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pythonnumpymatrixmatrix-multiplicationelementwise-operations
Malintha
Malintha

Reputation: 4776

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

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]], which equals

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

I have tried np.dot(a,b) and a*b but both give the result matrix([[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?

Upvotes: 185

Views: 512612

Answers (5)

cottontail
cottontail

Reputation: 23429

For ndarrays, * is elementwise multiplication (Hadamard product) while for numpy matrix objects, it is wrapper for np.dot (source code).

As the accepted answer mentions, np.multiply always returns an elementwise multiplication. Notably, it preserves the type of the object, if a matrix object is passed, the returned object will be matrix; if ndarrays are passed, an ndarray is returned.

If you have a np.matrix object, then you can convert it into an ndarray (via .A attribute) and use * for elementwise multiplication. However, note that unlike np.multiply which preserves the matrix type, it returns an ndarray (because we converted to ndarray before multiplication).

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

c = a.A * b.A

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

Then again, matrix is not recommended by the library itself and once it's removed from numpy, this answer (and arguably the question as well) will probably be obsolete.

Upvotes: 1

4rshdeep
4rshdeep

Reputation: 510

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

Upvotes: 19

Rahul K P
Rahul K P

Reputation: 16081

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

Upvotes: 260

rez
rez

Reputation: 2085

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)

Upvotes: 1

jtitusj
jtitusj

Reputation: 3084

just do this:

import numpy as np

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

a * b

Upvotes: 39

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