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unvech.m    84 lines (69 with data), 2.6 kB

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## Copyright (C) 2006 Michael Creel <michael.creel@uab.es>
## Copyright (C) 2009 Jaroslav Hajek <highegg@gmail.com>
## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## Copyright (c) 2011 CarnĂŤ Draug <carandraug+dev@gmail.com>
##
## 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 3 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} {@var{m} =} unvech (@var{v}, @var{scale})
## Performs the reverse of @code{vech} on the vector @var{v}.
##
## Given a Nx1 array @var{v} describing the lower triangular part of a
## matrix (as obtained from @code{vech}), it returns the full matrix.
##
## The upper triangular part of the matrix will be multiplied by @var{scale} such
## that 1 and -1 can be used for symmetric and antisymmetric matrix respectively.
## @var{scale} must be a scalar and defaults to 1.
##
## @seealso{vech, ind2sub}
## @end deftypefn
function M = unvech (v, scale = 1)
if ( nargin < 1 || nargin > 2 )
print_usage;
elseif ( !ismatrix (v) && any (size (v) != 1) )
error ("V must be a row or column matrix")
elseif ( !isnumeric (scale) || !isscalar (scale) )
error ("SCALE must be a scalar")
endif
N = length (v);
dim = (sqrt ( 1 + 8*N ) - 1)/2;
[r, c] = ind2sub_tril (dim, 1:N);
M = accumarray ([r; c].', v);
M += scale * tril (M, -1).';
endfunction
function [r c] = ind2sub_tril(N,idx)
%% Horrible lengthly check
if nargin < 2 ||( !isnumeric (N) && all(size(N)==1) )|| ...
!( ismatrix (idx) && any (size (idx)==1) )
print_usage;
endif
endofrow = 0.5*(1:N) .* (2*N:-1:N + 1);
c = lookup(endofrow, idx-1)+1;
r = N - endofrow(c) + idx ;
end
%!assert(unvech([1;0;0;1;0;1]), full(eye(3,3)) );
%!test %symmetric
%! dim = 10;
%! A = tril( floor ( 5*(2*rand(dim)-1) ) );
%! A += A.';
%! M = vech(A);
%! M = unvech(M, 1);
%! assert (A, M);
%!test %antisymmetric
%! dim = 10;
%! A = tril( floor ( 5*(2*rand(dim)-1) ) );
%! A -= A.';
%! M = vech(A);
%! M = unvech(M, -1);
%! assert (A, M);