To return the Norm of the matrix or vector in Linear Algebra, use the LA.norm() method in Python Numpy. The 1st parameter, x is an input array. If axis is None, x must be 1-D or 2-D, unless ord is None. If both axis and ord are None, the 2-norm of x.ravel will be returned. The 2nd parameter, ord is the order of the norm. The inf means numpy’s inf object. The default is None.The 3rd parameter axis, if an integer, specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies ... Read More

To get the Kronecker product of two arrays, use the numpy.kron() method in Python Numpy. Compute the Kronecker product, a composite array made of blocks of the second array scaled by the first.The function assumes that the number of dimensions of a and b are the same, if necessary, prepending the smallest with ones. If a.shape = (r0, r1, .., rN) and b.shape = (s0, s1, ..., sN), the Kronecker product has shape (r0*s0, r1*s1, ..., rN*SN). The elements are products of elements from a and b, organized explicitly by −kron(a, b)[k0, k1, ..., kN] = a[i0, i1, ..., iN] ... Read More

To raise a square matrix to the power n in Linear Algebra, use the numpy.linalg.matrix_power() in Python For positive integers n, the power is computed by repeated matrix squarings and matrix multiplications. If n == 0, the identity matrix of the same shape as M is returned. If n < 0, the inverse is computed and then raised to the abs(n).The return value is the same shape and type as M; if the exponent is positive or zero then the type of the elements is the same as those of M. If the exponent is negative the elements are floating-point. ... Read More

To get the lowest cost contraction order for an einsum expression, use the numpy.einsum+path() method in Python. The 1st parameter, subscripts specify the subscripts for summation. The 2nd parameter, operands are the arrays for the operation.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 operations, by disabling, or forcing summation over specified subscript labels.The resulting path indicates which terms of the input contraction should ... Read More

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

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

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