function c = tensor_mul(a, b, ka, kb)

% tensor_mul -- Tensor multiplication.
%  tensor_mul(a, b, ka, kb) returns the tensor-product a*b,
%   summed along the respective ka and kb directions, which
%   must have the same length.  If the directions are not
%   specified, the innermost ones are assumed.
%  tensor_mul('demo') demonstrates itself with two 2-by-2
%   random arrays.
%
% Also see: tensor_sol, tensor_test.
 
% Copyright (C) 1998 Dr. Charles R. Denham, ZYDECO.
%  All Rights Reserved.
%   Disclosure without explicit written consent from the
%    copyright owner does not constitute publication.
 
% Version of 16-Sep-1998 05:34:15.

if nargout > 0, c = []; end

if nargin < 1, help(mfilename), a = 'demo'; end

if isequal(a, 'demo')
	a = floor(rand(2, 2) * 10);
	b = floor(rand(2, 2) * 10);
	ka = 2; kb = 1;
	result = tensor_mul(a, b, ka, kb);
	begets(mfilename, 4, a, b, ka, kb, result)
	ka = 1; kb = 1;
	result = tensor_mul(a, b, ka, kb);
	begets(mfilename, 4, a, b, ka, kb, result)
	ka = 1; kb = 2;
	result = tensor_mul(a, b, ka, kb);
	begets(mfilename, 4, a, b, ka, kb, result)
	ka = 2; kb = 2;
	result = tensor_mul(a, b, ka, kb);
	begets(mfilename, 4, a, b, ka, kb, result)
	return
end

if nargin < 2, help(mfilename), return, end

% Size of factors.

sa = size(a);
sb = size(b);

% Default directions.

if nargin < 3, ka = length(sa); end
if nargin < 4, kb = 1; end

% Check size compatibilities.

if any(rem(ka, 1)) | ka < 1 | ka > length(sa)
	s = num2str(ka);
	warning([' ## First direction index incompatible: ' s '.'])
	return
end

if any(rem(kb, 1)) | kb < 1 | kb > length(sb)
	s = num2str(kb);
	warning([' ## Second direction index incompatible: ' s '.'])
	return
end

if sa(ka) ~= sb(kb)
	s = [int2str(sa(ka)) ' ~= ' int2str(sb(kb))];
	warning([' ## Specified directions not same length: ' s '.'])
	return
end

% Size of product.

sc = [sa sb];
sc(length(sa)+kb) = [];
sc(ka) = [];

% Permute a so ka is leftmost direction.

pa = 1:length(sa);
if ka > 1
	pa(ka) = -pa(ka);
	pa = abs(sort(pa));
	a = permute(a, pa);
end

% Permute b so kb is leftmost direction.

pb = 1:length(sb);
if kb > 1
	pb(kb) = -pb(kb);
	pb = abs(sort(pb));
	b = permute(b, pb);
end

% New sizes.

sa = size(a);
sb = size(b);

% Form two-dimensional arrays.

a = reshape(a, [sa(1) prod(sa)/sa(1)]);
b = reshape(b, [sb(1) prod(sb)/sb(1)]);

% Transpose a.

pa = 1:length(sa);
pa([1 2]) = pa([2 1]);
a = permute(a, pa);

% Matrix multiply and reshape.

c = reshape(a * b, sc);