Mercurial > octave-nkf
view liboctave/fCMatrix.cc @ 7948:af10baa63915 ss-3-1-50
3.1.50 snapshot
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 18 Jul 2008 17:42:48 -0400 |
| parents | 935be827eaf8 |
| children | 851803f7bb4d |
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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 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 "fCmplxDET.h" #include "fCmplxSCHUR.h" #include "fCmplxSVD.h" #include "fCmplxCHOL.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-fcm-fdm.h" #include "mx-fdm-fcm.h" #include "mx-fcm-fs.h" #include "mx-inlines.cc" #include "oct-cmplx.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 { FloatComplexDET retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr == 0 || nc == 0) { retval = FloatComplexDET (1.0, 0); } else { 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 = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (cgetrf, CGETRF, (nr, 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; retval = FloatComplexDET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<FloatComplex> z (2*nr); FloatComplex *pz = z.fortran_vec (); Array<float> rz (2*nr); 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 { FloatComplex c = 1.0; int e = 0; for (octave_idx_type i = 0; i < nc; i++) { if (ipvt(i) != (i+1)) c = -c; c *= atmp(i,i); if (c == static_cast<float> (0.0)) break; while (std::abs(c) < 0.5) { c *= 2.0; e--; } while (std::abs(c) >= 2.0) { c /= 2.0; e++; } } retval = FloatComplexDET (c, e); } } } 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); } FloatComplexMatrix FloatComplexMatrix::expm (void) const { FloatComplexMatrix retval; FloatComplexMatrix m = *this; octave_idx_type nc = columns (); // Preconditioning step 1: trace normalization to reduce dynamic // range of poles, but avoid making stable eigenvalues unstable. // trace shift value FloatComplex trshift = 0.0; for (octave_idx_type i = 0; i < nc; i++) trshift += m.elem (i, i); trshift /= nc; if (trshift.real () < 0.0) { trshift = trshift.imag (); if (trshift.real () > 709.0) trshift = 709.0; } for (octave_idx_type i = 0; i < nc; i++) m.elem (i, i) -= trshift; // Preconditioning step 2: eigenvalue balancing. // code follows development in AEPBAL FloatComplex *mp = m.fortran_vec (); octave_idx_type info, ilo, ihi,ilos,ihis; Array<float> dpermute (nc); Array<float> dscale (nc); // FIXME -- should pass job as a parameter in expm // Permute first char job = 'P'; F77_XFCN (cgebal, CGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), nc, mp, nc, ilo, ihi, dpermute.fortran_vec (), info F77_CHAR_ARG_LEN (1))); // then scale job = 'S'; F77_XFCN (cgebal, CGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), nc, mp, nc, ilos, ihis, dscale.fortran_vec (), info F77_CHAR_ARG_LEN (1))); // Preconditioning step 3: scaling. FloatColumnVector work (nc); float inf_norm; F77_XFCN (xclange, XCLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), nc, nc, m.fortran_vec (), nc, work.fortran_vec (), inf_norm F77_CHAR_ARG_LEN (1))); int sqpow = (inf_norm > 0.0 ? static_cast<int> (1.0 + log (inf_norm) / log (2.0)) : 0); // Check whether we need to square at all. if (sqpow < 0) sqpow = 0; if (sqpow > 0) { if (sqpow > 1023) sqpow = 1023; float scale_factor = 1.0; for (octave_idx_type i = 0; i < sqpow; i++) scale_factor *= 2.0; m = m / scale_factor; } // npp, dpp: pade' approx polynomial matrices. FloatComplexMatrix npp (nc, nc, 0.0); FloatComplex *pnpp = npp.fortran_vec (); FloatComplexMatrix dpp = npp; FloatComplex *pdpp = dpp.fortran_vec (); // Now powers a^8 ... a^1. int minus_one_j = -1; for (octave_idx_type j = 7; j >= 0; j--) { for (octave_idx_type i = 0; i < nc; i++) { octave_idx_type k = i * nc + i; pnpp[k] += padec[j]; pdpp[k] += minus_one_j * padec[j]; } npp = m * npp; pnpp = npp.fortran_vec (); dpp = m * dpp; pdpp = dpp.fortran_vec (); minus_one_j *= -1; } // Zero power. dpp = -dpp; for (octave_idx_type j = 0; j < nc; j++) { npp.elem (j, j) += 1.0; dpp.elem (j, j) += 1.0; } // Compute pade approximation = inverse (dpp) * npp. float rcon; retval = dpp.solve (npp, info, rcon, solve_singularity_warning); if (info < 0) return retval; // Reverse preconditioning step 3: repeated squaring. while (sqpow) { retval = retval * retval; sqpow--; } // Reverse preconditioning step 2: inverse balancing. // Done in two steps: inverse scaling, then inverse permutation // inverse scaling (diagonal transformation) for (octave_idx_type i = 0; i < nc; i++) for (octave_idx_type j = 0; j < nc; j++) retval(i,j) *= dscale(i) / dscale(j); OCTAVE_QUIT; // construct balancing permutation vector Array<octave_idx_type> iperm (nc); for (octave_idx_type i = 0; i < nc; i++) iperm(i) = i; // initialize to identity permutation // leading permutations in forward order for (octave_idx_type i = 0; i < (ilo-1); i++) { octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; octave_idx_type tmp = iperm(i); iperm(i) = iperm(swapidx); iperm(swapidx) = tmp; } // construct inverse balancing permutation vector Array<octave_idx_type> invpvec (nc); for (octave_idx_type i = 0; i < nc; i++) invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method OCTAVE_QUIT; FloatComplexMatrix tmpMat = retval; for (octave_idx_type i = 0; i < nc; i++) for (octave_idx_type j = 0; j < nc; j++) retval(i,j) = tmpMat(invpvec(i),invpvec(j)); OCTAVE_QUIT; for (octave_idx_type i = 0; i < nc; i++) iperm(i) = i; // initialize to identity permutation // trailing permutations must be done in reverse order for (octave_idx_type i = nc - 1; i >= ihi; i--) { octave_idx_type swapidx = static_cast<octave_idx_type> (dpermute(i)) - 1; octave_idx_type tmp = iperm(i); iperm(i) = iperm(swapidx); iperm(swapidx) = tmp; } // construct inverse balancing permutation vector for (octave_idx_type i = 0; i < nc; i++) invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method OCTAVE_QUIT; tmpMat = retval; for (octave_idx_type i = 0; i < nc; i++) for (octave_idx_type j = 0; j < nc; j++) retval(i,j) = tmpMat(invpvec(i),invpvec(j)); // Reverse preconditioning step 1: fix trace normalization. return exp (trshift) * retval; } // 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: *** */