torch.cholesky_solve¶
- torch.cholesky_solve(B, L, upper=False, *, out=None) Tensor ¶
Computes the solution of a system of linear equations with complex Hermitian or real symmetric positive-definite lhs 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.
Returns the solution of the following linear system:
Supports inputs of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if or is a batch of matrices then the output has the same batch dimensions.
- Parameters
B (Tensor) – right-hand side tensor of shape (*, n, k) where is zero or more batch dimensions
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 >>> B = torch.randn(3, 2) >>> torch.cholesky_solve(B, L) tensor([[ -8.1625, 19.6097], [ -5.8398, 14.2387], [ -4.3771, 10.4173]]) >>> A.inverse() @ B tensor([[ -8.1626, 19.6097], [ -5.8398, 14.2387], [ -4.3771, 10.4173]]) >>> 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) >>> B = torch.randn(2, 1, dtype=torch.complex64) >>> X = torch.cholesky_solve(B, L) >>> torch.dist(X, A.inverse() @ B) tensor(1.6881e-5)