function x = tensor_sol(a, b, ka, kx)

% tensor_sol -- Tensor solve.
%  tensor_sol(a, b, ka, kx) solves for tensor x in a*x = b,
%   for summations along the respective ka and kx directions.
%   If the directions are not specified, the innermost ones
%   are assumed.
%  tensor_sol('demo') demonstrates itself with two 2-by-2
%   random arrays.
%
% Also see: tensor_mul, 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, x = []; 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; kx = 1;
	result = tensor_sol(a, b, ka, kx);
	begets(mfilename, 4, a, b, ka, kx, result)
	ka = 1; kx = 1;
	result = tensor_sol(a, b, ka, kx);
	begets(mfilename, 4, a, b, ka, kx, result)
	ka = 1; kx = 2;
	result = tensor_sol(a, b, ka, kx);
	begets(mfilename, 4, a, b, ka, kx, result)
	ka = 2; kx = 2;
	result = tensor_sol(a, b, ka, kx);
	begets(mfilename, 4, a, b, ka, kx, 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, kx = 1; end

% Compatibility of sizes.

u = sa;
u(ka) = [];
v = sb(1:length(u));
if ~isequal(u, v)
	s = [mat2str(sa) ' vs ' mat2str(sb)];
	warning([' ## Incompatible sizes: ' s '.'])
	return
end

% Size of result.

sx = sb;
sx(1:length(sa)-1) = [];
ix = [1:length(sx) (kx-0.5)];
sx = [sx sa(ka)];
[ignore, ind] = sort(ix);
sx = sx(ind);

% 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(kx, 1)) | kx < 1 | kx > length(sx)
	s = num2str(kx);
	warning([' ## Second direction index incompatible: ' s '.'])
	return
end

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

% 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
sa = size(a);

% Form two-dimensional a.

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

% Transpose a.

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

% Form two-dimensional b.

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

% Matrix solve and reshape.

x = reshape(a \ b, sx);

% Inverse permutation of x.

px = 1:length(sx);
if kx > 1
	px(kx) = -px(kx);
	px = abs(sort(px));
	x = ipermute(x, px);
end