Find index of min element in matlab

Question

Here I have two matrix, one indicating cost and the other determines when to take into comparison.

cost =      [0.2 0.0 0.3; 0.4 0 0; 0.5 0 0];
available = [1   1   0  ; 1   0 0; 0   0 0];
available = logical(available);

I want to get the index of the min available element in the cost matrix, which in this case would compare 0.2 , 0.0 and 0.4 and return the index of 0.0 , which is (1, 2) or 4 in the cost matrix.

I tried

mul = cost .* available;     % Zero if not available, but I can't know if it is zero because cost is zero
mul(~mul) = nan;             % Set zero to be NaN
[minVal, minId] = min(mul)

This will help to get the min non-zero cost but if there exists zero elements which are available, it would be wrong.

So is there a better way to do so?

Answer 1

Here are two possible solutions. Both essentially involve converting all non-available costs to Inf .

%#Set up an example
Cost =      [0.2 0 0.3; 0.4 0 0; 0.5 0 0];
Available = [1   1   0; 1   0 0; 0   0 0];

%#Transform non-available costs to Inf
Cost(Available == 0) = Inf;

%#Obtain indices using find
[r, c] = find(Cost == min(min(Cost)))

%#Obtain linear indices and convert using ind2sub
[~, I1] = min(Cost(:));
[r2, c2] = ind2sub(size(Cost), I1);

Both solutions will only return the first minimum value in the instance that there is not a unique minimum. Also, the method will fail in the perverse case that all the available costs are Inf (but I guess you've got bigger problems if all your costs are infinite...).

I've done a few speed tests, and the second method is definitely faster, no matter what the dimensions of Cost , so should be strictly preferred. Also, if you only want linear indices and not subscript indices then you can of course drop the call to ind2sub . However, this doesn't give you huge savings in efficiency, so if there is a preference for subscript indices then you should use them.