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LanczosCGS_eigenValue.m
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LanczosCGS_eigenValue.m
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G = gallery('grcar',50);
v = ones(50,1);
% eigenV = eig(G)%LanczosCGS(G,v,50);
% size(eigenV)
% plot(eigenV,'*r')
h = figure;
eigenV = eig(G);
plot(eigenV,'*r')
axis tight manual
ax = gca;
ax.NextPlot = 'add';
loops = 50;
M(loops) = struct('cdata',[],'colormap',[]);
%h.Visible = 'off';
for j = 1:loops
eigenV = LanczosCGS(G,v,j)
plot(eigenV,'*b')
drawnow
M(j) = getframe;
end
h.Visible = 'on';
movie(M,12,2);
function RitzValues = LanczosCGS(A,v,k)
%note output has been changed from the original code
T = zeros(k+1,k);
v = v/norm(v); V = v;
w = A*v; a(1) = v'*w;
w = w - v*a(1); b(2) = norm(w);
v = w/b(2); V = [V v];
%forming of first column of T
t = [a(1) b(2) zeros(1,k-1)];
T(:,1) = t';
%solving eigenvalue problem
[y,mu] = eig(T(1,1));
Mu=[1];
Mu = [Mu, mu(1,1)];
r = [abs(T(2,1))*abs(y(1,1))];
Table=[Mu; T(k+1,k) r];
disp(Table)
for j=2:k
r = [];
%Lanczos iteration
w = A*v;
a(j) = v'*w;
w = w - b(j)*V(:,j-1)-a(j)*v;
b(j+1) = norm(w);
v = w/b(j+1);
V = [V v];
%forming of rest of the columns of T
t = [zeros(1,j-2) b(j) a(j) b(j+1) zeros(1,k-j)];
T(:,j) = t';
%solving eigenvalue problem
[y,mu] = eig(T(1:j,1:j));
Mu=[j];
for i=1:j
Mu = [Mu, mu(i,i)];
r = [r,abs(T(i+1,i))*abs(y(i,i))];
end
Table=[Mu; T(k+1,k) r];
%disp(Table)
end
RitzValues = diag(mu)
end