计算两个多维NumPy数组的克朗克乘积
给定一个m X n矩阵A和一个p X q矩阵B,它们的克朗克积是A⊗B,也叫它们的矩阵直积,是一个(m*p)X(n*q)矩阵。
A = | (a00) (a01) |
| (a10) (a11) |
B = | (b00) (b01) |
| (b10) (b11) |
A ⊗ B = | (a00)*(b00) (a00)*(b01) (a01)*(b00) (a01)*(b00) |
| (a00)*(b01) (a00)*(b11) (a01)*(b01) (a01)*(b11) |
| (a10)*(b00) (a10)*(b01) (a11)*(b00) (a11)*(b01) |
| (a10)*(b10) (a10)*(b11) (a11)*(b10) (a11)*(b11) |
两个给定的多维数组的克朗克积可以通过NumPy模块中的kron()方法来计算。kron()方法接收两个数组作为参数,并返回这两个数组的克朗克乘积。
语法:
numpy.kron(array1, array2)
下面是一些程序,描述了kron()方法在计算两个数组的克朗克乘积时的实现。
示例 1:
# Importing required modules
import numpy
# Creating arrays
array1 = numpy.array([[1, 2], [3, 4]])
print('Array1:\n', array1)
array2 = numpy.array([[5, 6], [7, 8]])
print('\nArray2:\n', array2)
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)
输出:
Array1:
[[1 2]
[3 4]]
Array2:
[[5 6]
[7 8]]
Array1 ⊗ Array2:
[[ 5 6 10 12]
[ 7 8 14 16]
[15 18 20 24]
[21 24 28 32]]
示例 2:
# Importing required modules
import numpy
# Creating arrays
array1 = numpy.array([[1, 2, 3]])
print('Array1:\n', array1)
array2 = numpy.array([[3, 2, 1]])
print('\nArray2:\n', array2)
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)
输出:
Array1:
[[1 2 3]]
Array2:
[[3 2 1]]
Array1 ⊗ Array2:
[[3 2 1 6 4 2 9 6 3]]
示例 3:
# Importing required modules
import numpy
# Creating arrays
array1 = numpy.array([[1, 2, 3], [4, 5, 6]])
print('Array1:\n', array1)
array2 = numpy.array([[1, 2], [3, 4], [5, 6]])
print('\nArray2:\n', array2)
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)
输出:
Array1:
[[1 2 3]
[4 5 6]]
Array2:
[[1 2]
[3 4]
[5 6]]
Array1 ⊗ Array2:
[[ 1 2 2 4 3 6]
[ 3 4 6 8 9 12]
[ 5 6 10 12 15 18]
[ 4 8 5 10 6 12]