From 01fa64bd8a8931544a1734de104e2fe72018694f Mon Sep 17 00:00:00 2001
From: Mario Mulansky <mario.mulansky@gmx.net>
Date: Wed, 28 Jan 2015 19:22:02 +0100
Subject: added missing py files

---
 pyspike/DiscreteFunc.py       | 242 ++++++++++++++++++++++++++++++++++++++++++
 pyspike/PieceWiseConstFunc.py | 168 +++++++++++++++++++++++++++++
 pyspike/PieceWiseLinFunc.py   | 197 ++++++++++++++++++++++++++++++++++
 3 files changed, 607 insertions(+)
 create mode 100644 pyspike/DiscreteFunc.py
 create mode 100644 pyspike/PieceWiseConstFunc.py
 create mode 100644 pyspike/PieceWiseLinFunc.py

diff --git a/pyspike/DiscreteFunc.py b/pyspike/DiscreteFunc.py
new file mode 100644
index 0000000..3e24284
--- /dev/null
+++ b/pyspike/DiscreteFunc.py
@@ -0,0 +1,242 @@
+"""
+Class representing discrete functions.
+
+Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
+
+Distributed under the BSD License
+
+"""
+from __future__ import print_function
+
+import numpy as np
+import collections
+
+
+##############################################################
+# DiscreteFunc
+##############################################################
+class DiscreteFunc(object):
+    """ A class representing values defined on a discrete set of points.
+    """
+
+    def __init__(self, x, y, multiplicity):
+        """ Constructs the discrete function.
+
+        :param x: array of length N defining the points at which the values are
+        defined.
+        :param y: array of length N degining the values at the points x.
+        :param multiplicity: array of length N defining the multiplicity of the
+        values.
+        """
+        # convert parameters to arrays, also ensures copying
+        self.x = np.array(x)
+        self.y = np.array(y)
+        self.mp = np.array(multiplicity)
+
+    def copy(self):
+        """ Returns a copy of itself
+
+        :rtype: :class:`DiscreteFunc`
+        """
+        return DiscreteFunc(self.x, self.y, self.mp)
+
+    def almost_equal(self, other, decimal=14):
+        """ Checks if the function is equal to another function up to `decimal`
+        precision.
+
+        :param other: another :class:`DiscreteFunc`
+        :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.y, other.y, atol=eps, rtol=0.0) and \
+            np.allclose(self.mp, other.mp, atol=eps, rtol=0.0)
+
+    def get_plottable_data(self, averaging_window_size=0):
+        """ Returns two arrays containing x- and y-coordinates for plotting
+        the interval sequence. The optional parameter `averaging_window_size`
+        determines the size of an averaging window to smoothen the profile. If
+        this value is 0, no averaging is performed.
+
+        :param averaging_window_size: size of the averaging window, default=0.
+        :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="Discrete function")
+        """
+
+        if averaging_window_size > 0:
+            # for the averaged profile we have to take the multiplicity into
+            # account. values with higher multiplicity should be consider as if
+            # they appeared several times. Hence we can not know how many
+            # entries we have to consider to the left and right. Rather, we
+            # will iterate until some wanted multiplicity is reached.
+
+            # the first value in self.mp contains the number of averaged
+            # profiles without any possible extra multiplicities
+            # (by implementation)
+            expected_mp = (averaging_window_size+1) * int(self.mp[0])
+            y_plot = np.zeros_like(self.y)
+            # compute the values in a loop, could be done in cython if required
+            for i in xrange(len(y_plot)):
+
+                if self.mp[i] >= expected_mp:
+                    # the current value contains already all the wanted
+                    # multiplicity
+                    y_plot[i] = self.y[i]/self.mp[i]
+                    continue
+
+                # first look to the right
+                y = self.y[i]
+                mp_r = self.mp[i]
+                j = i+1
+                while j < len(y_plot):
+                    if mp_r+self.mp[j] < expected_mp:
+                        # if we still dont reach the required multiplicity
+                        # we take the whole value
+                        y += self.y[j]
+                        mp_r += self.mp[j]
+                    else:
+                        # otherwise, just some fraction
+                        y += self.y[j] * (expected_mp - mp_r)/self.mp[j]
+                        mp_r += (expected_mp - mp_r)
+                        break
+                    j += 1
+
+                # same story to the left
+                mp_l = self.mp[i]
+                j = i-1
+                while j >= 0:
+                    if mp_l+self.mp[j] < expected_mp:
+                        y += self.y[j]
+                        mp_l += self.mp[j]
+                    else:
+                        y += self.y[j] * (expected_mp - mp_l)/self.mp[j]
+                        mp_l += (expected_mp - mp_l)
+                        break
+                    j -= 1
+                y_plot[i] = y/(mp_l+mp_r-self.mp[i])
+            return 1.0*self.x, y_plot
+
+        else:  # k = 0
+
+            return 1.0*self.x, 1.0*self.y/self.mp
+
+    def integral(self, interval=None):
+        """ Returns the integral over the given interval. For the discrete
+        function, this amounts to the sum over all values divided by the total
+        multiplicity.
+
+        :param interval: integration interval given as a pair of floats, or a
+                         sequence of pairs in case of multiple intervals, if
+                         None the integral over the whole function is computed.
+        :type interval: Pair, sequence of pairs, or None.
+        :returns: the integral
+        :rtype: float
+        """
+
+        def get_indices(ival):
+            """ Retuns the indeces surrounding the given interval"""
+            start_ind = np.searchsorted(self.x, ival[0], side='right')
+            end_ind = np.searchsorted(self.x, ival[1], side='left')
+            assert start_ind > 0 and end_ind < len(self.x), \
+                "Invalid averaging interval"
+            return start_ind, end_ind
+
+        if interval is None:
+            # no interval given, integrate over the whole spike train
+            # don't count the first value, which is zero by definition
+            return 1.0 * np.sum(self.y[1:-1]) / np.sum(self.mp[1:-1])
+
+        # 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):
+            # find the indices corresponding to the interval
+            start_ind, end_ind = get_indices(interval)
+            return (np.sum(self.y[start_ind:end_ind]) /
+                    np.sum(self.mp[start_ind:end_ind]))
+        else:
+            value = 0.0
+            multiplicity = 0.0
+            for ival in interval:
+                # find the indices corresponding to the interval
+                start_ind, end_ind = get_indices(ival)
+                value += np.sum(self.y[start_ind:end_ind])
+                multiplicity += np.sum(self.mp[start_ind:end_ind])
+        return value/multiplicity
+
+    def avrg(self, interval=None):
+        """ Computes the average of the interval sequence:
+        :math:`a = 1/N sum f_n ` where N is the number of intervals.
+
+        :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
+        """
+        return self.integral(interval)
+
+    def add(self, f):
+        """ Adds another `DiscreteFunc` function to this function.
+        Note: only functions defined on the same interval can be summed.
+
+        :param f: :class:`DiscreteFunc` 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"
+
+        # cython version
+        try:
+            from cython_add import add_discrete_function_cython as \
+                add_discrete_function_impl
+        except ImportError:
+            print("Warning: add_discrete_function_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 python_backend import add_discrete_function_python as \
+                add_discrete_function_impl
+
+        self.x, self.y, self.mp = \
+            add_discrete_function_impl(self.x, self.y, self.mp,
+                                       f.x, f.y, f.mp)
+
+    def mul_scalar(self, fac):
+        """ Multiplies the function with a scalar value
+
+        :param fac: Value to multiply
+        :type fac: double
+        :rtype: None
+        """
+        self.y *= fac
+
+
+def average_profile(profiles):
+    """ Computes the average profile from the given ISI- or SPIKE-profiles.
+
+    :param profiles: list of :class:`PieceWiseConstFunc` or
+                     :class:`PieceWiseLinFunc` representing ISI- or
+                     SPIKE-profiles to be averaged.
+    :returns: the averages profile :math:`<S_{isi}>` or :math:`<S_{spike}>`.
+    :rtype: :class:`PieceWiseConstFunc` or :class:`PieceWiseLinFunc`
+    """
+    assert len(profiles) > 1
+
+    avrg_profile = profiles[0].copy()
+    for i in xrange(1, len(profiles)):
+        avrg_profile.add(profiles[i])
+    avrg_profile.mul_scalar(1.0/len(profiles))  # normalize
+
+    return avrg_profile
diff --git a/pyspike/PieceWiseConstFunc.py b/pyspike/PieceWiseConstFunc.py
new file mode 100644
index 0000000..e639dfc
--- /dev/null
+++ b/pyspike/PieceWiseConstFunc.py
@@ -0,0 +1,168 @@
+"""
+Class representing piece-wise constant functions.
+
+Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
+
+Distributed under the BSD License
+
+"""
+from __future__ import print_function
+
+import numpy as np
+import collections
+
+
+##############################################################
+# PieceWiseConstFunc
+##############################################################
+class PieceWiseConstFunc(object):
+    """ A class representing a piece-wise constant function. """
+
+    def __init__(self, x, y):
+        """ Constructs the piece-wise const function.
+
+        :param x: array of length N+1 defining the edges of the intervals of
+                  the pwc function.
+        :param y: array of length N defining the function values at the
+                  intervals.
+        """
+        # convert parameters to arrays, also ensures copying
+        self.x = np.array(x)
+        self.y = np.array(y)
+
+    def copy(self):
+        """ Returns a copy of itself
+
+        :rtype: :class:`PieceWiseConstFunc`
+        """
+        return PieceWiseConstFunc(self.x, self.y)
+
+    def almost_equal(self, other, decimal=14):
+        """ Checks if the function is equal to another function up to `decimal`
+        precision.
+
+        :param other: another :class:`PieceWiseConstFunc`
+        :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.y, other.y, 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(2*len(self.y))
+        y_plot[::2] = self.y
+        y_plot[1::2] = self.y
+
+        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
+        """
+        if interval is None:
+            # no interval given, integrate over the whole spike train
+            a = np.sum((self.x[1:]-self.x[:-1]) * self.y)
+        else:
+            # 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"
+            # first the contribution from between the indices
+            a = np.sum((self.x[start_ind+1:end_ind+1] -
+                        self.x[start_ind:end_ind]) *
+                       self.y[start_ind:end_ind])
+            # correction from start to first index
+            a += (self.x[start_ind]-interval[0]) * self.y[start_ind-1]
+            # correction from last index to end
+            a += (interval[1]-self.x[end_ind]) * self.y[end_ind]
+        return a
+
+    def avrg(self, interval=None):
+        """ Computes the average of the piece-wise const function:
+        :math:`a = 1/T int_0^T f(x) dx` where T is the length of the interval.
+
+        :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 PieceWiseConst function to this function.
+        Note: only functions defined on the same interval can be summed.
+
+        :param f: :class:`PieceWiseConstFunc` 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"
+
+        # cython version
+        try:
+            from cython_add import add_piece_wise_const_cython as \
+                add_piece_wise_const_impl
+        except ImportError:
+            print("Warning: add_piece_wise_const_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 python_backend import add_piece_wise_const_python as \
+                add_piece_wise_const_impl
+
+        self.x, self.y = add_piece_wise_const_impl(self.x, self.y, f.x, f.y)
+
+    def mul_scalar(self, fac):
+        """ Multiplies the function with a scalar value
+
+        :param fac: Value to multiply
+        :type fac: double
+        :rtype: None
+        """
+        self.y *= fac
diff --git a/pyspike/PieceWiseLinFunc.py b/pyspike/PieceWiseLinFunc.py
new file mode 100644
index 0000000..58a20e5
--- /dev/null
+++ b/pyspike/PieceWiseLinFunc.py
@@ -0,0 +1,197 @@
+"""
+Class representing piece-wise linear functions.
+
+Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
+
+Distributed under the BSD License
+
+"""
+from __future__ import print_function
+
+import numpy as np
+import collections
+
+
+##############################################################
+# 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 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
+            integral = np.sum((self.x[1:]-self.x[:-1]) * 0.5*(self.y1+self.y2))
+        else:
+            # 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"
+            # 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 length of the interval.
+
+        :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_add import add_piece_wise_lin_cython as \
+                add_piece_wise_lin_impl
+        except ImportError:
+            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 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
-- 
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