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#! /usr/bin/python
#
# Copyrighted David Cournapeau
# Last Change: Sat Jun 09 10:00 PM 2007 J
"""This module implements some function of densities module in C for efficiency
reasons. gaussian, such as pdf estimation, confidence interval/ellipsoids,
etc..."""
__docformat__ = 'restructuredtext'
# This module uses a C implementation through ctypes, for diagonal cases
# TODO:
# - portable way to find/open the shared library
# - full cov matrice
# - test before inclusion
import numpy as N
import numpy.linalg as lin
#from numpy.random import randn
#from scipy.stats import chi2
#import densities as D
import ctypes
from ctypes import c_uint, c_int
from numpy.ctypeslib import ndpointer, load_library
ctypes_major = int(ctypes.__version__.split('.')[0])
if ctypes_major < 1:
raise ImportError(msg = "version of ctypes is %s, expected at least %s"\
% (ctypes.__version__, '1.0.1'))
# Requirements for diag gden
_gden = load_library('c_gden.so', __file__)
arg1 = ndpointer(dtype=N.float64)
arg2 = c_uint
arg3 = c_uint
arg4 = ndpointer(dtype=N.float64)
arg5 = ndpointer(dtype=N.float64)
arg6 = ndpointer(dtype=N.float64)
_gden.gden_diag.argtypes = [arg1, arg2, arg3, arg4, arg5, arg6]
_gden.gden_diag.restype = c_int
# Error classes
class DenError(Exception):
"""Base class for exceptions in this module.
Attributes:
expression -- input expression in which the error occurred
message -- explanation of the error"""
def __init__(self, message):
self.message = message
def __str__(self):
return self.message
# The following function do all the fancy stuff to check that parameters
# are Ok, and call the right implementation if args are OK.
def gauss_den(x, mu, va, log = False):
""" Compute multivariate Gaussian density at points x for
mean mu and variance va.
Vector are row vectors, except va which can be a matrix
(row vector variance for diagonal variance)
If log is True, than the log density is returned
(useful for underflow ?)"""
mu = N.atleast_2d(mu)
va = N.atleast_2d(va)
x = N.atleast_2d(x)
#=======================#
# Checking parameters #
#=======================#
if len(N.shape(mu)) != 2:
raise DenError("mu is not rank 2")
if len(N.shape(va)) != 2:
raise DenError("va is not rank 2")
if len(N.shape(x)) != 2:
raise DenError("x is not rank 2")
(n, d) = N.shape(x)
(dm0, dm1) = N.shape(mu)
(dv0, dv1) = N.shape(va)
# Check x and mu same dimension
if dm0 != 1:
msg = "mean must be a row vector!"
raise DenError(msg)
if dm1 != d:
msg = "x and mu not same dim"
raise DenError(msg)
# Check va and mu same size
if dv1 != d:
msg = "mu and va not same dim"
raise DenError(msg)
if dv0 != 1 and dv0 != d:
msg = "va not square"
raise DenError(msg)
#===============#
# Computation #
#===============#
if d == 1:
# scalar case
return _scalar_gauss_den(x[:, 0], mu[0, 0], va[0, 0], log)
elif dv0 == 1:
# Diagonal matrix case
return _diag_gauss_den(x, mu, va, log)
elif dv1 == dv0:
# full case
return _full_gauss_den(x, mu, va, log)
else:
raise DenError("variance mode not recognized, this is a bug")
# Those 3 functions do almost all the actual computation
def _scalar_gauss_den(x, mu, va, log):
""" This function is the actual implementation
of gaussian pdf in scalar case. It assumes all args
are conformant, so it should not be used directly
** Expect centered data (ie with mean removed) **
Call gauss_den instead"""
d = mu.size
inva = 1/va
fac = (2*N.pi) ** (-d/2.0) * N.sqrt(inva)
y = ((x-mu) ** 2) * -0.5 * inva
if not log:
y = fac * N.exp(y)
else:
y = y + log(fac)
return y
def _diag_gauss_den(x, mu, va, log):
""" This function is the actual implementation
of gaussian pdf in scalar case. It assumes all args
are conformant, so it should not be used directly
** Expect centered data (ie with mean removed) **
Call gauss_den instead"""
# Diagonal matrix case
d = mu.size
n = x.shape[0]
if not log:
y = N.zeros(n)
vat = va.copy()
# _gden.gden_diag(N.require(x, requirements = 'C'), n, d,
# N.require(mu, requirements = 'C'),
# N.require(inva, requirements = 'C'),
# N.require(y, requirements = 'C'))
x = N.require(x, requirements = 'C')
mu = N.require(mu, requirements = 'C')
vat = N.require(vat, requirements = 'C')
y = N.require(y, requirements = 'C')
_gden.gden_diag(x, n, d, mu, vat, y)
return y
# _gden.gden_diag.restype = c_int
# _gden.gden_diag.argtypes = [POINTER(c_double), c_uint, c_uint,
# POINTER(c_double), POINTER(c_double), POINTER(c_double)]
# y = N.zeros(n)
# inva= 1/va
# _gden.gden_diag(x.ctypes.data_as(POINTER(c_double)),
# n, d,
# mu.ctypes.data_as(POINTER(c_double)),
# inva.ctypes.data_as(POINTER(c_double)),
# y.ctypes.data_as(POINTER(c_double)))
else:
y = _scalar_gauss_den(x[:, 0], mu[0, 0], va[0, 0], log)
for i in range(1, d):
y += _scalar_gauss_den(x[:, i], mu[0, i], va[0, i], log)
return y
def _full_gauss_den(x, mu, va, log):
""" This function is the actual implementation
of gaussian pdf in full matrix case.
It assumes all args are conformant, so it should
not be used directly Call gauss_den instead
** Expect centered data (ie with mean removed) **
Does not check if va is definite positive (on inversible
for that matter), so the inverse computation and/or determinant
would throw an exception."""
d = mu.size
inva = lin.inv(va)
fac = 1 / N.sqrt( (2*N.pi) ** d * N.fabs(lin.det(va)))
# we are using a trick with sum to "emulate"
# the matrix multiplication inva * x without any explicit loop
y = N.dot((x-mu), inva)
y = -0.5 * N.sum(y * (x-mu), 1)
if not log:
y = fac * N.exp(y)
else:
y = y + N.log(fac)
return y
if __name__ == "__main__":
pass
##=========================================
## Test accuracy between pure and C python
##=========================================
#mu = N.array([2.0, 3])
#va = N.array([5.0, 3])
## Generate a multivariate gaussian of mean mu and covariance va
#nframes = 1e4
#X = randn(nframes, 2)
#Yc = N.dot(N.diag(N.sqrt(va)), X.transpose())
#Yc = Yc.transpose() + mu
#Y = D.gauss_den(Yc, mu, va)
#Yt = gauss_den(Yc, mu, va)
#print "Diff is " + str(N.sqrt(N.sum((Y-Yt) ** 2))/nframes/2)
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