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# torch.linalg.ldl_factor

torch.linalg.ldl_factor(A, *, hermitian=False, out=None)

  Computes a compact representation of the LDL factorization of a Hermitian or symmetric (possibly indefinite) matrix.

  When `A` is complex valued it can be Hermitian (`hermitian`= True) or symmetric (`hermitian`= False).

  The factorization is of the form the form A=L D L T A = L D L^T A=L D L T. If `hermitian` is True then transpose operation is the conjugate transpose.

  L L L (or U U U) and D D D are stored in compact form in `LD`. They follow the format specified by LAPACK’s sytrf function. These tensors may be used in `torch.linalg.ldl_solve()` to solve linear systems.

  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.

  Note

  When inputs are on a CUDA device, this function synchronizes that device with the CPU. For a version of this function that does not synchronize, see `torch.linalg.ldl_factor_ex()`.

  Parameters:

    A (Tensor) – tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of symmetric or Hermitian matrices.

  Keyword Arguments:

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

    - out (tuple, optional) – tuple of two tensors to write the output to. Ignored if None. Default: None.

  Returns:

    A named tuple (LD, pivots).

  Examples:

      >>> A = torch.randn(3, 3)
      >>> A = A @ A.mT # make symmetric
      >>> A
      tensor([[7.2079, 4.2414, 1.9428],
              [4.2414, 3.4554, 0.3264],
              [1.9428, 0.3264, 1.3823]])
      >>> LD, pivots = torch.linalg.ldl_factor(A)
      >>> LD
      tensor([[ 7.2079,  0.0000,  0.0000],
              [ 0.5884,  0.9595,  0.0000],
              [ 0.2695, -0.8513,  0.1633]])
      >>> pivots
      tensor([1, 2, 3], dtype=torch.int32)

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