MATLAB: How to compute distance efficiently with no loops

Question

I have matrices for points (not the same number of rows for P1 and P2) like this

P1=[12 45
    34 7 ]

and

P2= [1 42 25
     2 37 57 
     3 55 16]

What I what is to get the Manhattan (cityblock) distance between points in P1 (X and Y coordinates are in column 1 and 2) and those in P2 (X and Y are in column 2 and 3, the first one are indices of the points.

What I have been doing so far and works but very slow is with a nested for loop. But recently I saw pdist2 and I think it can help me avoid the loop.

But in the example, I need to put the whole matrix something like this

pdist2(P1,P2, 'cityblock');

But in my case, I want to use the columns of my matrices col as follows

abs(xP1(col1) - xP2(col2)) + abs(yP1(col2) - yP2(col3))

How can I do it or is there any faster way to do it (because i saw someone stating that even pdist uses nested for) since my matrices are quite big?

Answer 1

Most likely:

pdist2(P1, P2(:, [2 3]), 'cityblock')