# Copyright 2017 Joachim van der Herten
#
# 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.
from gpflow import settings
from gpflow.param import Parameterized, DataHolder, AutoFlow
import numpy as np
import tensorflow as tf
float_type = settings.dtypes.float_type
class DataTransform(Parameterized):
"""
Maps data in :class:`.Domain` U to :class:`.Domain` V.
Useful for scaling of data between domains.
"""
@AutoFlow((float_type, [None, None]))
def forward(self, X):
"""
Performs the transformation of U -> V
"""
return self.build_forward(X)
def build_forward(self, X):
"""
Tensorflow graph for the transformation of U -> V
:param X: N x P tensor
:return: N x Q tensor
"""
raise NotImplementedError
def backward(self, Y):
"""
Performs the transformation of V -> U. By default, calls the :meth:`.forward` transform on the inverted
transform object which requires implementation of __invert__. The method can be overwritten in subclasses if a
more efficient (direct) transformation is possible.
:param Y: N x Q matrix
:return: N x P matrix
"""
return (~self).forward(Y)
def assign(self, other):
raise NotImplementedError
def __invert__(self):
"""
Return a :class:`.DataTransform` object implementing the reverse transform V -> U
"""
raise NotImplementedError
class LinearTransform(DataTransform):
"""
A simple linear transform of the form
.. math::
\\mathbf Y = (\\mathbf A \\mathbf X^{T})^{T} + \\mathbf b \\otimes \\mathbf 1_{N}^{T}
"""
def __init__(self, A, b):
"""
:param A: scaling matrix. Either a P-dimensional vector, or a P x P transformation matrix. For the latter,
the inverse and backward methods are not guaranteed to work as A must be invertible.
It is also possible to specify a matrix with size P x Q with Q != P to achieve
a lower dimensional representation of X.
In this case, A is not invertible, hence inverse and backward transforms are not supported.
:param b: A P-dimensional offset vector.
"""
super(LinearTransform, self).__init__()
assert A is not None
assert b is not None
b = np.atleast_1d(b)
A = np.atleast_1d(A)
if len(A.shape) == 1:
A = np.diag(A)
assert (len(b.shape) == 1)
assert (len(A.shape) == 2)
self.A = DataHolder(A)
self.b = DataHolder(b)
def build_forward(self, X):
return tf.matmul(X, tf.transpose(self.A)) + self.b
@AutoFlow((float_type, [None, None]))
def backward(self, Y):
"""
Overwrites the default backward approach, to avoid an explicit matrix inversion.
"""
return self.build_backward(Y)
def build_backward(self, Y):
"""
TensorFlow implementation of the inverse mapping
"""
L = tf.cholesky(tf.transpose(self.A))
XT = tf.cholesky_solve(L, tf.transpose(Y-self.b))
return tf.transpose(XT)
def build_backward_variance(self, Yvar):
"""
Additional method for scaling variance backward (used in :class:`.Normalizer`). Can process both the diagonal
variances returned by predict_f, as well as full covariance matrices.
:param Yvar: size N x N x P or size N x P
:return: Yvar scaled, same rank and size as input
"""
rank = tf.rank(Yvar)
# Because TensorFlow evaluates both fn1 and fn2, the transpose can't be in the same line. If a full cov
# matrix is provided fn1 turns it into a rank 4, then tries to transpose it as a rank 3.
# Splitting it in two steps however works fine.
Yvar = tf.cond(tf.equal(rank, 2), lambda: tf.matrix_diag(tf.transpose(Yvar)), lambda: Yvar)
Yvar = tf.cond(tf.equal(rank, 2), lambda: tf.transpose(Yvar, perm=[1, 2, 0]), lambda: Yvar)
N = tf.shape(Yvar)[0]
D = tf.shape(Yvar)[2]
L = tf.cholesky(tf.square(tf.transpose(self.A)))
Yvar = tf.reshape(Yvar, [N * N, D])
scaled_var = tf.reshape(tf.transpose(tf.cholesky_solve(L, tf.transpose(Yvar))), [N, N, D])
return tf.cond(tf.equal(rank, 2), lambda: tf.reduce_sum(scaled_var, axis=1), lambda: scaled_var)
def assign(self, other):
"""
Assign the parameters of another :class:`LinearTransform`.
Useful to avoid graph re-compilation.
:param other: :class:`.LinearTransform` object
"""
assert other is not None
assert isinstance(other, LinearTransform)
self.A.set_data(other.A.value)
self.b.set_data(other.b.value)
def __invert__(self):
A_inv = np.linalg.inv(self.A.value.T)
return LinearTransform(A_inv, -np.dot(self.b.value, A_inv))
