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from __future__ import division 

from builtins import zip 

from builtins import range 

import unittest 

import numpy as np 

import lsst.utils.tests 

import lsst.sims.utils as utils 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

def controlAltAzFromRaDec(raRad_in, decRad_in, longRad, latRad, mjd): 

""" 

Converts RA and Dec to altitude and azimuth 

 

@param [in] raRad is the RA in radians 

(observed geocentric) 

 

@param [in] decRad is the Dec in radians 

(observed geocentric) 

 

@param [in] longRad is the longitude of the observer in radians 

(positive east of the prime meridian) 

 

@param [in[ latRad is the latitude of the observer in radians 

(positive north of the equator) 

 

@param [in] mjd is the universal time expressed as an MJD 

 

@param [out] altitude in radians 

 

@param [out[ azimuth in radians 

 

see: http://www.stargazing.net/kepler/altaz.html#twig04 

""" 

obs = utils.ObservationMetaData(mjd=utils.ModifiedJulianDate(UTC=mjd), 

site=utils.Site(longitude=np.degrees(longRad), 

latitude=np.degrees(latRad), 

name='LSST')) 

 

if hasattr(raRad_in, '__len__'): 

raRad, decRad = utils._observedFromICRS(raRad_in, decRad_in, obs_metadata=obs, 

epoch=2000.0, includeRefraction=True) 

else: 

raRad, decRad = utils._observedFromICRS(raRad_in, decRad_in, 

obs_metadata=obs, epoch=2000.0, includeRefraction=True) 

 

lst = utils.calcLmstLast(obs.mjd.UT1, longRad) 

last = lst[1] 

haRad = np.radians(last * 15.) - raRad 

 

sinDec = np.sin(decRad) 

cosLat = np.cos(latRad) 

sinLat = np.sin(latRad) 

sinAlt = sinDec*sinLat + np.cos(decRad)*cosLat*np.cos(haRad) 

altRad = np.arcsin(sinAlt) 

azRad = np.arccos((sinDec - sinAlt*sinLat) / (np.cos(altRad)*cosLat)) 

azRadOut = np.where(np.sin(haRad) >= 0.0, 2.0 * np.pi - azRad, azRad) 

if isinstance(altRad, float): 

return altRad, float(azRadOut) 

return altRad, azRadOut 

 

 

class CompoundCoordinateTransformationsTests(unittest.TestCase): 

 

def setUp(self): 

self.rng = np.random.RandomState(32) 

self.mjd = 57087.0 

self.tolerance = 1.0e-5 

 

def testExceptions(self): 

""" 

Test to make sure that methods complain when incorrect data types are passed. 

""" 

obs = utils.ObservationMetaData(pointingRA=55.0, pointingDec=-72.0, mjd=53467.8) 

 

raFloat = 1.1 

raList = np.array([0.2, 0.3]) 

 

decFloat = 1.1 

decList = np.array([0.2, 0.3]) 

 

self.assertRaises(RuntimeError, utils._altAzPaFromRaDec, raList, decFloat, obs) 

self.assertRaises(RuntimeError, utils._altAzPaFromRaDec, raFloat, decList, obs) 

utils._altAzPaFromRaDec(raFloat, decFloat, obs) 

utils._altAzPaFromRaDec(raList, decList, obs) 

 

self.assertRaises(RuntimeError, utils._raDecFromAltAz, raList, decFloat, obs) 

self.assertRaises(RuntimeError, utils._raDecFromAltAz, raFloat, decList, obs) 

utils._raDecFromAltAz(raFloat, decFloat, obs) 

utils._raDecFromAltAz(raList, decList, obs) 

 

self.assertRaises(RuntimeError, utils.altAzPaFromRaDec, raList, decFloat, obs) 

self.assertRaises(RuntimeError, utils.altAzPaFromRaDec, raFloat, decList, obs) 

utils.altAzPaFromRaDec(raFloat, decFloat, obs) 

utils.altAzPaFromRaDec(raList, decList, obs) 

 

self.assertRaises(RuntimeError, utils.raDecFromAltAz, raList, decFloat, obs) 

self.assertRaises(RuntimeError, utils.raDecFromAltAz, raFloat, decList, obs) 

utils.raDecFromAltAz(raFloat, decFloat, obs) 

utils.raDecFromAltAz(raList, decList, obs) 

 

def test_raDecFromAltAz(self): 

""" 

Test conversion of Alt, Az to Ra, Dec using data on the Sun 

 

This site gives the altitude and azimuth of the Sun as a function 

of time and position on the earth 

 

http://aa.usno.navy.mil/data/docs/AltAz.php 

 

This site gives the apparent geocentric RA, Dec of major celestial objects 

as a function of time 

 

http://aa.usno.navy.mil/data/docs/geocentric.php 

 

This site converts calendar dates into Julian Dates 

 

http://aa.usno.navy.mil/data/docs/JulianDate.php 

""" 

 

hours = np.radians(360.0 / 24.0) 

minutes = hours / 60.0 

seconds = minutes / 60.0 

 

longitude_list = [] 

latitude_list = [] 

mjd_list = [] 

alt_list = [] 

az_list = [] 

ra_app_list = [] 

dec_app_list = [] 

 

longitude_list.append(np.radians(-22.0 - 33.0 / 60.0)) 

latitude_list.append(np.radians(11.0 + 45.0 / 60.0)) 

mjd_list.append(2457364.958333 - 2400000.5) # 8 December 2015 11:00 UTC 

alt_list.append(np.radians(41.1)) 

az_list.append(np.radians(134.7)) 

ra_app_list.append(16.0 * hours + 59.0 * minutes + 16.665 * seconds) 

dec_app_list.append(np.radians(-22.0 - 42.0 / 60.0 - 2.94 / 3600.0)) 

 

longitude_list.append(np.radians(-22.0 - 33.0 / 60.0)) 

latitude_list.append(np.radians(11.0 + 45.0 / 60.0)) 

mjd_list.append(2457368.958333 - 2400000.5) # 12 December 2015 11:00 UTC 

alt_list.append(np.radians(40.5)) 

az_list.append(np.radians(134.7)) 

ra_app_list.append(17.0 * hours + 16.0 * minutes + 51.649 * seconds) 

dec_app_list.append(np.radians(-23.0 - 3 / 60.0 - 50.35 / 3600.0)) 

 

longitude_list.append(np.radians(145.0 + 23.0 / 60.0)) 

latitude_list.append(np.radians(-64.0 - 5.0 / 60.0)) 

mjd_list.append(2456727.583333 - 2400000.5) # 11 March 2014, 02:00 UTC 

alt_list.append(np.radians(29.5)) 

az_list.append(np.radians(8.2)) 

ra_app_list.append(23.0 * hours + 24.0 * minutes + 46.634 * seconds) 

dec_app_list.append(np.radians(-3.0 - 47.0 / 60.0 - 47.81 / 3600.0)) 

 

longitude_list.append(np.radians(145.0 + 23.0 / 60.0)) 

latitude_list.append(np.radians(-64.0 - 5.0 / 60.0)) 

mjd_list.append(2456731.583333 - 2400000.5) # 15 March 2014, 02:00 UTC 

alt_list.append(np.radians(28.0)) 

az_list.append(np.radians(7.8)) 

ra_app_list.append(23.0 * hours + 39.0 * minutes + 27.695 * seconds) 

dec_app_list.append(np.radians(-2.0 - 13.0 / 60.0 - 18.32 / 3600.0)) 

 

for longitude, latitude, mjd, alt, az, ra_app, dec_app in \ 

zip(longitude_list, latitude_list, mjd_list, alt_list, az_list, 

ra_app_list, dec_app_list): 

 

obs = utils.ObservationMetaData(site=utils.Site(longitude=np.degrees(longitude), 

latitude=np.degrees(latitude), name='LSST'), 

mjd=utils.ModifiedJulianDate(UTC=mjd)) 

 

ra_icrs, dec_icrs = utils._raDecFromAltAz(alt, az, obs) 

ra_test, dec_test = utils._appGeoFromICRS(ra_icrs, dec_icrs, mjd=obs.mjd) 

 

distance = np.degrees(utils.haversine(ra_app, dec_app, ra_test, dec_test)) 

# this is all the precision we have in the alt,az data taken from the USNO 

self.assertLess(distance, 0.1) 

 

correction = np.degrees(utils.haversine(ra_test, dec_test, ra_icrs, dec_icrs)) 

self.assertLess(distance, correction) 

 

def testAltAzRADecRoundTrip(self): 

""" 

Test that altAzPaFromRaDec and raDecFromAltAz really invert each other 

""" 

 

mjd = 58350.0 

 

alt_in = [] 

az_in = [] 

for alt in np.arange(0.0, 90.0, 10.0): 

for az in np.arange(0.0, 360.0, 10.0): 

alt_in.append(alt) 

az_in.append(az) 

 

alt_in = np.array(alt_in) 

az_in = np.array(az_in) 

 

for lon in (0.0, 90.0, 135.0): 

for lat in (60.0, 30.0, -60.0, -30.0): 

 

obs = utils.ObservationMetaData(mjd=mjd, 

site=utils.Site(longitude=lon, latitude=lat, name='LSST')) 

 

ra_in, dec_in = utils.raDecFromAltAz(alt_in, az_in, obs) 

 

self.assertIsInstance(ra_in, np.ndarray) 

self.assertIsInstance(dec_in, np.ndarray) 

 

self.assertFalse(np.isnan(ra_in).any(), msg='there were NaNs in ra_in') 

self.assertFalse(np.isnan(dec_in).any(), msg='there were NaNs in dec_in') 

 

# test that passing them in one at a time gives the same answer 

for ix in range(len(alt_in)): 

ra_f, dec_f = utils.raDecFromAltAz(alt_in[ix], az_in[ix], obs) 

self.assertIsInstance(ra_f, np.float) 

self.assertIsInstance(dec_f, np.float) 

self.assertAlmostEqual(ra_f, ra_in[ix], 12) 

self.assertAlmostEqual(dec_f, dec_in[ix], 12) 

 

alt_out, az_out, pa_out = utils.altAzPaFromRaDec(ra_in, dec_in, obs) 

 

self.assertFalse(np.isnan(pa_out).any(), msg='there were NaNs in pa_out') 

 

for alt_c, az_c, alt_t, az_t in \ 

zip(np.radians(alt_in), np.radians(az_in), np.radians(alt_out), np.radians(az_out)): 

distance = utils.arcsecFromRadians(utils.haversine(az_c, alt_c, az_t, alt_t)) 

self.assertLess(distance, 0.2) 

# not sure why 0.2 arcsec is the limiting precision of this test 

 

def testAltAzFromRaDec(self): 

""" 

Test conversion from RA, Dec to Alt, Az 

""" 

 

nSamples = 100 

ra = self.rng.random_sample(nSamples)*2.0*np.pi 

dec = (self.rng.random_sample(nSamples)-0.5)*np.pi 

lon_rad = 1.467 

lat_rad = -0.234 

controlAlt, controlAz = controlAltAzFromRaDec(ra, dec, 

lon_rad, lat_rad, 

self.mjd) 

 

obs = utils.ObservationMetaData(mjd=utils.ModifiedJulianDate(UTC=self.mjd), 

site=utils.Site(longitude=np.degrees(lon_rad), 

latitude=np.degrees(lat_rad), 

name='LSST')) 

 

# verify parallactic angle against an expression from 

# http://www.astro.washington.edu/groups/APO/Mirror.Motions/Feb.2000.Image.Jumps/report.html#Image%20motion%20directions 

# 

ra_obs, dec_obs = utils._observedFromICRS(ra, dec, obs_metadata=obs, epoch=2000.0, 

includeRefraction=True) 

 

lmst, last = utils.calcLmstLast(obs.mjd.UT1, lon_rad) 

hourAngle = np.radians(last * 15.0) - ra_obs 

controlSinPa = np.sin(hourAngle) * np.cos(lat_rad) / np.cos(controlAlt) 

 

testAlt, testAz, testPa = utils._altAzPaFromRaDec(ra, dec, obs) 

 

distance = utils.arcsecFromRadians(utils.haversine(controlAz, controlAlt, testAz, testAlt)) 

self.assertLess(distance.max(), 0.0001) 

self.assertLess(np.abs(np.sin(testPa) - controlSinPa).max(), self.tolerance) 

 

# test non-vectorized version 

for r, d in zip(ra, dec): 

controlAlt, controlAz = controlAltAzFromRaDec(r, d, lon_rad, lat_rad, self.mjd) 

testAlt, testAz, testPa = utils._altAzPaFromRaDec(r, d, obs) 

lmst, last = utils.calcLmstLast(obs.mjd.UT1, lon_rad) 

r_obs, dec_obs = utils._observedFromICRS(r, d, obs_metadata=obs, 

epoch=2000.0, includeRefraction=True) 

hourAngle = np.radians(last * 15.0) - r_obs 

controlSinPa = np.sin(hourAngle) * np.cos(lat_rad) / np.cos(controlAlt) 

distance = utils.arcsecFromRadians(utils.haversine(controlAz, controlAlt, testAz, testAlt)) 

self.assertLess(distance, 0.0001) 

self.assertLess(np.abs(np.sin(testPa) - controlSinPa), self.tolerance) 

 

def test_altAzPaFromRaDec_no_refraction(self): 

""" 

Test that altAzPaFromRaDec gives a sane answer when you turn off 

refraction. 

""" 

 

rng = np.random.RandomState(44) 

n_samples = 10 

n_batches = 10 

for i_batch in range(n_batches): 

# first, generate some sane RA, Dec values by generating sane 

# Alt, Az values with refraction and converting them into 

# RA, Dec 

alt_sane = rng.random_sample(n_samples)*45.0 + 45.0 

az_sane = rng.random_sample(n_samples)*360.0 

mjd_input = rng.random_sample(n_samples)*10000.0 + 40000.0 

mjd_list = utils.ModifiedJulianDate.get_list(TAI=mjd_input) 

 

ra_sane = [] 

dec_sane = [] 

obs_sane = [] 

for alt, az, mjd in zip(alt_sane, az_sane, mjd_list): 

obs = utils.ObservationMetaData(mjd=mjd) 

ra, dec = utils.raDecFromAltAz(alt, az, obs) 

ra_sane.append(ra) 

dec_sane.append(dec) 

obs_sane.append(obs) 

 

# Now, loop over our refracted RA, Dec, Alt, Az values. 

# Convert from RA, Dec to unrefracted Alt, Az. Then, apply refraction 

# with our applyRefraction method. Check that the resulting refracted 

# zenith distance is: 

# 1) within 0.1 arcsec of the zenith distance of the already refracted 

# alt value calculated above 

# 

# 2) closer to the zenith distance calculated above than to the 

# unrefracted zenith distance 

for ra, dec, obs, alt_ref, az_ref in \ 

zip(ra_sane, dec_sane, obs_sane, alt_sane, az_sane): 

 

alt, az, pa = utils.altAzPaFromRaDec(ra, dec, obs, 

includeRefraction = False) 

 

tanz, tanz3 = utils.refractionCoefficients(site=obs.site) 

refracted_zd = utils.applyRefraction(np.radians(90.0-alt), tanz, tanz3) 

 

# Check that the two independently refracted zenith distances agree 

# to within 0.1 arcsec 

self.assertLess(np.abs(utils.arcsecFromRadians(refracted_zd) - 

utils.arcsecFromRadians(np.radians(90.0-alt_ref))), 

0.1) 

 

# Check that the two refracted zenith distances are closer to each other 

# than to the unrefracted zenith distance 

self.assertLess(np.abs(np.degrees(refracted_zd)-(90.0-alt_ref)), 

np.abs((90.0-alt_ref) - (90.0-alt))) 

 

self.assertLess(np.abs(np.degrees(refracted_zd)-(90.0-alt_ref)), 

np.abs(np.degrees(refracted_zd) - (90.0-alt))) 

 

def test_raDecFromAltAz_noref(self): 

""" 

test that raDecFromAltAz correctly inverts altAzPaFromRaDec, even when 

refraction is turned off 

""" 

 

rng = np.random.RandomState(55) 

n_samples = 10 

n_batches = 10 

 

for i_batch in range(n_batches): 

d_sun = 0.0 

while d_sun < 45.0: # because ICRS->Observed transformation breaks down close to the sun 

 

alt_in = rng.random_sample(n_samples)*50.0 + 20.0 

az_in = rng.random_sample(n_samples)*360.0 

obs = utils.ObservationMetaData(mjd=43000.0) 

ra_in, dec_in = utils.raDecFromAltAz(alt_in, az_in, obs=obs, includeRefraction=False) 

 

d_sun = utils.distanceToSun(ra_in, dec_in, obs.mjd).min() 

 

alt_out, az_out, pa_out = utils.altAzPaFromRaDec(ra_in, dec_in, obs=obs, 

includeRefraction=False) 

 

dd = utils.haversine(np.radians(alt_out), np.radians(az_out), 

np.radians(alt_in), np.radians(az_in)) 

self.assertLess(utils.arcsecFromRadians(dd).max(), 0.01) 

 

def test_raDecAltAz_noRefraction_degVsRadians(self): 

""" 

Check that raDecFromAltAz and altAzPaFromRaDec are consistent in a degrees-versus-radians 

sense when refraction is turned off 

""" 

 

rng = np.random.RandomState(34) 

n_samples = 10 

ra_in = rng.random_sample(n_samples)*360.0 

dec_in = rng.random_sample(n_samples)*180.0 - 90.0 

mjd = 43000.0 

obs = utils.ObservationMetaData(mjd=mjd) 

alt, az, pa = utils.altAzPaFromRaDec(ra_in, dec_in, obs, includeRefraction=False) 

alt_rad, az_rad, pa_rad = utils._altAzPaFromRaDec(np.radians(ra_in), 

np.radians(dec_in), 

obs, includeRefraction=False) 

 

distance = utils.haversine(az_rad, alt_rad, 

np.radians(az), np.radians(alt)) 

self.assertLess(utils.arcsecFromRadians(distance).min(), 0.001) 

np.testing.assert_array_almost_equal(pa, np.degrees(pa_rad), decimal=12) 

 

ra, dec = utils.raDecFromAltAz(alt, az, obs, includeRefraction=False) 

ra_rad, dec_rad = utils._raDecFromAltAz(alt_rad, az_rad, obs, includeRefraction=False) 

distance = utils.haversine(ra_rad, dec_rad, np.radians(ra), np.radians(dec)) 

self.assertLess(utils.arcsecFromRadians(distance).min(), 0.001) 

 

 

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

pass 

 

402 ↛ 403line 402 didn't jump to line 403, because the condition on line 402 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()