How to get a set of elements from a matrix given a set of index pairs?

Hello,

For instance, Given:

A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
index_set = [1,1; 2,3; 3,1]
% I'd like to get
output = [A(1,1); A(2,3); A(3,1)];

I've tried:

output = diag(A(index_set(:,1), index_set(:,2)))

but I don't think this is an efficient solution.

Is there an efficient way of doing this? Thank you!

Answer 1

[John D'Errico]

If you want efficiency, assuming your real problem is much larger, then you need to learn how to use sub2ind. That means you need to start thinking about how MATLAB stores the elements of an array, so you will learn about using a single index into the elements of a multi-dimensional array.

sub2ind helps you here, and does so efficiently.

A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
index_set = [1,1; 2,3; 3,1];

A(sub2ind(size(A),index_set(:,1),index_set(:,2)))
ans =
     1
     6
     7

Answer 2

[Image Analyst]

Try this:

for k = 1 : size(index_set, 1);
  row = index_set(k, 1);
  col = index_set(k, 2);
  output(k) = A(row, col);
end

Of course the most efficient way was just

output = [A(1,1); A(2,3); A(3,1)];

which you already had. What was wrong with that?