NumPy: Get the qr factorization of a given array
Write a NumPy program to get the qr factorization of a given array.
Sample Solution:
Python Code :
# Importing the NumPy library
import numpy as np
# Create a 3x3 NumPy array 'a' with specified values and data type as int32
a = np.array([[4, 12, -14], [12, 37, -53], [-14, -53, 98]], dtype=np.int32)
# Display the original array 'a'
print("Original array:")
print(a)
# Compute the QR decomposition of the array 'a' using np.linalg.qr()
# QR decomposition provides two matrices 'q' (orthogonal/unitary) and 'r' (upper triangular)
q, r = np.linalg.qr(a)
# Display the 'q' and 'r' matrices obtained from QR factorization of the array
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: