How to efficiently create a matrix of random numbers generating independently?

Hi,

I want to have a 100-by-2000 matrix of random numbers. Each column of random numbers is generated by an independent stream. It means there should be 2000 independent streams.

I learn from "Help: Create three independent streams"

[s1,s2,s3] = RandStream.create('mrg32k3a','NumStreams',3);
r1 = rand(s1,100000,1); r2 = rand(s2,100000,1); r3 = rand(s3,100000,1);

It is very easy with 3 independent streams.

How can I efficiently create this matrix of random numbers from 2000 independent streams?

Thank you!

Are you sure that you need 2000 independent streams? Will you be able to distinguish it from rand(100, 20000)?

+1 Jan

My first attempt to generate the 100-by-2000 matrix with random numbers is simply using "rand" or "randi."

The three main steps involving random numbers generation in the script are as followed.

len=100;

R=2000;

y=zeros(len,R);

for n=1:2.1e7

N=(0:len:(R-1)*len)+randi(len,1,R); % Only one element in each column was randomly selected.

y(N)=-1+9*rand(1,R); % The selected element of y matrix was replaced with a random number uniformly distributed from -1 to 8.

A=find(deltaE>0); %Compare E values calculated from y values in each column

exp(-delta_E/k/T)>rand(1,length(A)); %Accept E values when it meets the criterion.

end

When this for-loop finished, I observed clearly that the y values in the last 200 to 500 columns fluctuated around zero or still are zero but the all other y values from column 1 to column 1500 vary between -1 and 8.

I don't understand why this happen. I expected all columns should vary between -1 and 8.

The goal I want to reach is that all the random number generating(random N, random y values, rand(1,length(A)) in each column is independent to each other. The calculation of E value in each column is a independent simulation (i.e. I want to do 2000 independent simulations simultaneously).

However,the present results I have is that some columns seems untouched.

How can I modify the script to accomplish my goal?

Thanks !