torch.linalg.ldl_factor_ex

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

This is a version of ldl_factor() that does not perform error checks unless check_errors= True. It also returns the info tensor returned by LAPACK’s sytrf. info stores integer error codes from the backend library. A positive integer indicates the diagonal element of $D$ that is zero. Division by 0 will occur if the result is used for solving a system of linear equations. info filled with zeros indicates that the factorization was successful. If check_errors=True and info contains positive integers, then a RuntimeError is thrown.

Note

When the inputs are on a CUDA device, this function synchronizes only when check_errors= True.

Warning

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

Parameters:

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

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.

• check_errors (bool, optional) – controls whether to check the content of info and raise an error if it is non-zero. Default: False.

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

Returns:

A named tuple (LD, pivots, info).

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, info = torch.linalg.ldl_factor_ex(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)
>>> info
tensor(0, dtype=torch.int32)