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NumPy: Get the lower-triangular L in the Cholesky decomposition of a given array

NumPy: Linear Algebra Exercise-16 with Solution

Write a NumPy program to get the lower-triangular L in the Cholesky decomposition of a given array.

Sample Solution:

Python Code :

import numpy as np
a = np.array([[4, 12, -16], [12, 37, -53], [-16, -53, 98]], dtype=np.int32)
print("Original array:")
print(a)
L = np.linalg.cholesky(a)
print("Lower-trianglular L in the Cholesky decomposition of the said array:")
print(L)

Sample Output:

Original array:
[[  4  12 -16]
 [ 12  37 -53]
 [-16 -53  98]]
Lower-triangular L in the Cholesky decomposition of the said array:
[[ 2.  0.  0.]
 [ 6.  1.  0.]
 [-8. -5.  3.]]

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