function [x, err_norm] = xabx(a, b, c, TRANSPOSE_FLAG)

% xabx -- Solve x*a + b*x = c for x.
%  xabx(a, b, c, 'TRANSPOSE_FLAG') solves the linear
%   system x*a + b*x = c for x.  If the TRANSPOSE_FLAG
%   is any string, then the system to be solved is
%   x'*a + b*x = c for x.
%  xabx(a, c, 'TRANSPOSE_FLAG') solves the linear
%   system x*a + a*x = c or x'*a + a*x = c for x.
%  [x, err_norm] = ... returns x and the error-norm.
 
% Copyright (C) 1997 Dr. Charles R. Denham, ZYDECO.
%  All Rights Reserved.
%   Disclosure without explicit written consent from the
%    copyright owner does not constitute publication.

if nargin < 1, help xabx, a = 2; end

if nargin < 2
   n = a;
   if isstr(n), n = eval(n); end
   a = fix(rand(n, n) .* 10);
   b = fix(rand(n, n) .* 10);
   c = fix(rand(n, n) .* 10);
   if n < 4, a, b, c, end
   if nargout > 0
      [x, err_norm] = xabx(a, b, c);
     else
      xabx(a, b, c)
   end
   return
end

flag = 0;

if nargin == 4
   if isstr(TRANSPOSE_FLAG)
      flag = 1;
   end
  elseif nargin == 3
   if isstr(c)
      flag = 1;
      c = b;
      b = a;
   end
  elseif nargin == 2
   c = b;
   b = a;
end

[ma, na] = size(a);
[mb, nb] = size(b);
[mc, nc] = size(c);

if na ~= nc | mb ~= mc
   error(' ## Incompatible data sizes.')
   return
end

% Construct u and v as index-arrays for x.

mv = nb; nv = nc;
v = zeros(mv, nv); v(:) = 1:prod(size(v));
u = v; if flag, u = u.'; end
[mu, nu] = size(u);

% Construct d to solve d * x(:) = c(:).

d = zeros(prod(size(v)), prod(size(c)));

% Assemble the x*a portion first.

k = 0;
for j = 1:na
   for i = 1:mu
      indices = u(i, :);
      k = k + 1;
      d(k, indices) = d(k, indices) + a(:, j).';
   end
end

% Assemble the b*x portion next.

k = 0;
for j = 1:nv
   for i = 1:mb
      indices = v(:, j);
      k = k + 1;
      d(k, indices) = d(k, indices) + b(i, :);
   end
end

% Solve the system.

v(:) = d \ c(:);   % v is already the right size.

% Error-norm.

if nargout ~= 1
   u = v; if flag, u = u'; end
   err_norm = norm(u*a + b*v - c);
end

% Output.

if nargout > 0
   x = v;
  else
   disp(' '), disp(['ans =']), disp(' '), disp(v), err_norm
end