| {"text": "#include <iostream>\n#include <Eigen/Dense>\n\ntemplate<typename T>\nT pseudoInverse(const T &a, double epsilon = std::numeric_limits<double>::epsilon())\n{\n //Eigen::DecompositionOptions flags;\n int flags;\n // For a non-square matrix\n if(a.cols()!=a.rows())\n {\n flags=Eigen::ComputeThinU | Eigen::ComputeThinV;\n }\n else\n {\n flags=Eigen::ComputeFullU | Eigen::ComputeFullV;\n }\n Eigen::JacobiSVD< T > svd(a ,flags);\n\n double tolerance = epsilon * std::max(a.cols(), a.rows()) *svd.singularValues().array().abs()(0);\n return svd.matrixV() * (svd.singularValues().array().abs() > tolerance).select(svd.singularValues().array().inverse(), 0).matrix().asDiagonal() * svd.matrixU().adjoint();\n}\n\n\n\ntemplate <class MatT>\nEigen::Matrix<typename MatT::Scalar, MatT::ColsAtCompileTime, MatT::RowsAtCompileTime>\npseudoinverse(const MatT &mat, typename MatT::Scalar tolerance = typename MatT::Scalar{1e-4}) // choose appropriately\n{\n typedef typename MatT::Scalar Scalar;\n auto svd = mat.jacobiSvd(Eigen::ComputeFullU | Eigen::ComputeFullV);\n const auto &singularValues = svd.singularValues();\n Eigen::Matrix<Scalar, MatT::ColsAtCompileTime, MatT::RowsAtCompileTime> singularValuesInv(mat.cols(), mat.rows());\n singularValuesInv.setZero();\n for (unsigned int i = 0; i < singularValues.size(); ++i) {\n if (singularValues(i) > tolerance)\n {\n singularValuesInv(i, i) = Scalar{1} / singularValues(i);\n }\n else\n {\n singularValuesInv(i, i) = Scalar{0};\n }\n }\n return svd.matrixV() * singularValuesInv * svd.matrixU().adjoint();\n}\n\n\n\nvoid SVD_Example()\n{\n/*\n\nAX=0;\nA, U, V=SVD(A);\nA* U(Index of last column)=0;\n\n1) Full SVD\n A mxn\n U mxm\n Σ mxn\n V* nxn\n\n\n2) Thin SVD\n A mxn\n U mxn\n Σ nxn\n V* nxn\n\n3) Compact SVD\n\n4) Truncated SVD\nRef: https://en.wikipedia.org/wiki/Singular_value_decomposition#Thin_SVD\n\n*/\n\n std::cout<<\"********************** 1) Full SVD ***********************************\" <<std::endl;\n\n Eigen::MatrixXd A;\n A.setRandom(3,4);\n std::cout<<\"Matrix A\" <<std::endl;\n std::cout<<A <<std::endl;\n Eigen::JacobiSVD<Eigen::MatrixXd> svd(A, Eigen::ComputeFullU | Eigen::ComputeFullV);\n\n\n std::cout<< \"Size of original matrix:\"<< A.rows()<<\",\"<<A.cols() <<std::endl;\n\n std::cout<< \"Size of U matrix:\"<< svd.matrixU().rows()<<\",\"<<svd.matrixU().cols() <<std::endl;\n\n std::cout<< \"Size of Σ matrix:\"<< svd.singularValues().rows()<<\",\"<<svd.singularValues().cols() <<std::endl;\n\n std::cout<< \"Size of V matrix:\"<< svd.matrixV().rows()<<\",\"<<svd.matrixV().cols() <<std::endl;\n\n std::cout << \"Its singular values are:\" << std::endl << svd.singularValues() << std::endl;\n\n Eigen::MatrixXd U=svd.matrixU();\n Eigen::MatrixXd V=svd.matrixV();\n Eigen::MatrixXd Sigma(U.rows(),V.cols());\n Eigen::MatrixXd identity=Eigen::MatrixXd::Identity(U.rows(),V.cols());\n\n Sigma=identity.array().colwise()* svd.singularValues().array();\n\n std::cout<<\"Matrix U\" <<std::endl;\n std::cout<<U <<std::endl;\n\n std::cout<<\"Matrix V\" <<std::endl;\n std::cout<<V <<std::endl;\n\n std::cout<<\"Matrix Sigma\" <<std::endl;\n std::cout<<Sigma <<std::endl;\n\n std::cout<<\"This should be very close to A\" <<std::endl;\n Eigen::MatrixXd A_reconstructed= U*Sigma*V.transpose();\n std::cout<<U*Sigma*V.transpose() <<std::endl;\n\n\n std::cout<<\"This should be zero vector (solution of the problem A*V.col( V.cols()-1))\" <<std::endl;\n std::cout<<A*V.col( V.cols()-1)<<std::endl;\n\n\n Eigen::MatrixXd diff = A - A_reconstructed;\n std::cout << \"diff:\\n\" << diff.array().abs().sum() << \"\\n\";\n\n\n std::cout<<\"********************** 2) Thin SVD ***********************************\" <<std::endl;\n Eigen::MatrixXd C;\n C.setRandom(27,18);\n Eigen::JacobiSVD<Eigen::MatrixXd> svd_thin( C, Eigen::ComputeThinU | Eigen::ComputeThinV);\n\n std::cout<< \"Size of original matrix:\"<< C.rows()<<\",\"<<C.cols() <<std::endl;\n\n std::cout<< \"Size of U matrix:\"<< svd_thin.matrixU().rows()<<\",\"<<svd_thin.matrixU().cols() <<std::endl;\n\n std::cout<< \"Size of Σ matrix:\"<< svd_thin.singularValues().rows()<<\",\"<<svd_thin.singularValues().cols() <<std::endl;\n\n std::cout<< \"Size of V matrix:\"<< svd_thin.matrixV().rows()<<\",\"<<svd_thin.matrixV().cols() <<std::endl;\n\n Eigen::MatrixXd C_reconstructed = svd_thin.matrixU() * svd_thin.singularValues().asDiagonal() * svd_thin.matrixV().transpose();\n\n std::cout << \"diff:\\n\" << (C - C_reconstructed).array().abs().sum() << \"\\n\";\n\n Eigen::MatrixXd pinv_C =svd_thin.matrixV()*svd_thin.singularValues().asDiagonal() * svd_thin.matrixU().transpose();\n\n// Eigen::MatrixXd pinv_C =svd.matrixV()*svd.singularValues().asDiagonal() ;\n\n// MatrixXd diff = Cp - C;\n// cout << \"diff:\\n\" << diff.array().abs().sum() << \"\\n\";\n\n std::cout<< \"Size of pinv_C matrix:\"<< pinv_C.rows()<<\",\"<<pinv_C.cols() <<std::endl;\n\n\n //std::cout << \"pinv_C*C:\\n\" << pinv_C*C << \"\\n\";\n\n\n Eigen::MatrixXd pinv = C.completeOrthogonalDecomposition().pseudoInverse();\n\n Eigen::MatrixXd pinv2 = pseudoInverse(C);\n\n std::cout << \"xxx\" << (pinv2*C).rows()<< \",\" <<(pinv2*C).cols() << \"\\n\";\n std::cout << \"xxx\" << (pinv2*C).array().abs().sum() << \"\\n\";\n\n std::cout << \"xxx\" << (pinv-pinv2).array().abs().sum() << \"\\n\";\n\n/*\nRef:\n https://gist.github.com/javidcf/25066cf85e71105d57b6\n https://eigen.tuxfamily.org/bz/show_bug.cgi?id=257#c8\n https://gist.github.com/pshriwise/67c2ae78e5db3831da38390a8b2a209f\n https://math.stackexchange.com/questions/19948/pseudoinverse-matrix-and-svd\n*/\n}\n\n\nint main()\n{\n\n}\n", "meta": {"hexsha": "b4422faf9ea3fa6005a5afc81a0a7732324bd66a", "size": 5645, "ext": "cpp", "lang": "C++", "max_stars_repo_path": "src/singular_value_decomposition.cpp", "max_stars_repo_name": "behnamasadi/Mastering_Eigen", "max_stars_repo_head_hexsha": "99edbc819c89a4805b777eef69044a1658d96206", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 4.0, "max_stars_repo_stars_event_min_datetime": "2019-04-14T16:54:17.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-13T15:55:08.000Z", "max_issues_repo_path": "src/singular_value_decomposition.cpp", "max_issues_repo_name": "behnamasadi/Mastering_Eigen", "max_issues_repo_head_hexsha": "99edbc819c89a4805b777eef69044a1658d96206", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "src/singular_value_decomposition.cpp", "max_forks_repo_name": "behnamasadi/Mastering_Eigen", "max_forks_repo_head_hexsha": "99edbc819c89a4805b777eef69044a1658d96206", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 2.0, "max_forks_repo_forks_event_min_datetime": "2019-12-25T10:08:09.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-06T14:27:32.000Z", "avg_line_length": 31.5363128492, "max_line_length": 175, "alphanum_fraction": 0.6047829938, "num_tokens": 1722, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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