# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)

import numpy as np
import pylab as pb
import sys, pdb
from GPLVM import GPLVM
from sparse_GP import sparse_GP
from GPy.util.linalg import pdinv
from ..likelihoods import Gaussian
from .. import kern

class Bayesian_GPLVM(sparse_GP, GPLVM):
    """
    Bayesian Gaussian Process Latent Variable Model

    :param Y: observed data
    :type Y: np.ndarray
    :param Q: latent dimensionality
    :type Q: int
    :param init: initialisation method for the latent space
    :type init: 'PCA'|'random'

    """
    def __init__(self, Y, Q, X = None, S = None, init='PCA', M=10, Z=None, kernel=None, **kwargs):
        if X == None:
            X = self.initialise_latent(init, Q, Y)

        if S is None:
            S = np.ones_like(X) * 1e-2#

        if Z is None:
            Z = np.random.permutation(X.copy())[:M]
        assert Z.shape[1]==X.shape[1]

        if kernel is None:
            kernel = kern.rbf(Q) + kern.white(Q)


        sparse_GP.__init__(self, X, Gaussian(Y), kernel, Z=Z, X_uncertainty=S, **kwargs)

    def _get_param_names(self):
        X_names = sum([['X_%i_%i'%(n,q) for q in range(self.Q)] for n in range(self.N)],[])
        S_names = sum([['S_%i_%i'%(n,q) for q in range(self.Q)] for n in range(self.N)],[])
        return (X_names + S_names + sparse_GP._get_param_names(self))

    def _get_params(self):
        """
        Horizontally stacks the parameters in order to present them to the optimizer.
        The resulting 1-D array has this structure:

        ===============================================================
        |       mu       |        S        |    Z    | theta |  beta  |
        ===============================================================

        """
        return np.hstack((self.X.flatten(), self.X_uncertainty.flatten(), sparse_GP._get_params(self)))

    def _set_params(self,x):
        N, Q = self.N, self.Q
        self.X = x[:self.X.size].reshape(N,Q).copy()
        self.X_uncertainty = x[(N*Q):(2*N*Q)].reshape(N,Q).copy()
        sparse_GP._set_params(self, x[(2*N*Q):])

    def dL_dmuS(self):
        dL_dmu_psi0, dL_dS_psi0 = self.kern.dpsi1_dmuS(self.dL_dpsi1,self.Z,self.X,self.X_uncertainty)
        dL_dmu_psi1, dL_dS_psi1 = self.kern.dpsi0_dmuS(self.dL_dpsi0,self.Z,self.X,self.X_uncertainty)
        dL_dmu_psi2, dL_dS_psi2 = self.kern.dpsi2_dmuS(self.dL_dpsi2,self.Z,self.X,self.X_uncertainty)
        dL_dmu = dL_dmu_psi0 + dL_dmu_psi1 + dL_dmu_psi2
        dL_dS = dL_dS_psi0 + dL_dS_psi1 + dL_dS_psi2

        dKL_dS = (1. - (1./self.X_uncertainty))*0.5
        dKL_dmu = self.X
        return np.hstack(((dL_dmu - dKL_dmu).flatten(), (dL_dS - dKL_dS).flatten()))

    def KL_divergence(self):
        var_mean = np.square(self.X).sum()
        var_S = np.sum(self.X_uncertainty - np.log(self.X_uncertainty))
        return 0.5*(var_mean + var_S) - 0.5*self.Q*self.N

    def log_likelihood(self):
        return sparse_GP.log_likelihood(self) - self.KL_divergence()

    def _log_likelihood_gradients(self):
        return np.hstack((self.dL_dmuS().flatten(), sparse_GP._log_likelihood_gradients(self)))

    def plot_latent(self, *args, **kwargs):
        input_1, input_2 = GPLVM.plot_latent(*args, **kwargs)
        pb.plot(m.Z[:, input_1], m.Z[:, input_2], '^w')