使用 NumPy 通过奇异值分解计算给定数组的因子

奇异值分解意味着当arr是二维数组时，它被分解为u和vh ，其中u和vh是二维酉数组， s是 a 的奇异值的一维数组。 numpy.linalg.svd()函数用于通过奇异值分解计算数组的因子。

Syntax : numpy.linalg.svd(a, full_matrices=True, compute_uv=True, hermitian=False)

Parameters : 

• a (…, M, N) array : A real or complex array with a.ndim >= 2.
• full_matrices(bool, optional) : If True (default), u and vh have the shapes (…, M, M) and (…, N, N), respectively. Otherwise, the shapes are (…, M, K) and (…, K, N), respectively, where K = min(M, N).
• compute_uv(bool, optional) : Whether or not to compute u and vh in addition to s. Its default value is True.
• hermitian(bool, optional) : If True, a is assumed to be Hermitian (symmetric if real-valued), enabling a more efficient method for finding singular values. Its default value is False.

以下是有关如何使用该函数的一些示例：

示例 1：

Python3

# Import numpy library
import numpy as np
  
# Create a numpy array
arr = np.array([[0, 0, 0, 0, 1], [2, 0, 0, 1, 3],
                [4, 0, 2, 0, 0], [3, 2, 0, 0, 1]],
               dtype=np.float32)
  
print("Original array:")
print(arr)
  
# Compute the factor by Singular Value 
# Decomposition
U, s, V = np.linalg.svd(arr, full_matrices=False)
  
# Print the result
print("\nFactor of the given array  by Singular Value Decomposition:")
print("\nU=", U, "\n\ns=", s, "\n\nV=", V)

输出 ：

示例 2：

Python3

# Import numpy library
import numpy as np
  
# Create a numpy array
arr = np.array([[8, 4, 0], [2, 5, 1], 
                [4, 0, 9]], dtype=np.float32)
  
print("Original array:")
print(arr)
  
# Compute the factor 
U, s, V = np.linalg.svd(arr, full_matrices=False)
  
# Print the result
print("\nFactor of the given array  by Singular Value Decomposition:")
print("\nU=", U, "\n\ns=", s, "\n\nV=", V)

输出 ：

示例 3：

Python3

# Import numpy library
import numpy as np
  
# Create a numpy array
arr = np.array([[8, 1], [0, 5]], dtype=np.float32)
print("Original array:")
print(arr)
  
# Compute the factor 
U, s, V = np.linalg.svd(arr, full_matrices=False)
  
# Print the result
print("\nFactor of the given array  by Singular Value Decomposition:")
print("\nU=", U, "\n\ns=", s, "\n\nV=", V)

输出 ：