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Copy pathTwoDpoissonFast.m
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TwoDpoissonFast.m
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N = 16;
% initialized rho_{i,j}
rho_init =[
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 2.50e+01 5.00e+01 5.00e+01 5.00e+01 2.50e+01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 5.00e+01 1.00e+02 1.00e+02 1.00e+02 5.00e+01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 5.00e+01 1.00e+02 1.00e+02 1.00e+02 5.00e+01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 5.00e+01 1.00e+02 1.00e+02 1.00e+02 5.00e+01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 2.50e+01 5.00e+01 5.00e+01 5.00e+01 2.50e+01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00
];
% Setting up S_N
SN = zeros(N-1,N-1);
for i = 1: N-1
for j = 1: N-1
SN(i,j) = sin(i*j*pi/N);
end
end
rho1 = zeros(size(SN));
rho2 = zeros(size(SN));
psi0 = zeros(size(SN));
psi1 = zeros(size(SN));
psi2 = zeros(size(SN));
% Calculating rho^{k,l} -- equation (5.4)
for i = 1: N-1
rho1(i,:) = (SN*rho_init(i,:)')';
end
for j = 1: N-1
rho2(:,j) = (SN*rho1(:,j));
end
rho3 = (4/N/N).*rho2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculating psi^{k,l} -- equation (5.6)
for i = 1: N-1
for j = 1: N-1
psi0(i,j) = rho3(i,j)/N/N/(4-2*(cos(i*pi/N)+cos(j*pi/N)));%/(pi*pi*(i^2 + j^2));
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculating equation (5.5)
for j = 1: N-1
psi1(:,j) = (SN*psi0(:,j));
end
for i = 1: N-1
psi2(i,:) = (SN*psi1(i,:)')';
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
contour(psi2);
colorbar;