% This program was used to test helmsolve submissions.
% DPO 05/2005

% Set parameters.

n = 10;
kappa = 5;

% Generate the Laplacian matrix K  using a program
% derived from an earlier homework, and generate
% a random true solution wtrue.
% The right-hand side is then generated
% to match K, kappa, and wtrue.

[K,f,rhs,h] = laplace2d(n);
wtrue = rand(n^2,1)
rhs = K*wtrue - kappa^2*wtrue;

% Call helmsolve.

f = reshape(rhs,n,n);
w = helmsolve(kappa,f);

% Reshape the solution as a vector 
% and compute the norm of the residual and
% the norm of the error.  
% Both of these norms should be very small.

wlong = reshape(w,n^2,1);

resid = norm(K*wlong - kappa^2*wlong -rhs)
err = norm(wtrue-wlong)

% The following line can be used for checking.
%wtrue = (K -kappa^2*speye(n^2))\rhs;