PyTorch torch.linalg.qr Function
Pytorch torch Reference Manual
torch.linalg.qrIt is a function in the PyTorch linear algebra module used to compute the QR decomposition of a matrix. QR decomposition factorizes matrix A as A = Q * R, where Q is an orthogonal matrix and R is an upper triangular matrix.
Function Definition
torch.linalg.qr(A, mode='reduced', out=None)
Parameters:
A(Tensor): Input matrix.mode(str, optional): 'reduced' returns the reduced decomposition, 'complete' returns the complete decomposition. Defaults to 'reduced'.out(tuple, optional): Output tuple.
Return Value:
tuple: Returns the tuple (Q, R).
Usage Example
Example
import torch
# Create matrix
A = torch.tensor([[12.0, -51.0, 4.0],
[6.0, 167.0, -68.0],
[-4.0, 24.0, -41.0]])
# QR decomposition
Q, R = torch.linalg.qr(A)
print("Matrix A:")
print(A)
print("nOrthogonal matrix Q:")
print(Q)
print("nUpper triangular matrix R:")
print(R)
print("nVerification: Q @ R =")
print(Q @ R)
# Create matrix
A = torch.tensor([[12.0, -51.0, 4.0],
[6.0, 167.0, -68.0],
[-4.0, 24.0, -41.0]])
# QR decomposition
Q, R = torch.linalg.qr(A)
print("Matrix A:")
print(A)
print("nOrthogonal matrix Q:")
print(Q)
print("nUpper triangular matrix R:")
print(R)
print("nVerification: Q @ R =")
print(Q @ R)
The output result is:
矩阵 A:
tensor([[ 12., -51., 4.],
[ 6., 167., -68.],
[ -4., 24., -41.]])
正交矩阵 Q:
tensor([[-0.8571, 0.3943, 0.3314],
[-0.4286, -0.9029, -0.0343],
[ 0.2857, -0.1714, 0.9428]])
上三角矩阵 R:
tensor([[ -14., -21., 14.],
[ 0., -175., 70.],
[ 0., 0., -35.]])
验证: Q @ R =
tensor([[ 12., -51., 4.],
[ 6., 167., -68.],
[ -4., 24., -41.]])
Other Extensions