## Copyright (C) 1996, 1997 Auburn University.  All rights reserved.
##
## 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, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c})
## @deftypefnx {Function File} {} lyap (@var{a}, @var{b})
##   Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart
##   algorithm (Communications of the ACM, 1972).
## 
##   If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns
##   the solution of the  Sylvester equation
##   @iftex
##     @tex
##       $$ A X + X B + C = 0 $$
##     @end tex
##   @end iftex
##   @ifinfo
##     @example
##       a x + x b + c = 0
##     @end example
##   @end ifinfo
##   If only @code{(a, b)} are specified, then @code{lyap} returns the
##   solution of the Lyapunov equation
##   @iftex
##     @tex
##       $$ A^T X + X A + B = 0 $$
##     @end tex
##   @end iftex
##   @ifinfo
##     @example
##       a' x + x a + b = 0
##     @end example
##   @end ifinfo
##   If @var{b} is not square, then @code{lyap} returns the solution of either
##   @iftex
##     @tex
##       $$ A^T X + X A + B^T B = 0 $$
##     @end tex
##   @end iftex
##   @ifinfo
##     @example
##       a' x + x a + b' b = 0
##     @end example
##   @end ifinfo
##   @noindent
##   or
##   @iftex
##     @tex
##       $$ A X + X A^T + B B^T = 0 $$
##     @end tex
##   @end iftex
##   @ifinfo
##     @example
##       a x + x a' + b b' = 0
##     @end example
##   @end ifinfo
##   @noindent
##   whichever is appropriate.
##
## Solves by using the Bartels-Stewart algorithm (1972).
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe

function x = lyap (a, b, c)

  if (nargin != 3 && nargin != 2)
    usage ("lyap (a, b {,c})");
  endif

  if ((n = is_square(a)) == 0)
    error ("lyap: a is not square");
  endif

  if (nargin == 2)

    ## Transform Lyapunov equation to Sylvester equation form.

    if ((m = is_square (b)) == 0)
      if ((m = rows (b)) == n)

	## solve a x + x a' + b b' = 0

	b = b * b';
	a = a';
      else

	## Try to solve a'x + x a + b' b = 0.

	m = columns (b);
	b = b' * b;
      endif

      if (m != n)
	error ("lyap: a, b not conformably dimensioned");
      endif
    endif

    ## Set up Sylvester equation.

    c = b;
    b = a;
    a = b';

  else

    ## Check dimensions.

    if ((m = is_square (b)) == 0)
      error ("lyap: b must be square in a sylvester equation");
    endif

    [n1, m1] = size(c);

    if (n != n1 || m != m1)
      error("lyap: a,b,c not conformably dimensioned");
    endif
  endif

  ## Call octave built-in function.

  x = syl (a, b, c);

endfunction