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import unittest 

import lsst.utils.tests 

import numpy as np 

import scipy 

from lsst.sims.photUtils import CosmologyObject 

from lsst.sims.photUtils.utils import comovingDistanceIntegrand, cosmologicalOmega 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

class CosmologyUnitTest(unittest.TestCase): 

 

def setUp(self): 

self.speedOfLight = 2.9979e5 # in km/sec 

 

def tearDown(self): 

del self.speedOfLight 

 

def testFlatLCDM(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for 

flat Lambda CDM models 

""" 

H0 = 50.0 

for Om0 in np.arange(start=0.1, stop=0.91, step=0.4): 

universe = CosmologyObject(H0=H0, Om0=Om0) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(1.0 - Om0 - universe.OmegaDarkEnergy(redshift=0.0), Og0+Onu0, 6) 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

self.assertEqual(universe.OmegaCurvature(), 0.0) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.1, step=2.0): 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl, = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testFlatW0Wa(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for 

flat models with w = w0 + wa * z / (1 + z) 

""" 

 

H0 = 96.0 

for Om0 in np.arange(start=0.1, stop=0.95, step=0.4): 

for w0 in np.arange(start=-1.1, stop=-0.89, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.11, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, w0=w0, wa=wa) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(1.0 - Om0 - universe.OmegaDarkEnergy(redshift=0.0), Og0+Onu0, 6) 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

self.assertEqual(universe.OmegaCurvature(), 0.0) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.1, step=2.0): 

 

wControl = w0 + wa*(1.0 - 1.0/(1.0+zz)) 

self.assertAlmostEqual(wControl, universe.w(redshift=zz), 6) 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0, 

w0=w0, wa=wa) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testFlatW0(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for flat 

models with constant w 

""" 

 

H0 = 96.0 

for Om0 in np.arange(start=0.1, stop=0.95, step=0.4): 

for w0 in np.arange(start=-1.5, stop=-0.49, step=1.0): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, w0=w0) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(1.0 - Om0 - universe.OmegaDarkEnergy(redshift=0.0), Og0+Onu0, 6) 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

self.assertEqual(universe.OmegaCurvature(), 0.0) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.1, step=2.0): 

 

self.assertAlmostEqual(w0, universe.w(redshift=zz), 6) 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0, 

w0=w0, wa=0.0) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testNonFlatLCDM(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for non-flat 

Lambda CDM models 

""" 

w0 = -1.0 

wa = 0.0 

H0 = 77.0 

 

for Om0 in np.arange(start=0.15, stop=0.96, step=0.4): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(universe.OmegaCurvature(redshift=0.0), Ok0, 10) 

self.assertAlmostEqual(1.0 - Ok0 - Om0 - universe.OmegaDarkEnergy(redshift=0.0), Og0+Onu0, 6) 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

Ode0 = universe.OmegaDarkEnergy(redshift=0.0) 

Ok0 = universe.OmegaCurvature(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.0, step=2.0): 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0, 

Ode0=Ode0) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(OkControl, universe.OmegaCurvature(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testNonFlatW0Wa(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for non-flat 

models with w = w0 + wa * z / (1+z) 

""" 

 

H0 = 60.0 

 

for Om0 in np.arange(start=0.15, stop=0.76, step=0.3): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop=-0.89, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.15, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(Ok0, universe.OmegaCurvature(redshift=0.0), 10) 

self.assertAlmostEqual(1.0 - Om0 - Ok0 - universe.OmegaDarkEnergy(redshift=0.0), 

Og0 + Onu0, 10) 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

Ode0 = universe.OmegaDarkEnergy(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.0, step=2.0): 

 

wControl = w0 + wa*(1.0 - 1.0/(1.0+zz)) 

self.assertAlmostEqual(wControl, universe.w(redshift=zz), 6) 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0, 

w0=w0, wa=wa, Ode0=Ode0) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(OkControl, universe.OmegaCurvature(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testNonFlatW0(self): 

""" 

Test the evolution of H and Omega_i as a function of redshift for non-flat 

models with constant w 

""" 

 

H0 = 60.0 

 

for Om0 in np.arange(start=0.15, stop=0.76, step=0.3): 

for Ok0 in np.arange(start=0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop = -0.89, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0) 

 

Og0 = universe.OmegaPhotons(redshift=0.0) 

Onu0 = universe.OmegaNeutrinos(redshift=0.0) 

 

self.assertAlmostEqual(universe.OmegaMatter(redshift=0.0), Om0, 10) 

self.assertAlmostEqual(Ok0, universe.OmegaCurvature(redshift=0.0), 10) 

self.assertAlmostEqual(1.0 - Om0 - Ok0 - universe.OmegaDarkEnergy(redshift=0.0), 

Og0+Onu0, 10) 

 

self.assertAlmostEqual(universe.H(redshift=0.0), H0, 10) 

 

Om0 = universe.OmegaMatter(redshift=0.0) 

Ode0 = universe.OmegaDarkEnergy(redshift=0.0) 

 

for zz in np.arange(start=0.0, stop=4.0, step=2.0): 

 

self.assertAlmostEqual(w0, universe.w(redshift=zz), 6) 

 

Hcontrol, OmControl, OdeControl, OgControl, OnuControl, \ 

OkControl = cosmologicalOmega(zz, H0, Om0, Og0=Og0, Onu0=Onu0, 

w0=w0, wa=0.0, Ode0=Ode0) 

 

self.assertAlmostEqual(OmControl, universe.OmegaMatter(redshift=zz), 6) 

self.assertAlmostEqual(OdeControl, universe.OmegaDarkEnergy(redshift=zz), 6) 

self.assertAlmostEqual(OgControl, universe.OmegaPhotons(redshift=zz), 6) 

self.assertAlmostEqual(OnuControl, universe.OmegaNeutrinos(redshift=zz), 6) 

self.assertAlmostEqual(OkControl, universe.OmegaCurvature(redshift=zz), 6) 

self.assertAlmostEqual(Hcontrol, universe.H(redshift=zz), 6) 

 

del universe 

 

def testComovingDistance(self): 

""" 

Test comoving distance calculation 

 

Note: this is comoving distance defined as X in the FRW metric 

 

ds^2 = -c^2 dt^2 + a^2 dX^2 + sin^2(X) dOmega^2 

 

where spatial curvature is accounted for in the sin function 

""" 

 

H0 = 73.0 

for Om0 in np.arange(start=0.15, stop=0.56, step=0.2): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop=-0.85, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.115, step=0.02): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

Og0 = universe.OmegaPhotons() 

Onu0 = universe.OmegaNeutrinos() 

Ode0 = universe.OmegaDarkEnergy() 

 

for zz in np.arange(start=0.1, stop=4.2, step=2.0): 

comovingControl = universe.comovingDistance(redshift=zz) 

 

comovingTest = \ 

self.speedOfLight*scipy.integrate.quad(comovingDistanceIntegrand, 0.0, zz, 

args=(H0, Om0, Ode0, 

Og0, Onu0, w0, wa))[0] 

 

self.assertAlmostEqual(comovingControl/comovingTest, 1.0, 4) 

 

def testLuminosityDistance(self): 

""" 

Test the calculation of the luminosity distance 

""" 

 

H0 = 73.0 

 

for Om0 in np.arange(start=0.15, stop=0.56, step=0.2): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop=-0.85, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.11, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

 

sqrtkCurvature = \ 

np.sqrt(np.abs(universe.OmegaCurvature()))*universe.H()/self.speedOfLight 

 

Og0 = universe.OmegaPhotons() 

Onu0 = universe.OmegaNeutrinos() 

Ode0 = universe.OmegaDarkEnergy() 

 

for zz in np.arange(start=0.1, stop=4.2, step=2.0): 

luminosityControl = universe.luminosityDistance(redshift=zz) 

 

comovingDistance = \ 

self.speedOfLight*scipy.integrate.quad(comovingDistanceIntegrand, 0.0, zz, 

args=(H0, Om0, Ode0, Og0, Onu0, w0, wa))[0] 

 

if universe.OmegaCurvature() < 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sin(nn) 

luminosityTest = (1.0+zz)*nn/sqrtkCurvature 

elif universe.OmegaCurvature() > 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sinh(nn) 

luminosityTest = (1.0+zz)*nn/sqrtkCurvature 

else: 

luminosityTest = (1.0+zz)*comovingDistance 

self.assertAlmostEqual(luminosityControl/luminosityTest, 1.0, 4) 

 

def testAngularDiameterDistance(self): 

""" 

Test the calculation of the angular diameter distance 

""" 

 

H0 = 56.0 

universe = CosmologyObject() 

for Om0 in np.arange(start=0.15, stop=0.56, step=0.2): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop=-0.85, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.11, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

 

sqrtkCurvature = \ 

np.sqrt(np.abs(universe.OmegaCurvature()))*universe.H()/self.speedOfLight 

 

Og0 = universe.OmegaPhotons() 

Onu0 = universe.OmegaNeutrinos() 

Ode0 = universe.OmegaDarkEnergy() 

 

for zz in np.arange(start=0.1, stop=4.2, step=2.0): 

angularControl = universe.angularDiameterDistance(redshift=zz) 

 

comovingDistance = \ 

self.speedOfLight*scipy.integrate.quad(comovingDistanceIntegrand, 0.0, zz, 

args=(H0, Om0, Ode0, Og0, Onu0, w0, wa))[0] 

 

if universe.OmegaCurvature() < 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sin(nn) 

angularTest = nn/sqrtkCurvature 

elif universe.OmegaCurvature() > 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sinh(nn) 

angularTest = nn/sqrtkCurvature 

else: 

angularTest = comovingDistance 

angularTest /= (1.0+zz) 

self.assertAlmostEqual(angularControl/angularTest, 1.0, 4) 

 

def testDistanceModulus(self): 

""" 

Test the calculation of the distance modulus out to a certain redshift 

""" 

H0 = 73.0 

 

universe = CosmologyObject() 

for Om0 in np.arange(start=0.15, stop=0.56, step=0.2): 

for Ok0 in np.arange(start=-0.1, stop=0.11, step=0.2): 

for w0 in np.arange(start=-1.1, stop=-0.85, step=0.2): 

for wa in np.arange(start=-0.1, stop=0.11, step=0.2): 

 

universe = CosmologyObject(H0=H0, Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

 

sqrtkCurvature = \ 

np.sqrt(np.abs(universe.OmegaCurvature()))*universe.H()/self.speedOfLight 

 

Og0 = universe.OmegaPhotons() 

Onu0 = universe.OmegaNeutrinos() 

Ode0 = universe.OmegaDarkEnergy() 

 

for zz in np.arange(start=0.1, stop=4.2, step=2.0): 

modulusControl = universe.distanceModulus(redshift=zz) 

 

comovingDistance = \ 

self.speedOfLight*scipy.integrate.quad(comovingDistanceIntegrand, 0.0, zz, 

args=(H0, Om0, Ode0, Og0, 

Onu0, w0, wa))[0] 

 

if universe.OmegaCurvature() < 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sin(nn) 

luminosityDistance = (1.0+zz)*nn/sqrtkCurvature 

elif universe.OmegaCurvature() > 0.0: 

nn = sqrtkCurvature*comovingDistance 

nn = np.sinh(nn) 

luminosityDistance = (1.0+zz)*nn/sqrtkCurvature 

else: 

luminosityDistance = (1.0+zz)*comovingDistance 

 

modulusTest = 5.0*np.log10(luminosityDistance) + 25.0 

self.assertAlmostEqual(modulusControl/modulusTest, 1.0, 4) 

 

def testDistanceModulusAtZero(self): 

""" 

Test to make sure that the distance modulus is set to zero if the distance modulus method 

returns a negative number 

""" 

universe = CosmologyObject() 

ztest = [0.0, 1.0, 2.0, 0.0, 3.0] 

mm = universe.distanceModulus(redshift=ztest) 

self.assertEqual(mm[0], 0.0) 

self.assertEqual(mm[3], 0.0) 

self.assertEqual(mm[1], 5.0*np.log10(universe.luminosityDistance(ztest[1])) + 25.0) 

self.assertEqual(mm[2], 5.0*np.log10(universe.luminosityDistance(ztest[2])) + 25.0) 

self.assertEqual(mm[4], 5.0*np.log10(universe.luminosityDistance(ztest[4])) + 25.0) 

 

def testGetCurrent(self): 

""" 

Test to make sure that getCurrent returns the activeCosmology 

""" 

 

for Om0 in np.arange(start=0.2, stop=0.5, step=0.29): 

for Ok0 in np.arange(start=-0.2, stop=0.2, step=0.39): 

for w0 in np.arange(start=-1.2, stop=-0.7, step=0.49): 

for wa in np.arange(start=-0.2, stop=0.2, step=0.39): 

universe = CosmologyObject(Om0=Om0, Ok0=Ok0, w0=w0, wa=wa) 

testUniverse = universe.getCurrent() 

 

for zz in np.arange(start=1.0, stop=2.1, step=1.0): 

self.assertEqual(universe.OmegaMatter(redshift=zz), 

testUniverse.Om(zz)) 

self.assertEqual(universe.OmegaDarkEnergy(redshift=zz), 

testUniverse.Ode(zz)) 

self.assertEqual(universe.OmegaPhotons(redshift=zz), 

testUniverse.Ogamma(zz)) 

self.assertEqual(universe.OmegaNeutrinos(redshift=zz), 

testUniverse.Onu(zz)) 

self.assertEqual(universe.OmegaCurvature(redshift=zz), 

testUniverse.Ok(zz)) 

 

 

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

pass 

 

459 ↛ 460line 459 didn't jump to line 460, because the condition on line 459 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()