PyTorch torch.linalg.cholesky function
Pytorch torch Reference Manual
torch.linalg.choleskyIt is a function in PyTorch's linear algebra module (linalg) used to compute the Cholesky decomposition of a symmetric positive definite matrix. It istorch.choleskythe recommended replacement function.
Function definition
torch.linalg.cholesky(A, upper=False, out=None)
Parameters:
A(Tensor): Input symmetric positive definite matrix.upper(bool, optional): If True, returns the upper triangular matrix; otherwise, returns the lower triangular matrix. Default is False.out(Tensor, optional): Output tensor.
Return value:
torch.Tensor: Returns the triangular matrix of the Cholesky decomposition.
Usage example
Example
import torch
# Create a symmetric positive definite matrix
A = torch.tensor([[4.0, 2.0, 2.0],
[2.0, 5.0, 3.0],
[2.0, 3.0, 6.0]], dtype=torch.float64)
# Cholesky decomposition
L = torch.linalg.cholesky(A)
print("Original matrix A:")
print(A)
print("nCholesky decomposition (lower triangular matrix L):")
print(L)
print("nVerification: L @ L.T = ")
print(L @ L.T)
# Create a symmetric positive definite matrix
A = torch.tensor([[4.0, 2.0, 2.0],
[2.0, 5.0, 3.0],
[2.0, 3.0, 6.0]], dtype=torch.float64)
# Cholesky decomposition
L = torch.linalg.cholesky(A)
print("Original matrix A:")
print(A)
print("nCholesky decomposition (lower triangular matrix L):")
print(L)
print("nVerification: L @ L.T = ")
print(L @ L.T)
The output result is:
原矩阵 A:
tensor([[4., 2., 2.],
[2., 5., 3.],
[2., 3., 6.]], dtype=torch.float64)
Cholesky 分解 (下三角矩阵 L):
tensor([[2.0000, 0.0000, 0.0000],
[1.0000, 2.0000, 0.0000],
[1.0000, 1.0000, 2.0000]], dtype=torch.float64)
验证: L @ L.T =
tensor([[4., 2., 2.],
[2., 5., 3.],
[2., 3., 6.]], dtype=torch.float64)
Other extensions