pypose.optim.kernel.Arctan

class pypose.optim.kernel.Arctan(delta=1.0)

The robust Arctan kernel cost function.

\[\bm{y}_i=\delta ^{2}\arctan \left ( \frac{\bm{x}_i}{\delta ^{2}}\right ) \]

where \(\delta\) (delta) is a hyperparameter, \(\bm{x}\) and \(\bm{y}\) are the input and output tensors, respectively.

Parameters:

delta (float, optional) – Specify the Arctan cost. Default: 1.0

Note

The input has to be a non-negative tensor and the output tensor has the same shape with the input.

Example

>>> import pypose.optim.kernel as ppok
>>> kernel = ppok.Arctan()
>>> input = torch.tensor([0, 0.5, 1, 2, 3])
>>> kernel(input)
tensor([0.0000, 0.4636, 0.7854, 1.1071, 1.2490])

forward(input)

Parameters:

input (torch.Tensor) – the input tensor (non-negative).