Broadcasting in Numpy

The issue of array shapes matters when trying to combine them by arithmetic operations. Here is a simple array of 4 rows and 3 columns:

>>> from numpy import ones >>> A = ones((4,3)) # 4 rows x 3 cols >>> A.shape (4, 3) >>> A array([[ 1., 1., 1.], [ 1., 1., 1.], [ 1., 1., 1.], [ 1., 1., 1.]])

Here is a second array of 4 rows x 1 col

>>> ones((4,1)) # 4 rows x 1 col array([[ 1.], [ 1.], [ 1.], [ 1.]])

We can add them, and in the process the second array is "broadcast" to the same shape as the first one:

>>> A + ones((4,1)) array([[ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.]])

An array of a single row and 3 cols works the same:

>>> ones((1,3)) # 1 row x 3 cols array([[ 1., 1., 1.]]) >>> A + ones((1,3)) array([[ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.]])

Now, it is possible to make a 1D array, e.g.:

>>> B = ones((3,)) # a 1D array >>> B array([ 1., 1., 1.]) >>> B.shape (3,)

And again, we can add A + B:

>>> A + B array([[ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.]])

But this doesn't work if the number of columns doesn't match:

>>> C = ones((4,)) # a 1D array >>> C.shape (4,) >>> C array([ 1., 1., 1., 1.]) >>> A + C Traceback (most recent call last): File "", line 1, in ValueError: shape mismatch: objects cannot be broadcast to a single shape

We need to call newaxis:

from numpy import newaxis >>> D = C[:,newaxis] >>> D.shape (4, 1) >>> A + D array([[ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.], [ 2., 2., 2.]])