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view liboctave/numeric/gsvd.cc @ 27918:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 06 Jan 2020 15:38:17 -0500 |
| parents | 84ff9953faa1 |
| children | 1891570abac8 |
line wrap: on
line source
/* Copyright (C) 1997-2019 The Octave Project Developers See the file COPYRIGHT.md in the top-level directory of this distribution or <https://octave.org/COPYRIGHT.html/>. 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 <vector> #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-shlib.h" namespace octave { static std::map<std::string, void *> gsvd_fcn; static bool have_DGGSVD3 = false; static bool gsvd_initialized = false; /* Hack to stringize macro results. */ #define xSTRINGIZE(x) #x #define STRINGIZE(x) xSTRINGIZE(x) static void initialize_gsvd (void) { if (gsvd_initialized) return; dynamic_library libs (""); if (! libs) { // FIXME: Should we throw an error if we cannot check the libraries? have_DGGSVD3 = false; return; } 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; } 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_ggsvd3_ptr<F77_DBLE>::type dggsvd3_type; typedef real_ggsvd_ptr<F77_DBLE>::type dggsvd_type; typedef real_ggsvd3_ptr<F77_REAL>::type sggsvd3_type; typedef real_ggsvd_ptr<F77_REAL>::type sggsvd_type; typedef comp_ggsvd3_ptr<F77_DBLE_CMPLX, F77_DBLE>::type zggsvd3_type; typedef comp_ggsvd_ptr<F77_DBLE_CMPLX, F77_DBLE>::type zggsvd_type; typedef comp_ggsvd3_ptr<F77_CMPLX, F77_REAL>::type cggsvd3_type; typedef comp_ggsvd_ptr<F77_CMPLX, F77_REAL>::type cggsvd_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, Matrix& 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.fortran_vec (), 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.fortran_vec (), 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, FloatMatrix& 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.fortran_vec (), 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.fortran_vec (), 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, ComplexMatrix& work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); Matrix rwork(2*n, 1); 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.fortran_vec ()), lwork, rwork.fortran_vec (), 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.fortran_vec ()), rwork.fortran_vec (), 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, FloatComplexMatrix& work, F77_INT lwork, F77_INT *iwork, F77_INT& info) { if (! gsvd_initialized) initialize_gsvd (); FloatMatrix rwork(2*n, 1); 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.fortran_vec ()), lwork, rwork.fortran_vec (), 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.fortran_vec ()), rwork.fortran_vec (), 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 T (); } else 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 T (); } else 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 T (); } else return right_sm; } template <typename T> T gsvd<T>::R_matrix (void) const { if (type != gsvd::Type::std) { (*current_liboctave_error_handler) ("gsvd: R not computed because type != gsvd::std"); return T (); } else return R; } template <typename T> gsvd<T>::gsvd (const T& a, const T& b, gsvd::Type gsvd_type) { 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: // 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 = 'N'; jobv = 'N'; jobq = 'N'; nrow_u = nrow_v = nrow_q = 1; break; default: break; } type = gsvd_type; if (! (jobu == 'N' || jobu == 'O')) left_smA.resize (nrow_u, m); P *u = left_smA.fortran_vec (); if (! (jobv == 'N' || jobv == 'O')) left_smB.resize (nrow_v, p); P *v = left_smB.fortran_vec (); if (! (jobq == 'N' || jobq == 'O')) right_sm.resize (nrow_q, n); P *q = right_sm.fortran_vec (); real_matrix alpha (n, 1); real_matrix beta (n, 1); std::vector<F77_INT> iwork (n); if (! gsvd_initialized) initialize_gsvd (); F77_INT lwork; if (have_DGGSVD3) { lwork = -1; T work_tmp (1, 1); 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.data (), info); lwork = static_cast<F77_INT> (std::abs (work_tmp(0, 0))); } else { lwork = 3*n; lwork = (lwork > m ? lwork : m); lwork = (lwork > p ? lwork : p) + n; } info = 0; T work (lwork, 1); 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.data (), info); if (info < 0) (*current_liboctave_error_handler) ("*ggsvd.f: argument %d illegal", -info); else { if (info > 0) (*current_liboctave_error_handler) ("*ggsvd.f: Jacobi-type procedure failed to converge."); else { F77_INT i, j; if (gsvd<T>::Type::std == gsvd_type) { R.resize(k+l, k+l); int astart = n-k-l; if (m - k - l >= 0) { astart = n-k-l; // 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 = k+l-1; i >=m; i--) { for (j = 0; j < m; j++) R.xelem(i, j) = 0.0; for (j = m; j < k+l; j++) R.xelem (i, j) = btmp.xelem (i - k, astart + j); } } } if (m-k-l >= 0) { // Fills in C and S sigmaA.resize (l, l); sigmaB.resize (l, l); for (i = 0; i < l; i++) { sigmaA.dgxelem(i) = alpha.elem(k+i); sigmaB.dgxelem(i) = beta.elem(k+i); } } else { // Fills in C and S sigmaA.resize (m-k, m-k); sigmaB.resize (m-k, m-k); for (i = 0; i < m-k; i++) { sigmaA.dgxelem(i) = alpha.elem(k+i); sigmaB.dgxelem(i) = beta.elem(k+i); } } } } } // Instantiations we need. template class gsvd<Matrix>; template class gsvd<FloatMatrix>; template class gsvd<ComplexMatrix>; template class gsvd<FloatComplexMatrix>; } }