This is a test.
Copyright (c) 2016 Theodore Gast, Chuyuan Fu, Chenfanfu Jiang, Joseph Teran
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If the code is used in an article, the following paper shall be cited: @techreport{qrsvd:2016, title={Implicit-shifted Symmetric QR Singular Value Decomposition of 3x3 Matrices}, author={Gast, Theodore and Fu, Chuyuan and Jiang, Chenfanfu and Teran, Joseph}, year={2016}, institution={University of California Los Angeles} }
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################################################################################ ImplicitQRSVD.h implements 2D and 3D polar decompositions and SVDs. Tools.h provides a random number generator and a timer. The code is tested with g++ 5.3. It uses std=c++14. It relies on Eigen3 and is header-only. ################################################################################ To run the benchmark: make; ./svd ################################################################################ To use the SVD code: (T may be float or double) 2D Polar: Eigen::Matrix<T, 2, 2> A,R,S; A<<1,2,3,4; JIXIE::polarDecomposition(A, R, S); // R will be the closest rotation to A // S will be symmetric 2D SVD: Eigen::Matrix<T, 2, 2> A; A<<1,2,3,4; Eigen::Matrix<T, 2, 1> S; Eigen::Matrix<T, 2, 2> U; Eigen::Matrix<T, 2, 2> V; JIXIE::singularValueDecomposition(A,U,S,V); // A = U S V' // U and V will be rotations // S will be singular values sorted by decreasing magnitude. Only the last one may be negative. 3D Polar: Eigen::Matrix<T, 3, 3> A,R,S; A<<1,2,3,4,5,6; JIXIE::polarDecomposition(A, R, S); // R will be the closest rotation to A // S will be symmetric 3D SVD: Eigen::Matrix<T, 3, 3> A; A<<1,2,3,4,5,6; Eigen::Matrix<T, 3, 1> S; Eigen::Matrix<T, 3, 3> U; Eigen::Matrix<T, 3, 3> V; JIXIE::singularValueDecomposition(A,U,S,V); // A = U S V' // U and V will be rotations // S will be singular values sorted by decreasing magnitude. Only the last one may be negative. ################################################################################