NumPy: Evaluate Einstein’s summation convention of two given multidimensional arrays

NumPy: Linear Algebra Exercise-5 with Solution

Write a NumPy program to evaluate Einstein’s summation convention of two given multidimensional arrays.

Note: In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.

Sample Solution :

Python Code :

import numpy as np
a = np.array([1,2,3])
b = np.array([0,1,0])
print("Original 1-d arrays:")
print(a)
print(b)
result =  np.einsum("n,n", a, b)
print("Einstein’s summation convention of the said arrays:")
print(result)
x = np.arange(9).reshape(3, 3)
y = np.arange(3, 12).reshape(3, 3)
print("Original Higher dimension:")
print(x)
print(y)
result = np.einsum("mk,kn", x, y)
print("Einstein’s summation convention of the said arrays:")
print(result)

Sample Output:

Original 1-d arrays:
[1 2 3]
[0 1 0]
Einstein’s summation convention of the said arrays:
2
Original Higher dimension:
[[0 1 2]
 [3 4 5]
 [6 7 8]]
[[ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
Einstein’s summation convention of the said arrays:
[[ 24  27  30]
 [ 78  90 102]
 [132 153 174]]

Python-Numpy Code Editor:

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