How can I select a three dimensional diagonal from a three dimensional array?

Question

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I have a scalar s.

I have a 3D array M(nx,nr,N), where in this case nx=100, nr=10, and N=30.

Dimension 1 takes index values from a vector X which has nx possible elements. Similarly for the r dimension. The N dimension is just a count n=1:N.

I have N observations of a variable, each with an index point (ix,ir,n). I can collect the indices for all N observations in three index vectors.

I then perform the following operation: Z=s<=M(IX,IX,:);

But all i really want as an outcome is the "diagonal" which picks the N points I am looking for.

M(IX(1),IR(1),1)

M(IX(2),IR(2),2)

etc

M(IX(N),IR(N),N)

How can I do this in one command?

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Answer 1

Matt J 2023-2-21

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out=M( sub2ind(size(M), IX,IR,1:N) );

Joao Miguel 2023-2-21

Brilliant. Thank you.