Source code for gpytorch.kernels.periodic_kernel

#!/usr/bin/env python3

import math

import torch

from ..constraints import Positive
from .kernel import Kernel


[docs]class PeriodicKernel(Kernel): r"""Computes a covariance matrix based on the periodic kernel between inputs :math:`\mathbf{x_1}` and :math:`\mathbf{x_2}`: .. math:: \begin{equation*} k_{\text{Periodic}}(\mathbf{x_1}, \mathbf{x_2}) = \exp \left( -2 \sum_i \frac{\sin ^2 \left( \frac{\pi}{p} (\mathbf{x_{1,i}} - \mathbf{x_{2,i}} ) \right)}{\lambda} \right) \end{equation*} where * :math:`p` is the period length parameter. * :math:`\lambda` is a lengthscale parameter. Equation is based on [David Mackay's Introduction to Gaussian Processes equation 47] (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.81.1927&rep=rep1&type=pdf) albeit without feature-specific lengthscales and period lengths. The exponential coefficient was changed and lengthscale is not squared to maintain backwards compatibility .. note:: This kernel does not have an `outputscale` parameter. To add a scaling parameter, decorate this kernel with a :class:`gpytorch.kernels.ScaleKernel`. .. note:: This kernel does not have an ARD lengthscale or period length option. Args: :attr:`batch_shape` (torch.Size, optional): Set this if you want a separate lengthscale for each batch of input data. It should be `b` if :attr:`x1` is a `b x n x d` tensor. Default: `torch.Size([])`. :attr:`active_dims` (tuple of ints, optional): Set this if you want to compute the covariance of only a few input dimensions. The ints corresponds to the indices of the dimensions. Default: `None`. :attr:`period_length_prior` (Prior, optional): Set this if you want to apply a prior to the period length parameter. Default: `None`. :attr:`lengthscale_prior` (Prior, optional): Set this if you want to apply a prior to the lengthscale parameter. Default: `None`. :attr:`lengthscale_constraint` (Constraint, optional): Set this if you want to apply a constraint to the value of the lengthscale. Default: `Positive`. :attr:`period_length_constraint` (Constraint, optional): Set this if you want to apply a constraint to the value of the period length. Default: `Positive`. :attr:`eps` (float): The minimum value that the lengthscale/period length can take (prevents divide by zero errors). Default: `1e-6`. Attributes: :attr:`lengthscale` (Tensor): The lengthscale parameter. Size = `*batch_shape x 1 x 1`. :attr:`period_length` (Tensor): The period length parameter. Size = `*batch_shape x 1 x 1`. Example: >>> x = torch.randn(10, 5) >>> # Non-batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel()) >>> >>> batch_x = torch.randn(2, 10, 5) >>> # Batch: Simple option >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel()) >>> # Batch: different lengthscale for each batch >>> covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.PeriodicKernel(batch_size=2)) >>> covar = covar_module(x) # Output: LazyVariable of size (2 x 10 x 10) """ has_lengthscale = True def __init__(self, period_length_prior=None, period_length_constraint=None, **kwargs): super(PeriodicKernel, self).__init__(**kwargs) if period_length_constraint is None: period_length_constraint = Positive() self.register_parameter( name="raw_period_length", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1, 1)) ) if period_length_prior is not None: self.register_prior( "period_length_prior", period_length_prior, lambda m: m.period_length, lambda m, v: m._set_period_length(v), ) self.register_constraint("raw_period_length", period_length_constraint) @property def period_length(self): return self.raw_period_length_constraint.transform(self.raw_period_length) @period_length.setter def period_length(self, value): self._set_period_length(value) def _set_period_length(self, value): if not torch.is_tensor(value): value = torch.as_tensor(value).to(self.raw_period_length) self.initialize(raw_period_length=self.raw_period_length_constraint.inverse_transform(value)) def forward(self, x1, x2, diag=False, **params): x1_ = x1.div(self.period_length).mul(math.pi) x2_ = x2.div(self.period_length).mul(math.pi) diff = x1_.unsqueeze(-2) - x2_.unsqueeze(-3) res = diff.sin().pow(2).sum(dim=-1).div(self.lengthscale).mul(-2.0).exp_() if diag: res = res.squeeze(0) return res