torch.cholesky_inverse — PyTorch 2.7 documentation (original) (raw)

torch.cholesky_inverse(L, upper=False, *, out=None) → Tensor¶

Computes the inverse of a complex Hermitian or real symmetric positive-definite matrix given its Cholesky decomposition.

Let AA be a complex Hermitian or real symmetric positive-definite matrix, and LL its Cholesky decomposition such that:

A=LLHA = LL^{\text{H}}

where LHL^{\text{H}} is the conjugate transpose when LL is complex, and the transpose when LL is real-valued.

Computes the inverse matrix A−1A^{-1}.

Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if AA is a batch of matrices then the output has the same batch dimensions.

Parameters

• L (Tensor) – tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of lower or upper triangular Cholesky decompositions of symmetric or Hermitian positive-definite matrices.
• upper (bool, optional) – flag that indicates whether LL is lower triangular or upper triangular. Default: False

Keyword Arguments

out (Tensor, optional) – output tensor. Ignored if None. Default: None.

Example:

A = torch.randn(3, 3) A = A @ A.T + torch.eye(3) * 1e-3 # Creates a symmetric positive-definite matrix L = torch.linalg.cholesky(A) # Extract Cholesky decomposition torch.cholesky_inverse(L) tensor([[ 1.9314, 1.2251, -0.0889], [ 1.2251, 2.4439, 0.2122], [-0.0889, 0.2122, 0.1412]]) A.inverse() tensor([[ 1.9314, 1.2251, -0.0889], [ 1.2251, 2.4439, 0.2122], [-0.0889, 0.2122, 0.1412]])

A = torch.randn(3, 2, 2, dtype=torch.complex64) A = A @ A.mH + torch.eye(2) * 1e-3 # Batch of Hermitian positive-definite matrices L = torch.linalg.cholesky(A) torch.dist(torch.inverse(A), torch.cholesky_inverse(L)) tensor(5.6358e-7)