In this article, we will discuss QR decomposition or QR factorization of a matrix. QR factorization of a matrix is the decomposition of a matrix say ‘A’ into ‘A=QR’ where Q is orthogonal and R is an upper-triangular matrix. We factorize the matrix using numpy.linalg.qr() function.
Syntax : numpy.linalg.qr(a, mode=’reduced’)
Parameters :
- a : matrix(M,N) which needs to be factored.
- mode : it is optional. It can be :
Below are some examples of how to use the above-described function :
Example 1: QR factorization of 2X2 matrix
Python3
# Import numpy package import numpy as np # Create a numpy array arr = np.array([[10,22],[13,6]]) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) |
Output :
Example 2: QR factorization of 2X4 matrix
Python3
# Import numpy package import numpy as np # Create a numpy array arr = np.array([[0, 1], [1, 0], [1, 1], [2, 2]]) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) |
Output :
Example 3: QR factorization of 3X3 matrix
Python3
# Import numpy package import numpy as np # Create a numpy array arr = np.array([[5, 11, -15], [12, 34, -51], [-24, -43, 92]], dtype=np.int32) # Find the QR factor of array q, r = np.linalg.qr(arr) # Print the result print("Decomposition of matrix:") print( "q=\n", q, "\nr=\n", r) |
Output :
