torch.logdet

torch.logdet(input) → Tensor

Calculates log determinant of a square matrix or batches of square matrices.

It returns -inf if the input has a determinant of zero, and NaN if it has a negative determinant.

Note

Backward through logdet() internally uses SVD results when input is not invertible. In this case, double backward through logdet() will be unstable in when input doesn’t have distinct singular values. See torch.linalg.svd() for details.

See also

torch.linalg.slogdet() computes the sign (resp. angle) and natural logarithm of the absolute value of the determinant of real-valued (resp. complex) square matrices.

Parameters

input (Tensor) – the input tensor of size (*, n, n) where * is zero or more batch dimensions.

Example:

>>> A = torch.randn(3, 3)
>>> torch.det(A)
tensor(0.2611)
>>> torch.logdet(A)
tensor(-1.3430)
>>> A
tensor([[[ 0.9254, -0.6213],
         [-0.5787,  1.6843]],

        [[ 0.3242, -0.9665],
         [ 0.4539, -0.0887]],

        [[ 1.1336, -0.4025],
         [-0.7089,  0.9032]]])
>>> A.det()
tensor([1.1990, 0.4099, 0.7386])
>>> A.det().log()
tensor([ 0.1815, -0.8917, -0.3031])