# Copyright 2018 Amazon.com, Inc. or its affiliates. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License").
# You may not use this file except in compliance with the License.
# A copy of the License is located at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# or in the "license" file accompanying this file. This file is distributed
# on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
# express or implied. See the License for the specific language governing
# permissions and limitations under the License.
from gluonts.mx import Tensor
[docs]class Kernel:
# noinspection PyMethodOverriding,PyPep8Naming
[docs] def kernel_matrix(self, x1: Tensor, x2: Tensor):
# raise error in the base Kernel class, implement in the concrete
# subclasses
raise NotImplementedError()
# noinspection PyMethodOverriding,PyPep8Naming
def _compute_square_dist(self, F, x1: Tensor, x2: Tensor) -> None:
r"""
Parameters
--------------------
F : ModuleType
A module that can either refer to the Symbol API or the NDArray
API in MXNet.
x1 : Tensor
Feature data of shape (batch_size, history_length, num_features).
x2 : Tensor
Feature data of shape (batch_size, history_length, num_features).
Returns
--------------------
Tensor
square distance matrix of shape (batch_size, history_length, history_length)
:math: `\|\mathbf{x_1}-\mathbf{x_2}\|_2^2 = (\mathbf{x_1}-\mathbf{x_2})^T(\mathbf{x_1}-\mathbf{x_2})
= \|\mathbf{x_1}\|_2^2 - 2\mathbf{x_1}^T\mathbf{x_2}
+ \|\mathbf{x_2}\|_2^2`.
""" # noqa: E501
feature_axis = 2
# Column vector: Add to math:`x_i^Tx_i` to every column in row i
x1_norm_square = (
F.norm(x1, ord=2, axis=feature_axis) ** 2
).expand_dims(2)
# Row vector: Add to math:`x_i^Tx_i` to every row in column i
x2_norm_square = (
F.norm(x2, ord=2, axis=feature_axis) ** 2
).expand_dims(1)
x1x2_trans = F.linalg.gemm2(x1, x2, transpose_b=True)
self.square_dist = F.broadcast_add(
F.broadcast_sub(x1_norm_square, 2 * x1x2_trans), x2_norm_square
)