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gauss.py
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gauss.py
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'''Module containing a DensityFunc abstract class, with common probability densities
@since: 2014
@author: Ben
'''
from __future__ import division
import numpy as np
class Gauss(object):
'''
Class for representing a multi-dimensional Gaussian distribution of dimension d,
given mean and covariance.
The covariance matrix has to be positive definite and non-singular.
Parameters
----------
mean : (d,) ndarray
mean of the distribution
cov : (d,d) ndarray
Covariance matrix.
Methods
-------
f
Returns the value of the density function
logf
Returns the log of the density function
likelihood
Returns the likelihood of the data
loglik
Reurns the log-likelihood of the data
sample
Returns samples drawn from the normal distribution with the given
mean and covariance
Example
-------
>>> from gauss import Gauss
>>> # Scalar example
>>> mean = [10.]
>>> cov = [[1.]]
>>> ga = Gauss(mean,cov)
>>> ga.f([10.])
0.398942280401
>>> x = np.array([[10.,10.,10.]])
>>> ga.likelihood(x)
0.0634936359342
>>> # Multivariate example
>>> mean = [10.0, 10.0]
>>> cov = [[ 1. 0.],[ 0. 10.]]
>>> ga = Gauss(mean,cov)
>>> ga.f(np.array([10.,10.])
0.050329212104487035
>>> x = np.array([[10.,10.,10.,10.],[10.,10.,10.,10.]])
>>> ga.likelihood(x)
336.4162389091777101e-06
'''
def __init__(self, mean=[0.,0.], cov=[[1.,0.],[0.,1.]]):
mean = np.array(mean); cov = np.array(cov)
d,n = cov.shape
self._dim = d
self._mean = mean.flatten()
self._cov = cov
self._covdet = np.linalg.det(2.0*np.pi*cov)
if self._covdet < 10e-25:
raise ValueError('The covariance matrix is singular.')
def f(self, x):
'''
Calculate the value of the normal distributions at x
Parameters
----------
x : (d,) ndarray
Evaluate a single d-dimensional samples x
Returns
-------
val : scalar
The value of the normal distribution at x.
'''
return np.exp(self.logf(x))
def logf(self, x):
'''
Calculate the log-density at x
Parameters
----------
x : (d,) ndarray
Evaluate the log-normal distribution at a single d-dimensional
sample x
Returns
-------
val : scalar
The value of the log of the normal distribution at x.
'''
if not len(x.shape)==1:
raise ValueError('The input vector needs to be of shape (d,)')
trans = x - self._mean
mal = -trans.dot(np.linalg.solve(self._cov,trans))/2.
return -0.5*np.log(self._covdet) + mal
def likelihood(self, x):
'''
Calculates the likelihood of the data set x for the normal
distribution.
Parameters
----------
x : (d,n) ndarray
Calculate the likelihood of n, d-dimensional samples
Returns
-------
val : scalar
The likelihood value
'''
return np.exp(self.loglik(x))
def loglik(self, x):
'''
Calculates the log-likelihood of the data set x for the normal
distribution.
Parameters
----------
x : (d,n) ndarray
Calculate the likelihood of n, d-dimensional samples
Returns
-------
val : scalar
The log-likelihood value
'''
return np.sum(np.apply_along_axis(self.logf, 0, x))
def sample(self, n=1):
'''
Calculates n independent points sampled from the normal distribution
Parameters
----------
n : int
The number of samples
Returns
-------
samples : (d,n) ndarray
n, d-dimensional samples
'''
return np.random.multivariate_normal(self._mean, self._cov, n).T