How to compute QR decomposition of a matrix in Pytorch?

In this article, we are going to discuss how to compute the QR decomposition of a matrix in Python using PyTorch.

torch.linalg.qr() method accepts a matrix and a batch of matrices as input. This method also supports the input of float, double, cfloat, and cdouble data types. It will return a named tuple (Q, R). Q is orthogonal in the real case and unitary in the complex case. R is the upper triangular with a real diagonal. The below syntax is used to compute the QR decomposition of a matrix.

Syntax: (Q, R) = torch.linalg.qr(matrix, mode)

Parameters:

• matrix (Tensor): input matrix.
• mode (str, optional): It’s an optional parameter. We have three modes reduced, complete, and r. Default value of this parameter is reduced.

Return: This method return a named tuple (Q, R).

Example 1:

In this example, we will understand how to compute the QR decomposition of a matrix in Pytorch.

Python3

# Import the required libraries
import torch

# create a matrix of size 3x3
matrix = torch.tensor([[1., 2., -3.], [4., 5., 6.], [7., -8., 9.]])

# display input matrix
print("\n Input Matrix: \n", matrix)

# compute the QR decomposition of input matrix
Q, R = torch.linalg.qr(matrix)

# display result
print("\n Q \n", Q)
print("\n R \n", R)

Output:

QR Decomposition of Square Matrix

Example 2:

In this example, we compute the QR decomposition of a matrix. and set the mode to complete.

Python3

# Import the required libraries
import torch

# create a matrix of size 3x3
matrix = torch.tensor([[9., 8., -7.], [6., 5., 4.], [3., 2., -1.]])

# display input matrix
print("\n Input Matrix: \n", matrix)

# compute the QR decomposition of input matrix
Q, R = torch.linalg.qr(matrix, mode='r')

# display result
print("\n Q \n", Q)
print("\n R \n", R)

Output:

QR Decomposition of Square Matrix

Example 3:

In this example, we compute the QR decomposition of a matrix. and set the mode to R.

Python3

# Import the required libraries
import torch

# create a matrix of size 3x3
matrix = torch.tensor([[1., 2., -3.], [6., 5., 4.], [7., 8., -9.]])

# display input matrix
print("\n Input Matrix: \n ", matrix)

# compute the QR decomposition of input matrix
Q, R = torch.linalg.qr(matrix, mode='r')

# display result
print("\n Q \n ", Q)
print("\n R \n ", R)

Output:

QR Decomposition of Square Matrix