/usr/share/octave/packages/3.2/linear-algebra-2.1.0/ndcovlt.m is in octave-linear-algebra 2.1.0-1.
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##
## Author: Jaroslav Hajek <highegg@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; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn{Function File} {@var{y} =} ndcovlt (@var{x}, @var{t1}, @var{t2}, @dots{})
## Computes an n-dimensional covariant linear transform of an n-d tensor, given a
## transformation matrix for each dimension. The number of columns of each transformation
## matrix must match the corresponding extent of @var{x}, and the number of rows determines
## the corresponding extent of @var{y}. For example:
##
## @example
## size (@var{x}, 2) == columns (@var{t2})
## size (@var{y}, 2) == rows (@var{t2})
## @end example
##
## The element @code{@var{y}(i1, i2, @dots{})} is defined as a sum of
##
## @example
## @var{x}(j1, j2, @dots{}) * @var{t1}(i1, j1) * @var{t2}(i2, j2) * @dots{}
## @end example
##
## over all j1, j2, @dots{}. For two dimensions, this reduces to
## @example
## @var{y} = @var{t1} * @var{x} * @var{t2}.'
## @end example
##
## [] passed as a transformation matrix is converted to identity matrix for
## the corresponding dimension.
##
## @end deftypefn
function y = ndcovlt (x, varargin)
nd = max (ndims (x), nargin - 1);
varargin = resize (varargin, 1, nd);
# check dimensions
for i = 1:nd
ti = varargin{i};
if (isnumeric (ti) && ndims (ti) == 2)
[r, c] = size (ti);
if (r + c == 0)
varargin{i} = eye (size (x, i));
elseif (c != size (x, i))
error ("ndcovt: dimension mismatch for x-th transformation matrix");
endif
else
error ("ndcovt: transformation matrices must be numeric 2d matrices");
endif
endfor
if (isempty (x))
szy = cellfun (@rows, varargin);
y = zeros (szy);
return
endif
ldp = [2:nd, 1];
## First transformation.
y = ldtrans (x, varargin{1});
## Always shift one dimension.
for i = 2:nd-1
y = ldtrans (permute (y, ldp), varargin{i});
endfor
## Permute to normal order now to save one permutation.
if (nd > 2)
y = ipermute (y, [nd-1:nd, 1:nd-2]);
endif
## Now multiply from the right.
szy = size (y);
szy(end+1:nd-1) = 1;
m = varargin{nd};
szy(nd) = rows (m);
y = reshape (y, [], size (y, nd));
y = reshape (y * m.', szy);
endfunction
function y = ldtrans (x, m)
sz = size (x);
sz(1) = rows (m);
y = reshape (m * x(:,:), sz);
endfunction
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