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# 

# LSST Data Management System 

# Copyright 2008-2017 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 

from builtins import range 

import unittest 

 

import numpy as np 

 

try: 

import scipy.special 

except ImportError: 

scipy = None 

 

import lsst.utils.tests 

import lsst.afw.geom 

import lsst.shapelet.tests 

 

 

class HermiteTransformMatrixTestCase(lsst.shapelet.tests.ShapeletTestCase): 

 

def setUp(self): 

np.random.seed(500) 

self.order = 4 

self.size = lsst.shapelet.computeSize(self.order) 

self.htm = lsst.shapelet.HermiteTransformMatrix(self.order) 

 

@staticmethod 

def ht(n): 

"""return a scipy poly1d for the nth 'alternate' Hermite polynomial (i.e. Hermite polynomial 

with shapeley normalization)""" 

return (scipy.poly1d([(2**n * np.pi**0.5 * scipy.special.gamma(n+1))**(-0.5)]) * 

scipy.special.hermite(n)) 

 

def testCoefficientMatrices(self): 

coeff = self.htm.getCoefficientMatrix() 

coeffInv = self.htm.getInverseCoefficientMatrix() 

self.assertFloatsAlmostEqual(np.identity(self.order+1), np.dot(coeff, coeffInv)) 

# Both matrices should be lower-triangular 

for i in range(0, self.order+1): 

for j in range(i+1, self.order+1): 

self.assertEqual(coeff[i, j], 0.0) 

self.assertEqual(coeffInv[i, j], 0.0) 

# test coefficient matrix values against scipy Hermite polynomials 

if scipy is None: 

print("Skipping Hermite polynomial tests that require SciPy") 

return 

for n in range(0, self.order+1): 

poly = self.ht(n) 

self.assertFloatsAlmostEqual(coeff[n, :n+1], poly.c[::-1], atol=1E-15) 

 

def testTransformMatrix(self): 

if scipy is None: 

print("Skipping transform tests that require SciPy") 

return 

 

s = lsst.afw.geom.LinearTransform.makeScaling(2.0, 1.5) 

r = lsst.afw.geom.LinearTransform.makeRotation(0.30*lsst.afw.geom.radians) 

transforms = [s, r, s*r*s] 

testPoints = np.random.randn(10, 2) 

for transform in transforms: 

m = self.htm.compute(transform) 

for testPoint in testPoints: 

assert(testPoint.size == 2) 

origPoint = lsst.afw.geom.Point2D(testPoint[0], testPoint[1]) 

transPoint = transform(origPoint) 

for i, inx, iny in lsst.shapelet.HermiteIndexGenerator(self.order): 

v1 = self.ht(inx)(transPoint.getX()) * self.ht(iny)(transPoint.getY()) 

v2 = 0.0 

for j, jnx, jny in lsst.shapelet.HermiteIndexGenerator(self.order): 

v2 += m[i, j] * self.ht(jnx)(origPoint.getX()) * self.ht(jny)(origPoint.getY()) 

self.assertFloatsAlmostEqual(v1, v2, rtol=1E-11) 

 

 

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

pass 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

102 ↛ 103line 102 didn't jump to line 103, because the condition on line 102 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()