#!/usr/bin/env python3

from typing import Optional, Tuple

from .kernel import Kernel

r"""
A Kernel decorator for kernels with additive structure. If a kernel decomposes
additively, then this module will be much more computationally efficient.

A kernel function k decomposes additively if it can be written as

.. math::

\begin{equation*}
k(\mathbf{x_1}, \mathbf{x_2}) = k'(x_1^{(1)}, x_2^{(1)}) + \ldots + k'(x_1^{(d)}, x_2^{(d)})
\end{equation*}

for some kernel :math:k' that operates on a subset of dimensions.

Given a b x n x d input, AdditiveStructureKernel computes d one-dimensional kernels
(using the supplied base_kernel), and then adds the component kernels together.
Unlike :class:~gpytorch.kernels.AdditiveKernel, AdditiveStructureKernel computes each
of the additive terms in batch, making it very fast.

Args:
:attr:base_kernel (Kernel):
The kernel to approximate with KISS-GP
:attr:num_dims (int):
The dimension of the input data.
:attr:active_dims (tuple of ints, optional):
Passed down to the base_kernel.
"""

@property
def is_stationary(self) -> bool:
"""
Kernel is stationary if the base kernel is stationary.
"""
return self.base_kernel.is_stationary

def __init__(
self,
base_kernel: Kernel,
num_dims: int,
active_dims: Optional[Tuple[int, ...]] = None,
):
self.base_kernel = base_kernel
self.num_dims = num_dims

def forward(self, x1, x2, diag=False, last_dim_is_batch=False, **params):
if last_dim_is_batch:
raise RuntimeError("AdditiveStructureKernel does not accept the last_dim_is_batch argument.")

res = self.base_kernel(x1, x2, diag=diag, last_dim_is_batch=True, **params)
res = res.sum(-2 if diag else -3)
return res

def prediction_strategy(self, train_inputs, train_prior_dist, train_labels, likelihood):
return self.base_kernel.prediction_strategy(train_inputs, train_prior_dist, train_labels, likelihood)

def num_outputs_per_input(self, x1, x2):
return self.base_kernel.num_outputs_per_input(x1, x2)