Mercurial > octave
view liboctave/numeric/gsvd.cc @ 30300:4ee01c14fccd
Rewrite gsvd function and return *correct* 3rd output (bug #60273).
Correctly use the API interface to LAPACK which Octave got wrong for
certain matrix combinations. Perform post-processing on LAPACK results
to return Matlab-compatible outputs.
* libinterp/corefcn/gsvd.cc (gsvd_type): Add second input (nargin) to be able
to distinguish the type of gsvd to generate.
* libinterp/corefcn/gsvd.cc (do_gsvd): Add another input (nargin) to be able
to calculate the correct gsvd type. Update code for API change in liboctave
which now returns a full Matrix for singular values rather than a DiagMatrix.
Sort singular values in ascending order for compatibility with Matlab.
* libinterp/corefcn/gsvd.cc (Fgsvd): Update documation to warn about
rank-deficient input case. Add new input validation to check that number
of columns of A and B match. Move special check for empty matrices from
libinterp to liboctave. Update all BIST tests for new behavior of gsvd
code in liboctave.
* liboctave/numeric/gsvd.h (gsvd): Remove member variable R from gsvd class.
* liboctave/numeric/gsvd.h (gsvd::singular_values_A, gsvd_singular_values_B):
Change return type to T::real_matrix_type from T::real_diag_matrix_type.
* liboctave/numeric/gsvd.h (gsvd::ggsvd): Change default gsvd::Type to "std"
from "economy".
* liboctave/numeric/gsvd.cc: Add #includes for <algorithm>, <undordered_map>,
and "oct-locbuf.h". Change gsvd_fcn from std::map to std::unordered_map.
* liboctave/numeric/gsvd.cc (initialize_gsvd): Throw an error if Octave is
unable to connect to LAPACK library.
* liboctave/numeric/gsvd.cc (ggsvd): Change function prototype to not use
references to Octave Matrix datatypes, but rather point directly to
underlying plain old datatype. For example, use "double *" rather than
"Matrix&". Replace scratch memory instances created with Matrix() with
OCTAVE_LOCAL_BUFFER which relies on C++ STL.
* liboctave/numeric/gsvd.cc (left_singular_matrix_A, left_singular_matrix_B,
right_singular_matrix): Use the fact that current_liboctave_error_handler never
returns to eliminate else branch of if/else code.
* liboctave/numeric/gsvd.cc (R_matrix): Delete unused function.
* liboctave/numeric/gsvd.cc (gsvd): Add input validation for empty matrices.
Simplify 'job' values processing which seems to have been fixed in LAPACK 3.0.
Replace scratch memory created with std::vector with OCTAVE_LOCAL_BUFFER.
Replace scratch memory created with Octave Matrix classes with
OCTAVE_LOCAL_BUFFER. Use initializer list to std::max to simplify code.
Re-code interface to LAPACK to extract 'R' matrix. Post-process to calculate
third output of gsvd as X = Q*R'. Correct algorithm to extract singular values
from LAPACK..
author | Rik <rik@octave.org> |
---|---|
date | Wed, 08 Sep 2021 16:08:03 -0700 |
parents | a6ab7069a87c |
children | 4fa09c269dde |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1997-2021 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/>. // //////////////////////////////////////////////////////////////////////// #ifdef HAVE_CONFIG_H # include <config.h> #endif #include <algorithm> #include <unordered_map> #include "CMatrix.h" #include "dDiagMatrix.h" #include "dMatrix.h" #include "fCMatrix.h" #include "fDiagMatrix.h" #include "fMatrix.h" #include "gsvd.h" #include "lo-error.h" #include "lo-lapack-proto.h" #include "oct-locbuf.h" #include "oct-shlib.h" namespace octave { static std::unordered_map<std::string, void *> gsvd_fcn; static bool have_DGGSVD3 = false; static bool gsvd_initialized = false; /* Hack to stringize results of F77_FUNC macro. */ #define xSTRINGIZE(x) #x #define STRINGIZE(x) xSTRINGIZE(x) static void initialize_gsvd (void) { if (gsvd_initialized) return; dynamic_library libs (""); if (! libs) (*current_liboctave_error_handler) ("gsvd: unable to query LAPACK library"); have_DGGSVD3 = (libs.search (STRINGIZE (F77_FUNC (dggsvd3, DGGSVD3))) != nullptr); if (have_DGGSVD3) { gsvd_fcn["dg"] = libs.search (STRINGIZE (F77_FUNC (dggsvd3, DGGSVD3))); gsvd_fcn["sg"] = libs.search (STRINGIZE (F77_FUNC (sggsvd3, SGGSVD3))); gsvd_fcn["zg"] = libs.search (STRINGIZE (F77_FUNC (zggsvd3, ZGGSVD3))); gsvd_fcn["cg"] = libs.search (STRINGIZE (F77_FUNC (cggsvd3, CGGSVD3))); } else { gsvd_fcn["dg"] = libs.search (STRINGIZE (F77_FUNC (dggsvd, DGGSVD))); gsvd_fcn["sg"] = libs.search (STRINGIZE (F77_FUNC (sggsvd, SGGSVD))); gsvd_fcn["zg"] = libs.search (STRINGIZE (F77_FUNC (zggsvd, ZGGSVD))); gsvd_fcn["cg"] = libs.search (STRINGIZE (F77_FUNC (cggsvd, CGGSVD))); } gsvd_initialized = true; } /* Clean up macro namespace as soon as we are done using them */ #undef xSTRINGIZE #undef STRINGIZE template<class T1> struct real_ggsvd_ptr { typedef F77_RET_T (*type) (F77_CONST_CHAR_ARG_DECL, // JOBU F77_CONST_CHAR_ARG_DECL, // JOBV F77_CONST_CHAR_ARG_DECL, // JOBQ const F77_INT&, // M const F77_INT&, // N const F77_INT&, // P F77_INT &, // K F77_INT &, // L T1*, // A(LDA,N) const F77_INT&, // LDA T1*, // B(LDB,N) const F77_INT&, // LDB T1*, // ALPHA(N) T1*, // BETA(N) T1*, // U(LDU,M) const F77_INT&, // LDU T1*, // V(LDV,P) const F77_INT&, // LDV T1*, // Q(LDQ,N) const F77_INT&, // LDQ T1*, // WORK F77_INT*, // IWORK(N) F77_INT& // INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); }; template<class T1> struct real_ggsvd3_ptr { typedef F77_RET_T (*type) (F77_CONST_CHAR_ARG_DECL, // JOBU F77_CONST_CHAR_ARG_DECL, // JOBV F77_CONST_CHAR_ARG_DECL, // JOBQ const F77_INT&, // M const F77_INT&, // N const F77_INT&, // P F77_INT &, // K F77_INT &, // L T1*, // A(LDA,N) const F77_INT&, // LDA T1*, // B(LDB,N) const F77_INT&, // LDB T1*, // ALPHA(N) T1*, // BETA(N) T1*, // U(LDU,M) const F77_INT&, // LDU T1*, // V(LDV,P) const F77_INT&, // LDV T1*, // Q(LDQ,N) const F77_INT&, // LDQ T1*, // WORK const F77_INT&, // LWORK F77_INT*, // IWORK(N) F77_INT& // INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); }; template<class T1, class T2> struct comp_ggsvd_ptr { typedef F77_RET_T (*type) (F77_CONST_CHAR_ARG_DECL, // JOBU F77_CONST_CHAR_ARG_DECL, // JOBV F77_CONST_CHAR_ARG_DECL, // JOBQ const F77_INT&, // M const F77_INT&, // N const F77_INT&, // P F77_INT &, // K F77_INT &, // L T1*, // A(LDA,N) const F77_INT&, // LDA T1*, // B(LDB,N) const F77_INT&, // LDB T2*, // ALPHA(N) T2*, // BETA(N) T1*, // U(LDU,M) const F77_INT&, // LDU T1*, // V(LDV,P) const F77_INT&, // LDV T1*, // Q(LDQ,N) const F77_INT&, // LDQ T1*, // WORK T2*, // RWORK F77_INT*, // IWORK(N) F77_INT& // INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); }; template<class T1, class T2> struct comp_ggsvd3_ptr { typedef F77_RET_T (*type) (F77_CONST_CHAR_ARG_DECL, // JOBU F77_CONST_CHAR_ARG_DECL, // JOBV F77_CONST_CHAR_ARG_DECL, // JOBQ const F77_INT&, // M const F77_INT&, // N const F77_INT&, // P F77_INT &, // K F77_INT &, // L T1*, // A(LDA,N) const F77_INT&, // LDA T1*, // B(LDB,N) const F77_INT&, // LDB T2*, // ALPHA(N) T2*, // BETA(N) T1*, // U(LDU,M) const F77_INT&, // LDU T1*, // V(LDV,P) const F77_INT&, // LDV T1*, // Q(LDQ,N) const F77_INT&, // LDQ T1*, // WORK const F77_INT&, // LWORK T2*, // RWORK F77_INT*, // IWORK(N) F77_INT& // INFO F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); }; // template specializations typedef real_ggsvd_ptr<F77_DBLE>::type dggsvd_type; typedef real_ggsvd3_ptr<F77_DBLE>::type dggsvd3_type; typedef real_ggsvd_ptr<F77_REAL>::type sggsvd_type; typedef real_ggsvd3_ptr<F77_REAL>::type sggsvd3_type; typedef comp_ggsvd_ptr<F77_DBLE_CMPLX, F77_DBLE>::type zggsvd_type; typedef comp_ggsvd3_ptr<F77_DBLE_CMPLX, F77_DBLE>::type zggsvd3_type; typedef comp_ggsvd_ptr<F77_CMPLX, F77_REAL>::type cggsvd_type; typedef comp_ggsvd3_ptr<F77_CMPLX, F77_REAL>::type cggsvd3_type; namespace math { template <> void gsvd<Matrix>::ggsvd (char& jobu, char& jobv, char& jobq, F77_INT m, F77_INT n, F77_INT p, F77_INT& k, F77_INT& l, double *tmp_dataA, F77_INT m1, double *tmp_dataB, F77_INT p1, Matrix& alpha, Matrix& beta, double *u, F77_INT nrow_u, double *v, F77_INT nrow_v, double *q, F77_INT nrow_q, double *work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); if (have_DGGSVD3) { dggsvd3_type f_ptr = reinterpret_cast<dggsvd3_type> (gsvd_fcn["dg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, tmp_dataA, m1, tmp_dataB, p1, alpha.fortran_vec (), beta.fortran_vec (), u, nrow_u, v, nrow_v, q, nrow_q, work, lwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } else { dggsvd_type f_ptr = reinterpret_cast<dggsvd_type> (gsvd_fcn["dg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, tmp_dataA, m1, tmp_dataB, p1, alpha.fortran_vec (), beta.fortran_vec (), u, nrow_u, v, nrow_v, q, nrow_q, work, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } } template <> void gsvd<FloatMatrix>::ggsvd (char& jobu, char& jobv, char& jobq, F77_INT m, F77_INT n, F77_INT p, F77_INT& k, F77_INT& l, float *tmp_dataA, F77_INT m1, float *tmp_dataB, F77_INT p1, FloatMatrix& alpha, FloatMatrix& beta, float *u, F77_INT nrow_u, float *v, F77_INT nrow_v, float *q, F77_INT nrow_q, float *work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); if (have_DGGSVD3) { sggsvd3_type f_ptr = reinterpret_cast<sggsvd3_type> (gsvd_fcn["sg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, tmp_dataA, m1, tmp_dataB, p1, alpha.fortran_vec (), beta.fortran_vec (), u, nrow_u, v, nrow_v, q, nrow_q, work, lwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } else { sggsvd_type f_ptr = reinterpret_cast<sggsvd_type> (gsvd_fcn["sg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, tmp_dataA, m1, tmp_dataB, p1, alpha.fortran_vec (), beta.fortran_vec (), u, nrow_u, v, nrow_v, q, nrow_q, work, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } } template <> void gsvd<ComplexMatrix>::ggsvd (char& jobu, char& jobv, char& jobq, F77_INT m, F77_INT n, F77_INT p, F77_INT& k, F77_INT& l, Complex *tmp_dataA, F77_INT m1, Complex *tmp_dataB, F77_INT p1, Matrix& alpha, Matrix& beta, Complex *u, F77_INT nrow_u, Complex *v, F77_INT nrow_v, Complex *q, F77_INT nrow_q, Complex *work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); OCTAVE_LOCAL_BUFFER(double, rwork, 2*n); if (have_DGGSVD3) { zggsvd3_type f_ptr = reinterpret_cast<zggsvd3_type> (gsvd_fcn["zg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, F77_DBLE_CMPLX_ARG (tmp_dataA), m1, F77_DBLE_CMPLX_ARG (tmp_dataB), p1, alpha.fortran_vec (), beta.fortran_vec (), F77_DBLE_CMPLX_ARG (u), nrow_u, F77_DBLE_CMPLX_ARG (v), nrow_v, F77_DBLE_CMPLX_ARG (q), nrow_q, F77_DBLE_CMPLX_ARG (work), lwork, rwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } else { zggsvd_type f_ptr = reinterpret_cast<zggsvd_type> (gsvd_fcn["zg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, F77_DBLE_CMPLX_ARG (tmp_dataA), m1, F77_DBLE_CMPLX_ARG (tmp_dataB), p1, alpha.fortran_vec (), beta.fortran_vec (), F77_DBLE_CMPLX_ARG (u), nrow_u, F77_DBLE_CMPLX_ARG (v), nrow_v, F77_DBLE_CMPLX_ARG (q), nrow_q, F77_DBLE_CMPLX_ARG (work), rwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } } template <> void gsvd<FloatComplexMatrix>::ggsvd (char& jobu, char& jobv, char& jobq, F77_INT m, F77_INT n, F77_INT p, F77_INT& k, F77_INT& l, FloatComplex *tmp_dataA, F77_INT m1, FloatComplex *tmp_dataB, F77_INT p1, FloatMatrix& alpha, FloatMatrix& beta, FloatComplex *u, F77_INT nrow_u, FloatComplex *v, F77_INT nrow_v, FloatComplex *q, F77_INT nrow_q, FloatComplex *work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); OCTAVE_LOCAL_BUFFER(float, rwork, 2*n); if (have_DGGSVD3) { cggsvd3_type f_ptr = reinterpret_cast<cggsvd3_type> (gsvd_fcn["cg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, F77_CMPLX_ARG (tmp_dataA), m1, F77_CMPLX_ARG (tmp_dataB), p1, alpha.fortran_vec (), beta.fortran_vec (), F77_CMPLX_ARG (u), nrow_u, F77_CMPLX_ARG (v), nrow_v, F77_CMPLX_ARG (q), nrow_q, F77_CMPLX_ARG (work), lwork, rwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } else { cggsvd_type f_ptr = reinterpret_cast<cggsvd_type> (gsvd_fcn["cg"]); f_ptr (F77_CONST_CHAR_ARG2 (&jobu, 1), F77_CONST_CHAR_ARG2 (&jobv, 1), F77_CONST_CHAR_ARG2 (&jobq, 1), m, n, p, k, l, F77_CMPLX_ARG (tmp_dataA), m1, F77_CMPLX_ARG (tmp_dataB), p1, alpha.fortran_vec (), beta.fortran_vec (), F77_CMPLX_ARG (u), nrow_u, F77_CMPLX_ARG (v), nrow_v, F77_CMPLX_ARG (q), nrow_q, F77_CMPLX_ARG (work), rwork, iwork, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1)); } } template <typename T> T gsvd<T>::left_singular_matrix_A (void) const { if (type == gsvd::Type::sigma_only) (*current_liboctave_error_handler) ("gsvd: U not computed because type == gsvd::sigma_only"); return left_smA; } template <typename T> T gsvd<T>::left_singular_matrix_B (void) const { if (type == gsvd::Type::sigma_only) (*current_liboctave_error_handler) ("gsvd: V not computed because type == gsvd::sigma_only"); return left_smB; } template <typename T> T gsvd<T>::right_singular_matrix (void) const { if (type == gsvd::Type::sigma_only) (*current_liboctave_error_handler) ("gsvd: X not computed because type == gsvd::sigma_only"); return right_sm; } template <typename T> gsvd<T>::gsvd (const T& a, const T& b, gsvd::Type gsvd_type) { if (a.isempty () || b.isempty ()) (*current_liboctave_error_handler) ("gsvd: A and B cannot be empty matrices"); F77_INT info; F77_INT m = to_f77_int (a.rows ()); F77_INT n = to_f77_int (a.cols ()); F77_INT p = to_f77_int (b.rows ()); T atmp = a; P *tmp_dataA = atmp.fortran_vec (); T btmp = b; P *tmp_dataB = btmp.fortran_vec (); char jobu = 'U'; char jobv = 'V'; char jobq = 'Q'; F77_INT nrow_u = m; F77_INT nrow_v = p; F77_INT nrow_q = n; F77_INT k, l; switch (gsvd_type) { case gsvd<T>::Type::sigma_only: // FIXME: In LAPACK 3.0, problem below seems to be fixed, // so we now set jobX = 'N'. // // For calculating sigma_only, 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)]. jobu = jobv = jobq = 'N'; nrow_u = nrow_v = nrow_q = 1; break; default: break; } type = gsvd_type; if (jobu != 'N') left_smA.resize (nrow_u, m); P *u = left_smA.fortran_vec (); if (jobv != 'N') left_smB.resize (nrow_v, p); P *v = left_smB.fortran_vec (); if (jobq != 'N') right_sm.resize (nrow_q, n); P *q = right_sm.fortran_vec (); real_matrix alpha (n, 1); real_matrix beta (n, 1); OCTAVE_LOCAL_BUFFER(F77_INT, iwork, n); if (! gsvd_initialized) initialize_gsvd (); F77_INT lwork; if (have_DGGSVD3) { lwork = -1; P work_tmp; gsvd<T>::ggsvd (jobu, jobv, jobq, m, n, p, k, l, tmp_dataA, m, tmp_dataB, p, alpha, beta, u, nrow_u, v, nrow_v, q, nrow_q, &work_tmp, lwork, iwork, info); lwork = static_cast<F77_INT> (std::abs (work_tmp)); } else { lwork = std::max ({3*n, m, p}) + n; } info = 0; OCTAVE_LOCAL_BUFFER(P, work, lwork); gsvd<T>::ggsvd (jobu, jobv, jobq, m, n, p, k, l, tmp_dataA, m, tmp_dataB, p, alpha, beta, u, nrow_u, v, nrow_v, q, nrow_q, work, lwork, iwork, info); if (info < 0) (*current_liboctave_error_handler) ("*ggsvd.f: argument %d illegal", -info); if (info > 0) (*current_liboctave_error_handler) ("*ggsvd.f: Jacobi-type procedure failed to converge"); F77_INT i, j; if (gsvd_type != gsvd<T>::Type::sigma_only) { // Size according to LAPACK is k+l,k+l, but this needs // to be nxn for Matlab compatibility. T R (n, n, 0.0); int astart = n-k-l; if (m - k - l >= 0) { // R is stored in A(1:K+L,N-K-L+1:N) for (i = 0; i < k+l; i++) for (j = 0; j < k+l; j++) R.xelem (i, j) = atmp.xelem (i, astart + j); } else { // (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) // ( 0 R22 R23 ) for (i = 0; i < m; i++) for (j = 0; j < k+l; j++) R.xelem (i, j) = atmp.xelem (i, astart + j); // and R33 is stored in B(M-K+1:L,N+M-K-L+1:N) for (i = m; i < k + l; i++) for (j = n - l - k + m; j < n; j++) R.xelem (i, j) = btmp.xelem (i - k, j); } // Output X = Q*R' // FIXME: Is there a way to call BLAS multiply directly // with flags so that R is transposed? right_sm = right_sm * R.hermitian (); } // Fill in C and S F77_INT rank; bool fill_ptn; if (m-k-l >= 0) { rank = l; fill_ptn = true; } else { rank = m-k; fill_ptn = false; } if (gsvd_type == gsvd<T>::Type::sigma_only) { // Return column vector with results sigmaA.resize (k+l, 1); sigmaB.resize (k+l, 1); if (fill_ptn) { for (i = 0; i < k; i++) { sigmaA.xelem (i) = 1.0; sigmaB.xelem (i) = 0.0; } for (i = k, j = k+l-1; i < k+l; i++, j--) { sigmaA.xelem (i) = alpha.xelem (i); sigmaB.xelem (i) = beta.xelem (i); } } else { for (i = 0; i < k; i++) { sigmaA.xelem (i) = 1.0; sigmaB.xelem (i) = 0.0; } for (i = k; i < m; i++) { sigmaA.xelem (i) = alpha.xelem (i); sigmaB.xelem (i) = beta.xelem (i); } for (i = m; i < k+l; i++) { sigmaA.xelem (i) = 0.0; sigmaB.xelem (i) = 1.0; } } } else // returning all matrices { // Number of columns according to LAPACK is k+l, but this needs // to be n for Matlab compatibility. sigmaA.resize (m, n); sigmaB.resize (p, n); for (i = 0; i < k; i++) sigmaA.xelem (i,i) = 1.0; for (i = 0; i < rank; i++) { sigmaA.xelem (k+i,k+i) = alpha.xelem (k+i); sigmaB.xelem (i,k+i) = beta.xelem (k+i); } if (! fill_ptn) { for (i = m; i < n; i++) sigmaB.xelem (i-k, i) = 1.0; } } } // Instantiations needed in octave::math namespace. template class gsvd<Matrix>; template class gsvd<FloatMatrix>; template class gsvd<ComplexMatrix>; template class gsvd<FloatComplexMatrix>; } }