// Matrix manipulations.
/*
Copyright (C) 1996, 1997 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 2, 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, write to the Free
Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.
*/
#if defined (__GNUG__) && defined (USE_PRAGMA_INTERFACE_IMPLEMENTATION)
#pragma implementation
#endif
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <cfloat>
#include <iostream>
#include "Array-util.h"
#include "byte-swap.h"
#include "dMatrix.h"
#include "dbleAEPBAL.h"
#include "dbleDET.h"
#include "dbleSCHUR.h"
#include "dbleSVD.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 int&, double*, const int&, int&,
int&, double*, int&
F77_CHAR_ARG_LEN_DECL);
F77_RET_T
F77_FUNC (dgebak, DGEBAK) (F77_CONST_CHAR_ARG_DECL,
F77_CONST_CHAR_ARG_DECL,
const int&, const int&, const int&, double*,
const int&, double*, const int&, int&
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 int&, const int&, const int&,
const double&, const double*, const int&,
const double*, const int&, const double&,
double*, const int&
F77_CHAR_ARG_LEN_DECL
F77_CHAR_ARG_LEN_DECL);
F77_RET_T
F77_FUNC (dgetrf, DGETRF) (const int&, const int&, double*, const int&,
int*, int&);
F77_RET_T
F77_FUNC (dgetrs, DGETRS) (F77_CONST_CHAR_ARG_DECL, const int&, const int&,
const double*, const int&,
const int*, double*, const int&, int&
F77_CHAR_ARG_LEN_DECL);
F77_RET_T
F77_FUNC (dgetri, DGETRI) (const int&, double*, const int&, const int*,
double*, const int&, int&);
F77_RET_T
F77_FUNC (dgecon, DGECON) (F77_CONST_CHAR_ARG_DECL, const int&, double*,
const int&, const double&, double&,
double*, int*, int&
F77_CHAR_ARG_LEN_DECL);
F77_RET_T
F77_FUNC (dgelss, DGELSS) (const int&, const int&, const int&,
double*, const int&, double*,
const int&, double*, double&, int&,
double*, const int&, int&);
// 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 int&, Complex*);
F77_RET_T
F77_FUNC (cfftf, CFFTF) (const int&, Complex*, Complex*);
F77_RET_T
F77_FUNC (cfftb, CFFTB) (const int&, 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 int&, const int&, const int&,
const double*, const int&, const double*,
const int&, const double*, const int&,
double&, int&
F77_CHAR_ARG_LEN_DECL
F77_CHAR_ARG_LEN_DECL);
F77_RET_T
F77_FUNC (xdlange, XDLANGE) (F77_CONST_CHAR_ARG_DECL, const int&,
const int&, const double*,
const int&, double*, double&
F77_CHAR_ARG_LEN_DECL);
}
// Matrix class.
Matrix::Matrix (const RowVector& rv)
: MArray2<double> (1, rv.length (), 0.0)
{
for (int 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 (int 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 (int i = 0; i < a.length (); i++)
elem (i, i) = a.elem (i, i);
}
// XXX FIXME XXX -- could we use a templated mixed-type copy function
// here?
Matrix::Matrix (const boolMatrix& a)
: MArray2<double> (a.rows (), a.cols ())
{
for (int i = 0; i < a.rows (); i++)
for (int 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 (int i = 0; i < a.rows (); i++)
for (int 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 (int i = 0; i < rows (); i++)
for (int 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, int r, int c)
{
Array2<double>::insert (a, r, c);
return *this;
}
Matrix&
Matrix::insert (const RowVector& a, int r, int c)
{
int 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 (int i = 0; i < a_len; i++)
xelem (r, c+i) = a.elem (i);
}
return *this;
}
Matrix&
Matrix::insert (const ColumnVector& a, int r, int c)
{
int 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 (int i = 0; i < a_len; i++)
xelem (r+i, c) = a.elem (i);
}
return *this;
}
Matrix&
Matrix::insert (const DiagMatrix& a, int r, int c)
{
int a_nr = a.rows ();
int 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);
int a_len = a.length ();
if (a_len > 0)
{
make_unique ();
for (int i = 0; i < a_len; i++)
xelem (r+i, c+i) = a.elem (i, i);
}
return *this;
}
Matrix&
Matrix::fill (double val)
{
int nr = rows ();
int nc = cols ();
if (nr > 0 && nc > 0)
{
make_unique ();
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
xelem (i, j) = val;
}
return *this;
}
Matrix&
Matrix::fill (double val, int r1, int c1, int r2, int c2)
{
int nr = rows ();
int 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) { int tmp = r1; r1 = r2; r2 = tmp; }
if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; }
if (r2 >= r1 && c2 >= c1)
{
make_unique ();
for (int j = c1; j <= c2; j++)
for (int i = r1; i <= r2; i++)
xelem (i, j) = val;
}
return *this;
}
Matrix
Matrix::append (const Matrix& a) const
{
int nr = rows ();
int nc = cols ();
if (nr != a.rows ())
{
(*current_liboctave_error_handler) ("row dimension mismatch for append");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nr != 1)
{
(*current_liboctave_error_handler) ("row dimension mismatch for append");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nr != a.length ())
{
(*current_liboctave_error_handler) ("row dimension mismatch for append");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nr != a.rows ())
{
(*current_liboctave_error_handler) ("row dimension mismatch for append");
return *this;
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nc != a.cols ())
{
(*current_liboctave_error_handler)
("column dimension mismatch for stack");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nc != a.length ())
{
(*current_liboctave_error_handler)
("column dimension mismatch for stack");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nc != 1)
{
(*current_liboctave_error_handler)
("column dimension mismatch for stack");
return Matrix ();
}
int 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
{
int nr = rows ();
int nc = cols ();
if (nc != a.cols ())
{
(*current_liboctave_error_handler)
("column dimension mismatch for stack");
return Matrix ();
}
int 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)
{
int 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)
{
int 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 (int r1, int c1, int r2, int c2) const
{
if (r1 > r2) { int tmp = r1; r1 = r2; r2 = tmp; }
if (c1 > c2) { int tmp = c1; c1 = c2; c2 = tmp; }
int new_r = r2 - r1 + 1;
int new_c = c2 - c1 + 1;
Matrix result (new_r, new_c);
for (int j = 0; j < new_c; j++)
for (int i = 0; i < new_r; i++)
result.xelem (i, j) = elem (r1+i, c1+j);
return result;
}
Matrix
Matrix::extract_n (int r1, int c1, int nr, int nc) const
{
Matrix result (nr, nc);
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
result.xelem (i, j) = elem (r1+i, c1+j);
return result;
}
// extract row or column i.
RowVector
Matrix::row (int i) const
{
int nc = cols ();
if (i < 0 || i >= rows ())
{
(*current_liboctave_error_handler) ("invalid row selection");
return RowVector ();
}
RowVector retval (nc);
for (int j = 0; j < nc; j++)
retval.xelem (j) = elem (i, j);
return retval;
}
RowVector
Matrix::row (char *s) const
{
if (! s)
{
(*current_liboctave_error_handler) ("invalid row selection");
return RowVector ();
}
char c = *s;
if (c == 'f' || c == 'F')
return row (0);
else if (c == 'l' || c == 'L')
return row (rows () - 1);
else
{
(*current_liboctave_error_handler) ("invalid row selection");
return RowVector ();
}
}
ColumnVector
Matrix::column (int i) const
{
int nr = rows ();
if (i < 0 || i >= cols ())
{
(*current_liboctave_error_handler) ("invalid column selection");
return ColumnVector ();
}
ColumnVector retval (nr);
for (int j = 0; j < nr; j++)
retval.xelem (j) = elem (j, i);
return retval;
}
ColumnVector
Matrix::column (char *s) const
{
if (! s)
{
(*current_liboctave_error_handler) ("invalid column selection");
return ColumnVector ();
}
char c = *s;
if (c == 'f' || c == 'F')
return column (0);
else if (c == 'l' || c == 'L')
return column (cols () - 1);
else
{
(*current_liboctave_error_handler) ("invalid column selection");
return ColumnVector ();
}
}
Matrix
Matrix::inverse (void) const
{
int info;
double rcond;
return inverse (info, rcond, 0, 0);
}
Matrix
Matrix::inverse (int& info) const
{
double rcond;
return inverse (info, rcond, 0, 0);
}
Matrix
Matrix::inverse (int& info, double& rcond, int force, int calc_cond) const
{
Matrix retval;
int nr = rows ();
int nc = cols ();
if (nr != nc || nr == 0 || nc == 0)
(*current_liboctave_error_handler) ("inverse requires square matrix");
else
{
Array<int> ipvt (nr);
int *pipvt = ipvt.fortran_vec ();
retval = *this;
double *tmp_data = retval.fortran_vec ();
Array<double> z(1);
int 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<int> (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(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)
{
int dgecon_info = 0;
// Now calculate the condition number for non-singular matrix.
char job = '1';
Array<int> iz (nc);
int *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
{
int 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;
}
}
}
return retval;
}
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 ();
int r = sigma.length () - 1;
int nr = rows ();
int 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;
int nr = rows ();
int nc = cols ();
int npts, nsamples;
if (nr == 1 || nc == 1)
{
npts = nr > nc ? nr : nc;
nsamples = 1;
}
else
{
npts = nr;
nsamples = nc;
}
int 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 (int 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;
int nr = rows ();
int nc = cols ();
int npts, nsamples;
if (nr == 1 || nc == 1)
{
npts = nr > nc ? nr : nc;
nsamples = 1;
}
else
{
npts = nr;
nsamples = nc;
}
int 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 (int j = 0; j < nsamples; j++)
{
OCTAVE_QUIT;
F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave);
}
for (int 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;
int nr = rows ();
int nc = cols ();
int npts, nsamples;
if (nr == 1 || nc == 1)
{
npts = nr > nc ? nr : nc;
nsamples = 1;
}
else
{
npts = nr;
nsamples = nc;
}
int 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 (int 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 (int j = 0; j < nsamples; j++)
{
OCTAVE_QUIT;
for (int i = 0; i < npts; i++)
prow[i] = tmp_data[i*nr + j];
F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave);
for (int i = 0; i < npts; i++)
tmp_data[i*nr + j] = prow[i];
}
return retval;
}
ComplexMatrix
Matrix::ifourier2d (void) const
{
ComplexMatrix retval;
int nr = rows ();
int nc = cols ();
int npts, nsamples;
if (nr == 1 || nc == 1)
{
npts = nr > nc ? nr : nc;
nsamples = 1;
}
else
{
npts = nr;
nsamples = nc;
}
int 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 (int j = 0; j < nsamples; j++)
{
OCTAVE_QUIT;
F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave);
}
for (int 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 (int j = 0; j < nsamples; j++)
{
OCTAVE_QUIT;
for (int i = 0; i < npts; i++)
prow[i] = tmp_data[i*nr + j];
F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave);
for (int i = 0; i < npts; i++)
tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts);
}
return retval;
}
#endif
DET
Matrix::determinant (void) const
{
int info;
double rcond;
return determinant (info, rcond, 0);
}
DET
Matrix::determinant (int& info) const
{
double rcond;
return determinant (info, rcond, 0);
}
DET
Matrix::determinant (int& info, double& rcond, int calc_cond) const
{
DET retval;
int nr = rows ();
int nc = cols ();
if (nr == 0 || nc == 0)
{
double d[2];
d[0] = 1.0;
d[1] = 0.0;
retval = DET (d);
}
else
{
Array<int> ipvt (nr);
int *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(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<int> iz (nc);
int *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 d[2] = { 1., 0.};
for (int i=0; i<nc; i++)
{
if (ipvt(i) != (i+1)) d[0] = -d[0];
d[0] *= atmp(i,i);
if (d[0] == 0.) break;
while (fabs(d[0]) < 1.)
{
d[0] = 10. * d[0];
d[1] = d[1] - 1.0;
}
while (fabs(d[0]) >= 10.)
{
d[0] = 0.1 * d[0];
d[1] = d[1] + 1.0;
}
}
retval = DET (d);
}
}
}
}
return retval;
}
Matrix
Matrix::solve (const Matrix& b) const
{
int info;
double rcond;
return solve (b, info, rcond, 0);
}
Matrix
Matrix::solve (const Matrix& b, int& info) const
{
double rcond;
return solve (b, info, rcond, 0);
}
Matrix
Matrix::solve (const Matrix& b, int& info, double& rcond) const
{
return solve (b, info, rcond, 0);
}
Matrix
Matrix::solve (const Matrix& b, int& info, double& rcond,
solve_singularity_handler sing_handler) const
{
Matrix retval;
int nr = rows ();
int nc = cols ();
if (nr == 0 || nc == 0 || nr != nc || nr != b.rows ())
(*current_liboctave_error_handler)
("matrix dimension mismatch solution of linear equations");
else
{
info = 0;
Array<int> ipvt (nr);
int *pipvt = ipvt.fortran_vec ();
Matrix atmp = *this;
double *tmp_data = atmp.fortran_vec ();
Array<double> z (4 * nc);
double *pz = z.fortran_vec ();
Array<int> iz (nc);
int *piz = iz.fortran_vec ();
// Calculate the norm of the matrix, for later use.
double anorm = atmp.abs().sum().row(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 = -2;
if (sing_handler)
sing_handler (rcond);
else
(*current_liboctave_error_handler)
("matrix singular to machine precision");
}
else
{
// 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);
}
else
{
retval = b;
double *result = retval.fortran_vec ();
int b_nc = b.cols ();
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");
}
}
}
}
return retval;
}
ComplexMatrix
Matrix::solve (const ComplexMatrix& b) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b);
}
ComplexMatrix
Matrix::solve (const ComplexMatrix& b, int& info) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b, info);
}
ComplexMatrix
Matrix::solve (const ComplexMatrix& b, int& info, double& rcond) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b, info, rcond);
}
ComplexMatrix
Matrix::solve (const ComplexMatrix& b, int& 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
{
int info; double rcond;
return solve (b, info, rcond);
}
ColumnVector
Matrix::solve (const ColumnVector& b, int& info) const
{
double rcond;
return solve (b, info, rcond);
}
ColumnVector
Matrix::solve (const ColumnVector& b, int& info, double& rcond) const
{
return solve (b, info, rcond, 0);
}
ColumnVector
Matrix::solve (const ColumnVector& b, int& info, double& rcond,
solve_singularity_handler sing_handler) const
{
ColumnVector retval;
int nr = rows ();
int nc = cols ();
if (nr == 0 || nc == 0 || nr != nc || nr != b.length ())
(*current_liboctave_error_handler)
("matrix dimension mismatch solution of linear equations");
else
{
info = 0;
Array<int> ipvt (nr);
int *pipvt = ipvt.fortran_vec ();
Matrix atmp = *this;
double *tmp_data = atmp.fortran_vec ();
Array<double> z (4 * nc);
double *pz = z.fortran_vec ();
Array<int> iz (nc);
int *piz = iz.fortran_vec ();
// Calculate the norm of the matrix, for later use.
double anorm = atmp.abs().sum().row(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 = -2;
if (sing_handler)
sing_handler (rcond);
else
(*current_liboctave_error_handler)
("matrix singular to machine precision");
}
else
{
// 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);
}
else
{
retval = b;
double *result = retval.fortran_vec ();
job = 'N';
F77_XFCN (dgetrs, DGETRS, (F77_CONST_CHAR_ARG2 (&job, 1),
nr, 1, tmp_data, nr, pipvt,
result, b.length(), info
F77_CHAR_ARG_LEN (1)));
if (f77_exception_encountered)
(*current_liboctave_error_handler)
("unrecoverable error in dgetrs");
}
}
}
}
return retval;
}
ComplexColumnVector
Matrix::solve (const ComplexColumnVector& b) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b);
}
ComplexColumnVector
Matrix::solve (const ComplexColumnVector& b, int& info) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b, info);
}
ComplexColumnVector
Matrix::solve (const ComplexColumnVector& b, int& info, double& rcond) const
{
ComplexMatrix tmp (*this);
return tmp.solve (b, info, rcond);
}
ComplexColumnVector
Matrix::solve (const ComplexColumnVector& b, int& 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
{
int info;
int rank;
return lssolve (b, info, rank);
}
Matrix
Matrix::lssolve (const Matrix& b, int& info) const
{
int rank;
return lssolve (b, info, rank);
}
Matrix
Matrix::lssolve (const Matrix& b, int& info, int& rank) const
{
Matrix retval;
int nrhs = b.cols ();
int m = rows ();
int n = cols ();
if (m == 0 || n == 0 || m != b.rows ())
(*current_liboctave_error_handler)
("matrix dimension mismatch in solution of least squares problem");
else
{
Matrix atmp = *this;
double *tmp_data = atmp.fortran_vec ();
int nrr = m > n ? m : n;
Matrix result (nrr, nrhs, 0.0);
for (int j = 0; j < nrhs; j++)
for (int i = 0; i < m; i++)
result.elem (i, j) = b.elem (i, j);
double *presult = result.fortran_vec ();
int len_s = m < n ? m : n;
Array<double> s (len_s);
double *ps = s.fortran_vec ();
double rcond = -1.0;
// Ask DGELSS what the dimension of WORK should be.
int lwork = -1;
Array<double> work (1);
F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps,
rcond, rank, work.fortran_vec (),
lwork, info));
if (f77_exception_encountered)
(*current_liboctave_error_handler) ("unrecoverable error in dgelss");
else
{
lwork = static_cast<int> (work(0));
work.resize (lwork);
F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult,
nrr, ps, rcond, rank,
work.fortran_vec (), lwork, info));
if (f77_exception_encountered)
(*current_liboctave_error_handler)
("unrecoverable error in dgelss");
else
{
retval.resize (n, nrhs);
for (int j = 0; j < nrhs; j++)
for (int i = 0; i < n; i++)
retval.elem (i, j) = result.elem (i, j);
}
}
}
return retval;
}
ComplexMatrix
Matrix::lssolve (const ComplexMatrix& b) const
{
ComplexMatrix tmp (*this);
int info;
int rank;
return tmp.lssolve (b, info, rank);
}
ComplexMatrix
Matrix::lssolve (const ComplexMatrix& b, int& info) const
{
ComplexMatrix tmp (*this);
int rank;
return tmp.lssolve (b, info, rank);
}
ComplexMatrix
Matrix::lssolve (const ComplexMatrix& b, int& info, int& rank) const
{
ComplexMatrix tmp (*this);
return tmp.lssolve (b, info, rank);
}
ColumnVector
Matrix::lssolve (const ColumnVector& b) const
{
int info;
int rank;
return lssolve (b, info, rank);
}
ColumnVector
Matrix::lssolve (const ColumnVector& b, int& info) const
{
int rank;
return lssolve (b, info, rank);
}
ColumnVector
Matrix::lssolve (const ColumnVector& b, int& info, int& rank) const
{
ColumnVector retval;
int nrhs = 1;
int m = rows ();
int n = cols ();
if (m == 0 || n == 0 || m != b.length ())
(*current_liboctave_error_handler)
("matrix dimension mismatch in solution of least squares problem");
else
{
Matrix atmp = *this;
double *tmp_data = atmp.fortran_vec ();
int nrr = m > n ? m : n;
ColumnVector result (nrr);
for (int i = 0; i < m; i++)
result.elem (i) = b.elem (i);
double *presult = result.fortran_vec ();
int len_s = m < n ? m : n;
Array<double> s (len_s);
double *ps = s.fortran_vec ();
double rcond = -1.0;
// Ask DGELSS what the dimension of WORK should be.
int lwork = -1;
Array<double> work (1);
F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult, nrr, ps,
rcond, rank, work.fortran_vec (),
lwork, info));
if (f77_exception_encountered)
(*current_liboctave_error_handler) ("unrecoverable error in dgelss");
else
{
lwork = static_cast<int> (work(0));
work.resize (lwork);
F77_XFCN (dgelss, DGELSS, (m, n, nrhs, tmp_data, m, presult,
nrr, ps, rcond, rank,
work.fortran_vec (), lwork, info));
if (f77_exception_encountered)
(*current_liboctave_error_handler)
("unrecoverable error in dgelss");
else
{
retval.resize (n);
for (int i = 0; i < n; i++)
retval.elem (i) = result.elem (i);
}
}
}
return retval;
}
ComplexColumnVector
Matrix::lssolve (const ComplexColumnVector& b) const
{
ComplexMatrix tmp (*this);
return tmp.lssolve (b);
}
ComplexColumnVector
Matrix::lssolve (const ComplexColumnVector& b, int& info) const
{
ComplexMatrix tmp (*this);
return tmp.lssolve (b, info);
}
ComplexColumnVector
Matrix::lssolve (const ComplexColumnVector& b, int& info, int& rank) const
{
ComplexMatrix tmp (*this);
return tmp.lssolve (b, info, rank);
}
// 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;
int 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 (int i = 0; i < nc; i++)
trshift += m.elem (i, i);
trshift /= nc;
if (trshift > 0.0)
{
for (int 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 ();
int 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;
}
int sqpow = (int) (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 (int 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.
int minus_one_j = -1;
for (int 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 (int 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 (int i = 0; i < nc; i++)
for (int j = 0; j < nc; j++)
retval(i,j) *= dscale(i) / dscale(j);
OCTAVE_QUIT;
// construct balancing permutation vector
Array<int> iperm (nc);
for (int i = 0; i < nc; i++)
iperm(i) = i; // identity permutation
// leading permutations in forward order
for (int i = 0; i < (ilo-1); i++)
{
int swapidx = static_cast<int> (dpermute(i)) - 1;
int tmp = iperm(i);
iperm(i) = iperm (swapidx);
iperm(swapidx) = tmp;
}
// trailing permutations must be done in reverse order
for (int i = nc - 1; i >= ihi; i--)
{
int swapidx = static_cast<int> (dpermute(i)) - 1;
int tmp = iperm(i);
iperm(i) = iperm(swapidx);
iperm(swapidx) = tmp;
}
// construct inverse balancing permutation vector
Array<int> invpvec (nc);
for (int i = 0; i < nc; i++)
invpvec(iperm(i)) = i; // Thanks to R. A. Lippert for this method
OCTAVE_QUIT;
Matrix tmpMat = retval;
for (int i = 0; i < nc; i++)
for (int 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)
{
int nr = rows ();
int nc = cols ();
int a_nr = a.rows ();
int a_nc = a.cols ();
if (nr != a_nr || nc != a_nc)
{
gripe_nonconformant ("operator +=", nr, nc, a_nr, a_nc);
return *this;
}
for (int i = 0; i < a.length (); i++)
elem (i, i) += a.elem (i, i);
return *this;
}
Matrix&
Matrix::operator -= (const DiagMatrix& a)
{
int nr = rows ();
int nc = cols ();
int a_nr = a.rows ();
int a_nc = a.cols ();
if (nr != a_nr || nc != a_nc)
{
gripe_nonconformant ("operator -=", nr, nc, a_nr, a_nc);
return *this;
}
for (int i = 0; i < a.length (); i++)
elem (i, i) -= a.elem (i, i);
return *this;
}
// unary operations
boolMatrix
Matrix::operator ! (void) const
{
int nr = rows ();
int nc = cols ();
boolMatrix b (nr, nc);
for (int j = 0; j < nc; j++)
for (int 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;
int len = v.length ();
if (len != 0)
{
int 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
{
int nr = rows ();
int nc = cols ();
boolMatrix retval (nr, nc);
for (int j = 0; j < nc; j++)
for (int 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 (int i = 0; i < length (); i++)
d[i] = f (d[i]);
return *this;
}
bool
Matrix::any_element_is_negative (bool neg_zero) const
{
int nel = nelem ();
if (neg_zero)
{
for (int i = 0; i < nel; i++)
if (lo_ieee_signbit (elem (i)))
return true;
}
else
{
for (int i = 0; i < nel; i++)
if (elem (i) < 0)
return true;
}
return false;
}
bool
Matrix::any_element_is_inf_or_nan (void) const
{
int nel = nelem ();
for (int i = 0; i < nel; i++)
{
double val = elem (i);
if (xisinf (val) || xisnan (val))
return true;
}
return false;
}
bool
Matrix::all_elements_are_int_or_inf_or_nan (void) const
{
int nel = nelem ();
for (int 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
{
int nel = nelem ();
if (nel > 0)
{
max_val = elem (0);
min_val = elem (0);
}
else
return false;
for (int 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
{
int nel = nelem ();
for (int i = 0; i < nel; i++)
{
double val = elem (i);
if (! (octave_is_NaN_or_NA (val) || xisinf (val))
&& fabs (val) > FLT_MAX)
return true;
}
return false;
}
// XXX FIXME XXX 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
{
int nr = rows ();
int nc = cols ();
Matrix retval (nr, nc);
for (int j = 0; j < nc; j++)
for (int 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 (int k) const
{
int nnr = rows ();
int nnc = cols ();
if (k > 0)
nnc -= k;
else if (k < 0)
nnr += k;
ColumnVector d;
if (nnr > 0 && nnc > 0)
{
int ndiag = (nnr < nnc) ? nnr : nnc;
d.resize (ndiag);
if (k > 0)
{
for (int i = 0; i < ndiag; i++)
d.elem (i) = elem (i, i+k);
}
else if (k < 0)
{
for (int i = 0; i < ndiag; i++)
d.elem (i) = elem (i-k, i);
}
else
{
for (int 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<int> dummy_idx;
return row_min (dummy_idx);
}
ColumnVector
Matrix::row_min (Array<int>& idx_arg) const
{
ColumnVector result;
int nr = rows ();
int nc = cols ();
if (nr > 0 && nc > 0)
{
result.resize (nr);
idx_arg.resize (nr);
for (int i = 0; i < nr; i++)
{
int idx_j;
double tmp_min = octave_NaN;
for (idx_j = 0; idx_j < nc; idx_j++)
{
tmp_min = elem (i, idx_j);
if (! octave_is_NaN_or_NA (tmp_min))
break;
}
for (int j = idx_j+1; j < nc; j++)
{
double tmp = elem (i, j);
if (octave_is_NaN_or_NA (tmp))
continue;
else if (tmp < tmp_min)
{
idx_j = j;
tmp_min = tmp;
}
}
result.elem (i) = tmp_min;
idx_arg.elem (i) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_j;
}
}
return result;
}
ColumnVector
Matrix::row_max (void) const
{
Array<int> dummy_idx;
return row_max (dummy_idx);
}
ColumnVector
Matrix::row_max (Array<int>& idx_arg) const
{
ColumnVector result;
int nr = rows ();
int nc = cols ();
if (nr > 0 && nc > 0)
{
result.resize (nr);
idx_arg.resize (nr);
for (int i = 0; i < nr; i++)
{
int idx_j;
double tmp_max = octave_NaN;
for (idx_j = 0; idx_j < nc; idx_j++)
{
tmp_max = elem (i, idx_j);
if (! octave_is_NaN_or_NA (tmp_max))
break;
}
for (int j = idx_j+1; j < nc; j++)
{
double tmp = elem (i, j);
if (octave_is_NaN_or_NA (tmp))
continue;
else if (tmp > tmp_max)
{
idx_j = j;
tmp_max = tmp;
}
}
result.elem (i) = tmp_max;
idx_arg.elem (i) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_j;
}
}
return result;
}
RowVector
Matrix::column_min (void) const
{
Array<int> dummy_idx;
return column_min (dummy_idx);
}
RowVector
Matrix::column_min (Array<int>& idx_arg) const
{
RowVector result;
int nr = rows ();
int nc = cols ();
if (nr > 0 && nc > 0)
{
result.resize (nc);
idx_arg.resize (nc);
for (int j = 0; j < nc; j++)
{
int idx_i;
double tmp_min = octave_NaN;
for (idx_i = 0; idx_i < nr; idx_i++)
{
tmp_min = elem (idx_i, j);
if (! octave_is_NaN_or_NA (tmp_min))
break;
}
for (int i = idx_i+1; i < nr; i++)
{
double tmp = elem (i, j);
if (octave_is_NaN_or_NA (tmp))
continue;
else if (tmp < tmp_min)
{
idx_i = i;
tmp_min = tmp;
}
}
result.elem (j) = tmp_min;
idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_min) ? 0 : idx_i;
}
}
return result;
}
RowVector
Matrix::column_max (void) const
{
Array<int> dummy_idx;
return column_max (dummy_idx);
}
RowVector
Matrix::column_max (Array<int>& idx_arg) const
{
RowVector result;
int nr = rows ();
int nc = cols ();
if (nr > 0 && nc > 0)
{
result.resize (nc);
idx_arg.resize (nc);
for (int j = 0; j < nc; j++)
{
int idx_i;
double tmp_max = octave_NaN;
for (idx_i = 0; idx_i < nr; idx_i++)
{
tmp_max = elem (idx_i, j);
if (! octave_is_NaN_or_NA (tmp_max))
break;
}
for (int i = idx_i+1; i < nr; i++)
{
double tmp = elem (i, j);
if (octave_is_NaN_or_NA (tmp))
continue;
else if (tmp > tmp_max)
{
idx_i = i;
tmp_max = tmp;
}
}
result.elem (j) = tmp_max;
idx_arg.elem (j) = octave_is_NaN_or_NA (tmp_max) ? 0 : idx_i;
}
}
return result;
}
std::ostream&
operator << (std::ostream& os, const Matrix& a)
{
for (int i = 0; i < a.rows (); i++)
{
for (int 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)
{
int nr = a.rows ();
int nc = a.cols ();
if (nr < 1 || nc < 1)
is.clear (std::ios::badbit);
else
{
double tmp;
for (int i = 0; i < nr; i++)
for (int 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;
// XXX FIXME XXX -- 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.
int a_nr = a.rows ();
int b_nr = b.rows ();
double scale;
int 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
{
// XXX FIXME XXX -- check info?
retval = -ua*cx*ub.transpose ();
}
return retval;
}
// matrix by matrix -> matrix operations
Matrix
operator * (const Matrix& m, const Matrix& a)
{
Matrix retval;
int nr = m.rows ();
int nc = m.cols ();
int a_nr = a.rows ();
int 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
{
int ld = nr;
int lda = a_nr;
retval.resize (nr, a_nc);
double *c = retval.fortran_vec ();
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;
}
// XXX FIXME XXX -- 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)
{
int nr = m.rows ();
int nc = m.columns ();
EMPTY_RETURN_CHECK (Matrix);
Matrix result (nr, nc);
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
{
OCTAVE_QUIT;
result (i, j) = xmin (d, m (i, j));
}
return result;
}
Matrix
min (const Matrix& m, double d)
{
int nr = m.rows ();
int nc = m.columns ();
EMPTY_RETURN_CHECK (Matrix);
Matrix result (nr, nc);
for (int j = 0; j < nc; j++)
for (int 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)
{
int nr = a.rows ();
int 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 (int j = 0; j < nc; j++)
for (int 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)
{
int nr = m.rows ();
int nc = m.columns ();
EMPTY_RETURN_CHECK (Matrix);
Matrix result (nr, nc);
for (int j = 0; j < nc; j++)
for (int i = 0; i < nr; i++)
{
OCTAVE_QUIT;
result (i, j) = xmax (d, m (i, j));
}
return result;
}
Matrix
max (const Matrix& m, double d)
{
int nr = m.rows ();
int nc = m.columns ();
EMPTY_RETURN_CHECK (Matrix);
Matrix result (nr, nc);
for (int j = 0; j < nc; j++)
for (int 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)
{
int nr = a.rows ();
int 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 (int j = 0; j < nc; j++)
for (int 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: ***
*/
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