在Python中获取两个不同维度数组的克罗内克积
要获取不同维度的两个数组的克罗内克积,可以使用 Python NumPy 中的 numpy.kron() 方法。计算克罗内克积,这是一个由第二个数组的块组成的复合数组,由第一个数组缩放。
该函数假设 a 和 b 的维度数相同,如有必要,则用 1 补充最小的维度。如果 a.shape = (r0,r1,..,rN) 且 b.shape = (s0,s1,...,sN),则克罗内克积的形状为 (r0*s0, r1*s1, ..., rN*SN)。元素是由 a 和 b 中的元素的乘积组成,通过 - 明确组织。
# kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
步骤
首先,导入所需的库:
import numpy as np
使用 arange() 和 reshape() 方法创建两个不同维度的 NumPy 数组:
arr1 = np.arange(20).reshape((2,5,2)) arr2 = np.arange(6).reshape((2,3))
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)
要获取两个数组的克罗内克积,请在 Python 中使用 numpy.kron() 方法:
print("\nResult (Kronecker product)...\n",np.kron(arr1, arr2))
示例
import numpy as np # Creating two numpy arrays with different dimensions using the arange() and reshape() method arr1 = np.arange(20).reshape((2,5,2)) arr2 = np.arange(6).reshape((2,3)) # Display the arrays print("Array1...\n",arr1) print("\nArray2...\n",arr2) # Check the Dimensions of both the array print("\nDimensions of Array1...\n",arr1.ndim) print("\nDimensions of Array2...\n",arr2.ndim) # Check the Shape of both the array print("\nShape of Array1...\n",arr1.shape) print("\nShape of Array2...\n",arr2.shape) # To get the Kronecker product of two arrays, use the numpy.kron() method in Python Numpy print("\nResult (Kronecker product)...\n",np.kron(arr1, arr2))
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输出
Array1... [[[ 0 1] [ 2 3] [ 4 5] [ 6 7] [ 8 9]] [[10 11] [12 13] [14 15] [16 17] [18 19]]] Array2... [[0 1 2] [3 4 5]] Dimensions of Array1... 3 Dimensions of Array2... 2 Shape of Array1... (2, 5, 2) Shape of Array2... (2, 3) Result (Kronecker product)... [[[ 0 0 0 0 1 2] [ 0 0 0 3 4 5] [ 0 2 4 0 3 6] [ 6 8 10 9 12 15] [ 0 4 8 0 5 10] [12 16 20 15 20 25] [ 0 6 12 0 7 14] [18 24 30 21 28 35] [ 0 8 16 0 9 18] [24 32 40 27 36 45]] [[ 0 10 20 0 11 22] [30 40 50 33 44 55] [ 0 12 24 0 13 26] [36 48 60 39 52 65] [ 0 14 28 0 15 30] [42 56 70 45 60 75] [ 0 16 32 0 17 34] [48 64 80 51 68 85] [ 0 18 36 0 19 38] [54 72 90 57 76 95]]]
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