function [  ] = myNiceProgram(  )
%MYNICEPROGRAM Joli programme qui resout
%  une equation de Laplace par des
%  differences finies sur un rectangle
%
%   Programme dedie a Gregoire et Jean-Francois
%   

close all;
factor = 20;
nx = 7*factor;
ny = 4*factor;
n = nx*ny
h = 2/(ny-1);
%A = sparse(n,n)
%for i=1:n
%    A(i,i) = 1;
%end
A = spdiags(ones(n,1),0,n,n);

%A = diag(ones(n,1));
B = zeros(n,1);
for i = 2:nx-1
    for j = 2:ny-1
        index = i + (j-1)*nx;
        A(index,index) = 4;
        A(index,index+1) = -1;
        A(index,index-1) = -1;
        A(index,index+nx) = -1;
        A(index,index-nx) = -1;
            B(index) = 1;

    end
end

A = A./(h*h);

spy(A)

tic
U = A\B;
toc

figure
U = reshape(U,nx,ny)';
X = linspace(-2,2,nx);
Y = linspace(-1,1,ny);
contourf(X,Y,U); 
axis off; axis equal;

figure
mesh(X,Y,U);
view(2); axis off; axis equal;


end