Calculate outer product of given two vectors in Python using NumPy

The outer product of two vectors is the matrix obtained by multiplying each element of vector A by each element of vector B. The outer product of vectors a and b is a ⊗ b. Below is the mathematical formula for calculating the outer product.

a ⊗ b = [a[0] * b, a[1] * b, ..., a[m-1] * b]

where,

• a, b are vectors.

• # Represents the element-wise multiplication of two vectors.

The output of the outer product is a matrix, where i and j are the elements of the matrix, where the i-th row is the vector obtained by multiplying the i-th element of the vector 'a' by the i-th element of the vector 'b' .

Use Numpy to calculate outer product

In Numpy, we have a function called outer(), which is used to calculate the outer product of two vectors.

grammar

The following is the syntax of the outer() function -

np.outer(array1, array2)

where,

• The outside is a function.

• array1 and array2 are input arrays.

Example

In the following example, we try to use the outer() function to calculate the outer product of two numpy arrays -

import numpy as np
a = np.array([34,23,90,34])
b = np.array([90,34,43,23])
print("The input arrays:",a,b)
outer_product = np.outer(a,b)
print("The Outer product of the given input arrays:",outer_product) 

Output

The input arrays: [34 23 90 34] [90 34 43 23]
The Outer product of the given input arrays: [[3060 1156 1462 782]
[2070 782 989 529]
[8100 3060 3870 2070]
[3060 1156 1462 782]]

Example

Let's look at another example where we use the outer() function to calculate the outer product of a two-dimensional array -

import numpy as np
a = np.array([[34,23],[90,34]])
b = np.array([[90,34],[43,23]])
print("The input arrays:",a,b)
outer_product = np.outer(a,b)
print("The Outer product of the given input arrays:",outer_product)

Output

The following is the output of the outer product of two arrays.

The input arrays: [[34 23]
[90 34]] [[90 34]
[43 23]]
The Outer product of the given input arrays: [[3060 1156 1462 782]
[2070 782 989 529]
[8100 3060 3870 2070]
[3060 1156 1462 782]]

Example

Now, let's try to calculate the outer product of a 3D array.

import numpy as np
a = np.array([[[34,23],[90,34]],[[12,5],[14,5]]])
b = np.array([[[90,34],[43,23]],[[1,22],[7,2]]])
print("The input arrays:",a,b)
outer_product = np.outer(a,b)
print("The Outer product of the given input arrays:",outer_product)

Output

The input arrays: [[[34 23]
[90 34]]
[[12 5]
[14 5]]] [[[90 34]
[43 23]]
[[ 1 22]
[ 7 2]]]
The Outer product of the given input arrays: [[3060 1156 1462 782 34 748 238 68]
[2070 782 989 529 23 506 161 46]
[8100 3060 3870 2070 90 1980 630 180]
[3060 1156 1462 782 34 748 238 68]
[1080 408 516 276 12 264 84 24]
[ 450 170 215 115 5 110 35 10]
[1260 476 602 322 14 308 98 28]
[ 450 170 215 115 5 110 35 10]]

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