# Element-wise matrix multiplication in NumPy

## Element-wise matrix multiplication in NumPy

Contents

Problem Description:

I’m making my first real foray into Python and NumPy to do some image processing. I have an image loaded as a 3 dimensional NumPy Array, where axis 0 represents image bands, while axes 1 and 2 represent columns and rows of pixels. From this, I need to take the 3×1 matrix representing each pixel and perform a few operations which result in another 3×1 matrix, which will be used to build a results image.

My first approach (simplified and with random data) looks like this:

``````import numpy as np
import random

factor = np.random.rand(3,3)
input = np.random.rand(3,100,100)
results = np.zeros((3,100,100))

for x in range(100):
for y in range(100):
results[:,x,y] = np.dot(factor,input[:,x,y])
``````

But this strikes me as inelegant and inefficient. Is there a way to do this in an element-wise fasion, e.g.:

``````results = np.dot(factor,input,ElementWiseOnAxis0)
``````

In trying to find a solution to this problem I came across this question, which is obviously quite similar. However, the author was unable to solve the problem to their satisfaction. I am hoping that either something has changed since 2012, or my problem is sufficiently different from theirs to make it more easily solvable.

## Solution – 1

Numpy arrays use element-wise multiplication by default. Check out numpy.einsum and numpy.tensordot. I think what you’re looking for is something like this:

``````results = np.einsum('ij,jkl->ikl',factor,input)
``````
Rate this post
We use cookies in order to give you the best possible experience on our website. By continuing to use this site, you agree to our use of cookies.