Mercurial > octave
view liboctave/numeric/svd.cc @ 31202:434b5a1b9498
isequal.m: Add ability to compare Java objects (bug #62930)
* isequal.m: Add elseif clause to detect Java objects and use built-in Java
"equals" method for comparison. Add BIST test for Java object comparison.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 25 Aug 2022 15:35:25 -0700 |
parents | 796f54d4ddbf |
children | d17ee5e7b66c |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1994-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cassert> #include <algorithm> #include <unordered_map> #include "CMatrix.h" #include "dDiagMatrix.h" #include "dMatrix.h" #include "fCMatrix.h" #include "fDiagMatrix.h" #include "fMatrix.h" #include "lo-error.h" #include "lo-lapack-proto.h" #include "svd.h" // class to compute optimal work space size (lwork) for DGEJSV and SGEJSV template<typename T> class gejsv_lwork { public: gejsv_lwork () = delete; // Unfortunately, dgejsv and sgejsv do not provide estimation of 'lwork'. // Thus, we have to estimate it according to corresponding LAPACK // documentation and related source codes (e.g. cgejsv). // In LAPACKE (C interface to LAPACK), the memory handling code in // LAPACKE_dgejsv() (lapacke_dgejsv.c, last visit 2019-02-17) uses // the minimum required working space. In contrast, here the optimal // working space size is computed, at the cost of much longer code. static F77_INT optimal (char& joba, char& jobu, char& jobv, F77_INT m, F77_INT n); private: typedef typename T::element_type P; // functions could be called from GEJSV static F77_INT geqp3_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, F77_INT *jpvt, P *tau, P *work, F77_INT lwork, F77_INT& info); static F77_INT geqrf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info); static F77_INT gelqf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info); static F77_INT ormlq_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info); static F77_INT ormqr_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info); }; #define GEJSV_REAL_QP3_LWORK(f, F) \ F77_XFCN (f, F, (m, n, a, lda, jpvt, tau, work, lwork, info)) #define GEJSV_REAL_QR_LWORK(f, F) \ F77_XFCN (f, F, (m, n, a, lda, tau, work, lwork, info)) #define GEJSV_REAL_ORM_LWORK(f, F) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&side, 1), \ F77_CONST_CHAR_ARG2 (&trans, 1), \ m, n, k, a, lda, tau, \ c, ldc, work, lwork, info \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1))) // For Matrix template<> F77_INT gejsv_lwork<Matrix>::geqp3_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, F77_INT *jpvt, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QP3_LWORK (dgeqp3, DGEQP3); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<Matrix>::geqrf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QR_LWORK (dgeqrf, DGEQRF); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<Matrix>::gelqf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QR_LWORK (dgelqf, DGELQF); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<Matrix>::ormlq_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_ORM_LWORK (dormlq, DORMLQ); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<Matrix>::ormqr_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_ORM_LWORK (dormqr, DORMQR); return static_cast<F77_INT> (work[0]); } // For FloatMatrix template<> F77_INT gejsv_lwork<FloatMatrix>::geqp3_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, F77_INT *jpvt, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QP3_LWORK (sgeqp3, SGEQP3); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<FloatMatrix>::geqrf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QR_LWORK (sgeqrf, SGEQRF); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<FloatMatrix>::gelqf_lwork (F77_INT m, F77_INT n, P *a, F77_INT lda, P *tau, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_QR_LWORK (sgelqf, SGELQF); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<FloatMatrix>::ormlq_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_ORM_LWORK (sormlq, SORMLQ); return static_cast<F77_INT> (work[0]); } template<> F77_INT gejsv_lwork<FloatMatrix>::ormqr_lwork (char& side, char& trans, F77_INT m, F77_INT n, F77_INT k, P *a, F77_INT lda, P *tau, P *c, F77_INT ldc, P *work, F77_INT lwork, F77_INT& info) { GEJSV_REAL_ORM_LWORK (sormqr, SORMQR); return static_cast<F77_INT> (work[0]); } #undef GEJSV_REAL_QP3_LWORK #undef GEJSV_REAL_QR_LWORK #undef GEJSV_REAL_ORM_LWORK template<typename T> F77_INT gejsv_lwork<T>::optimal (char& joba, char& jobu, char& jobv, F77_INT m, F77_INT n) { F77_INT lwork = -1; std::vector<P> work (2); // dummy work space // variables that mimic running environment of gejsv F77_INT lda = std::max<F77_INT> (m, 1); F77_INT ierr = 0; char side = 'L'; char trans = 'N'; std::vector<P> mat_a (1); P *a = mat_a.data (); // dummy input matrix std::vector<F77_INT> vec_jpvt = {0}; P *tau = work.data (); P *u = work.data (); P *v = work.data (); bool need_lsvec = jobu == 'U' || jobu == 'F'; bool need_rsvec = jobv == 'V' || jobv == 'J'; F77_INT lw_pocon = 3 * n; // for [s,d]pocon F77_INT lw_geqp3 = geqp3_lwork (m, n, a, lda, vec_jpvt.data (), tau, work.data (), -1, ierr); F77_INT lw_geqrf = geqrf_lwork (m, n, a, lda, tau, work.data (), -1, ierr); if (! (need_lsvec || need_rsvec) ) { // only SIGMA is needed if (! (joba == 'E' || joba == 'G') ) lwork = std::max<F77_INT> ({2*m + n, n + lw_geqp3, n + lw_geqrf, 7}); else lwork = std::max<F77_INT> ({2*m + n, n + lw_geqp3, n + lw_geqrf, n + n*n + lw_pocon, 7}); } else if (need_rsvec && ! need_lsvec) { // SIGMA and the right singular vectors are needed F77_INT lw_gelqf = gelqf_lwork (n, n, a, lda, tau, work.data (), -1, ierr); trans = 'T'; F77_INT lw_ormlq = ormlq_lwork (side, trans, n, n, n, a, lda, tau, v, n, work.data (), -1, ierr); lwork = std::max<F77_INT> ({2*m + n, n + lw_geqp3, n + lw_pocon, n + lw_gelqf, 2*n + lw_geqrf, n + lw_ormlq}); } else if (need_lsvec && ! need_rsvec) { // SIGMA and the left singular vectors are needed F77_INT n1 = (jobu == 'U') ? n : m; // size of U is m x n1 F77_INT lw_ormqr = ormqr_lwork (side, trans, m, n1, n, a, lda, tau, u, m, work.data (), -1, ierr); lwork = std::max<F77_INT> ({2*m + n, n + lw_geqp3, n + lw_pocon, 2*n + lw_geqrf, n + lw_ormqr}); } else // full SVD is needed { if (jobv == 'V') lwork = std::max (2*m + n, 6*n + 2*n*n); else if (jobv == 'J') lwork = std::max<F77_INT> ({2*m + n, 4*n + n*n, 2*n + n*n + 6}); F77_INT n1 = (jobu == 'U') ? n : m; // size of U is m x n1 F77_INT lw_ormqr = ormqr_lwork (side, trans, m, n1, n, a, lda, tau, u, m, work.data (), -1, ierr); lwork = std::max (lwork, n + lw_ormqr); } return lwork; } namespace octave { namespace math { template <typename T> T svd<T>::left_singular_matrix (void) const { if (m_type == svd::Type::sigma_only) (*current_liboctave_error_handler) ("svd: U not computed because type == svd::sigma_only"); return m_left_sm; } template <typename T> T svd<T>::right_singular_matrix (void) const { if (m_type == svd::Type::sigma_only) (*current_liboctave_error_handler) ("svd: V not computed because type == svd::sigma_only"); return m_right_sm; } // GESVD specializations #define GESVD_REAL_STEP(f, F) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobu, 1), \ F77_CONST_CHAR_ARG2 (&jobv, 1), \ m, n, tmp_data, m1, s_vec, u, m1, vt, \ nrow_vt1, work.data (), lwork, info \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1))) #define GESVD_COMPLEX_STEP(f, F, CMPLX_ARG) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobu, 1), \ F77_CONST_CHAR_ARG2 (&jobv, 1), \ m, n, CMPLX_ARG (tmp_data), \ m1, s_vec, CMPLX_ARG (u), m1, \ CMPLX_ARG (vt), nrow_vt1, \ CMPLX_ARG (work.data ()), \ lwork, rwork.data (), info \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1))) // DGESVD template<> OCTAVE_API void svd<Matrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, double *tmp_data, F77_INT m1, double *s_vec, double *u, double *vt, F77_INT nrow_vt1, std::vector<double>& work, F77_INT& lwork, F77_INT& info) { GESVD_REAL_STEP (dgesvd, DGESVD); lwork = static_cast<F77_INT> (work[0]); work.reserve (lwork); GESVD_REAL_STEP (dgesvd, DGESVD); } // SGESVD template<> OCTAVE_API void svd<FloatMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, float *tmp_data, F77_INT m1, float *s_vec, float *u, float *vt, F77_INT nrow_vt1, std::vector<float>& work, F77_INT& lwork, F77_INT& info) { GESVD_REAL_STEP (sgesvd, SGESVD); lwork = static_cast<F77_INT> (work[0]); work.reserve (lwork); GESVD_REAL_STEP (sgesvd, SGESVD); } // ZGESVD template<> OCTAVE_API void svd<ComplexMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, Complex *tmp_data, F77_INT m1, double *s_vec, Complex *u, Complex *vt, F77_INT nrow_vt1, std::vector<Complex>& work, F77_INT& lwork, F77_INT& info) { std::vector<double> rwork (5 * std::max (m, n)); GESVD_COMPLEX_STEP (zgesvd, ZGESVD, F77_DBLE_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); GESVD_COMPLEX_STEP (zgesvd, ZGESVD, F77_DBLE_CMPLX_ARG); } // CGESVD template<> OCTAVE_API void svd<FloatComplexMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, FloatComplex *tmp_data, F77_INT m1, float *s_vec, FloatComplex *u, FloatComplex *vt, F77_INT nrow_vt1, std::vector<FloatComplex>& work, F77_INT& lwork, F77_INT& info) { std::vector<float> rwork (5 * std::max (m, n)); GESVD_COMPLEX_STEP (cgesvd, CGESVD, F77_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); GESVD_COMPLEX_STEP (cgesvd, CGESVD, F77_CMPLX_ARG); } #undef GESVD_REAL_STEP #undef GESVD_COMPLEX_STEP // GESDD specializations #define GESDD_REAL_STEP(f, F) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobz, 1), \ m, n, tmp_data, m1, s_vec, u, m1, vt, nrow_vt1, \ work.data (), lwork, iwork, info \ F77_CHAR_ARG_LEN (1))) #define GESDD_COMPLEX_STEP(f, F, CMPLX_ARG) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobz, 1), m, n, \ CMPLX_ARG (tmp_data), m1, \ s_vec, CMPLX_ARG (u), m1, \ CMPLX_ARG (vt), nrow_vt1, \ CMPLX_ARG (work.data ()), lwork, \ rwork.data (), iwork, info \ F77_CHAR_ARG_LEN (1))) // DGESDD template<> OCTAVE_API void svd<Matrix>::gesdd (char& jobz, F77_INT m, F77_INT n, double *tmp_data, F77_INT m1, double *s_vec, double *u, double *vt, F77_INT nrow_vt1, std::vector<double>& work, F77_INT& lwork, F77_INT *iwork, F77_INT& info) { GESDD_REAL_STEP (dgesdd, DGESDD); lwork = static_cast<F77_INT> (work[0]); work.reserve (lwork); GESDD_REAL_STEP (dgesdd, DGESDD); } // SGESDD template<> OCTAVE_API void svd<FloatMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, float *tmp_data, F77_INT m1, float *s_vec, float *u, float *vt, F77_INT nrow_vt1, std::vector<float>& work, F77_INT& lwork, F77_INT *iwork, F77_INT& info) { GESDD_REAL_STEP (sgesdd, SGESDD); lwork = static_cast<F77_INT> (work[0]); work.reserve (lwork); GESDD_REAL_STEP (sgesdd, SGESDD); } // ZGESDD template<> OCTAVE_API void svd<ComplexMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, Complex *tmp_data, F77_INT m1, double *s_vec, Complex *u, Complex *vt, F77_INT nrow_vt1, std::vector<Complex>& work, F77_INT& lwork, F77_INT *iwork, F77_INT& info) { F77_INT min_mn = std::min (m, n); F77_INT max_mn = std::max (m, n); F77_INT lrwork; if (jobz == 'N') lrwork = 7*min_mn; else lrwork = min_mn * std::max (5*min_mn+5, 2*max_mn+2*min_mn+1); std::vector<double> rwork (lrwork); GESDD_COMPLEX_STEP (zgesdd, ZGESDD, F77_DBLE_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); GESDD_COMPLEX_STEP (zgesdd, ZGESDD, F77_DBLE_CMPLX_ARG); } // CGESDD template<> OCTAVE_API void svd<FloatComplexMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, FloatComplex *tmp_data, F77_INT m1, float *s_vec, FloatComplex *u, FloatComplex *vt, F77_INT nrow_vt1, std::vector<FloatComplex>& work, F77_INT& lwork, F77_INT *iwork, F77_INT& info) { F77_INT min_mn = std::min (m, n); F77_INT max_mn = std::max (m, n); F77_INT lrwork; if (jobz == 'N') lrwork = 7*min_mn; else lrwork = min_mn * std::max (5*min_mn+5, 2*max_mn+2*min_mn+1); std::vector<float> rwork (lrwork); GESDD_COMPLEX_STEP (cgesdd, CGESDD, F77_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); GESDD_COMPLEX_STEP (cgesdd, CGESDD, F77_CMPLX_ARG); } #undef GESDD_REAL_STEP #undef GESDD_COMPLEX_STEP // GEJSV specializations #define GEJSV_REAL_STEP(f, F) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&joba, 1), \ F77_CONST_CHAR_ARG2 (&jobu, 1), \ F77_CONST_CHAR_ARG2 (&jobv, 1), \ F77_CONST_CHAR_ARG2 (&jobr, 1), \ F77_CONST_CHAR_ARG2 (&jobt, 1), \ F77_CONST_CHAR_ARG2 (&jobp, 1), \ m, n, tmp_data, m1, s_vec, u, m1, v, nrow_v1, \ work.data (), lwork, iwork.data (), info \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1))) #define GEJSV_COMPLEX_STEP(f, F, CMPLX_ARG) \ F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&joba, 1), \ F77_CONST_CHAR_ARG2 (&jobu, 1), \ F77_CONST_CHAR_ARG2 (&jobv, 1), \ F77_CONST_CHAR_ARG2 (&jobr, 1), \ F77_CONST_CHAR_ARG2 (&jobt, 1), \ F77_CONST_CHAR_ARG2 (&jobp, 1), \ m, n, CMPLX_ARG (tmp_data), m1, \ s_vec, CMPLX_ARG (u), m1, \ CMPLX_ARG (v), nrow_v1, \ CMPLX_ARG (work.data ()), lwork, \ rwork.data (), lrwork, iwork.data (), info \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1) \ F77_CHAR_ARG_LEN (1))) // DGEJSV template<> void svd<Matrix>::gejsv (char& joba, char& jobu, char& jobv, char& jobr, char& jobt, char& jobp, F77_INT m, F77_INT n, P *tmp_data, F77_INT m1, DM_P *s_vec, P *u, P *v, F77_INT nrow_v1, std::vector<P>& work, F77_INT& lwork, std::vector<F77_INT>& iwork, F77_INT& info) { lwork = gejsv_lwork<Matrix>::optimal (joba, jobu, jobv, m, n); work.reserve (lwork); GEJSV_REAL_STEP (dgejsv, DGEJSV); } // SGEJSV template<> void svd<FloatMatrix>::gejsv (char& joba, char& jobu, char& jobv, char& jobr, char& jobt, char& jobp, F77_INT m, F77_INT n, P *tmp_data, F77_INT m1, DM_P *s_vec, P *u, P *v, F77_INT nrow_v1, std::vector<P>& work, F77_INT& lwork, std::vector<F77_INT>& iwork, F77_INT& info) { lwork = gejsv_lwork<FloatMatrix>::optimal (joba, jobu, jobv, m, n); work.reserve (lwork); GEJSV_REAL_STEP (sgejsv, SGEJSV); } // ZGEJSV template<> void svd<ComplexMatrix>::gejsv (char& joba, char& jobu, char& jobv, char& jobr, char& jobt, char& jobp, F77_INT m, F77_INT n, P *tmp_data, F77_INT m1, DM_P *s_vec, P *u, P *v, F77_INT nrow_v1, std::vector<P>& work, F77_INT& lwork, std::vector<F77_INT>& iwork, F77_INT& info) { F77_INT lrwork = -1; // work space size query std::vector<double> rwork (1); work.reserve (2); GEJSV_COMPLEX_STEP (zgejsv, ZGEJSV, F77_DBLE_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); lrwork = static_cast<F77_INT> (rwork[0]); rwork.reserve (lrwork); F77_INT liwork = static_cast<F77_INT> (iwork[0]); iwork.reserve (liwork); GEJSV_COMPLEX_STEP (zgejsv, ZGEJSV, F77_DBLE_CMPLX_ARG); } // CGEJSV template<> void svd<FloatComplexMatrix>::gejsv (char& joba, char& jobu, char& jobv, char& jobr, char& jobt, char& jobp, F77_INT m, F77_INT n, P *tmp_data, F77_INT m1, DM_P *s_vec, P *u, P *v, F77_INT nrow_v1, std::vector<P>& work, F77_INT& lwork, std::vector<F77_INT>& iwork, F77_INT& info) { F77_INT lrwork = -1; // work space size query std::vector<float> rwork (1); work.reserve (2); GEJSV_COMPLEX_STEP (cgejsv, CGEJSV, F77_CMPLX_ARG); lwork = static_cast<F77_INT> (work[0].real ()); work.reserve (lwork); lrwork = static_cast<F77_INT> (rwork[0]); rwork.reserve (lrwork); F77_INT liwork = static_cast<F77_INT> (iwork[0]); iwork.reserve (liwork); GEJSV_COMPLEX_STEP (cgejsv, CGEJSV, F77_CMPLX_ARG); } #undef GEJSV_REAL_STEP #undef GEJSV_COMPLEX_STEP template<typename T> svd<T>::svd (const T& a, svd::Type type, svd::Driver driver) : m_type (type), m_driver (driver), m_left_sm (), m_sigma (), m_right_sm () { F77_INT info; F77_INT m = to_f77_int (a.rows ()); F77_INT n = to_f77_int (a.cols ()); if (m == 0 || n == 0) { switch (m_type) { case svd::Type::std: m_left_sm = T (m, m, 0); for (F77_INT i = 0; i < m; i++) m_left_sm.xelem (i, i) = 1; m_sigma = DM_T (m, n); m_right_sm = T (n, n, 0); for (F77_INT i = 0; i < n; i++) m_right_sm.xelem (i, i) = 1; break; case svd::Type::economy: m_left_sm = T (m, 0, 0); m_sigma = DM_T (0, 0); m_right_sm = T (n, 0, 0); break; case svd::Type::sigma_only: default: m_sigma = DM_T (0, 1); break; } return; } T atmp = a; P *tmp_data = atmp.fortran_vec (); F77_INT min_mn = (m < n ? m : n); char jobu = 'A'; char jobv = 'A'; F77_INT ncol_u = m; F77_INT nrow_vt = n; F77_INT nrow_s = m; F77_INT ncol_s = n; switch (m_type) { case svd::Type::economy: jobu = jobv = 'S'; ncol_u = nrow_vt = nrow_s = ncol_s = min_mn; break; case svd::Type::sigma_only: // Note: for this case, both jobu and jobv should be 'N', but there // seems to be a bug in dgesvd from Lapack V2.0. To demonstrate the // bug, set both jobu and jobv to 'N' and find the singular values of // [eye(3), eye(3)]. The result is [-sqrt(2), -sqrt(2), -sqrt(2)]. // // For Lapack 3.0, this problem seems to be fixed. jobu = jobv = 'N'; ncol_u = nrow_vt = 1; break; default: break; } if (! (jobu == 'N' || jobu == 'O')) m_left_sm.resize (m, ncol_u); P *u = m_left_sm.fortran_vec (); m_sigma.resize (nrow_s, ncol_s); DM_P *s_vec = m_sigma.fortran_vec (); if (! (jobv == 'N' || jobv == 'O')) { if (m_driver == svd::Driver::GEJSV) m_right_sm.resize (n, nrow_vt); else m_right_sm.resize (nrow_vt, n); } P *vt = m_right_sm.fortran_vec (); // Query _GESVD for the correct dimension of WORK. F77_INT lwork = -1; std::vector<P> work (1); const F77_INT f77_int_one = static_cast<F77_INT> (1); F77_INT m1 = std::max (m, f77_int_one); F77_INT nrow_vt1 = std::max (nrow_vt, f77_int_one); if (m_driver == svd::Driver::GESVD) gesvd (jobu, jobv, m, n, tmp_data, m1, s_vec, u, vt, nrow_vt1, work, lwork, info); else if (m_driver == svd::Driver::GESDD) { assert (jobu == jobv); char jobz = jobu; std::vector<F77_INT> iwork (8 * std::min (m, n)); gesdd (jobz, m, n, tmp_data, m1, s_vec, u, vt, nrow_vt1, work, lwork, iwork.data (), info); } else if (m_driver == svd::Driver::GEJSV) { bool transposed = false; if (n > m) { // GEJSV only accepts m >= n, thus we need to transpose here transposed = true; std::swap (m, n); m1 = std::max (m, f77_int_one); nrow_vt1 = std::max (n, f77_int_one); // we have m > n if (m_type == svd::Type::sigma_only) nrow_vt1 = 1; std::swap (jobu, jobv); atmp = atmp.hermitian (); tmp_data = atmp.fortran_vec (); // Swap pointers of U and V. u = m_right_sm.fortran_vec (); vt = m_left_sm.fortran_vec (); } // translate jobu and jobv from gesvd to gejsv. std::unordered_map<char, std::string> job_svd2jsv; job_svd2jsv['A'] = "FJ"; job_svd2jsv['S'] = "UV"; job_svd2jsv['O'] = "WW"; job_svd2jsv['N'] = "NN"; jobu = job_svd2jsv[jobu][0]; jobv = job_svd2jsv[jobv][1]; char joba = 'F'; // 'F': most conservative char jobr = 'R'; // 'R' is recommended. char jobt = 'N'; // or 'T', but that requires U and V appear together char jobp = 'N'; // use 'P' if denormal is poorly implemented. std::vector<F77_INT> iwork (std::max<F77_INT> (m + 3*n, 1)); gejsv (joba, jobu, jobv, jobr, jobt, jobp, m, n, tmp_data, m1, s_vec, u, vt, nrow_vt1, work, lwork, iwork, info); if (iwork[2] == 1) (*current_liboctave_warning_with_id_handler) ("Octave:convergence", "svd: (driver: GEJSV) " "Denormal occured, possible loss of accuracy."); if (info < 0) (*current_liboctave_error_handler) ("svd: (driver: GEJSV) Illegal argument at #%d", static_cast<int> (-info)); else if (info > 0) (*current_liboctave_warning_with_id_handler) ("Octave:convergence", "svd: (driver: GEJSV) " "Fail to converge within max sweeps, " "possible inaccurate result."); if (transposed) // put things that need to transpose back here std::swap (m, n); } else (*current_liboctave_error_handler) ("svd: unknown driver"); // LAPACK can return -0 which is a small problem (bug #55710). for (octave_idx_type i = 0; i < m_sigma.diag_length (); i++) { if (! m_sigma.dgxelem (i)) m_sigma.dgxelem (i) = DM_P (0); } // GESVD and GESDD return VT instead of V, GEJSV return V. if (! (jobv == 'N' || jobv == 'O') && (m_driver != svd::Driver::GEJSV)) m_right_sm = m_right_sm.hermitian (); } // Instantiations we need. template class svd<Matrix>; template class svd<FloatMatrix>; template class svd<ComplexMatrix>; template class svd<FloatComplexMatrix>; } }