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# 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])

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