##### https://github.com/GPflow/GPflow
Tip revision: 6fd1a26
conditionals.py
``````# Copyright 2016 Valentine Svensson, James Hensman, alexggmatthews
#
# 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
#
#
# 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 warnings
import tensorflow as tf

from gpflow.decors import name_scope
from gpflow import settings

@name_scope()
def conditional(Xnew, X, kern, f, full_cov=False, q_sqrt=None, whiten=False):
"""
Given F, representing the GP at the points X, produce the mean and
(co-)variance of the GP at the points Xnew.

Additionally, there may be Gaussian uncertainty about F as represented by
q_sqrt. In this case `f` represents the mean of the distribution and
q_sqrt the square-root of the covariance.

Additionally, the GP may have been centered (whitened) so that
p(v) = N( 0, I)
f = L v
thus
p(f) = N(0, LL^T) = N(0, K).
In this case 'f' represents the values taken by v.

The method can either return the diagonals of the covariance matrix for
each output of the full covariance matrix (full_cov).

We assume K independent GPs, represented by the columns of f (and the
last dimension of q_sqrt).

- Xnew is a data matrix, size N x D
- X are data points, size M x D
- kern is a GPflow kernel
- f is a data matrix, M x K, representing the function values at X, for K functions.
- q_sqrt (optional) is a matrix of standard-deviations or Cholesky
matrices, size M x K or M x M x K
- whiten (optional) is a boolean: whether to whiten the representation
as described above.

These functions are now considered deprecated, subsumed into this one:
gp_predict
gaussian_gp_predict
gp_predict_whitened
gaussian_gp_predict_whitened

"""

# compute kernel stuff
num_data = tf.shape(X)[0]  # M
num_func = tf.shape(f)[1]  # K
Kmn = kern.K(X, Xnew)
Kmm = kern.K(X) + tf.eye(num_data, dtype=settings.tf_float) * settings.numerics.jitter_level
Lm = tf.cholesky(Kmm)

# Compute the projection matrix A
A = tf.matrix_triangular_solve(Lm, Kmn, lower=True)

# compute the covariance due to the conditioning
if full_cov:
fvar = kern.K(Xnew) - tf.matmul(A, A, transpose_a=True)
shape = tf.stack([num_func, 1, 1])
else:
fvar = kern.Kdiag(Xnew) - tf.reduce_sum(tf.square(A), 0)
shape = tf.stack([num_func, 1])
fvar = tf.tile(tf.expand_dims(fvar, 0), shape)  # K x N x N or K x N

# another backsubstitution in the unwhitened case
if not whiten:
A = tf.matrix_triangular_solve(tf.transpose(Lm), A, lower=False)

# construct the conditional mean
fmean = tf.matmul(A, f, transpose_a=True)

if q_sqrt is not None:
if q_sqrt.get_shape().ndims == 2:
LTA = A * tf.expand_dims(tf.transpose(q_sqrt), 2)  # K x M x N
elif q_sqrt.get_shape().ndims == 3:
L = tf.matrix_band_part(tf.transpose(q_sqrt, (2, 0, 1)), -1, 0)  # K x M x M
A_tiled = tf.tile(tf.expand_dims(A, 0), tf.stack([num_func, 1, 1]))
LTA = tf.matmul(L, A_tiled, transpose_a=True)  # K x M x N
else:  # pragma: no cover
raise ValueError("Bad dimension for q_sqrt: %s" %
str(q_sqrt.get_shape().ndims))
if full_cov:
fvar = fvar + tf.matmul(LTA, LTA, transpose_a=True)  # K x N x N
else:
fvar = fvar + tf.reduce_sum(tf.square(LTA), 1)  # K x N
fvar = tf.transpose(fvar)  # N x K or N x N x K

return fmean, fvar

def gp_predict(Xnew, X, kern, F, full_cov=False):
warnings.warn('gp_predict is deprecated: use conditonal(...) instead',
DeprecationWarning)
return conditional(Xnew, X, kern, F,
full_cov=full_cov, q_sqrt=None, whiten=False)

def gaussian_gp_predict(Xnew, X, kern, q_mu, q_sqrt, num_columns,
full_cov=False):
warnings.warn('gp_predict is deprecated: use conditonal(...) instead',
DeprecationWarning)
return conditional(Xnew, X, kern, q_mu,
full_cov=full_cov, q_sqrt=q_sqrt, whiten=False)

def gaussian_gp_predict_whitened(Xnew, X, kern, q_mu, q_sqrt, num_columns,
full_cov=False):
warnings.warn('gp_predict is deprecated: use conditonal(...) instead',
DeprecationWarning)
return conditional(Xnew, X, kern, q_mu,
full_cov=full_cov, q_sqrt=q_sqrt, whiten=True)

def gp_predict_whitened(Xnew, X, kern, V, full_cov=False):
warnings.warn('gp_predict is deprecated: use conditonal(...) instead',
DeprecationWarning)
return conditional(Xnew, X, kern, V,
full_cov=full_cov, q_sqrt=None, whiten=True)
``````