It seems I am getting lost in something potentially silly. I have an n-dimensional numpy array, and I want to multiply it with a vector (1d array) along some dimension (which can change!). As an example, say I want to multiply a 2d array by a 1d array along axis 0 of the first array, I can do something like this:
a=np.arange(20).reshape((5,4))
b=np.ones(5)
c=a*b[:,np.newaxis]
Easy, but I would like to extend this idea to n-dimensions (for a, while b is always 1d) and to any axis. In other words, I would like to know how to generate a slice with the np.newaxis at the right place. Say that a is 3d and I want to multiply along axis=1, I would like to generate the slice which would correctly give:
c=a*b[np.newaxis,:,np.newaxis]
I.e. given the number of dimensions of a (say 3), and the axis along which I want to multiply (say axis=1), how do I generate and pass the slice:
np.newaxis,:,np.newaxis
Thanks.
Solution Code -
import numpy as np
# Given axis along which elementwise multiplication with broadcasting
# is to be performed
given_axis = 1
# Create an array which would be used to reshape 1D array, b to have
# singleton dimensions except for the given axis where we would put -1
# signifying to use the entire length of elements along that axis
dim_array = np.ones((1,a.ndim),int).ravel()
dim_array[given_axis] = -1
# Reshape b with dim_array and perform elementwise multiplication with
# broadcasting along the singleton dimensions for the final output
b_reshaped = b.reshape(dim_array)
mult_out = a*b_reshaped
Sample run for a demo of the steps -
In [149]: import numpy as np
In [150]: a = np.random.randint(0,9,(4,2,3))
In [151]: b = np.random.randint(0,9,(2,1)).ravel()
In [152]: whos
Variable Type Data/Info
-------------------------------
a ndarray 4x2x3: 24 elems, type `int32`, 96 bytes
b ndarray 2: 2 elems, type `int32`, 8 bytes
In [153]: given_axis = 1
Now, we would like to perform elementwise multiplications along given axis = 1. Let's create dim_array:
In [154]: dim_array = np.ones((1,a.ndim),int).ravel()
...: dim_array[given_axis] = -1
...:
In [155]: dim_array
Out[155]: array([ 1, -1, 1])
Finally, reshape b & perform the elementwise multiplication:
In [156]: b_reshaped = b.reshape(dim_array)
...: mult_out = a*b_reshaped
...:
Check out the whos info again and pay special attention to b_reshaped & mult_out:
In [157]: whos
Variable Type Data/Info
---------------------------------
a ndarray 4x2x3: 24 elems, type `int32`, 96 bytes
b ndarray 2: 2 elems, type `int32`, 8 bytes
b_reshaped ndarray 1x2x1: 2 elems, type `int32`, 8 bytes
dim_array ndarray 3: 3 elems, type `int32`, 12 bytes
given_axis int 1
mult_out ndarray 4x2x3: 24 elems, type `int32`, 96 bytes