fracdiff.torch.fdiff#

fracdiff.torch.fdiff(input, n, dim=-1, prepend=None, append=None, window=10, mode='same')[source]#

Computes the n-th differentiation along the given dimension.

This is an extension of torch.diff() to fractional differentiation. See fracdiff.torch.Fracdiff for details.

Note

For integer n, the output is the same as torch.diff() and the parameters window and mode are ignored.

Shape:

  • input: \((N, *, L_{\mathrm{in}})\), where where \(*\) means any number of additional dimensions.

  • output: \((N, *, L_{\mathrm{out}})\), where \(L_{\mathrm{out}}\) is given by \(L_{\mathrm{in}}\) if mode=”same” and \(L_{\mathrm{in}} - \mathrm{window} - 1\) if mode=”valid”. If prepend and/or append are provided, then \(L_{\mathrm{out}}\) increases by the number of elements in each of these tensors.

Examples

>>> from fracdiff.torch import fdiff
...
>>> input = torch.tensor([1, 2, 4, 7, 0])
>>> fdiff(input, 0.5, mode="same", window=3)
tensor([ 1.0000,  1.5000,  2.8750,  4.7500, -4.0000])

>>> fdiff(input, 0.5, mode="valid", window=3)
tensor([ 2.8750,  4.7500, -4.0000])

>>> fdiff(input, 0.5, mode="valid", window=3, prepend=[1, 1])
tensor([ 0.3750,  1.3750,  2.8750,  4.7500, -4.0000])

>>> input = torch.arange(10).reshape(2, 5)
>>> fdiff(input, 0.5)
tensor([[0.0000, 1.0000, 1.5000, 1.8750, 2.1875],
        [5.0000, 3.5000, 3.3750, 3.4375, 3.5547]])