inv_cholesky

sionna.phy.utils.inv_cholesky(tensor: torch.Tensor) → torch.Tensor

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 \(\mathbf{A}=\mathbf{L}\mathbf{L}^{\textsf{H}}\).

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.]])