import tensorflow as tf
import numpy as np
from .param import Param
from .model import GPModel
from . import transforms
from . import conditionals
from .mean_functions import Zero
from .tf_hacks import eye
from . import kullback_leiblers


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=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.
        """
        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]

        # these variables used for minibatching
        self._tfX = tf.Variable(self.X, name="tfX")
        self._tfY = tf.Variable(self.Y, name="tfY")
        self.minibatch = minibatch

        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)

    def __getstate__(self):
        d = GPModel.__getstate__(self)
        d.pop('_tfX')
        d.pop('_tfY')
        return d

    def __setstate__(self, d):
        GPModel.__setstate__(self, d)
        self._tfX = tf.Variable(self.X, name="tfX")
        self._tfY = tf.Variable(self.Y, name="tfY")

    @property
    def minibatch(self):
        if self._minibatch is None:
            return len(self.X)
        else:
            return self._minibatch

    @minibatch.setter
    def minibatch(self, val):
        self._minibatch = val

    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,
                                                           self.num_latent)
            else:
                KL = kullback_leiblers.gauss_kl_white(self.q_mu,
                                                      self.q_sqrt,
                                                      self.num_latent)
        else:
            K = self.kern.K(self.Z) + eye(self.num_inducing) * 1e-6
            if self.q_diag:
                KL = kullback_leiblers.gauss_kl_diag(self.q_mu,
                                                     self.q_sqrt,
                                                     K,
                                                     self.num_latent)
            else:
                KL = kullback_leiblers.gauss_kl(self.q_mu,
                                                self.q_sqrt,
                                                K,
                                                self.num_latent)
        return KL

    def _compile(self, optimizer=None):
        """
        compile the tensorflow function "self._objective"
        """
        opt_step = GPModel._compile(self, optimizer)

        def obj(x):
            if self.minibatch / float(len(self.X)) > 0.5:
                ss = np.random.permutation(len(self.X))[:self.minibatch]
            else:
                # This is much faster than above, and for N >> minibatch,
                # it doesn't make much difference. This actually
                # becomes the limit when N is around 10**6, which isn't
                # uncommon when using SVI.
                ss = np.random.randint(len(self.X), size=self.minibatch)
            return self._session.run([self._minusF, self._minusG],
                                     feed_dict={self._free_vars: x,
                                                self._tfX: self.X[ss, :],
                                                self._tfY: self.Y[ss, :]})
        self._objective = obj
        return opt_step

    def optimize(self, method='L-BFGS-B', tol=None,
                 callback=None, max_iters=1000, **kw):
        def calc_feed_dict():
            ss = np.random.randint(len(self.dX), size=self.minibatch)
            return {self.X: self.dX[ss, :], self.Y: self.dY[ss, :]}

        return GPModel.optimize(self, method, tol, callback,
                                max_iters, calc_feed_dict, **kw)

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

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

        # Get conditionals
        if self.whiten:
            cond_fn = conditionals.gaussian_gp_predict_whitened
        else:
            cond_fn = conditionals.gaussian_gp_predict
        fmean, fvar = cond_fn(self._tfX, self.Z, self.kern,
                              self.q_mu, self.q_sqrt, self.num_latent)

        # add in mean function to conditionals.
        fmean += self.mean_function(self._tfX)

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

        Nbatch = tf.cast(tf.shape(self._tfX)[0], tf.float64)
        minibatch_scale = len(self.X) / Nbatch

        return tf.reduce_sum(var_exp) * minibatch_scale - KL

    def build_predict(self, Xnew, full_cov=False):
        if self.whiten:
            cond_fn = conditionals.gaussian_gp_predict_whitened
        else:
            cond_fn = conditionals.gaussian_gp_predict
        mu, var = cond_fn(Xnew, self.Z, self.kern,
                          self.q_mu, self.q_sqrt, self.num_latent, full_cov)
        return mu + self.mean_function(Xnew), var