# Copyright 2016 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
#
# 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
import tensorflow as tf
from .model import GPModel
from .param import Param, DataHolder
from .conditionals import conditional
from .priors import Gaussian
from .mean_functions import Zero


class SGPMC(GPModel):
    """
    This is the Sparse Variational GP using MCMC (SGPMC). The key reference is

    ::

      @inproceedings{hensman2015mcmc,
        title={MCMC for Variatinoally Sparse Gaussian Processes},
        author={Hensman, James and Matthews, Alexander G. de G.
                and Filippone, Maurizio and Ghahramani, Zoubin},
        booktitle={Proceedings of NIPS},
        year={2015}
      }

    The latent function values are represented by centered
    (whitened) variables, so

    .. math::
       :nowrap:

       \\begin{align}
       \\mathbf v & \\sim N(0, \\mathbf I) \\\\
       \\mathbf u &= \\mathbf L\\mathbf v
       \\end{align}

    with

    .. math::
        \\mathbf L \\mathbf L^\\top = \\mathbf K


    """
    def __init__(self, X, Y, kern, likelihood, Z,
                 mean_function=Zero(), num_latent=None):
        """
        X is a data matrix, size N x D
        Y is a data matrix, size N x R
        Z is a data matrix, of inducing inputs, size M x D
        kern, likelihood, mean_function are appropriate GPflow objects

        """
        X = DataHolder(X, on_shape_change='pass')
        Y = DataHolder(Y, on_shape_change='pass')
        GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
        self.num_data = X.shape[0]
        self.num_inducing = Z.shape[0]
        self.num_latent = num_latent or Y.shape[1]
        self.Z = DataHolder(Z, on_shape_change='raise')
        self.V = Param(np.zeros((self.num_inducing, self.num_latent)))
        self.V.prior = Gaussian(0., 1.)

    def build_likelihood(self):
        """
        This function computes the optimal density for v, q*(v), up to a constant
        """
        # get the (marginals of) q(f): exactly predicting!
        fmean, fvar = self.build_predict(self.X, full_cov=False)
        return tf.reduce_sum(self.likelihood.variational_expectations(fmean, fvar, self.Y))

    def build_predict(self, Xnew, full_cov=False):
        """
        Xnew is a data matrix, point at which we want to predict

        This method computes

            p(F* | (U=LV) )

        where F* are points on the GP at Xnew, F=LV are points on the GP at Z,

        """
        mu, var = conditional(Xnew, self.Z, self.kern, self.V,
                              full_cov=full_cov, q_sqrt=None, whiten=True)
        return mu + self.mean_function(Xnew), var