-
Notifications
You must be signed in to change notification settings - Fork 0
/
ArnoldiMovi.m
58 lines (48 loc) · 933 Bytes
/
ArnoldiMovi.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
dimension = 50;
G = gallery('grcar',dimension);
v = ones(dimension,1);
% eigenV = eig(G)%LanczosCGS(G,v,50);
% size(eigenV)
% plot(eigenV,'*r')
h = figure;
eigenV_Ref = eig(G);
plot(eigenV_Ref,'*r');
axis tight manual
ax = gca;
ax.NextPlot = 'replacechildren';
loops = dimension;
M(loops) = struct('cdata',[],'colormap',[]);
h.Visible = 'off';
for j = 1:loops
j
eigenV = ArnoldiRitz(G,v,j);
size(eigenV)
plot(eigenV_Ref,'*r');
hold on;
plot(eigenV,'*b');
hold off;
drawnow
axis([-1,3, -4, 4])
M(j) = getframe;
end
h.Visible = 'on';
movie(M);
function RitzValues = ArnoldiRitz(A,v,k)
v = v/norm(v);
V = v; H = [];
n = size(v);
for j=1:k
w = A*v;
q = w;
for l = 1:size(V,2)
w = w-V(:,l)*(V(:,l)'*w);
end
g = norm(w);
v = w/g;
h = V'*q;
V = [V v];
H = [H,h; zeros(1,j-1),g];
end
H_kk = H(1:k,1:k);
RitzValues = eig(H_kk);
end