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# 

# LSST Data Management System 

# 

# Copyright 2008-2016 AURA/LSST. 

# 

# 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 <https://www.lsstcorp.org/LegalNotices/>. 

# 

import os 

import unittest 

import numpy 

 

import lsst.utils.tests 

import lsst.afw.geom.ellipses 

import lsst.afw.image 

import lsst.afw.detection 

import lsst.shapelet.tests 

import lsst.meas.modelfit 

 

try: 

import scipy.stats 

except ImportError: 

scipy = None 

 

 

class MixtureTestCase(lsst.utils.tests.TestCase): 

 

def setUp(self): 

numpy.random.seed(500) 

self.rng = lsst.afw.math.Random("MT19937", 500) 

 

@staticmethod 

def makeRandomMixture(nDim, nComponents, df=float("inf")): 

componentList = [] 

for i in range(nComponents): 

mu = numpy.random.randn(nDim)*4 

a = numpy.random.randn(nDim+1, nDim) 

sigma = numpy.dot(a.transpose(), a) + numpy.identity(nDim) 

componentList.append(lsst.meas.modelfit.Mixture.Component(numpy.random.rand(), mu, sigma)) 

return lsst.meas.modelfit.Mixture(nDim, componentList, df) 

 

def testSwig(self): 

"""Test that Swig correctly wrapped tricky things. 

""" 

l1 = [] 

l1.append(lsst.meas.modelfit.MixtureComponent(1)) 

l1.append(lsst.meas.modelfit.MixtureComponent(1)) 

l1.append(lsst.meas.modelfit.MixtureComponent(1)) 

l1[0].weight = 1.0 

l1[0].setMu(numpy.array([1.0], dtype=float)) 

l1[0].setSigma(numpy.array([[4.0]], dtype=float)) 

l1[1].weight = 0.5 

l1[2].weight = 0.5 

m1 = lsst.meas.modelfit.Mixture(1, l1) 

self.assertEqual(m1[0].weight, 0.5) 

self.assertEqual([0.5, 0.25, 0.25], [c.weight for c in m1]) 

self.assertFloatsAlmostEqual(m1[0].getMu(), numpy.array([1.0], dtype=float)) 

self.assertFloatsAlmostEqual(m1[0].getSigma(), numpy.array([4.0], dtype=float)) 

self.assertFloatsAlmostEqual(m1.evaluate(m1[1], numpy.array([0.0], dtype=float)), 

m1[1].weight*(2.0*numpy.pi)**(-0.5)) 

self.assertFloatsAlmostEqual(m1.evaluate(numpy.array([0.0], dtype=float)), 

(m1[0].weight*numpy.exp(-0.125)/2 + m1[1].weight + m1[2].weight) * 

(2.0*numpy.pi)**(-0.5)) 

 

def testGaussian(self): 

"""Test that our implementations for a single-component Gaussian are correct. 

""" 

m = self.makeRandomMixture(2, 1) 

mu = m[0].getMu() 

sigma = m[0].getSigma() 

fisher = numpy.linalg.inv(sigma) 

x = numpy.random.randn(20, 2) 

p = numpy.zeros(20, dtype=float) 

m.evaluate(x, p) 

z = ((x - mu)[:, numpy.newaxis, :] * fisher[numpy.newaxis, :, :, ] * 

(x - mu)[:, :, numpy.newaxis]).sum(axis=2).sum(axis=1) 

self.assertFloatsAlmostEqual(p, numpy.exp(-0.5*z) / numpy.linalg.det(2*numpy.pi*sigma)**0.5) 

x = numpy.zeros((1000000, 2), dtype=float) 

m.draw(self.rng, x) 

self.assertFloatsAlmostEqual(x.mean(axis=0), mu, rtol=2E-2) 

self.assertFloatsAlmostEqual(numpy.cov(x, rowvar=False), sigma, rtol=3E-2) 

if scipy is None: 

return 

self.assertGreater(scipy.stats.normaltest(x[:, 0])[1], 0.05) 

self.assertGreater(scipy.stats.normaltest(x[:, 1])[1], 0.05) 

 

def testStudentsT(self): 

"""Test that our implementations for a single-component Student's T are correct. 

""" 

if scipy is None: 

return 

for df in [4, 8]: 

m = self.makeRandomMixture(1, 1, df=df) 

mu = m[0].getMu() 

sigma = m[0].getSigma() 

x = numpy.random.randn(20, 1) 

p = numpy.zeros(20, dtype=float) 

m.evaluate(x, p) 

x = x.reshape(20) 

z = (x - mu)/(sigma**0.5) 

self.assertFloatsAlmostEqual(p, scipy.stats.t.pdf(z, df)/sigma**0.5) 

x = numpy.zeros((1000000, 1), dtype=float) 

m.draw(self.rng, x) 

self.assertFloatsAlmostEqual(x.mean(), mu, rtol=5E-2) 

self.assertFloatsAlmostEqual(x.var(), sigma * df / (df - 2), rtol=5E-2) 

self.assertLess(scipy.stats.normaltest(x)[1], 0.05) 

 

def testPersistence(self): 

"""Test table-based persistence of Mixtures""" 

filename = "testMixturePersistence.fits" 

mix1 = self.makeRandomMixture(3, 4, df=3.5) 

mix1.writeFits(filename) 

mix2 = lsst.meas.modelfit.Mixture.readFits(filename) 

self.assertEqual(mix1.getDegreesOfFreedom(), mix2.getDegreesOfFreedom()) 

self.assertEqual(len(mix1), len(mix2)) 

for c1, c2 in zip(mix1, mix2): 

self.assertFloatsAlmostEqual(c1.weight, c2.weight) 

self.assertFloatsAlmostEqual(c1.getMu(), c2.getMu()) 

self.assertFloatsAlmostEqual(c1.getSigma(), c2.getSigma()) 

os.remove(filename) 

 

def testDerivatives(self): 

epsilon = 1E-7 

g = self.makeRandomMixture(3, 4) 

t = self.makeRandomMixture(4, 3, df=4.0) 

 

def doTest(mixture, point): 

n = mixture.getDimension() 

# Compute numeric first derivatives 

testPoints = numpy.zeros((2*n, n), dtype=float) 

testPoints[:, :] = point[numpy.newaxis, :] 

for i in range(n): 

testPoints[i, i] += epsilon 

testPoints[n+i, i] -= epsilon 

testValues = numpy.zeros(2*n, dtype=float) 

mixture.evaluate(testPoints, testValues) 

numericGradient = numpy.zeros(n, dtype=float) 

for i in range(n): 

numericGradient[i] = (testValues[i] - testValues[n+i]) / (2.0 * epsilon) 

# Compute numeric second derivatives from analytic first derivatives 

numericHessian = numpy.zeros((n, n), dtype=float) 

testGrad1 = numpy.zeros(n, dtype=float) 

testGrad2 = numpy.zeros(n, dtype=float) 

testHessian = numpy.zeros((n, n), dtype=float) 

for i in range(n): 

testPoint = point.copy() 

testPoint[i] += epsilon 

mixture.evaluateDerivatives(testPoint, testGrad1, testHessian) 

testPoint[i] -= 2.0*epsilon 

mixture.evaluateDerivatives(testPoint, testGrad2, testHessian) 

numericHessian[i, :] = (testGrad1 - testGrad2) / (2.0 * epsilon) 

# Compute analytic derivatives and compare 

analyticGradient = numpy.zeros(n, dtype=float) 

analyticHessian = numpy.zeros((n, n), dtype=float) 

mixture.evaluateDerivatives(point, analyticGradient, analyticHessian) 

self.assertFloatsAlmostEqual(analyticGradient, numericGradient, rtol=1.5E-6) 

self.assertFloatsAlmostEqual(analyticHessian, numericHessian, rtol=1E-6) 

 

for x in numpy.random.randn(10, g.getDimension()): 

doTest(g, x) 

 

for x in numpy.random.randn(10, t.getDimension()): 

doTest(t, x) 

 

 

class TestMemory(lsst.utils.tests.MemoryTestCase): 

pass 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

188 ↛ 189line 188 didn't jump to line 189, because the condition on line 188 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()