Unexpected pdist2 behavior?

According to the documentation, the function

D = pdist2(X,Y,distance)

returns the pairwise distance between rows in X and rows in Y, where the distance, specified with

distance

can be a custom function handle. So for example, I know that all the points in X and Y all lie on the same 3D cylinder, and I want the distance to be the cylindrical geodesic distance, I could set

distance = @cylindricalGeodesic;

However, what I get when using this is not the pair-wise distance between points in X and points in Y:

>> a = [ 1 1 0; -1 1 0];
>> b = [sqrt(2) 0 1;1 1 1];
>> pdist2(a,b,@cylindricalGeodesic)

ans =

      1.1107    2.2214
      1.1107    2.2214

>> for i = 1:2;for j = 1:2;d(i,j) = cylindricalGeodesic(a(i,:),b(j,:));end;end;d

d =

      1.4946    1.0000
      3.4790    2.4361

I fully accept this may just be me overlooking something silly, but this behavior seems very unexpected to me: that pdist2 is not equivalent to the pairwise application of the distance function?

[dpb]

I can't seem to find a TMW-supplied function cylindricalGeodesic; what's it?

[nccrabb]

A custom-defined function

function d = cylindricalGeodesic(x,y)

that computes the distance of the cylindrical geodesic connecting x and y, where x,y are 1 by 3 (it verifies the points are co-cylindrical internally)

[nccrabb]

Actually, I think I just answered my own question: the documentation makes it seem like the second argument of the distance function must be able to handle an arbitrary number of rows? Is that true?

[nccrabb]

I just modified the function so that y is an arbitrary number of rows, and it works now:

>> pdist2(a,b,@cylindricalGeodesic)

ans =

      1.4946    1.0000
      3.4790    2.4361

Answer 1

[Bruno Luong]

In the DOC of PDIST2 it has been mentioned that the custom distance must able to accept second parameter of (m x 3) as m points in R^3.

I suspect you don't do it and this screws up PDIST2