Subtracting numpy arrays of different shape efficiently

Question

Using the excellent broadcasting rules of numpy you can subtract a shape (3,) array v from a shape (5,3) array X with

X - v

The result is a shape (5,3) array in which each row i is the difference X[i] - v.

Is there a way to subtract a shape (n,3) array w from X so that each row of w is subtracted form the whole array X without explicitly using a loop?

Catacaustic

What would be the shape of the output array? – Judenberg

We need to subtract n shape (3,) vectors from a shape (5,3) array so the result would be a shape (5,3,n) array. – Catacaustic

I think it would be (5,n,3) rather, no? Because the last axis would be the rows. – Judenberg

In fact the ordering dosen't matter since I could use swapaxes the achieve the desired ordering (in my case (n,5,3)). – Catacaustic

Answer 1

You need to extend the dimensions of X with None/np.newaxis to form a 3D array and then do subtraction by w. This would bring in broadcasting into play for this 3D operation and result in an output with a shape of (5,n,3). The implementation would look like this -

X[:,None] - w  # or X[:,np.newaxis] - w

Instead, if the desired ordering is (n,5,3), then you need to extend the dimensions of w instead, like so -

X - w[:,None] # or X - w[:,np.newaxis] 

Sample run -

In [39]: X
Out[39]: 
array([[5, 5, 4],
       [8, 1, 8],
       [0, 1, 5],
       [0, 3, 1],
       [6, 2, 5]])

In [40]: w
Out[40]: 
array([[8, 5, 1],
       [7, 8, 6]])

In [41]: (X[:,None] - w).shape
Out[41]: (5, 2, 3)

In [42]: (X - w[:,None]).shape
Out[42]: (2, 5, 3)

Judenberg