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# 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.abc
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.abc.Sequence), \
"Invalid value for `interval`. None, Sequence or Tuple \
expected."
# check if interval is a sequence of intervals
if not isinstance(interval[0], collections.abc.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:
pyspike.NoCythonWarn()
# 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
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