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PyTorch – How to compute QR decomposition of a matrix?
torch.linalg.qr() computes the QR decomposition of a matrix or a batch of matrices. It accepts matrix and batch of matrices of float, double, cfloat and cdouble data types.
It returns a named tuple (Q, R). Q is orthogonal when the matrix is real valued and unitary when matrix is complex valued. And R is an upper triangular matrix.
Syntax
(Q, R) = torch.linalg.qr(mat, mode='reduced')
Parameters
Mat – Square matrix or a batch of square matrices.
mode – It decides mode of QR decomposition. It is set to one of three modes, 'reduced', 'complete', and 'r'. Default is set to 'reduced'. It's an optional parameter.
Steps
Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.
import torch
Create a matrix or batch of matrices. Here we define a matrix (a 2D torch tensor) of size [3, 2].
mat = torch.tensor([[1.,12.],[14.,5.],[17.,-8.]])
Compute QR decomposition of the input matrix or batch of matrices using torch.linalg.qr(mat). Here mat is the input matrix.
Q, R = torch.linalg.qr(A)
Display Q and R.
print("Q:
", Q)
print("R:
", R)Example 1
In this Python program, we compute the QR decomposition of a matrix. We have not given mode parameter. It's set to 'reduced' by default.
# import necessary libraries
import torch
# create a matrix
mat = torch.tensor([[1.,12.],[14.,5.],[17.,-8.]])
print("Matrix:
", mat)
# compute QR decomposition
Q, R = torch.linalg.qr(mat)
# print Q and S matrices
print("Q:
",Q)
print("R:
",R)Output
It will produce the following output −
Matrix: tensor([[ 1., 12.], [14., 5.], [17., -8.]]) Q: tensor([[-0.0454, 0.8038], [-0.6351, 0.4351], [-0.7711, -0.4056]]) R: tensor([[-22.0454, 2.4495], [ 0.0000, 15.0665]])
Example 2
In this Python program, we compute the QR decomposition of a matrix. We set mode to 'r'.
# import necessary libraries
import torch
# create a matrix
mat = torch.tensor([[1.,12.],[14.,5.],[17.,-8.]])
print("Matrix:
", mat)
# compute QR decomposition
Q, R = torch.linalg.qr(mat, mode = 'r')
# print Q and S matrices
print("Q:
",Q)
print("R:
",R)Output
It will produce the following output −
Matrix: tensor([[ 1., 12.], [14., 5.], [17., -8.]]) Q: tensor([]) R: tensor([[-22.0454, 2.4495], [ 0.0000, 15.0665]])
Example 3
In this Python3 program we compute the QR decomposition of a matrix. We set mode to 'complete'.
# import necessary libraries
import torch
# create a matrix
mat = torch.tensor([[1.,12.],[14.,5.],[17.,-8.]])
print("Matrix:
", mat)
# compute QR decomposition
Q, R = torch.linalg.qr(mat, mode = 'complete')
# print Q and S matrices
print("Q:
", Q)
print("R:
", R)Output
It will produce the following output −
Matrix: tensor([[ 1., 12.], [14., 5.], [17., -8.]]) Q: tensor([[-0.0454, 0.8038, 0.5931], [-0.6351, 0.4351, -0.6383], [-0.7711, -0.4056, 0.4907]]) R: tensor([[-22.0454, 2.4495], [ 0.0000, 15.0665], [ 0.0000, 0.0000]])
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