/usr/lib/python2.7/dist-packages/csb/statistics/maxent.py is in python-csb 1.2.3+dfsg-3.
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A Maximum-Entropy model for backbone torsion angles.
Reference: Rowicka and Otwinowski 2004
"""
import numpy
from csb.statistics.pdf import BaseDensity
class MaxentModel(BaseDensity):
"""
Fourier expansion of a biangular log-probability density
"""
def __init__(self, n, beta=1.):
"""
@param n: order of the fourier expansion
@type n: int
@param beta: inverse temperature
@type beta: float
"""
super(MaxentModel, self).__init__()
self._n = int(n)
self._cc = numpy.zeros((self._n, self._n))
self._ss = numpy.zeros((self._n, self._n))
self._cs = numpy.zeros((self._n, self._n))
self._sc = numpy.zeros((self._n, self._n))
self._beta = float(beta)
@property
def beta(self):
"""
Inverse temperature
@rtype: float
"""
return self._beta
@property
def n(self):
"""
Order of the fourier expansion
@rtype: int
"""
return self._n
def load_old(self, aa, f_name):
"""
Load set of expansion coefficients from isd.
@param aa: Amino acid type
@param f_name: File containing ramachandran definition
"""
import os
params, _energies = eval(open(os.path.expanduser(f_name)).read())
params = params[self._n - 1]
for k, l, x, f, g in params[aa]:
if f == 'cos' and g == 'cos':
self._cc[k, l] = -x
elif f == 'cos' and g == 'sin':
self._cs[k, l] = -x
elif f == 'sin' and g == 'cos':
self._sc[k, l] = -x
elif f == 'sin' and g == 'sin':
self._ss[k, l] = -x
def load(self, aa, f_name):
"""
Load set of expansion coefficients from isd+.
@param aa: Amino acid type
@param f_name: File containing ramachandran definition
"""
import os
from numpy import reshape, array
from csb.io import load
f_name = os.path.expanduser(f_name)
params, _energies = load(f_name)
params = params[self._n]
a, b, c, d = params[aa]
a, b, c, d = reshape(array(a), (self._n, self._n)).astype('d'), \
reshape(array(b), (self._n, self._n)).astype('d'), \
reshape(array(c), (self._n, self._n)).astype('d'), \
reshape(array(d), (self._n, self._n)).astype('d')
# Not a typo, I accidently swichted cos*sin and sin*cos
self._cc, self._cs, self._sc, self._ss = -a, -c, -b, -d
def _periodicities(self):
return numpy.arange(self._n)
def log_prob(self, x, y):
"""
Return the energy at positions (x,y).
@param x: x-coordinates for evaluation
@type x: array-like
@param y: y-coordinates for evaluation
@type y: array-like
"""
return -self.energy(x, y)
def set(self, coef):
"""
Set the fourier expansion coefficients and calculations the
new partation function.
@param coef: expansion coefficents
@type coef: array like, with shape (4,n,n)
"""
self._cc[:, :], self._ss[:, :], self._cs[:, :], self._sc[:, :] = \
numpy.reshape(coef, (4, self._n, self._n))
self.normalize()
def get(self):
"""
Return current expansion coefficients.
"""
return numpy.array([self._cc, self._ss, self._cs, self._sc])
def energy(self, x, y=None):
"""
Return the energy at positions (x,y).
@param x: x-coordinates for evaluation
@type x: array-like
@param y: y-coordinates for evaluation
@type y: array-like
"""
from numpy import sin, cos, dot, multiply
k = self._periodicities()
cx, sx = cos(multiply.outer(k, x)), sin(multiply.outer(k, x))
if y is not None:
cy, sy = cos(multiply.outer(k, y)), sin(multiply.outer(k, y))
else:
cy, sy = cx, sx
return dot(dot(cx.T, self._cc), cy) + \
dot(dot(cx.T, self._cs), sy) + \
dot(dot(sx.T, self._sc), cy) + \
dot(dot(sx.T, self._ss), sy)
def sample_weights(self):
"""
Create a random set of expansion coefficients.
"""
from numpy import add
from numpy.random import standard_normal
k = self._periodicities()
k = add.outer(k ** 2, k ** 2)
self.set([standard_normal(k.shape) for i in range(4)])
self.normalize(True)
def prob(self, x, y):
"""
Return the probability of the configurations x cross y.
"""
from csb.numeric import exp
return exp(-self.beta * self(x, y))
def z(self):
"""
Calculate the partion function .
"""
from scipy.integrate import dblquad
from numpy import pi
return dblquad(self.prob, 0., 2 * pi, lambda x: 0., lambda x: 2 * pi)
def log_z(self, n=500, integration='simpson'):
"""
Calculate the log partion function.
"""
from numpy import pi, linspace, max
from csb.numeric import log, exp
if integration == 'simpson':
from csb.numeric import simpson_2d
x = linspace(0., 2 * pi, 2 * n + 1)
dx = x[1] - x[0]
f = -self.beta * self.energy(x)
f_max = max(f)
f -= f_max
I = simpson_2d(exp(f))
return log(I) + f_max + 2 * log(dx)
elif integration == 'trapezoidal':
from csb.numeric import trapezoidal_2d
x = linspace(0., 2 * pi, n)
dx = x[1] - x[0]
f = -self.beta * self.energy(x)
f_max = max(f)
f -= f_max
I = trapezoidal_2d(exp(f))
return log(I) + f_max + 2 * log(dx)
else:
raise NotImplementedError(
'Choose from trapezoidal and simpson-rule Integration')
def entropy(self, n=500):
"""
Calculate the entropy of the model.
@param n: number of integration points for numerical integration
@type n: integer
"""
from csb.numeric import trapezoidal_2d
from numpy import pi, linspace, max
from csb.numeric import log, exp
x = linspace(0., 2 * pi, n)
dx = x[1] - x[0]
f = -self.beta * self.energy(x)
f_max = max(f)
log_z = log(trapezoidal_2d(exp(f - f_max))) + f_max + 2 * log(dx)
average_energy = trapezoidal_2d(f * exp(f - f_max))\
* exp(f_max + 2 * log(dx) - log_z)
return -average_energy + log_z
def calculate_statistics(self, data):
"""
Calculate the sufficient statistics for the data.
"""
from numpy import cos, sin, dot, multiply
k = self._periodicities()
cx = cos(multiply.outer(k, data[:, 0]))
sx = sin(multiply.outer(k, data[:, 0]))
cy = cos(multiply.outer(k, data[:, 1]))
sy = sin(multiply.outer(k, data[:, 1]))
return dot(cx, cy.T), dot(sx, sy.T), dot(cx, sy.T), dot(sx, cy.T)
def normalize(self, normalize_full=True):
"""
Remove parameter, which do not have any influence on the model
and compute the partition function.
@param normalize_full: compute partition function
@type normalize_full: boolean
"""
self._cc[0, 0] = 0.
self._ss[:, 0] = 0.
self._ss[0, :] = 0.
self._cs[:, 0] = 0.
self._sc[0, :] = 0.
if normalize_full:
self._cc[0, 0] = self.log_z()
class MaxentPosterior(object):
"""
Object to hold and calculate the posterior (log)probability
given an exponential family model and corresponding data.
"""
def __init__(self, model, data):
"""
@param model: MaxentModel
@param data: two dimensonal data
"""
self._model = model
self._data = numpy.array(data)
self._stats = self.model.calculate_statistics(self._data)
self._log_likelihoods = []
@property
def model(self):
return self._model
@model.setter
def model(self, value):
self._model = value
self._stats = self.model.calculate_statistics(self._data)
@property
def data(self):
return self._data
@data.setter
def data(self, value):
self._data = numpy.array(value)
self._stats = self.model.calculate_statistics(value)
@property
def stats(self):
return self._stats
def __call__(self, weights=None, n=100):
"""
Returns the log posterior likelihood
@param weights: optional expansion coefficients of the model,
if none are specified those of the model are used
@param n: number of integration point for calculating the partition function
"""
from numpy import sum
if weights is not None:
self.model.set(weights)
a = sum(self._stats[0] * self.model._cc)
b = sum(self._stats[1] * self.model._ss)
c = sum(self._stats[2] * self.model._cs)
d = sum(self._stats[3] * self.model._sc)
log_z = self.data.shape[0] * self.model.log_z(n=n)
log_likelihood = -self.model.beta * (a + b + c + d) - log_z
self._log_likelihoods.append(log_likelihood)
return log_likelihood
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