# Class representing piece-wise linear functions.
# Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
# Distributed under the BSD License

from __future__ import absolute_import, print_function

import numpy as np
import collections
import pyspike


##############################################################
# PieceWiseLinFunc
##############################################################
class PieceWiseLinFunc:
    """ A class representing a piece-wise linear function. """

    def __init__(self, x, y1, y2):
        """ Constructs the piece-wise linear function.

        :param x: array of length N+1 defining the edges of the intervals of
                  the pwc function.
        :param y1: array of length N defining the function values at the left
                  of the intervals.
        :param y2: array of length N defining the function values at the right
                  of the intervals.
        """
        # convert to array, which also ensures copying
        self.x = np.array(x)
        self.y1 = np.array(y1)
        self.y2 = np.array(y2)

    def __call__(self, t):
        """ Returns the function value for the given time t. If t is a list of
        times, the corresponding list of values is returned.

        :param: time t, or list of times
        :returns: function value(s) at that time(s).
        """
        def intermediate_value(x0, x1, y0, y1, x):
            """ computes the intermediate value of a linear function """
            return y0 + (y1-y0)*(x-x0)/(x1-x0)

        assert np.all(t >= self.x[0]) and np.all(t <= self.x[-1]), \
            "Invalid time: " + str(t)

        ind = np.searchsorted(self.x, t, side='right')

        if isinstance(t, collections.Sequence):
            # t is a sequence of values
            # correct the cases t == x[0], t == x[-1]
            ind[ind == 0] = 1
            ind[ind == len(self.x)] = len(self.x)-1
            value = intermediate_value(self.x[ind-1],
                                       self.x[ind],
                                       self.y1[ind-1],
                                       self.y2[ind-1],
                                       t)
            # correct the values at exact spike times: there the value should
            # be the at half of the step
            # obtain the 'left' side indices for t
            ind_l = np.searchsorted(self.x, t, side='left')
            # if left and right side indices differ, the time t has to appear
            # in self.x
            ind_at_spike = np.logical_and(np.logical_and(ind != ind_l,
                                                         ind > 1),
                                          ind < len(self.x))
            # get the corresponding indices for the resulting value array
            val_ind = np.arange(len(ind))[ind_at_spike]
            # and for the values in self.x, y1, y2
            xy_ind = ind[ind_at_spike]
            # the values are defined as the average of the left and right limit
            value[val_ind] = 0.5 * (self.y1[xy_ind-1] + self.y2[xy_ind-2])
            return value
        else:  # t is a single value
            # specific check for interval edges
            if t == self.x[0]:
                return self.y1[0]
            if t == self.x[-1]:
                return self.y2[-1]
            # check if we are on any other exact spike time
            if sum(self.x == t) > 0:
                # use the middle of the left and right Spike value
                return 0.5 * (self.y1[ind-1] + self.y2[ind-2])
            return intermediate_value(self.x[ind-1],
                                      self.x[ind],
                                      self.y1[ind-1],
                                      self.y2[ind-1],
                                      t)

    def copy(self):
        """ Returns a copy of itself

        :rtype: :class:`PieceWiseLinFunc`
        """
        return PieceWiseLinFunc(self.x, self.y1, self.y2)

    def almost_equal(self, other, decimal=14):
        """ Checks if the function is equal to another function up to `decimal`
        precision.

        :param other: another :class:`PieceWiseLinFunc`
        :returns: True if the two functions are equal up to `decimal` decimals,
                  False otherwise
        :rtype: bool
        """
        eps = 10.0**(-decimal)
        return np.allclose(self.x, other.x, atol=eps, rtol=0.0) and \
            np.allclose(self.y1, other.y1, atol=eps, rtol=0.0) and \
            np.allclose(self.y2, other.y2, atol=eps, rtol=0.0)

    def get_plottable_data(self):
        """ Returns two arrays containing x- and y-coordinates for immeditate
        plotting of the piece-wise function.

        :returns: (x_plot, y_plot) containing plottable data
        :rtype: pair of np.array

        Example::

            x, y = f.get_plottable_data()
            plt.plot(x, y, '-o', label="Piece-wise const function")
        """
        x_plot = np.empty(2*len(self.x)-2)
        x_plot[0] = self.x[0]
        x_plot[1::2] = self.x[1:]
        x_plot[2::2] = self.x[1:-1]
        y_plot = np.empty_like(x_plot)
        y_plot[0::2] = self.y1
        y_plot[1::2] = self.y2
        return x_plot, y_plot

    def integral(self, interval=None):
        """ Returns the integral over the given interval.

        :param interval: integration interval given as a pair of floats, if
                         None the integral over the whole function is computed.
        :type interval: Pair of floats or None.
        :returns: the integral
        :rtype: float
        """

        def intermediate_value(x0, x1, y0, y1, x):
            """ computes the intermediate value of a linear function """
            return y0 + (y1-y0)*(x-x0)/(x1-x0)

        if interval is None:
            # no interval given, integrate over the whole spike train
            return np.sum((self.x[1:]-self.x[:-1]) * 0.5*(self.y1+self.y2))

        # find the indices corresponding to the interval
        start_ind = np.searchsorted(self.x, interval[0], side='right')
        end_ind = np.searchsorted(self.x, interval[1], side='left')-1
        assert start_ind > 0 and end_ind < len(self.x), \
            "Invalid averaging interval"
        if start_ind > end_ind:
            print(start_ind, end_ind, self.x[start_ind])
            # contribution from between two closest edges
            y_x0 = intermediate_value(self.x[start_ind-1],
                                        self.x[start_ind],
                                        self.y1[start_ind-1],
                                        self.y2[start_ind-1],
                                        interval[0])
            y_x1 = intermediate_value(self.x[start_ind-1],
                                        self.x[start_ind],
                                        self.y1[start_ind-1],
                                        self.y2[start_ind-1],
                                        interval[1])
            print(y_x0, y_x1, interval[1] - interval[0])
            integral = (y_x0 + y_x1) * 0.5 * (interval[1] - interval[0])
            print(integral)
        else:
            # first the contribution from between the indices
            integral = np.sum((self.x[start_ind+1:end_ind+1] -
                            self.x[start_ind:end_ind]) *
                            0.5*(self.y1[start_ind:end_ind] +
                                self.y2[start_ind:end_ind]))
            # correction from start to first index
            integral += (self.x[start_ind]-interval[0]) * 0.5 * \
                        (self.y2[start_ind-1] +
                        intermediate_value(self.x[start_ind-1],
                                            self.x[start_ind],
                                            self.y1[start_ind-1],
                                            self.y2[start_ind-1],
                                            interval[0]))
            # correction from last index to end
            integral += (interval[1]-self.x[end_ind]) * 0.5 * \
                        (self.y1[end_ind] +
                        intermediate_value(self.x[end_ind], self.x[end_ind+1],
                                            self.y1[end_ind], self.y2[end_ind],
                                            interval[1]
                                            ))
        return integral

    def avrg(self, interval=None):
        """ Computes the average of the piece-wise linear function:
        :math:`a = 1/T \int_0^T f(x) dx` where T is the interval length.

        :param interval: averaging interval given as a pair of floats, a
                         sequence of pairs for averaging multiple intervals, or
                         None, if None the average over the whole function is
                         computed.
        :type interval: Pair, sequence of pairs, or None.
        :returns: the average a.
        :rtype: float

        """

        if interval is None:
            # no interval given, average over the whole spike train
            return self.integral() / (self.x[-1]-self.x[0])

        # check if interval is as sequence
        assert isinstance(interval, collections.Sequence), \
            "Invalid value for `interval`. None, Sequence or Tuple expected."
        # check if interval is a sequence of intervals
        if not isinstance(interval[0], collections.Sequence):
            # just one interval
            a = self.integral(interval) / (interval[1]-interval[0])
        else:
            # several intervals
            a = 0.0
            int_length = 0.0
            for ival in interval:
                a += self.integral(ival)
                int_length += ival[1] - ival[0]
            a /= int_length
        return a

    def add(self, f):
        """ Adds another PieceWiseLin function to this function.
        Note: only functions defined on the same interval can be summed.

        :param f: :class:`PieceWiseLinFunc` function to be added.
        :rtype: None
        """
        assert self.x[0] == f.x[0], "The functions have different intervals"
        assert self.x[-1] == f.x[-1], "The functions have different intervals"

        # python implementation
        # from .python_backend import add_piece_wise_lin_python
        # self.x, self.y1, self.y2 = add_piece_wise_lin_python(
        #     self.x, self.y1, self.y2, f.x, f.y1, f.y2)

        # cython version
        try:
            from .cython.cython_add import add_piece_wise_lin_cython as \
                add_piece_wise_lin_impl
        except ImportError:
            if not(pyspike.disable_backend_warning):
                print("Warning: add_piece_wise_lin_cython not found. Make \
sure that PySpike is installed by running\n \
'python setup.py build_ext --inplace'! \n \
Falling back to slow python backend.")
            # use python backend
            from .cython.python_backend import add_piece_wise_lin_python as \
                add_piece_wise_lin_impl

        self.x, self.y1, self.y2 = add_piece_wise_lin_impl(
            self.x, self.y1, self.y2, f.x, f.y1, f.y2)

    def mul_scalar(self, fac):
        """ Multiplies the function with a scalar value

        :param fac: Value to multiply
        :type fac: double
        :rtype: None
        """
        self.y1 *= fac
        self.y2 *= fac
