# Copyright 2017-2020 The GPflow Contributors. 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.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License 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.
import numpy as np # pylint: disable=unused-import # Used by Sphinx to generate documentation.
import tensorflow as tf
from check_shapes import check_shapes
from ..base import TensorLike, TensorType
from ..inducing_variables import InducingPatches, InducingPoints, Multiscale
from ..kernels import Convolutional, Kernel, SquaredExponential
from .dispatch import Kuf
[docs]@Kuf.register(InducingPoints, Kernel, TensorLike)
@check_shapes(
"inducing_variable: [M, D, 1]",
"Xnew: [batch..., N, D]",
"return: [M, batch..., N]",
)
def Kuf_kernel_inducingpoints(
inducing_variable: InducingPoints, kernel: Kernel, Xnew: TensorType
) -> tf.Tensor:
return kernel(inducing_variable.Z, Xnew)
[docs]@Kuf.register(Multiscale, SquaredExponential, TensorLike)
@check_shapes(
"inducing_variable: [M, D, 1]",
"Xnew: [batch..., N, D]",
"return: [M, batch..., N]",
)
def Kuf_sqexp_multiscale(
inducing_variable: Multiscale, kernel: SquaredExponential, Xnew: TensorType
) -> tf.Tensor:
Xnew, _ = kernel.slice(Xnew, None)
Zmu, Zlen = kernel.slice(inducing_variable.Z, inducing_variable.scales)
idlengthscales = kernel.lengthscales + Zlen
d = inducing_variable._cust_square_dist(Xnew, Zmu, idlengthscales[None, :, :])
lengthscales = tf.reduce_prod(kernel.lengthscales / idlengthscales, 1)
lengthscales = tf.reshape(lengthscales, (1, -1))
return tf.transpose(kernel.variance * tf.exp(-0.5 * d) * lengthscales)
[docs]@Kuf.register(InducingPatches, Convolutional, object)
@check_shapes(
"inducing_variable: [M, D, 1]",
"Xnew: [batch..., N, D2]",
"return: [M, batch..., N]",
)
def Kuf_conv_patch(
inducing_variable: InducingPatches, kernel: Convolutional, Xnew: TensorType
) -> tf.Tensor:
Xp = kernel.get_patches(Xnew) # [N, num_patches, patch_len]
bigKzx = kernel.base_kernel.K(
inducing_variable.Z, Xp
) # [M, N, P] -- thanks to broadcasting of kernels
Kzx = tf.reduce_sum(bigKzx * kernel.weights if hasattr(kernel, "weights") else bigKzx, [2])
return Kzx / kernel.num_patches