python-scipyHow do I use Python Scipy to calculate a QR decomposition?

The QR decomposition is the factorization of a matrix into an orthogonal matrix and an upper triangular matrix. To calculate a QR decomposition in Python Scipy, the scipy.linalg.qr function can be used.

import scipy
import numpy as np

A = np.array([[1,2,3],[4,5,6],[7,8,9]])
Q, R = scipy.linalg.qr(A)
print(Q)
print(R)

Output example

[[-0.12309149  0.90453403  0.40824829]
 [-0.49236596  0.30151134 -0.81649658]
 [-0.86164044 -0.30151134  0.40824829]]
[[-8.12403840e+00 -9.60113630e+00 -1.10782342e+01]
 [ 0.00000000e+00  9.04534034e-01  1.80906807e+00]
 [ 0.00000000e+00  0.00000000e+00 -1.11164740e-15]]

The scipy.linalg.qr function takes the matrix A as an argument and returns two matrices, Q and R. Q is an orthogonal matrix, and R is an upper triangular matrix. In the example code, the matrix A is a 3x3 matrix, and the output is two 3x3 matrices.

Parts of the code:

• import scipy: imports the scipy library
• import numpy as np: imports the numpy library with the alias np
• A = np.array([[1,2,3],[4,5,6],[7,8,9]]): creates a 3x3 matrix A
• Q, R = scipy.linalg.qr(A): calculates the QR decomposition of A and assigns the orthogonal matrix Q to the variable Q and the upper triangular matrix R to the variable R
• print(Q): prints the matrix Q
• print(R): prints the matrix R

Helpful links

• Scipy QR Decomposition Documentation
• Numpy Array Documentation

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