inv_cholesky#

sionna.phy.utils.inv_cholesky(tensor: torch.Tensor) → torch.Tensor[source]#

Inverse of the Cholesky decomposition of a matrix

Given a batch of \(M \times M\) Hermitian positive definite matrices \(\mathbf{A}\), this function computes \(\mathbf{L}^{-1}\), where \(\mathbf{L}\) is the Cholesky decomposition, such that \(\mathbf{A}=\mathbf{L}\mathbf{L}^{\textsf{H}}\).

Note

This function assumes that every input matrix is Hermitian positive definite. Factorization errors are deliberately not checked because doing so synchronizes CUDA execution and prevents CUDA graph capture. Results are undefined when the precondition is violated.

Parameters:: tensor (torch.Tensor) – […, M, M], torch.float | torch.complex. Input tensor of rank greater than one.
Outputs:: inv_chol – […, M, M], torch.float | torch.complex. A tensor of the same shape and type as tensor containing the inverse of the Cholesky decomposition of its last two dimensions.

Examples

>>> import torch
>>> from sionna.phy.utils.linalg import inv_cholesky
>>> a = torch.eye(2)
>>> inv_cholesky(a)
tensor([[1., 0.],
        [0., 1.]])