# 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.
from typing import Optional

import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp

from ..base import Parameter
from ..conditionals import conditional
from ..config import default_float, default_jitter
from ..kernels import Kernel
from ..likelihoods import Likelihood
from ..mean_functions import MeanFunction
from ..utilities import to_default_float
from .model import Data, GPModel, MeanAndVariance


class GPMC(GPModel):
    def __init__(self,
                 data: Data,
                 kernel: Kernel,
                 likelihood: Likelihood,
                 mean_function: Optional[MeanFunction] = None,
                 num_latent: int = 1):
        """
        data is a tuple of X, Y with X, a data matrix, size [N, D] and Y, a data matrix, size [N, R]
        kernel, likelihood, mean_function are appropriate GPflow objects

        This is a vanilla implementation of a GP with a non-Gaussian
        likelihood. The latent function values are represented by centered
        (whitened) variables, so

            v ~ N(0, I)
            f = Lv + m(x)

        with

            L L^T = K

        """
        super().__init__(kernel, likelihood, mean_function, num_latent)
        self.data = data
        self.num_data = data[0].shape[0]
        self.V = Parameter(np.zeros((self.num_data, self.num_latent)))
        self.V.prior = tfp.distributions.Normal(loc=to_default_float(0.), scale=to_default_float(1.))

    def log_likelihood(self, *args, **kwargs) -> tf.Tensor:
        r"""
        Construct a tf function to compute the likelihood of a general GP
        model.

            \log p(Y, V | theta).

        """
        x_data, y_data = self.data
        K = self.kernel(x_data)
        L = tf.linalg.cholesky(K + tf.eye(tf.shape(x_data)[0], dtype=default_float()) * default_jitter())
        F = tf.linalg.matmul(L, self.V) + self.mean_function(x_data)

        return tf.reduce_sum(self.likelihood.log_prob(F, y_data))

    def predict_f(self, Xnew: tf.Tensor, full_cov=False, full_output_cov=False) -> MeanAndVariance:
        """
        Xnew is a data matrix, point at which we want to predict

        This method computes

            p(F* | (F=LV) )

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

        """
        x_data, y_data = self.data
        mu, var = conditional(Xnew, x_data, self.kernel, self.V, full_cov=full_cov, q_sqrt=None, white=True)
        return mu + self.mean_function(Xnew), var