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行列分解ライブラリredsvdを公開ã—ã¾ã—㟠- DO++
大è¦æ¨¡ç–Žè¡Œåˆ—å‘ã‘ã®è¡Œåˆ—分解ライブラリredsvdを公開ã—ã¾ã—ãŸï¼Ž redsvd 大è¦æ¨¡ç–Žè¡Œåˆ—å‘ã‘ã®ç‰¹ç•°å€¤åˆ†è§£ã‚„主æˆåˆ†åˆ†æžï¼Œå›ºæœ‰å€¤åˆ†è§£ã‚’è¡Œã†ãƒ©ã‚¤ãƒ–ラリredsvdを公開ã—ã¾ã—ãŸï¼Ž ä¿®æ£BSDライセンスã§å…¬é–‹ã—ã¦ãŠã‚Šï¼Œã‚³ãƒžãƒ³ãƒ‰ãƒ©ã‚¤ãƒ³ã‹ã‚‰ä½¿ãˆã‚‹ä»–，C++ライブラリãŒç”¨æ„ã•ã‚Œã¦ã„ã¾ã™ï¼Ž 例ãˆã°ï¼Œè¡Œã¨åˆ—æ•°ãŒãã‚Œãžã‚Œ10万，éžé›¶ã®è¦ç´ ãŒ1000万ã‹ã‚‰ãªã‚‹ç–Žè¡Œåˆ—ã«å¯¾ã™ã‚‹ä¸Šä½20ä½ã¾ã§ã®ç‰¹ç•°å€¤åˆ†è§£ã‚’ç´„2秒ã§å‡¦ç†ã—ã¾ã™ï¼Ž 特異値分解ã¨ã‹ï¼Œä½¿ã£ã¦ã„る技術ã®è©³ç´°ã¨ã‹å¿œç”¨äº‹ä¾‹ã‚’以下ã«ç°¡å˜ã«ç´¹ä»‹ã—ã¾ã—ãŸã®ã§ï¼Œèˆˆå‘³ã®ã‚ã‚‹æ–¹ã¯å‚考ã«ã—ã¦ãã ã•ã„． 特異値分解ã¨ã¯ ã¾ãšè¡Œåˆ—ã‚’é©å½“ã«å¾©ç¿’ã—ã¾ã™ï¼Žè¡Œåˆ—Xã®è»¢ç½®ã‚’X^tã¨è¡¨ã™ã“ã¨ã«ã—ã¾ã™ï¼Žã¾ãŸIã‚’å˜ä½è¡Œåˆ—ã¨ã—，Oã‚’å…¨ã¦ã®æˆåˆ†ãŒ0ã§ã‚る零行列ã¨ã—ã¾ã™ï¼Žã¾ãŸï¼Œè¡Œåˆ—XX^t=Iã§ã‚るよã†ãªXを直交行列ã¨å‘¼ã³ã¾ã™ï¼ŽXãŒç›´äº¤è¡Œåˆ—ã®æ™‚，Xvã¯ãƒ™ã‚¯ãƒˆãƒ«vã‚’é•·ã•ã‚’変ãˆãšã«å›žè»¢ã•ã›ã¾ã™ï¼Žã“ã“ã§ã¯
SVDLIBC
A C Library for Computing Singular Value Decompositions version 1.4 SVDLIBC is a C library written by Doug Rohde. It was based on the SVDPACKC library, which was written by Michael Berry, Theresa Do, Gavin O'Brien, Vijay Krishna and Sowmini Varadhan at the University of Tennessee. SVDLIBC is made available under a BSD License. SVDLIBC offers a cleaned-up version of the code with a new library inte
SVDLIBC
SVDLIBC is a C library based on the SVDPACKC library, which was written by Michael Berry, Theresa Do, Gavin O'Brien, Vijay Krishna and Sowmini Varadhan. SVDLIBC offers a cleaned-up version of the code with a sane library interface and a front-end executable that performs matrix file type conversions, along with computing singular value decompositions. Currently the only SVDPACKC algorithm implemen
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SINGULAR VALUE Decomposition SVD
Example with O-matrix /Mathlab O>(u,s,v)=svd(x) O>x { [ 1 , 2 ] [ 2 , 3 ] [ 3 , 4 ] } O>[u,s,v]=svd(x) O>u { [ -0.338098 , 0.847952 , 0.408248 ] [ -0.550649 , 0.173547 , -0.816497 ] [ -0.763201 , -0.500857 , 0.408248 ] } O>s { [ 6.54676 , 0 ] [ 0 , 0.374153 ] [ 0 , 0 ] } O>v { [ -0.569595 , -0.821926 ] [ -0.821926 , 0.569595 ] } O>[e,d]=eigen(x'x) O>[e,d]=eigen(x'*x) O>e { [ (0.569595,0) , (-0.821
SVD decomposition - C++, C#, Java library
SVD decomposition The singular value decomposition of MxN matrix A is its representation as A = U W VT, where U is an orthogonal MxM matrix, V - orthogonal NxN matrix. The diagonal elements of matrix W are non-negative numbers in descending order, all off-diagonal elements are zeros. The matrix W consists mainly of zeros, so we only need the first min(M,N) columns (three, in the example above) of
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