How can't a matrix be generated randomly?

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 !

Answer 1

[Kye Taylor]

If I understand you correctly, each column represents a different trial. What does the iteration variable n (going from 1 to 2.1e7) represent? Also, the line of code

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

makes no assignment and seems to be independent of your matrix y... unless delta_E is calculated using y somehow?

Can you describe what your goals is in more detail?

In the meantime, the following code creates a 100-by-2000 double array... selects a random entry in each column and assigns a random number between -1 and 8 to that entry.

y = zeros(100,2000);
randomRowIndex = randi(100,1,2000); % select random row for each column
randomLinearIndex= sub2ind(size(y), randomRowIndex, 1:2000); % linear index
y(randomLinearIndex) = randi(10,size(randomLinearIndex)) - 2; % the random #s

[Peter Perkins]

Perhaps even simpler, that last line could be

randi([-1 8],size(randomLinearIndex));