from collections.abc import Iterable
from typing import List, Optional, Union

import tensorflow as tf

from ..base import Parameter
from ..utilities import positive
from .base import Combination, Kernel


class ChangePoints(Combination):
    r"""
    The ChangePoints kernel defines a fixed number of change-points along a 1d
    input space where different kernels govern different parts of the space.

    The kernel is by multiplication and addition of the base kernels with
    sigmoid functions (σ). A single change-point kernel is defined as:

        K₁(x, x') * (1 - σ(x)) * (1 - σ(x')) + K₂(x, x') * σ(x) * σ(x')

    where K₁ is deactivated around the change-point and K₂ is activated. The
    single change-point version can be found in \citet{lloyd2014}. Each sigmoid
    is a logistic function defined as:

        σ(x) = 1 / (1 + exp{-s(x - x₀)})

    parameterized by location "x₀" and steepness "s".

    @incollection{lloyd2014,
      author = {Lloyd, James Robert et al},
      title = {Automatic Construction and Natural-language Description of Nonparametric Regression Models},
      booktitle = {Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence},
      year = {2014},
      url = {http://dl.acm.org/citation.cfm?id=2893873.2894066},
    }
    """
    def __init__(self,
                 kernels: List[Kernel],
                 locations: List[float],
                 steepness: Union[float, List[float]] = 1.0,
                 name: Optional[str] = None):
        """
        :param kernels: list of kernels defining the different regimes
        :param locations: list of change-point locations in the 1d input space
        :param steepness: the steepness parameter(s) of the sigmoids, this can be
            common between them or decoupled
        """
        if len(kernels) != len(locations) + 1:
            raise ValueError("Number of kernels ({nk}) must be one more than the number of "
                             "changepoint locations ({nl})".format(nk=len(kernels), nl=len(locations)))

        if isinstance(steepness, Iterable) and len(steepness) != len(locations):
            raise ValueError("Dimension of steepness ({ns}) does not match number of changepoint "
                             "locations ({nl})".format(ns=len(steepness), nl=len(locations)))

        super().__init__(kernels, name=name)

        self.locations = Parameter(locations)
        self.steepness = Parameter(steepness, transform=positive())

    def _set_kernels(self, kernels: List[Kernel]):
        # it is not clear how to flatten out nested change-points
        self.kernels = list(kernels)

    def K(self, X: tf.Tensor, X2: Optional[tf.Tensor] = None, presliced: bool = False) -> tf.Tensor:
        sig_X = self._sigmoids(X)  # N x 1 x Ncp
        sig_X2 = self._sigmoids(X2) if X2 is not None else sig_X

        # `starters` are the sigmoids going from 0 -> 1, whilst `stoppers` go 
        # from 1 -> 0, dimensions are N x N x Ncp
        starters = sig_X * tf.transpose(sig_X2, perm=(1, 0, 2))
        stoppers = (1 - sig_X) * tf.transpose((1 - sig_X2), perm=(1, 0, 2))

        # prepend `starters` with ones and append ones to `stoppers` since the
        # first kernel has no start and the last kernel has no end
        N = tf.shape(X)[0]
        ones = tf.ones((N, N, 1), dtype=X.dtype)
        starters = tf.concat([ones, starters], axis=2)
        stoppers = tf.concat([stoppers, ones], axis=2)

        # now combine with the underlying kernels
        kernel_stack = tf.stack([k(X, X2) for k in self.kernels], axis=2)
        return tf.reduce_sum(kernel_stack * starters * stoppers, axis=2)

    def K_diag(self, X: tf.Tensor, presliced: bool = False) -> tf.Tensor:
        N = tf.shape(X)[0]
        sig_X = tf.reshape(self._sigmoids(X), (N, -1))  # N x Ncp

        ones = tf.ones((N, 1), dtype=X.dtype)
        starters = tf.concat([ones, sig_X * sig_X], axis=1)  # N x Ncp
        stoppers = tf.concat([(1 - sig_X) * (1 - sig_X), ones], axis=1)

        kernel_stack = tf.stack([k(X, full=False) for k in self.kernels], axis=1)
        return tf.reduce_sum(kernel_stack * starters * stoppers, axis=1)

    def _sigmoids(self, X: tf.Tensor) -> tf.Tensor:
        locations = tf.sort(self.locations)  # ensure locations are ordered
        locations = tf.reshape(locations, (1, 1, -1))
        steepness = tf.reshape(self.steepness, (1, 1, -1))
        return tf.sigmoid(steepness * (X[:, :, None] - locations))