# HG changeset patch
# User Jordi Gutiérrez Hermoso <jordigh@octave.org>
# Date 1345133525 14400
# Node ID 3a33f93c9e62937a69cb920b2f3adb7cfd7de4f2
# Parent  82d51d6e470c23c748a53a6fd8b82c3d5e7e1614# Parent  045ae93e8fe9a7b4b2ddd1b66caa36a4129bb7a7
Merge in polyeig

diff -r 82d51d6e470c -r 3a33f93c9e62 NEWS
--- a/NEWS	Tue Aug 14 15:54:43 2012 -0400
+++ b/NEWS	Thu Aug 16 12:12:05 2012 -0400
@@ -82,11 +82,10 @@
       
  ** Other new functions added in 3.8.0:
 
-      betaincinv   erfcinv      splinefit
-      cmpermute    findfigs     tetramesh
-      cmunique     fminsearch   rgbplot     
-      colorcube    lines        shrinkfaces 
-
+      betaincinv   erfcinv      polyeig      shrinkfaces 
+      cmpermute    findfigs     splinefit
+      cmunique     fminsearch   tetramesh
+      colorcube    lines        rgbplot     
  ** Deprecated functions.
 
     The following functions were deprecated in Octave 3.4 and have been
diff -r 82d51d6e470c -r 3a33f93c9e62 doc/interpreter/poly.txi
--- a/doc/interpreter/poly.txi	Tue Aug 14 15:54:43 2012 -0400
+++ b/doc/interpreter/poly.txi	Thu Aug 16 12:12:05 2012 -0400
@@ -84,6 +84,8 @@
 
 @DOCSTRING(roots)
 
+@DOCSTRING(polyeig)
+
 @DOCSTRING(compan)
 
 @DOCSTRING(mpoles)
diff -r 82d51d6e470c -r 3a33f93c9e62 scripts/help/unimplemented.m
--- a/scripts/help/unimplemented.m	Tue Aug 14 15:54:43 2012 -0400
+++ b/scripts/help/unimplemented.m	Thu Aug 16 12:12:05 2012 -0400
@@ -310,7 +310,6 @@
   "plotbrowser",
   "plotedit",
   "plottools",
-  "polyeig",
   "prefdir",
   "preferences",
   "printdlg",
diff -r 82d51d6e470c -r 3a33f93c9e62 scripts/polynomial/polyeig.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/polynomial/polyeig.m	Thu Aug 16 12:12:05 2012 -0400
@@ -0,0 +1,84 @@
+## Copyright (C) 2012 Fotios Kasolis
+##
+## 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/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
+## @deftypefnx {Function File} {[ @var{v}, @var{z} ] =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
+## Solve the polynomial eigenvalue problem of degree @var{l}.
+##
+## Given a @var{n*n} matrix polynomial @var{C(s)} = @var{C0 + C1 s + @dots{} + Cl s^l} polyeig 
+## solves the eigenvalue problem (@var{C0} + @var{C1} + @dots{} + @var{Cl})v = 0.
+## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial. @var{z} is a
+## @var{lxn} vector and @var{v} is a @var{(n x n)l} matrix with columns that correspond to
+## the eigenvectors.
+## @seealso{eig, eigs, compan}
+## @end deftypefn
+
+## Author: Fotios Kasolis
+
+function [ z, varargout ] = polyeig (varargin)
+  
+  if ( nargout > 2 )
+    print_usage ();
+  endif
+
+  nin = numel (varargin);
+
+  n = zeros (1, nin);
+
+  for cnt = 1 : nin
+    if ! ( issquare (varargin{cnt}) )
+       error ("polyeig: coefficients must be square matrices");
+    endif
+    n(cnt) = size (varargin{cnt}, 1);
+  endfor
+
+  if numel (unique (n)) > 1
+       error ("polyeig: coefficients must have the same dimensions");
+  endif
+  n = unique (n);
+
+  # matrix polynomial degree
+  l = nin - 1;
+
+  # form needed matrices
+  C = [ zeros(n * (l - 1), n), eye(n * (l - 1)); -cell2mat(varargin(1 : end - 1)) ];
+  D = [ eye(n * (l - 1)), zeros(n * (l - 1), n); zeros(n, n * (l - 1)), varargin{end} ];
+
+  % solve generalized eigenvalue problem
+  if ( isequal (nargout, 1) )
+    z = eig (C, D);
+  else
+    [ z, v ] = eig (C, D);
+    varargout{1} = v;
+    % return n-element eigenvectors normalized so
+    % that the infinity-norm = 1
+    z = z(1:n,:);
+    % max() takes the abs if complex:
+    t = max(z);
+    z /= diag(t);
+  endif
+
+endfunction
+
+%!test
+%! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1];
+%! [v,z] = polyeig (C0, C1);
+%! assert (isequal (z(1), -8), true);
+%! d = C0*v + C1*v*z
+%! assert (isequal (norm(d), 0.0), true);