在Python中使用爱因斯坦求和约定进行矩阵向量乘法

对于使用爱因斯坦求和约定进行矩阵向量乘法，可以在Python中使用numpy.einsum()方法。第一个参数是下标，它指定了用逗号分隔的下标标签列表作为求和的下标。第二个参数是操作数，这些是进行操作的数组。

einsum()方法对操作数执行了爱因斯坦求和约定。使用爱因斯坦求和约定，许多常见的多维线性代数数组操作可以用简单的方式表示。在隐式模式下，einsum计算这些值。

在显式模式下，einsum提供了进一步的灵活性，用于计算可能不被认为是经典爱因斯坦求和操作的其他数组操作，通过禁用或强制求和指定的下标标签。

步骤

首先，导入所需的库 –

import numpy as np

创建两个使用array()方法的numpy一维数组−

arr1 = np.arange(25).reshape(5,5)
arr2 = np.arange(5)

显示数组 –

print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

检查两个数组的维度 –

print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

检查两个数组的形状-

print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

对于使用爱因斯坦求和约定的矩阵向量乘法，在Python中使用numpy.einsum()方法-

print("\nResult (Matrix Vector multiplication)...\n",np.einsum('ij,j', arr1, arr2))

示例

import numpy as np

# Creating two numpy One-Dimensional array using the array() method
arr1 = np.arange(25).reshape(5,5)
arr2 = np.arange(5)

# Display the arrays
print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

# For Matrix Vector multiplication with Einstein summation convention, use the numpy.einsum() method in Python.
print("\nResult (Matrix Vector multiplication)...\n",np.einsum('ij,j', arr1, arr2))

输出

Array1...
[[ 0 1 2 3 4]
[ 5 6 7 8 9]
[10 11 12 13 14]
[15 16 17 18 19]
[20 21 22 23 24]]

Array2...
[0 1 2 3 4]

Dimensions of Array1...
2

Dimensions of Array2...
1

Shape of Array1...
(5, 5)

Shape of Array2...
(5,)

Result (Matrix Vector multiplication)...
[ 30 80 130 180 230]