unvech function for possible inclusion in Octave

[Michael Creel]

Hello all,

Below is an unvech function, that I'm offering for inclusion in Octave. This 
just reverses the vech operator. For example:

octave:1> a = rand(3,3);
octave:2> a = a'*a
a =

  0.41979  0.59313  0.49142
  0.59313  1.52968  0.45800
  0.49142  0.45800  0.71002

octave:3> b = vech(a)
b =

  0.41979
  0.59313
  0.49142
  1.52968
  0.45800
  0.71002

octave:4> unvech(b)
ans =

  0.41979  0.59313  0.49142
  0.59313  1.52968  0.45800
  0.49142  0.45800  0.71002

octave:5>

An example where this can be useful is if a covariance matrix needs to be 
passed as part of a parameter vector. This lets you easily reconstruct the 
covariance matrix.

Cheers, Michael


## Copyright (C) 2006  Michael Creel <address@hidden>
##
## 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, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## -*- 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.

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
        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
endfunction