#######################
# DCProgs computes missed-events likelihood as described in
# Hawkes, Jalali and Colquhoun (1990, 1992)
#
# Copyright (C) 2013 University College London
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#########################
""" Some pure python methods used to access/complement the c++ bindings. """
__docformat__ = "restructuredtext en"
__all__ = ['network', 'find_roots', 'plot_roots',
'missed_events_pdf', 'ideal_pdf', 'intervals_to_series', 'series_to_intervals',
'plot_time_series', 'plot_time_intervals' ]
def network(qmatrix):
""" Creates networkx graph object from a :class:`QMatrix` object.
Vertices have an "open" attribute to indicate whether they are open or shut. Edges have a
"k+" and "k-" attribute containing the transition rates for the node with smaller index to
the node with larger index, and vice-versa.
:param qmatrix:
A :class:`QMatrix` instance for which to construct a graph
:return: A `networkx.Graph` object which contains all the information held by the qmatrix
object, but in a graph format.
"""
from networkx import Graph
graph = Graph()
for i in range(qmatrix.nopen): graph.add_node(i, open=True)
for j in range(qmatrix.nshut): graph.add_node(i+j, open=False)
for i in range(qmatrix.matrix.shape[0]):
for j in range(i, qmatrix.matrix.shape[1]):
if abs(qmatrix.matrix[i,j]) > 1e-8:
graph.add_edge(i, j)
graph[i][j]['k+'] = qmatrix.matrix[i, j]
graph[i][j]['k-'] = qmatrix.matrix[j, i]
return graph
[docs]def find_roots(determinant, intervals=None, tolerance=1e-12, **kwargs):
""" Computes roots for each interval.
:param determinant:
A function or functor of a single variable.
:param intervals:
A list of items `[(a0, b0), ..., (a1, b1)]`, where `(a, b)` is the interval over which to
look for roots.
If this object is None (default), then uses :py:meth:`find_root_intervals` to figure out
the intervals.
:param tolerance:
Tolerance criteria. Used to determine multiplicity.
:param kwargs:
Passed on to :py:meth:`brentq` and :py:meth:`find_root_intervals`.
:returns: A list of items `(root, multiplicity)`.
"""
from scipy.optimize import fminbound
from numpy import abs, count_nonzero
from inspect import getargspec
from .likelihood import find_root_intervals, eig, brentq
if intervals is None:
# Create dictionary of keyword arguments
names, varargs, keywords, defaults = getargspec(find_root_intervals)
intervals_kwargs = {'tolerance': tolerance}
for name in names[-len(defaults):]:
if name in kwargs: intervals_kwargs[name] = kwargs[name]
intervals = [u[0] for u in find_root_intervals(determinant, **intervals_kwargs)]
names, varargs, keywords, defaults = getargspec(brentq)
brentq_kwargs = {}
for name in names[-len(defaults):]:
if name in kwargs: brentq_kwargs[name] = kwargs[name]
result = []
for interval in intervals:
# left, right: limit of interval.
left, right = determinant(interval)
if left * right < 0: root = brentq(determinant, *interval, **brentq_kwargs)[0]
elif left < 0:
root, value, ierr, numfunc = fminbound(lambda x: -determinant(x), left, right)
if abs(value) > tolerance: continue
else:
root, value, ierr, numfunc = fminbound(determinant, left, right, full_output=True)
if abs(value) > tolerance: continue
H = determinant.H(root)
if len(H) > 1:
# Use Eigen's eigenvalue pb so that we can do long doubles.
eigenvalues = eig(determinant.H(root))[0]
multiplicity = count_nonzero(abs(eigenvalues - root) < tolerance)
else: multiplicity = 1
if left * right < 0:
if multiplicity == 0 or multiplicity % 2 != 1: multiplicity = 1
else:
if multiplicity == 0 or multiplicity % 2 != 0: multiplicity = 2
result.append((root, multiplicity));
return result;
def plot_roots(determinant, intervals=None, figure=None, main=None, lines=None, size=1000,
tolerance=1e-8, ax=None):
""" Computes and plots roots.
:param determinant:
A function or functor of a single variable.
:param intervals:
A list of items `[(a0, b0), ..., (a1, b1)]`, where `(a, b)` is the interval over which to
look for roots.
If this object is None (default), then uses :py:meth:`find_root_intervals` to figure out
the intervals.
:param main:
A dictionary of values with which to plot the determinant.
:param lines:
A dictionary of values with which to plot the roots.
:returns: A figure
"""
from matplotlib import pyplot as plt
from numpy import arange, min, max, array
from .likelihood import find_root_intervals
if intervals is None:
intervals = [u[0] for u in find_root_intervals(determinant)]
intervals = array(intervals)
if main is None: main = {}
if lines is None: lines = {}
roots = find_roots(determinant, intervals, tolerance)
mini = min([u[0] for u in roots])
maxi = max([u[0] for u in roots])
diff = maxi - mini
maxi += diff * 0.05
mini -= diff * 0.05
x = arange(mini, maxi+(maxi-mini)/float(size)*0.5, (maxi-mini)/float(size))
y = determinant(x)
if ax is None:
figure = plt.figure()
ax = figure.add_subplot(111)
ax.plot(x, y, **main)
ax.set_xlim((mini, maxi))
ymin, ymax = min(y), max(y)
ymin = ymin - (ymax - ymin) * 0.05
ymax = ymax + (ymax - ymin) * 0.05
ax.set_ylim((ymin, ymax))
for root in roots:
ax.plot([root[0], root[0]], [ymin, 0], **lines)
ax.plot([x[0], x[-1]], [0, 0])
return figure
def _create_pdf(phi, g, shut):
""" Creates pdf from knowledge of phi, g and whether open or shut."""
from numpy import dot, sum, zeros_like
if shut:
def missed_events_pdf(t):
result = zeros_like(t)
for i, u in enumerate(t.flat):
result.itemset(i, sum(dot(phi, g.fa(float(u)))))
return result
else:
def missed_events_pdf(t):
result = zeros_like(t)
for i, u in enumerate(t.flat):
result.itemset(i, sum(dot(phi, g.af(float(u)))))
return result
return missed_events_pdf
def missed_events_pdf(qmatrix, tau, nmax=2, shut=False, tcrit=None):
""" A function to compute missed-events pdf """
from .likelihood import MissedEventsG
g = MissedEventsG(qmatrix, tau, nmax)
if tcrit is not None:
phi = g.final_CHS_occupancies(tcrit) if shut else g.initial_CHS_occupancies(tcrit)
else:
phi = g.final_occupancies if shut else g.initial_occupancies
return _create_pdf(phi, g, shut)
def ideal_pdf(qmatrix, shut=False):
""" A function to compute ideal pdf """
from .likelihood import IdealG
g = IdealG(qmatrix)
phi = g.final_occupancies if shut else g.initial_occupancies
return _create_pdf(phi, g, shut)
def exponential_pdfs(qmatrix, tau, shut=False, tcrit=None):
""" Returns a list of function that make up the asymptotic pdf.
This is mostly to re-plot Hawkes et al (1992).
"""
from operator import itemgetter
from functools import partial
from numpy import dot, sum, exp
from .likelihood import MissedEventsG, ApproxSurvivor
g = MissedEventsG(qmatrix, tau)
if tcrit is not None:
phi = g.final_CHS_occupancies(tcrit) if shut else g.initial_CHS_occupancies(tcrit)
else:
phi = g.final_occupancies if shut else g.initial_occupancies
if shut:
components = ApproxSurvivor(qmatrix, tau).fa_components
else:
components = ApproxSurvivor(qmatrix, tau).af_components
components = sorted(components, key=itemgetter(1))
def function(coef, root, t): return coef * exp(root * (t-tau))
results = []
if shut:
for matrix, root in components:
coef = sum(dot(phi, dot(matrix, g.fa_factor)))
results.append(partial(function, coef, root))
else:
for matrix, root in components:
coef = sum(dot(phi, dot(matrix, g.af_factor)))
results.append(partial(function, coef, root))
return results
def intervals_to_series(intervals, start=0):
""" Converts time intervals to time series. """
from numpy import zeros
from .. import internal_dtype
result = zeros(len(intervals)+1, dtype=internal_dtype)
result[0] = start
for i, z in enumerate(intervals): result[i+1] = result[i] + z
return result
def series_to_intervals(series, start=0):
""" Converts time intervals to time series. """
return series[1:] - series[:-1]
def plot_time_series(series, ax=None, **kwargs):
""" Plots time series """
from numpy import array, min, max, arange
from matplotlib.pylab import figure
x = [series[0]] + [series[i//2] for i in range(2, 2*len(series)-1)]
y = (arange(0, len(x)) % 4 >= 2).astype('int')
if ax is None:
fig = figure()
ax = fig.add_subplot(111)
ax.plot(x, 0.1 + array(y), **kwargs)
ax.set_xlabel("time")
ax.set_ylim((0, 1.2))
ax.set_xlim((min(x)-0.1, max(x)+0.1))
ax.yaxis.set_visible(False)
def plot_time_intervals(series, start=0, ax = None):
""" Plots time intervals """
return plot_time_series(series_to_intervals(series, start), ax=ax)