How to use the prod function on non-zero elements?

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I have a matrix with zeros in its main diagonal. I would like to take the product of the elements in each row (excluding the 0) so as to get a column vector. How can I make it using a vectorized code? E.g.
A = [0 1 2; 2 0 4; 7 8 0];
I want to get:
[1*2; 2*4; 7*8]
Thank you.

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Azzi Abdelmalek
Azzi Abdelmalek 2014-3-28
编辑:Azzi Abdelmalek 2014-3-28
A = [0 1 2; 2 0 4; 7 8 0];
B=A
B(~A)=1 % replace 0 elements by 1
out=prod(B,2)

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