torch.linalg.ldl_solve

torch.linalg.ldl_solve(LD, pivots, B, *, hermitian=False, out=None) → Tensor

Computes the solution of a system of linear equations using the LDL factorization.

LD and pivots are the compact representation of the LDL factorization and are expected to be computed by torch.linalg.ldl_factor_ex(). hermitian argument to this function should be the same as the corresponding arguments in torch.linalg.ldl_factor_ex().

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

Warning

This function is “experimental” and it may change in a future PyTorch release.

Parameters

• LD (Tensor) – the n times n matrix or the batch of such matrices of size (*, n, n) where * is one or more batch dimensions.

• pivots (Tensor) – the pivots corresponding to the LDL factorization of LD.

• B (Tensor) – right-hand side tensor of shape (*, n, k).

Keyword Arguments

• hermitian (bool, optional) – whether to consider the decomposed matrix to be Hermitian or symmetric. For real-valued matrices, this switch has no effect. Default: False.

• out (tuple, optional) – output tensor. B may be passed as out and the result is computed in-place on B. Ignored if None. Default: None.

Examples:

>>> A = torch.randn(2, 3, 3)
>>> A = A @ A.mT # make symmetric
>>> LD, pivots, info = torch.linalg.ldl_factor_ex(A)
>>> B = torch.randn(2, 3, 4)
>>> X = torch.linalg.ldl_solve(LD, pivots, B)
>>> torch.linalg.norm(A @ X - B)
>>> tensor(0.0001)