# 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 copy
from typing import Any, Callable, List, Optional
import tensorflow as tf
import tensorflow_probability as tfp
from check_shapes import check_shapes
[docs]@check_shapes(
"value: []",
"return: [N, N]",
)
def eye(num: int, value: tf.Tensor, dtype: Optional[tf.DType] = None) -> tf.Tensor:
if dtype is not None:
value = tf.cast(value, dtype)
return tf.linalg.diag(tf.fill([num], value))
[docs]@check_shapes(
"tensor: [any...]",
"return: [transposed_any...]",
)
def leading_transpose(tensor: tf.Tensor, perm: List[Any], leading_dim: int = 0) -> tf.Tensor:
"""
Transposes tensors with leading dimensions.
Leading dimensions in permutation list represented via ellipsis `...` and is of type
List[Union[int, type(...)] (please note, due to mypy issues, List[Any] is used instead). When
leading dimensions are found, `transpose` method considers them as a single grouped element
indexed by 0 in `perm` list. So, passing `perm=[-2, ..., -1]`, you assume that your input tensor
has [..., A, B] shape, and you want to move leading dims between A and B dimensions. Dimension
indices in permutation list can be negative or positive. Valid positive indices start from 1 up
to the tensor rank, viewing leading dimensions `...` as zero index.
Example::
a = tf.random.normal((1, 2, 3, 4, 5, 6))
# [..., A, B, C],
# where A is 1st element,
# B is 2nd element and
# C is 3rd element in
# permutation list,
# leading dimensions are [1, 2, 3]
# which are 0th element in permutation list
b = leading_transpose(a, [3, -3, ..., -2]) # [C, A, ..., B]
sess.run(b).shape
output> (6, 4, 1, 2, 3, 5)
:param tensor: TensorFlow tensor.
:param perm: List of permutation indices.
:returns: TensorFlow tensor.
:raises ValueError: when `...` cannot be found.
"""
perm = copy.copy(perm)
idx = perm.index(...)
perm[idx] = leading_dim
rank = tf.rank(tensor)
perm_tf = perm % rank
leading_dims = tf.range(rank - len(perm) + 1)
perm = tf.concat([perm_tf[:idx], leading_dims, perm_tf[idx + 1 :]], 0)
return tf.transpose(tensor, perm)
[docs]@check_shapes(
"a: [a_shape...]",
"b: [b_shape...]",
"return: [a_shape..., b_shape...]",
)
def broadcasting_elementwise(
op: Callable[[tf.Tensor, tf.Tensor], tf.Tensor], a: tf.Tensor, b: tf.Tensor
) -> tf.Tensor:
"""
Apply binary operation `op` to every pair in tensors `a` and `b`.
:param op: binary operator on tensors, e.g. tf.add, tf.substract
"""
flatres = op(tf.reshape(a, [-1, 1]), tf.reshape(b, [1, -1]))
return tf.reshape(flatres, tf.concat([tf.shape(a), tf.shape(b)], 0))
[docs]@check_shapes(
"X: [batch..., N, D]",
"X2: [batch2..., N2, D]",
"return: [batch..., N, batch2..., N2] if X2 is not None",
"return: [batch..., N, N] if X2 is None",
)
def square_distance(X: tf.Tensor, X2: Optional[tf.Tensor]) -> tf.Tensor:
"""
Returns ||X - X2ᵀ||²
Due to the implementation and floating-point imprecision, the
result may actually be very slightly negative for entries very
close to each other.
"""
if X2 is None:
Xs = tf.reduce_sum(tf.square(X), axis=-1, keepdims=True)
dist = -2 * tf.matmul(X, X, transpose_b=True)
dist += Xs + tf.linalg.adjoint(Xs)
return dist
Xs = tf.reduce_sum(tf.square(X), axis=-1)
X2s = tf.reduce_sum(tf.square(X2), axis=-1)
dist = -2 * tf.tensordot(X, X2, [[-1], [-1]])
dist += broadcasting_elementwise(tf.add, Xs, X2s)
return dist
[docs]@check_shapes(
"X: [batch..., N, D]",
"X2: [batch2..., N2, D]",
"return: [batch..., N, batch2..., N2, D] if X2 is not None",
"return: [batch..., N, N, D] if X2 is None",
)
def difference_matrix(X: tf.Tensor, X2: Optional[tf.Tensor]) -> tf.Tensor:
"""
Returns (X - X2ᵀ)
"""
if X2 is None:
X2 = X
diff = X[..., :, tf.newaxis, :] - X2[..., tf.newaxis, :, :]
return diff
Xshape = tf.shape(X)
X2shape = tf.shape(X2)
X = tf.reshape(X, (-1, Xshape[-1]))
X2 = tf.reshape(X2, (-1, X2shape[-1]))
diff = X[:, tf.newaxis, :] - X2[tf.newaxis, :, :]
diff = tf.reshape(diff, tf.concat((Xshape[:-1], X2shape[:-1], [Xshape[-1]]), 0))
return diff
[docs]@check_shapes(
"X: [N, D]",
"latent_dim: []",
"return: [N, Q]",
)
def pca_reduce(X: tf.Tensor, latent_dim: tf.Tensor) -> tf.Tensor:
"""
Linearly reduce the dimensionality of the input points `X` to `latent_dim` dimensions.
:param X: Data to reduce.
:param latent_dim: Number of latent dimension, Q < D.
:return: PCA projection array.
"""
if latent_dim > X.shape[1]: # pragma: no cover
raise ValueError("Cannot have more latent dimensions than observed")
X_cov = tfp.stats.covariance(X)
evals, evecs = tf.linalg.eigh(X_cov)
W = evecs[:, -latent_dim:]
return (X - tf.reduce_mean(X, axis=0, keepdims=True)) @ W