phd/randspec.m at master · kunegis/phd · GitHub

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%
% Draw the spectral transformation generated by a random sampling of a
% sparse graph.
%
% OUTPUT
%	img-eps/randspec.eps
%	img-eps/randspec.st.eps
%

path(path, '../webstore/analysis');
path(path, '../webstore/matlab');

font_size = 20;

n = 1000;
d = 3;
testsize = .24;
k = 100;

r = d * n;
a = sprand(n, n, r / (n*n));
[x y z] = find(a);

r = size(x,1);

p = randperm(r);

x = x(p);
y = y(p);
z = z(p);

r2 = round(r * testsize);
r1 = r - r2;

x1 = x(1:r1);
y1 = y(1:r1);
z1 = z(1:r1);

x2 = x(1+r1:end);
y2 = y(1+r1:end);
z2 = z(1+r1:end);

a1 = spconvert([x1 y1 z1]);
a2 = spconvert([x2 y2 z2]);

a1(n,n) = 0;
a2(n,n) = 0;

a1 = a1 + a1';
a2 = a2 + a2';

[u1, d1] = eigs(a1, k);

ubu = u1' * a2 * u1;

%
% UBU plot
%
imageubu(ubu);

print('-depsc', 'img-eps/randspec.eps');  close all;

%
% Spectral transformation plot
%

plot(diag(d1), diag(ubu), 'ok');

gridxy([0], [0], 'LineStyle', '--');
set(gca, 'FontSize', font_size);

xlabel('\lambda_k', 'FontSize', font_size);
ylabel('f(\lambda_k)', 'FontSize', font_size);

print('-depsc', 'img-eps/randspec.st.eps');  close all;