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# 

# Developed for the LSST Data Management System. 

# This product includes software developed by the LSST Project 

# (https://www.lsst.org). 

# See the COPYRIGHT file at the top-level directory of this distribution 

# for details of code ownership. 

# 

# 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 GNU General Public License 

# along with this program. If not, see <https://www.gnu.org/licenses/>. 

# 

 

""" 

Tests for Angle 

 

Run with: 

angle.py 

or 

python 

>>> import angle; angle.run() 

""" 

import itertools 

import math 

import unittest 

 

import numpy as np 

 

import lsst.utils.tests 

import lsst.geom 

 

 

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

"""A test case for Angle""" 

 

def setUp(self): 

self.pi = lsst.geom.Angle(math.pi, lsst.geom.radians) 

self.d = 180*lsst.geom.degrees 

 

def testCtor(self): 

self.assertEqual(self.pi, math.pi) 

self.assertEqual(self.pi, lsst.geom.Angle(math.pi)) 

self.assertEqual(self.pi, self.d) 

 

dd = lsst.geom.Angle(180, lsst.geom.degrees) 

self.assertEqual(self.d, dd) 

dd = lsst.geom.Angle(60*180, lsst.geom.arcminutes) 

self.assertEqual(self.d, dd) 

dd = lsst.geom.Angle(60*60*180, lsst.geom.arcseconds) 

self.assertEqual(self.d, dd) 

dd = lsst.geom.Angle(60*60*180*1000, lsst.geom.milliarcseconds) 

self.assertEqual(self.d, dd) 

 

def testArithmetic(self): 

self.assertTrue(lsst.geom.isAngle(self.pi)) 

self.assertFalse(lsst.geom.isAngle(self.pi.asRadians())) 

self.assertFalse(lsst.geom.isAngle(math.pi)) 

 

with self.assertRaises(TypeError): 

self.pi - math.pi # subtracting a float from an Angle 

self.assertEqual(self.pi - math.pi*lsst.geom.radians, 0) 

self.assertEqual(self.pi - self.d, 0) # can subtract Angles 

 

with self.assertRaises(TypeError): 

self.pi + math.pi # adding a float to an Angle 

 

with self.assertRaises(NotImplementedError): 

self.pi*lsst.geom.degrees # self.pi is already an Angle 

 

self.assertEqual((self.pi + self.d).asAngularUnits(lsst.geom.degrees), 

360) 

self.assertEqual((self.pi).asRadians(), math.pi) 

self.assertEqual((self.pi/2).asDegrees(), 90) 

self.assertEqual((self.pi*2).asArcminutes(), 360*60) 

self.assertEqual((self.pi*2).asArcseconds(), 360*60*60) 

self.assertEqual((self.pi*2).asMilliarcseconds(), 360*60*60*1000) 

self.assertEqual((-self.pi).asRadians(), -math.pi) 

 

with self.assertRaises(TypeError): 

2.0 / self.pi # dividing a float by an Angle 

with self.assertRaises(TypeError): 

self.pi / self.pi 

 

# automatic conversion to double 

self.assertEqual(math.sin(self.pi/2), 1.0) 

 

def testAbs(self): 

self.assertEqual(abs(0.0*lsst.geom.degrees - self.pi), self.pi) 

 

def testPi(self): 

self.assertEqual(lsst.geom.PI, math.pi) 

 

def testComparison(self): 

a2 = 2.0 * lsst.geom.arcseconds 

a1 = 0.5 * lsst.geom.arcseconds 

a3 = 0.5 * lsst.geom.arcseconds 

self.assertEqual(a1, a3) 

self.assertNotEqual(a1, a2) 

self.assertLessEqual(a1, a2) 

self.assertLess(a1, a2) 

self.assertGreater(a2, a1) 

self.assertGreaterEqual(a2, a1) 

 

self.assertFalse(a1 != a3) 

self.assertFalse(a1 == a2) 

self.assertFalse(a1 >= a2) 

self.assertFalse(a1 > a2) 

self.assertFalse(a2 < a1) 

self.assertFalse(a2 <= a1) 

 

self.assertTrue(a1 == float(a1)) 

self.assertTrue(float(a1) == a1) 

 

def testTrig(self): 

self.assertEqual(math.cos(self.d), -1.0) 

self.assertAlmostEqual(math.sin(self.d), 0.0, places=15) 

thirty = 30.*lsst.geom.degrees 

self.assertAlmostEqual(math.sin(thirty), 0.5, places=15) 

 

def testSeparation(self): 

"""Tests whether angle differences are computed as expected. 

 

Wrapping accuracy is assumed tested by testWrap. 

""" 

angleBase = 0.0*lsst.geom.degrees 

angleWrap = 360.0*lsst.geom.degrees 

angleHalf = -180.0*lsst.geom.degrees 

angleOdd = 32.0*lsst.geom.degrees 

 

self.checkWrappedAngle(angleBase.separation(angleWrap), 

0.0*lsst.geom.degrees) 

self.checkWrappedAngle(angleWrap.separation(angleBase), 

0.0*lsst.geom.degrees) 

 

self.checkWrappedAngle(angleBase.separation(angleHalf), angleHalf) 

self.checkWrappedAngle(angleHalf.separation(angleBase), angleHalf) 

 

self.checkWrappedAngle(angleWrap.separation(angleHalf), angleHalf) 

self.checkWrappedAngle(angleHalf.separation(angleWrap), angleHalf) 

 

self.checkWrappedAngle(angleOdd.separation(angleBase), angleOdd) 

self.checkWrappedAngle(angleBase.separation(angleOdd), -angleOdd) 

 

self.checkWrappedAngle(angleOdd.separation(angleWrap), angleOdd) 

self.checkWrappedAngle(angleWrap.separation(angleOdd), -angleOdd) 

 

def checkWrappedAngle(self, observed, expected): 

"""Tests whether an angle wrapped to [-pi, pi) both matches its expected 

value and strictly satisfies its range restriction. 

""" 

obs = observed.asRadians() 

exp = expected.asRadians() 

self.assertAlmostEqual(obs, exp, delta=np.finfo(float).eps) 

self.assertGreaterEqual(obs, -math.pi) 

self.assertLess(obs, math.pi) 

 

def testWrap(self): 

eps = np.finfo(float).eps 

self.assertNotEqual(1 + eps, eps) 

for wrap, offset, epsMult in itertools.product( 

(-1000, -10, -1, 0, 1, 10, 1000), 

(-2*math.pi, -math.pi, -math.pi*0.5, 0.0, math.pi*0.5, math.pi*0.75, math.pi, math.pi*2.0), 

(-3, -2, -1, 0, 1, 2, 3), 

): 

angRad = (offset + (wrap*math.pi)) * (1 + (eps*epsMult)) 

ang = angRad * lsst.geom.radians 

 

posAng = (angRad * lsst.geom.radians).wrap() 

self.assertAnglesAlmostEqual(ang, posAng) 

posAngRad = posAng.asRadians() 

posAngDeg = posAng.asDegrees() 

posAngArcmin = posAng.asArcminutes() 

posAngArcsec = posAng.asArcseconds() 

posAngMilliarcsec = posAng.asMilliarcseconds() 

# the code promises 0 <= posAng for all units 

self.assertGreaterEqual(posAngRad, 0) 

self.assertGreaterEqual(posAngDeg, 0) 

self.assertGreaterEqual(posAngArcmin, 0) 

self.assertGreaterEqual(posAngArcsec, 0) 

self.assertGreaterEqual(posAngMilliarcsec, 0) 

# wrap promises posAng < 2*pi only for radians, 

# but it seems to work for all units 

self.assertLess(posAngRad, 2*math.pi) 

self.assertLess(posAngDeg, 360) 

self.assertLess(posAngArcmin, 360 * 60) 

self.assertLess(posAngArcsec, 360 * 3600) 

self.assertLess(posAngMilliarcsec, 360 * 3.6e6) 

 

ctrAng = (angRad * lsst.geom.radians).wrapCtr() 

self.assertAnglesAlmostEqual(ang, ctrAng) 

ctrAngRad = ctrAng.asRadians() 

ctrAngDeg = ctrAng.asDegrees() 

ctrAngArcmin = ctrAng.asArcminutes() 

ctrAngArcsec = ctrAng.asArcseconds() 

ctrAngMilliarcsec = ctrAng.asMilliarcseconds() 

# wrapCtr promises -pi <= ctrAngRad < pi only for radians, 

# but it seems to work for all units 

self.assertGreaterEqual(ctrAngRad, -math.pi) 

self.assertGreaterEqual(ctrAngDeg, -180) 

self.assertGreaterEqual(ctrAngArcmin, -180 * 60) 

self.assertGreaterEqual(ctrAngArcsec, -180 * 3600) 

self.assertGreaterEqual(ctrAngMilliarcsec, -180 * 3.6e6) 

self.assertLess(ctrAngRad, math.pi) 

self.assertLess(ctrAngDeg, 180) 

self.assertLess(ctrAngArcmin, 180 * 60) 

self.assertLess(ctrAngArcsec, 180 * 3600) 

 

for refAngBase, refAngWrap, refEpsMult in itertools.product( 

(-math.pi, 0.0, math.pi, math.pi*2.0), 

range(-10, 11, 2), 

(-3, -2, -1, 0, 1, 2, 3), 

): 

refAngRad = refAngBase * (1 + (eps * refEpsMult)) + refAngWrap * math.pi * 2.0 

refAng = refAngRad * lsst.geom.radians 

refAngDeg = refAng.asDegrees() 

refAngArcmin = refAng.asArcminutes() 

refAngArcsec = refAng.asArcseconds() 

refAngMilliarcsec = refAng.asMilliarcseconds() 

nearAng = (angRad * lsst.geom.radians).wrapNear(refAng) 

self.assertAnglesAlmostEqual(ang, nearAng) 

nearAngRad = nearAng.asRadians() 

nearAngDeg = nearAng.asDegrees() 

nearAngArcmin = nearAng.asArcminutes() 

nearAngArcsec = nearAng.asArcseconds() 

nearAngMilliarcsec = nearAng.asMilliarcseconds() 

 

fudgeFactor = 5 # 1 and 2 are too small for one case, 3 works; 5 has margin 

relEps = max(1, nearAngRad / math.pi, refAngRad / math.pi) * eps * fudgeFactor 

piWithSlop = math.pi * (1 + relEps) 

oneEightyWithSlop = 180 * (1 + relEps) 

 

# wrapNear promises nearAngRad - refAngRad >= -pi 

# for radians but has known failures due to 

# roundoff error for other units and for < pi 

self.assertGreaterEqual(nearAngRad - refAngRad, -math.pi) 

self.assertGreaterEqual(nearAngDeg - refAngDeg, -oneEightyWithSlop) 

self.assertGreaterEqual(nearAngArcmin - refAngArcmin, -oneEightyWithSlop * 60) 

self.assertGreaterEqual(nearAngArcsec - refAngArcsec, -oneEightyWithSlop * 3600) 

self.assertGreaterEqual(nearAngMilliarcsec - refAngMilliarcsec, -oneEightyWithSlop * 3.6e6) 

self.assertLessEqual(nearAngRad - refAngRad, piWithSlop) 

self.assertLessEqual(nearAngDeg - refAngDeg, oneEightyWithSlop) 

self.assertLessEqual(nearAngArcmin - refAngArcmin, oneEightyWithSlop * 60) 

self.assertLessEqual(nearAngArcsec - refAngArcsec, oneEightyWithSlop * 3600) 

self.assertLessEqual(nearAngMilliarcsec - refAngMilliarcsec, oneEightyWithSlop * 3.6e6) 

 

 

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

pass 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

263 ↛ 264line 263 didn't jump to line 264, because the condition on line 263 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()