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#!/usr/bin/env python 

# 

# LSST Data Management System 

# Copyright 2008-2013 LSST Corporation. 

# 

# This product includes software developed by the 

# LSST Project (http://www.lsst.org/). 

# 

# 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. 

# 

# You should have received a copy of the LSST License Statement and 

# the GNU General Public License along with this program. If not, 

# see <http://www.lsstcorp.org/LegalNotices/>. 

# 

 

from __future__ import absolute_import, division, print_function 

 

__all__ = ("fitMixture", "SemiEmpiricalPriorConfig", 

"SoftenedLinearPriorControl") 

 

from builtins import range 

 

import numpy as np 

 

from lsst.pex.config import makeConfigClass 

from lsst.utils import continueClass 

 

from ..mixture import Mixture 

from .priors import (SemiEmpiricalPriorControl, SemiEmpiricalPrior, 

SoftenedLinearPriorControl, SoftenedLinearPrior, 

MixturePrior) 

 

 

SemiEmpiricalPriorConfig = makeConfigClass(SemiEmpiricalPriorControl) 

 

SoftenedLinearPriorConfig = makeConfigClass(SoftenedLinearPriorControl) 

 

 

@continueClass # noqa 

class SemiEmpiricalPrior: 

 

ConfigClass = SemiEmpiricalPriorConfig 

 

 

@continueClass # noqa 

class SoftenedLinearPrior: 

 

ConfigClass = SoftenedLinearPriorConfig 

 

 

def fitMixture(data, nComponents, minFactor=0.25, maxFactor=4.0, 

nIterations=20, df=float("inf")): 

"""Fit a ``Mixture`` distribution to a set of (e1, e2, r) data points, 

returing a ``MixturePrior`` object. 

 

Parameters 

---------- 

data : numpy.ndarray 

array of data points to fit; shape=(N,3) 

nComponents : int 

number of components in the mixture distribution 

minFactor : float 

ellipticity variance of the smallest component in the initial mixture, 

relative to the measured variance 

maxFactor : float 

ellipticity variance of the largest component in the initial mixture, 

relative to the measured variance 

nIterations : int 

number of expectation-maximization update iterations 

df : float 

number of degrees of freedom for component Student's T distributions 

(inf=Gaussian). 

""" 

components = Mixture.ComponentList() 

rMu = data[:, 2].mean() 

rSigma = data[:, 2].var() 

eSigma = 0.5*(data[:, 0].var() + data[:, 1].var()) 

mu = np.array([0.0, 0.0, rMu], dtype=float) 

baseSigma = np.array([[eSigma, 0.0, 0.0], 

[0.0, eSigma, 0.0], 

[0.0, 0.0, rSigma]]) 

for factor in np.linspace(minFactor, maxFactor, nComponents): 

sigma = baseSigma.copy() 

sigma[:2, :2] *= factor 

components.append(Mixture.Component(1.0, mu, sigma)) 

mixture = Mixture(3, components, df) 

restriction = MixturePrior.getUpdateRestriction() 

for i in range(nIterations): 

mixture.updateEM(data, restriction) 

return mixture