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unvech.m

## Copyright (C) 2006  Michael Creel <michael.creel@uab.es>
##
## This program 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 of the License, or
## (at your option) any later version.
##
## This program 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 this program; If not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} unvech (@var{v})
## Performs the reverse of "vech". Generates a symmetric matrix from the lower
## triangular elements, received as a vector @var{v}.
## @end deftypefn

# Note: this uses a double loop. A C version would be a lot faster for large matrices.
## Adapted-By:  Ben Hall <benjamin.hall@pw.utc.com>

function x = unvech (v)

      if (nargin != 1)
            usage ("unvech (v)");
      endif

      if (! isvector(v))
            usage ("unvech (v)");
      endif

      # find out dimension of symmetric matrix
      p = length(v);
      g = -(1 - sqrt(1 + 8*p))/2;

      if (mod(g,1) != 0)
            error("unvech: the input vector does not generate a square matrix");
      endif

      x = zeros(g,g);

      # fill in the symmetric matrix, the obvious way
#     k = 1;
#     for i = 1:g
#           for j = i:g
#                 x(i,j) = v(k);
#                 if (i != j) x(j,i) = v(k); endif
#                 k = k + 1;
#           endfor
#     endfor

      # fill in the symmetric matrix, a more clever way
      ii = repmat( 1:g, [g 1] );
      idx= find( ii <= ii' );
      x(idx) = v;
      x = x + x' - diag(diag(x));
endfunction

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