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NumPy: Get the qr factorization of a given array

NumPy: Linear Algebra Exercise-17 with Solution

Write a NumPy program to get the qr factorization of a given array.

Sample Solution:

Python Code :

import numpy as np
a = np.array([[4, 12, -14], [12, 37, -53], [-14, -53, 98]], dtype=np.int32)
print("Original array:")
print(a)
q, r = np.linalg.qr(a)
print("qr factorization of the said array:")
print( "q=\n", q, "\nr=\n", r)

Sample Output:

Original array:
[[  4  12 -14]
 [ 12  37 -53]
 [-14 -53  98]]
qr factorization of the said array:
q=
 [[-0.21199958 -0.27930103  0.93650794]
 [-0.63599873 -0.68815735 -0.34920635]
 [ 0.74199852 -0.66964945 -0.03174603]] 
r=
 [[ -18.86796226  -65.4018692   109.39178122]
 [   0.            6.67798664  -25.24309237]
 [   0.            0.            2.28571429]]

Python-Numpy Code Editor:

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Previous: Write a NumPy program to get the lower-triangular L in the Cholesky decomposition of a given array.
Next: Write a NumPy program to compute the factor of a given array by Singular Value Decomposition.

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m