# Copyright 2016 James Hensman, Valentine Svensson, alexggmatthews, fujiisoup
# 
# 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
from .model import GPModel
from .densities import multivariate_normal
from .mean_functions import Zero
from . import likelihoods
from .tf_wraps import eye
from .param import DataHolder


class GPR(GPModel):
    """
    Gaussian Process Regression.

    This is a vanilla implementation of GP regression with a Gaussian
    likelihood.  Multiple columns of Y are treated independently.

    The log likelihood i this models is sometimes referred to as the 'marginal log likelihood', and is given by

    .. math::

       \\log p(\\mathbf y \\,|\\, \\mathbf f) = \\mathcal N\\left(\\mathbf y\,|\, 0, \\mathbf K + \\sigma_n \\mathbf I\\right)
    """
    def __init__(self, X, Y, kern, mean_function=Zero()):
        """
        X is a data matrix, size N x D
        Y is a data matrix, size N x R
        kern, mean_function are appropriate GPflow objects
        """
        likelihood = likelihoods.Gaussian()
        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_latent = Y.shape[1]

    def build_likelihood(self):
        """
        Construct a tensorflow function to compute the likelihood.

            \log p(Y | theta).

        """
        K = self.kern.K(self.X) + eye(tf.shape(self.X)[0]) * self.likelihood.variance
        L = tf.cholesky(K)
        m = self.mean_function(self.X)

        return multivariate_normal(self.Y, m, L)

    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* | Y )

        where F* are points on the GP at Xnew, Y are noisy observations at X.

        """
        Kx = self.kern.K(self.X, Xnew)
        K = self.kern.K(self.X) + eye(tf.shape(self.X)[0]) * self.likelihood.variance
        L = tf.cholesky(K)
        A = tf.matrix_triangular_solve(L, Kx, lower=True)
        V = tf.matrix_triangular_solve(L, self.Y - self.mean_function(self.X))
        fmean = tf.matmul(tf.transpose(A), V) + self.mean_function(Xnew)
        if full_cov:
            fvar = self.kern.K(Xnew) - tf.matmul(tf.transpose(A), A)
            shape = tf.stack([1, 1, tf.shape(self.Y)[1]])
            fvar = tf.tile(tf.expand_dims(fvar, 2), shape)
        else:
            fvar = self.kern.Kdiag(Xnew) - tf.reduce_sum(tf.square(A), 0)
            fvar = tf.tile(tf.reshape(fvar, (-1, 1)), [1, tf.shape(self.Y)[1]])
        return fmean, fvar