How to get element-wise matrix multiplication (Hadamard product) in numpy?

138
votes

I have two matrices 

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

and I want to get the element-wise product, [[1*5,2*6], [3*7,4*8]], equaling

[[5,12], [21,32]]

I have tried

print(np.dot(a,b))

and

print(a*b)

but both give the result

[[19 22], [43 50]]

which is the matrix product, not the element-wise product. How can I get the the element-wise product (aka Hadamard product) using built-in functions?

4
pythonnumpymatrixmatrix-multiplicationelementwise-operations
Are you sure a and b aren't NumPy's matrix type? With this class, * returns the inner product, not element-wise. But for the usual ndarray class, * means element-wise product. – bnaecker
are a and b numpy arrays? Also, in your question above, you are using x and y for computation instead of a and b. Is that just a typo? – jtitusj
a and b are numpy matrix type elements – Malintha
Always use numpy arrays, and not numpy matrices. See what the numpy docs say about this. Also note that from python 3.5+, you can use @ for matrix multiplication with numpy arrays, which means there should be absolutely no good reason to use matrices over arrays. – Praveen
To be picky, a and b are lists. They will work in np.dot; but not in a*b. If you use np.array(a) or np.matrix(a), * works but with different results. – hpaulj

4 Answers

202
votes

For elementwise multiplication of matrix objects, you can use numpy.multiply:

import numpy as np
a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
np.multiply(a,b)

Result 

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

However, you should really use array instead of matrix. matrix objects have all sorts of horrible incompatibilities with regular ndarrays. With ndarrays, you can just use * for elementwise multiplication:

a * b

If you're on Python 3.5+, you don't even lose the ability to perform matrix multiplication with an operator, because @ does matrix multiplication now:

a @ b  # matrix multiplication
38
votes

just do this:

import numpy as np

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

a * b
12
votes
import numpy as np
x = np.array([[1,2,3], [4,5,6]])
y = np.array([[-1, 2, 0], [-2, 5, 1]])

x*y
Out: 
array([[-1,  4,  0],
       [-8, 25,  6]])

%timeit x*y
1000000 loops, best of 3: 421 ns per loop

np.multiply(x,y)
Out: 
array([[-1,  4,  0],
       [-8, 25,  6]])

%timeit np.multiply(x, y)
1000000 loops, best of 3: 457 ns per loop

Both np.multiply and * would yield element wise multiplication known as the Hadamard Product

%timeit is ipython magic

1
votes

Try this:

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

#This would result a 'numpy.ndarray'
result = np.array(a) * np.array(b)

Here, np.array(a) returns a 2D array of type ndarray and multiplication of two ndarray would result element wise multiplication. So the result would be:

result = [[5, 12], [21, 32]]

If you wanna get a matrix, the do it with this:

result = np.mat(result)