Mercurial > hg > octave-nkf
view liboctave/CMatrix.cc @ 11521:00fe5069b70e
update bootstrap scripts from gnulib sources
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 02:58:24 -0500 |
| parents | 141b3fb5cef7 |
| children | fd0a3ac60b0e |
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// Matrix manipulations. /* Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 John W. Eaton Copyright (C) 2008, 2009 Jaroslav Hajek Copyright (C) 2009 VZLU Prague, a.s. 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 <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include <cfloat> #include <iostream> #include <vector> // FIXME #include <sys/types.h> #include "Array-util.h" #include "CMatrix.h" #include "CmplxAEPBAL.h" #include "CmplxCHOL.h" #include "CmplxSCHUR.h" #include "CmplxSVD.h" #include "DET.h" #include "f77-fcn.h" #include "functor.h" #include "lo-error.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-base.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" // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgebal, ZGEBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type&, octave_idx_type&, double*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgemm, ZGEMM) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const Complex&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xzdotu, XZDOTU) (const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, Complex&); F77_RET_T F77_FUNC (xzdotc, XZDOTC) (const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, Complex&); F77_RET_T F77_FUNC (zsyrk, ZSYRK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex&, const Complex*, const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zherk, ZHERK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double&, const Complex*, const octave_idx_type&, const double&, Complex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgetrf, ZGETRF) (const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (zgetrs, ZGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgetri, ZGETRI) (const octave_idx_type&, Complex*, const octave_idx_type&, const octave_idx_type*, Complex*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (zgecon, ZGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, Complex*, const octave_idx_type&, const double&, double&, Complex*, double*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgelsy, ZGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, Complex*, const octave_idx_type&, double*, octave_idx_type&); F77_RET_T F77_FUNC (zgelsd, ZGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, double*, double&, octave_idx_type&, Complex*, const octave_idx_type&, double*, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (zpotrf, ZPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zpocon, ZPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, Complex*, const octave_idx_type&, const double&, double&, Complex*, double*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zpotrs, ZPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ztrtri, ZTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const Complex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ztrcon, ZTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const Complex*, const octave_idx_type&, double&, Complex*, double*, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ztrtrs, ZTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zlartg, ZLARTG) (const Complex&, const Complex&, double&, Complex&, Complex&); F77_RET_T F77_FUNC (ztrsyl, ZTRSYL) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, double&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xzlange, XZLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex*, const octave_idx_type&, double*, double& F77_CHAR_ARG_LEN_DECL); } static const Complex Complex_NaN_result (octave_NaN, octave_NaN); // Complex Matrix class ComplexMatrix::ComplexMatrix (const Matrix& a) : MArray<Complex> (a) { } ComplexMatrix::ComplexMatrix (const RowVector& rv) : MArray<Complex> (rv) { } ComplexMatrix::ComplexMatrix (const ColumnVector& cv) : MArray<Complex> (cv) { } ComplexMatrix::ComplexMatrix (const DiagMatrix& a) : MArray<Complex> (a.rows (), a.cols (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) : MArray<Complex> (rv) { } ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) : MArray<Complex> (cv) { } ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) : MArray<Complex> (a.rows (), a.cols (), 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) : MArray<Complex> (a) { } ComplexMatrix::ComplexMatrix (const charMatrix& a) : MArray<Complex> (a.rows (), a.cols (), 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) : MArray<Complex> (re.rows (), re.cols ()) { 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 (length (), data (), a.data ()); } bool ComplexMatrix::operator != (const ComplexMatrix& a) const { return !(*this == a); } bool ComplexMatrix::is_hermitian (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (is_square () && 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"); return *this; } 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.length (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } 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.length (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } 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"); return *this; } 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) { Array<Complex>::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.length (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } 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.length (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } 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"); return *this; } 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"); return *this; } if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } 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"); return *this; } if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } 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"); return *this; } 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"); return *this; } octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.length ()); 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.length ()) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return *this; } 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"); return *this; } 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"); return *this; } 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"); return *this; } octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.length ()); 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.length ()) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return *this; } 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"); return *this; } 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"); return *this; } 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.length ()) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return *this; } 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"); return *this; } octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.length (), 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"); return *this; } 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"); return *this; } 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.length ()) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return *this; } 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"); return *this; } octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.length (), 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"); return *this; } 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> (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) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } return index (idx_vector (r1, r2+1), 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 (idx_vector (r1, r1 + nr), idx_vector (c1, c1 + nc)); } // extract row or column i. ComplexRowVector ComplexMatrix::row (octave_idx_type i) const { return index (idx_vector (i), idx_vector::colon); } ComplexColumnVector ComplexMatrix::column (octave_idx_type i) const { return index (idx_vector::colon, idx_vector (i)); } 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, int force, int 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, int force, int calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr == 0 || nc == 0) (*current_liboctave_error_handler) ("inverse requires square matrix"); else { int typ = mattype.type (); char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); char udiag = 'N'; retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_XFCN (ztrtri, ZTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { octave_idx_type 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, tmp_data, nr, rcon, 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, int force, int calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); else { Array<octave_idx_type> ipvt (nr, 1); octave_idx_type *pipvt = ipvt.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); Array<Complex> z(1, 1); octave_idx_type lwork = -1; // Query the optimum work array size. F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, z.fortran_vec (), lwork, info)); lwork = static_cast<octave_idx_type> (std::real(z(0))); lwork = (lwork < 2 *nc ? 2*nc : lwork); z.resize (lwork, 1); Complex *pz = z.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. double anorm; if (calc_cond) anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zgetrf, ZGETRF, (nc, nc, tmp_data, nr, pipvt, 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) { // Now calculate the condition number for non-singular matrix. octave_idx_type zgecon_info = 0; char job = '1'; Array<double> rz (2 * nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, zgecon_info F77_CHAR_ARG_LEN (1))); if (zgecon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore contents. else { octave_idx_type zgetri_info = 0; F77_XFCN (zgetri, ZGETRI, (nc, tmp_data, nr, pipvt, 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, int force, int 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.is_hermitian ()) { ComplexCHOL chol (*this, info, 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.is_hermitian ()) ret = finverse(mattype, info, rcon, force, calc_cond); if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) ret = ComplexMatrix (rows (), columns (), Complex (octave_Inf, 0.)); } return ret; } ComplexMatrix ComplexMatrix::pseudo_inverse (double tol) const { ComplexMatrix retval; ComplexSVD result (*this, SVD::economy); DiagMatrix S = result.singular_values (); ComplexMatrix U = result.left_singular_matrix (); ComplexMatrix V = result.right_singular_matrix (); ColumnVector sigma = S.diag (); octave_idx_type r = sigma.length () - 1; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (tol <= 0.0) { if (nr > nc) tol = nr * sigma.elem (0) * DBL_EPSILON; else tol = nc * sigma.elem (0) * DBL_EPSILON; } 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 { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); 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 { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); 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 extern "C" { // Note that the original complex fft routines were not written for // double complex arguments. They have been modified by adding an // implicit double precision (a-h,o-z) statement at the beginning of // each subroutine. F77_RET_T F77_FUNC (zffti, ZFFTI) (const octave_idx_type&, Complex*); F77_RET_T F77_FUNC (zfftf, ZFFTF) (const octave_idx_type&, Complex*, Complex*); F77_RET_T F77_FUNC (zfftb, ZFFTB) (const octave_idx_type&, Complex*, Complex*); } ComplexMatrix ComplexMatrix::fourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn, 1); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); } return retval; } ComplexMatrix ComplexMatrix::ifourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn, 1); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<double> (npts); return retval; } ComplexMatrix ComplexMatrix::fourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn, 1); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftf, ZFFTF) (npts, &tmp_data[npts*j], pwsave); } npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (nn, 1); pwsave = wsave.fortran_vec (); Array<Complex> tmp (npts, 1); Complex *prow = tmp.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (zfftf, ZFFTF) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i]; } return retval; } ComplexMatrix ComplexMatrix::ifourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn, 1); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftb, ZFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<double> (npts); npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (nn, 1); pwsave = wsave.fortran_vec (); Array<Complex> tmp (npts, 1); Complex *prow = tmp.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (zfftb, ZFFTB) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); } return retval; } #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, int calc_cond) const { MatrixType mattype (*this); return determinant (mattype, info, rcon, calc_cond); } ComplexDET ComplexMatrix::determinant (MatrixType& mattype, octave_idx_type& info, double& rcon, int calc_cond) const { ComplexDET retval (1.0); octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); else { 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 (octave_idx_type i = 0; i < nc; i++) retval *= elem (i,i); } else if (typ == MatrixType::Hermitian) { ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); info = 0; double anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); char job = 'L'; F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 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 (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; for (octave_idx_type 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<octave_idx_type> ipvt (nr, 1); octave_idx_type *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. double anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, 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 (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (2 * nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); } if (info != 0) { info = -1; retval = ComplexDET (); } else { for (octave_idx_type 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_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); else if (nr == 0 || nc == 0) rcon = octave_Inf; else { 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 (); octave_idx_type info = 0; char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (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, tmp_data, nr, rcon, 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 (); octave_idx_type info = 0; char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (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, tmp_data, nr, rcon, 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; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); if (typ == MatrixType::Hermitian) { octave_idx_type info = 0; char job = 'L'; anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, 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 (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } if (typ == MatrixType::Full) { octave_idx_type info = 0; Array<octave_idx_type> ipvt (nr, 1); octave_idx_type *pipvt = ipvt.fortran_vec (); if(anorm < 0.) anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (2 * nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zgetrf, ZGETRF, (nr, nr, 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, tmp_data, nr, anorm, rcon, 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; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Upper || typ == MatrixType::Upper) { octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Upper) { (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); } else { const Complex *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (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, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); char uplo = 'U'; char trans = get_blas_char (transt); char dia = 'N'; 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, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Lower || typ == MatrixType::Lower) { octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Lower) { (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); } else { const Complex *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (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, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); char uplo = 'L'; char trans = get_blas_char (transt); char dia = 'N'; 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, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } 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; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else if (nr == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix, for later use. double anorm = -1.; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); // 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 (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (nc, 1); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, result, b.rows(), info F77_CHAR_ARG_LEN (1))); } else { mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } } } if (typ == MatrixType::Full) { info = 0; Array<octave_idx_type> ipvt (nr, 1); octave_idx_type *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Array<Complex> z (2 * nc, 1); Complex *pz = z.fortran_vec (); Array<double> rz (2 * nc, 1); double *prz = rz.fortran_vec (); // Calculate the norm of the matrix, for later use. if (anorm < 0.) anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zgetrf, ZGETRF, (nr, nr, tmp_data, nr, pipvt, 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 (*current_liboctave_error_handler) ("matrix singular to machine precision"); mattype.mark_as_rectangular (); } else { if (calc_cond) { // Now calculate the condition number for // non-singular matrix. char job = '1'; F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, pipvt, result, b.rows(), info F77_CHAR_ARG_LEN (1))); } else mattype.mark_as_rectangular (); } } } return retval; } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, 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 (typ, tmp, info, rcon, sing_handler, singular_fallback, transt); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } 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, false, transt); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcon, sing_handler, false, 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"); return ComplexMatrix (); } // 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 &typ, const ColumnVector& b) const { octave_idx_type info; double rcon; return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (typ, ComplexColumnVector (b), info, rcon, sing_handler, transt); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { ComplexMatrix tmp (b); tmp = solve (typ, 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, 0); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } 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, 0); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } 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, 0); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (ComplexColumnVector (b), info, rcon, 0); } 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, 0); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } 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; octave_idx_type nrhs = b.cols (); octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else if (m== 0 || n == 0 || b.cols () == 0) retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = ComplexMatrix (maxmn, nrhs); for (octave_idx_type j = 0; j < nrhs; j++) for (octave_idx_type 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 (minmn, 1); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<Complex> work (1, 1); octave_idx_type 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)); octave_idx_type 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); #if defined (HAVE_LOG2) double tmp = log2 (dminmn / dsmlsizp1); #else double tmp = log (dminmn / dsmlsizp1) / log (2.0); #endif octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type 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 (lrwork, 1); double *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (liwork, 1); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); // 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) { octave_idx_type 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 octave_idx_type lworkaround = 4*m + m*m + addend; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } else if (m >= n) { octave_idx_type lworkaround = 2*m + m*nrhs; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } lwork = static_cast<octave_idx_type> (std::real (work(0))); work.resize (lwork, 1); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); 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; octave_idx_type nrhs = 1; octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.length ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); else if (m == 0 || n == 0 || b.cols () == 0) retval = ComplexColumnVector (n, Complex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = ComplexColumnVector (maxmn); for (octave_idx_type 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 (minmn, 1); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<Complex> work (1, 1); octave_idx_type 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); #if defined (HAVE_LOG2) double tmp = log2 (dminmn / dsmlsizp1); #else double tmp = log (dminmn / dsmlsizp1) / log (2.0); #endif octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); if (lrwork < 1) lrwork = 1; Array<double> rwork (lrwork, 1); double *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (liwork, 1); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); lwork = static_cast<octave_idx_type> (std::real (work(0))); work.resize (lwork, 1); rwork.resize (static_cast<octave_idx_type> (rwork(0)), 1); iwork.resize (iwork(0), 1); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); if (rank < minmn) { if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } 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; octave_idx_type len = v.length (); if (len != 0) { octave_idx_type a_len = a.length (); 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, v.data (), len, a.data (), 1, 0.0, 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 = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) { gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); return *this; } 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 = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) { gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); return *this; } 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 = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) { gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); return *this; } 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 = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) { gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); return *this; } 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) { gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc); return *this; } if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_add2 (length (), 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) { gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc); return *this; } if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_sub2 (length (), d, a.data ()); return *this; } // unary operations boolMatrix ComplexMatrix::operator ! (void) const { if (any_element_is_nan ()) gripe_nan_to_logical_conversion (); return do_mx_unary_op<bool, Complex> (*this, mx_inline_not); } // other operations bool ComplexMatrix::any_element_is_nan (void) const { return do_mx_check<Complex> (*this, mx_inline_any_nan); } bool ComplexMatrix::any_element_is_inf_or_nan (void) const { return ! do_mx_check<Complex> (*this, mx_inline_all_finite); } // Return true if no elements have imaginary components. bool ComplexMatrix::all_elements_are_real (void) const { return do_mx_check<Complex> (*this, mx_inline_all_real); } // Return nonzero if any element of CM has a non-integer real or // imaginary part. Also extract the largest and smallest (real or // imaginary) values and return them in MAX_VAL and MIN_VAL. bool ComplexMatrix::all_integers (double& max_val, double& min_val) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { Complex val = elem (0, 0); double r_val = std::real (val); double i_val = std::imag (val); max_val = r_val; min_val = r_val; if (i_val > max_val) max_val = i_val; if (i_val < max_val) min_val = i_val; } else return false; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { Complex val = elem (i, j); double r_val = std::real (val); double i_val = std::imag (val); if (r_val > max_val) max_val = r_val; if (i_val > max_val) max_val = i_val; if (r_val < min_val) min_val = r_val; if (i_val < min_val) min_val = i_val; if (D_NINT (r_val) != r_val || D_NINT (i_val) != i_val) return false; } return true; } bool ComplexMatrix::too_large_for_float (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { Complex val = elem (i, j); double r_val = std::real (val); double i_val = std::imag (val); if ((! (xisnan (r_val) || xisinf (r_val)) && fabs (r_val) > FLT_MAX) || (! (xisnan (i_val) || xisinf (i_val)) && fabs (i_val) > FLT_MAX)) return true; } return false; } // FIXME Do these really belong here? Maybe they should be // in a base class? boolMatrix ComplexMatrix::all (int dim) const { return do_mx_red_op<bool, Complex> (*this, dim, mx_inline_all); } boolMatrix ComplexMatrix::any (int dim) const { return do_mx_red_op<bool, Complex> (*this, dim, mx_inline_any); } ComplexMatrix ComplexMatrix::cumprod (int dim) const { return do_mx_cum_op<Complex, Complex> (*this, dim, mx_inline_cumprod); } ComplexMatrix ComplexMatrix::cumsum (int dim) const { return do_mx_cum_op<Complex, Complex> (*this, dim, mx_inline_cumsum); } ComplexMatrix ComplexMatrix::prod (int dim) const { return do_mx_red_op<Complex, Complex> (*this, dim, mx_inline_prod); } ComplexMatrix ComplexMatrix::sum (int dim) const { return do_mx_red_op<Complex, Complex> (*this, dim, mx_inline_sum); } ComplexMatrix ComplexMatrix::sumsq (int dim) const { return do_mx_red_op<double, Complex> (*this, dim, mx_inline_sumsq); } Matrix ComplexMatrix::abs (void) const { return do_mx_unary_map<double, Complex, std::abs> (*this); } ComplexMatrix ComplexMatrix::diag (octave_idx_type k) const { return MArray<Complex>::diag (k); } 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 (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_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_min = elem (i, idx_j); if (! xisnan (tmp_min)) { abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (xisnan (tmp)) continue; double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp < abs_min) { idx_j = j; tmp_min = tmp; abs_min = abs_tmp; } } if (xisnan (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 (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_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_max = elem (i, idx_j); if (! xisnan (tmp_max)) { abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (xisnan (tmp)) continue; double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp > abs_max) { idx_j = j; tmp_max = tmp; abs_max = abs_tmp; } } if (xisnan (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 (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_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_min = elem (idx_i, j); if (! xisnan (tmp_min)) { abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (xisnan (tmp)) continue; double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp < abs_min) { idx_i = i; tmp_min = tmp; abs_min = abs_tmp; } } if (xisnan (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 (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_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_max = elem (idx_i, j); if (! xisnan (tmp_max)) { abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (xisnan (tmp)) continue; double abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp > abs_max) { idx_i = i; tmp_max = tmp; abs_max = abs_tmp; } } if (xisnan (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_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 goto done; } } done: return is; } ComplexMatrix Givens (const Complex& x, const Complex& y) { double cc; Complex cs, temp_r; F77_FUNC (zlartg, ZLARTG) (x, y, cc, cs, 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 ComplexSCHUR as (a, "U"); ComplexSCHUR 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. octave_idx_type a_nr = a.rows (); octave_idx_type b_nr = b.rows (); double scale; octave_idx_type 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, pa, a_nr, pb, b_nr, 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],1e-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, trb = transb != blas_no_trans; bool cja = transa == blas_conj_trans, cjb = transb == blas_conj_trans; octave_idx_type a_nr = tra ? a.cols () : a.rows (); octave_idx_type a_nc = tra ? a.rows () : a.cols (); octave_idx_type b_nr = trb ? b.cols () : b.rows (); octave_idx_type b_nc = trb ? b.rows () : b.cols (); if (a_nc != b_nr) gripe_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); else { 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) { octave_idx_type lda = a.rows (); retval = ComplexMatrix (a_nr, b_nc); 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, a.data (), lda, 0.0, c, a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = std::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, a.data (), lda, 0.0, c, a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = retval.xelem (i,j); } } else { octave_idx_type lda = a.rows (), tda = a.cols (); octave_idx_type ldb = b.rows (), tdb = b.cols (); retval = ComplexMatrix (a_nr, b_nc); Complex *c = retval.fortran_vec (); if (b_nc == 1 && a_nr == 1) { if (cja == cjb) { F77_FUNC (xzdotu, XZDOTU) (a_nc, a.data (), 1, b.data (), 1, *c); if (cja) *c = std::conj (*c); } else if (cja) F77_FUNC (xzdotc, XZDOTC) (a_nc, a.data (), 1, b.data (), 1, *c); else F77_FUNC (xzdotc, XZDOTC) (a_nc, b.data (), 1, a.data (), 1, *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, a.data (), lda, b.data (), 1, 0.0, 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, b.data (), ldb, a.data (), 1, 0.0, 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, a.data (), lda, b.data (), ldb, 0.0, 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) = xmin (c, m (i, j)); } return result; } ComplexMatrix min (const ComplexMatrix& m, const Complex& c) { 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) = xmin (m (i, j), c); } return result; } 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 expecting args of same size"); return ComplexMatrix (); } EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { int columns_are_real_only = 1; 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 = 0; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) result (i, j) = xmin (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) = xmin (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) = xmax (c, m (i, j)); } return result; } ComplexMatrix max (const ComplexMatrix& m, const Complex& c) { 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) = xmax (m (i, j), c); } return result; } 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 expecting args of same size"); return ComplexMatrix (); } EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { int columns_are_real_only = 1; 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 = 0; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result (i, j) = xmax (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) = xmax (a (i, j), b (i, j)); } } } return result; } ComplexMatrix linspace (const ComplexColumnVector& x1, const ComplexColumnVector& x2, octave_idx_type n) { if (n < 1) n = 1; octave_idx_type m = x1.length (); if (x2.length () != m) (*current_liboctave_error_handler) ("linspace: vectors must be of equal length"); NoAlias<ComplexMatrix> retval; retval.clear (m, n); for (octave_idx_type i = 0; i < m; i++) retval(i, 0) = x1(i); // The last column is not needed while using delta. Complex *delta = &retval(0, n-1); for (octave_idx_type i = 0; i < m; i++) delta[i] = (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(i, j) = x1(i) + static_cast<double> (j)*delta[i]; for (octave_idx_type i = 0; i < m; i++) retval(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)