[FIXED] Efficient way to compute distance matrix in NumPy

Issue

I have this sample array:

In [38]: arr
Out[38]: array([  0,  44, 121, 154, 191])

The above is just a sample whereas my actual array size is pretty huge. So, what is an efficient way to compute a distance matrix?

The result should be:

In [41]: res
Out[41]: 
array([[   0,   44,  121,  154,  191],
       [ -44,    0,   77,  110,  147],
       [-121,  -77,    0,   33,   70],
       [-154, -110,  -33,    0,   37],
       [-191, -147,  -70,  -37,    0]])

I wrote a for loop based implementation which is too slow. Could this be vectorized for efficiency reasons?

Solution

There's subtract.outer, which effectively performs broadcasted subtraction between two arrays.

Apply the ufunc op to all pairs (a, b) with a in A and b in B.

Let M = A.ndim, N = B.ndim. Then the result, C, of op.outer(A, B) is an array of dimension M + N such that:

C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = 
     op(A[i_0, ..., i_{M-1}],B[j_0, ..., j_{N-1}])

np.subtract.outer(arr, arr).T

Or,

arr - arr[:, None] # essentially the same thing as above

array([[   0,   44,  121,  154,  191],
       [ -44,    0,   77,  110,  147],
       [-121,  -77,    0,   33,   70],
       [-154, -110,  -33,    0,   37],
       [-191, -147,  -70,  -37,    0]])

Answered By - cs95