from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import abc

import six

from tensorflow.python.framework import tensor_shape
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops.distributions import categorical
from tensorflow.python.ops.distributions import normal


@six.add_metaclass(abc.ABCMeta)
class LossFunction(object):
    """Abstract core class for loss functions.
    Note that unlike typical loss functions used in neural networks these are
    summed and not averaged across cases in the batch, since this is what the
    users of this class (FisherEstimator and MatrixVectorProductComputer) will
    be expecting. The implication of this is that you will may want to
    normalize things like Fisher-vector products by the batch size when you
    use this class.  It depends on the use case.
    """

    @abc.abstractproperty
    def targets(self):
        """The targets being predicted by the model.
        Returns:
          None or Tensor of appropriate shape for calling self._evaluate() on.
        """
        pass

    @abc.abstractproperty
    def inputs(self):
        """The inputs to the loss function (excluding the targets)."""
        pass

    @property
    def input_minibatches(self):
        """A `list` of inputs to the loss function, separated by minibatch.
        Typically there will be one minibatch per tower in a multi-tower setup.
        Returns a list consisting of `self.inputs` by default; `LossFunction`s
        supporting registering multiple minibatches should override this method.
        Returns:
          A `list` of `Tensor`s representing
        """
        return [self.inputs]

    @property
    def num_registered_minibatches(self):
        """Number of minibatches registered for this LossFunction.
        Typically equal to the number of towers in a multi-tower setup.
        Returns:
          An `int` representing the number of registered minibatches.
        """
        return len(self.input_minibatches)

    def evaluate(self):
        """Evaluate the loss function on the targets."""
        if self.targets is not None:
            # We treat the targets as "constant".  It's only the inputs that get
            # "back-propped" through.
            return self._evaluate(array_ops.stop_gradient(self.targets))
        else:
            raise Exception("Cannot evaluate losses with unspecified targets.")

    @abc.abstractmethod
    def _evaluate(self, targets):
        """Evaluates the negative log probability of the targets.
        Args:
          targets: Tensor that distribution can calculate log_prob() of.
        Returns:
          negative log probability of each target, summed across all targets.
        """
        pass

    @abc.abstractmethod
    def multiply_hessian(self, vector):
        """Right-multiply a vector by the Hessian.
        Here the 'Hessian' is the Hessian matrix (i.e. matrix of 2nd-derivatives)
        of the loss function with respect to its inputs.
        Args:
          vector: The vector to multiply.  Must be the same shape(s) as the
            'inputs' property.
        Returns:
          The vector right-multiplied by the Hessian.  Will be of the same shape(s)
          as the 'inputs' property.
        """
        pass

    @abc.abstractmethod
    def multiply_hessian_factor(self, vector):
        """Right-multiply a vector by a factor B of the Hessian.
        Here the 'Hessian' is the Hessian matrix (i.e. matrix of 2nd-derivatives)
        of the loss function with respect to its inputs.  Typically this will be
        block-diagonal across different cases in the batch, since the loss function
        is typically summed across cases.
        Note that B can be any matrix satisfying B * B^T = H where H is the Hessian,
        but will agree with the one used in the other methods of this class.
        Args:
          vector: The vector to multiply.  Must be of the shape given by the
            'hessian_factor_inner_shape' property.
        Returns:
          The vector right-multiplied by B.  Will be of the same shape(s) as the
          'inputs' property.
        """
        pass

    @abc.abstractmethod
    def multiply_hessian_factor_transpose(self, vector):
        """Right-multiply a vector by the transpose of a factor B of the Hessian.
        Here the 'Hessian' is the Hessian matrix (i.e. matrix of 2nd-derivatives)
        of the loss function with respect to its inputs.  Typically this will be
        block-diagonal across different cases in the batch, since the loss function
        is typically summed across cases.
        Note that B can be any matrix satisfying B * B^T = H where H is the Hessian,
        but will agree with the one used in the other methods of this class.
        Args:
          vector: The vector to multiply.  Must be the same shape(s) as the
            'inputs' property.
        Returns:
          The vector right-multiplied by B^T.  Will be of the shape given by the
          'hessian_factor_inner_shape' property.
        """
        pass

    @abc.abstractmethod
    def multiply_hessian_factor_replicated_one_hot(self, index):
        """Right-multiply a replicated-one-hot vector by a factor B of the Hessian.
        Here the 'Hessian' is the Hessian matrix (i.e. matrix of 2nd-derivatives)
        of the loss function with respect to its inputs.  Typically this will be
        block-diagonal across different cases in the batch, since the loss function
        is typically summed across cases.
        A 'replicated-one-hot' vector means a tensor which, for each slice along the
        batch dimension (assumed to be dimension 0), is 1.0 in the entry
        corresponding to the given index and 0 elsewhere.
        Note that B can be any matrix satisfying B * B^T = H where H is the Hessian,
        but will agree with the one used in the other methods of this class.
        Args:
          index: A tuple representing in the index of the entry in each slice that
            is 1.0. Note that len(index) must be equal to the number of elements
            of the 'hessian_factor_inner_shape' tensor minus one.
        Returns:
          The vector right-multiplied by B^T. Will be of the same shape(s) as the
          'inputs' property.
        """
        pass

    @abc.abstractproperty
    def hessian_factor_inner_shape(self):
        """The shape of the tensor returned by multiply_hessian_factor."""
        pass

    @abc.abstractproperty
    def hessian_factor_inner_static_shape(self):
        """Static version of hessian_factor_inner_shape."""
        pass


@six.add_metaclass(abc.ABCMeta)
class NegativeLogProbLoss(LossFunction):
    """Abstract core class for loss functions that are negative log probs."""

    def __init__(self, seed=None):
        self._default_seed = seed
        super(NegativeLogProbLoss, self).__init__()

    @property
    def inputs(self):
        return self.params

    @abc.abstractproperty
    def params(self):
        """Parameters to the underlying distribution."""
        pass

    @abc.abstractmethod
    def multiply_fisher(self, vector):
        """Right-multiply a vector by the Fisher.
        Args:
          vector: The vector to multiply.  Must be the same shape(s) as the
            'inputs' property.
        Returns:
          The vector right-multiplied by the Fisher.  Will be of the same shape(s)
          as the 'inputs' property.
        """
        pass

    @abc.abstractmethod
    def multiply_fisher_factor(self, vector):
        """Right-multiply a vector by a factor B of the Fisher.
        Here the 'Fisher' is the Fisher information matrix (i.e. expected outer-
        product of gradients) with respect to the parameters of the underlying
        probability distribtion (whose log-prob defines the loss). Typically this
        will be block-diagonal across different cases in the batch, since the
        distribution is usually (but not always) conditionally iid across different
        cases.
        Note that B can be any matrix satisfying B * B^T = F where F is the Fisher,
        but will agree with the one used in the other methods of this class.
        Args:
          vector: The vector to multiply.  Must be of the shape given by the
            'fisher_factor_inner_shape' property.
        Returns:
          The vector right-multiplied by B. Will be of the same shape(s) as the
          'inputs' property.
        """
        pass

    @abc.abstractmethod
    def multiply_fisher_factor_transpose(self, vector):
        """Right-multiply a vector by the transpose of a factor B of the Fisher.
        Here the 'Fisher' is the Fisher information matrix (i.e. expected outer-
        product of gradients) with respect to the parameters of the underlying
        probability distribtion (whose log-prob defines the loss). Typically this
        will be block-diagonal across different cases in the batch, since the
        distribution is usually (but not always) conditionally iid across different
        cases.
        Note that B can be any matrix satisfying B * B^T = F where F is the Fisher,
        but will agree with the one used in the other methods of this class.
        Args:
          vector: The vector to multiply.  Must be the same shape(s) as the
            'inputs' property.
        Returns:
          The vector right-multiplied by B^T.  Will be of the shape given by the
          'fisher_factor_inner_shape' property.
        """
        pass

    @abc.abstractmethod
    def multiply_fisher_factor_replicated_one_hot(self, index):
        """Right-multiply a replicated-one-hot vector by a factor B of the Fisher.
        Here the 'Fisher' is the Fisher information matrix (i.e. expected outer-
        product of gradients) with respect to the parameters of the underlying
        probability distribtion (whose log-prob defines the loss). Typically this
        will be block-diagonal across different cases in the batch, since the
        distribution is usually (but not always) conditionally iid across different
        cases.
        A 'replicated-one-hot' vector means a tensor which, for each slice along the
        batch dimension (assumed to be dimension 0), is 1.0 in the entry
        corresponding to the given index and 0 elsewhere.
        Note that B can be any matrix satisfying B * B^T = H where H is the Fisher,
        but will agree with the one used in the other methods of this class.
        Args:
          index: A tuple representing in the index of the entry in each slice that
            is 1.0. Note that len(index) must be equal to the number of elements
            of the 'fisher_factor_inner_shape' tensor minus one.
        Returns:
          The vector right-multiplied by B. Will be of the same shape(s) as the
          'inputs' property.
        """
        pass

    @abc.abstractproperty
    def fisher_factor_inner_shape(self):
        """The shape of the tensor returned by multiply_fisher_factor."""
        pass

    @abc.abstractproperty
    def fisher_factor_inner_static_shape(self):
        """Static version of fisher_factor_inner_shape."""
        pass

    @abc.abstractmethod
    def sample(self, seed):
        """Sample 'targets' from the underlying distribution."""
        pass

    def evaluate_on_sample(self, seed=None):
        """Evaluates the log probability on a random sample.
        Args:
          seed: int or None. Random seed for this draw from the distribution.
        Returns:
          Log probability of sampled targets, summed across examples.
        """
        if seed is None:
            seed = self._default_seed
        # We treat the targets as "constant".  It's only the inputs that get
        # "back-propped" through.
        return self._evaluate(array_ops.stop_gradient(self.sample(seed)))


# TODO(jamesmartens): should this just inherit from object to avoid "diamond"
# inheritance, or is there a better way?
class NaturalParamsNegativeLogProbLoss(NegativeLogProbLoss):
    """Base class for neg log prob losses whose inputs are 'natural' parameters.
    Note that the Hessian and Fisher for natural parameters of exponential-
    family models are the same, hence the purpose of this class.
    See here: https://arxiv.org/abs/1412.1193
    'Natural parameters' are defined for exponential-family models. See for
    example: https://en.wikipedia.org/wiki/Exponential_family
    """

    def multiply_hessian(self, vector):
        return self.multiply_fisher(vector)

    def multiply_hessian_factor(self, vector):
        return self.multiply_fisher_factor(vector)

    def multiply_hessian_factor_transpose(self, vector):
        return self.multiply_fisher_factor_transpose(vector)

    def multiply_hessian_factor_replicated_one_hot(self, index):
        return self.multiply_fisher_factor_replicated_one_hot(index)

    @property
    def hessian_factor_inner_shape(self):
        return self.fisher_factor_inner_shape

    @property
    def hessian_factor_inner_static_shape(self):
        return self.fisher_factor_inner_shape


class DistributionNegativeLogProbLoss(NegativeLogProbLoss):
    """Base class for neg log prob losses that use the TF Distribution classes."""

    def __init__(self, seed=None):
        super(DistributionNegativeLogProbLoss, self).__init__(seed=seed)

    @abc.abstractproperty
    def dist(self):
        """The underlying tf.distributions.Distribution."""
        pass

    def _evaluate(self, targets):
        return -math_ops.reduce_sum(self.dist.log_prob(targets))

    def sample(self, seed):
        return self.dist.sample(seed=seed)


class NormalMeanNegativeLogProbLoss(DistributionNegativeLogProbLoss,
                                    NaturalParamsNegativeLogProbLoss):
    """Neg log prob loss for a normal distribution parameterized by a mean vector.
    Note that the covariance is treated as a constant 'var' times the identity.
    Also note that the Fisher for such a normal distribution with respect the mean
    parameter is given by:
       F = (1/var) * I
    See for example https://www.ii.pwr.edu.pl/~tomczak/PDF/[JMT]Fisher_inf.pdf.
    """

    def __init__(self, mean, var=0.5, targets=None, seed=None):
        self._mean = mean
        self._var = var
        self._targets = targets
        super(NormalMeanNegativeLogProbLoss, self).__init__(seed=seed)

    @property
    def targets(self):
        return self._targets

    @property
    def dist(self):
        return normal.Normal(loc=self._mean, scale=math_ops.sqrt(self._var))

    @property
    def params(self):
        return self._mean

    def multiply_fisher(self, vector):
        return (1. / self._var) * vector

    def multiply_fisher_factor(self, vector):
        return self._var**-0.5 * vector

    def multiply_fisher_factor_transpose(self, vector):
        return self.multiply_fisher_factor(vector)  # it's symmetric in this case

    def multiply_fisher_factor_replicated_one_hot(self, index):
        assert len(index) == 1, "Length of index was {}".format(len(index))
        ones_slice = array_ops.expand_dims(
            array_ops.ones(array_ops.shape(self._mean)[:1], dtype=self._mean.dtype),
            axis=-1)
        output_slice = self._var**-0.5 * ones_slice
        return insert_slice_in_zeros(output_slice, 1, int(self._mean.shape[1]),
                                     index[0])

    @property
    def fisher_factor_inner_shape(self):
        return array_ops.shape(self._mean)

    @property
    def fisher_factor_inner_static_shape(self):
        return self._mean.shape


class NormalMeanVarianceNegativeLogProbLoss(DistributionNegativeLogProbLoss):
    """Negative log prob loss for a normal distribution with mean and variance.
    This class parameterizes a multivariate normal distribution with n independent
    dimensions. Unlike `NormalMeanNegativeLogProbLoss`, this class does not
    assume the variance is held constant. The Fisher Information for n = 1
    is given by,
    F = [[1 / variance,                0],
         [           0, 0.5 / variance^2]]
    where the parameters of the distribution are concatenated into a single
    vector as [mean, variance]. For n > 1, the mean parameter vector is
    concatenated with the variance parameter vector.
    See https://www.ii.pwr.edu.pl/~tomczak/PDF/[JMT]Fisher_inf.pdf for derivation.
    """

    def __init__(self, mean, variance, targets=None, seed=None):
        assert len(mean.shape) == 2, "Expect 2D mean tensor."
        assert len(variance.shape) == 2, "Expect 2D variance tensor."
        self._mean = mean
        self._variance = variance
        self._scale = math_ops.sqrt(variance)
        self._targets = targets
        super(NormalMeanVarianceNegativeLogProbLoss, self).__init__(seed=seed)

    @property
    def targets(self):
        return self._targets

    @property
    def dist(self):
        return normal.Normal(loc=self._mean, scale=self._scale)

    @property
    def params(self):
        return self._mean, self._variance

    def _concat(self, mean, variance):
        return array_ops.concat([mean, variance], axis=-1)

    def _split(self, params):
        return array_ops.split(params, 2, axis=-1)

    @property
    def _fisher_mean(self):
        return 1. / self._variance

    @property
    def _fisher_mean_factor(self):
        return 1. / self._scale

    @property
    def _fisher_var(self):
        return 1. / (2 * math_ops.square(self._variance))

    @property
    def _fisher_var_factor(self):
        return 1. / (math_ops.sqrt(2.) * self._variance)

    def multiply_fisher(self, vecs):
        mean_vec, var_vec = vecs
        return (self._fisher_mean * mean_vec, self._fisher_var * var_vec)

    def multiply_fisher_factor(self, vecs):
        mean_vec, var_vec = self._split(vecs)
        return (self._fisher_mean_factor * mean_vec,
                self._fisher_var_factor * var_vec)

    def multiply_fisher_factor_transpose(self, vecs):
        mean_vec, var_vec = vecs
        return self._concat(self._fisher_mean_factor * mean_vec,
                            self._fisher_var_factor * var_vec)

    def multiply_fisher_factor_replicated_one_hot(self, index):
        assert len(index) == 1, "Length of index was {}".format(len(index))
        index = index[0]

        if index < int(self._mean.shape[-1]):
            # Index corresponds to mean parameter.
            mean_slice = self._fisher_mean_factor[:, index]
            mean_slice = array_ops.expand_dims(mean_slice, axis=-1)
            mean_output = insert_slice_in_zeros(mean_slice, 1, int(
                self._mean.shape[1]), index)
            var_output = array_ops.zeros_like(mean_output)
        else:
            index -= int(self._mean.shape[-1])
            # Index corresponds to variance parameter.
            var_slice = self._fisher_var_factor[:, index]
            var_slice = array_ops.expand_dims(var_slice, axis=-1)
            var_output = insert_slice_in_zeros(var_slice, 1,
                                               int(self._variance.shape[1]), index)
            mean_output = array_ops.zeros_like(var_output)

        return mean_output, var_output

    @property
    def fisher_factor_inner_shape(self):
        return array_ops.concat(
            [
                array_ops.shape(self._mean)[:-1],
                2 * array_ops.shape(self._mean)[-1:]
            ],
            axis=0)

    @property
    def fisher_factor_inner_static_shape(self):
        shape = self._mean.shape.as_list()
        return tensor_shape.TensorShape(shape[-1:] + [2 * shape[-1]])

    def multiply_hessian(self, vector):
        raise NotImplementedError()

    def multiply_hessian_factor(self, vector):
        raise NotImplementedError()

    def multiply_hessian_factor_transpose(self, vector):
        raise NotImplementedError()

    def multiply_hessian_factor_replicated_one_hot(self, index):
        raise NotImplementedError()

    @property
    def hessian_factor_inner_shape(self):
        raise NotImplementedError()

    @property
    def hessian_factor_inner_static_shape(self):
        raise NotImplementedError()


class CategoricalLogitsNegativeLogProbLoss(DistributionNegativeLogProbLoss,
                                           NaturalParamsNegativeLogProbLoss):
    """Neg log prob loss for a categorical distribution parameterized by logits.
    Note that the Fisher (for a single case) of a categorical distribution, with
    respect to the natural parameters (i.e. the logits), is given by:
    F = diag(p) - p*p^T
    where p = softmax(logits).  F can be factorized as F = B * B^T where
    B = diag(q) - p*q^T
    where q is the entry-wise square root of p. This is easy to verify using the
    fact that q^T*q = 1.
    """

    def __init__(self, logits, targets=None, seed=None):
        """Instantiates a CategoricalLogitsNegativeLogProbLoss.
        Args:
          logits: Tensor of shape [batch_size, output_size]. Parameters for
            underlying distribution.
          targets: None or Tensor of shape [output_size]. Each elements contains an
            index in [0, output_size).
          seed: int or None. Default random seed when sampling.
        """
        self._logits_components = []
        self._targets_components = []
        self.register_additional_minibatch(logits, targets=targets)
        super(CategoricalLogitsNegativeLogProbLoss, self).__init__(seed=seed)

    def register_additional_minibatch(self, logits, targets=None):
        """Register an additiona minibatch's worth of parameters.
        Args:
          logits: Tensor of shape [batch_size, output_size]. Parameters for
            underlying distribution.
          targets: None or Tensor of shape [batch_size, output_size].  Each row must
            be a one-hot vector.
        """
        self._logits_components.append(logits)
        self._targets_components.append(targets)

    @property
    def _logits(self):
        return array_ops.concat(self._logits_components, axis=0)

    @property
    def input_minibatches(self):
        return self._logits_components

    @property
    def targets(self):
        if all(target is None for target in self._targets_components):
            return None
        return array_ops.concat(self._targets_components, axis=0)

    @property
    def dist(self):
        return categorical.Categorical(logits=self._logits)

    @property
    def _probs(self):
        return self.dist.probs

    @property
    def _sqrt_probs(self):
        return math_ops.sqrt(self._probs)

    @property
    def params(self):
        return self._logits

    def multiply_fisher(self, vector):
        probs = self._probs
        return vector * probs - probs * math_ops.reduce_sum(
            vector * probs, axis=1, keep_dims=True)

    def multiply_fisher_factor(self, vector):
        probs = self._probs
        sqrt_probs = self._sqrt_probs
        return sqrt_probs * vector - probs * math_ops.reduce_sum(
            sqrt_probs * vector, axis=1, keep_dims=True)

    def multiply_fisher_factor_transpose(self, vector):
        probs = self._probs
        sqrt_probs = self._sqrt_probs
        return sqrt_probs * vector - sqrt_probs * math_ops.reduce_sum(
            probs * vector, axis=1, keep_dims=True)

    def multiply_fisher_factor_replicated_one_hot(self, index):
        assert len(index) == 1, "Length of index was {}".format(len(index))
        probs = self._probs
        sqrt_probs = self._sqrt_probs
        sqrt_probs_slice = array_ops.expand_dims(sqrt_probs[:, index[0]], -1)
        padded_slice = insert_slice_in_zeros(sqrt_probs_slice, 1,
                                             int(sqrt_probs.shape[1]), index[0])
        return padded_slice - probs * sqrt_probs_slice

    @property
    def fisher_factor_inner_shape(self):
        return array_ops.shape(self._logits)

    @property
    def fisher_factor_inner_static_shape(self):
        return self._logits.shape


def insert_slice_in_zeros(slice_to_insert, dim, dim_size, position):
    """Inserts slice into a larger tensor of zeros.
    Forms a new tensor which is the same shape as slice_to_insert, except that
    the dimension given by 'dim' is expanded to the size given by 'dim_size'.
    'position' determines the position (index) at which to insert the slice within
    that dimension.
    Assumes slice_to_insert.shape[dim] = 1.
    Args:
      slice_to_insert: The slice to insert.
      dim: The dimension which to expand with zeros.
      dim_size: The new size of the 'dim' dimension.
      position: The position of 'slice_to_insert' in the new tensor.
    Returns:
      The new tensor.
    Raises:
      ValueError: If the slice's shape at the given dim is not 1.
    """
    slice_shape = slice_to_insert.shape
    if slice_shape[dim] != 1:
        raise ValueError("Expected slice_to_insert.shape to have {} dim of 1, but "
                         "was {}".format(dim, slice_to_insert.shape[dim]))

    before = [0] * int(len(slice_shape))
    after = before[:]
    before[dim] = position
    after[dim] = dim_size - position - 1

    return array_ops.pad(slice_to_insert, list(zip(before, after)))
