Numpy columnwise subtraction; subtract (k,n) array from values in a (k,) array

Question

Say I have

x=np.random.random((3,10))
y=np.array([1,10,100])

and I want to subtract the values in each column of x from y. I can do this like so:

np.array([y]*10).T-x

However, this involves the creation of a new array of 10 times the size of y (in this case). I could also imagine using a for loop. Can anyone suggest a better way of doing this?

Answer 1

Something like this?

>>> (y - x.T).T
array([[  8.79354250e-01,   5.30104393e-01,   7.78342126e-01,
          4.56857161e-02,   5.32181828e-01,   1.47155126e-01,
          3.39654176e-01,   3.72693537e-01,   4.32737024e-01,
          7.55366710e-01],
       [  9.53976069e+00,   9.51725133e+00,   9.00439583e+00,
          9.65411497e+00,   9.55728110e+00,   9.35189161e+00,
          9.72451832e+00,   9.20089714e+00,   9.60367043e+00,
          9.41722649e+00],
       [  9.99248465e+01,   9.96932738e+01,   9.93110996e+01,
          9.94116657e+01,   9.98695626e+01,   9.92118001e+01,
          9.93602275e+01,   9.99518088e+01,   9.98442735e+01,
          9.93865628e+01]])

Answer 2

Just stack y vertically and subtract x. For example:

y[:, None] - x    # insert a new axis into y (creating a new view of y)

or

np.vstack(y) - x  # stack y vertically (creating a copy of y)

This works because y now has shape (3, 1) and so can be broadcast with your x which has shape (3, 10).

x and y can be broadcast together if each trailing dimension (i.e. starting from the end of the shape tuple) of x is equal to the trailing dimension of y, or if one of the compared dimensions is 1. In this example, the trailing dimension of y was changed to 1, so that the two arrays are compatible.