Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / dlyapchol.m

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+## Copyright (C) 2010   Lukas F. Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope 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.
+##
+## LTI Syncope 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 LTI Syncope.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {@var{u} =} dlyapchol (@var{a}, @var{b})
+## @deftypefnx{Function File} {@var{u} =} dlyapchol (@var{a}, @var{b}, @var{e})
+## Compute Cholesky factor of discrete-time Lyapunov equations.
+##
+## @strong{Equations}
+## @example
+## @group
+## A U' U A'  -  U' U  +  B B'  =  0           (Lyapunov Equation)
+##
+## A U' U A'  -  E U' U E'  +  B B'  =  0      (Generalized Lyapunov Equation)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB03OD and SG03BD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{dlyap, lyap, lyapchol}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.2.1
+
+function [u, scale] = dlyapchol (a, b, e)
+
+  switch (nargin)
+    case 2
+      
+      if (! is_real_square_matrix (a))
+        ## error ("dlyapchol: a must be real and square");
+        error ("dlyapchol: %s must be real and square", \
+                inputname (1));
+      endif
+
+      if (! is_real_matrix (b))
+        ## error ("dlyapchol: b must be real")
+        error ("dlyapchol: %s must be real", \
+                inputname (2))
+      endif
+  
+      if (rows (a) != rows (b))
+        ## error ("dlyapchol: a and b must have the same number of rows");
+        error ("dlyapchol: %s and %s must have the same number of rows", \
+                inputname (1), inputname (2));
+      endif
+
+      [u, scale] = slsb03od (a.', b.', true);
+
+      ## NOTE: TRANS = 'T' not suitable because we need U' U, not U U'
+
+    case 3
+
+      if (! is_real_square_matrix (a, e))
+        ## error ("dlyapchol: a, e must be real and square");
+        error ("dlyapchol: %s, %s must be real and square", \
+                inputname (1), inputname (3));
+      endif
+
+      if (! is_real_matrix (b))
+        ## error ("dlyapchol: b must be real");
+        error ("dlyapchol: %s must be real", \
+                inputname (2));
+      endif
+
+      if (rows (b) != rows (a) || rows (e) != rows (a))
+        ## error ("dlyapchol: a, b, e must have the same number of rows");
+        error ("dlyapchol: %s, %s, %s must have the same number of rows", \
+                inputname (1), inputname (2), inputname (3));
+      endif
+
+      [u, scale] = slsg03bd (a.', e.', b.', true);
+
+      ## NOTE: TRANS = 'T' not suitable because we need U' U, not U U'
+
+    otherwise
+      print_usage ();
+
+  endswitch
+
+  if (scale < 1)
+    warning ("dlyapchol: solution scaled by %g to prevent overflow", scale);
+  endif
+
+endfunction
+
+
+## TODO: add tests