Leverage QR Decomposition of large-sized real and complex matrices of an arbitrary shape using the variety of methods: Gram-Schmidt Orthogonalization, Schwarz-Rutishauser Algorithm, Householder Reflections, and surveying the performance.
Source codes in Python 3.9.x (64-bit) / Intel® Distribution for Python 2021.1.1 using the latest Numpy 1.20.2 library, Microsoft Visual Studio 2019 Python's project:
To perform QR decomposition of a randomly generated matrix A of an arbitrary shape, download the project and run the code in your Python-environment:
Please don't forget to import the following Py-modules to your project, as well as to define a real or complex matrix A (see example below):
example.py:
import numpy as np
import numpy.linalg as lin
from qr_gschmidt import *
from qr_gs_schwrt import *
from qr_householder import *
# An example of a `real` matrix A of shape (5,4):
A = [[1.0,7.0,2.0,4.0],
[2.0,3.0,6.0,8.0],
[1.0,9.0,5.0,4.0],
[2.0,6.0,8.0,3.0],
[3.0,5.0,2.0,7.0]]
# An example of a `complex` matrix A of shape (5,4):
A = [[2.5+3.7j,7.0-2.2j,1.8-2.6j,4.1+1.8j],
[6.4-2.1j,3.1+1.7j,3.3+1.4j,1.3+1.1j],
[8.5-4.6j,9.2-6.4j,5.8+3.6j,4.6+2.7j],
[2.0-3.2j,4.4-5.1j,8.1+1.1j,3.5+4.4j],
[0.0+6.8j,5.0+8.9j,5.5+4.6j,7.1+6.8j]]
Use the following sub-routines below in your code to perform QR decomposition of a matrix A into an orthogonal matrix Q and upper triangular matrix R:
QR Decomposition Using Gram-Schmidt Orthogonalization
Q, R = qr_gram_schmidt(A)
QR Decomposition Using Schwarz-Rutishauser Algorithm
Q, R = qr_gram_schmidt_mod(A)
QR Decomposition Using Householder Reflections
Q, R = qr_householder(A)
CPOL © 2021 Arthur V. Ratz