Hi I am trying to covert this distance formula for rectilinear distance from matlab to python. X1 and X2 are two matrices of two dimensional points and could be differing lengths.
nd = size(X1); n = nd(1);
d = nd(2);
m = size(X2,1);
D = abs(X1(:,ones(1,m)) - X2(:,ones(1,n))') + ...
abs(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))');
I think the problem I am having most in python is appending the ones matrices with X1 and X2 since they are np.arrays.
First your code:
octave:1> X1=[0,1,2,3;2,3,1,1]'
octave:2> X2=[2,3,2;4,2,4]'
<your code>
octave:21> D
D =
4 3 4
2 3 2
3 2 3
4 1 4
Matching numpy code:
X1=np.array([[0,1,2,3],[2,3,1,1]]).T
X2=np.array([[2,3,2],[4,2,4]]).T
D=np.abs(X1[:,None,:]-X2[None,:,:]).sum(axis=-1)
produces, D:
array([[4, 3, 4],
[2, 3, 2],
[3, 2, 3],
[4, 1, 4]])
numpy broadcasts automatically, so it doesn't need the ones() to expand the dimensions. Instead I use None (same as np.newaxis) to create new dimensions. The difference is then 3D, which is then summed on the last axis.
I forgot how spoilt we are with the numpy broadcasting. Though newer Octave has something similar:
D = sum(abs(reshape(X1,[],1,2)-reshape(X2,1,[],2)),3)
