YouTipPytorch Torch Linalg Cholesky
# PyTorch torch.linalg.cholesky Function
* * PyTorch torch Reference](#)
`torch.linalg.cholesky` is a function in PyTorch's linear algebra module (linalg) for computing the Cholesky decomposition of symmetric positive-definite matrices. It is the recommended replacement for `torch.cholesky`.
### Function Definition
torch.linalg.cholesky(A, upper=False, out=None)
**Parameters**:
* `A` (Tensor): Input symmetric positive-definite matrix.
* `upper` (bool, optional): If True, returns upper triangular matrix; otherwise returns lower triangular matrix. Default: False.
* `out` (Tensor, optional): Output tensor.
**Returns**:
* `torch.Tensor`: Returns the triangular matrix from 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)
Output:
Original matrix A: tensor([[4., 2., 2.], [2., 5., 3.], [2., 3., 6.]], dtype=torch.float64)Cholesky decomposition (Lower triangular matrix L): tensor([[2.0000, 0.0000, 0.0000], [1.0000, 2.0000, 0.0000], [1.0000, 1.0000, 2.0000]], dtype=torch.float64)Verification: L @ L.T = tensor([[4., 2., 2.], [2., 5., 3.], [2., 3., 6.]], dtype=torch.float64)
* * PyTorch torch Reference](#)