Getting inf in matrix?

I wrote a code where I’m implementing an algorithm. The code works, but the values in my Z matrix are all inf and I don’t know why. I added a picture so you can see it. r in R^d should a sample drawn uniformly at random from the Fourier transformation of the Gaussian kernel. Gamma is just numbers uniformly at random in (0,2pi). cos(...) is at maximum 1, so I don’t understand why I get inf. Help is appreciated!

n=2000;

d=1000;

s=50;

Gamma=10;

S=randn(n,s);

U=qr(randn(s,d));

F=randn(n,d);

D=zeros(s,s);

for i=1:s

D(i,i)=1-(i-1)/d;

end

X = S*D*U + F/Gamma;

% This is the data matrix

-----------------------------------

function [G_2] = rnca(A,m)

[n,d]=size(A);

G=zeros(n,n);

for k=1:n

for j=1:n

G(k,j)=(1/2*pi)^(d/2)*exp(-norm(A(k,:)-A(j,:))^2/2);

end

end

Z=zeros(n,m);

gamma=0+(2*pi-0)*rand(1,m);

D=fft(G);

r=D(randsample(size(D,1),m),1:d);

for i=1:n

for l=1:m

Z(i,l)=sqrt(2/m)*cos(dot(r(l,:),A(i,:))+gamma(l));

end

end

G_2=Z*Z';

end

[James Tursa]

We can't run pictures. Please post your code as text.

[Walter Roberson]

r is not in R^d because the fourier transform is complex valued. You are taking cos of a complex number and the result of that has value that is exponential growth.

[Desiree]

So how can I fix it?

[Walter Roberson]

is your expectation that the fft will produce a lot of values that are exactly 0? doesn't happen much due to roundoff even for cases that theory say should be 0.

[Desiree]

The values of fft(G) are huge... which I guess it isn't supposed to be...

[Walter Roberson]

what is mean(G)?

[Desiree]

Now I discovered that I missed () when defining G matrix as I forgot to put () on 2*pi.

Now indeed the fft(G) reproduces lots of 0 values and Z ain't inf anymore. So I guess now it is fine?