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////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 1996-2021 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// 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
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////
#if defined (HAVE_CONFIG_H)
# include "config.h"
#endif
#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
DEFUN (sylvester, args, ,
doc: /* -*- texinfo -*-
@deftypefn {} {@var{X} =} sylvester (@var{A}, @var{B}, @var{C})
Solve the Sylvester equation.
The Sylvester equation is defined as:
@tex
$$
A X + X B = C
$$
@end tex
@ifnottex
@example
A X + X B = C
@end example
@end ifnottex
The solution is computed using standard @sc{lapack} subroutines.
For example:
@example
@group
sylvester ([1, 2; 3, 4], [5, 6; 7, 8], [9, 10; 11, 12])
@result{} [ 0.50000, 0.66667; 0.66667, 0.50000 ]
@end group
@end example
@end deftypefn */)
{
if (args.length () != 3)
print_usage ();
octave_value retval;
octave_value arg_a = args(0);
octave_value arg_b = args(1);
octave_value arg_c = args(2);
octave_idx_type a_nr = arg_a.rows ();
octave_idx_type a_nc = arg_a.columns ();
octave_idx_type b_nr = arg_b.rows ();
octave_idx_type b_nc = arg_b.columns ();
octave_idx_type c_nr = arg_c.rows ();
octave_idx_type c_nc = arg_c.columns ();
bool isfloat = arg_a.is_single_type ()
|| arg_b.is_single_type ()
|| arg_c.is_single_type ();
if (arg_a.isempty () || arg_b.isempty () || arg_c.isempty ())
{
if (isfloat)
return ovl (FloatMatrix ());
else
return ovl (Matrix ());
}
// Arguments are not empty, so check for correct dimensions.
if (a_nr != a_nc)
err_square_matrix_required ("sylvester", "A");
if (b_nr != b_nc)
err_square_matrix_required ("sylvester", "B");
if (a_nr != c_nr || b_nr != c_nc)
err_nonconformant ();
if (isfloat)
{
if (arg_a.iscomplex ()
|| arg_b.iscomplex ()
|| arg_c.iscomplex ())
{
// Do everything in complex arithmetic;
FloatComplexMatrix ca = arg_a.float_complex_matrix_value ();
FloatComplexMatrix cb = arg_b.float_complex_matrix_value ();
FloatComplexMatrix cc = arg_c.float_complex_matrix_value ();
retval = Sylvester (ca, cb, cc);
}
else
{
// Do everything in real arithmetic.
FloatMatrix ca = arg_a.float_matrix_value ();
FloatMatrix cb = arg_b.float_matrix_value ();
FloatMatrix cc = arg_c.float_matrix_value ();
retval = Sylvester (ca, cb, cc);
}
}
else
{
if (arg_a.iscomplex ()
|| arg_b.iscomplex ()
|| arg_c.iscomplex ())
{
// Do everything in complex arithmetic;
ComplexMatrix ca = arg_a.complex_matrix_value ();
ComplexMatrix cb = arg_b.complex_matrix_value ();
ComplexMatrix cc = arg_c.complex_matrix_value ();
retval = Sylvester (ca, cb, cc);
}
else
{
// Do everything in real arithmetic.
Matrix ca = arg_a.matrix_value ();
Matrix cb = arg_b.matrix_value ();
Matrix cc = arg_c.matrix_value ();
retval = Sylvester (ca, cb, cc);
}
}
return retval;
}
/*
%!assert (sylvester ([1, 2; 3, 4], [5, 6; 7, 8], [9, 10; 11, 12]), [1/2, 2/3; 2/3, 1/2], sqrt (eps))
%!assert (sylvester (single ([1, 2; 3, 4]), single ([5, 6; 7, 8]), single ([9, 10; 11, 12])), single ([1/2, 2/3; 2/3, 1/2]), sqrt (eps ("single")))
## Test input validation
%!error sylvester ()
%!error sylvester (1)
%!error sylvester (1,2)
%!error sylvester (1, 2, 3, 4)
%!error <A must be a square matrix> sylvester (ones (2,3), ones (2,2), ones (2,2))
%!error <B must be a square matrix> sylvester (ones (2,2), ones (2,3), ones (2,2))
%!error <nonconformant matrices> sylvester (ones (2,2), ones (2,2), ones (3,3))
*/
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