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# 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)

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