Create a matrix of random numbers with different distributions in each entry

Say I have a matrix and I want to add an error to each of the elements, the error should be normally distributed around the element with variance of 0.1 of the value of the element.

That is how I implemented this:

A = [1 2 3 ; 4 5 6 ; 7 8 9]
sz=size(A);
sigma = 0.1*A;
err = zeros(sz);
for i=1:sz(1)
    for j=1:sz(2)
        pd = makedist('Normal','sigma',sigma(i,j));
        err(i,j)=random(pd);
    end
end

Result = A + err;

This is ok for 9 elemens but it is very time consuming when my matrix is 3000X3000

Is there any more efficient way to do so?

Answer 1

[Thiago Henrique Gomes Lobato]

Your code does basically this:

A = [1 2 3 ; 4 5 6 ; 7 8 9]
Result = A + randn(size(A))*0.1;

In your question however you seem to mean that the variance should be 0.1 of the element value, if this is the case do this:

A = [1 2 3 ; 4 5 6 ; 7 8 9]
Result = A.*(1+randn(size(A))*0.1)

I'm not sure what you actually want but those two solutions should solve it way faster than a loop

[Pavel Penshin]

Hi I have fixed the code, the line changed is:

sigma = 0.1*A;

Now I have a matrix of variances as I wanted.

I don't think this

A.*randn(size(A))*0.1 

- acheves the errors matrix that I need.

[Thiago Henrique Gomes Lobato]

No, but what you wrote is different than what was in my answer

Result = A.*(1+randn(size(A))*0.1)

this gives you the desired behaviour, you need to multiply A with 1+randn(size(A))*0.1, or, in other words, your A is equal to itself plus a normal distributed random value with variance equals to A times 0.1

[Pavel Penshin]

doest this mean that effectively my error matrix is satisfying the condition that

err(i,j) = rand(makedist('Normal','sigma',0.1*A(i,j)))

Because I need the errors matrix itself as well.

[Thiago Henrique Gomes Lobato]

Yes. If you need the error matrix you can do it like this:

err    = A.*randn(size(A))*0.1
Result = A+err;