Copyright (c) 2016 Theodore Gast, Chuyuan Fu, Chenfanfu Jiang, Joseph Teran
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The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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. ################################################################################