What does the command A(~A) really do in matlab

Question

I was looking to find the most efficient way to find the non zero minimum of a matrix and found this on a forum :

Let the data be a matrix A.

A(~A) = nan;
minNonZero = min(A);

This is very short and efficient (at least in number of code lines) but I don't understand what happens when we do this. I can't find any documentation about this since it's not an operation on matrices like +,-,\,... would be.

Could anyone explain me or give me a link or something that could help me understand what is done ? Thank you !

Answer 1

It uses logical indexing

~ in Matlab is the not operator. When used on a double array, it finds all elements equal to zero. e.g.:

~[0 3 4 0]

Results in the logical matrix

[1 0 0 1]

i.e. it's a quick way to find all the zero elements

So if A = [0 3 4 0] then ~A = [1 0 0 1] so now A(~A) = A([1 0 0 1]). A([1 0 0 1]) uses logical indexing to only affect the elements that are true so in this case element 1 and element 4.

Finally A(~A) = NaN will replace all the elements in A that were equal to 0 with NaN which min ignores and thus you find the smallest non-zero element.