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Diffstat (limited to 'pyspike/DiscreteFunc.py')
| -rw-r--r-- | pyspike/DiscreteFunc.py | 250 |
1 files changed, 250 insertions, 0 deletions
diff --git a/pyspike/DiscreteFunc.py b/pyspike/DiscreteFunc.py new file mode 100644 index 0000000..caad290 --- /dev/null +++ b/pyspike/DiscreteFunc.py @@ -0,0 +1,250 @@ +# Class representing discrete 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 + + +############################################################## +# 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 range(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 two values: the sum over all values and the + sum over all multiplicities. + + :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 summed values and the summed multiplicity + :rtype: pair of float + """ + + value = 0.0 + multiplicity = 0.0 + + 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 + value = 1.0 * np.sum(self.y[1:-1]) + multiplicity = np.sum(self.mp[1:-1]) + else: + # 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) + value = np.sum(self.y[start_ind:end_ind]) + multiplicity = np.sum(self.mp[start_ind:end_ind]) + else: + 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, normalize=True): + """ 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 + """ + val, mp = self.integral(interval) + if normalize: + if mp > 0: + return val/mp + else: + return 1.0 + else: + return val + + 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.cython_add import add_discrete_function_cython as \ + add_discrete_function_impl + except ImportError: + if not(pyspike.disable_backend_warning): + 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 .cython.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 range(1, len(profiles)): + avrg_profile.add(profiles[i]) + avrg_profile.mul_scalar(1.0/len(profiles)) # normalize + + return avrg_profile |