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
