij,jk -> ik\"(a,b) returns :(a * b) and ein\"ij,kj -> ki\"(a,b) returns :(b * transpose(a)) . in a way you should be familiar with. The nucleus is represented as a N-nanometer by M-nanometer grid, and at each 1nm * 1nm square is known whether or not it is filled by something. G. Parsian, Data . When we represent matrices in this form, we do not need to keep entries for the cells that have values of zero to save large amount of disk space. PyMR is a Python 2. We deﬁne requirements for the design of serverless big data applications, present a prototype for matrix multiplication using FaaS, and discuss and synthesize insights from results of extensive experimentation. What we want to do We will write a simple MapReduce program (see also Wikipedia ) for Hadoop in Python but without using Jython to translate our code to Java jar files. Aug 29, 2015 · Matrix Multiplication with MapReduce 33 Comments Posted by Maruf Aytekin on February 16, 2015 Matrix-vector and matrix-matrix calculations fit nicely into the MapReduce style of computing. The MapReduce contains two important tasks, namely Map and Reduce. Map-Reduce. Integer matrix-matrix and matrix-vector Distributed matrix factorization with mapreduce using a series of broadcast-joins (SS, CB, MS, AA, VM), pp. Matrix-matrix product • Basic matrix multiplication on a 2-D grid • Matrix multiplication is an important application in HPC and appears in many areas (linear algebra) • C = A * B where A, B, and C are matrices (two-dimensional arrays) • A restricted case is when B has only one column, matrix-vector product, which appears in 1957: Minimum degree sparse matrix reordering (Harry Markowitz) 1961: QR algorithm (V. Jan 25, 2021 · We need to extract it using the command tar –zxvf eclipse-committers-photon-R-linux-gtk. 0-m2 m4. Many fields such as Machine Learning and Optimization have adapted their algorithms to handle such clusters. js) and Approach2 (multiply_map_aggregate. 5https://github. MapReduce, from one job to another, takes time to upload the file and start the job again. Basic Matrix Multiplication Operators. When performance or resources are a matter of concern Cubert Script is a developer-friendly language that takes out the hints, guesswork and surprises when running the script. \" Computi (Concurrent Replication-based Matrix Multiplication) along with a parallel algorithm, Marlin, for large-scale matrix multiplication on uted data-parallel platforms, such as Hadoop MapReduce of naively using the general shuffle me Cannon principle parallel matrix multiplication algorithm implementation, and Source: https: //github. function mapReduce(input, map, reduce) {// Map: var mapperOutput = []. Mon 11/14: No recitation : Tue 11/15: srini Experiment MapReduce: Result for Matrix Multiplication 38 MapReduce The speedup of using software-based atomic add over the system one increases as the input matrices get larger (up to 13. 1) Simple Moving Average for Companies Stock Data. e. There are 2 main reasons why interpreted Python code is slower than code in a compiled lanauge such as C (or other compiled langauge): Using MapReduce, we could achieve N times throughput by having N workers running in parallel. Existing GPUbased SOM algorithms take a similar approach in finding the best matching unit, but they do not necessarily use matrix operations to derive the distance matrix [34,46]. ,1. sin ( xs ) # np. Tensor-matrix-multiplication(TTM)referstomultiplyingTalong any mode n, by a matrix of size K ×Ln (for some K). pi , 100 ) ys = np . Importance Sampling for Learning Edge opicsT (ISLE) Microsoft Research, 2000+ LOC [Github] Sep 21, 2020 · The course includes video lectures, case studies, peer-to-peer engagements and use of computational tools and platforms (such as R/RStudio, and Git/Github), and a reproducible research project. Knowing the working of matrix multiplication in a distributed system provides important insights on understanding the cost of our algorithms. Apr 10, 2019 · MRQL (the MapReduce Query Language) is an SQL-like query language for large-scale data analysis on a cluster of computers. sum (axis = 1). Gittens et al. com Li Pu A. Mahoney. The essence of the transformation is to unroll the input patches (a 3D matrix) and lters (a 4D matrix) in 2D in a way that a single matrix-matrix multiplication produces the unrolled version of the output in 2D. 10 of Mahout it became obvious that using Hadoop MapReduce. dblp-2011 3. Map Reduce paradigm is usually used to aggregate data at a large scale. Methods used in the 4 Apr 2019 How to find top-N records using MapReduce Now to do so we just multiply the key with -1 in mapper, so that after sorting higher numbers Other Links: GitHub Repository Matrix Multiplication With 1 MapReduce Step. UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. How to do matrix multiplication in R? Machine Learning Recipes,do, matrix, multiplication, r: What is mapply in R? Machine Learning Recipes,what, is, mapply, r: What is sapply in R? Machine Learning Recipes,what, is, sapply, r: How to find lagged differences in R? Machine Learning Recipes,find, lagged, differences, r: How to find variance and MapReduce/Hadoop, where data must be read from disk on eachiteration. Use of MapReduce has flourished since its premier, as illustrated by an in-depth example of its use in WordCount. Aug 02, 2016 · Next we show various attempts for scalable implementation of matrix multiplication using spark, and the winning method which combines numpy matrix multiplication along with spark’s broadcast and MapReduce Word Count Example. 18. ,0. 38) 13KB Synchronous-100x100-Matrix-Multiplication-using-Multiple-Threads：开发了一个程序，用于通过使用多个线程将两个大型矩阵 Nov 29, 2017 · Generalized matrix multiplication with semiring? Closing since I think this is out of reach of easy contributions. Each cell of the matrix is labelled as Aij and Bij. 7, which is an open source (Apache project) machine learning library. Dec 15, 2014 · This can be an important way to tune performance. Matrix Multiplication With 1 MapReduce Step. ,0. Matrix-multiplication kernels like gemm (dense-dense) and csrmm (sparse-dense), and utility kernels like csrcsc (sparse-transpose), sort (Parallel Sample Sort), and map-reduce are implemented in the framework. Let m be an NxM matrix and v a M vector. Design a MapReduce algorithm to compute matrix multiplication: A x B Mar 27, 2012 · Puzzle: Since there's so much other stuff in the nucleus, like proteins, it is sometimes troublesome finding room for a genome. new array wrappers are not covered, and only one level of wrapping is supported. Under Review: 2017. ∇ x ( p) T J ( i) ( θ) = ( δ ( i) T W) ⋅ 1 { i = p } ∈ R 1 × ( 2 w + 1) d, where the gradient with respect to the ( p, q) -th entry x ( p) q of the matrix x is given by. #MapReduce #MatrixMultiplication Apr 02, 2018 · Matrix Multiplication In MIPS. And more generally, taking a sum of outer products of corresponding rows and columns of the input matrices, always returns the desired matrix multiplication result. Trigger module in display ad project owner & core member Object: the old ad engine built reverse index from tag to ad, and this scheme suffered from long reverse index, the engine needed to do hard pruning when searching which hurt CTR. MPI Programming Matrix Multiplication Operators. matrix (np. 17. Here, the role of Mapper is to map the keys to the existing values and the role of Reducer is to aggregate the keys of common values. Matrix multiplication uses a generated function to return a matrix-product with at most one application of transpose , such that e. N. com/jfkelley/hadoop-matrix-mult After the submatrix multiplication, there's another MapReduce job that simply does the same Then iterate through just those sections of the arrays and multiply elem 9 Mar 2018 Sparse Matrix Matrix Multiplication. 2-CDH3U2 ← Matrix Multiplication using MapReduce – 1 Step Solution A celebrated example of an embarrassingly parallel problem is shared-memory matrix multiplication in which for two n n matrices, the multiplication process is split into n2 tasks, each responsible for calculating one element of the result matrix . Among them: matrix multiplication , similarity join [112,121,14,23], multi-way join using map-reduce offers a scalable Having that said, the ground is prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. ones ((3, 3)) + 3) m2 = m1 * (m2 + m1) m4 = 1. Moreover, Pegasus provides fast algorithms for GIM-V in MapReduce, a distributed computing platform multiplication operations . Section 5 will discuss https://github. Matrix Multiplication Map-Reduce. Shi, \"Performance Prediction and Evaluation of a Solution Space Compact Parallel Program using the Steady State Timing Model\", Poster, Future of My personal list of journals I use for my research and projects where I wrote one-sentence summaries. These operations are low-level, but for your convenience wrapped using high-level constructs. We write ++ for concatenation, so \"foo\" ++ \"bar\" is \"foobar\". Sparse matrix-vector multiplication (SpMV) is an important kernel that is considered critical for the performance of compute-intensive applications. Use an algorithm that does not require looking through every single possible matrix. Apr 29, 2013 · Sparse matrix computations in MapReduce!Austin Benson Tall-and-skinny matrix computations in MapReduceTuesday!Joe Buck Extending MapReduce for scientiﬁc computing!Chunsheng Feng Large scale video analytics on pivotal HadoopWednesday!Joe Nichols Post-processing CFD dynamics data in MapReduce !Lavanya Ramakrishnan Evaluating MapReduce and combining the matrix multiplication with the MapReduce is only 4 articles that we will discuss and com pare through this paper. Matrix Multiplication using Map-Reduce A specification ixs,iy is a matrix multiplication if ixs consists of two 2-tuples that share one index-label and iy is a permutation of the two-nonshared index-labels of the ixs. MapReduce is an attractive framework because it allows us to decompose the inner products involved in computing document similarity into separate multiplication and summation stages in a way that is well matched to efcient disk access using MapReduce minimize #syncs 8md Ours FPGA acceleration with small on-chip BRAM minimize data transfers (4m+4)d . Using item collaborative filtering algorithm to build co-ocurrence matrix by users' rating towards different movies from Netflix Prize Data Set. Thus, matrix multiplication is the major focus of performance optimization for many big data analytical algorithms or or applications. “Efficient Kernel Management on GPUs”. plot ( xs , ys ); 1 vala: Matrix[Float] //MxN 2 valb: Matrix[Float] //NxP 3 valc = Map(M, P){(i,j) => 4 //OuterMapfunction(f1) 5 Fold(N)(0. However, computing the inverse of a matrix using MapReduce is difficult when the order of the matrix is large. This is the function in C that will be implemented. e. In the following, we give an overview of backend-specific physical matrix multiplication operators in SystemML as well as their internally used matrix multiplication block operations. a ++ (b ++ c) = (a ++ b) ++ c. A matrix is a set of numerical and non-numerical data arranged in a fixed number of rows and column. 2. If you want uniformly spaced vectors, use the : operator. Stack Overflow. Cubert provides a novel sparse matrix multiplication algorithm that is best suited for analytics with large-scale graphs. first_10_even_numbers = 0: 2: 21 first_10_even_numbers = 0 2 4 6 8 10 12 14 16 18 20 A mode-n unfolding refers to the matrix of size Ln ×bL n obtained by arranging the mode-n fibers as the columns in a lexicographic order. What can we do with MapReduce? Models & Algorithms • Communication-processor tradeoffs for 1 round of MapReduce – Upper bounds for database join queries [Afrati,Ullman2010] – Upper and lower bounds for finding triangles, matrix multiplication, finding neighboring strings [Afrati, Sarma, Salihoglu, Ullman 2012] 5 compression idea from the sparse matrix-vector multiplication literature , into the Ligra shared-memory graph processing framework . the result will be the format of mat2. 2nd-row 1st column. Implementing matrix multiplication using MR and optimizing it using Combiner. A MapReduce program is defined via user-specified map and reduce functions, and we will learn how to write such programs in the Apache Hadoop and Spark projects. We propose a novel parallel execution model called pin-and-slide, which implements the column view of the matrix-vector mul-tiplication. ], [ 2. N. smaller/simpler) approximation of the original matrix A. rustlearn - a machine learning framework featuring logistic regression, support vector machines, decision trees and random forests. This code performs matrix vector multiplication using map reduce, which enables fast computations for large amounts of data. 3. At a high level, SVD is an algorithm that decomposes a matrix A into the best lower rank (i. Performance of matrix multiplication and random tensor contractions for rank-k update matrix/tensor shapes on a Xeon E5-2690 v3 processor. An extra MapReduce Job has to be run initially in order to retrieve the values. An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. 4. choose the year of your choice and select any one of the data text-file for analyzing. Installed multi node Hadoop 2. Using the best currently known parallel matrix multiplication [Wil12, LG14], our algorithm dynamically maintains the number of k-cliques in O min m 0:469k 235;( + m)0 :469k+0 amor-tized work w. Mathematically, it decomposes A into a two unitary matrices and a diagonal A matrix is a set of numerical and non-numerical data arranged in a fixed number of rows and column. By interpreting the matrix-vector multiplication in the column view, we can restrict the computation to just a subset of the May 21, 2015 · Jeffrey Dean and Sanjay Ghemawat. One of these systems is SystemML , which provides a high-level language for expressing some matrix operations such as matrix multiplication, division, and transpose Keywords: Item Collaborative Filter, Matrix Multiplication, MapReduce, Java, Hadoop - A movie recommender system is built to recommend movies in a similar style to users using raw data from Netflix. Jun 15, 2019 · Map Reduce paradigm is the soul of distributed parallel processing in Big Data. This is because the MapReduce works efficiently only with BIG data. In Proc eed- ings/42nd IEEE Symposium on Fo undations of Computer Science: October 14-17, 2001, Las Use same MapReduce job for operations w/o dependencies sFA Optimizations: Minimize Intermediary Data Recompute X and Y at each job rather than storing and exchanging Dec 27, 2015 · For multiplication, the key is to build rpos[], rpos[i] means in matrix N row i starts at rpos[i] position in datas[]. 01 import systemml as sml import numpy as np m1 = sml. Apr 05, 2019 · The below picture illustrates calculating an image’s class values for all 10 classes in a single step via matrix multiplication. One of the most important topic from university exam point of view. This is still not a complete solution though, e. Matrix-vector multiplication. 0f){k => 6 //Innermapfunction(f2) 7 a(i,k) * b(k,j) 8}{(x,y) => 9 //Combinefunction(r) 10 x + y 11} 12} Figure 1: Example of using Map and Fold in a Scala-based lan-guage for computing an untiled matrix multiplication using in-ner products. • Obtained a user’s rating matrix of films from the Netflix data using the Item Collaborative Filtering Algorithm, then obtained the co-occurrence matrix of the films, and finally merged both matrices to obtain a recommendation list. By-product: large-scale sparse matrix multiplication based on MapReduce. 1 and hadoop with Python 2. using matrix multiplication as example. ones ((3, 3)) + 3) m2 = m1 * (m2 + m1) m4 = 1. Mahout’s linear algebra DSL has an abstraction called DistributedRowMatrix (DRM) which models a matrix that is partitioned by rows and stored in the memory of a cluster of machines. We use 5 for this project, but you may want to increase this number for large datasets. If you like my post - Do follow me on this blog - Matrix Multiplication Using MapReduce Programming In mathematics , matrix mult map-reduce operation, we can perform grouping and aggregat ion, with I and K as the grouping attributes and the sum of V × W as the aggregation. . Each block is sent to each process, and the copied sub blocks are multiplied together and the results added to the partial results in the C sub-blocks. RecSys-2013-ZhuangCJL #matrix #memory management #parallel #performance A fast parallel SGD for matrix factorization in shared memory systems ( YZ , WSC , YCJ , CJL ), pp. For unidirectional (causal) attention, where tokens do not attend to other tokens appearing later in the input sequence, we slightly modify the approach to use prefix-sum computations, which only store running totals of matrix computations rather than mrjob fully supports Amazon’s Elastic MapReduce (EMR) service, which allows you to buy time on a Hadoop cluster on an hourly basis. matrix-matrix multiplication using * matrix-vector multiplication using * element-wise multiplication (Hadamard product) using . Pseudocode: First Map-Reduce job: Oct 25, 2016 · Mapper For a matrix multiplication of the form AB, we must provide in the mapper, the number of rows of A, referenced as row_a in the code, and the number of columns of B, referenced as col_b (The number of columns of A and number of rows of B are always same, else multiplication won't be possible). Most matrices are sparse so large amount of cells have value zero. Semi-External Memory Sparse Matrix Multiplication on Billion-node Graphs in a Multicore Architecture. Here's a small example to illustrate it. 20. Array operations - slicing, dicing, searching¶ Table of Contents Array operations - slicing, dicing, searchingArray slicingnD array slicingArray dicingArray broadcastingDeep copyArray searchingC •Similar to MapReduce •Aggregate multiple messages to same recipient from same server into a single message •Also executed at the receiver side to save space •Aggregators •Master collects data from vertices at the end of a superstep •Workers aggregate locally and use tree-based structure to aggregate to master This paper presents a MapReduce algorithm for computing pairwise document similarity in large document collections. What do we Outline a Map-Reduce program that calculates the vector x. ICALP-v2-2012-BaldeschiHLS #keyword #multi #on the On Multiple Keyword Sponsored Search Auctions with Budgets ( RCB , MH , SL , MS ), pp. Hence, the resulting product has the same number of rows as A and columns as B. 15 Dec 2014 map-reduce method for multiplying large, sparse matrices using Elasticsearch as As always, the code is available in the GitHub repository. Implementing the matrix multiplication with Map Reduce jobs to find the recommender movie(s). Below picture shows process for transpose: Below shows the process for 2 triple tuple matrix multiplication: check my code on github: link Matrix Multiplication: 2 MapReduce steps! Matrix M can be thought of as a relation with tuples (i, j, m ij) ! Matrix N can be thought of as a relation with tuples (j, k, n jk) ! Map operation creates these tuples ! Map: Join of M and N brings us closer to M X N by creating: Relation (i, j, k, m ij, n jk) or the relation (i, j, k, m ij X n jk) ! Nov 05, 2020 · MapReduce is a programming model and an associated implementation for processing and generating large datasets that is amenable to a broad variety of real-world tasks. Fast monte carlo algorithms for matrices iii: Computing a compressed approximate matrix decomposition, SIAM Journal of Computing, 2005. As the usual dense GEMM, the computation partitions the output matrix into tiles. Map-Reduce for each vertex D B A C Block Matrix Multiplication Let’s look at Block Matrix Multiplication (on the board and on GitHub) Experiment MapReduce: Result for Matrix Multiplication 38 MapReduce The speedup of using software-based atomic add over the system one increases as the input matrices get larger (up to 13. The ‘Iterative’ in the name of GIM-V denotes that we apply the £G opera- based on fast matrix multiplication. Blue line shows the 0. options. Graph reachability, using Matrix-Matrix multiplication of adjacency matrices. MapReduce is a processing technique and a program model for distributed computing based on java. The Map-reduce programming model is a common data-handling model Array-based distributed computations are another abstraction, used in all forms of parallelism. Graphs, and Matrix Multiplication using MapReduce, Spark, and MASS. Feb 01, 2013 · We extended the MapReduce SOM algorithm by moving all calculations on local nodes to the GPU with the matrix-based Euclidean distance matrix and reduction algorithm described above. A discussion about each of this operations is available below, if you want to go ahead of this section, click here. 39 is a matrix of residuals, assuming: s i. data. In the following, we give an overview of backend-specific physical matrix multiplication operators in SystemML as well as their internally used matrix multiplication block operations. Matrix Multiplication performed using Hadoop. Implementing matrix multiplication using MR and optimizing it using Combiner. . What we want to do We will write a simple MapReduce program (see also the MapReduce article on Wikipedia ) for Hadoop in Python but without using Jython to translate our Around version 0. UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. A MapReduce job can be enhanced by sampling local data, which cannot be used for future analysis. During the vector-matrix multiplication, each node will use its portion of the updated u vector, then estimate the v vector based on the multiplication of its putations as a single matrix-matrix multiplication (GEMM). Kublanovskaya, J. The RMM plan in Figure 1 im-plements a replication-based strategy in a single MapReduce version of matrix multiplication using recursive block matrix decomposition View MapReduceBlockMatrixProduct. Distributed engine neutral allreduceBlock() operator api for Spark and H2O. Unfortunately there is no acceleration routine for integers. Also, due to the inherent complexity of high-order computation, experience from prior work in other ﬁelds can not easily be applied to tensors. 8 Weeks. webbase-2001 Describe how you stored the connectivity matrix on disk and how you computed the transition matrix. Lecture 16 (5/28): Complexity Measures for MapReduce, Triangle Counting in a Graph The sum of these outer products matches the result we obtained in the previous slide using the traditional definition of matrix multiplication. concat. We show that serverless big data processing can lower oper- We also consider distributed MapReduce computations for training clustering models such as k-means and collaborative filtering models based on matrix factorization. 1. TensorFlow. In this case, each task needs one row of the ﬁrst input matrix and one Map Reduce Reduce. A breakdown of basic MapReduce terms and functions follows. matrix (np. 3 and use Different Algorithmic Techniques to Solve Following problems using Hadoop Map-Reduce. com/nm4archana/BigDataAnalysis-Comet. (For example Facebook) 4) K-mers counting using long DNA sequence in FASTA format 5) installing putations as a single matrix-matrix multiplication (GEMM). split (\"\\t\") index, value = map (int, [index,value]) if curr_index == prev_index: value_list. Integer factorization must be adaptable to MapReduce and must be parallizable (more than 1 Map or Reduce task) The emergence of large distributed clusters of commodity machines has brought with it a slew of new algorithms and tools. Finally the basic process of MapReduce is shown. You can still represent them using linear models. Irregular algorithms, however, depend on the input. I have published LSH package I developed for Apache Spark on GitHub. g. Diverse types of matrix classes/matrix multiplication are accommodated. MapReduce in distributed model training Using the MapReduce strategy, if we can split the training data on separate workers, compute Map functions in parallel, and aggregate the results in a Reduce function, we will be able to achieve distributed model Github. a mapreduce program of matrix multiplication. Green = true positive male, yellow = true positive female, red halo = misclassification. The ultimate goal is to make the algorithm as e cient as possible for any input . By using Monoids, we can take advantage of sparsity (we deal with a lot of sparse matrices, where almost all values are a zero in some Monoid). The operation is denoted Z = T×n A. matrix (np. Report this profile Addition of numbers, matrix multiplication inside a docker and using MapReduce as the programming model. Map the input matrices line by line and emits the matrix element. ee) Performance Prediction of Sparse Matrix Multiplication on a Distributed BigData Processing Environment. The sum of these outer products matches the result we obtained in the previous slide using the traditional definition of matrix multiplication. A naïve approach would be to extend an eﬃcient matrix multiplication algorithm, replacing the dot product by the distance function. xs = np . Contribute to ashkang/cs222_fin development by creating an account on GitHub. 99 “ Joel takes you on a journey from being data-curious to getting a thorough understanding Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision (SJ, RK, FM), pp. [J14] Yun Liang, Xiuhong Li. . Shi, \"How to achieve a 47000x speed up on the GPU/CUDA using matrix multiplication,\" Technical Report, Amax corporation, June 2009. Use a reducer to multiply value for same indices. His current research topic covers big data platforms, large-scale distributed computing resource manangement, cloud computing, and peer-to-peer systems. dot(a,b) array([[ 0. You can generate uniformly spaced vectors, using 2 methods. pdf such as MapReduce [Srirama et al, FGCS 2012] • Designed a classification on how the algorithms can be adapted to MR – Algorithm single MapReduce job • Monte Carlo, RSA breaking – Algorithm nMapReduce jobs • CLARA (Clustering), Matrix Multiplication – Each iteration in algorithm single MapReduce job • PAM (Clustering) Aug 29, 2015 · Posts about Machine Learning written by Maruf Aytekin. jl package. Ofeishat . Optimized Matrix Multiplication using Shared Virtual Memory In OpenCL 2. MATRIX MULTIPLICATION: Project to Read a file containing two 3 X 3 Matrices and calculate their Vector Product. 3 were implemented by their corresponding distributed primitives in Spark: I. The A sub-blocks are rolled one step to the left and the B Representing non-linearity using Polynomial Regression¶ Sometimes, when you plot the response variable with one of the predictors, it may not take a linear form. GitHub Gist: instantly share code, notes, and snippets. 249–256. Marlin contains several distributed matrix operations and especially focuses on matrix multiplication which is a funda-mental kernel of high performance scientiﬁc computing. test_naive. The matrix is denoted as T (n). straightforward, but the fact that matrix multiplication itself can be accomplished in multiple ways complicates matters. Individualpair-wiseremotememory distributed matrix multiplication Dec 29, 2017 · These techniques first partition matrix X into blocks and then exploit the block-matrix multiplication when learning U and V. Based on the observa-tion, Pegasus implements a very important primitive called GIM-V (Generalized Iterated Matrix-Vector multiplication) which is a generalization of the plain matrix-vector multi-plication. 20. A distributed, MapReduce-based SOM also builds on the batch formulation described in Equation 2 . . Amatname in fn: return 1 else: return 2 def joinmap(self, key, line): mtype = self. 281–284. io/Bulk. The chunk of X assigned to the node and the corresponding norms of X are kept in the GPU memory between subsequent epochs, and the weight vectors are copied to the 'sparse' is a matrix class based on a dictionary to store data using 2-element tuples (i,j) as keys (i is the row and j the column index). 1. the FFT, LU, and dense matrix–matrix multiplication. In this part of the code, the matrix multiplication begins, again, by implementing three MapReduce jobs. Policy: Printed material is allowed. i. There was a mix of similar problems presented in assignment 1 and assignment 2 that we had to solve them using MapReduce paradigm. Sep 10, 2012 · cost of the algorithm• determined by the amount of data that has to be sent over the network in the matrix multiplication step• for each user, we have to process the square of the number of his interactions → cost is dominated by the densest rows of A• distribution of interactions per user is usually heavy tailed → small number of Github. You have seen many of the stream operations before, in Question 5 of Exercise 7, including map, reduce, filter, and forEach • Matrix multiplication • Dynamic programming External Memory Model • Addition and subtraction are fast, multiplication is fast • MapReduce model: peated matrix-vector multiplications. 249–256. Designing e cient irregular algorithms is a challenge. 6. y * dz # [dz/dx * dL/dz] dy = self . push({key: key, value: value});}; map(row, emit); return emitArray;})); // Group tuples with the same key: var reducerInput = {}; mapperOutput. This was Jul 30, 2013 · MapReduce Algorithms: Having presented the video lectures on the topic, in which Prof. Using functions from various compiled languages in Python¶. ▫ SPGEMM: KKTRI: Triangle Counting using SpGEMM. Dec 14, 2016 · Data-Intensive Computing and MapReduce/Hadoop : For more info, see the MapReduce paper, it's pretty readable. js First of all lets recap the multiplication formula: import arraymancer proc customSigmoid2[T: SomeFloat](t: Tensor[T]): Tensor[T] = result = map_inline(t): 1 / (1 + exp(-x)) Now in a single loop over t, Arraymancer will do 1 / (1 + exp (-x)) for each x found. So, the whitespace or the indentation of the very first line of the program must be maintained all throughout the code. What we want to do We will write a simple MapReduce program (see also Wikipedia ) for Hadoop in Python but without using Jython to translate our code to Java jar files. Video: Youtube Map-Reduce! Ranking (e. MapReduce in distributed model training Using the MapReduce strategy, if we can split the training data on separate workers, compute Map functions in parallel, and aggregate the results in a Reduce function, we will be able to achieve distributed model We can use the logistic regression results to classify subjects as male or female based on their height and weight, using 0. Using the old API in the Mapper and Reducer. 281–284. Length. The MRQL query language is powerful enough to express most common data analysis tasks over many forms of raw in-situ data, such as XML and JSON documents, binary files, and CSV documents. js) To run the code mongo < multiply_map_reduce. txt. g. Mimir inherits the core principles of existing MapReduce frameworks, such as MR-MPI, while redesigning the execution model to incorporate a number of sophisticated optimization techniques that achieve similar or better performance with significant reduction in the amount of memory used. Thu 11/10: yuvraj: Virtual Machines : See also the book chapter on Virtual Machines from the Wisconsin OS book. Figure 4 illustrates how output splitting a ects weight and Using the Maven POM to manage your project is an easy way to start. BSPmodel. rithms are often iterative, using repeated read-only data access and I/O-bound matrix-vector multiplications to converge to an optimal model. requests in parallel by using the underlying multiple ﬂash memory packages. Subtypes of StaticArray will provide fast implementations of common array and linear algebra operations. With both the item-item similarity matrix and the user-item vectors, it’s now possible to multiply them together and generate recommendations for users. M. inline. MatrixMulOutput. NOTE: Please note that the Mapper function does not have access to the i, j, and k values directly. The MRQL query processing system can evaluate MRQL queries in two modes: in MapReduce mode on top of Apache Hadoop or in Bulk Synchronous Parallel (BSP) mode on top of Apache Hama. For example: MapReduce workflow: InputFormat, RecordReader, InputSplits, Map tasks, Combiners, Shuffle/Sort, Reduce tasks, OutputFormat. 55 folds) Ratio of FastPath to CompletePath memory accesses: 30:0 for software-based atomic and 3:28 for system-provided atomic implementations Since multiplication is done element-wise, you need to specifically perform a dot product to perform matrix multiplication. sum(B[i, :] * C[:, j]) Mapreduce and matrix multiplication November 2, 2016 The homework questions are due at the 23:59 on Tuesday 15 November. Specifically, the matrix multiplication operations described in Eq. Mar 12, 2018 · GitHub. 2. 0 2D card game 2048 (Android Studio, Java) Solely developed android game on windows platform using android studio. This method, however, is very inefficient as it would require to compute a matrix multiplication and the square root of a matrix at each step. parseLong(job. If you want a specific number of elements within a range, then use the linspace function. You can check it out from here. It is used to solve problems where problem of size N is solved using solution of problems of size N - 1 (or smaller). An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. Distributed matrix factorization with mapreduce using a series of broadcast-joins (SS, CB, MS, AA, VM), pp. Input are two matrix A and B python - How to write Mapreduce code for matrix multiplication which does not use any list of size more than 10 - Stack Overflow. One method for computing Pi (even though not the most efficient) generates a number of points in a square with side = 2. But MapReduce tries to use commodity machines to solve big data problems. js for ML using JavaScript TensorFlow 1 version, View source on GitHub the inner 2 dimensions specify valid matrix multiplication dimensions, and any level matrix computation primitives with MapReduce through the case study two basic primitives, matrix multiplication and finding linear solution, and goes into . 2. F ast monte-carlo algorithms for appr oximate matrix multiplication. ]]) >>>a[0,0]=1 >>>a[1,1]=1 >>>b =np. file') if self. StaticArrays provides a framework for implementing statically sized arrays in Julia, using the abstract type StaticArray{Size,T,N} <: AbstractArray{T,N}. The algorithm we’ll be using is a two-pass matrix multiplication algorithm for MapReduce. , PageRank) requires iterated matrix-vector multiplication with matrix containing millions of rows and columns ! Computing with social networks involves graphs with hundreds of millions of nodes and billions of edges ! Map-Reduce is a parallel programming paradigm, a software-stack that will help to address big data Used Blocked Matrix Multiplication technique to improve the convergence rate,by performing the nontrivial computation in the reduce steps. It is deployed on expensive hardware such as HPC or supercomputers. Our idea is to speed up distributed NMF in a new, orthogonal direction: by reducing the problem size of each NLS subproblem within NMF, which in turn decreases the overall computation cost. Please cite any references you use. mrjob has basic support for Google Cloud Dataproc (Dataproc) which allows you to buy time on a Hadoop cluster on a minute-by-minute basis. split()] row = int(vals) A key feature is the capability for users to write callback functions, called after each iteration, thus enabling customization for specific applications. The general algorithm matrix-vector multiplication (SpMV) and sparse matrix-matrix multiplication (SpGEMM), a systematic study on applying blocking techniques to tensors has not yet been conducted. List the top-10 vertices for graphs 1,2 & 4. Difference between MapReduce and Pig. Assume you have two matrices A and B in a sparse matrix format, where each record is of the form i, j, value. linspace ( 0 , 2 np . Do you have any idea, about the matrix multiplication example which I mentioned in question, that why this works fine with hadoop standalone mode but does not work with hadoop distributed mode at the point of checking answers? – waqas Nov 30 '11 at 13:39 Matrix multiplication using MPI. Matrix-vector and matrix-matrix calculations fit nicely into the MapReduce style of computing. Big Data Project On A Commodity Search System For Online Shopping Using Web Mining Big Data Project On A data mining framework to analyze road accident data Big Data Project On A neuro-fuzzy agent based group decision HR system for candidate ranking Big Data Project On A Profile-Based Big Data Architecture for Agricultural Context Big Data Project On A Queuing Method for GSoC Results and Summary. Thus, Meta-MapReduce enhances the standard MapReduce and can be implemented into the state-of-the-art MapReduce systems, such as Spark, Pregel , or modern Hadoop. $docker run -v Matrix multiplication is an important application in. In MapReduce word count example, we find out the frequency of each word. You might want an order 2 or 3 curve. General-purpose, heavy- and An example of how multi-method-based dispatch might work for a binary operation like matrix multiplication. 1. 6. xs = np . If the multiplication type computes in parallel, then the package computation is also parallel. 0-m2 m4. e. 快速矩阵乘法 Fast and Stable matrix multiplication Coppersmith and Winograd's Algorithm 时间复杂度O(n^2. ∙ 0 ∙ share While performing distributed computations in today's cloud-based platforms, execution speed variations among compute nodes can significantly reduce the performance and create bottlenecks like stragglers. Stage 2. Naive Bayes classifier to classify text documents Latent semantic analysis (LSA) Rsa breaking using a more efficient integer factorization than trial division. parsemat() vals = [float(v) for v in line. 1. I got it right. MapReduce. PRELIMINARY A. Feb 16, 2015 · Matrix Data Model for MapReduce. ones ((3, 3)) + 2) m2 = sml. There are two main security concerns in outsourcing computation: guaranteeing that the server performs the computation correctly, and protecting the privacy of the client’s data. The first is Map Only with CAP3 DNA Sequence Assembly, followed by Classic MapReduce with Pair-wise Sequences and High-Energy Physics, Iterative with K-means clustering, PageRank and Multi-dimensional Scaling, and finally Loosely Synchronous with Matrix Multiplication Algorithms. Sparse Matrix Multiplication in Map Reduce. CS231n, Convolutional Neural Networks for Visual Recognition, Stanford University; CS224d, Deep Learning for Natural Language Processing, Stanford University You can now run all stages of the rewrite system for a program (in this example for matrix multiplication): scripts / compiled_scripts / HighLevelRewrite highLevel / mmTransposedA scripts / compiled_scripts / MemoryMappingRewrite -- gr10 mmTransposedA scripts / compiled_scripts / ParameterRewrite - f highLevel / mm . MPI is a SPMD model of distributed computing, where each process is completely independent and one just controls the memory handling. ,3. Aug 25, 2017 · Matrix Multiplication using MapReduce Programming in Java. json mmTransposedA Jul 14, 2020 · MapReduce Program – Finding The Average Age of Male and Female Died in Titanic Disaster; MapReduce – Understanding With Real-Life Example; How to find top-N records using MapReduce; How to Execute WordCount Program in MapReduce using Cloudera Distribution Hadoop(CDH) Matrix Multiplication With 1 MapReduce Step; MapReduce – Combiners matrix multiplication operations within the NMF algorithms. An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. It uses a distributed file system called GFS, which is Google File System. Matrix Multiplication with Spark. ], [ 0. Plagiarism checking with MapReduce Manages: Pelle Jakovits ([email protected] 22 706. ####MapReduce problems#### Count number of words in a book; Total number of words in a book; tf-idf calculations for ranking; Cosine distance measure between 2 documents; Matrix multiplication in MapReduce Aug 13, 2016 · Matrix Computations and Optimization in Apache Spark Reza Bosagh Zadeh Stanford and Matroid 475 Via Ortega Stanford, CA 94305 Xiangrui Meng Databricks 160 Spear Street, 13th Floor San Francisco, CA 94105 Alexander Ulanov HP Labs 1501 Page Mill Rd Palo Alto, CA 94304 [email protected] zeros(4). e. Jueon Park, and Kyungyong Lee, The 8th International Workshop on Autonomic Management of high performance Grid and Cloud Computing (AMGCC'20), Accepted, 07/2020. OSDI’04 ,San Francisco, CA; Petros Drineas, Ravi Kannan, and Michael W. edu Burak Yavuz Databricks 160 Spear Street, 13th Floor San Francisco, CA 94105 [email protected] the code works perfectly fine with smaller matrices but when the files becomes large the mapping p Nov 12, 2020 · Matrix B is also a 2×2 matrix where number of rows(j)=2 and number of columns(k)=2. Data Analysis of huge amount of open Github Data, where we tried to find some deep patterns among popularity and spatial distributions of programming languages and users on Github. Moreover, your code has two steps, that means two jobs. Course content Because using map is equivalent to for loops, with an extra code we can always write a general mapping utility: >>> def mymap(aFunc, aSeq): result = [] for x in aSeq: result. It may be possible to switch between MapReduce and MPI to perform scalable matrix inversion in these The next step is PageRank, a fairly straightforward linear algebra problem. Lecture 15 (5/26): Partitioning for PageRank Lecture 15, Partitioning for Pagerank. While some arrays — like Array itself — are implemented using a linear chunk of memory and directly use a linear index in their implementations, other arrays — like Diagonal — need the full set of cartesian indices to do their lookup (see IndexStyle to Feb 08, 2010 · This posting gives an example of how to use Mapreduce, Python and Numpy to parallelize a linear machine learning classifier algorithm for Hadoop Streaming. get(\"NumberOfDocuments\"));} The variable N can then be used with the map and reduce functions. 5 × 10 5 and the number of nonzero elements equal to 6 × 10 5. By using Rings, we can do matrix multiplication over things other than numbers (which on occasion we have done). 1. sin ( xs ) # np. We use dense() to create a dense in-memory matrix from our toy dataset and use drmParallelize to load it into the cluster, “mimicking” a large, partitioned • Used Netflix data to offer movie recommendations to users based on their previous favorites. , 2015. CS231n, Convolutional Neural Networks for Visual Recognition, Stanford University; CS224d, Deep Learning for Natural Language Processing, Stanford University Publication: M. Syntax of Mongo mapReduce() Following is the syntax of mapReduce() function that could be used in Mongo Shell > db. Figure 4 illustrates how output splitting a�ects weight and In modern processors, integer division can be 10-50 times slower than multiplication. AWS Elastic MapReduce, an adaptation of Apache Hadoop to Matrix Multiplication: 2 MapReduce steps! Matrix M can be thought of as a relation with tuples (i, j, m ij) ! Matrix N can be thought of as a relation with tuples (j, k, n jk) ! Map operation creates these tuples ! Map: Join of M and N brings us closer to M X N by creating: Relation (i, j, k, m ij, n jk) or the relation (i, j, k, m ij X n jk) ! Jul 26, 2016 · Outline • Introduction • DFS • MapReduce • Examples • Matrix Calculation on Hadoop 3. Advices [edit \| edit source] In this section, you will see some advices that can help you to desing a Python source Refactor compression package and add functionalities including quantization for lossy compression, binary cell operations, left matrix multiplication. For sparse computations, they usually depend on the nonzero pattern of the matrix. per batch of updates where mis de-ﬁned as the maximum number of edges in the graph be- Jun 15, 2013 · For those who prefer reading a code instead of text - GitHub: Approach1(multiply_map_reduce. For example : mat1 is 2×3 means mat2 will be 3×2. Implement SELECT MAX(<field>) FROM <table> GROUP BY <field> with MapReduce. 8 May 2015 https://github. . In all cases, Twister outperforms or is close to the competition. Implementations in CUDA Sep 2015 – Sep 2015 2. 7. . Create a matrix of processes of size p1/2 1/2 x p so that each process can maintain a block of A matrix and a block of B matrix. X-rays) are sent through an object from various angles Google MapReduce. Combiner Edit the “MapTask” method to add support for running a Combiner. The repository provides demo programs for implementations of basic algorithms on Spark 2. h. apply([], input. N(0;˙2). Many applications in different areas exist already for MapReduce. pi , 100 ) ys = np . Matrix Multiplication with MapReduce Big Data possibly now has become the most used term in the tech world for this decade. 95% c Thanks Thomas. Mark Kröll 击 see https://hadoopecosystemtable. 7. in a way you should be familiar with. Android4. Mo 09 Dezember 2013 How to use Jekyll with GitHub ; Di 05 Juli 2016 Pythons map, reduce and filter as list Matrix multiplication on multiple cores in Jun 25, 2012 · Translating to MapReduce: rethinking matrix multiplication It’s now possible to use MapReduce to multiply the user vectors computed in step 1, and the co-occurrence matrix from step 2, to produce a recommendation vector from which the algorithm can derive recommendations. Matrix-Vector multiplication As an example if we consider a Matrix-Vector multiplication (taken from the book Mining Massive Data Sets by Jure Leskovec, Anand Rajaraman et al To store the past gradients, we will use a matrix G. International Journal of Computer Science and Information Technology (IJCSIT) 9 (5): 29 - 37 ( October 2017 Figure 1 shows the general matrix multiplication (GEMM) operation by using the block sparse format. Look for “# [ADD COMBINER HERE]” for the place one would add this. 2 minute read. the rule of matrix multiplication is mat1 columns is equal to mat2 rows values. It may help if you checkout my introduction to map-reduce and an example here. To do so, we are taking input from the user for row number, column number, first matrix elements and second matrix elements. Contribute to JaredP94/MapReduce-Matrix-Multiplication development by creating an account on GitHub. GitHub Gist: instantly share code, notes, and snippets. MapReduce is a programming model that Google came up with to handle computation of their huge large scale data. The examples below use the einsum / notation for the elements of tensors, namely m[i,j] for element i,j of the matrix m, instead of the more mathematical notation m_ij. #!/usr/bin/env python import sys from operator import itemgetter prev_index = None value_list = [] for line in sys. Dijkstra's algorithm. GPU Accelerated Computing with C and C++, which also has some videos. Combiner Edit the “MapTask” method to add support for running a Sparse matrix multiplication for hadoop. Matrix Multiplication Operators. to implement matrix inversion using other parallelization platforms such as MPI, a MapReduce matrix inversion technique that can be used as a pluggable component in complex Hadoop data analysis workﬂows is highly desirable. The instruction sets are typed, and instructions designed to operate on packed doubles can’t operate on packed ints without explicit casting. (Duh!) Map takes data and converts it into another set of data, where individual elements are broken down into tuples (key/value pairs). rusty-machine - a pure-rust machine learning library. - Use MapReduce to calculate tag similarity in twitter and improves the speed from 90min to 36min. e. 0 and measured the performance of the same with previous implementations. 5 In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. ]]) Matrix Multiplication Examples (both using global memory and shared memory) CUDA C Programming Guide; CUDA Toolkit documentation, which includes CUDA installation, C programming guide, APIs for cuBlas, cuFFT etc, tools, compiler SDK, and others. “Limitations and Challenges of HDFS and MapReduce” by Weets et al. 10 of Mahout it became obvious that using Hadoop MapReduce was causing more pain than it was solving, due to massively redundant data reads required 1 Problems Suited for MapReduce 2 MapReduce: Applications Matrix-Vector Multiplication Information Retrieval 3 Hadoop Ecosystem Designing a Big Data System Big Data Storage Technologies Slides are partially based on Slides “Mining Massive Datasets” by Jure Leskovec. What inference can you derive from using PageRank on the these datasets. The minimum is found by a multi-step reduction algorithm. 10 Matrix Multiplication with One MapReduce Step . 6. sin is a universal function plt . Jan 17, 2021 · Matrix Multiplication With 1 MapReduce Step; Hadoop - copyFromLocal Command go to this GitHub Repo and download the receptacle organizer as a speed as For advanced use of the CUDA, you can use the driver API wrappers in CUDA. 1. per batch of updates where mis de-ﬁned as the maximum number of edges in the graph be- Matrix multiplication: n^3/p + (n^2/p^{2/3}) \\cdot g + l: Sorting (n \\log n)/p + (n/p)\\cdot g + l: Fast Fourier Transform (n \\log n)/p + (n/p)\\cdot g + l: LU Decomposition: n^3/p + (n^2/p^{1/2})\\cdot g + p^{1/2}\\cdot l: Cholesky Factorisation: n^3/p + (n^2/p^{1/2})\\cdot g + p^{1/2}\\cdot l: Algebraic Path Problem (Shortest Paths) Distributed ﬁle systems and map-reduce as a tool for creating parallel 2. with callbacks. Assume you have two matrices A and B in a sparse matrix format, where each record is of the form i, j, value. For matrix computation library built on top of Spark which is an distributed in-memory cluster computing framework. Ex. Vogelstein, Carey E. reshape(2,2) >>>b array([[0, 1], [2, 3]]) >>>ab array([[ 0. Using the new API in the Mapper and Reducer. Remember, a combiner runs the reduce task at the end of the map task in order to save communication cost of sending to multiple reducers. tar. Specifically, for building MapReduce jobs, you only need to have the hadoop-client dependency, which contains all the Hadoop client-side classes needed to interact with HDFS and MapReduce. The goal is to calculate A B. [experimental] New python bindings with supports for several builtin s, matrix operations, federated tensors and lineage traces. Lowering XLA HLO to I E 6 func @mnist_predict(%input: tensor<1x28x28x1xf32>) /> tensor<1x10xf32> {%1 = mhlo. hollywood-2011 2. PageRank) Gradient descent methods Stochastic SVD Tall skinny QR This paper presents a MapReduce algorithm for computing pairwise document similarity in large document collections. I couldn't find a simple way to do this within the EMR framework, though I bet there is a way to do it. import systemml as sml import numpy as np m1 = sml. On the left are the full matrix organized in blocks and its internal memory representation: compressed values and block indices. The essence of the transformation is to unroll the input patches (a 3D matrix) and �lters (a 4D matrix) in 2D in a way that a single matrix-matrix multiplication produces the unrolled version of the output in 2D. Common operations include synchronizing the GPU, inspecting its properties, starting the profiler, etc. Sparse Matrix-Vector Multiplication { Size of Distributed Matrix Multiplication Using Speed Adaptive Coding 04/15/2019 ∙ by Krishna Narra , et al. Da Zheng, Disa Mhembere, Joshua T. Figure 1 and Figure 2 show two alternative MapReduce plans for matrix multiplication (details of the two plans will be discussed in Section IV). MapReduce is an attractive framework because it allows us to decompose the inner products involved in computing document similarity into separate multiplication and summation stages in a way that is well matched to efcient disk access May 12, 2018 · On Intel CPUs, SSE instruction sets use up to 128 bit registers (xmm, four ints), AVX and AVX2 use up to 256 bit registers (ymm, eight ints), and AVX512 use up to 512 bit registers (zmm, sixteen ints). 1957: Minimum degree sparse matrix reordering (Harry Markowitz) 1961: QR algorithm (V. Curtis Huttenhower, John Quackenbush, Lorenzo Trippa & Christine Choirat. Thus, r u v ≈ x T u ⋅ θ v, where x u, θ v ∈ R f are the u t h Map-Reduce also makes short work of dealing with large matrices and can crunch matrix operations like matrix addition, subtraction, multiplication etc. 2 and the deflation operation defined in Eq. Implement inner join between two tables with MapReduce. Design a MapReduce algorithm to compute matrix multiplication: A x B Matrix Multiplication. The common matrix operations such as 'dot' for the inner product, multiplication/division by a scalar, indexing/slicing, etc. forEach(function(keyValue) Example matrix multiplication in distributed environment using R, MPI and Hadoop MapReduce - aaparo/MultMatrix Use Git or checkout with SVN using the web URL. And more generally, taking a sum of outer products of corresponding rows and columns of the input matrices, always returns the desired matrix multiplication result. No electronic device (except for electronic calculator). The class will cover widely used distributed algorithms in academia Dynamic programming is well known algorithm design method. Matthews Author content It can be used in conjunction with other functionality like Map, Reduce, Filter in Python. append(aFunc(x)) return result >>> list(map(sqr, [1, 2, 3])) [1, 4, 9] >>> mymap(sqr, [1, 2, 3]) [1, 4, 9] >>> Aug 25, 2011 · In-Database Operations • Matrix and vector multiplication: Av SELECT 1, array_accum(row_number, vectorv) FROM A array_accum(x,v) is a custom function. Both of these are considered to be whitespaces when you code. Figures - uploaded by Devin A. Current Apache Mahout: Beyond MapReduce Matrix Multiplication. Note: Matrix operations for floats are accelerated using BLAS (Intel MKL, OpenBLAS, Apple Accelerate …). ,0. 1. Ligra+ is able to represent a variety of synthetic and real-world graphs using General Matrix-Vector multiplication: y <- alpha A * x + beta * y Source Edit proc gemv [T: SomeInteger] (alpha: T; A: Tensor [T]; x: Tensor [T]; beta: T; y: var Tensor [T]) { } {. Clearly it holds that. 11 Jan 2009 Okay, so how can we compute PageRank using MapReduce? we'll take is to use MapReduce to repeatedly multiply a vector by the matrix M 23 Feb 2021 Multiplies matrix a by matrix b, producing a * b. Say the co-occurrence matrix for 4 items is Courses ¶. It also discusses various hadoop/mapreduce-specific approaches how to potentially improve or extend the example. MapReduce¶ MapReduce was designed by Google to address the problem of large-scale data processing. append ( (index,value)) else: if prev_index: value_list = sorted (value_list,key=itemgetter (0)) i In this video u will learn about Matrix Multiplication using Map Reduce in Big-Data. p. The 27 Jun 2020 Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers. Francis) 1964: Sinkhorn (Richard Sinkhorn) 1965: Golub-Reinsch SVD (Gene Golub) 1969: Sparse matrix ordering (Elizabeth Cuthill, James McKee) 1969: Strassen matrix multiplication (Volker Strassen) INTRODUCTION TO DATA SCIENCE JOHN P DICKERSON Lecture #4 –9/5/2019 CMSC320 Tuesdays & Thursdays 5:00pm –6:15pm Graph reachability, using Matrix-Matrix multiplication of adjacency matrices. Download [edit \| edit source] The source code is available on Github. One purpose of matrix decomposition is reducing calculations cost while solving a system of linear equations by decomposing the coefficients matrix into a product of two triangular matrices. MapReduce • Programming Model for Large-Volume Data Processing • Specialized for frequent use case: aggregation queries – Map every input object to set of key/value pairs – Reduce (aggregate) all mapped values for same key into one result for that key • Use this structure as explicit API for cluster computing May 01, 2018 · You fit this matrix to approximate your original matrix, as closely as possible, by multiplying the low-rank matrices together, which fills in the entries missing in the original matrix. Using MapReduce, we could achieve N times throughput by having N workers running in parallel. Here, we will discuss the implementation of matrix multiplication on various communication networks like mesh and hypercube. 99 CAN$45. Taifi and Y. 1. Qatawneh , and H. Now One step matrix multiplication has 1 mapper and 1 reducer. In a nutshell, we reduce the size of each NLS subproblem, by employing a matrix sketching technique: Having that said, the ground is prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. Aug 02, 2016 · Next we show various attempts for scalable implementation of matrix multiplication using spark, and the winning method which combines numpy matrix multiplication along with spark’s broadcast and Courses ¶. View on GitHub Spark. Challenge: Make linear https://github. ones ((3, 3)) + 2) m2 = sml. Published: December 08, 2018 Hi everyone, this is the final (summarizing) blog post for my Google Summer of Code project. the FFT, LU, and dense matrix matrix multiplication. For both classes, few matrix operations dominate the overall algorithm runtime, apart from the costs for the initial read from distributed le system or object storage. F. In fact, large-scale matrix multiplication can hardly be handled by the single-node matrix computation libraries due to hardware resource limitation. The unit of Parallel Matrix Multiplication on Open MPI. github. Fortunately, the authors in proposed a method of matrix inversion using MapReduce. js mongo < multiply_map_aggregate. 26 >>>a =np. Straggler Robust Distributed Matrix Inverse Approximation 03/05/2020 ∙ by Neophytos Charalambides , et al. ], [ 0. The reduce( ) step in the MapReduce Algorithm for matrix multiplication Facts: The final step in the MapReduce algorithm is to produce the matrix A × B. In this example did the matrix multiplication. git. There are many parallel computation prototype for matrix multiplication using FaaS, and discuss and synthesize insights entry-barriers of. This workload tests the Naive Bayesian (a popular classification algorithm for knowledge discovery and data mining) trainer in Mahout 0. However, I want to tell you something, if your file is not big enough, you will not see an improvement in term of execution speed. 3. Besides matrix-vector multi-plication (e. There are Python 2. map(function(row) { var emitArray = []; var emit = function(key, value) {emitArray. 7 codes and learning notes for Spark 2. In SpMV, the optimal selection of storage format is one of the key aspects of enabling the best performance. source The code is available on my GitHub account of the converting a collection to stream using stream method; reading from a file using Files. the result is the same as mat2. Use of ufuncs is an esssential aspect of vectorization and typically much more computtionally efficient than using an explicit loop over each element. Dec 29, 2017 · Background Matrix factorization is a well established pattern discovery tool that has seen numerous applications in biomedical data analytics, such as gene expression co-clustering, patient stratification, and gene-disease association mining. Using the best currently known parallel matrix multiplication [Wil12, LG14], our algorithm dynamically maintains the number of k-cliques in O min m 0:469k 235;( + m)0 :469k+0 amor-tized work w. One, you can multiply BIG matrices in a memory efficient way, without needing to pull everything out of SQL. Our extended framework, which we call Ligra+, uses less space than Ligra, while providing comparable or improved performance. 2-CDH3U2 ← Matrix Multiplication using MapReduce – 2 Step Solution A Movie recommender system using Netflix movie data and currently on the stage of achieving matrix multiplication, use the item-collaborative algorithm and Hadoop MapReduce Auto Complete Apr 2018 traditional matrix-vector multiplication requires): 1. Then matrix-vector multiplication m * v is defined as: w[i] = sum_j m[i,j] * v[j]. The verifiable computation of Gennaro, Gentry and Parno addresses both concerns for Mimir: Mimir is a new implementation of MapReduce over MPI. Nov 20, 2020 · Matrices represented using COO format Matrix Multiplication Using Two Passes. Use Git or checkout with SVN using the web URL. This can be parallelized easily (just matrix-vector multiplication) but needs to chain together multiple MapReduce tasks. Spring 09 Publication: M. Jul 14, 2013 · The advantage of the above logic is, we can use a distributed map reduce model for compute with multiple map-reduce tasks - Constructing the co-occurrence matrix, Finding the dot product for each user etc. mapReduce # Python 3 my_strings = ['a', 'b', 'c', 'd', 'e'] my_numbers = [1,2,3,4,5] results = list(zip(my_strings, my_numbers)) print(results) As a bonus, can you guess what would happen in the above session if my_strings and my_numbers are not of the same length? Large-scale machine learning is another important use of MapReduce. A well-known matrix factorization method is Singular value decomposition (SVD). 522–532. Thursday, August 25, 11 30 The Mahout In Action (Chapter 6) book contains a recommendation method based on matrix multiplication that uses co-occurrence data (C) in combination with user preferences (U) to generate user recommendations (R). com/awslabs/lambda-refarch- mapreduce/. To put it in a crude analogy, Page Rank, Inverted Index and Matrix Multiplication - asarraf/Algorithm- Implementation-Using-Map-Reduce. arange(4). rb. x is a shorthand for the elements of the first tensor argument. * Distributed performance bug fixes. 1–12. To maximize parallelism, the Gram matrix is calculated, that is, a matrix of the distances between every data instance and the nodes of the SOM. } General Matrix-Vector multiplication: y <- alpha * A * x + beta * y Source Edit proc gemm [T: SomeFloat \| Complex] (alpha: T; A, B: The product of matrices A and B is calculated by multiplying the elements of rows in A with the corresponding columns in B, and then adding the resulting values to produce a single value for each row in A and each column in B. The Formula is: Mapper for Matrix A (k, v)=((i, k), (A, j, Aij)) for all k That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. to distributed matrix multiplication and distributed learning. regCG, for example, only lines 4 and 9 access matrix X; all other computations are inexpensive operations over small vectors or scalars. 5 as a cutoff, as shown in the plot below. com/Cloveryww/MPI-parallel-algorithms/tree/master/ cannon Since the algorithm and the lower hair collection task results when us 26 Nov 2018 Map Reduce (Part 3). sum (axis = 1). matrix (np. I'm working on the matrix multiplication using mapreduce. G. assign(vi;vnew) : decide how to update vi with vnew. Nov 29, 2017 · MapReduce, by Google, in 2004; Hadoop (fair mode), Spark (easy mode) MPI (hard mode) Matrix multiplication A = BxC for i in range(m): for j in range(n): for k in range(r): A[i][j] += B[i][k] * C[k][j] Matrix multiplication Vectorized for i in range(m): for j in range(n): A[i, j] = np. Problem Motivation Apr 04, 2019 · Other Links: GitHub Repository. Eq. The is similar to the process of generating the Row Number as explained in the previous post. It involves the matrix Oct 08, 2019 · In Cholesky method, a positive-definite matrix is written as the matrix multiplication of a lower-triangular matrix and its transpose. RecSys-2013-ZhuangCJL #memory management #parallel #performance A fast parallel SGD for matrix factorization in shared memory systems ( YZ , WSC , YCJ , CJL ), pp. 5 cutoff. GitHub Gist: instantly share code, notes, and snippets. Google’s MapReduce (Example)1 Classic example: word count. , non-causal attention where there is no notion of past and future. com/kokkos/kokkos- kernels \"Graph twiddling in a mapreduce world. Matrix-Vector Multiplication. ACM Transactions on Embedded Computing Systems (TECS), Vol 16, Issue 4, May 2017. Databases 2 Application 1: Matrix-Vector Multiplication. rstrip (). 55 folds) Ratio of FastPath to CompletePath memory accesses: 30:0 for software-based atomic and 3:28 for system-provided atomic implementations Matrix factorization (MF) factorizes a matrix R ∈ R m × n (with N z non-zero elements) into two low-rank matrices X ∈ R m × f and Θ ∈ R n × f, such that R ≈ X ⋅ Θ T. The output should be similar with the input. Matrix Multiplication With MapReduce. require ' rubygems ': require ' matrix ': require '. plot ( xs , ys ); Apr 09, 2013 · OutcomesRecognize relationships between matrix methods andthings you’ve already been doing\" Example SQL queries as matrix computationsUnderstand how to use Hadoop to compute thesematrix methods at scale for BigData\" Example Recommenders with social network infoUnderstand some of the issues that could arise. combine2(mi;j;vj) : combine mi;j and vj. Priebe, and Randal Burns. /matrix_block_mixin ' Mar 28, 2012 · That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. Background MapReduce and Spark Matrix Multiplication Note: also with row/column vector rhs Note: 1:N join. Matrix multiplication is an important multiplication design in parallel computation. Please turn in source codes, compilation, submission scripts used and also output les. 28 Mar 2012 P is a matrix = MN with element pik in row i and column k, where pik =∑j mijnjk Relational Representations: M = M(I, J, V ), with… Matrix Multiplication using MapReduce – 2 Step Solution Source Code: GitHub. ]]) >>>np. 2 A New Parallel Matrix Multiplication Algorithm on Hex-Cell Network (PMMHC) Using IMAN1 Super Computer E. input. However, such a straightforward approach does not apply to matrix tri-factorization because, as we show in the Methods section, the learning of any block of U and V depends on factor S . 0. May 12, 2018 · On Intel CPUs, SSE instruction sets use up to 128 bit registers (xmm, four ints), AVX and AVX2 use up to 256 bit registers (ymm, eight ints), and AVX512 use up to 512 bit registers (zmm, sixteen ints). Contribute to tangsttw/Matrix- Multiplication-MapReduce development by creating an account on GitHub. ,3. Report this profile Addition of numbers, matrix multiplication inside a docker and using MapReduce as the programming model. reshape(2,2) >>>a array([[ 0. y = y return z def backward ( dz ): dx = self . Lecture 14, Matrix Computations and Optimization in Apache Spark, Sparse matrix multiplication using SQL, Sparse matrix multiplication in MapReduce. Everybody is talking about it and everybody have their own understanding towards it which has made its definition quite ambiguous. My Personal Notes arrow_drop_up. Dec 16, 2019 · Outsourcing computation has gained significant attention in recent years in particular due to the prevalence of cloud computing. Use the output from the Stage 1 Reducer and pass along the same input to the Stage 2 reducer, where all the values having same index pairs are summed up to get the final output value. 04/27/18 - Large-scale machine learning and data mining applications require computer systems to perform massive computations that need to be May 02, 2018 · One kernel that can be parallelized using SPMD parallelism is dense matrix-matrix multiplication, in which we multiply two input matrices A and B to produce an output matrix C. Introduction Modern data-mining or ML applications, called «big-data analysis» requires us to manage massive amounts of data quickly. Here two passes symbolises the fact that we will need two map reduce jobs to compute the matrix multiplication. Then we are performing multiplication on the matrices entered by the user. 13. This matrix at each step will be updated and extended. After scaling genotype and expression data to unit variance with matrix-vector multiplications (or matrix-matrix with a small second matrix), and (2) closed-form algorithms with transpose-self matrix multiplication. x * dz # [dz/dy * dL/dz] return [ dx , dy ] “Scale-free Sparse Matrix-Vector Multiplication on Many-Core Architectures, “ IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), Vol 36, Issue 12, Dec 2017. Large Scale Machine Learning: Page: Gradient descent with large data, stochastic gradient descent, mini-batch gradient descent, map reduce, data parallelism, and online learning. It is crucial for perfor-mance to t the data into single-node or distributed main memory and enable fast matrix-vector opera-tions on in-memory data. The aim of this library is to easily design prototypes of algorithms using MapReduce. The product of a n x n matrix M by a vector v of length n is given by Dec 25, 2020 · Matrix Multiplication At Scale Using Map Reduce Matrix multiplication is the one of the most fundamental operation that most of the machine learning algorithms rely on. Taifi and Y. Optimizations Around version 0. x = x # must keep these around! self . For any u and v, such tat 1 ≤ u ≤ m and 1 ≤ v ≤ n, r u v is the (i, j) entry of R. toNumPy () Output: array ([[ - 60. This file shows the output of the resultant matrix obtained by multiplying matrix A and B in the format \"(row,column) value\" Contribute to JaredP94/MapReduce-Matrix-Multiplication development by creating an account on GitHub. It takes the value v and puts it in the row indexed by x. Feb 08, 2015 · Write a MapReduce query to remove the last 10 characters from each string of nucleotides, then remove any duplicates generated. A file containing two Matrices - MatrixA and MatrixB, was fetched from the Hadoop Distributed File System (HDFS) as an input for the Map Reduce task. - Use OpenMP and SSE to improve the speed of matrix multiplication over 86 times and kmeans 11 times. As the instructor pointed out, there are reasons this approach isn't insane. a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c max (a, max (b, c)) = max (max (a, b), c) min (a, min (b, c)) = min (min (a, b), c) Strings with string-concatenation form a semigroup. There are 2 implementations of the 3 Feb 2018 PDF \| On Dec 1, 2017, Mais Haj Qasem and others published Matrix multiplication of big data using MapReduce: A review \| Find, read and cite 4. Map Reduce Example for Sparse Matrix Multiplication. in a way you should be familiar with. Here, we will discuss the implementation of matrix multiplication on various communication networks like mesh and hypercube. The definition is motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. Write a MapReduce query to remove the last 10 characters from each string of nucleotides, then remove any duplicates generated. distributed map reduce In this module, we will learn about the MapReduce paradigm, and how it can be used to write distributed programs that analyze data represented as key-value pairs. It takes in 6 parameters: n: number of rows in A; m: number of I would like to apply map-reduce to deal with matrix multiplication in python with Hadoop. Jul 28, 2020 · Analyzing weather data of Fairbanks, Alaska to find cold and hot days using MapReduce Hadoop. , line 9), we have vector-matrix multiplication, often caused by the rewrite X>v !(v>> > > 2 Implement SELECT * FROM <table> WHERE <condition> with MapReduce. jl. 1 Matrix Multiplication Hadoop Implementation . * DRM row sampling api. Illustrates how a variety of coercion-based defaults can be specified to make life easy on the implementer, while still easily allowing for dispatch to optimal implementation-specific routines whenever it's desired. You might want to examine the Hadoop code for Word Count and Matrix multiplication. DATA/DATA SCIENCE Data Science from Scratch ISBN: 978-1-491-90142-7 US $39. So, several papers have studied the problem of multiplying matrices using a large number of processors (CPUs) in parallel. Kyungyong Lee is an assistant professor in the College of Computer Science at Kookmin University. The instruction sets are typed, and instructions designed to operate on packed doubles can’t operate on packed ints without explicit casting. In this post, we will be writing a map-reduce program to do Matrix Multiplication You need Hadoop’s HDFS and map GitHub Gist: star and fork jaganadhg's gists by creating an account on GitHub. Jun 23, 2014 · To the best of our knowledge, there are no matrix inversion algorithms using MapReduce, although there are several software systems for other matrix operations using MapReduce. FlashMatrix: Parallel, Scalable Data Analysis with Generalized Matrix Operations using Commodity SSDs. Here we reduce the output received from mapper into actual 2D array for matrices A and B and calculate the matrix multiplication based on usual formula. • Irregular algorithms Penetrating rays (e. Instructors. (1) can be minimised with respect to and solved for , yielding a large matrix multiplication problem, a formulation that is employed by the R package Matrix eQTL , which allows for fast eQTL analysis on a desktop computer. matrix',default='A', dest='Amatname') def parsemat(self): \"\"\" Return 1 if this is the A matrix, otherwise return 2\"\"\" fn = get_jobconf_value('map. Matrix factorization learns a latent data model that takes a data matrix and transforms it into a latent feature space enabling generalization, noise 1 Mar 2018 implement by naive algorithm(without partition) and advanced algorithm(with partition) - AiningWang/Matrix-Multiplication-using-MapReduce. d. . I hope these programs will help people understand the power of distributed parallel computing via map-reduce on Spark platform. An AggBinaryOp hop can be compiled into the following physical operators. collection. Howe outlined, together with the theory, some solutions to the assignments, we started to make our hands really dirty. Pros . UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. 09, May 20. F. lines method; using the generate method (provide a Supplier) or iterate method (providing the initial value and incremental operation). Hi all. 550 Architecture of Machine Learning Systems based on fast matrix multiplication. Mar 29, 2012 · Posted by Venkata (Ravi) Adusumilli on March 29, 2012 in Hadoop, MapReduce Tags: Hadoop 0. toNumPy () Output: array ([[ - 60. The JobConfigurable#configure has to be implemented in the Mapper and Reducer class. Apr 14, 2012 · Prepare for Matrix Multiplication. stdin: curr_index, index, value = line. g. enron 4. But somehow the generation of the <Key> <value> pair and the operation in the 1. For running unit tests, use junit, and for writing MapReduce tests, use mrunit. Jan 27, 2021 · // The slave process receives the sub portion of the Matrix A which assigned by Root : MPI_Recv(&matrix_a, rowsN, MPI_DOUBLE, source, 1, MPI_COMM_WORLD, &status); // The slave process receives the Matrix B: MPI_Recv(&matrix_b, NN, MPI_DOUBLE, source, 1, MPI_COMM_WORLD, &status); // Matrix multiplication: for (int k = 0; k<N; k++) Mar 31, 2012 · P is a matrix = MN with element p ik in row i and column k, where p ik =∑ j m ij n jk. We represent matrix M as a relation , with tuples , and matrix N as a relation , with tuples . Monte Carlo Integration. 19. Implementation . Also a variation for pair-wise distance matrix of two different inputs x and y: sqDist(x,y), dsqDist(x,y). py. 1 Matrix Multiply and Computer Architectures Homework question 1 Matrix multiplication with MapReduce If A is an m × p matrix and B is an p × n matrix, then the product of A and B is the m × n matrix C = AB, where the (i, j) th element of C is computed as the inner product of the ith row of A with the jth column of B: This is a dot product—simple arithmetic if m, p, and n are small. The map takes ( le, content) pair, and emits (word, 1) pairs for each word in the content. MapReduce: Simplified Data Processing on Large Clusters. Step 1: We can download the dataset from this Link , For various cities in different years. At first it was a little brain-breaky, but then we did the map-reduce version, which was brain-breakier. Written by Luka Kerr on April 2, 2018 I’ve been learning MIPS assembly for about 2 weeks now at uni and wanted to share how i’ve implemented a simple matrix multiplication function in MIPS. That said, the ground is now prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. linspace ( 0 , 2 * np . Clustering with KMeans: Page: Clustering with KMeans in scikit-learn. “Matrix factorizations at scale: A comparison of scientific data analytics in Spark and C+MPI using three case studies”, 2016 IEEE International Conference on Big Data (Big Data), pages 204–213, Dec 2016. I will explain LSH and how to use this package as well as the details of the implementation below. \"Git-a\" -rec It further employs a content-based filtering approach, coupled with Apache Spark to develop a recommender system, for Github users. Use of ufuncs is an esssential aspect of vectorization and typically much more computtionally efficient than using an explicit loop over each element. For these setups, coding has been utilized primarily to handle failed or straggling (delayed) workers –, where some workers fail or are signiﬁcantly slower than the other workers, causing a signiﬁcant delay in the overall computation time. e. g. 2) Matrix Multiplication 3) Find Mutual Friends for Social Media Data. Contribute to kdave2/Matrix- Multiplication-Hadoop-Map-Reduce development by creating an account on GitHub. Map, Reduce and Filter functions in Python make writing code much more easier (less lines of code) and I think they are optimized internally which will make them more faster than writing custom code which will most Sparse linear algebra Matrix Multiplication Spectral methods FFT N-Body methods GEM Structured grids SRAD Unstructured grids CFD solver MapReduce Combinational logic CRC Graph traversal Breadth-First Search (BFS) Dynamic programming Needleman-Wunsch Backtrack and branch-and-bound Graphical models Hidden Markov Model Map Reduce Triplets Block Matrix Multiplication Let’s look at Block Matrix Multiplication (on the board and on GitHub) Created Date: Oct 23, 2020 · The above analysis is relevant for so-called bidirectional attention, i. This model defines data abstraction as key-value pairs and computation flow as “map, shuffle and then reduce”. Matrix multiplication is an important multiplication design in parallel computation. MapReduce is a parallel fram ework for big da ta, which That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. p. private static Long N; public void configure(JobConf job) {N = Long. Designed a 4x4 grid layout of game card. We consider numerical computations using dataflow graphs, with a focus on learning deep neural networks for image classification and other classification tasks. x library which implements a MapReduce algorithm. reshape (%input) : (tensor<1x28x28x1xf32>) /> tensor Matrix multiplication in C. – Description of AdaGrad. First: The Map Function\":Foreachmatrixelementm ij,producethekeyvaluepair j, (M,i,m ij) # 21 hours ago · mapreduce python 3, Jan 28, 2020 · You can indent using tabs and spaces in Python. 4. That is, we can implement matrix multiplication as the cascade of two map-reduce operations, as follows. sin is a universal function plt . are overloaded for convenience. The : operator takes syntax start:spacing:end. We classify the matrix multiplication problems into Apr 26, 2012 · Posted by Venkata (Ravi) Adusumilli on April 26, 2012 in Hadoop, MapReduce Tags: Hadoop 0. 3. sh Matrix_Reducer. github. ∙ 0 ∙ share A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. gz Step 2: Move the eclipse folder to the home directory In this step, you can see how to move the eclipse folder to the home directory. Example MapReduce Algorithms Matrix-vector multiplication Power iteration (e. A trivial implementation is trivial, but users are likely to want fast versions that are hard to write. io/. Graph Processing using Map-Reduce 2. Oct 10, 2017 · Using MapReduce Programming In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. The value for cell (i, j) of matrix C is computed by taking the dot product of row i in matrix A and column j in matrix B. If A is an m × p matrix and B is an p × n matrix, then the product of A and B is the m × n matrix C = AB, where the (i, j)th element of C is computed as the. In the Figure 1 (a), we experiment large and sparse matrix multiplication from two random Bernoulli square matrices with dimension roughly equal to 1. Parallel Matrix Multiplication Algorithms Grid-based approach - The grid-based algorithms , regard processors as residing on a two- or three- Coverage: vectors norms (ℓ 2-norm, ℓ 1-norm, ℓ p-norm, ℓ ∞-norm), vector inner product, matrix multiplication, matrix trace, matrix Frobenius norm, scalar function differential, convex function, use Numpy to construct vectors and matrices. Matrix multiplication in C: We can add, subtract, multiply and divide 2 matrices. 20. matrix multiplication using mapreduce github iomeviewer-weezy-l-y-incompetence-laguna-adair\"> matrix multiplication using mapreduce github Kublanovskaya, J. Examples of Lambda are given below. • Standard http://jwbuurlage. MapReduce. Francis) 1964: Sinkhorn (Richard Sinkhorn) 1965: Golub-Reinsch SVD (Gene Golub) 1969: Sparse matrix ordering (Elizabeth Cuthill, James McKee) 1969: Strassen matrix multiplication (Volker Strassen) The implementation for the multiplication gate with input scalars x and y and output scalar z is class MultiplyGate ( object ): def forward ( x , y ): z = x * y self . combineAlli(x1;:::;xn) : combine all the results from combine2() for node i. g. g. 3. I just want to code a matrix multiplication problem in MapReduce using python for very large sparse matrix. An AggBinaryOp hop can be compiled into the following physical operators. h. This relates mostly to (a) matrix multiplication deficiencies, and (b) handling parallelism. Test naive algorithm locally. Basic Matrix Multiplication Operators. May 15, 2013 · Does anyone need MapReduce?122• I tried to do book recommendations withlinear algebra• Basically, doing matrix multiplication toproduce the full user/item matrix withblanks filled in• My Mac wound up freezing• 185,973 books x 77,805 users =14,469,629,265– assuming 2 bytes per float = 28 GB of RAM• So it doesn’t necessarily take that much tohave some use for MapReduce of the loss J ( i) ( θ) of the i th window vector with respect to the matrix x of window vectors is given by. I built a jar file using the code below. Jun 21, 2020 · MapReduce Program – Finding The Average Age of Male and Female Died in Titanic Disaster; MapReduce – Understanding With Real-Life Example; How to find top-N records using MapReduce; How to Execute WordCount Program in MapReduce using Cloudera Distribution Hadoop(CDH) Matrix Multiplication With 1 MapReduce Step; MapReduce – Combiners 1. element 3 in matrix A is called A21 i. 15 minute read. Introductory example is calculation of Fibonacci numbers where F(N) (problem of size N) is calculated as sum of F(N - 2) and F(N - 1) (problems of size N - 2 and N - 1). KEY: block num (a_block, b_block) VALUE: [(row, col, value), ,( )]//numbers in the block // implement matrix multiplication of the blocks locally res = 0 for i = row of ele in this a block: for k = col of ele in this b block: for j = 0 to n-1: res += A[i][j] * B[j][k] Test. Aug 17, 2018 · Besides matrix-vector and matrix-matrix calculations, relational-algebra operations fit well into the MapReduce style of computing. deeplearn-rs - deeplearn-rs provides simple networks that use matrix multiplication, addition, and ReLU under the MIT license. This file contains the implementation of reducer. Specifically, use test your implementation on the following graphs, 1. Table 2 summarizes the core operations of important ML algorithms. com&nbs 15 Dec 2014 in this area (Hadoop, Map-Reduce and Spark) work exercises. Rawashdeh , M. From the implementation point of view, Before the MapReduce model, MPI was the main tool used to process big data. 2166 II. Certain common operations, like broadcast or matrix multiplication, do know how to deal with array wrappers by using the Adapt. ein\"ij,jk -> ik\"(a,b) returns :(a * b) and ein\"ij,kj -> ki\"(a,b) returns :(b * transpose(a)) . in a way you should be familiar with. The nucleus is represented as a N-nanometer by M-nanometer grid, and at each 1nm * 1nm square is known whether or not it is filled by something. G. Parsian, Data . When we represent matrices in this form, we do not need to keep entries for the cells that have values of zero to save large amount of disk space. PyMR is a Python 2. We deﬁne requirements for the design of serverless big data applications, present a prototype for matrix multiplication using FaaS, and discuss and synthesize insights from results of extensive experimentation. What we want to do We will write a simple MapReduce program (see also Wikipedia ) for Hadoop in Python but without using Jython to translate our code to Java jar files. Aug 29, 2015 · Matrix Multiplication with MapReduce 33 Comments Posted by Maruf Aytekin on February 16, 2015 Matrix-vector and matrix-matrix calculations fit nicely into the MapReduce style of computing. The MapReduce contains two important tasks, namely Map and Reduce. Map-Reduce. Integer matrix-matrix and matrix-vector Distributed matrix factorization with mapreduce using a series of broadcast-joins (SS, CB, MS, AA, VM), pp. Matrix-matrix product • Basic matrix multiplication on a 2-D grid • Matrix multiplication is an important application in HPC and appears in many areas (linear algebra) • C = A * B where A, B, and C are matrices (two-dimensional arrays) • A restricted case is when B has only one column, matrix-vector product, which appears in 1957: Minimum degree sparse matrix reordering (Harry Markowitz) 1961: QR algorithm (V. Jan 25, 2021 · We need to extract it using the command tar –zxvf eclipse-committers-photon-R-linux-gtk. 0-m2 m4. Many fields such as Machine Learning and Optimization have adapted their algorithms to handle such clusters. js) and Approach2 (multiply_map_aggregate. 5https://github. MapReduce, from one job to another, takes time to upload the file and start the job again. Basic Matrix Multiplication Operators. When performance or resources are a matter of concern Cubert Script is a developer-friendly language that takes out the hints, guesswork and surprises when running the script. \" Computi (Concurrent Replication-based Matrix Multiplication) along with a parallel algorithm, Marlin, for large-scale matrix multiplication on uted data-parallel platforms, such as Hadoop MapReduce of naively using the general shuffle me Cannon principle parallel matrix multiplication algorithm implementation, and Source: https: //github. function mapReduce(input, map, reduce) {// Map: var mapperOutput = []. Mon 11/14: No recitation : Tue 11/15: srini Experiment MapReduce: Result for Matrix Multiplication 38 MapReduce The speedup of using software-based atomic add over the system one increases as the input matrices get larger (up to 13. 1) Simple Moving Average for Companies Stock Data. e. There are 2 main reasons why interpreted Python code is slower than code in a compiled lanauge such as C (or other compiled langauge): Using MapReduce, we could achieve N times throughput by having N workers running in parallel. Existing GPUbased SOM algorithms take a similar approach in finding the best matching unit, but they do not necessarily use matrix operations to derive the distance matrix [34,46]. ,1. sin ( xs ) # np. Tensor-matrix-multiplication(TTM)referstomultiplyingTalong any mode n, by a matrix of size K ×Ln (for some K). pi , 100 ) ys = np . Importance Sampling for Learning Edge opicsT (ISLE) Microsoft Research, 2000+ LOC [Github] Sep 21, 2020 · The course includes video lectures, case studies, peer-to-peer engagements and use of computational tools and platforms (such as R/RStudio, and Git/Github), and a reproducible research project. Knowing the working of matrix multiplication in a distributed system provides important insights on understanding the cost of our algorithms. Apr 10, 2019 · MRQL (the MapReduce Query Language) is an SQL-like query language for large-scale data analysis on a cluster of computers. sum (axis = 1). Gittens et al. com Li Pu A. Mahoney. The essence of the transformation is to unroll the input patches (a 3D matrix) and lters (a 4D matrix) in 2D in a way that a single matrix-matrix multiplication produces the unrolled version of the output in 2D. 10 of Mahout it became obvious that using Hadoop MapReduce. dblp-2011 3. Map Reduce paradigm is usually used to aggregate data at a large scale. Methods used in the 4 Apr 2019 How to find top-N records using MapReduce Now to do so we just multiply the key with -1 in mapper, so that after sorting higher numbers Other Links: GitHub Repository Matrix Multiplication With 1 MapReduce Step. UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. How to do matrix multiplication in R? Machine Learning Recipes,do, matrix, multiplication, r: What is mapply in R? Machine Learning Recipes,what, is, mapply, r: What is sapply in R? Machine Learning Recipes,what, is, sapply, r: How to find lagged differences in R? Machine Learning Recipes,find, lagged, differences, r: How to find variance and MapReduce/Hadoop, where data must be read from disk on eachiteration. Use of MapReduce has flourished since its premier, as illustrated by an in-depth example of its use in WordCount. Aug 02, 2016 · Next we show various attempts for scalable implementation of matrix multiplication using spark, and the winning method which combines numpy matrix multiplication along with spark’s broadcast and MapReduce Word Count Example. 18. ,0. 38) 13KB Synchronous-100x100-Matrix-Multiplication-using-Multiple-Threads：开发了一个程序，用于通过使用多个线程将两个大型矩阵 Nov 29, 2017 · Generalized matrix multiplication with semiring? Closing since I think this is out of reach of easy contributions. Each cell of the matrix is labelled as Aij and Bij. 7, which is an open source (Apache project) machine learning library. Dec 15, 2014 · This can be an important way to tune performance. Matrix Multiplication With 1 MapReduce Step. ,0. Matrix-multiplication kernels like gemm (dense-dense) and csrmm (sparse-dense), and utility kernels like csrcsc (sparse-transpose), sort (Parallel Sample Sort), and map-reduce are implemented in the framework. Let m be an NxM matrix and v a M vector. Design a MapReduce algorithm to compute matrix multiplication: A x B Mar 27, 2012 · Puzzle: Since there's so much other stuff in the nucleus, like proteins, it is sometimes troublesome finding room for a genome. new array wrappers are not covered, and only one level of wrapping is supported. Under Review: 2017. ∇ x ( p) T J ( i) ( θ) = ( δ ( i) T W) ⋅ 1 { i = p } ∈ R 1 × ( 2 w + 1) d, where the gradient with respect to the ( p, q) -th entry x ( p) q of the matrix x is given by. #MapReduce #MatrixMultiplication Apr 02, 2018 · Matrix Multiplication In MIPS. And more generally, taking a sum of outer products of corresponding rows and columns of the input matrices, always returns the desired matrix multiplication result. Trigger module in display ad project owner & core member Object: the old ad engine built reverse index from tag to ad, and this scheme suffered from long reverse index, the engine needed to do hard pruning when searching which hurt CTR. MPI Programming Matrix Multiplication Operators. matrix (np. 17. Here, the role of Mapper is to map the keys to the existing values and the role of Reducer is to aggregate the keys of common values. Matrix multiplication uses a generated function to return a matrix-product with at most one application of transpose , such that e. N. com/jfkelley/hadoop-matrix-mult After the submatrix multiplication, there's another MapReduce job that simply does the same Then iterate through just those sections of the arrays and multiply elem 9 Mar 2018 Sparse Matrix Matrix Multiplication. 2-CDH3U2 ← Matrix Multiplication using MapReduce – 1 Step Solution A celebrated example of an embarrassingly parallel problem is shared-memory matrix multiplication in which for two n n matrices, the multiplication process is split into n2 tasks, each responsible for calculating one element of the result matrix . Among them: matrix multiplication , similarity join [112,121,14,23], multi-way join using map-reduce offers a scalable Having that said, the ground is prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. ones ((3, 3)) + 3) m2 = m1 * (m2 + m1) m4 = 1. Moreover, Pegasus provides fast algorithms for GIM-V in MapReduce, a distributed computing platform multiplication operations . Section 5 will discuss https://github. Matrix Multiplication Map-Reduce. Shi, \"Performance Prediction and Evaluation of a Solution Space Compact Parallel Program using the Steady State Timing Model\", Poster, Future of My personal list of journals I use for my research and projects where I wrote one-sentence summaries. These operations are low-level, but for your convenience wrapped using high-level constructs. We write ++ for concatenation, so \"foo\" ++ \"bar\" is \"foobar\". Sparse matrix-vector multiplication (SpMV) is an important kernel that is considered critical for the performance of compute-intensive applications. Use an algorithm that does not require looking through every single possible matrix. Apr 29, 2013 · Sparse matrix computations in MapReduce!Austin Benson Tall-and-skinny matrix computations in MapReduceTuesday!Joe Buck Extending MapReduce for scientiﬁc computing!Chunsheng Feng Large scale video analytics on pivotal HadoopWednesday!Joe Nichols Post-processing CFD dynamics data in MapReduce !Lavanya Ramakrishnan Evaluating MapReduce and combining the matrix multiplication with the MapReduce is only 4 articles that we will discuss and com pare through this paper. Matrix Multiplication using Map-Reduce A specification ixs,iy is a matrix multiplication if ixs consists of two 2-tuples that share one index-label and iy is a permutation of the two-nonshared index-labels of the ixs. MapReduce is an attractive framework because it allows us to decompose the inner products involved in computing document similarity into separate multiplication and summation stages in a way that is well matched to efcient disk access using MapReduce minimize #syncs 8md Ours FPGA acceleration with small on-chip BRAM minimize data transfers (4m+4)d . Using item collaborative filtering algorithm to build co-ocurrence matrix by users' rating towards different movies from Netflix Prize Data Set. Thus, matrix multiplication is the major focus of performance optimization for many big data analytical algorithms or or applications. “Efficient Kernel Management on GPUs”. plot ( xs , ys ); 1 vala: Matrix[Float] //MxN 2 valb: Matrix[Float] //NxP 3 valc = Map(M, P){(i,j) => 4 //OuterMapfunction(f1) 5 Fold(N)(0. However, computing the inverse of a matrix using MapReduce is difficult when the order of the matrix is large. This is the function in C that will be implemented. e. In the following, we give an overview of backend-specific physical matrix multiplication operators in SystemML as well as their internally used matrix multiplication block operations. a ++ (b ++ c) = (a ++ b) ++ c. A matrix is a set of numerical and non-numerical data arranged in a fixed number of rows and column. 2. If you want uniformly spaced vectors, use the : operator. Stack Overflow. Cubert provides a novel sparse matrix multiplication algorithm that is best suited for analytics with large-scale graphs. first_10_even_numbers = 0: 2: 21 first_10_even_numbers = 0 2 4 6 8 10 12 14 16 18 20 A mode-n unfolding refers to the matrix of size Ln ×bL n obtained by arranging the mode-n fibers as the columns in a lexicographic order. What can we do with MapReduce? Models & Algorithms • Communication-processor tradeoffs for 1 round of MapReduce – Upper bounds for database join queries [Afrati,Ullman2010] – Upper and lower bounds for finding triangles, matrix multiplication, finding neighboring strings [Afrati, Sarma, Salihoglu, Ullman 2012] 5 compression idea from the sparse matrix-vector multiplication literature , into the Ligra shared-memory graph processing framework . the result will be the format of mat2. 2nd-row 1st column. Implementing matrix multiplication using MR and optimizing it using Combiner. A MapReduce program is defined via user-specified map and reduce functions, and we will learn how to write such programs in the Apache Hadoop and Spark projects. We propose a novel parallel execution model called pin-and-slide, which implements the column view of the matrix-vector mul-tiplication. ], [ 2. N. smaller/simpler) approximation of the original matrix A. rustlearn - a machine learning framework featuring logistic regression, support vector machines, decision trees and random forests. This code performs matrix vector multiplication using map reduce, which enables fast computations for large amounts of data. 3. At a high level, SVD is an algorithm that decomposes a matrix A into the best lower rank (i. Performance of matrix multiplication and random tensor contractions for rank-k update matrix/tensor shapes on a Xeon E5-2690 v3 processor. An extra MapReduce Job has to be run initially in order to retrieve the values. An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. 4. choose the year of your choice and select any one of the data text-file for analyzing. Installed multi node Hadoop 2. Using the best currently known parallel matrix multiplication [Wil12, LG14], our algorithm dynamically maintains the number of k-cliques in O min m 0:469k 235;( + m)0 :469k+0 amor-tized work w. Mathematically, it decomposes A into a two unitary matrices and a diagonal A matrix is a set of numerical and non-numerical data arranged in a fixed number of rows and column. By interpreting the matrix-vector multiplication in the column view, we can restrict the computation to just a subset of the May 21, 2015 · Jeffrey Dean and Sanjay Ghemawat. One of these systems is SystemML , which provides a high-level language for expressing some matrix operations such as matrix multiplication, division, and transpose Keywords: Item Collaborative Filter, Matrix Multiplication, MapReduce, Java, Hadoop - A movie recommender system is built to recommend movies in a similar style to users using raw data from Netflix. Jun 15, 2019 · Map Reduce paradigm is the soul of distributed parallel processing in Big Data. This is because the MapReduce works efficiently only with BIG data. In Proc eed- ings/42nd IEEE Symposium on Fo undations of Computer Science: October 14-17, 2001, Las Use same MapReduce job for operations w/o dependencies sFA Optimizations: Minimize Intermediary Data Recompute X and Y at each job rather than storing and exchanging Dec 27, 2015 · For multiplication, the key is to build rpos[], rpos[i] means in matrix N row i starts at rpos[i] position in datas[]. 01 import systemml as sml import numpy as np m1 = sml. Apr 05, 2019 · The below picture illustrates calculating an image’s class values for all 10 classes in a single step via matrix multiplication. One of the most important topic from university exam point of view. This is still not a complete solution though, e. Matrix-vector multiplication. 0f){k => 6 //Innermapfunction(f2) 7 a(i,k) * b(k,j) 8}{(x,y) => 9 //Combinefunction(r) 10 x + y 11} 12} Figure 1: Example of using Map and Fold in a Scala-based lan-guage for computing an untiled matrix multiplication using in-ner products. • Obtained a user’s rating matrix of films from the Netflix data using the Item Collaborative Filtering Algorithm, then obtained the co-occurrence matrix of the films, and finally merged both matrices to obtain a recommendation list. By-product: large-scale sparse matrix multiplication based on MapReduce. 1 and hadoop with Python 2. using matrix multiplication as example. ones ((3, 3)) + 3) m2 = m1 * (m2 + m1) m4 = 1. Mahout’s linear algebra DSL has an abstraction called DistributedRowMatrix (DRM) which models a matrix that is partitioned by rows and stored in the memory of a cluster of machines. We use 5 for this project, but you may want to increase this number for large datasets. If you like my post - Do follow me on this blog - Matrix Multiplication Using MapReduce Programming In mathematics , matrix mult map-reduce operation, we can perform grouping and aggregat ion, with I and K as the grouping attributes and the sum of V × W as the aggregation. . Each block is sent to each process, and the copied sub blocks are multiplied together and the results added to the partial results in the C sub-blocks. RecSys-2013-ZhuangCJL #matrix #memory management #parallel #performance A fast parallel SGD for matrix factorization in shared memory systems ( YZ , WSC , YCJ , CJL ), pp. For unidirectional (causal) attention, where tokens do not attend to other tokens appearing later in the input sequence, we slightly modify the approach to use prefix-sum computations, which only store running totals of matrix computations rather than mrjob fully supports Amazon’s Elastic MapReduce (EMR) service, which allows you to buy time on a Hadoop cluster on an hourly basis. matrix-matrix multiplication using * matrix-vector multiplication using * element-wise multiplication (Hadamard product) using . Pseudocode: First Map-Reduce job: Oct 25, 2016 · Mapper For a matrix multiplication of the form AB, we must provide in the mapper, the number of rows of A, referenced as row_a in the code, and the number of columns of B, referenced as col_b (The number of columns of A and number of rows of B are always same, else multiplication won't be possible). Most matrices are sparse so large amount of cells have value zero. Semi-External Memory Sparse Matrix Multiplication on Billion-node Graphs in a Multicore Architecture. Here's a small example to illustrate it. 20. Array operations - slicing, dicing, searching¶ Table of Contents Array operations - slicing, dicing, searchingArray slicingnD array slicingArray dicingArray broadcastingDeep copyArray searchingC •Similar to MapReduce •Aggregate multiple messages to same recipient from same server into a single message •Also executed at the receiver side to save space •Aggregators •Master collects data from vertices at the end of a superstep •Workers aggregate locally and use tree-based structure to aggregate to master This paper presents a MapReduce algorithm for computing pairwise document similarity in large document collections. What do we Outline a Map-Reduce program that calculates the vector x. ICALP-v2-2012-BaldeschiHLS #keyword #multi #on the On Multiple Keyword Sponsored Search Auctions with Budgets ( RCB , MH , SL , MS ), pp. Hence, the resulting product has the same number of rows as A and columns as B. 15 Dec 2014 map-reduce method for multiplying large, sparse matrices using Elasticsearch as As always, the code is available in the GitHub repository. Implementing the matrix multiplication with Map Reduce jobs to find the recommender movie(s). Below picture shows process for transpose: Below shows the process for 2 triple tuple matrix multiplication: check my code on github: link Matrix Multiplication: 2 MapReduce steps! Matrix M can be thought of as a relation with tuples (i, j, m ij) ! Matrix N can be thought of as a relation with tuples (j, k, n jk) ! Map operation creates these tuples ! Map: Join of M and N brings us closer to M X N by creating: Relation (i, j, k, m ij, n jk) or the relation (i, j, k, m ij X n jk) ! Nov 05, 2020 · MapReduce is a programming model and an associated implementation for processing and generating large datasets that is amenable to a broad variety of real-world tasks. Fast monte carlo algorithms for matrices iii: Computing a compressed approximate matrix decomposition, SIAM Journal of Computing, 2005. As the usual dense GEMM, the computation partitions the output matrix into tiles. Map-Reduce for each vertex D B A C Block Matrix Multiplication Let’s look at Block Matrix Multiplication (on the board and on GitHub) Experiment MapReduce: Result for Matrix Multiplication 38 MapReduce The speedup of using software-based atomic add over the system one increases as the input matrices get larger (up to 13. The ‘Iterative’ in the name of GIM-V denotes that we apply the £G opera- based on fast matrix multiplication. Blue line shows the 0. options. Graph reachability, using Matrix-Matrix multiplication of adjacency matrices. MapReduce is a processing technique and a program model for distributed computing based on java. The Map-reduce programming model is a common data-handling model Array-based distributed computations are another abstraction, used in all forms of parallelism. Graphs, and Matrix Multiplication using MapReduce, Spark, and MASS. Feb 01, 2013 · We extended the MapReduce SOM algorithm by moving all calculations on local nodes to the GPU with the matrix-based Euclidean distance matrix and reduction algorithm described above. A discussion about each of this operations is available below, if you want to go ahead of this section, click here. 39 is a matrix of residuals, assuming: s i. data. In the following, we give an overview of backend-specific physical matrix multiplication operators in SystemML as well as their internally used matrix multiplication block operations. Matrix Multiplication performed using Hadoop. Implementing matrix multiplication using MR and optimizing it using Combiner. . What we want to do We will write a simple MapReduce program (see also the MapReduce article on Wikipedia ) for Hadoop in Python but without using Jython to translate our Around version 0. UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. A MapReduce job can be enhanced by sampling local data, which cannot be used for future analysis. During the vector-matrix multiplication, each node will use its portion of the updated u vector, then estimate the v vector based on the multiplication of its putations as a single matrix-matrix multiplication (GEMM). Kublanovskaya, J. The RMM plan in Figure 1 im-plements a replication-based strategy in a single MapReduce version of matrix multiplication using recursive block matrix decomposition View MapReduceBlockMatrixProduct. Distributed engine neutral allreduceBlock() operator api for Spark and H2O. Unfortunately there is no acceleration routine for integers. Also, due to the inherent complexity of high-order computation, experience from prior work in other ﬁelds can not easily be applied to tensors. 8 Weeks. webbase-2001 Describe how you stored the connectivity matrix on disk and how you computed the transition matrix. Lecture 16 (5/28): Complexity Measures for MapReduce, Triangle Counting in a Graph The sum of these outer products matches the result we obtained in the previous slide using the traditional definition of matrix multiplication. concat. We show that serverless big data processing can lower oper- We also consider distributed MapReduce computations for training clustering models such as k-means and collaborative filtering models based on matrix factorization. 1. TensorFlow. In this case, each task needs one row of the ﬁrst input matrix and one Map Reduce Reduce. A breakdown of basic MapReduce terms and functions follows. matrix (np. 3 and use Different Algorithmic Techniques to Solve Following problems using Hadoop Map-Reduce. com/nm4archana/BigDataAnalysis-Comet. (For example Facebook) 4) K-mers counting using long DNA sequence in FASTA format 5) installing putations as a single matrix-matrix multiplication (GEMM). split (\"\\t\") index, value = map (int, [index,value]) if curr_index == prev_index: value_list. Integer factorization must be adaptable to MapReduce and must be parallizable (more than 1 Map or Reduce task) The emergence of large distributed clusters of commodity machines has brought with it a slew of new algorithms and tools. Finally the basic process of MapReduce is shown. You can still represent them using linear models. Irregular algorithms, however, depend on the input. I have published LSH package I developed for Apache Spark on GitHub. g. Diverse types of matrix classes/matrix multiplication are accommodated. MapReduce in distributed model training Using the MapReduce strategy, if we can split the training data on separate workers, compute Map functions in parallel, and aggregate the results in a Reduce function, we will be able to achieve distributed model Github. a mapreduce program of matrix multiplication. Green = true positive male, yellow = true positive female, red halo = misclassification. The ultimate goal is to make the algorithm as e cient as possible for any input . By using Monoids, we can take advantage of sparsity (we deal with a lot of sparse matrices, where almost all values are a zero in some Monoid). The operation is denoted Z = T×n A. matrix (np. Report this profile Addition of numbers, matrix multiplication inside a docker and using MapReduce as the programming model. Map the input matrices line by line and emits the matrix element. ee) Performance Prediction of Sparse Matrix Multiplication on a Distributed BigData Processing Environment. The sum of these outer products matches the result we obtained in the previous slide using the traditional definition of matrix multiplication. A naïve approach would be to extend an eﬃcient matrix multiplication algorithm, replacing the dot product by the distance function. xs = np . Contribute to ashkang/cs222_fin development by creating an account on GitHub. 99 “ Joel takes you on a journey from being data-curious to getting a thorough understanding Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision (SJ, RK, FM), pp. [J14] Yun Liang, Xiuhong Li. . Shi, \"How to achieve a 47000x speed up on the GPU/CUDA using matrix multiplication,\" Technical Report, Amax corporation, June 2009. Use a reducer to multiply value for same indices. His current research topic covers big data platforms, large-scale distributed computing resource manangement, cloud computing, and peer-to-peer systems. dot(a,b) array([[ 0. You can generate uniformly spaced vectors, using 2 methods. pdf such as MapReduce [Srirama et al, FGCS 2012] • Designed a classification on how the algorithms can be adapted to MR – Algorithm single MapReduce job • Monte Carlo, RSA breaking – Algorithm nMapReduce jobs • CLARA (Clustering), Matrix Multiplication – Each iteration in algorithm single MapReduce job • PAM (Clustering) Aug 29, 2015 · Posts about Machine Learning written by Maruf Aytekin. jl package. Ofeishat . Optimized Matrix Multiplication using Shared Virtual Memory In OpenCL 2. MATRIX MULTIPLICATION: Project to Read a file containing two 3 X 3 Matrices and calculate their Vector Product. 3 were implemented by their corresponding distributed primitives in Spark: I. The A sub-blocks are rolled one step to the left and the B Representing non-linearity using Polynomial Regression¶ Sometimes, when you plot the response variable with one of the predictors, it may not take a linear form. GitHub Gist: instantly share code, notes, and snippets. 249–256. Marlin contains several distributed matrix operations and especially focuses on matrix multiplication which is a funda-mental kernel of high performance scientiﬁc computing. test_naive. The matrix is denoted as T (n). straightforward, but the fact that matrix multiplication itself can be accomplished in multiple ways complicates matters. Individualpair-wiseremotememory distributed matrix multiplication Dec 29, 2017 · These techniques first partition matrix X into blocks and then exploit the block-matrix multiplication when learning U and V. Based on the observa-tion, Pegasus implements a very important primitive called GIM-V (Generalized Iterated Matrix-Vector multiplication) which is a generalization of the plain matrix-vector multi-plication. 20. A distributed, MapReduce-based SOM also builds on the batch formulation described in Equation 2 . . Amatname in fn: return 1 else: return 2 def joinmap(self, key, line): mtype = self. 281–284. io/Bulk. The chunk of X assigned to the node and the corresponding norms of X are kept in the GPU memory between subsequent epochs, and the weight vectors are copied to the 'sparse' is a matrix class based on a dictionary to store data using 2-element tuples (i,j) as keys (i is the row and j the column index). 1. the FFT, LU, and dense matrix–matrix multiplication. In this part of the code, the matrix multiplication begins, again, by implementing three MapReduce jobs. Policy: Printed material is allowed. i. There was a mix of similar problems presented in assignment 1 and assignment 2 that we had to solve them using MapReduce paradigm. Sep 10, 2012 · cost of the algorithm• determined by the amount of data that has to be sent over the network in the matrix multiplication step• for each user, we have to process the square of the number of his interactions → cost is dominated by the densest rows of A• distribution of interactions per user is usually heavy tailed → small number of Github. You have seen many of the stream operations before, in Question 5 of Exercise 7, including map, reduce, filter, and forEach • Matrix multiplication • Dynamic programming External Memory Model • Addition and subtraction are fast, multiplication is fast • MapReduce model: peated matrix-vector multiplications. 249–256. Designing e cient irregular algorithms is a challenge. 6. y * dz # [dz/dx * dL/dz] dy = self . push({key: key, value: value});}; map(row, emit); return emitArray;})); // Group tuples with the same key: var reducerInput = {}; mapperOutput. This was Jul 30, 2013 · MapReduce Algorithms: Having presented the video lectures on the topic, in which Prof. Using functions from various compiled languages in Python¶. ▫ SPGEMM: KKTRI: Triangle Counting using SpGEMM. Dec 14, 2016 · Data-Intensive Computing and MapReduce/Hadoop : For more info, see the MapReduce paper, it's pretty readable. js First of all lets recap the multiplication formula: import arraymancer proc customSigmoid2[T: SomeFloat](t: Tensor[T]): Tensor[T] = result = map_inline(t): 1 / (1 + exp(-x)) Now in a single loop over t, Arraymancer will do 1 / (1 + exp (-x)) for each x found. So, the whitespace or the indentation of the very first line of the program must be maintained all throughout the code. What we want to do We will write a simple MapReduce program (see also Wikipedia ) for Hadoop in Python but without using Jython to translate our code to Java jar files. Video: Youtube Map-Reduce! Ranking (e. MapReduce in distributed model training Using the MapReduce strategy, if we can split the training data on separate workers, compute Map functions in parallel, and aggregate the results in a Reduce function, we will be able to achieve distributed model We can use the logistic regression results to classify subjects as male or female based on their height and weight, using 0. Using the old API in the Mapper and Reducer. 281–284. Length. The MRQL query language is powerful enough to express most common data analysis tasks over many forms of raw in-situ data, such as XML and JSON documents, binary files, and CSV documents. js) To run the code mongo < multiply_map_reduce. txt. g. Mimir inherits the core principles of existing MapReduce frameworks, such as MR-MPI, while redesigning the execution model to incorporate a number of sophisticated optimization techniques that achieve similar or better performance with significant reduction in the amount of memory used. Thu 11/10: yuvraj: Virtual Machines : See also the book chapter on Virtual Machines from the Wisconsin OS book. Figure 4 illustrates how output splitting a ects weight and Using the Maven POM to manage your project is an easy way to start. BSPmodel. rithms are often iterative, using repeated read-only data access and I/O-bound matrix-vector multiplications to converge to an optimal model. requests in parallel by using the underlying multiple ﬂash memory packages. Subtypes of StaticArray will provide fast implementations of common array and linear algebra operations. With both the item-item similarity matrix and the user-item vectors, it’s now possible to multiply them together and generate recommendations for users. M. inline. MatrixMulOutput. NOTE: Please note that the Mapper function does not have access to the i, j, and k values directly. The MRQL query processing system can evaluate MRQL queries in two modes: in MapReduce mode on top of Apache Hadoop or in Bulk Synchronous Parallel (BSP) mode on top of Apache Hama. For example: MapReduce workflow: InputFormat, RecordReader, InputSplits, Map tasks, Combiners, Shuffle/Sort, Reduce tasks, OutputFormat. 55 folds) Ratio of FastPath to CompletePath memory accesses: 30:0 for software-based atomic and 3:28 for system-provided atomic implementations Since multiplication is done element-wise, you need to specifically perform a dot product to perform matrix multiplication. sum(B[i, :] * C[:, j]) Mapreduce and matrix multiplication November 2, 2016 The homework questions are due at the 23:59 on Tuesday 15 November. Specifically, the matrix multiplication operations described in Eq. Mar 12, 2018 · GitHub. 2. 0 2D card game 2048 (Android Studio, Java) Solely developed android game on windows platform using android studio. This method, however, is very inefficient as it would require to compute a matrix multiplication and the square root of a matrix at each step. parseLong(job. If you want a specific number of elements within a range, then use the linspace function. You can check it out from here. It is used to solve problems where problem of size N is solved using solution of problems of size N - 1 (or smaller). An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. Distributed matrix factorization with mapreduce using a series of broadcast-joins (SS, CB, MS, AA, VM), pp. Input are two matrix A and B python - How to write Mapreduce code for matrix multiplication which does not use any list of size more than 10 - Stack Overflow. One method for computing Pi (even though not the most efficient) generates a number of points in a square with side = 2. But MapReduce tries to use commodity machines to solve big data problems. js for ML using JavaScript TensorFlow 1 version, View source on GitHub the inner 2 dimensions specify valid matrix multiplication dimensions, and any level matrix computation primitives with MapReduce through the case study two basic primitives, matrix multiplication and finding linear solution, and goes into . 2. F ast monte-carlo algorithms for appr oximate matrix multiplication. ]]) >>>a[0,0]=1 >>>a[1,1]=1 >>>b =np. file') if self. StaticArrays provides a framework for implementing statically sized arrays in Julia, using the abstract type StaticArray{Size,T,N} <: AbstractArray{T,N}. The algorithm we’ll be using is a two-pass matrix multiplication algorithm for MapReduce. , PageRank) requires iterated matrix-vector multiplication with matrix containing millions of rows and columns ! Computing with social networks involves graphs with hundreds of millions of nodes and billions of edges ! Map-Reduce is a parallel programming paradigm, a software-stack that will help to address big data Used Blocked Matrix Multiplication technique to improve the convergence rate,by performing the nontrivial computation in the reduce steps. It is deployed on expensive hardware such as HPC or supercomputers. Our idea is to speed up distributed NMF in a new, orthogonal direction: by reducing the problem size of each NLS subproblem within NMF, which in turn decreases the overall computation cost. Please cite any references you use. mrjob has basic support for Google Cloud Dataproc (Dataproc) which allows you to buy time on a Hadoop cluster on a minute-by-minute basis. split()] row = int(vals) A key feature is the capability for users to write callback functions, called after each iteration, thus enabling customization for specific applications. The general algorithm matrix-vector multiplication (SpMV) and sparse matrix-matrix multiplication (SpGEMM), a systematic study on applying blocking techniques to tensors has not yet been conducted. List the top-10 vertices for graphs 1,2 & 4. Difference between MapReduce and Pig. Assume you have two matrices A and B in a sparse matrix format, where each record is of the form i, j, value. linspace ( 0 , 2 np . Do you have any idea, about the matrix multiplication example which I mentioned in question, that why this works fine with hadoop standalone mode but does not work with hadoop distributed mode at the point of checking answers? – waqas Nov 30 '11 at 13:39 Matrix multiplication using MPI. Matrix-vector and matrix-matrix calculations fit nicely into the MapReduce style of computing. Big Data Project On A Commodity Search System For Online Shopping Using Web Mining Big Data Project On A data mining framework to analyze road accident data Big Data Project On A neuro-fuzzy agent based group decision HR system for candidate ranking Big Data Project On A Profile-Based Big Data Architecture for Agricultural Context Big Data Project On A Queuing Method for GSoC Results and Summary. Thus, Meta-MapReduce enhances the standard MapReduce and can be implemented into the state-of-the-art MapReduce systems, such as Spark, Pregel , or modern Hadoop.$ docker run -v Matrix multiplication is an important application in. In MapReduce word count example, we find out the frequency of each word. You might want an order 2 or 3 curve. General-purpose, heavy- and An example of how multi-method-based dispatch might work for a binary operation like matrix multiplication. 1. 6. xs = np . If the multiplication type computes in parallel, then the package computation is also parallel. 0-m2 m4. e. 快速矩阵乘法 Fast and Stable matrix multiplication Coppersmith and Winograd's Algorithm 时间复杂度O(n^2. ∙ 0 ∙ share While performing distributed computations in today's cloud-based platforms, execution speed variations among compute nodes can significantly reduce the performance and create bottlenecks like stragglers. Stage 2. Naive Bayes classifier to classify text documents Latent semantic analysis (LSA) Rsa breaking using a more efficient integer factorization than trial division. parsemat() vals = [float(v) for v in line. 1. I got it right. MapReduce. PRELIMINARY A. Feb 16, 2015 · Matrix Data Model for MapReduce. ones ((3, 3)) + 2) m2 = sml. There are two main security concerns in outsourcing computation: guaranteeing that the server performs the computation correctly, and protecting the privacy of the client’s data. The first is Map Only with CAP3 DNA Sequence Assembly, followed by Classic MapReduce with Pair-wise Sequences and High-Energy Physics, Iterative with K-means clustering, PageRank and Multi-dimensional Scaling, and finally Loosely Synchronous with Matrix Multiplication Algorithms. Sparse Matrix Multiplication in Map Reduce. CS231n, Convolutional Neural Networks for Visual Recognition, Stanford University; CS224d, Deep Learning for Natural Language Processing, Stanford University You can now run all stages of the rewrite system for a program (in this example for matrix multiplication): scripts / compiled_scripts / HighLevelRewrite highLevel / mmTransposedA scripts / compiled_scripts / MemoryMappingRewrite -- gr10 mmTransposedA scripts / compiled_scripts / ParameterRewrite - f highLevel / mm . MPI is a SPMD model of distributed computing, where each process is completely independent and one just controls the memory handling. ,3. Aug 25, 2017 · Matrix Multiplication using MapReduce Programming in Java. json mmTransposedA Jul 14, 2020 · MapReduce Program – Finding The Average Age of Male and Female Died in Titanic Disaster; MapReduce – Understanding With Real-Life Example; How to find top-N records using MapReduce; How to Execute WordCount Program in MapReduce using Cloudera Distribution Hadoop(CDH) Matrix Multiplication With 1 MapReduce Step; MapReduce – Combiners matrix multiplication operations within the NMF algorithms. An extra MapReduce Job has to be run initially in order to add the Row Number as Key to every row. It uses a distributed file system called GFS, which is Google File System. Matrix Multiplication with Spark. ], [ 0. Plagiarism checking with MapReduce Manages: Pelle Jakovits ([email protected] 22 706. ####MapReduce problems#### Count number of words in a book; Total number of words in a book; tf-idf calculations for ranking; Cosine distance measure between 2 documents; Matrix multiplication in MapReduce Aug 13, 2016 · Matrix Computations and Optimization in Apache Spark Reza Bosagh Zadeh Stanford and Matroid 475 Via Ortega Stanford, CA 94305 Xiangrui Meng Databricks 160 Spear Street, 13th Floor San Francisco, CA 94105 Alexander Ulanov HP Labs 1501 Page Mill Rd Palo Alto, CA 94304 [email protected] zeros(4). e. Jueon Park, and Kyungyong Lee, The 8th International Workshop on Autonomic Management of high performance Grid and Cloud Computing (AMGCC'20), Accepted, 07/2020. OSDI’04 ,San Francisco, CA; Petros Drineas, Ravi Kannan, and Michael W. edu Burak Yavuz Databricks 160 Spear Street, 13th Floor San Francisco, CA 94105 [email protected] the code works perfectly fine with smaller matrices but when the files becomes large the mapping p Nov 12, 2020 · Matrix B is also a 2×2 matrix where number of rows(j)=2 and number of columns(k)=2. Data Analysis of huge amount of open Github Data, where we tried to find some deep patterns among popularity and spatial distributions of programming languages and users on Github. Moreover, your code has two steps, that means two jobs. Course content Because using map is equivalent to for loops, with an extra code we can always write a general mapping utility: >>> def mymap(aFunc, aSeq): result = [] for x in aSeq: result. It may be possible to switch between MapReduce and MPI to perform scalable matrix inversion in these The next step is PageRank, a fairly straightforward linear algebra problem. Lecture 15 (5/26): Partitioning for PageRank Lecture 15, Partitioning for Pagerank. While some arrays — like Array itself — are implemented using a linear chunk of memory and directly use a linear index in their implementations, other arrays — like Diagonal — need the full set of cartesian indices to do their lookup (see IndexStyle to Feb 08, 2010 · This posting gives an example of how to use Mapreduce, Python and Numpy to parallelize a linear machine learning classifier algorithm for Hadoop Streaming. get(\"NumberOfDocuments\"));} The variable N can then be used with the map and reduce functions. 5 × 10 5 and the number of nonzero elements equal to 6 × 10 5. By using Rings, we can do matrix multiplication over things other than numbers (which on occasion we have done). 1. sin ( xs ) # np. We use dense() to create a dense in-memory matrix from our toy dataset and use drmParallelize to load it into the cluster, “mimicking” a large, partitioned • Used Netflix data to offer movie recommendations to users based on their previous favorites. , 2015. CS231n, Convolutional Neural Networks for Visual Recognition, Stanford University; CS224d, Deep Learning for Natural Language Processing, Stanford University Publication: M. Syntax of Mongo mapReduce() Following is the syntax of mapReduce() function that could be used in Mongo Shell > db. Figure 4 illustrates how output splitting a�ects weight and In modern processors, integer division can be 10-50 times slower than multiplication. AWS Elastic MapReduce, an adaptation of Apache Hadoop to Matrix Multiplication: 2 MapReduce steps! Matrix M can be thought of as a relation with tuples (i, j, m ij) ! Matrix N can be thought of as a relation with tuples (j, k, n jk) ! Map operation creates these tuples ! Map: Join of M and N brings us closer to M X N by creating: Relation (i, j, k, m ij, n jk) or the relation (i, j, k, m ij X n jk) ! Jul 26, 2016 · Outline • Introduction • DFS • MapReduce • Examples • Matrix Calculation on Hadoop 3. Advices [edit \| edit source] In this section, you will see some advices that can help you to desing a Python source Refactor compression package and add functionalities including quantization for lossy compression, binary cell operations, left matrix multiplication. For sparse computations, they usually depend on the nonzero pattern of the matrix. per batch of updates where mis de-ﬁned as the maximum number of edges in the graph be- Jun 15, 2013 · For those who prefer reading a code instead of text - GitHub: Approach1(multiply_map_reduce. For example : mat1 is 2×3 means mat2 will be 3×2. Implement SELECT MAX(<field>) FROM <table> GROUP BY <field> with MapReduce. 8 May 2015 https://github. . In all cases, Twister outperforms or is close to the competition. Implementations in CUDA Sep 2015 – Sep 2015 2. 7. . Create a matrix of processes of size p1/2 1/2 x p so that each process can maintain a block of A matrix and a block of B matrix. X-rays) are sent through an object from various angles Google MapReduce. Combiner Edit the “MapTask” method to add support for running a Combiner. The repository provides demo programs for implementations of basic algorithms on Spark 2. h. apply([], input. N(0;˙2). Many applications in different areas exist already for MapReduce. pi , 100 ) ys = np . Matrix Multiplication with MapReduce Big Data possibly now has become the most used term in the tech world for this decade. 95% c Thanks Thomas. Mark Kröll 击 see https://hadoopecosystemtable. 7. in a way you should be familiar with. Android4. Mo 09 Dezember 2013 How to use Jekyll with GitHub ; Di 05 Juli 2016 Pythons map, reduce and filter as list Matrix multiplication on multiple cores in Jun 25, 2012 · Translating to MapReduce: rethinking matrix multiplication It’s now possible to use MapReduce to multiply the user vectors computed in step 1, and the co-occurrence matrix from step 2, to produce a recommendation vector from which the algorithm can derive recommendations. Matrix-Vector multiplication As an example if we consider a Matrix-Vector multiplication (taken from the book Mining Massive Data Sets by Jure Leskovec, Anand Rajaraman et al To store the past gradients, we will use a matrix G. International Journal of Computer Science and Information Technology (IJCSIT) 9 (5): 29 - 37 ( October 2017 Figure 1 shows the general matrix multiplication (GEMM) operation by using the block sparse format. Look for “# [ADD COMBINER HERE]” for the place one would add this. 2 minute read. the rule of matrix multiplication is mat1 columns is equal to mat2 rows values. It may help if you checkout my introduction to map-reduce and an example here. To do so, we are taking input from the user for row number, column number, first matrix elements and second matrix elements. Contribute to JaredP94/MapReduce-Matrix-Multiplication development by creating an account on GitHub. GitHub Gist: instantly share code, notes, and snippets. MapReduce is a programming model that Google came up with to handle computation of their huge large scale data. The examples below use the einsum / notation for the elements of tensors, namely m[i,j] for element i,j of the matrix m, instead of the more mathematical notation m_ij. #!/usr/bin/env python import sys from operator import itemgetter prev_index = None value_list = [] for line in sys. Dijkstra's algorithm. GPU Accelerated Computing with C and C++, which also has some videos. Combiner Edit the “MapTask” method to add support for running a Sparse matrix multiplication for hadoop. Matrix Multiplication Operators. to implement matrix inversion using other parallelization platforms such as MPI, a MapReduce matrix inversion technique that can be used as a pluggable component in complex Hadoop data analysis workﬂows is highly desirable. The instruction sets are typed, and instructions designed to operate on packed doubles can’t operate on packed ints without explicit casting. (Duh!) Map takes data and converts it into another set of data, where individual elements are broken down into tuples (key/value pairs). rusty-machine - a pure-rust machine learning library. - Use MapReduce to calculate tag similarity in twitter and improves the speed from 90min to 36min. e. 0 and measured the performance of the same with previous implementations. 5 In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. ]]) Matrix Multiplication Examples (both using global memory and shared memory) CUDA C Programming Guide; CUDA Toolkit documentation, which includes CUDA installation, C programming guide, APIs for cuBlas, cuFFT etc, tools, compiler SDK, and others. “Limitations and Challenges of HDFS and MapReduce” by Weets et al. 10 of Mahout it became obvious that using Hadoop MapReduce was causing more pain than it was solving, due to massively redundant data reads required 1 Problems Suited for MapReduce 2 MapReduce: Applications Matrix-Vector Multiplication Information Retrieval 3 Hadoop Ecosystem Designing a Big Data System Big Data Storage Technologies Slides are partially based on Slides “Mining Massive Datasets” by Jure Leskovec. What inference can you derive from using PageRank on the these datasets. The minimum is found by a multi-step reduction algorithm. 10 Matrix Multiplication with One MapReduce Step . 6. sin is a universal function plt . Jan 17, 2021 · Matrix Multiplication With 1 MapReduce Step; Hadoop - copyFromLocal Command go to this GitHub Repo and download the receptacle organizer as a speed as For advanced use of the CUDA, you can use the driver API wrappers in CUDA. 1. per batch of updates where mis de-ﬁned as the maximum number of edges in the graph be- Matrix multiplication: n^3/p + (n^2/p^{2/3}) \\cdot g + l: Sorting (n \\log n)/p + (n/p)\\cdot g + l: Fast Fourier Transform (n \\log n)/p + (n/p)\\cdot g + l: LU Decomposition: n^3/p + (n^2/p^{1/2})\\cdot g + p^{1/2}\\cdot l: Cholesky Factorisation: n^3/p + (n^2/p^{1/2})\\cdot g + p^{1/2}\\cdot l: Algebraic Path Problem (Shortest Paths) Distributed ﬁle systems and map-reduce as a tool for creating parallel 2. with callbacks. Assume you have two matrices A and B in a sparse matrix format, where each record is of the form i, j, value. For matrix computation library built on top of Spark which is an distributed in-memory cluster computing framework. Ex. Vogelstein, Carey E. reshape(2,2) >>>b array([[0, 1], [2, 3]]) >>>ab array([[ 0. Using the new API in the Mapper and Reducer. Remember, a combiner runs the reduce task at the end of the map task in order to save communication cost of sending to multiple reducers. tar. Specifically, for building MapReduce jobs, you only need to have the hadoop-client dependency, which contains all the Hadoop client-side classes needed to interact with HDFS and MapReduce. The goal is to calculate A B. [experimental] New python bindings with supports for several builtin s, matrix operations, federated tensors and lineage traces. Lowering XLA HLO to I E 6 func @mnist_predict(%input: tensor<1x28x28x1xf32>) /> tensor<1x10xf32> {%1 = mhlo. hollywood-2011 2. PageRank) Gradient descent methods Stochastic SVD Tall skinny QR This paper presents a MapReduce algorithm for computing pairwise document similarity in large document collections. I couldn't find a simple way to do this within the EMR framework, though I bet there is a way to do it. import systemml as sml import numpy as np m1 = sml. On the left are the full matrix organized in blocks and its internal memory representation: compressed values and block indices. The essence of the transformation is to unroll the input patches (a 3D matrix) and �lters (a 4D matrix) in 2D in a way that a single matrix-matrix multiplication produces the unrolled version of the output in 2D. Common operations include synchronizing the GPU, inspecting its properties, starting the profiler, etc. Sparse Matrix-Vector Multiplication { Size of Distributed Matrix Multiplication Using Speed Adaptive Coding 04/15/2019 ∙ by Krishna Narra , et al. Da Zheng, Disa Mhembere, Joshua T. Figure 1 and Figure 2 show two alternative MapReduce plans for matrix multiplication (details of the two plans will be discussed in Section IV). MapReduce is an attractive framework because it allows us to decompose the inner products involved in computing document similarity into separate multiplication and summation stages in a way that is well matched to efcient disk access May 12, 2018 · On Intel CPUs, SSE instruction sets use up to 128 bit registers (xmm, four ints), AVX and AVX2 use up to 256 bit registers (ymm, eight ints), and AVX512 use up to 512 bit registers (zmm, sixteen ints). 1957: Minimum degree sparse matrix reordering (Harry Markowitz) 1961: QR algorithm (V. Curtis Huttenhower, John Quackenbush, Lorenzo Trippa & Christine Choirat. Thus, r u v ≈ x T u ⋅ θ v, where x u, θ v ∈ R f are the u t h Map-Reduce also makes short work of dealing with large matrices and can crunch matrix operations like matrix addition, subtraction, multiplication etc. 2 and the deflation operation defined in Eq. Implement inner join between two tables with MapReduce. Design a MapReduce algorithm to compute matrix multiplication: A x B Matrix Multiplication. The common matrix operations such as 'dot' for the inner product, multiplication/division by a scalar, indexing/slicing, etc. forEach(function(keyValue) Example matrix multiplication in distributed environment using R, MPI and Hadoop MapReduce - aaparo/MultMatrix Use Git or checkout with SVN using the web URL. And more generally, taking a sum of outer products of corresponding rows and columns of the input matrices, always returns the desired matrix multiplication result. No electronic device (except for electronic calculator). The class will cover widely used distributed algorithms in academia Dynamic programming is well known algorithm design method. Matthews Author content It can be used in conjunction with other functionality like Map, Reduce, Filter in Python. append(aFunc(x)) return result >>> list(map(sqr, [1, 2, 3])) [1, 4, 9] >>> mymap(sqr, [1, 2, 3]) [1, 4, 9] >>> Aug 25, 2011 · In-Database Operations • Matrix and vector multiplication: Av SELECT 1, array_accum(row_number, vectorv) FROM A array_accum(x,v) is a custom function. Both of these are considered to be whitespaces when you code. Figures - uploaded by Devin A. Current Apache Mahout: Beyond MapReduce Matrix Multiplication. Note: Matrix operations for floats are accelerated using BLAS (Intel MKL, OpenBLAS, Apple Accelerate …). ,0. 1. Ligra+ is able to represent a variety of synthetic and real-world graphs using General Matrix-Vector multiplication: y <- alpha A * x + beta * y Source Edit proc gemv [T: SomeInteger] (alpha: T; A: Tensor [T]; x: Tensor [T]; beta: T; y: var Tensor [T]) { } {. Clearly it holds that. 11 Jan 2009 Okay, so how can we compute PageRank using MapReduce? we'll take is to use MapReduce to repeatedly multiply a vector by the matrix M 23 Feb 2021 Multiplies matrix a by matrix b, producing a * b. Say the co-occurrence matrix for 4 items is Courses ¶. It also discusses various hadoop/mapreduce-specific approaches how to potentially improve or extend the example. MapReduce¶ MapReduce was designed by Google to address the problem of large-scale data processing. append ( (index,value)) else: if prev_index: value_list = sorted (value_list,key=itemgetter (0)) i In this video u will learn about Matrix Multiplication using Map Reduce in Big-Data. p. The 27 Jun 2020 Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers. Francis) 1964: Sinkhorn (Richard Sinkhorn) 1965: Golub-Reinsch SVD (Gene Golub) 1969: Sparse matrix ordering (Elizabeth Cuthill, James McKee) 1969: Strassen matrix multiplication (Volker Strassen) INTRODUCTION TO DATA SCIENCE JOHN P DICKERSON Lecture #4 –9/5/2019 CMSC320 Tuesdays & Thursdays 5:00pm –6:15pm Graph reachability, using Matrix-Matrix multiplication of adjacency matrices. Download [edit \| edit source] The source code is available on Github. One purpose of matrix decomposition is reducing calculations cost while solving a system of linear equations by decomposing the coefficients matrix into a product of two triangular matrices. MapReduce • Programming Model for Large-Volume Data Processing • Specialized for frequent use case: aggregation queries – Map every input object to set of key/value pairs – Reduce (aggregate) all mapped values for same key into one result for that key • Use this structure as explicit API for cluster computing May 01, 2018 · You fit this matrix to approximate your original matrix, as closely as possible, by multiplying the low-rank matrices together, which fills in the entries missing in the original matrix. Using MapReduce, we could achieve N times throughput by having N workers running in parallel. Here, we will discuss the implementation of matrix multiplication on various communication networks like mesh and hypercube. 99 CAN $45. Taifi and Y. 1. Qatawneh , and H. Now One step matrix multiplication has 1 mapper and 1 reducer. In a nutshell, we reduce the size of each NLS subproblem, by employing a matrix sketching technique: Having that said, the ground is prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. Aug 02, 2016 · Next we show various attempts for scalable implementation of matrix multiplication using spark, and the winning method which combines numpy matrix multiplication along with spark’s broadcast and Courses ¶. View on GitHub Spark. Challenge: Make linear https://github. ones ((3, 3)) + 2) m2 = sml. Published: December 08, 2018 Hi everyone, this is the final (summarizing) blog post for my Google Summer of Code project. the FFT, LU, and dense matrix matrix multiplication. For both classes, few matrix operations dominate the overall algorithm runtime, apart from the costs for the initial read from distributed le system or object storage. F. In fact, large-scale matrix multiplication can hardly be handled by the single-node matrix computation libraries due to hardware resource limitation. The unit of Parallel Matrix Multiplication on Open MPI. github. Fortunately, the authors in proposed a method of matrix inversion using MapReduce. js mongo < multiply_map_aggregate. 26 >>>a =np. Straggler Robust Distributed Matrix Inverse Approximation 03/05/2020 ∙ by Neophytos Charalambides , et al. ], [ 0. The reduce( ) step in the MapReduce Algorithm for matrix multiplication Facts: The final step in the MapReduce algorithm is to produce the matrix A × B. In this example did the matrix multiplication. git. There are many parallel computation prototype for matrix multiplication using FaaS, and discuss and synthesize insights entry-barriers of. This workload tests the Naive Bayesian (a popular classification algorithm for knowledge discovery and data mining) trainer in Mahout 0. However, I want to tell you something, if your file is not big enough, you will not see an improvement in term of execution speed. 3. Besides matrix-vector multi-plication (e. There are Python 2. map(function(row) { var emitArray = []; var emit = function(key, value) {emitArray. 7 codes and learning notes for Spark 2. In SpMV, the optimal selection of storage format is one of the key aspects of enabling the best performance. source The code is available on my GitHub account of the converting a collection to stream using stream method; reading from a file using Files. the result is the same as mat2. Use of ufuncs is an esssential aspect of vectorization and typically much more computtionally efficient than using an explicit loop over each element. Dec 29, 2017 · Background Matrix factorization is a well established pattern discovery tool that has seen numerous applications in biomedical data analytics, such as gene expression co-clustering, patient stratification, and gene-disease association mining. Using the best currently known parallel matrix multiplication [Wil12, LG14], our algorithm dynamically maintains the number of k-cliques in O min m 0:469k 235;( + m)0 :469k+0 amor-tized work w. One, you can multiply BIG matrices in a memory efficient way, without needing to pull everything out of SQL. Our extended framework, which we call Ligra+, uses less space than Ligra, while providing comparable or improved performance. 2-CDH3U2 ← Matrix Multiplication using MapReduce – 2 Step Solution A Movie recommender system using Netflix movie data and currently on the stage of achieving matrix multiplication, use the item-collaborative algorithm and Hadoop MapReduce Auto Complete Apr 2018 traditional matrix-vector multiplication requires): 1. Then matrix-vector multiplication m * v is defined as: w[i] = sum_j m[i,j] * v[j]. The verifiable computation of Gennaro, Gentry and Parno addresses both concerns for Mimir: Mimir is a new implementation of MapReduce over MPI. Nov 20, 2020 · Matrices represented using COO format Matrix Multiplication Using Two Passes. Use Git or checkout with SVN using the web URL. This can be parallelized easily (just matrix-vector multiplication) but needs to chain together multiple MapReduce tasks. Spring 09 Publication: M. Jul 14, 2013 · The advantage of the above logic is, we can use a distributed map reduce model for compute with multiple map-reduce tasks - Constructing the co-occurrence matrix, Finding the dot product for each user etc. mapReduce # Python 3 my_strings = ['a', 'b', 'c', 'd', 'e'] my_numbers = [1,2,3,4,5] results = list(zip(my_strings, my_numbers)) print(results) As a bonus, can you guess what would happen in the above session if my_strings and my_numbers are not of the same length? Large-scale machine learning is another important use of MapReduce. A well-known matrix factorization method is Singular value decomposition (SVD). 522–532. Thursday, August 25, 11 30 The Mahout In Action (Chapter 6) book contains a recommendation method based on matrix multiplication that uses co-occurrence data (C) in combination with user preferences (U) to generate user recommendations (R). com/awslabs/lambda-refarch- mapreduce/. To put it in a crude analogy, Page Rank, Inverted Index and Matrix Multiplication - asarraf/Algorithm- Implementation-Using-Map-Reduce. arange(4). rb. x is a shorthand for the elements of the first tensor argument. * Distributed performance bug fixes. 1–12. To maximize parallelism, the Gram matrix is calculated, that is, a matrix of the distances between every data instance and the nodes of the SOM. } General Matrix-Vector multiplication: y <- alpha * A * x + beta * y Source Edit proc gemm [T: SomeFloat \| Complex] (alpha: T; A, B: The product of matrices A and B is calculated by multiplying the elements of rows in A with the corresponding columns in B, and then adding the resulting values to produce a single value for each row in A and each column in B. The Formula is: Mapper for Matrix A (k, v)=((i, k), (A, j, Aij)) for all k That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. to distributed matrix multiplication and distributed learning. regCG, for example, only lines 4 and 9 access matrix X; all other computations are inexpensive operations over small vectors or scalars. 5 as a cutoff, as shown in the plot below. com/Cloveryww/MPI-parallel-algorithms/tree/master/ cannon Since the algorithm and the lower hair collection task results when us 26 Nov 2018 Map Reduce (Part 3). sum (axis = 1). matrix (np. I'm working on the matrix multiplication using mapreduce. G. assign(vi;vnew) : decide how to update vi with vnew. Nov 29, 2017 · MapReduce, by Google, in 2004; Hadoop (fair mode), Spark (easy mode) MPI (hard mode) Matrix multiplication A = BxC for i in range(m): for j in range(n): for k in range(r): A[i][j] += B[i][k] * C[k][j] Matrix multiplication Vectorized for i in range(m): for j in range(n): A[i, j] = np. Problem Motivation Apr 04, 2019 · Other Links: GitHub Repository. Eq. The is similar to the process of generating the Row Number as explained in the previous post. It involves the matrix Oct 08, 2019 · In Cholesky method, a positive-definite matrix is written as the matrix multiplication of a lower-triangular matrix and its transpose. RecSys-2013-ZhuangCJL #memory management #parallel #performance A fast parallel SGD for matrix factorization in shared memory systems ( YZ , WSC , YCJ , CJL ), pp. 5 cutoff. GitHub Gist: instantly share code, notes, and snippets. Google’s MapReduce (Example)1 Classic example: word count. , non-causal attention where there is no notion of past and future. com/kokkos/kokkos- kernels \"Graph twiddling in a mapreduce world. Matrix-Vector Multiplication. ACM Transactions on Embedded Computing Systems (TECS), Vol 16, Issue 4, May 2017. Databases 2 Application 1: Matrix-Vector Multiplication. rstrip (). 55 folds) Ratio of FastPath to CompletePath memory accesses: 30:0 for software-based atomic and 3:28 for system-provided atomic implementations Matrix factorization (MF) factorizes a matrix R ∈ R m × n (with N z non-zero elements) into two low-rank matrices X ∈ R m × f and Θ ∈ R n × f, such that R ≈ X ⋅ Θ T. The output should be similar with the input. Matrix Multiplication With MapReduce. require ' rubygems ': require ' matrix ': require '. plot ( xs , ys ); Apr 09, 2013 · OutcomesRecognize relationships between matrix methods andthings you’ve already been doing\" Example SQL queries as matrix computationsUnderstand how to use Hadoop to compute thesematrix methods at scale for BigData\" Example Recommenders with social network infoUnderstand some of the issues that could arise. combine2(mi;j;vj) : combine mi;j and vj. Priebe, and Randal Burns. /matrix_block_mixin ' Mar 28, 2012 · That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. Background MapReduce and Spark Matrix Multiplication Note: also with row/column vector rhs Note: 1:N join. Matrix multiplication is an important multiplication design in parallel computation. Please turn in source codes, compilation, submission scripts used and also output les. 28 Mar 2012 P is a matrix = MN with element pik in row i and column k, where pik =∑j mijnjk Relational Representations: M = M(I, J, V ), with… Matrix Multiplication using MapReduce – 2 Step Solution Source Code: GitHub. ]]) >>>np. 2 A New Parallel Matrix Multiplication Algorithm on Hex-Cell Network (PMMHC) Using IMAN1 Super Computer E. input. However, such a straightforward approach does not apply to matrix tri-factorization because, as we show in the Methods section, the learning of any block of U and V depends on factor S . 0. May 12, 2018 · On Intel CPUs, SSE instruction sets use up to 128 bit registers (xmm, four ints), AVX and AVX2 use up to 256 bit registers (ymm, eight ints), and AVX512 use up to 512 bit registers (zmm, sixteen ints). Contribute to tangsttw/Matrix- Multiplication-MapReduce development by creating an account on GitHub. ,3. Report this profile Addition of numbers, matrix multiplication inside a docker and using MapReduce as the programming model. reshape(2,2) >>>a array([[ 0. y = y return z def backward ( dz ): dx = self . Lecture 14, Matrix Computations and Optimization in Apache Spark, Sparse matrix multiplication using SQL, Sparse matrix multiplication in MapReduce. Everybody is talking about it and everybody have their own understanding towards it which has made its definition quite ambiguous. My Personal Notes arrow_drop_up. Dec 16, 2019 · Outsourcing computation has gained significant attention in recent years in particular due to the prevalence of cloud computing. Use the output from the Stage 1 Reducer and pass along the same input to the Stage 2 reducer, where all the values having same index pairs are summed up to get the final output value. 04/27/18 - Large-scale machine learning and data mining applications require computer systems to perform massive computations that need to be May 02, 2018 · One kernel that can be parallelized using SPMD parallelism is dense matrix-matrix multiplication, in which we multiply two input matrices A and B to produce an output matrix C. Introduction Modern data-mining or ML applications, called «big-data analysis» requires us to manage massive amounts of data quickly. Here two passes symbolises the fact that we will need two map reduce jobs to compute the matrix multiplication. Then we are performing multiplication on the matrices entered by the user. 13. This matrix at each step will be updated and extended. After scaling genotype and expression data to unit variance with matrix-vector multiplications (or matrix-matrix with a small second matrix), and (2) closed-form algorithms with transpose-self matrix multiplication. x * dz # [dz/dy * dL/dz] return [ dx , dy ] “Scale-free Sparse Matrix-Vector Multiplication on Many-Core Architectures, “ IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), Vol 36, Issue 12, Dec 2017. Large Scale Machine Learning: Page: Gradient descent with large data, stochastic gradient descent, mini-batch gradient descent, map reduce, data parallelism, and online learning. It is crucial for perfor-mance to t the data into single-node or distributed main memory and enable fast matrix-vector opera-tions on in-memory data. The aim of this library is to easily design prototypes of algorithms using MapReduce. The product of a n x n matrix M by a vector v of length n is given by Dec 25, 2020 · Matrix Multiplication At Scale Using Map Reduce Matrix multiplication is the one of the most fundamental operation that most of the machine learning algorithms rely on. Taifi and Y. Optimizations Around version 0. x = x # must keep these around! self . For any u and v, such tat 1 ≤ u ≤ m and 1 ≤ v ≤ n, r u v is the (i, j) entry of R. toNumPy () Output: array ([[ - 60. This file shows the output of the resultant matrix obtained by multiplying matrix A and B in the format \"(row,column) value\" Contribute to JaredP94/MapReduce-Matrix-Multiplication development by creating an account on GitHub. It takes the value v and puts it in the row indexed by x. Feb 08, 2015 · Write a MapReduce query to remove the last 10 characters from each string of nucleotides, then remove any duplicates generated. A file containing two Matrices - MatrixA and MatrixB, was fetched from the Hadoop Distributed File System (HDFS) as an input for the Map Reduce task. - Use OpenMP and SSE to improve the speed of matrix multiplication over 86 times and kmeans 11 times. As the instructor pointed out, there are reasons this approach isn't insane. a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c max (a, max (b, c)) = max (max (a, b), c) min (a, min (b, c)) = min (min (a, b), c) Strings with string-concatenation form a semigroup. There are 2 implementations of the 3 Feb 2018 PDF \| On Dec 1, 2017, Mais Haj Qasem and others published Matrix multiplication of big data using MapReduce: A review \| Find, read and cite 4. Map Reduce Example for Sparse Matrix Multiplication. in a way you should be familiar with. Here, we will discuss the implementation of matrix multiplication on various communication networks like mesh and hypercube. The definition is motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. Write a MapReduce query to remove the last 10 characters from each string of nucleotides, then remove any duplicates generated. distributed map reduce In this module, we will learn about the MapReduce paradigm, and how it can be used to write distributed programs that analyze data represented as key-value pairs. It takes in 6 parameters: n: number of rows in A; m: number of I would like to apply map-reduce to deal with matrix multiplication in python with Hadoop. Jul 28, 2020 · Analyzing weather data of Fairbanks, Alaska to find cold and hot days using MapReduce Hadoop. , line 9), we have vector-matrix multiplication, often caused by the rewrite X>v !(v>> > > 2 Implement SELECT * FROM <table> WHERE <condition> with MapReduce. jl. 1 Matrix Multiplication Hadoop Implementation . * DRM row sampling api. Illustrates how a variety of coercion-based defaults can be specified to make life easy on the implementer, while still easily allowing for dispatch to optimal implementation-specific routines whenever it's desired. You might want to examine the Hadoop code for Word Count and Matrix multiplication. DATA/DATA SCIENCE Data Science from Scratch ISBN: 978-1-491-90142-7 US$39. So, several papers have studied the problem of multiplying matrices using a large number of processors (CPUs) in parallel. Kyungyong Lee is an assistant professor in the College of Computer Science at Kookmin University. The instruction sets are typed, and instructions designed to operate on packed doubles can’t operate on packed ints without explicit casting. In this post, we will be writing a map-reduce program to do Matrix Multiplication You need Hadoop’s HDFS and map GitHub Gist: star and fork jaganadhg's gists by creating an account on GitHub. Jun 23, 2014 · To the best of our knowledge, there are no matrix inversion algorithms using MapReduce, although there are several software systems for other matrix operations using MapReduce. FlashMatrix: Parallel, Scalable Data Analysis with Generalized Matrix Operations using Commodity SSDs. Here we reduce the output received from mapper into actual 2D array for matrices A and B and calculate the matrix multiplication based on usual formula. • Irregular algorithms Penetrating rays (e. Instructors. (1) can be minimised with respect to and solved for , yielding a large matrix multiplication problem, a formulation that is employed by the R package Matrix eQTL , which allows for fast eQTL analysis on a desktop computer. matrix',default='A', dest='Amatname') def parsemat(self): \"\"\" Return 1 if this is the A matrix, otherwise return 2\"\"\" fn = get_jobconf_value('map. Matrix factorization learns a latent data model that takes a data matrix and transforms it into a latent feature space enabling generalization, noise 1 Mar 2018 implement by naive algorithm(without partition) and advanced algorithm(with partition) - AiningWang/Matrix-Multiplication-using-MapReduce. d. . I hope these programs will help people understand the power of distributed parallel computing via map-reduce on Spark platform. An AggBinaryOp hop can be compiled into the following physical operators. collection. Howe outlined, together with the theory, some solutions to the assignments, we started to make our hands really dirty. Pros . UPDATE: Please note that the Mapper function does not have access to the Row Number (in this case i, and k) directly. 09, May 20. F. lines method; using the generate method (provide a Supplier) or iterate method (providing the initial value and incremental operation). Hi all. 550 Architecture of Machine Learning Systems based on fast matrix multiplication. Mar 29, 2012 · Posted by Venkata (Ravi) Adusumilli on March 29, 2012 in Hadoop, MapReduce Tags: Hadoop 0. toNumPy () Output: array ([[ - 60. The JobConfigurable#configure has to be implemented in the Mapper and Reducer class. Apr 14, 2012 · Prepare for Matrix Multiplication. stdin: curr_index, index, value = line. g. enron 4. But somehow the generation of the <Key> <value> pair and the operation in the 1. For running unit tests, use junit, and for writing MapReduce tests, use mrunit. Jan 27, 2021 · // The slave process receives the sub portion of the Matrix A which assigned by Root : MPI_Recv(&matrix_a, rowsN, MPI_DOUBLE, source, 1, MPI_COMM_WORLD, &status); // The slave process receives the Matrix B: MPI_Recv(&matrix_b, NN, MPI_DOUBLE, source, 1, MPI_COMM_WORLD, &status); // Matrix multiplication: for (int k = 0; k<N; k++) Mar 31, 2012 · P is a matrix = MN with element p ik in row i and column k, where p ik =∑ j m ij n jk. We represent matrix M as a relation , with tuples , and matrix N as a relation , with tuples . Monte Carlo Integration. 19. Implementation . Also a variation for pair-wise distance matrix of two different inputs x and y: sqDist(x,y), dsqDist(x,y). py. 1 Matrix Multiply and Computer Architectures Homework question 1 Matrix multiplication with MapReduce If A is an m × p matrix and B is an p × n matrix, then the product of A and B is the m × n matrix C = AB, where the (i, j) th element of C is computed as the inner product of the ith row of A with the jth column of B: This is a dot product—simple arithmetic if m, p, and n are small. The map takes ( le, content) pair, and emits (word, 1) pairs for each word in the content. MapReduce: Simplified Data Processing on Large Clusters. Step 1: We can download the dataset from this Link , For various cities in different years. At first it was a little brain-breaky, but then we did the map-reduce version, which was brain-breakier. Written by Luka Kerr on April 2, 2018 I’ve been learning MIPS assembly for about 2 weeks now at uni and wanted to share how i’ve implemented a simple matrix multiplication function in MIPS. That said, the ground is now prepared for the purpose of this tutorial: writing a Hadoop MapReduce program in a more Pythonic way, i. linspace ( 0 , 2 * np . Clustering with KMeans: Page: Clustering with KMeans in scikit-learn. “Matrix factorizations at scale: A comparison of scientific data analytics in Spark and C+MPI using three case studies”, 2016 IEEE International Conference on Big Data (Big Data), pages 204–213, Dec 2016. I will explain LSH and how to use this package as well as the details of the implementation below. \"Git-a\" -rec It further employs a content-based filtering approach, coupled with Apache Spark to develop a recommender system, for Github users. Use of ufuncs is an esssential aspect of vectorization and typically much more computtionally efficient than using an explicit loop over each element. For these setups, coding has been utilized primarily to handle failed or straggling (delayed) workers –, where some workers fail or are signiﬁcantly slower than the other workers, causing a signiﬁcant delay in the overall computation time. e. g. 2) Matrix Multiplication 3) Find Mutual Friends for Social Media Data. Contribute to kdave2/Matrix- Multiplication-Hadoop-Map-Reduce development by creating an account on GitHub. Map, Reduce and Filter functions in Python make writing code much more easier (less lines of code) and I think they are optimized internally which will make them more faster than writing custom code which will most Sparse linear algebra Matrix Multiplication Spectral methods FFT N-Body methods GEM Structured grids SRAD Unstructured grids CFD solver MapReduce Combinational logic CRC Graph traversal Breadth-First Search (BFS) Dynamic programming Needleman-Wunsch Backtrack and branch-and-bound Graphical models Hidden Markov Model Map Reduce Triplets Block Matrix Multiplication Let’s look at Block Matrix Multiplication (on the board and on GitHub) Created Date: Oct 23, 2020 · The above analysis is relevant for so-called bidirectional attention, i. This model defines data abstraction as key-value pairs and computation flow as “map, shuffle and then reduce”. Matrix multiplication is an important multiplication design in parallel computation. MapReduce is a parallel fram ework for big da ta, which That is, we can implement matrix multiplication as the cascade of two MapReduce operations, as follows. p. private static Long N; public void configure(JobConf job) {N = Long. Designed a 4x4 grid layout of game card. We consider numerical computations using dataflow graphs, with a focus on learning deep neural networks for image classification and other classification tasks. x library which implements a MapReduce algorithm. reshape (%input) : (tensor<1x28x28x1xf32>) /> tensor Matrix multiplication in C. – Description of AdaGrad. First: The Map Function\":Foreachmatrixelementm ij,producethekeyvaluepair j, (M,i,m ij) # 21 hours ago · mapreduce python 3, Jan 28, 2020 · You can indent using tabs and spaces in Python. 4. That is, we can implement matrix multiplication as the cascade of two map-reduce operations, as follows. sin is a universal function plt . are overloaded for convenience. The : operator takes syntax start:spacing:end. We classify the matrix multiplication problems into Apr 26, 2012 · Posted by Venkata (Ravi) Adusumilli on April 26, 2012 in Hadoop, MapReduce Tags: Hadoop 0. 3. sh Matrix_Reducer. github. ∙ 0 ∙ share A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. gz Step 2: Move the eclipse folder to the home directory In this step, you can see how to move the eclipse folder to the home directory. Example MapReduce Algorithms Matrix-vector multiplication Power iteration (e. A trivial implementation is trivial, but users are likely to want fast versions that are hard to write. io/. Graph Processing using Map-Reduce 2. Oct 10, 2017 · Using MapReduce Programming In mathematics, matrix multiplication or the matrix product is a binary operation that produces a matrix from two matrices. The value for cell (i, j) of matrix C is computed by taking the dot product of row i in matrix A and column j in matrix B. If A is an m × p matrix and B is an p × n matrix, then the product of A and B is the m × n matrix C = AB, where the (i, j)th element of C is computed as the. In the Figure 1 (a), we experiment large and sparse matrix multiplication from two random Bernoulli square matrices with dimension roughly equal to 1. Parallel Matrix Multiplication Algorithms Grid-based approach - The grid-based algorithms , regard processors as residing on a two- or three- Coverage: vectors norms (ℓ 2-norm, ℓ 1-norm, ℓ p-norm, ℓ ∞-norm), vector inner product, matrix multiplication, matrix trace, matrix Frobenius norm, scalar function differential, convex function, use Numpy to construct vectors and matrices. Matrix multiplication in C: We can add, subtract, multiply and divide 2 matrices. 20. matrix multiplication using mapreduce github\n\nMatrix multiplication using mapreduce github" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.855038,"math_prob":0.88209856,"size":85719,"snap":"2021-21-2021-25","text_gpt3_token_len":19682,"char_repetition_ratio":0.19087674,"word_repetition_ratio":0.15476191,"special_character_ratio":0.22583091,"punctuation_ratio":0.12318703,"nsfw_num_words":3,"has_unicode_error":false,"math_prob_llama3":0.9918775,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-11T03:45:37Z\",\"WARC-Record-ID\":\"<urn:uuid:862db7a7-8be7-4b13-966c-95cbbd10ed9a>\",\"Content-Length\":\"183045\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aa73976b-c453-497a-8f4a-8676248a95b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:066cc9ee-1ff2-49e3-97ca-779a04790fc9>\",\"WARC-IP-Address\":\"172.67.176.106\",\"WARC-Target-URI\":\"https://cemxpu.burgerfi8518.site/matrix-multiplication-using-mapreduce-github.html\",\"WARC-Payload-Digest\":\"sha1:GDP3ONC2XXKL7VIT72CCABL23NEXKNUW\",\"WARC-Block-Digest\":\"sha1:CDH5UL2ENZYKZGJWLM3PHB7LT77FYBJW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991641.5_warc_CC-MAIN-20210511025739-20210511055739-00325.warc.gz\"}"}
https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/	[ "# ALGEBRA PRECALCULUS\n\nI want lớn prove sầu this (where each angle may be negative sầu or greater than \\$180^circ\\$):\n\nWhen \\$A+B+C = 180^circ\\$ \beginequation* an A + ung B + ung C = ã A: ung B: ã C. endequation\n\nWe know that\beginequation an(A+B) = frac an A+ ung B1- ung Achảy Bendequation* và that \beginequation* extvà that~A+B = 180^circ-C.endequation*\n\nTherefore \\$ an(A+B) = - an C.\\$\n\nFrom here, I got stuông chồng.\n\nBạn đang xem: Algebra precalculus", null, "", null, "cảnh báo that\\$\\$ hithptquocgia2016.comrmImleft(e^ipi ight)=0 ag1\\$\\$Thus, if \\$a+b+c=pi\\$,\\$\\$\beginalign0&= hithptquocgia2016.comrmImleft(e^iae^ibe^ic ight)\\&= hithptquocgia2016.comrmImBig(\big(cos(a)+isin(a)\big)\big(cos(b)+isin(b)\big)\big(cos(c)+isin(c)\big)Big)\\<4pt>&=sin(a)cos(b)cos(c)+cos(a)sin(b)cos(c)+cos(a)cos(b)sin(c)\\&-sin(a)sin(b)sin(c) ag2endalign\\$\\$Dividing \\$(2)\\$ by \\$cos(a)cos(b)cos(c)\\$ yields\\$\\$ an(a)+ an(b)+ an(c)= an(a) an(b) an(c) ag3\\$\\$", null, "HINT\n\n\\$A+B+C = 180\\$\n\n\\$A+B = 180 - C\\$\n\nWe\"ll apply tangent function:\n\n\\$ ã (A+B) = chảy (180 - C)\\$\n\nWe\"ll consider the identity:\n\n\\$ an(x+y) = fracchảy x + ã y1-chảy xchảy y\\$\n\n\\$frac ã A + chảy B1- ã A an B = fracchảy 180 - ung C1+ ã 180 ung C\\$\n\nBut \\$ ã 180 = 0\\$, therefore, we\"ll get:\n\n\\$fracchảy A + chảy 1- ã A an B\\$ = \\$frac0 - chảy C1+0\\$\n\n\\$fracchảy A + ã B1- ã A ung B = -chảy C\\$\n\nWe\"ll multiply by \\$(1- ung Achảy B)\\$:\n\n\\$ ã A + chảy B = -chảy C + an A ung B an C\\$\n\nHence\n\n\\$chảy A + an B+ an C = an A an B ã C\\$\n\nShare\nCite\nFollow\nanswered Aug 27 \"13 at 14:22", null, "ShobhitShobhit\n\\$endgroup\\$\n15\n\\$\begingroup\\$\nHere is a geometric proof, for the case that all three angles are acute:", null, "\\$QRUV\\$ are collinear because \\$B+90^circ+(90^circ-B)=180^circ\\$.\n\n\\$STV\\$ are collinear because \\$A+B+C=180^circ\\$, so \\$angle QSV=angle UTV=C\\$.\n\nXem thêm:\n\nSimilar triangles \\$ riangle PQRsim riangle TRS\\$ & \\$ riangle RTU syên riangle SRQ\\$ give sầu \\$displaystylefracQPRQ = fracRTSR = fracTURQ\\$, and therefore \\$TU=QP=1\\$.\n\nThen,\\$\\$\beginalign& ã A + ã B + ã C = QR+RU+UV = QV \\&= QP.. fracQRQP, fracQSQR , fracQVQS = 1 cdot an(A) an(B) an(C) endalign\\$\\$\n\nWhen one of the angles is obtuse, let it (without loss of generality) be \\$C\\$. Then a similar diagram can be drawn, except that \\$V\\$ is to lớn the left of \\$Q\\$, và \\$UV\\$, \\$QV\\$ count as negative lengths.\n\nShare\nCite\nFollow\nedited Jun 11 \"15 at 14:54\nanswered May 17 \"15 at 13:55", null, "hmakholm left over Monicahmakholm left over Monica\n\\$endgroup\\$\n0\n4\n\\$\begingroup\\$\nHINT:\n\nUsing \\$displaystyle an(A+B)=fracchảy A+chảy B1- an A ã B,\\$\n\nwe can prove sầu \\$\\$ an(A+B+C)=fracsum_ extcycchảy A-prod ã A1-sum_ extcycchảy Achảy B\\$\\$\n\nNow, if \\$A+B+C=n180^circ,\\$ where \\$n\\$ is any integer we know \\$ an(n180^circ)=0\\$\n\nShare\nCite\nFollow\nedited Nov 16 \"13 at 17:27\nMichael Hardy\n1\nanswered Aug 27 \"13 at 14:41\nlab bhattacharjeelab bhattacharjee" ]	[ null, "https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/imager_1_7193_700.jpg", null, "https://thithptquocgianăm 2016.com/tana-tanb-tanc-tanatanbtanc/imager_2_7193_700.jpg", null, "https://thithptquocgianăm 2016.com/tana-tanb-tanc-tanatanbtanc/imager_3_7193_700.jpg", null, "https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/imager_4_7193_700.jpg", null, "https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/imager_5_7193_700.jpg", null, "https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/imager_6_7193_700.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.50949204,"math_prob":0.9993272,"size":3886,"snap":"2023-14-2023-23","text_gpt3_token_len":1602,"char_repetition_ratio":0.10510046,"word_repetition_ratio":0.06110283,"special_character_ratio":0.38317037,"punctuation_ratio":0.07193396,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99988127,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-29T21:45:13Z\",\"WARC-Record-ID\":\"<urn:uuid:2d759d2a-0f44-4444-8847-afa76908124d>\",\"Content-Length\":\"37663\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b21162f7-590e-421c-b0d4-a78cd8f23e79>\",\"WARC-Concurrent-To\":\"<urn:uuid:76987f23-1ea7-4fab-aa40-bd19bdb02d39>\",\"WARC-IP-Address\":\"172.67.189.184\",\"WARC-Target-URI\":\"https://thithptquocgia2016.com/tana-tanb-tanc-tanatanbtanc/\",\"WARC-Payload-Digest\":\"sha1:MJLYRRMNLZUITOKV3FEOFBRALSR3ZRHX\",\"WARC-Block-Digest\":\"sha1:Y7WY6XEN4FZFDHOJRGEA5MOYCAPBOHD6\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224644913.39_warc_CC-MAIN-20230529205037-20230529235037-00367.warc.gz\"}"}