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

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Pavel Penshin
Pavel Penshin 2020-2-23
评论： Thiago Henrique Gomes Lobato 2020-2-23
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?

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Thiago Henrique Gomes Lobato
编辑：Thiago Henrique Gomes Lobato 2020-2-23
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
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Pavel Penshin
Pavel Penshin 2020-2-23
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.

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