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For Tensor contraction with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein summation ... Read More
To compute outer product of vectors with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered ... Read More
Suppose, there is a building that has center coordinates xc, yc, and height h. We don't know the center coordinates of the building, but we are provided with n pieces of information that contain x and y coordinates and an altitude value a. The altitude of coordinates (x, y) is the maximum of (h - |x - xc| - |y - yc|, 0). We have to find out the center coordinates and the height of the building. The coordinate xi is given in the array x, yi is given in teg array y, and ai is given in array a.So, ... Read More
To perform scalar multiplication with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values. In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical ... Read More
For Matrix Vector multiplication with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein ... Read More
To compute inner product of vectors with Einstein summation convention, use the numpy.einsum() method in Python. The 1st parameter is the subscript. It specifies the subscripts for summation as comma separated list of subscript labels. The 2nd parameter is the operands. These are the arrays for the operation.The einsum() method evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered ... Read More
Suppose, we are given two integers n and m and there are k tuples of integers that contain four integer numbers {ai, bi, ci, di}. Four arrays a, b, c, d are given, and a[i] signifies the i-th tuple's a value. Now, let us consider a sequence dp that has n positive integers and 1
Given two tensors, a and b, and an array_like object containing two array_like objects, (a_axes, b_axes), sum the products of a’s and b’s elements (components) over the axes specified by a_axes and b_axes. The third argument can be a single non-negative integer_like scalar, N; if it is such, then the last N dimensions of a and the first N dimensions of b are summed over.StepsAt first, import the required libraries −import numpy as npCreating two numpy arrays with different dimensions using the array() method −arr1 = np.array(range(1, 9)) arr1.shape = (2, 2, 2) arr2 = np.array(('p', 'q', 'r', 's'), ... Read More
Suppose n stations are connected by m tracks. The stations are named from 1 to n. The tracks are bidirectional, and we have to reach station dest from station src. Thes source and destination stations of the i-th railroad is given in the array 'roads' where roads[i] is of the format {station1, station2}. From the j-th station, a train leaves for all stations that are connected with the station at the multiples of time kj and each train takes tj amount of time to reach the destination. The values are given in an array 'departure' where each element is of ... Read More
Suppose, we are given a grid of dimensions h * w. The cells in the grid can contain either a bulb or obstacles. A light bulb cell illuminates the cells in its right, left, up, and down and the light can shine through the cells unless an obstacle cell blocks the light. An obstacle cell can not be illuminated and it blocks the light from a bulb cell from reaching the other cells. We are given the grid in an array of strings, where '#' represents an obstacle and '.' represents a vacant cell. We have only one bulb and ... Read More