How can I perform element-wise matrix multiplication (Hadamard product) in Python using NumPy?

General Discussions
1

How can I perform element-wise matrix multiplication (Hadamard product) in Python using NumPy?

I have two matrices:

a = np.matrix([[1, 2], [3, 4]])
b = np.matrix([[5, 6], [7, 8]])

and I want to calculate the element-wise product:

[[1*5, 2*6], [3*7, 4*8]]

which results in:

matrix([[5, 12], [21, 32]])

I have tried np.dot(a, b) and a * b, but both return the matrix product instead of the element-wise product, resulting in:

matrix([[19, 22], [43, 50]])

How can I perform element-wise multiplication in Python, also known as the Hadamard product, using NumPy’s built-in functions?

2

The np.multiply() function provides a direct way to perform element-wise multiplication between two matrices.

import numpy as np

a = np.matrix([[1, 2], [3, 4]])
b = np.matrix([[5, 6], [7, 8]])

result = np.multiply(a, b)
print(result)
This will output:

matrix([[ 5, 12],
        [21, 32]])
3

In NumPy, you can directly use the * operator to achieve element-wise multiplication between two matrices (or arrays). This is equivalent to the Hadamard product.

import numpy as np

a = np.matrix([[1, 2], [3, 4]])
b = np.matrix([[5, 6], [7, 8]])

result = a * b
print(result)
This will give:

matrix([[ 5, 12],
        [21, 32]])
4

You can achieve element-wise multiplication by iterating through the elements using nested list comprehension. Here’s an example:

import numpy as np

a = np.matrix([[1, 2], [3, 4]])
b = np.matrix([[5, 6], [7, 8]])

result = np.matrix([[a[i,j] * b[i,j] for j in range(a.shape[1])] for i in range(a.shape[0])])
print(result)

This will output:

matrix([[ 5, 12],
        [21, 32]])