Mercurial > hg > octave-lyh
view liboctave/fCMatrix.cc @ 8535:75e6ab186761
lexer debugging functions
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 19 Jan 2009 16:53:30 -0500 |
| parents | c187f0e3a7ee |
| children | 5114ea5a41b5 |
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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 Jaroslav Hajek 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 #ifdef HAVE_SYS_TYPES_H #include <sys/types.h> #endif #include "Array-util.h" #include "fCMatrix.h" #include "DET.h" #include "fCmplxSCHUR.h" #include "fCmplxSVD.h" #include "fCmplxCHOL.h" #include "f77-fcn.h" #include "functor.h" #include "lo-error.h" #include "oct-locbuf.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-base.h" #include "mx-fcm-fdm.h" #include "mx-fdm-fcm.h" #include "mx-fcm-fs.h" #include "mx-inlines.cc" #include "oct-cmplx.h" #include "oct-norm.h" #if defined (HAVE_FFTW3) #include "oct-fftw.h" #endif // 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 (cgebal, CGEBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type&, octave_idx_type&, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (sgebak, SGEBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, float*, const octave_idx_type&, float*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgemm, CGEMM) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgemv, CGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xcdotu, XCDOTU) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex&); F77_RET_T F77_FUNC (xcdotc, XCDOTC) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex&); F77_RET_T F77_FUNC (csyrk, CSYRK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cherk, CHERK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgetrf, CGETRF) (const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (cgetrs, CGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const octave_idx_type*, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgetri, CGETRI) (const octave_idx_type&, FloatComplex*, const octave_idx_type&, const octave_idx_type*, FloatComplex*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (cgecon, CGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const float&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgelsy, CGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type*, float&, octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, octave_idx_type&); F77_RET_T F77_FUNC (cgelsd, CGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, float&, octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (cpotrf, CPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cpocon, CPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const float&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cpotrs, CPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrtri, CTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrcon, CTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrtrs, CTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex*, 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 (cffti, CFFTI) (const octave_idx_type&, FloatComplex*); F77_RET_T F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, FloatComplex*, FloatComplex*); F77_RET_T F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, FloatComplex*, FloatComplex*); F77_RET_T F77_FUNC (clartg, CLARTG) (const FloatComplex&, const FloatComplex&, float&, FloatComplex&, FloatComplex&); F77_RET_T F77_FUNC (ctrsyl, CTRSYL) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xclange, XCLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float*, float& F77_CHAR_ARG_LEN_DECL); } static const FloatComplex FloatComplex_NaN_result (octave_Float_NaN, octave_Float_NaN); // FloatComplex Matrix class FloatComplexMatrix::FloatComplexMatrix (const FloatMatrix& a) : MArray2<FloatComplex> (a.rows (), a.cols ()) { for (octave_idx_type j = 0; j < cols (); j++) for (octave_idx_type i = 0; i < rows (); i++) elem (i, j) = a.elem (i, j); } FloatComplexMatrix::FloatComplexMatrix (const FloatRowVector& rv) : MArray2<FloatComplex> (1, rv.length (), 0.0) { for (octave_idx_type i = 0; i < rv.length (); i++) elem (0, i) = rv.elem (i); } FloatComplexMatrix::FloatComplexMatrix (const FloatColumnVector& cv) : MArray2<FloatComplex> (cv.length (), 1, 0.0) { for (octave_idx_type i = 0; i < cv.length (); i++) elem (i, 0) = cv.elem (i); } FloatComplexMatrix::FloatComplexMatrix (const FloatDiagMatrix& a) : MArray2<FloatComplex> (a.rows (), a.cols (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexRowVector& rv) : MArray2<FloatComplex> (1, rv.length (), 0.0) { for (octave_idx_type i = 0; i < rv.length (); i++) elem (0, i) = rv.elem (i); } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexColumnVector& cv) : MArray2<FloatComplex> (cv.length (), 1, 0.0) { for (octave_idx_type i = 0; i < cv.length (); i++) elem (i, 0) = cv.elem (i); } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexDiagMatrix& a) : MArray2<FloatComplex> (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? FloatComplexMatrix::FloatComplexMatrix (const boolMatrix& a) : MArray2<FloatComplex> (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) = a.elem (i, j); } FloatComplexMatrix::FloatComplexMatrix (const charMatrix& a) : MArray2<FloatComplex> (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) = a.elem (i, j); } bool FloatComplexMatrix::operator == (const FloatComplexMatrix& a) const { if (rows () != a.rows () || cols () != a.cols ()) return false; return mx_inline_equal (data (), a.data (), length ()); } bool FloatComplexMatrix::operator != (const FloatComplexMatrix& a) const { return !(*this == a); } bool FloatComplexMatrix::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 FloatComplexMatrix& FloatComplexMatrix::insert (const FloatMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatRowVector& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatColumnVector& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatDiagMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexMatrix& a, octave_idx_type r, octave_idx_type c) { Array2<FloatComplex>::insert (a, r, c); return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexRowVector& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexColumnVector& 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; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexDiagMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::fill (float 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; } FloatComplexMatrix& FloatComplexMatrix::fill (const FloatComplex& 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; } FloatComplexMatrix& FloatComplexMatrix::fill (float 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; } FloatComplexMatrix& FloatComplexMatrix::fill (const FloatComplex& 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; } FloatComplexMatrix FloatComplexMatrix::append (const FloatMatrix& 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; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatRowVector& 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; FloatComplexMatrix retval (nr, nc + a.length ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatColumnVector& 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; FloatComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatDiagMatrix& 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; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexMatrix& 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; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexRowVector& 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; FloatComplexMatrix retval (nr, nc + a.length ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexColumnVector& 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; FloatComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexDiagMatrix& 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; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatMatrix& 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; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatRowVector& 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; FloatComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatColumnVector& 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; FloatComplexMatrix retval (nr + a.length (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatDiagMatrix& 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; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexMatrix& 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; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexRowVector& 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; FloatComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexColumnVector& 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; FloatComplexMatrix retval (nr + a.length (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexDiagMatrix& 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; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix conj (const FloatComplexMatrix& a) { octave_idx_type a_len = a.length (); FloatComplexMatrix retval; if (a_len > 0) retval = FloatComplexMatrix (mx_inline_conj_dup (a.data (), a_len), a.rows (), a.cols ()); return retval; } // resize is the destructive equivalent for this one FloatComplexMatrix FloatComplexMatrix::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; } octave_idx_type new_r = r2 - r1 + 1; octave_idx_type new_c = c2 - c1 + 1; FloatComplexMatrix result (new_r, new_c); for (octave_idx_type j = 0; j < new_c; j++) for (octave_idx_type i = 0; i < new_r; i++) result.xelem (i, j) = elem (r1+i, c1+j); return result; } FloatComplexMatrix FloatComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const { FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) result.xelem (i, j) = elem (r1+i, c1+j); return result; } // extract row or column i. FloatComplexRowVector FloatComplexMatrix::row (octave_idx_type i) const { octave_idx_type nc = cols (); if (i < 0 || i >= rows ()) { (*current_liboctave_error_handler) ("invalid row selection"); return FloatComplexRowVector (); } FloatComplexRowVector retval (nc); for (octave_idx_type j = 0; j < cols (); j++) retval.xelem (j) = elem (i, j); return retval; } FloatComplexColumnVector FloatComplexMatrix::column (octave_idx_type i) const { octave_idx_type nr = rows (); if (i < 0 || i >= cols ()) { (*current_liboctave_error_handler) ("invalid column selection"); return FloatComplexColumnVector (); } FloatComplexColumnVector retval (nr); for (octave_idx_type j = 0; j < nr; j++) retval.xelem (j) = elem (j, i); return retval; } FloatComplexMatrix FloatComplexMatrix::inverse (void) const { octave_idx_type info; float rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (octave_idx_type& info) const { float rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (octave_idx_type& info, float& rcon, int force, int calc_cond) const { MatrixType mattype (*this); return inverse (mattype, info, rcon, force, calc_cond); } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype) const { octave_idx_type info; float rcon; return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const { float rcon; return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatComplexMatrix 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; FloatComplex *tmp_data = retval.fortran_vec (); F77_XFCN (ctrtri, CTRTRI, (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 (FloatComplex, cwork, 2*nr); OCTAVE_LOCAL_BUFFER (float, rwork, nr); F77_XFCN (ctrcon, CTRCON, (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; } FloatComplexMatrix FloatComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatComplexMatrix 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); octave_idx_type *pipvt = ipvt.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); Array<FloatComplex> z(1); octave_idx_type lwork = -1; // Query the optimum work array size. F77_XFCN (cgetri, CGETRI, (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); FloatComplex *pz = z.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. float anorm; if (calc_cond) anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (cgetrf, CGETRF, (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<float> rz (2 * nc); float *prz = rz.fortran_vec (); F77_XFCN (cgecon, CGECON, (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 (cgetri, CGETRI, (nc, tmp_data, nr, pipvt, pz, lwork, zgetri_info)); if (zgetri_info != 0) info = -1; } if (info != 0) mattype.mark_as_rectangular(); } return retval; } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { int typ = mattype.type (false); FloatComplexMatrix 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 ()) { FloatComplexCHOL 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 = FloatComplexMatrix (rows (), columns (), FloatComplex (octave_Float_Inf, 0.)); } return ret; } FloatComplexMatrix FloatComplexMatrix::pseudo_inverse (float tol) const { FloatComplexMatrix retval; FloatComplexSVD result (*this, SVD::economy); FloatDiagMatrix S = result.singular_values (); FloatComplexMatrix U = result.left_singular_matrix (); FloatComplexMatrix V = result.right_singular_matrix (); FloatColumnVector 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 = FloatComplexMatrix (nc, nr, 0.0); else { FloatComplexMatrix Ur = U.extract (0, 0, nr-1, r); FloatDiagMatrix D = FloatDiagMatrix (sigma.extract (0, r)) . inverse (); FloatComplexMatrix Vr = V.extract (0, 0, nc-1, r); retval = Vr * D * Ur.hermitian (); } return retval; } #if defined (HAVE_FFTW3) FloatComplexMatrix FloatComplexMatrix::fourier (void) const { size_t nr = rows (); size_t nc = cols (); FloatComplexMatrix 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 FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::fft (in, out, npts, nsamples); return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier (void) const { size_t nr = rows (); size_t nc = cols (); FloatComplexMatrix 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 FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::ifft (in, out, npts, nsamples); return retval; } FloatComplexMatrix FloatComplexMatrix::fourier2d (void) const { dim_vector dv(rows (), cols ()); FloatComplexMatrix retval (rows (), cols ()); const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::fftNd (in, out, 2, dv); return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier2d (void) const { dim_vector dv(rows (), cols ()); FloatComplexMatrix retval (rows (), cols ()); const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::ifftNd (in, out, 2, dv); return retval; } #else FloatComplexMatrix FloatComplexMatrix::fourier (void) const { FloatComplexMatrix 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<FloatComplex> wsave (nn); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { OCTAVE_QUIT; F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); } return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier (void) const { FloatComplexMatrix 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<FloatComplex> wsave (nn); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { OCTAVE_QUIT; F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<float> (npts); return retval; } FloatComplexMatrix FloatComplexMatrix::fourier2d (void) const { FloatComplexMatrix 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<FloatComplex> wsave (nn); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { OCTAVE_QUIT; F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); } npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (nn); pwsave = wsave.fortran_vec (); Array<FloatComplex> tmp (npts); FloatComplex *prow = tmp.fortran_vec (); F77_FUNC (cffti, CFFTI) (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 (cfftf, CFFTF) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i]; } return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier2d (void) const { FloatComplexMatrix 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<FloatComplex> wsave (nn); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { OCTAVE_QUIT; F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<float> (npts); npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (nn); pwsave = wsave.fortran_vec (); Array<FloatComplex> tmp (npts); FloatComplex *prow = tmp.fortran_vec (); F77_FUNC (cffti, CFFTI) (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 (cfftb, CFFTB) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i] / static_cast<float> (npts); } return retval; } #endif FloatComplexDET FloatComplexMatrix::determinant (void) const { octave_idx_type info; float rcon; return determinant (info, rcon, 0); } FloatComplexDET FloatComplexMatrix::determinant (octave_idx_type& info) const { float rcon; return determinant (info, rcon, 0); } FloatComplexDET FloatComplexMatrix::determinant (octave_idx_type& info, float& rcon, int calc_cond) const { MatrixType mattype (*this); return determinant (mattype, info, rcon, calc_cond); } FloatComplexDET FloatComplexMatrix::determinant (MatrixType& mattype, octave_idx_type& info, float& rcon, int calc_cond) const { FloatComplexDET 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 { int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); 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) { FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); info = 0; float anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); char job = 'L'; F77_XFCN (cpotrf, CPOTRF, (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<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (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); octave_idx_type *pipvt = ipvt.fortran_vec (); FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. float anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); F77_XFCN (cgetrf, CGETRF, (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 = FloatComplexDET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (2 * nc); float *prz = rz.fortran_vec (); F77_XFCN (cgecon, CGECON, (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 = FloatComplexDET (); } else { for (octave_idx_type i = 0; i < nc; i++) { FloatComplex c = atmp(i,i); retval *= (ipvt(i) != (i+1)) ? -c : c; } } } } } return retval; } float FloatComplexMatrix::rcond (void) const { MatrixType mattype (*this); return rcond (mattype); } float FloatComplexMatrix::rcond (MatrixType &mattype) const { float 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 FloatComplex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (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 FloatComplex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (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) { float anorm = -1.0; FloatComplexMatrix atmp = *this; FloatComplex *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 (cpotrf, CPOTRF, (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<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (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); octave_idx_type *pipvt = ipvt.fortran_vec (); if(anorm < 0.) anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (2 * nc); float *prz = rz.fortran_vec (); F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info)); if (info != 0) { rcon = 0.0; mattype.mark_as_rectangular (); } else { char job = '1'; F77_XFCN (cgecon, CGECON, (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; } FloatComplexMatrix FloatComplexMatrix::utsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { FloatComplexMatrix 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 = FloatComplexMatrix (nc, b.cols (), FloatComplex (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 FloatComplex *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (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 float 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; FloatComplex *result = retval.fortran_vec (); char uplo = 'U'; char trans = 'N'; char dia = 'N'; F77_XFCN (ctrtrs, CTRTRS, (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; } FloatComplexMatrix FloatComplexMatrix::ltsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { FloatComplexMatrix 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 = FloatComplexMatrix (nc, b.cols (), FloatComplex (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 FloatComplex *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (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 float 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; FloatComplex *result = retval.fortran_vec (); char uplo = 'L'; char trans = 'N'; char dia = 'N'; F77_XFCN (ctrtrs, CTRTRS, (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; } FloatComplexMatrix FloatComplexMatrix::fsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { FloatComplexMatrix 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 = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0)); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix, for later use. float anorm = -1.; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (cpotrf, CPOTRF, (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<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (nc); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (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 float 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; FloatComplex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (cpotrs, CPOTRS, (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); octave_idx_type *pipvt = ipvt.fortran_vec (); FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); Array<FloatComplex> z (2 * nc); FloatComplex *pz = z.fortran_vec (); Array<float> rz (2 * nc); float *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 (cgetrf, CGETRF, (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 (cgecon, CGECON, (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 float 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; FloatComplex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (cgetrs, CGETRS, (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; } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool singular_fallback) const { FloatComplexMatrix tmp (b); return solve (typ, tmp, info, rcon, sing_handler, singular_fallback); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool singular_fallback) const { FloatComplexMatrix 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); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcon, sing_handler, false); 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 FloatComplexMatrix (); } // 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; } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b) const { octave_idx_type info; float rcon; return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info) const { float rcon; return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { return solve (typ, FloatComplexColumnVector (b), info, rcon, sing_handler); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { FloatComplexMatrix tmp (b); return solve (typ, tmp, info, rcon, sing_handler).column(static_cast<octave_idx_type> (0)); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { FloatComplexMatrix tmp (b); return solve (tmp, info, rcon, sing_handler); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b) const { octave_idx_type info; float rcon; return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info) const { float rcon; return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { return solve (FloatComplexColumnVector (b), info, rcon, sing_handler); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { FloatComplexMatrix 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 = FloatComplexMatrix (n, b.cols (), FloatComplex (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 = FloatComplexMatrix (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; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); FloatComplex *pretval = retval.fortran_vec (); Array<float> s (minmn); float *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<FloatComplex> work (1); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 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 ("CGELSD", 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. float dminmn = static_cast<float> (minmn); float dsmlsizp1 = static_cast<float> (smlsiz+1); #if defined (HAVE_LOG2) float tmp = log2 (dminmn / dsmlsizp1); #else float 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<float> rwork (lrwork); float *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (liwork); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (cgelsd, CGELSD, (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 >= 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); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); if (rank < minmn) (*current_liboctave_warning_handler) ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", m, n, rank, rcon); if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } return retval; } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { FloatComplexColumnVector 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 = FloatComplexColumnVector (n, FloatComplex (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 = FloatComplexColumnVector (maxmn); for (octave_idx_type i = 0; i < m; i++) retval.elem (i) = b.elem (i); } else retval = b; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); FloatComplex *pretval = retval.fortran_vec (); Array<float> s (minmn); float *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<FloatComplex> work (1); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 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. float dminmn = static_cast<float> (minmn); float dsmlsizp1 = static_cast<float> (smlsiz+1); #if defined (HAVE_LOG2) float tmp = log2 (dminmn / dsmlsizp1); #else float 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<float> rwork (lrwork); float *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (liwork); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (cgelsd, CGELSD, (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); rwork.resize (static_cast<octave_idx_type> (rwork(0))); iwork.resize (iwork(0)); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); if (rank < minmn) { if (rank < minmn) (*current_liboctave_warning_handler) ("zgelsd: rank deficient %dx%d matrix, rank = %d, tol = %e", m, n, rank, rcon); if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } return retval; } // Constants for matrix exponential calculation. static float padec [] = { 5.0000000000000000e-1, 1.1666666666666667e-1, 1.6666666666666667e-2, 1.6025641025641026e-3, 1.0683760683760684e-4, 4.8562548562548563e-6, 1.3875013875013875e-7, 1.9270852604185938e-9, }; static void solve_singularity_warning (float rcon) { (*current_liboctave_warning_handler) ("singular matrix encountered in expm calculation, rcond = %g", rcon); } // column vector by row vector -> matrix operations FloatComplexMatrix operator * (const FloatColumnVector& v, const FloatComplexRowVector& a) { FloatComplexColumnVector tmp (v); return tmp * a; } FloatComplexMatrix operator * (const FloatComplexColumnVector& a, const FloatRowVector& b) { FloatComplexRowVector tmp (b); return a * tmp; } FloatComplexMatrix operator * (const FloatComplexColumnVector& v, const FloatComplexRowVector& a) { FloatComplexMatrix retval; octave_idx_type len = v.length (); if (len != 0) { octave_idx_type a_len = a.length (); retval.resize (len, a_len); FloatComplex *c = retval.fortran_vec (); F77_XFCN (cgemm, CGEMM, (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 FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatDiagMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatDiagMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatComplexDiagMatrix& 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; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatComplexDiagMatrix& 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 FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatMatrix& 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; FloatComplex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_add2 (d, a.data (), length ()); return *this; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatMatrix& 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; FloatComplex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_subtract2 (d, a.data (), length ()); return *this; } // unary operations boolMatrix FloatComplexMatrix::operator ! (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); boolMatrix b (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) b.elem (i, j) = elem (i, j) == static_cast<float> (0.0); return b; } // other operations FloatMatrix FloatComplexMatrix::map (dmapper fcn) const { return MArray2<FloatComplex>::map<float> (func_ptr (fcn)); } FloatComplexMatrix FloatComplexMatrix::map (cmapper fcn) const { return MArray2<FloatComplex>::map<FloatComplex> (func_ptr (fcn)); } boolMatrix FloatComplexMatrix::map (bmapper fcn) const { return MArray2<FloatComplex>::map<bool> (func_ptr (fcn)); } bool FloatComplexMatrix::any_element_is_nan (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++) { FloatComplex val = elem (i, j); if (xisnan (val)) return true; } return false; } bool FloatComplexMatrix::any_element_is_inf_or_nan (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++) { FloatComplex val = elem (i, j); if (xisinf (val) || xisnan (val)) return true; } return false; } // Return true if no elements have imaginary components. bool FloatComplexMatrix::all_elements_are_real (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++) { float ip = std::imag (elem (i, j)); if (ip != 0.0 || lo_ieee_signbit (ip)) return false; } } return true; } // 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 FloatComplexMatrix::all_integers (float& max_val, float& min_val) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { FloatComplex val = elem (0, 0); float r_val = std::real (val); float 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++) { FloatComplex val = elem (i, j); float r_val = std::real (val); float 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 FloatComplexMatrix::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++) { FloatComplex val = elem (i, j); float r_val = std::real (val); float 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 FloatComplexMatrix::all (int dim) const { // FIXME Can't use MX_ALL_OP as need to static cast to float to the ROW // and COL expressions #define ROW_EXPR \ if (elem (i, j) == static_cast<float> (0.0)) \ { \ retval.elem (i, 0) = false; \ break; \ } #define COL_EXPR \ if (elem (i, j) == static_cast<float> (0.0)) \ { \ retval.elem (0, j) = false; \ break; \ } MX_BASE_REDUCTION_OP (boolMatrix, ROW_EXPR, COL_EXPR, true, true); #undef ROW_EXPR #undef COL_EXPR } boolMatrix FloatComplexMatrix::any (int dim) const { // FIXME Can't use MX_ANY_OP as need to static cast to float to the ROW // and COL expressions #define ROW_EXPR \ if (elem (i, j) != static_cast<float> (0.0)) \ { \ retval.elem (i, 0) = true; \ break; \ } #define COL_EXPR \ if (elem (i, j) != static_cast<float> (0.0)) \ { \ retval.elem (0, j) = true; \ break; \ } MX_BASE_REDUCTION_OP (boolMatrix, ROW_EXPR, COL_EXPR, false, false); #undef ROW_EXPR #undef COL_EXPR } FloatComplexMatrix FloatComplexMatrix::cumprod (int dim) const { MX_CUMULATIVE_OP (FloatComplexMatrix, FloatComplex, *=); } FloatComplexMatrix FloatComplexMatrix::cumsum (int dim) const { MX_CUMULATIVE_OP (FloatComplexMatrix, FloatComplex, +=); } FloatComplexMatrix FloatComplexMatrix::prod (int dim) const { MX_REDUCTION_OP (FloatComplexMatrix, *=, 1.0, 1.0); } FloatComplexMatrix FloatComplexMatrix::sum (int dim) const { MX_REDUCTION_OP (FloatComplexMatrix, +=, 0.0, 0.0); } FloatComplexMatrix FloatComplexMatrix::sumsq (int dim) const { #define ROW_EXPR \ FloatComplex d = elem (i, j); \ retval.elem (i, 0) += d * conj (d) #define COL_EXPR \ FloatComplex d = elem (i, j); \ retval.elem (0, j) += d * conj (d) MX_BASE_REDUCTION_OP (FloatComplexMatrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); #undef ROW_EXPR #undef COL_EXPR } FloatMatrix FloatComplexMatrix::abs (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); FloatMatrix retval (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) retval (i, j) = std::abs (elem (i, j)); return retval; } FloatComplexMatrix FloatComplexMatrix::diag (octave_idx_type k) const { return MArray2<FloatComplex>::diag (k); } bool FloatComplexMatrix::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 FloatComplexMatrix::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; } FloatComplexColumnVector FloatComplexMatrix::row_min (void) const { Array<octave_idx_type> dummy_idx; return row_min (dummy_idx); } FloatComplexColumnVector FloatComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const { FloatComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (nr); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; FloatComplex tmp_min; float abs_min = octave_Float_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++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float 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) = FloatComplex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_min; idx_arg.elem (i) = idx_j; } } } return result; } FloatComplexColumnVector FloatComplexMatrix::row_max (void) const { Array<octave_idx_type> dummy_idx; return row_max (dummy_idx); } FloatComplexColumnVector FloatComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const { FloatComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (nr); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; FloatComplex tmp_max; float abs_max = octave_Float_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++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float 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) = FloatComplex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_max; idx_arg.elem (i) = idx_j; } } } return result; } FloatComplexRowVector FloatComplexMatrix::column_min (void) const { Array<octave_idx_type> dummy_idx; return column_min (dummy_idx); } FloatComplexRowVector FloatComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const { FloatComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (nc); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; FloatComplex tmp_min; float abs_min = octave_Float_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++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float 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) = FloatComplex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_min; idx_arg.elem (j) = idx_i; } } } return result; } FloatComplexRowVector FloatComplexMatrix::column_max (void) const { Array<octave_idx_type> dummy_idx; return column_max (dummy_idx); } FloatComplexRowVector FloatComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const { FloatComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (nc); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; FloatComplex tmp_max; float abs_max = octave_Float_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++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float 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) = FloatComplex_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 FloatComplexMatrix& 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, FloatComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr < 1 || nc < 1) is.clear (std::ios::badbit); else { FloatComplex tmp; for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = 0; j < nc; j++) { tmp = octave_read_complex (is); if (is) a.elem (i, j) = tmp; else goto done; } } done: return is; } FloatComplexMatrix Givens (const FloatComplex& x, const FloatComplex& y) { float cc; FloatComplex cs, temp_r; F77_FUNC (clartg, CLARTG) (x, y, cc, cs, temp_r); FloatComplexMatrix 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; } FloatComplexMatrix Sylvester (const FloatComplexMatrix& a, const FloatComplexMatrix& b, const FloatComplexMatrix& c) { FloatComplexMatrix retval; // FIXME -- need to check that a, b, and c are all the same // size. // Compute Schur decompositions FloatComplexSCHUR as (a, "U"); FloatComplexSCHUR bs (b, "U"); // Transform c to new coordinates. FloatComplexMatrix ua = as.unitary_matrix (); FloatComplexMatrix sch_a = as.schur_matrix (); FloatComplexMatrix ub = bs.unitary_matrix (); FloatComplexMatrix sch_b = bs.schur_matrix (); FloatComplexMatrix 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 (); float scale; octave_idx_type info; FloatComplex *pa = sch_a.fortran_vec (); FloatComplex *pb = sch_b.fortran_vec (); FloatComplex *px = cx.fortran_vec (); F77_XFCN (ctrsyl, CTRSYL, (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; } FloatComplexMatrix operator * (const FloatComplexMatrix& m, const FloatMatrix& a) { FloatComplexMatrix tmp (a); return m * tmp; } FloatComplexMatrix operator * (const FloatMatrix& m, const FloatComplexMatrix& a) { FloatComplexMatrix tmp (m); return tmp * 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) */ /* 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([rv*M;rv*M],[rv;rv]*M,1e-14) %!assert(2*rv*cv,[rv,rv]*[cv;cv],1e-14) */ static const char * get_blas_trans_arg (bool trans, bool conj) { static char blas_notrans = 'N', blas_trans = 'T', blas_conj_trans = 'C'; return trans ? (conj ? &blas_conj_trans : &blas_trans) : &blas_notrans; } // the general GEMM operation FloatComplexMatrix xgemm (bool transa, bool conja, const FloatComplexMatrix& a, bool transb, bool conjb, const FloatComplexMatrix& b) { FloatComplexMatrix retval; // conjugacy is ignored if no transpose conja = conja && transa; conjb = conjb && transb; octave_idx_type a_nr = transa ? a.cols () : a.rows (); octave_idx_type a_nc = transa ? a.rows () : a.cols (); octave_idx_type b_nr = transb ? b.cols () : b.rows (); octave_idx_type b_nc = transb ? 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.resize (a_nr, b_nc, 0.0); else if (a.data () == b.data () && a_nr == b_nc && transa != transb) { octave_idx_type lda = a.rows (); retval.resize (a_nr, b_nc); FloatComplex *c = retval.fortran_vec (); const char *ctransa = get_blas_trans_arg (transa, conja); if (conja || conjb) { F77_XFCN (cherk, CHERK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (ctransa, 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 (int j = 0; j < a_nr; j++) for (int i = 0; i < j; i++) retval.xelem (j,i) = std::conj (retval.xelem (i,j)); } else { F77_XFCN (csyrk, CSYRK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (ctransa, 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 (int j = 0; j < a_nr; j++) for (int 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.resize (a_nr, b_nc); FloatComplex *c = retval.fortran_vec (); if (b_nc == 1 && a_nr == 1) { if (conja == conjb) { F77_FUNC (xcdotu, XCDOTU) (a_nc, a.data (), 1, b.data (), 1, *c); if (conja) *c = std::conj (*c); } else if (conjb) F77_FUNC (xcdotc, XCDOTC) (a_nc, a.data (), 1, b.data (), 1, *c); else F77_FUNC (xcdotc, XCDOTC) (a_nc, b.data (), 1, a.data (), 1, *c); } else if (b_nc == 1 && ! conjb) { const char *ctransa = get_blas_trans_arg (transa, conja); F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (ctransa, 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 && ! conja) { const char *crevtransb = get_blas_trans_arg (! transb, conjb); F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (crevtransb, 1), ldb, tdb, 1.0, b.data (), ldb, a.data (), 1, 0.0, c, 1 F77_CHAR_ARG_LEN (1))); } else { const char *ctransa = get_blas_trans_arg (transa, conja); const char *ctransb = get_blas_trans_arg (transb, conjb); F77_XFCN (cgemm, CGEMM, (F77_CONST_CHAR_ARG2 (ctransa, 1), F77_CONST_CHAR_ARG2 (ctransb, 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; } FloatComplexMatrix operator * (const FloatComplexMatrix& a, const FloatComplexMatrix& b) { return xgemm (false, false, a, false, false, 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); FloatComplexMatrix min (const FloatComplex& c, const FloatComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } FloatComplexMatrix min (const FloatComplexMatrix& m, const FloatComplex& c) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } FloatComplexMatrix min (const FloatComplexMatrix& a, const FloatComplexMatrix& 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 FloatComplexMatrix (); } EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } FloatComplexMatrix max (const FloatComplex& c, const FloatComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } FloatComplexMatrix max (const FloatComplexMatrix& m, const FloatComplex& c) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } FloatComplexMatrix max (const FloatComplexMatrix& a, const FloatComplexMatrix& 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 FloatComplexMatrix (); } EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix 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; } MS_CMP_OPS(FloatComplexMatrix, std::real, FloatComplex, std::real) MS_BOOL_OPS(FloatComplexMatrix, FloatComplex, static_cast<float> (0.0)) SM_CMP_OPS(FloatComplex, std::real, FloatComplexMatrix, std::real) SM_BOOL_OPS(FloatComplex, FloatComplexMatrix, static_cast<float> (0.0)) MM_CMP_OPS(FloatComplexMatrix, std::real, FloatComplexMatrix, std::real) MM_BOOL_OPS(FloatComplexMatrix, FloatComplexMatrix, static_cast<float> (0.0)) /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */