Mercurial > octave
view liboctave/array/CMatrix.cc @ 29902:3cb8519fed0f
Use LU factorization to solve (close to) singular full matrices.
* liboctave/array/CMatrix.cc (ComplexMatrix::fsolve),
liboctave/array/dMatrix.cc (Matrix::fsolve),
liboctave/array/fCMatrix.cc (FloatComplexMatrix::fsolve),
liboctave/array/fMatrix.cc (FloatMatrix::fsolve): Continue with LU
decomposition also for (close to) singular full matrices.
See also: https://octave.discourse.group/t/1365
| author | Markus Mützel <markus.muetzel@gmx.de> |
|---|---|
| date | Wed, 21 Jul 2021 18:51:54 +0200 |
| parents | 32f4357ac8d9 |
| children | 7faff48840eb |
line wrap: on
line source
//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1994-2021 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/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <algorithm> #include <complex> #include <istream> #include <limits> #include <ostream> #include "Array-util.h" #include "CDiagMatrix.h" #include "CMatrix.h" #include "CNDArray.h" #include "CRowVector.h" #include "DET.h" #include "boolMatrix.h" #include "chMatrix.h" #include "chol.h" #include "dDiagMatrix.h" #include "dMatrix.h" #include "dRowVector.h" #include "lo-blas-proto.h" #include "lo-error.h" #include "lo-ieee.h" #include "lo-lapack-proto.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-cm-dm.h" #include "mx-cm-s.h" #include "mx-dm-cm.h" #include "mx-inlines.cc" #include "mx-op-defs.h" #include "oct-cmplx.h" #include "oct-fftw.h" #include "oct-locbuf.h" #include "oct-norm.h" #include "schur.h" #include "svd.h" static const Complex Complex_NaN_result (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); // Complex Matrix class ComplexMatrix::ComplexMatrix (const Matrix& a) : ComplexNDArray (a) { } ComplexMatrix::ComplexMatrix (const RowVector& rv) : ComplexNDArray (rv) { } ComplexMatrix::ComplexMatrix (const ColumnVector& cv) : ComplexNDArray (cv) { } ComplexMatrix::ComplexMatrix (const DiagMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const MDiagArray2<double>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const DiagArray2<double>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) : ComplexNDArray (rv) { } ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) : ComplexNDArray (cv) { } ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const MDiagArray2<Complex>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const DiagArray2<Complex>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } // FIXME: could we use a templated mixed-type copy function here? ComplexMatrix::ComplexMatrix (const boolMatrix& a) : ComplexNDArray (a) { } ComplexMatrix::ComplexMatrix (const charMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.rows (); i++) for (octave_idx_type j = 0; j < a.cols (); j++) elem (i, j) = static_cast<unsigned char> (a.elem (i, j)); } ComplexMatrix::ComplexMatrix (const Matrix& re, const Matrix& im) : ComplexNDArray (re.dims ()) { if (im.rows () != rows () || im.cols () != cols ()) (*current_liboctave_error_handler) ("complex: internal error"); octave_idx_type nel = numel (); for (octave_idx_type i = 0; i < nel; i++) xelem (i) = Complex (re(i), im(i)); } bool ComplexMatrix::operator == (const ComplexMatrix& a) const { if (rows () != a.rows () || cols () != a.cols ()) return false; return mx_inline_equal (numel (), data (), a.data ()); } bool ComplexMatrix::operator != (const ComplexMatrix& a) const { return !(*this == a); } bool ComplexMatrix::ishermitian (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (issquare () && nr > 0) { for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = i; j < nc; j++) if (elem (i, j) != conj (elem (j, i))) return false; return true; } return false; } // destructive insert/delete/reorder operations ComplexMatrix& ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_nr >0 && a_nc > 0) { make_unique (); for (octave_idx_type j = 0; j < a_nc; j++) for (octave_idx_type i = 0; i < a_nr; i++) xelem (r+i, c+j) = a.elem (i, j); } return *this; } ComplexMatrix& ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r, c+i) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) { ComplexNDArray::insert (a, r, c); return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); for (octave_idx_type i = 0; i < a_len; i++) elem (r, c+i) = a.elem (i); return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } ComplexMatrix& ComplexMatrix::fill (double val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (const Complex& val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >= c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >=c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } ComplexMatrix ComplexMatrix::append (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::stack (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix conj (const ComplexMatrix& a) { return do_mx_unary_map<Complex, Complex, std::conj<double>> (a); } // resize is the destructive equivalent for this one ComplexMatrix ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const { if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } return index (octave::idx_vector (r1, r2+1), octave::idx_vector (c1, c2+1)); } ComplexMatrix ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const { return index (octave::idx_vector (r1, r1 + nr), octave::idx_vector (c1, c1 + nc)); } // extract row or column i. ComplexRowVector ComplexMatrix::row (octave_idx_type i) const { return index (octave::idx_vector (i), octave::idx_vector::colon); } ComplexColumnVector ComplexMatrix::column (octave_idx_type i) const { return index (octave::idx_vector::colon, octave::idx_vector (i)); } // Local function to calculate the 1-norm. static double norm1 (const ComplexMatrix& a) { double anorm = 0.0; RowVector colsum = a.abs ().sum ().row (0); for (octave_idx_type i = 0; i < colsum.numel (); i++) { double sum = colsum.xelem (i); if (octave::math::isinf (sum) || octave::math::isnan (sum)) { anorm = sum; // Pass Inf or NaN to output break; } else anorm = std::max (anorm, sum); } return anorm; } ComplexMatrix ComplexMatrix::inverse (void) const { octave_idx_type info; double rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (octave_idx_type& info) const { double rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { MatrixType mattype (*this); return inverse (mattype, info, rcon, force, calc_cond); } ComplexMatrix ComplexMatrix::inverse (MatrixType& mattype) const { octave_idx_type info; double rcon; return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (MatrixType& mattype, octave_idx_type& info) const { double rcon; return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::tinverse (MatrixType& mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { ComplexMatrix retval; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); if (nr != nc || nr == 0 || nc == 0) (*current_liboctave_error_handler) ("inverse requires square matrix"); int typ = mattype.type (); char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); char udiag = 'N'; retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_INT tmp_info = 0; F77_XFCN (ztrtri, ZTRTRI,(F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, tmp_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); info = tmp_info; // Throw away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { F77_INT ztrcon_info = 0; char job = '1'; OCTAVE_LOCAL_BUFFER (Complex, cwork, 2*nr); OCTAVE_LOCAL_BUFFER (double, rwork, nr); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (cwork), rwork, ztrcon_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (ztrcon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore matrix contents. return retval; } ComplexMatrix ComplexMatrix::finverse (MatrixType& mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { ComplexMatrix retval; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); if (nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); Array<Complex> z (dim_vector (1, 1)); F77_INT lwork = -1; // Query the optimum work array size. F77_INT tmp_info = 0; F77_XFCN (zgetri, ZGETRI, (nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (z.fortran_vec ()), lwork, tmp_info)); lwork = static_cast<F77_INT> (std::real (z(0))); lwork = (lwork < 2 * nc ? 2 * nc : lwork); z.resize (dim_vector (lwork, 1)); Complex *pz = z.fortran_vec (); info = 0; tmp_info = 0; // Calculate norm of the matrix (always, see bug #45577) for later use. double anorm = norm1 (retval); // Work around bug #45577, LAPACK crashes Octave if norm is NaN // and bug #46330, segfault with matrices containing Inf & NaN if (octave::math::isnan (anorm) || octave::math::isinf (anorm)) info = -1; else { F77_XFCN (zgetrf, ZGETRF, (nc, nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, tmp_info)); info = tmp_info; } // Throw away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { F77_INT zgecon_info = 0; // Now calculate the condition number for non-singular matrix. char job = '1'; Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, zgecon_info F77_CHAR_ARG_LEN (1))); if (zgecon_info != 0) info = -1; } if ((info == -1 && ! force) || octave::math::isnan (anorm) || octave::math::isinf (anorm)) retval = *this; // Restore contents. else { F77_INT zgetri_info = 0; F77_XFCN (zgetri, ZGETRI, (nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (pz), lwork, zgetri_info)); if (zgetri_info != 0) info = -1; } if (info != 0) mattype.mark_as_rectangular (); return retval; } ComplexMatrix ComplexMatrix::inverse (MatrixType& mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { int typ = mattype.type (false); ComplexMatrix ret; if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Upper || typ == MatrixType::Lower) ret = tinverse (mattype, info, rcon, force, calc_cond); else { if (mattype.ishermitian ()) { octave::math::chol<ComplexMatrix> chol (*this, info, true, calc_cond); if (info == 0) { if (calc_cond) rcon = chol.rcond (); else rcon = 1.0; ret = chol.inverse (); } else mattype.mark_as_unsymmetric (); } if (! mattype.ishermitian ()) ret = finverse (mattype, info, rcon, force, calc_cond); if ((calc_cond || mattype.ishermitian ()) && rcon == 0.0) { if (numel () == 1) ret = ComplexMatrix (1, 1, 0.0); else ret = ComplexMatrix (rows (), columns (), Complex (octave::numeric_limits<double>::Inf (), 0.0)); } } return ret; } ComplexMatrix ComplexMatrix::pseudo_inverse (double tol) const { ComplexMatrix retval; octave::math::svd<ComplexMatrix> result (*this, octave::math::svd<ComplexMatrix>::Type::economy); DiagMatrix S = result.singular_values (); ComplexMatrix U = result.left_singular_matrix (); ComplexMatrix V = result.right_singular_matrix (); ColumnVector sigma = S.extract_diag (); octave_idx_type r = sigma.numel () - 1; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (tol <= 0.0) { tol = std::max (nr, nc) * sigma.elem (0) * std::numeric_limits<double>::epsilon (); if (tol == 0) tol = std::numeric_limits<double>::min (); } while (r >= 0 && sigma.elem (r) < tol) r--; if (r < 0) retval = ComplexMatrix (nc, nr, 0.0); else { ComplexMatrix Ur = U.extract (0, 0, nr-1, r); DiagMatrix D = DiagMatrix (sigma.extract (0, r)).inverse (); ComplexMatrix Vr = V.extract (0, 0, nc-1, r); retval = Vr * D * Ur.hermitian (); } return retval; } #if defined (HAVE_FFTW) ComplexMatrix ComplexMatrix::fourier (void) const { std::size_t nr = rows (); std::size_t nc = cols (); ComplexMatrix retval (nr, nc); std::size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = (nr > nc ? nr : nc); nsamples = 1; } else { npts = nr; nsamples = nc; } const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave::fftw::fft (in, out, npts, nsamples); return retval; } ComplexMatrix ComplexMatrix::ifourier (void) const { std::size_t nr = rows (); std::size_t nc = cols (); ComplexMatrix retval (nr, nc); std::size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = (nr > nc ? nr : nc); nsamples = 1; } else { npts = nr; nsamples = nc; } const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave::fftw::ifft (in, out, npts, nsamples); return retval; } ComplexMatrix ComplexMatrix::fourier2d (void) const { dim_vector dv (rows (), cols ()); ComplexMatrix retval (rows (), cols ()); const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave::fftw::fftNd (in, out, 2, dv); return retval; } ComplexMatrix ComplexMatrix::ifourier2d (void) const { dim_vector dv (rows (), cols ()); ComplexMatrix retval (rows (), cols ()); const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave::fftw::ifftNd (in, out, 2, dv); return retval; } #else ComplexMatrix ComplexMatrix::fourier (void) const { (*current_liboctave_error_handler) ("support for FFTW was unavailable or disabled when liboctave was built"); return ComplexMatrix (); } ComplexMatrix ComplexMatrix::ifourier (void) const { (*current_liboctave_error_handler) ("support for FFTW was unavailable or disabled when liboctave was built"); return ComplexMatrix (); } ComplexMatrix ComplexMatrix::fourier2d (void) const { (*current_liboctave_error_handler) ("support for FFTW was unavailable or disabled when liboctave was built"); return ComplexMatrix (); } ComplexMatrix ComplexMatrix::ifourier2d (void) const { (*current_liboctave_error_handler) ("support for FFTW was unavailable or disabled when liboctave was built"); return ComplexMatrix (); } #endif ComplexDET ComplexMatrix::determinant (void) const { octave_idx_type info; double rcon; return determinant (info, rcon, 0); } ComplexDET ComplexMatrix::determinant (octave_idx_type& info) const { double rcon; return determinant (info, rcon, 0); } ComplexDET ComplexMatrix::determinant (octave_idx_type& info, double& rcon, bool calc_cond) const { MatrixType mattype (*this); return determinant (mattype, info, rcon, calc_cond); } ComplexDET ComplexMatrix::determinant (MatrixType& mattype, octave_idx_type& info, double& rcon, bool calc_cond) const { ComplexDET retval (1.0); info = 0; rcon = 0.0; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); volatile int typ = mattype.type (); // Even though the matrix is marked as singular (Rectangular), we may // still get a useful number from the LU factorization, because it always // completes. if (typ == MatrixType::Unknown) typ = mattype.type (*this); else if (typ == MatrixType::Rectangular) typ = MatrixType::Full; if (typ == MatrixType::Lower || typ == MatrixType::Upper) { for (F77_INT i = 0; i < nc; i++) retval *= elem (i,i); } else if (typ == MatrixType::Hermitian) { ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); double anorm; if (calc_cond) anorm = norm1 (*this); F77_INT tmp_info = 0; char job = 'L'; F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { if (calc_cond) { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) rcon = 0.0; } for (F77_INT i = 0; i < nc; i++) retval *= atmp(i,i); retval = retval.square (); } } else if (typ != MatrixType::Full) (*current_liboctave_error_handler) ("det: invalid dense matrix type"); if (typ == MatrixType::Full) { Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); info = 0; // Calculate norm of the matrix (always, see bug #45577) for later use. double anorm = norm1 (*this); F77_INT tmp_info = 0; // Work around bug #45577, LAPACK crashes Octave if norm is NaN if (octave::math::isnan (anorm)) info = -1; else { F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, tmp_info)); info = tmp_info; } // Throw away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -1; retval = ComplexDET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; } if (info != 0) { info = -1; retval = ComplexDET (); } else { for (F77_INT i = 0; i < nc; i++) { Complex c = atmp(i,i); retval *= (ipvt(i) != (i+1)) ? -c : c; } } } } return retval; } double ComplexMatrix::rcond (void) const { MatrixType mattype (*this); return rcond (mattype); } double ComplexMatrix::rcond (MatrixType& mattype) const { double rcon = octave::numeric_limits<double>::NaN (); F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); if (nr == 0 || nc == 0) rcon = octave::numeric_limits<double>::Inf (); else { volatile int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper) { const Complex *tmp_data = fortran_vec (); F77_INT info = 0; char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0; } else if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Lower) { const Complex *tmp_data = fortran_vec (); F77_INT info = 0; char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } else if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) { double anorm = -1.0; if (typ == MatrixType::Hermitian) { F77_INT info = 0; char job = 'L'; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); anorm = norm1 (atmp); F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, info F77_CHAR_ARG_LEN (1))); if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } if (typ == MatrixType::Full) { F77_INT info = 0; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); if (anorm < 0.0) anorm = norm1 (atmp); Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); // Work around bug #45577, LAPACK crashes Octave if norm is NaN if (octave::math::isnan (anorm)) info = -1; else F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, info)); if (info != 0) { rcon = 0.0; mattype.mark_as_rectangular (); } else { char job = '1'; F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } } else rcon = 0.0; } return rcon; } ComplexMatrix ComplexMatrix::utsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { ComplexMatrix retval; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); if (nr != b_nr) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b_nc == 0) retval = ComplexMatrix (nc, b_nc, Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); rcon = 1.0; info = 0; if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); const Complex *tmp_data = fortran_vec (); retval = b; Complex *result = retval.fortran_vec (); char uplo = 'U'; char trans = get_blas_char (transt); char dia = 'N'; F77_INT tmp_info = 0; F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), nr, tmp_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); info = tmp_info; if (calc_cond) { char norm = '1'; uplo = 'U'; dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } } return retval; } ComplexMatrix ComplexMatrix::ltsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { ComplexMatrix retval; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); if (nr != b_nr) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b_nc == 0) retval = ComplexMatrix (nc, b_nc, Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); rcon = 1.0; info = 0; if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); const Complex *tmp_data = fortran_vec (); retval = b; Complex *result = retval.fortran_vec (); char uplo = 'L'; char trans = get_blas_char (transt); char dia = 'N'; F77_INT tmp_info = 0; F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), nr, tmp_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); info = tmp_info; if (calc_cond) { char norm = '1'; uplo = 'L'; dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } } return retval; } ComplexMatrix ComplexMatrix::fsolve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; F77_INT nr = octave::to_f77_int (rows ()); F77_INT nc = octave::to_f77_int (cols ()); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); if (nr != nc || nr != b_nr) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b_nc == 0) retval = ComplexMatrix (nc, b_nc, Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix for later use when determining rcon. double anorm = -1.0; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); // The norm of the matrix for later use when determining rcon. if (calc_cond) anorm = norm1 (atmp); F77_INT tmp_info = 0; F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; // Throw away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { if (calc_cond) { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), b_nr, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; } else { mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } } } if (typ == MatrixType::Full) { info = 0; Array<F77_INT> ipvt (dim_vector (nr, 1)); F77_INT *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); // Calculate the norm of the matrix, for later use. if (calc_cond && anorm < 0.0) anorm = norm1 (atmp); F77_INT tmp_info = 0; // Work around bug #45577, LAPACK crashes Octave if norm is NaN // and bug #46330, segfault with matrices containing Inf & NaN if (octave::math::isnan (anorm) || octave::math::isinf (anorm)) info = -2; else { F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, tmp_info)); info = tmp_info; } // Throw away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (); mattype.mark_as_rectangular (); } else { if (calc_cond) { // Calculate the condition number for non-singular matrix. char job = '1'; F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); char job = 'N'; F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (result), b_nr, tmp_info F77_CHAR_ARG_LEN (1))); info = tmp_info; } else mattype.mark_as_rectangular (); } } if (octave::math::isinf (anorm)) { retval = ComplexMatrix (b_nr, b_nc, Complex (0, 0)); mattype.mark_as_full (); } } return retval; } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const Matrix& b) const { octave_idx_type info; double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info) const { double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { ComplexMatrix tmp (b); return solve (mattype, tmp, info, rcon, sing_handler, singular_fallback, transt); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const ComplexMatrix& b) const { octave_idx_type info; double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (mattype, b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (MatrixType& mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { ComplexMatrix retval; int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (transt == blas_trans) return transpose ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (transt == blas_conj_trans) retval = hermitian ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, info, rcon, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); // Rectangular or one of the above solvers flags a singular matrix if (singular_fallback && mattype.type () == MatrixType::Rectangular) { octave_idx_type rank; retval = lssolve (b, info, rank, rcon); } return retval; } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ColumnVector& b) const { octave_idx_type info; double rcon; return solve (mattype, ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (mattype, ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (mattype, ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (mattype, ComplexColumnVector (b), info, rcon, sing_handler, transt); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b) const { octave_idx_type info; double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (mattype, b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (mattype, b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (MatrixType& mattype, const ComplexColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { ComplexMatrix tmp (b); tmp = solve (mattype, tmp, info, rcon, sing_handler, true, transt); return tmp.column (static_cast<octave_idx_type> (0)); } ComplexMatrix ComplexMatrix::solve (const Matrix& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { ComplexMatrix tmp (b); return solve (tmp, info, rcon, sing_handler, transt); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, nullptr); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, true, transt); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b) const { octave_idx_type info; double rcon; return solve (ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (ComplexColumnVector (b), info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (ComplexColumnVector (b), info, rcon, sing_handler, transt); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, nullptr); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, transt); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { ComplexMatrix retval; F77_INT m = octave::to_f77_int (rows ()); F77_INT n = octave::to_f77_int (cols ()); F77_INT b_nr = octave::to_f77_int (b.rows ()); F77_INT b_nc = octave::to_f77_int (b.cols ()); F77_INT nrhs = b_nc; // alias for code readability if (m != b_nr) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m == 0 || n == 0 || b_nc == 0) retval = ComplexMatrix (n, b_nc, Complex (0.0, 0.0)); else { volatile F77_INT minmn = (m < n ? m : n); F77_INT maxmn = (m > n ? m : n); rcon = -1.0; if (m != n) { retval = ComplexMatrix (maxmn, nrhs); for (F77_INT j = 0; j < nrhs; j++) for (F77_INT i = 0; i < m; i++) retval.elem (i, j) = b.elem (i, j); } else retval = b; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Complex *pretval = retval.fortran_vec (); Array<double> s (dim_vector (minmn, 1)); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. F77_INT lwork = -1; Array<Complex> work (dim_vector (1, 1)); F77_INT smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); F77_INT mnthr; F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), m, n, nrhs, -1, mnthr F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. double dminmn = static_cast<double> (minmn); double dsmlsizp1 = static_cast<double> (smlsiz+1); double tmp = octave::math::log2 (dminmn / dsmlsizp1); F77_INT nlvl = static_cast<F77_INT> (tmp) + 1; if (nlvl < 0) nlvl = 0; F77_INT lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + std::max ((smlsiz+1)*(smlsiz+1), n*(1+nrhs) + 2*nrhs); if (lrwork < 1) lrwork = 1; Array<double> rwork (dim_vector (lrwork, 1)); double *prwork = rwork.fortran_vec (); F77_INT liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<F77_INT> iwork (dim_vector (liwork, 1)); F77_INT *piwork = iwork.fortran_vec (); F77_INT tmp_info = 0; F77_INT tmp_rank = 0; F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, tmp_rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, tmp_info)); info = tmp_info; rank = tmp_rank; // The workspace query is broken in at least LAPACK 3.0.0 // through 3.1.1 when n >= mnthr. The obtuse formula below // should provide sufficient workspace for ZGELSD to operate // efficiently. if (n > m && n >= mnthr) { F77_INT addend = m; if (2*m-4 > addend) addend = 2*m-4; if (nrhs > addend) addend = nrhs; if (n-3*m > addend) addend = n-3*m; const F77_INT lworkaround = 4*m + m*m + addend; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } else if (m >= n) { F77_INT lworkaround = 2*m + m*nrhs; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } lwork = static_cast<F77_INT> (std::real (work(0))); work.resize (dim_vector (lwork, 1)); double anorm = norm1 (*this); if (octave::math::isinf (anorm)) { rcon = 0.0; retval = ComplexMatrix (n, b_nc, 0.0); } else if (octave::math::isnan (anorm)) { rcon = octave::numeric_limits<double>::NaN (); retval = ComplexMatrix (n, b_nc, octave::numeric_limits<double>::NaN ()); } else { F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, tmp_rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, tmp_info)); info = tmp_info; rank = tmp_rank; if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } return retval; } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { ComplexColumnVector retval; F77_INT nrhs = 1; F77_INT m = octave::to_f77_int (rows ()); F77_INT n = octave::to_f77_int (cols ()); F77_INT b_nel = octave::to_f77_int (b.numel ()); if (m != b_nel) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m == 0 || n == 0) retval = ComplexColumnVector (n, Complex (0.0, 0.0)); else { volatile F77_INT minmn = (m < n ? m : n); F77_INT maxmn = (m > n ? m : n); rcon = -1.0; if (m != n) { retval = ComplexColumnVector (maxmn); for (F77_INT i = 0; i < m; i++) retval.elem (i) = b.elem (i); } else retval = b; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Complex *pretval = retval.fortran_vec (); Array<double> s (dim_vector (minmn, 1)); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. F77_INT lwork = -1; Array<Complex> work (dim_vector (1, 1)); F77_INT smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. double dminmn = static_cast<double> (minmn); double dsmlsizp1 = static_cast<double> (smlsiz+1); double tmp = octave::math::log2 (dminmn / dsmlsizp1); F77_INT nlvl = static_cast<F77_INT> (tmp) + 1; if (nlvl < 0) nlvl = 0; F77_INT lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); if (lrwork < 1) lrwork = 1; Array<double> rwork (dim_vector (lrwork, 1)); double *prwork = rwork.fortran_vec (); F77_INT liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<F77_INT> iwork (dim_vector (liwork, 1)); F77_INT *piwork = iwork.fortran_vec (); F77_INT tmp_info = 0; F77_INT tmp_rank = 0; F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, tmp_rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, tmp_info)); info = tmp_info; rank = tmp_rank; lwork = static_cast<F77_INT> (std::real (work(0))); work.resize (dim_vector (lwork, 1)); rwork.resize (dim_vector (static_cast<F77_INT> (rwork(0)), 1)); iwork.resize (dim_vector (iwork(0), 1)); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, tmp_rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, tmp_info)); info = tmp_info; rank = tmp_rank; if (rank < minmn) { if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n); } } return retval; } // column vector by row vector -> matrix operations ComplexMatrix operator * (const ColumnVector& v, const ComplexRowVector& a) { ComplexColumnVector tmp (v); return tmp * a; } ComplexMatrix operator * (const ComplexColumnVector& a, const RowVector& b) { ComplexRowVector tmp (b); return a * tmp; } ComplexMatrix operator * (const ComplexColumnVector& v, const ComplexRowVector& a) { ComplexMatrix retval; F77_INT len = octave::to_f77_int (v.numel ()); if (len != 0) { F77_INT a_len = octave::to_f77_int (a.numel ()); retval = ComplexMatrix (len, a_len); Complex *c = retval.fortran_vec (); F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), len, a_len, 1, 1.0, F77_CONST_DBLE_CMPLX_ARG (v.data ()), len, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), len F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } return retval; } // matrix by diagonal matrix -> matrix operations ComplexMatrix& ComplexMatrix::operator += (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator += (const ComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const ComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } // matrix by matrix -> matrix operations ComplexMatrix& ComplexMatrix::operator += (const Matrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_add2 (numel (), d, a.data ()); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const Matrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_sub2 (numel (), d, a.data ()); return *this; } // other operations boolMatrix ComplexMatrix::all (int dim) const { return ComplexNDArray::all (dim); } boolMatrix ComplexMatrix::any (int dim) const { return ComplexNDArray::any (dim); } ComplexMatrix ComplexMatrix::cumprod (int dim) const { return ComplexNDArray::cumprod (dim); } ComplexMatrix ComplexMatrix::cumsum (int dim) const { return ComplexNDArray::cumsum (dim); } ComplexMatrix ComplexMatrix::prod (int dim) const { return ComplexNDArray::prod (dim); } ComplexMatrix ComplexMatrix::sum (int dim) const { return ComplexNDArray::sum (dim); } ComplexMatrix ComplexMatrix::sumsq (int dim) const { return ComplexNDArray::sumsq (dim); } Matrix ComplexMatrix::abs (void) const { return ComplexNDArray::abs (); } ComplexMatrix ComplexMatrix::diag (octave_idx_type k) const { return ComplexNDArray::diag (k); } ComplexDiagMatrix ComplexMatrix::diag (octave_idx_type m, octave_idx_type n) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1 && nc != 1) (*current_liboctave_error_handler) ("diag: expecting vector argument"); return ComplexDiagMatrix (*this, m, n); } bool ComplexMatrix::row_is_real_only (octave_idx_type i) const { bool retval = true; octave_idx_type nc = columns (); for (octave_idx_type j = 0; j < nc; j++) { if (std::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } bool ComplexMatrix::column_is_real_only (octave_idx_type j) const { bool retval = true; octave_idx_type nr = rows (); for (octave_idx_type i = 0; i < nr; i++) { if (std::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } ComplexColumnVector ComplexMatrix::row_min (void) const { Array<octave_idx_type> dummy_idx; return row_min (dummy_idx); } ComplexColumnVector ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const { ComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; Complex tmp_min; double abs_min = octave::numeric_limits<double>::NaN (); for (idx_j = 0; idx_j < nc; idx_j++) { tmp_min = elem (i, idx_j); if (! octave::math::isnan (tmp_min)) { abs_min = (real_only ? tmp_min.real () : std::abs (tmp_min)); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = (real_only ? tmp.real () : std::abs (tmp)); if (abs_tmp < abs_min) { idx_j = j; tmp_min = tmp; abs_min = abs_tmp; } } if (octave::math::isnan (tmp_min)) { result.elem (i) = Complex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_min; idx_arg.elem (i) = idx_j; } } } return result; } ComplexColumnVector ComplexMatrix::row_max (void) const { Array<octave_idx_type> dummy_idx; return row_max (dummy_idx); } ComplexColumnVector ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const { ComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; Complex tmp_max; double abs_max = octave::numeric_limits<double>::NaN (); for (idx_j = 0; idx_j < nc; idx_j++) { tmp_max = elem (i, idx_j); if (! octave::math::isnan (tmp_max)) { abs_max = (real_only ? tmp_max.real () : std::abs (tmp_max)); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = (real_only ? tmp.real () : std::abs (tmp)); if (abs_tmp > abs_max) { idx_j = j; tmp_max = tmp; abs_max = abs_tmp; } } if (octave::math::isnan (tmp_max)) { result.elem (i) = Complex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_max; idx_arg.elem (i) = idx_j; } } } return result; } ComplexRowVector ComplexMatrix::column_min (void) const { Array<octave_idx_type> dummy_idx; return column_min (dummy_idx); } ComplexRowVector ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const { ComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; Complex tmp_min; double abs_min = octave::numeric_limits<double>::NaN (); for (idx_i = 0; idx_i < nr; idx_i++) { tmp_min = elem (idx_i, j); if (! octave::math::isnan (tmp_min)) { abs_min = (real_only ? tmp_min.real () : std::abs (tmp_min)); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = (real_only ? tmp.real () : std::abs (tmp)); if (abs_tmp < abs_min) { idx_i = i; tmp_min = tmp; abs_min = abs_tmp; } } if (octave::math::isnan (tmp_min)) { result.elem (j) = Complex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_min; idx_arg.elem (j) = idx_i; } } } return result; } ComplexRowVector ComplexMatrix::column_max (void) const { Array<octave_idx_type> dummy_idx; return column_max (dummy_idx); } ComplexRowVector ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const { ComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; Complex tmp_max; double abs_max = octave::numeric_limits<double>::NaN (); for (idx_i = 0; idx_i < nr; idx_i++) { tmp_max = elem (idx_i, j); if (! octave::math::isnan (tmp_max)) { abs_max = (real_only ? tmp_max.real () : std::abs (tmp_max)); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = (real_only ? tmp.real () : std::abs (tmp)); if (abs_tmp > abs_max) { idx_i = i; tmp_max = tmp; abs_max = abs_tmp; } } if (octave::math::isnan (tmp_max)) { result.elem (j) = Complex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_max; idx_arg.elem (j) = idx_i; } } } return result; } // i/o std::ostream& operator << (std::ostream& os, const ComplexMatrix& a) { for (octave_idx_type i = 0; i < a.rows (); i++) { for (octave_idx_type j = 0; j < a.cols (); j++) { os << ' '; octave::write_value<Complex> (os, a.elem (i, j)); } os << "\n"; } return os; } std::istream& operator >> (std::istream& is, ComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr > 0 && nc > 0) { Complex tmp; for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = 0; j < nc; j++) { tmp = octave::read_value<Complex> (is); if (is) a.elem (i, j) = tmp; else return is; } } return is; } ComplexMatrix Givens (const Complex& x, const Complex& y) { double cc; Complex cs, temp_r; F77_FUNC (zlartg, ZLARTG) (F77_CONST_DBLE_CMPLX_ARG (&x), F77_CONST_DBLE_CMPLX_ARG (&y), cc, F77_DBLE_CMPLX_ARG (&cs), F77_DBLE_CMPLX_ARG (&temp_r)); ComplexMatrix g (2, 2); g.elem (0, 0) = cc; g.elem (1, 1) = cc; g.elem (0, 1) = cs; g.elem (1, 0) = -conj (cs); return g; } ComplexMatrix Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, const ComplexMatrix& c) { ComplexMatrix retval; // FIXME: need to check that a, b, and c are all the same size. // Compute Schur decompositions octave::math::schur<ComplexMatrix> as (a, "U"); octave::math::schur<ComplexMatrix> bs (b, "U"); // Transform c to new coordinates. ComplexMatrix ua = as.unitary_matrix (); ComplexMatrix sch_a = as.schur_matrix (); ComplexMatrix ub = bs.unitary_matrix (); ComplexMatrix sch_b = bs.schur_matrix (); ComplexMatrix cx = ua.hermitian () * c * ub; // Solve the sylvester equation, back-transform, and return the solution. F77_INT a_nr = octave::to_f77_int (a.rows ()); F77_INT b_nr = octave::to_f77_int (b.rows ()); double scale; F77_INT info; Complex *pa = sch_a.fortran_vec (); Complex *pb = sch_b.fortran_vec (); Complex *px = cx.fortran_vec (); F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), 1, a_nr, b_nr, F77_DBLE_CMPLX_ARG (pa), a_nr, F77_DBLE_CMPLX_ARG (pb), b_nr, F77_DBLE_CMPLX_ARG (px), a_nr, scale, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // FIXME: check info? retval = ua * cx * ub.hermitian (); return retval; } ComplexMatrix operator * (const ComplexMatrix& m, const Matrix& a) { if (m.columns () > std::min (m.rows (), a.columns ()) / 10) return ComplexMatrix (real (m) * a, imag (m) * a); else return m * ComplexMatrix (a); } ComplexMatrix operator * (const Matrix& m, const ComplexMatrix& a) { if (a.rows () > std::min (m.rows (), a.columns ()) / 10) return ComplexMatrix (m * real (a), m * imag (a)); else return ComplexMatrix (m) * a; } /* ## Simple Dot Product, Matrix-Vector, and Matrix-Matrix Unit tests %!assert ([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) %!assert ([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) %!assert ([1+i 2+i ; 3+i 4+i ] * [5+i 6+i ; 7+i 8+i], [17 + 15i 20 + 17i; 41 + 19i 48 + 21i], 1e-14) %!assert ([1 i]*[i 0]', -i) ## Test some simple identities %!shared M, cv, rv %! M = randn (10,10) + i*rand (10,10); %! cv = randn (10,1) + i*rand (10,1); %! rv = randn (1,10) + i*rand (1,10); %!assert ([M*cv,M*cv], M*[cv,cv], 1e-14) %!assert ([M.'*cv,M.'*cv], M.'*[cv,cv], 1e-14) %!assert ([M'*cv,M'*cv], M'*[cv,cv], 1e-14) %!assert ([rv*M;rv*M], [rv;rv]*M, 1e-14) %!assert ([rv*M.';rv*M.'], [rv;rv]*M.', 1e-14) %!assert ([rv*M';rv*M'], [rv;rv]*M', 1e-14) %!assert (2*rv*cv, [rv,rv]*[cv;cv], 2e-14) */ static inline char get_blas_trans_arg (bool trans, bool conj) { return trans ? (conj ? 'C' : 'T') : 'N'; } // the general GEMM operation ComplexMatrix xgemm (const ComplexMatrix& a, const ComplexMatrix& b, blas_trans_type transa, blas_trans_type transb) { ComplexMatrix retval; bool tra = transa != blas_no_trans; bool trb = transb != blas_no_trans; bool cja = transa == blas_conj_trans; bool cjb = transb == blas_conj_trans; F77_INT a_nr = octave::to_f77_int (tra ? a.cols () : a.rows ()); F77_INT a_nc = octave::to_f77_int (tra ? a.rows () : a.cols ()); F77_INT b_nr = octave::to_f77_int (trb ? b.cols () : b.rows ()); F77_INT b_nc = octave::to_f77_int (trb ? b.rows () : b.cols ()); if (a_nc != b_nr) octave::err_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); if (a_nr == 0 || a_nc == 0 || b_nc == 0) retval = ComplexMatrix (a_nr, b_nc, 0.0); else if (a.data () == b.data () && a_nr == b_nc && tra != trb) { F77_INT lda = octave::to_f77_int (a.rows ()); // FIXME: looking at the reference BLAS, it appears that it // should not be necessary to initialize the output matrix if // BETA is 0 in the call to ZHERK, but ATLAS appears to // use the result matrix before zeroing the elements. retval = ComplexMatrix (a_nr, b_nc, 0.0); Complex *c = retval.fortran_vec (); const char ctra = get_blas_trans_arg (tra, cja); if (cja || cjb) { F77_XFCN (zherk, ZHERK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (F77_INT j = 0; j < a_nr; j++) for (F77_INT i = 0; i < j; i++) retval.xelem (j,i) = octave::math::conj (retval.xelem (i,j)); } else { F77_XFCN (zsyrk, ZSYRK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (F77_INT j = 0; j < a_nr; j++) for (F77_INT i = 0; i < j; i++) retval.xelem (j,i) = retval.xelem (i,j); } } else { F77_INT lda = octave::to_f77_int (a.rows ()); F77_INT tda = octave::to_f77_int (a.cols ()); F77_INT ldb = octave::to_f77_int (b.rows ()); F77_INT tdb = octave::to_f77_int (b.cols ()); retval = ComplexMatrix (a_nr, b_nc, 0.0); Complex *c = retval.fortran_vec (); if (b_nc == 1 && a_nr == 1) { if (cja == cjb) { F77_FUNC (xzdotu, XZDOTU) (a_nc, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_DBLE_CMPLX_ARG (c)); if (cja) *c = octave::math::conj (*c); } else if (cja) F77_FUNC (xzdotc, XZDOTC) (a_nc, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_DBLE_CMPLX_ARG (c)); else F77_FUNC (xzdotc, XZDOTC) (a_nc, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_DBLE_CMPLX_ARG (c)); } else if (b_nc == 1 && ! cjb) { const char ctra = get_blas_trans_arg (tra, cja); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (&ctra, 1), lda, tda, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), 1 F77_CHAR_ARG_LEN (1))); } else if (a_nr == 1 && ! cja && ! cjb) { const char crevtrb = get_blas_trans_arg (! trb, cjb); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (&crevtrb, 1), ldb, tdb, 1.0, F77_CONST_DBLE_CMPLX_ARG (b.data ()), ldb, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), 1 F77_CHAR_ARG_LEN (1))); } else { const char ctra = get_blas_trans_arg (tra, cja); const char ctrb = get_blas_trans_arg (trb, cjb); F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 (&ctra, 1), F77_CONST_CHAR_ARG2 (&ctrb, 1), a_nr, b_nc, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, F77_CONST_DBLE_CMPLX_ARG (b.data ()), ldb, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } } return retval; } ComplexMatrix operator * (const ComplexMatrix& a, const ComplexMatrix& b) { return xgemm (a, b); } // FIXME: it would be nice to share code among the min/max functions below. #define EMPTY_RETURN_CHECK(T) \ if (nr == 0 || nc == 0) \ return T (nr, nc); ComplexMatrix min (const Complex& c, const ComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::min (c, m(i, j)); } return result; } ComplexMatrix min (const ComplexMatrix& m, const Complex& c) { return min (c, m); } ComplexMatrix min (const ComplexMatrix& a, const ComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg min requires same size arguments"); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { bool columns_are_real_only = true; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (std::imag (a(i, j)) != 0.0 || std::imag (b(i, j)) != 0.0) { columns_are_real_only = false; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) result(i, j) = octave::math::min (std::real (a(i, j)), std::real (b(i, j))); } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::min (a(i, j), b(i, j)); } } } return result; } ComplexMatrix max (const Complex& c, const ComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (c, m(i, j)); } return result; } ComplexMatrix max (const ComplexMatrix& m, const Complex& c) { return max (c, m); } ComplexMatrix max (const ComplexMatrix& a, const ComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg max requires same size arguments"); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { bool columns_are_real_only = true; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (std::imag (a(i, j)) != 0.0 || std::imag (b(i, j)) != 0.0) { columns_are_real_only = false; break; } } // FIXME: is it so much faster? if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (std::real (a(i, j)), std::real (b(i, j))); } } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (a(i, j), b(i, j)); } } } return result; } ComplexMatrix linspace (const ComplexColumnVector& x1, const ComplexColumnVector& x2, octave_idx_type n) { octave_idx_type m = x1.numel (); if (x2.numel () != m) (*current_liboctave_error_handler) ("linspace: vectors must be of equal length"); ComplexMatrix retval; if (n < 1) { retval.clear (m, 0); return retval; } retval.clear (m, n); for (octave_idx_type i = 0; i < m; i++) retval.xelem (i, 0) = x1(i); // The last column is unused so temporarily store delta there Complex *delta = &retval.xelem (0, n-1); for (octave_idx_type i = 0; i < m; i++) delta[i] = (x1(i) == x2(i)) ? 0 : (x2(i) - x1(i)) / (n - 1.0); for (octave_idx_type j = 1; j < n-1; j++) for (octave_idx_type i = 0; i < m; i++) retval.xelem (i, j) = x1(i) + static_cast<double> (j)*delta[i]; for (octave_idx_type i = 0; i < m; i++) retval.xelem (i, n-1) = x2(i); return retval; } MS_CMP_OPS (ComplexMatrix, Complex) MS_BOOL_OPS (ComplexMatrix, Complex) SM_CMP_OPS (Complex, ComplexMatrix) SM_BOOL_OPS (Complex, ComplexMatrix) MM_CMP_OPS (ComplexMatrix, ComplexMatrix) MM_BOOL_OPS (ComplexMatrix, ComplexMatrix)