torch.cholesky_inverse¶
- 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 be a complex Hermitian or real symmetric positive-definite matrix, and its Cholesky decomposition such that:
where is the conjugate transpose when is complex, and the transpose when is real-valued.
Computes the inverse matrix .
Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if 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 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)