Mercurial > octave-nkf
view liboctave/dMatrix.cc @ 7076:0bade2dc44a1
[project @ 2007-10-29 18:09:57 by jwe]
| author | jwe |
|---|---|
| date | Mon, 29 Oct 2007 18:09:57 +0000 |
| parents | b48d486f641d |
| children | 6d3e53a2f963 |
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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> #include "Array-util.h" #include "byte-swap.h" #include "dMatrix.h" #include "dbleAEPBAL.h" #include "dbleDET.h" #include "dbleSCHUR.h" #include "dbleSVD.h" #include "dbleCHOL.h" #include "f77-fcn.h" #include "lo-error.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-base.h" #include "mx-m-dm.h" #include "mx-dm-m.h" #include "mx-inlines.cc" #include "oct-cmplx.h" #include "quit.h" #if defined (HAVE_FFTW3) #include "oct-fftw.h" #endif // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (dgebal, DGEBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&, octave_idx_type&, double*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgemm, DGEMM) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const double&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, const double&, double*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, const double&, double*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xddot, XDDOT) (const octave_idx_type&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, double&); F77_RET_T F77_FUNC (dgetrf, DGETRF) (const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgetri, DGETRI) (const octave_idx_type&, double*, const octave_idx_type&, const octave_idx_type*, double*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, const octave_idx_type&, const double&, double&, double*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgelsy, DGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, double&, octave_idx_type&, double*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (dgelsd, DGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, double*, const octave_idx_type&, double*, const octave_idx_type&, double*, double&, octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (dpotrf, DPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double *, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpocon, DPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, double*, const octave_idx_type&, const double&, double&, double*, octave_idx_type*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dpotrs, DPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dtrtri, DTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dtrcon, DTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double*, const octave_idx_type&, double&, double*, 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 (dtrtrs, DTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); // Note that the original complex fft routines were not written for // double complex arguments. They have been modified by adding an // implicit double precision (a-h,o-z) statement at the beginning of // each subroutine. F77_RET_T F77_FUNC (cffti, CFFTI) (const octave_idx_type&, Complex*); F77_RET_T F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, Complex*, Complex*); F77_RET_T F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, Complex*, Complex*); F77_RET_T F77_FUNC (dlartg, DLARTG) (const double&, const double&, double&, double&, double&); F77_RET_T F77_FUNC (dtrsyl, DTRSYL) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, double&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double*, const octave_idx_type&, double*, double& F77_CHAR_ARG_LEN_DECL); } // Matrix class. Matrix::Matrix (const RowVector& rv) : MArray2<double> (1, rv.length (), 0.0) { for (octave_idx_type i = 0; i < rv.length (); i++) elem (0, i) = rv.elem (i); } Matrix::Matrix (const ColumnVector& cv) : MArray2<double> (cv.length (), 1, 0.0) { for (octave_idx_type i = 0; i < cv.length (); i++) elem (i, 0) = cv.elem (i); } Matrix::Matrix (const DiagMatrix& a) : MArray2<double> (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? Matrix::Matrix (const boolMatrix& a) : MArray2<double> (a.rows (), a.cols ()) { 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); } Matrix::Matrix (const charMatrix& a) : MArray2<double> (a.rows (), a.cols ()) { 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 Matrix::operator == (const Matrix& a) const { if (rows () != a.rows () || cols () != a.cols ()) return false; return mx_inline_equal (data (), a.data (), length ()); } bool Matrix::operator != (const Matrix& a) const { return !(*this == a); } bool Matrix::is_symmetric (void) const { if (is_square () && rows () > 0) { for (octave_idx_type i = 0; i < rows (); i++) for (octave_idx_type j = i+1; j < cols (); j++) if (elem (i, j) != elem (j, i)) return false; return true; } return false; } Matrix& Matrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) { Array2<double>::insert (a, r, c); return *this; } Matrix& Matrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.length (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r, c+i) = a.elem (i); } return *this; } Matrix& Matrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.length (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } Matrix& Matrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) { (*current_liboctave_error_handler) ("range error for insert"); return *this; } fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } Matrix& Matrix::fill (double val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } Matrix& Matrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) { (*current_liboctave_error_handler) ("range error for fill"); return *this; } if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; } if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; } if (r2 >= r1 && c2 >= c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } Matrix Matrix::append (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return Matrix (); } octave_idx_type nc_insert = nc; Matrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } Matrix Matrix::append (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return Matrix (); } octave_idx_type nc_insert = nc; Matrix retval (nr, nc + a.length ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } Matrix Matrix::append (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.length ()) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return Matrix (); } octave_idx_type nc_insert = nc; Matrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } Matrix Matrix::append (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) { (*current_liboctave_error_handler) ("row dimension mismatch for append"); return *this; } octave_idx_type nc_insert = nc; Matrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } Matrix Matrix::stack (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return Matrix (); } octave_idx_type nr_insert = nr; Matrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } Matrix Matrix::stack (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.length ()) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return Matrix (); } octave_idx_type nr_insert = nr; Matrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } Matrix Matrix::stack (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return Matrix (); } octave_idx_type nr_insert = nr; Matrix retval (nr + a.length (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } Matrix Matrix::stack (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) { (*current_liboctave_error_handler) ("column dimension mismatch for stack"); return Matrix (); } octave_idx_type nr_insert = nr; Matrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } Matrix real (const ComplexMatrix& a) { octave_idx_type a_len = a.length (); Matrix retval; if (a_len > 0) retval = Matrix (mx_inline_real_dup (a.data (), a_len), a.rows (), a.cols ()); return retval; } Matrix imag (const ComplexMatrix& a) { octave_idx_type a_len = a.length (); Matrix retval; if (a_len > 0) retval = Matrix (mx_inline_imag_dup (a.data (), a_len), a.rows (), a.cols ()); return retval; } Matrix Matrix::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; Matrix 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; } Matrix Matrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const { Matrix 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. RowVector Matrix::row (octave_idx_type i) const { octave_idx_type nc = cols (); if (i < 0 || i >= rows ()) { (*current_liboctave_error_handler) ("invalid row selection"); return RowVector (); } RowVector retval (nc); for (octave_idx_type j = 0; j < nc; j++) retval.xelem (j) = elem (i, j); return retval; } ColumnVector Matrix::column (octave_idx_type i) const { octave_idx_type nr = rows (); if (i < 0 || i >= cols ()) { (*current_liboctave_error_handler) ("invalid column selection"); return ColumnVector (); } ColumnVector retval (nr); for (octave_idx_type j = 0; j < nr; j++) retval.xelem (j) = elem (j, i); return retval; } Matrix Matrix::inverse (void) const { octave_idx_type info; double rcond; MatrixType mattype (*this); return inverse (mattype, info, rcond, 0, 0); } Matrix Matrix::inverse (octave_idx_type& info) const { double rcond; MatrixType mattype (*this); return inverse (mattype, info, rcond, 0, 0); } Matrix Matrix::inverse (octave_idx_type& info, double& rcond, int force, int calc_cond) const { MatrixType mattype (*this); return inverse (mattype, info, rcond, force, calc_cond); } Matrix Matrix::inverse (MatrixType& mattype) const { octave_idx_type info; double rcond; return inverse (mattype, info, rcond, 0, 0); } Matrix Matrix::inverse (MatrixType &mattype, octave_idx_type& info) const { double rcond; return inverse (mattype, info, rcond, 0, 0); } Matrix Matrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcond, int force, int calc_cond) const { Matrix 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; double *tmp_data = retval.fortran_vec (); F77_XFCN (dtrtri, DTRTRI, (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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrtri"); else { // Throw-away extra info LAPACK gives so as to not change output. rcond = 0.0; if (info != 0) info = -1; else if (calc_cond) { octave_idx_type dtrcon_info = 0; char job = '1'; OCTAVE_LOCAL_BUFFER (double, work, 3 * nr); OCTAVE_LOCAL_BUFFER (octave_idx_type, iwork, nr); F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, tmp_data, nr, rcond, work, iwork, dtrcon_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrcon"); if (dtrcon_info != 0) info = -1; } } if (info == -1 && ! force) retval = *this; // Restore matrix contents. } return retval; } Matrix Matrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcond, int force, int calc_cond) const { Matrix 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 { Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); retval = *this; double *tmp_data = retval.fortran_vec (); Array<double> z(1); octave_idx_type lwork = -1; // Query the optimum work array size. F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, z.fortran_vec (), lwork, info)); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgetri"); return retval; } lwork = static_cast<octave_idx_type> (z(0)); lwork = (lwork < 2 *nc ? 2*nc : lwork); z.resize (lwork); double *pz = z.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. double anorm = 0; if (calc_cond) anorm = retval.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (dgetrf, DGETRF, (nc, nc, tmp_data, nr, pipvt, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); else { // Throw-away extra info LAPACK gives so as to not change output. rcond = 0.0; if (info != 0) info = -1; else if (calc_cond) { octave_idx_type dgecon_info = 0; // Now calculate the condition number for non-singular matrix. char job = '1'; Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcond, pz, piz, dgecon_info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgecon"); if (dgecon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore matrix contents. else { octave_idx_type dgetri_info = 0; F77_XFCN (dgetri, DGETRI, (nc, tmp_data, nr, pipvt, pz, lwork, dgetri_info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgetri"); if (dgetri_info != 0) info = -1; } } if (info != 0) mattype.mark_as_rectangular(); } return retval; } Matrix Matrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcond, int force, int calc_cond) const { int typ = mattype.type (false); Matrix ret; if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Upper || typ == MatrixType::Lower) ret = tinverse (mattype, info, rcond, force, calc_cond); else { if (mattype.is_hermitian ()) { CHOL chol (*this, info, calc_cond); if (info == 0) { if (calc_cond) rcond = chol.rcond (); else rcond = 1.0; ret = chol.inverse (); } else mattype.mark_as_unsymmetric (); } if (!mattype.is_hermitian ()) ret = finverse(mattype, info, rcond, force, calc_cond); if ((mattype.is_hermitian () || calc_cond) && rcond == 0.) ret = Matrix (rows (), columns (), octave_Inf); } return ret; } Matrix Matrix::pseudo_inverse (double tol) const { SVD result (*this, SVD::economy); DiagMatrix S = result.singular_values (); Matrix U = result.left_singular_matrix (); Matrix V = result.right_singular_matrix (); ColumnVector sigma = S.diag (); octave_idx_type r = sigma.length () - 1; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (tol <= 0.0) { if (nr > nc) tol = nr * sigma.elem (0) * DBL_EPSILON; else tol = nc * sigma.elem (0) * DBL_EPSILON; } while (r >= 0 && sigma.elem (r) < tol) r--; if (r < 0) return Matrix (nc, nr, 0.0); else { Matrix Ur = U.extract (0, 0, nr-1, r); DiagMatrix D = DiagMatrix (sigma.extract (0, r)) . inverse (); Matrix Vr = V.extract (0, 0, nc-1, r); return Vr * D * Ur.transpose (); } } #if defined (HAVE_FFTW3) ComplexMatrix Matrix::fourier (void) const { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } const double *in (fortran_vec ()); Complex *out (retval.fortran_vec ()); octave_fftw::fft (in, out, npts, nsamples); return retval; } ComplexMatrix Matrix::ifourier (void) const { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } ComplexMatrix tmp (*this); Complex *in (tmp.fortran_vec ()); Complex *out (retval.fortran_vec ()); octave_fftw::ifft (in, out, npts, nsamples); return retval; } ComplexMatrix Matrix::fourier2d (void) const { dim_vector dv(rows (), cols ()); const double *in = fortran_vec (); ComplexMatrix retval (rows (), cols ()); octave_fftw::fftNd (in, retval.fortran_vec (), 2, dv); return retval; } ComplexMatrix Matrix::ifourier2d (void) const { dim_vector dv(rows (), cols ()); ComplexMatrix retval (*this); Complex *out (retval.fortran_vec ()); octave_fftw::ifftNd (out, out, 2, dv); return retval; } #else ComplexMatrix Matrix::fourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn); Complex *pwsave = wsave.fortran_vec (); retval = ComplexMatrix (*this); Complex *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; } ComplexMatrix Matrix::ifourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn); Complex *pwsave = wsave.fortran_vec (); retval = ComplexMatrix (*this); Complex *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<double> (npts); return retval; } ComplexMatrix Matrix::fourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn); Complex *pwsave = wsave.fortran_vec (); retval = ComplexMatrix (*this); Complex *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<Complex> tmp (npts); Complex *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; } ComplexMatrix Matrix::ifourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (nn); Complex *pwsave = wsave.fortran_vec (); retval = ComplexMatrix (*this); Complex *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<double> (npts); npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (nn); pwsave = wsave.fortran_vec (); Array<Complex> tmp (npts); Complex *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<double> (npts); } return retval; } #endif DET Matrix::determinant (void) const { octave_idx_type info; double rcond; return determinant (info, rcond, 0); } DET Matrix::determinant (octave_idx_type& info) const { double rcond; return determinant (info, rcond, 0); } DET Matrix::determinant (octave_idx_type& info, double& rcond, int calc_cond) const { DET retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr == 0 || nc == 0) { retval = DET (1.0, 0); } else { Array<octave_idx_type> ipvt (nr); octave_idx_type *pipvt = ipvt.fortran_vec (); Matrix atmp = *this; double *tmp_data = atmp.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. double anorm = 0; if (calc_cond) anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); else { // Throw-away extra info LAPACK gives so as to not change output. rcond = 0.0; if (info != 0) { info = -1; retval = DET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<double> z (4 * nc); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcond, pz, piz, info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgecon"); } if (info != 0) { info = -1; retval = DET (); } else { double 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 == 0.0) break; while (fabs (c) < 0.5) { c *= 2.0; e--; } while (fabs (c) >= 2.0) { c /= 2.0; e++; } } retval = DET (c, e); } } } } return retval; } Matrix Matrix::utsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix 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 = Matrix (nc, b.cols (), 0.0); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Upper || typ == MatrixType::Upper) { octave_idx_type b_nc = b.cols (); rcond = 1.; info = 0; if (typ == MatrixType::Permuted_Upper) { (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); } else { const double *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<double> z (3 * nc); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcond, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrcon"); if (info != 0) info = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { info = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } if (info == 0) { retval = b; double *result = retval.fortran_vec (); char uplo = 'U'; char trans = 'N'; char dia = 'N'; F77_XFCN (dtrtrs, DTRTRS, (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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrtrs"); } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix Matrix::ltsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix 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 = Matrix (nc, b.cols (), 0.0); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Lower || typ == MatrixType::Lower) { octave_idx_type b_nc = b.cols (); rcond = 1.; info = 0; if (typ == MatrixType::Permuted_Lower) { (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); } else { const double *tmp_data = fortran_vec (); if (calc_cond) { char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<double> z (3 * nc); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dtrcon, DTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcond, pz, piz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrcon"); if (info != 0) info = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { info = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } if (info == 0) { retval = b; double *result = retval.fortran_vec (); char uplo = 'L'; char trans = 'N'; char dia = 'N'; F77_XFCN (dtrtrs, DTRTRS, (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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrtrs"); } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix Matrix::fsolve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler, bool calc_cond) const { Matrix 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 = Matrix (nc, b.cols (), 0.0); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix, for later use. double anorm = -1.; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; Matrix atmp = *this; double *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpotrf"); else { // Throw-away extra info LAPACK gives so as to not change output. rcond = 0.0; if (info != 0) { info = -2; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { if (calc_cond) { Array<double> z (3 * nc); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcond, pz, piz, info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpocon"); if (info != 0) info = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { info = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } if (info == 0) { retval = b; double *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (dpotrs, DPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, result, b.rows(), info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dpotrs"); } 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 (); Matrix atmp = *this; double *tmp_data = atmp.fortran_vec (); if(anorm < 0.) anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); Array<double> z (4 * nc); double *pz = z.fortran_vec (); Array<octave_idx_type> iz (nc); octave_idx_type *piz = iz.fortran_vec (); F77_XFCN (dgetrf, DGETRF, (nr, nr, tmp_data, nr, pipvt, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgetrf"); else { // Throw-away extra info LAPACK gives so as to not change output. rcond = 0.0; if (info != 0) { info = -2; if (sing_handler) sing_handler (rcond); 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 (dgecon, DGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcond, pz, piz, info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgecon"); if (info != 0) info = -2; volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) { info = -2; if (sing_handler) sing_handler (rcond); else (*current_liboctave_error_handler) ("matrix singular to machine precision, rcond = %g", rcond); } } if (info == 0) { retval = b; double *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, pipvt, result, b.rows(), info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgetrs"); } else mattype.mark_as_rectangular (); } } } else if (typ != MatrixType::Hermitian) (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } Matrix Matrix::solve (MatrixType &typ, const Matrix& b) const { octave_idx_type info; double rcond; return solve (typ, b, info, rcond, 0); } Matrix Matrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (typ, b, info, rcond, 0); } Matrix Matrix::solve (MatrixType &mattype, const Matrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { Matrix 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, rcond, sing_handler, false); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcond, sing_handler, false); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, info, rcond, sing_handler, true); else if (typ != MatrixType::Rectangular) { (*current_liboctave_error_handler) ("unknown matrix type"); return Matrix (); } // 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, rcond); } return retval; } ComplexMatrix Matrix::solve (MatrixType &typ, const ComplexMatrix& b) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b); } ComplexMatrix Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b, info); } ComplexMatrix Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b, info, rcond); } ComplexMatrix Matrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler, bool singular_fallback) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b, info, rcond, sing_handler, singular_fallback); } ColumnVector Matrix::solve (MatrixType &typ, const ColumnVector& b) const { octave_idx_type info; double rcond; return solve (typ, b, info, rcond); } ColumnVector Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info) const { double rcond; return solve (typ, b, info, rcond); } ColumnVector Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (typ, b, info, rcond, 0); } ColumnVector Matrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { Matrix tmp (b); return solve (typ, tmp, info, rcond, sing_handler).column(static_cast<octave_idx_type> (0)); } ComplexColumnVector Matrix::solve (MatrixType &typ, const ComplexColumnVector& b) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b); } ComplexColumnVector Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b, info); } ComplexColumnVector Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { ComplexMatrix tmp (*this); return tmp.solve (typ, b, info, rcond); } ComplexColumnVector Matrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (*this); return tmp.solve(typ, b, info, rcond, sing_handler); } Matrix Matrix::solve (const Matrix& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond, 0); } Matrix Matrix::solve (const Matrix& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond, 0); } Matrix Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } Matrix Matrix::solve (const Matrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, info, rcond, sing_handler); } ComplexMatrix Matrix::solve (const ComplexMatrix& b) const { ComplexMatrix tmp (*this); return tmp.solve (b); } ComplexMatrix Matrix::solve (const ComplexMatrix& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); return tmp.solve (b, info); } ComplexMatrix Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond) const { ComplexMatrix tmp (*this); return tmp.solve (b, info, rcond); } ComplexMatrix Matrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (*this); return tmp.solve (b, info, rcond, sing_handler); } ColumnVector Matrix::solve (const ColumnVector& b) const { octave_idx_type info; double rcond; return solve (b, info, rcond); } ColumnVector Matrix::solve (const ColumnVector& b, octave_idx_type& info) const { double rcond; return solve (b, info, rcond); } ColumnVector Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond) const { return solve (b, info, rcond, 0); } ColumnVector Matrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { MatrixType mattype (*this); return solve (mattype, b, info, rcond, sing_handler); } ComplexColumnVector Matrix::solve (const ComplexColumnVector& b) const { ComplexMatrix tmp (*this); return tmp.solve (b); } ComplexColumnVector Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); return tmp.solve (b, info); } ComplexColumnVector Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond) const { ComplexMatrix tmp (*this); return tmp.solve (b, info, rcond); } ComplexColumnVector Matrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcond, solve_singularity_handler sing_handler) const { ComplexMatrix tmp (*this); return tmp.solve (b, info, rcond, sing_handler); } Matrix Matrix::lssolve (const Matrix& b) const { octave_idx_type info; octave_idx_type rank; double rcond; return lssolve (b, info, rank, rcond); } Matrix Matrix::lssolve (const Matrix& b, octave_idx_type& info) const { octave_idx_type rank; double rcond; return lssolve (b, info, rank, rcond); } Matrix Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const { double rcond; return lssolve (b, info, rank, rcond); } Matrix Matrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank, double &rcond) const { Matrix 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 = Matrix (n, b.cols (), 0.0); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcond = -1.0; if (m != n) { retval = Matrix (maxmn, nrhs, 0.0); 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; Matrix atmp = *this; double *tmp_data = atmp.fortran_vec (); double *pretval = retval.fortran_vec (); Array<double> s (minmn); double *ps = s.fortran_vec (); // Ask DGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<double> work (1); // FIXME: Can SMLSIZ be other than 25? octave_idx_type liwork = 3 * minmn * 25 + 11 * minmn; Array<octave_idx_type> iwork (liwork); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcond, rank, work.fortran_vec (), lwork, piwork, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgelsd"); else { lwork = static_cast<octave_idx_type> (work(0)); work.resize (lwork); F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcond, rank, work.fortran_vec (), lwork, piwork, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgelsd"); else { if (rank < minmn) (*current_liboctave_warning_handler) ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); if (s.elem (0) == 0.0) rcond = 0.0; else rcond = s.elem (minmn - 1) / s.elem (0); } } } return retval; } ComplexMatrix Matrix::lssolve (const ComplexMatrix& b) const { ComplexMatrix tmp (*this); octave_idx_type info; octave_idx_type rank; double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexMatrix Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); octave_idx_type rank; double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexMatrix Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { ComplexMatrix tmp (*this); double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexMatrix Matrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, double& rcond) const { ComplexMatrix tmp (*this); return tmp.lssolve (b, info, rank, rcond); } ColumnVector Matrix::lssolve (const ColumnVector& b) const { octave_idx_type info; octave_idx_type rank; double rcond; return lssolve (b, info, rank, rcond); } ColumnVector Matrix::lssolve (const ColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; double rcond; return lssolve (b, info, rank, rcond); } ColumnVector Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { double rcond; return lssolve (b, info, rank, rcond); } ColumnVector Matrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double &rcond) const { ColumnVector 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) retval = ColumnVector (n, 0.0); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcond = -1.0; if (m != n) { retval = ColumnVector (maxmn, 0.0); for (octave_idx_type i = 0; i < m; i++) retval.elem (i) = b.elem (i); } else retval = b; Matrix atmp = *this; double *tmp_data = atmp.fortran_vec (); double *pretval = retval.fortran_vec (); Array<double> s (minmn); double *ps = s.fortran_vec (); // Ask DGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<double> work (1); // FIXME: Can SMLSIZ be other than 25? octave_idx_type liwork = 3 * minmn * 25 + 11 * minmn; Array<octave_idx_type> iwork (liwork); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcond, rank, work.fortran_vec (), lwork, piwork, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgelsd"); else { lwork = static_cast<octave_idx_type> (work(0)); work.resize (lwork); F77_XFCN (dgelsd, DGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcond, rank, work.fortran_vec (), lwork, piwork, info)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgelsd"); else if (rank < minmn) { if (rank < minmn) (*current_liboctave_warning_handler) ("dgelsd: rank deficient %dx%d matrix, rank = %d", m, n, rank); if (s.elem (0) == 0.0) rcond = 0.0; else rcond = s.elem (minmn - 1) / s.elem (0); } } } return retval; } ComplexColumnVector Matrix::lssolve (const ComplexColumnVector& b) const { ComplexMatrix tmp (*this); octave_idx_type info; octave_idx_type rank; double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexColumnVector Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const { ComplexMatrix tmp (*this); octave_idx_type rank; double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexColumnVector Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { ComplexMatrix tmp (*this); double rcond; return tmp.lssolve (b, info, rank, rcond); } ComplexColumnVector Matrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double &rcond) const { ComplexMatrix tmp (*this); return tmp.lssolve (b, info, rank, rcond); } // Constants for matrix exponential calculation. static double 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, }; Matrix Matrix::expm (void) const { Matrix retval; Matrix m = *this; if (numel () == 1) return Matrix (1, 1, exp (m(0))); 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 volatile double trshift = 0.0; for (octave_idx_type i = 0; i < nc; i++) trshift += m.elem (i, i); trshift /= nc; if (trshift > 0.0) { for (octave_idx_type i = 0; i < nc; i++) m.elem (i, i) -= trshift; } // Preconditioning step 2: balancing; code follows development // in AEPBAL double *p_m = m.fortran_vec (); octave_idx_type info, ilo, ihi, ilos, ihis; Array<double> dpermute (nc); Array<double> dscale (nc); // permutation first char job = 'P'; F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), nc, p_m, nc, ilo, ihi, dpermute.fortran_vec (), info F77_CHAR_ARG_LEN (1))); // then scaling job = 'S'; F77_XFCN (dgebal, DGEBAL, (F77_CONST_CHAR_ARG2 (&job, 1), nc, p_m, nc, ilos, ihis, dscale.fortran_vec (), info F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dgebal"); return retval; } // Preconditioning step 3: scaling. ColumnVector work(nc); double inf_norm; F77_XFCN (xdlange, XDLANGE, (F77_CONST_CHAR_ARG2 ("I", 1), nc, nc, m.fortran_vec (), nc, work.fortran_vec (), inf_norm F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) { (*current_liboctave_error_handler) ("unrecoverable error in dlange"); return retval; } octave_idx_type sqpow = static_cast<octave_idx_type> (inf_norm > 0.0 ? (1.0 + log (inf_norm) / log (2.0)) : 0.0); // Check whether we need to square at all. if (sqpow < 0) sqpow = 0; if (sqpow > 0) { double 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. Matrix npp (nc, nc, 0.0); Matrix dpp = npp; // Now powers a^8 ... a^1. octave_idx_type minus_one_j = -1; for (octave_idx_type j = 7; j >= 0; j--) { npp = m * npp + padec[j] * m; dpp = m * dpp + (minus_one_j * padec[j]) * m; 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. retval = dpp.solve (npp, info); // Reverse preconditioning step 3: repeated squaring. while (sqpow) { retval = retval * retval; sqpow--; } // Reverse preconditioning step 2: inverse balancing. // apply inverse scaling to computed exponential 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; // 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; } // 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 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; Matrix 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. if (trshift > 0.0) retval = exp (trshift) * retval; return retval; } Matrix& Matrix::operator += (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) { 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& Matrix::operator -= (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) { 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; } // unary operations boolMatrix Matrix::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); return b; } // column vector by row vector -> matrix operations Matrix operator * (const ColumnVector& v, const RowVector& a) { Matrix retval; octave_idx_type len = v.length (); if (len != 0) { octave_idx_type a_len = a.length (); retval.resize (len, a_len); double *c = retval.fortran_vec (); F77_XFCN (dgemm, DGEMM, (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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgemm"); } return retval; } // other operations. Matrix Matrix::map (d_d_Mapper f) const { Matrix b (*this); return b.apply (f); } boolMatrix Matrix::map (b_d_Mapper f) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); boolMatrix retval (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) retval(i,j) = f (elem(i,j)); return retval; } Matrix& Matrix::apply (d_d_Mapper f) { double *d = fortran_vec (); // Ensures only one reference to my privates! for (octave_idx_type i = 0; i < length (); i++) d[i] = f (d[i]); return *this; } bool Matrix::any_element_is_negative (bool neg_zero) const { octave_idx_type nel = nelem (); if (neg_zero) { for (octave_idx_type i = 0; i < nel; i++) if (lo_ieee_signbit (elem (i))) return true; } else { for (octave_idx_type i = 0; i < nel; i++) if (elem (i) < 0) return true; } return false; } bool Matrix::any_element_is_inf_or_nan (void) const { octave_idx_type nel = nelem (); for (octave_idx_type i = 0; i < nel; i++) { double val = elem (i); if (xisinf (val) || xisnan (val)) return true; } return false; } bool Matrix::any_element_not_one_or_zero (void) const { octave_idx_type nel = nelem (); for (octave_idx_type i = 0; i < nel; i++) { double val = elem (i); if (val != 0 && val != 1) return true; } return false; } bool Matrix::all_elements_are_int_or_inf_or_nan (void) const { octave_idx_type nel = nelem (); for (octave_idx_type i = 0; i < nel; i++) { double val = elem (i); if (xisnan (val) || D_NINT (val) == val) continue; else return false; } return true; } // Return nonzero if any element of M is not an integer. Also extract // the largest and smallest values and return them in MAX_VAL and MIN_VAL. bool Matrix::all_integers (double& max_val, double& min_val) const { octave_idx_type nel = nelem (); if (nel > 0) { max_val = elem (0); min_val = elem (0); } else return false; for (octave_idx_type i = 0; i < nel; i++) { double val = elem (i); if (val > max_val) max_val = val; if (val < min_val) min_val = val; if (D_NINT (val) != val) return false; } return true; } bool Matrix::too_large_for_float (void) const { octave_idx_type nel = nelem (); for (octave_idx_type i = 0; i < nel; i++) { double val = elem (i); if (! (xisnan (val) || xisinf (val)) && fabs (val) > FLT_MAX) return true; } return false; } // FIXME Do these really belong here? Maybe they should be // in a base class? boolMatrix Matrix::all (int dim) const { MX_ALL_OP (dim); } boolMatrix Matrix::any (int dim) const { MX_ANY_OP (dim); } Matrix Matrix::cumprod (int dim) const { MX_CUMULATIVE_OP (Matrix, double, *=); } Matrix Matrix::cumsum (int dim) const { MX_CUMULATIVE_OP (Matrix, double, +=); } Matrix Matrix::prod (int dim) const { MX_REDUCTION_OP (Matrix, *=, 1.0, 1.0); } Matrix Matrix::sum (int dim) const { MX_REDUCTION_OP (Matrix, +=, 0.0, 0.0); } Matrix Matrix::sumsq (int dim) const { #define ROW_EXPR \ double d = elem (i, j); \ retval.elem (i, 0) += d * d #define COL_EXPR \ double d = elem (i, j); \ retval.elem (0, j) += d * d MX_BASE_REDUCTION_OP (Matrix, ROW_EXPR, COL_EXPR, 0.0, 0.0); #undef ROW_EXPR #undef COL_EXPR } Matrix Matrix::abs (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); Matrix retval (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) retval (i, j) = fabs (elem (i, j)); return retval; } ColumnVector Matrix::diag (void) const { return diag (0); } ColumnVector Matrix::diag (octave_idx_type k) const { octave_idx_type nnr = rows (); octave_idx_type nnc = cols (); if (k > 0) nnc -= k; else if (k < 0) nnr += k; ColumnVector d; if (nnr > 0 && nnc > 0) { octave_idx_type ndiag = (nnr < nnc) ? nnr : nnc; d.resize (ndiag); if (k > 0) { for (octave_idx_type i = 0; i < ndiag; i++) d.elem (i) = elem (i, i+k); } else if (k < 0) { for (octave_idx_type i = 0; i < ndiag; i++) d.elem (i) = elem (i-k, i); } else { for (octave_idx_type i = 0; i < ndiag; i++) d.elem (i) = elem (i, i); } } else (*current_liboctave_error_handler) ("diag: requested diagonal out of range"); return d; } ColumnVector Matrix::row_min (void) const { Array<octave_idx_type> dummy_idx; return row_min (dummy_idx); } ColumnVector Matrix::row_min (Array<octave_idx_type>& idx_arg) const { ColumnVector 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++) { octave_idx_type idx_j; double tmp_min = octave_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_min = elem (i, idx_j); if (! xisnan (tmp_min)) break; } for (octave_idx_type j = idx_j+1; j < nc; j++) { double tmp = elem (i, j); if (xisnan (tmp)) continue; else if (tmp < tmp_min) { idx_j = j; tmp_min = tmp; } } result.elem (i) = tmp_min; idx_arg.elem (i) = xisnan (tmp_min) ? 0 : idx_j; } } return result; } ColumnVector Matrix::row_max (void) const { Array<octave_idx_type> dummy_idx; return row_max (dummy_idx); } ColumnVector Matrix::row_max (Array<octave_idx_type>& idx_arg) const { ColumnVector 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++) { octave_idx_type idx_j; double tmp_max = octave_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_max = elem (i, idx_j); if (! xisnan (tmp_max)) break; } for (octave_idx_type j = idx_j+1; j < nc; j++) { double tmp = elem (i, j); if (xisnan (tmp)) continue; else if (tmp > tmp_max) { idx_j = j; tmp_max = tmp; } } result.elem (i) = tmp_max; idx_arg.elem (i) = xisnan (tmp_max) ? 0 : idx_j; } } return result; } RowVector Matrix::column_min (void) const { Array<octave_idx_type> dummy_idx; return column_min (dummy_idx); } RowVector Matrix::column_min (Array<octave_idx_type>& idx_arg) const { RowVector 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++) { octave_idx_type idx_i; double tmp_min = octave_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_min = elem (idx_i, j); if (! xisnan (tmp_min)) break; } for (octave_idx_type i = idx_i+1; i < nr; i++) { double tmp = elem (i, j); if (xisnan (tmp)) continue; else if (tmp < tmp_min) { idx_i = i; tmp_min = tmp; } } result.elem (j) = tmp_min; idx_arg.elem (j) = xisnan (tmp_min) ? 0 : idx_i; } } return result; } RowVector Matrix::column_max (void) const { Array<octave_idx_type> dummy_idx; return column_max (dummy_idx); } RowVector Matrix::column_max (Array<octave_idx_type>& idx_arg) const { RowVector 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++) { octave_idx_type idx_i; double tmp_max = octave_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_max = elem (idx_i, j); if (! xisnan (tmp_max)) break; } for (octave_idx_type i = idx_i+1; i < nr; i++) { double tmp = elem (i, j); if (xisnan (tmp)) continue; else if (tmp > tmp_max) { idx_i = i; tmp_max = tmp; } } result.elem (j) = tmp_max; idx_arg.elem (j) = xisnan (tmp_max) ? 0 : idx_i; } } return result; } std::ostream& operator << (std::ostream& os, const Matrix& a) { for (octave_idx_type i = 0; i < a.rows (); i++) { for (octave_idx_type j = 0; j < a.cols (); j++) { os << " "; octave_write_double (os, a.elem (i, j)); } os << "\n"; } return os; } std::istream& operator >> (std::istream& is, Matrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr < 1 || nc < 1) is.clear (std::ios::badbit); else { double tmp; for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = 0; j < nc; j++) { tmp = octave_read_double (is); if (is) a.elem (i, j) = tmp; else goto done; } } done: return is; } Matrix Givens (double x, double y) { double cc, s, temp_r; F77_FUNC (dlartg, DLARTG) (x, y, cc, s, temp_r); Matrix g (2, 2); g.elem (0, 0) = cc; g.elem (1, 1) = cc; g.elem (0, 1) = s; g.elem (1, 0) = -s; return g; } Matrix Sylvester (const Matrix& a, const Matrix& b, const Matrix& c) { Matrix retval; // FIXME -- need to check that a, b, and c are all the same // size. // Compute Schur decompositions. SCHUR as (a, "U"); SCHUR bs (b, "U"); // Transform c to new coordinates. Matrix ua = as.unitary_matrix (); Matrix sch_a = as.schur_matrix (); Matrix ub = bs.unitary_matrix (); Matrix sch_b = bs.schur_matrix (); Matrix cx = ua.transpose () * c * ub; // Solve the sylvester equation, back-transform, and return the // solution. octave_idx_type a_nr = a.rows (); octave_idx_type b_nr = b.rows (); double scale; octave_idx_type info; double *pa = sch_a.fortran_vec (); double *pb = sch_b.fortran_vec (); double *px = cx.fortran_vec (); F77_XFCN (dtrsyl, DTRSYL, (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))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dtrsyl"); else { // FIXME -- check info? retval = -ua*cx*ub.transpose (); } return retval; } // matrix by matrix -> matrix operations /* Simple Dot Product, Matrix-Vector and Matrix-Matrix Unit tests %!assert([1 2 3] * [ 4 ; 5 ; 6], 32, 1e-14) %!assert([1 2 ; 3 4 ] * [5 ; 6], [17 ; 39 ], 1e-14) %!assert([1 2 ; 3 4 ] * [5 6 ; 7 8], [19 22; 43 50], 1e-14) */ /* Test some simple identities %!shared M, cv, rv %! M = randn(10,10); %! cv = randn(10,1); %! rv = randn(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) */ Matrix operator * (const Matrix& m, const Matrix& a) { Matrix retval; octave_idx_type nr = m.rows (); octave_idx_type nc = m.cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nc != a_nr) gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); else { if (nr == 0 || nc == 0 || a_nc == 0) retval.resize (nr, a_nc, 0.0); else { octave_idx_type ld = nr; octave_idx_type lda = a_nr; retval.resize (nr, a_nc); double *c = retval.fortran_vec (); if (a_nc == 1) { if (nr == 1) F77_FUNC (xddot, XDDOT) (nc, m.data (), 1, a.data (), 1, *c); else { F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), nr, nc, 1.0, m.data (), ld, a.data (), 1, 0.0, c, 1 F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgemv"); } } else { F77_XFCN (dgemm, DGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), nr, a_nc, nc, 1.0, m.data (), ld, a.data (), lda, 0.0, c, nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("unrecoverable error in dgemm"); } } } return retval; } // 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); Matrix min (double d, const Matrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (Matrix); Matrix 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 (d, m (i, j)); } return result; } Matrix min (const Matrix& m, double d) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (Matrix); Matrix 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), d); } return result; } Matrix min (const Matrix& a, const Matrix& 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 Matrix (); } EMPTY_RETURN_CHECK (Matrix); Matrix 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 (a (i, j), b (i, j)); } return result; } Matrix max (double d, const Matrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (Matrix); Matrix 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 (d, m (i, j)); } return result; } Matrix max (const Matrix& m, double d) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (Matrix); Matrix 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), d); } return result; } Matrix max (const Matrix& a, const Matrix& 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 Matrix (); } EMPTY_RETURN_CHECK (Matrix); Matrix 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 (a (i, j), b (i, j)); } return result; } MS_CMP_OPS(Matrix, , double, ) MS_BOOL_OPS(Matrix, double, 0.0) SM_CMP_OPS(double, , Matrix, ) SM_BOOL_OPS(double, Matrix, 0.0) MM_CMP_OPS(Matrix, , Matrix, ) MM_BOOL_OPS(Matrix, Matrix, 0.0) /* ;;; Local Variables: *** ;;; mode: C++ *** ;;; End: *** */