Get the QR factorization of a given NumPy array (original) (raw)
Last Updated : 29 Aug, 2020
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 as np
arr = np.array([[ 10 , 22 ],[ 13 , 6 ]])
q, r = np.linalg.qr(arr)
print ( "Decomposition of matrix:" )
print ( "q=\n" , q, "\nr=\n" , r)
Output :
Example 2: QR factorization of 2X4 matrix
Python3
import numpy as np
arr = np.array([[ 0 , 1 ], [ 1 , 0 ], [ 1 , 1 ], [ 2 , 2 ]])
q, r = np.linalg.qr(arr)
print ( "Decomposition of matrix:" )
print ( "q=\n" , q, "\nr=\n" , r)
Output :
Example 3: QR factorization of 3X3 matrix
Python3
import numpy as np
arr = np.array([[ 5 , 11 , - 15 ], [ 12 , 34 , - 51 ],
`` [ - 24 , - 43 , 92 ]], dtype = np.int32)
q, r = np.linalg.qr(arr)
print ( "Decomposition of matrix:" )
print ( "q=\n" , q, "\nr=\n" , r)
Output :
