(Python Example for Beginners)
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)
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 Example – Write a NumPy program to evaluate Einstein’s summation convention of two given multidimensional arrays
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