about random number and matrix

If I have only one random number rand(1) , R1 (1X N) and R2(1XN) are both vector of size N.

R1=a*[0:n-1];
R2=b*[0:n-1];
R2=rand(1)+R2; % add rand(1) to every element in R2
del=R1-R2' ; % "row vector-column vector" is interpreted as "matrix-matrix" with appropriate duplication of rows and columns

But i want to do monte carlo simulation so I need a lot of rand(1). For example rand(1000000,1). But i dont want to use any loops since it is unefficient.

How can I still do the two steps above ?

[Ameer Hamza]

"But i dont want to use any loops since it is unefficient."

not necessarily:

https://www.mathworks.com/matlabcentral/answers/467159-for-loop-faster-than-vectorized

https://www.mathworks.com/matlabcentral/answers/301008-vectorized-code-slower-than-loops

[Walter Roberson]

Suppose you have the J'th entry in R1, the K'th entry in R2, and the L'th entry in rand(1000000,1), then where in del would you like the result to go, and how would you calculate it in terms of R1(J), R2(K), rands(L) ?

[Zichao Wang]

for example in one random number case, i need find some certain elemnts(fulfill some up and down bondary) in del and dont need R1 and R2 anymore.

[Walter Roberson]

That did not answer my question.

Your R1 is length n, and your R2 is length n as well, and you have 1000000 random numbers. What size of output of del do you want? n x n x 1000000 ? n x n x 1000000 x 1000000 ?

[Zichao Wang]

I am not sure . I want each random can generate a corrponding del. So i need 100000 of del (n X n)

so n x n x 1000000 i guess

Answer 1

[Walter Roberson]

R1=a*[0:n-1];
R2=b*[0:n-1];
R2=rand(1, 1, 100000)+R2.'; % add rand to every element in R2
del=R1-R2 ; % "row vector-column vector" is interpreted as "matrix-matrix" with appropriate duplication of rows and columns

[Zichao Wang]

how can i select element in this del ? still the same?

[Walter Roberson]

del(:,:,K)

is the n x n array that is appropriate to the K'th random number .

Just like in your code, R1 varies as you go "across", and R2 varies as you go "down". The 100000 random values go "out"

[Zichao Wang]

What if I want to plot all the del(:,:,K) as a histogram ?

[Zichao Wang]

and i find that in that way del is 1X N X 100000 not exactly N X N X 100000

[Walter Roberson]

Please re-check.

>> a = rand; b = rand; n = 5; R1=a*[0:n-1]; R2=b*[0:n-1]; R2=rand(1, 1, 100000)+R2.'; del=R1-R2 ;
>> size(del)

ans =

           5           5      100000

[Walter Roberson]

NB = 20;    %number of bins
mind = min(del(:)); maxd = max(del(:));
bins = linspace(mind,maxd,NB); centers = mean([bins(1:end-1);bins(2:end)]);

counts = arrayfun(@(R,C) histcounts(del(R,C,:), bins), ndgrid(1:n,1:n), meshgrid(1:n,1:n), 'uniform', 0);
h = arrayfun(@(idx) bar(subplot(n,n,idx), centers, counts{idx}), 1:n^2);