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NumPy: Compute the factor of a given array by Singular Value Decomposition

NumPy: Linear Algebra Exercise-18 with Solution

Write a NumPy program to compute the factor of a given array by Singular Value Decomposition.

Sample Solution:

Python Code :

import numpy as np
a = np.array([[1, 0, 0, 0, 2], [0, 0, 3, 0, 0], [0, 0, 0, 0, 0], [0, 2, 0, 0, 0]], dtype=np.float32)
print("Original array:")
print(a)
U, s, V = np.linalg.svd(a, full_matrices=False)
q, r = np.linalg.qr(a)
print("Factor of a given array  by Singular Value Decomposition:")
print("U=\n", U, "\ns=\n", s, "\nV=\n", V)

Sample Output:

Original array:
[[ 1.  0.  0.  0.  2.]
 [ 0.  0.  3.  0.  0.]
 [ 0.  0.  0.  0.  0.]
 [ 0.  2.  0.  0.  0.]]
Factor of a given array  by Singular Value Decomposition:
U=
 [[ 0.  1.  0.  0.]
 [ 1.  0.  0.  0.]
 [ 0.  0.  0. -1.]
 [ 0.  0.  1.  0.]] 
s=
 [ 3.          2.23606801  2.          0.        ] 
V=
 [[-0.          0.          1.         -0.          0.        ]
 [ 0.44721359 -0.         -0.         -0.          0.89442718]
 [-0.          1.          0.         -0.          0.        ]
 [ 0.          0.          0.          1.          0.        ]]

Python Code Editor:


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Python: Tips of the Day

Getting the last element of a list:

some_list[-1] is the shortest and most Pythonic.

In fact, you can do much more with this syntax. The some_list[-n] syntax gets the nth-to-last element. So some_list[-1] gets the last element, some_list[-2] gets the second to last, etc, all the way down to some_list[-len(some_list)], which gives you the first element.

You can also set list elements in this way. For instance:

>>> some_list = [1, 2, 3]
>>> some_list[-1] = 5 # Set the last element
>>> some_list[-2] = 3 # Set the second to last element
>>> some_list
[1, 3, 5]

Note that getting a list item by index will raise an IndexError if the expected item doesn't exist. This means that some_list[-1] will raise an exception if some_list is empty, because an empty list can't have a last element.

Ref: https://bit.ly/3d8TfFP