function u = fps(p, isSlope)

% fps -- Fast Poisson solver with boundary values.
%  fps(p) solves laplacian(u) = p for u, assuming the
%   boundary values are given along the perimeter of p
%   and the laplacians are given in the interior.
%  fps(p, isSlope) solves using the perimeter of p
%   as values of slope, if isSlope is logically TRUE.
%  fps([m n]) demonstrates itself with an n-by-n array
%   (default = [20 20]), with an off-center spike.
 
% Copyright (C) 1998 Dr. Charles R. Denham, ZYDECO.
%  All Rights Reserved.
%   Disclosure without explicit written consent from the
%    copyright owner does not constitute publication.

% Reference: Press, et al., Numerical Recipes,
%    Cambridge University Press, 1986 and later.
 
% Version of 23-Oct-1998 09:02:58.
% Revised    26-Oct-1998 14:29:11.
% Revised    28-Oct-1998 15:36:22.

% NB -- I am not happy with the zero-slope solution.
%  The graphs don't look correst, and they need
%  some scaling.

if nargin < 1, help(mfilename), p = 'demo'; end
if nargin < 2, isSlope = 0; end

if ischar(isSlope), isSlope = eval(isSlope); end
isSlope == any(isSlope(:));

if isequal(p, 'demo'), p = 20; end
if ischar(p), p = eval(p); end
if length(p) == 1, p = [p p]; end

if length(p) == 2
	theSize = p;
	p = zeros(theSize);
	[m, n] = size(p);
	p(ceil(m/3), ceil(n/3)) = 1;
	if nargout > 0
		u = feval(mfilename, p, isSlope);
	else
		feval(mfilename, p, isSlope)
	end
	return
end

% Fold the boundary into source terms.

if ~isSlope
	theFactor = -1;   % Boundary-value scheme.
else
	theFactor = +2;   % Boundary-slope scheme.
end

q = p;
for i = 1:2
	q = q.';
	q(2:end-1, 2:end-3:end-1) = ...
		q(2:end-1, 2:end-3:end-1) + theFactor * q(2:end-1, 1:end-1:end);
end

% Extract the interior.

q = q(2:end-1, 2:end-1);

% Symmetry: odd if 'value'; even if 'slope'.

if ~isSlope
	theSign = -1;   % Odd-symmetry, sine-transform scheme.
else
	theSign = +1;   % Even-symmetry, cosine-transform scheme.
end

[m, n] = size(q);
q = [zeros(m, 1) q zeros(m, 1) theSign*fliplr(q)];
q = [zeros(1, 2*n+2); q; zeros(1, 2*n+2); theSign*flipud(q)];

% Fast Poisson Transform.

res = fpt(q);

% Retain relevant piece.

if ~isSlope
	result = p;
	result(2:end-1, 2:end-1) = res(2:m+1, 2:n+1);
else
	result = res(1:m+2, 1:n+2);
end

% Output or plot solution.

if nargout > 0
	u = result;
else
	subplot(2, 2, 1), surf(p), axis tight
	title('Laplacian Data'), xlabel('x'), ylabel('y'), zlabel('p')
	subplot(2, 2, 2), surf(result), axis tight
	title('Poisson Solution'), xlabel('x'), ylabel('y'), zlabel('u')
	subplot(2, 2, 3), plot(p), axis tight
	xlabel('x'), ylabel('p')
	subplot(2, 2, 4), plot(result), axis tight
	xlabel('x'), ylabel('u')
	figure(gcf)
end