specify rows and columns to find min value?

I have a matrix, N, and a matrix RC, and what I want is to search for a minimum value in N based on values in RC for rows and columns. Each value in RC specifies a row and col that needs to be searched in N with column 1 representing row values and column 2 representing col values. How would I go about doing this? I tried doing

[minval, minidx] = min(min(N(RC(:,1), RC(:,2))))

but it is producing incorrect results leading me to believe there is an error in my logic. rmin and cmin are 2 and 1, respectively, which is not a pair in the RC matrix.

N = [0 1 5 12 1; 1 23 4 75 5; 11 29 2 5 9; 23 3 5 8 0; 12 11 23 48 0];
RC = [1 3; 2 5; 2 3; 5 1; 2 4; 1 1; 1 5; 3 3];
[minval, minidx] = min(min(N(RC(:,1), RC(:,2))));
[rmin, cmin] = ind2sub(size(N), minidx)

[Stephen23]

@Andrew Poissant? so what are the expected results? What output do you want from your example data?

[Andrew Poissant]

What I expect is minval = 0 and rmin = 1, cmin = 1.

[Stephen23]

See my answer for a simpler and more efficient solution.

Answer 1

[Star Strider]

This works:

N = [0 1 5 12 1; 1 23 4 75 5; 11 29 2 5 9; 23 3 5 8 0; 12 11 23 48 0];
RC = [1 3; 2 5; 2 3; 5 1; 2 4; 1 1; 1 5; 3 3];

idx = sub2ind(size(N), RC(:,1), RC(:,2));                           % Define ‘Eligible’ Elements As Linear Index Vector
minval = min(N(idx));                                               % Minimum of ‘Eligible’ Values
minidx = find(N(:)==minval);                                        % Location Of All Values Of ‘Eligible’ Minimum (Linear Index)
[~,minA] = ismember(idx, minidx);                                   % Find All ‘Eligible’ Minima
[rmin,cmin] = ind2sub(size(N),intersect(minidx,idx));               % Recover Row, Column Indices Of All ‘Eligible’ Minimum
fprintf('\nMinimum of A = %d, at [%2d,%2d]\n', [minval*ones(size(rmin,1),1), rmin, cmin]')

Minimum of A = 0, at [ 1, 1]

Answer 2

[Stephen23]

>> N = [0,1,5,12,1;1,23,4,75,5;11,29,2,5,9;23,3,5,8,0;12,11,23,48,0];
>> RC = [1,3;2,5;2,3;5,1;2,4;1,1;1,5;3,3];
>> [val,Y] = min(N(sub2ind(size(N),RC(:,1),RC(:,2))));
>> pos = RC(Y,:)
pos = 1     1
>> val
val = 0