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Get the QR factorization of a given NumPy array
• 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 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 :

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