Find extremum of multidimensional matrix in matlab

Question

I am trying to find the Extremum of a 3-dim matrix along the 2nd dimension.

I started with [~,index] = max(abs(mat),[],2), but I don't know how to advance from here. How is the index vector to be used together with the original matrix. Or is there a completely different solution to this problem?

To illustrate the task assume the following matrix:

mat(:,:,1) =
    23     8    -4
    -1   -26    46
mat(:,:,2) =
     5   -27    12
     2    -1    18
mat(:,:,3) =
   -10    49    39
   -13   -46    41
mat(:,:,4) =
    30   -24    18
   -40   -16   -36

The expected result would then be

ext(:,:,1) =
    23
   -46
ext(:,:,2) =
   -27
    18
ext(:,:,3) =
    49
   -46
ext(:,:,4) =
    30
   -40

I don't know how to use the index vector with mat to get the desired result ext.

Answer 1

Use ndgrid to generate the values along dimensions 1 and 3, and then sub2ind to combine the three indices into a linear index:

[~, jj] = max(abs(mat),[],2); %// jj: returned by max
[ii, ~, kk] = ndgrid(1:size(mat,1),1,1:size(mat,3)); %// ii, kk: all combinations
result = mat(sub2ind(size(mat), ii, jj, kk));

---

A fancier, one-line alternative:

result = max(complex(mat),[],2);

This works because, acccording to max documentation,

For complex input A, max returns the complex number with the largest complex modulus (magnitude), computed with max(abs(A)).

Answer 2

1) If you want to find a maximum just along, let's say, 2d dimension, your variable index will be a matrix having dimensions (N,1,M), where N and M are number of elements of your matrix in the first and third dimensions respectively. In order to remove dummy dimensions, there is function squeeze() exist: index=squeeze(index) After that size(index) gives N,M

2) Depending on your problem, you probably need matlab function ind2sub(). First, you take a slice of your matrix, than find its maximum with linear indexing, and than you can restore your indicies with int2sub(). Here is an example for a 2D matrix:

M = randn(5,5);
[C,I] = max(M(:));
[index1,index2] = ind2sub(size(M),I);

Same method allows to find the absolute maximal element in whole 3D matrix.