# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
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# 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
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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# See the License for the specific language governing permissions and
# limitations under the License.
import copy
from typing import Any, List, Optional, Union
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
[docs]def cast(
value: Union[tf.Tensor, np.ndarray], dtype: tf.DType, name: Optional[str] = None
) -> tf.Tensor:
if not tf.is_tensor(value):
# TODO(awav): Release TF2.2 resolves this issue
# workaround for https://github.com/tensorflow/tensorflow/issues/35938
return tf.convert_to_tensor(value, dtype, name=name)
return tf.cast(value, dtype, name=name)
[docs]def eye(num: int, value: tf.Tensor, dtype: Optional[tf.DType] = None) -> tf.Tensor:
if dtype is not None:
value = cast(value, dtype)
return tf.linalg.diag(tf.fill([num], value))
[docs]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]def broadcasting_elementwise(op, a, b):
"""
Apply binary operation `op` to every pair in tensors `a` and `b`.
:param op: binary operator on tensors, e.g. tf.add, tf.substract
:param a: tf.Tensor, shape [n_1, ..., n_a]
:param b: tf.Tensor, shape [m_1, ..., m_b]
:return: tf.Tensor, shape [n_1, ..., n_a, m_1, ..., m_b]
"""
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]def square_distance(X, X2):
"""
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.
This function can deal with leading dimensions in X and X2.
In the sample case, where X and X2 are both 2 dimensional,
for example, X is [N, D] and X2 is [M, D], then a tensor of shape
[N, M] is returned. If X is [N1, S1, D] and X2 is [N2, S2, D]
then the output will be [N1, S1, N2, S2].
"""
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]def difference_matrix(X, X2):
"""
Returns (X - X2ᵀ)
This function can deal with leading dimensions in X and X2.
For example, If X has shape [M, D] and X2 has shape [N, D],
the output will have shape [M, N, D]. If X has shape [I, J, M, D]
and X2 has shape [K, L, N, D], the output will have shape
[I, J, M, K, L, N, D].
"""
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]def pca_reduce(X: tf.Tensor, latent_dim: tf.Tensor) -> tf.Tensor:
"""
A helpful function for linearly reducing the dimensionality of the input
points X to `latent_dim` dimensions.
:param X: data array of size N (number of points) x D (dimensions)
:param latent_dim: Number of latent dimensions Q < D
:return: PCA projection array of size [N, Q].
"""
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