# Copyright 2016 James Hensman, Valentine Svensson, alexggmatthews, Mark van der Wilk
#
# 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 __future__ import absolute_import
import tensorflow as tf
import numpy as np
from .param import Param
from .model import GPModel
from . import transforms, conditionals, kullback_leiblers
from .mean_functions import Zero
from ._settings import settings
from .minibatch import MinibatchData
float_type = settings.dtypes.float_type


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

    ::

      @inproceedings{hensman2014scalable,
        title={Scalable Variational Gaussian Process Classification},
        author={Hensman, James and Matthews,
                Alexander G. de G. and Ghahramani, Zoubin},
        booktitle={Proceedings of AISTATS},
        year={2015}
      }

    """
    def __init__(self, X, Y, kern, likelihood, Z, mean_function=Zero(),
                 num_latent=None, q_diag=False, whiten=True, minibatch_size=None):
        """
        - X is a data matrix, size N x D
        - Y is a data matrix, size N x R
        - kern, likelihood, mean_function are appropriate GPflow objects
        - Z is a matrix of pseudo inputs, size M x D
        - num_latent is the number of latent process to use, default to
          Y.shape[1]
        - q_diag is a boolean. If True, the covariance is approximated by a
          diagonal matrix.
        - whiten is a boolean. If True, we use the whitened representation of
          the inducing points.
        """
        # sort out the X, Y into MiniBatch objects.
        if minibatch_size is None:
            minibatch_size = X.shape[0]
        self.num_data = X.shape[0]
        X = MinibatchData(X, minibatch_size, np.random.RandomState(0))
        Y = MinibatchData(Y, minibatch_size, np.random.RandomState(0))

        # init the super class, accept args
        GPModel.__init__(self, X, Y, kern, likelihood, mean_function)
        self.q_diag, self.whiten = q_diag, whiten
        self.Z = Param(Z)
        self.num_latent = num_latent or Y.shape[1]
        self.num_inducing = Z.shape[0]

        # init variational parameters
        self.q_mu = Param(np.zeros((self.num_inducing, self.num_latent)))
        if self.q_diag:
            self.q_sqrt = Param(np.ones((self.num_inducing, self.num_latent)),
                                transforms.positive)
        else:
            q_sqrt = np.array([np.eye(self.num_inducing)
                               for _ in range(self.num_latent)]).swapaxes(0, 2)
            self.q_sqrt = Param(q_sqrt, transforms.LowerTriangular(self.num_inducing, self.num_latent))

    def build_prior_KL(self):
        if self.whiten:
            if self.q_diag:
                KL = kullback_leiblers.gauss_kl_white_diag(self.q_mu, self.q_sqrt)
            else:
                KL = kullback_leiblers.gauss_kl_white(self.q_mu, self.q_sqrt)
        else:
            K = self.kern.Kzz(self.Z) + tf.eye(self.num_inducing, dtype=float_type) * settings.numerics.jitter_level
            if self.q_diag:
                KL = kullback_leiblers.gauss_kl_diag(self.q_mu, self.q_sqrt, K)
            else:
                KL = kullback_leiblers.gauss_kl(self.q_mu, self.q_sqrt, K)
        return KL

    def build_likelihood(self):
        """
        This gives a variational bound on the model likelihood.
        """

        # Get prior KL.
        KL = self.build_prior_KL()

        # Get conditionals
        fmean, fvar = self.build_predict(self.X, full_cov=False)

        # Get variational expectations.
        var_exp = self.likelihood.variational_expectations(fmean, fvar, self.Y)

        # re-scale for minibatch size
        scale = tf.cast(self.num_data, settings.dtypes.float_type) /\
            tf.cast(tf.shape(self.X)[0], settings.dtypes.float_type)

        return tf.reduce_sum(var_exp) * scale - KL

    def build_predict(self, Xnew, full_cov=False):
        mu, var = conditionals.conditional(Xnew, self.Z, self.kern, self.q_mu,
                                           q_sqrt=self.q_sqrt, full_cov=full_cov, whiten=self.whiten)
        return mu + self.mean_function(Xnew), var
