def test_tdb2tt():
epsilon = 1e-16
tt0 = c.tdb2tt(T0)[1]
ttA = c.tdb2tt(TA)[1]
ttB = c.tdb2tt(TB)[1]
t = array([T0, TA, TB])
v = timescales.tdb_minus_tt(t)
eq(v, [tt0, ttA, ttB], epsilon)
def test_tdb2tt(self):
self.delta = 1e-16
tt0 = c.tdb2tt(T0)[1]
ttA = c.tdb2tt(TA)[1]
ttB = c.tdb2tt(TB)[1]
t = array([T0, TA, TB])
v = timescales.tdb_minus_tt(t)
self.eq(v, [tt0, ttA, ttB])
def output_subroutine_tests(dates):
date_floats = [d for d in dates if not isinstance(d, list)]
delta_t_floats = [+39.707, +57.1136, +63.8285, +66.7846]
def shorter_cal_date(jd):
y, m, d, h = novas.cal_date(jd)
return y, m, d + h / 24.0 - 0.5
for i, jd in enumerate(date_floats):
cal_date = call(shorter_cal_date, jd)
output(
locals(), """\
def test_calendar_date_{i}():
compare(timelib.calendar_date({jd!r}), array({cal_date}), 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.era(jd)
output(
locals(), """\
def test_earth_rotation_angle_date{i}():
compare(earthlib.earth_rotation_angle({jd!r}) * 360.0, {angle!r},
0.000001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
angles = novas.e_tilt(jd)
output(
locals(), """\
def test_earth_tilt_date{i}(ts):
compare(nutationlib.earth_tilt(ts.tdb_jd({jd!r})),
array({angles}), 0.00001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
terms = novas.ee_ct(jd, 0.0, 0)
output(
locals(), """\
def test_equation_of_the_equinoxes_complimentary_terms_date{i}():
compare(nutationlib.equation_of_the_equinoxes_complimentary_terms({jd!r}),
array({terms!r}), 0.0000000000000001 * arcsecond)
""")
vector = (1.1, 1.2, 1.3)
tie1 = novas.frame_tie(vector, 0)
tie2 = novas.frame_tie(vector, -1)
output(
locals(), """\
def test_forward_frame_tie():
compare(framelib.ICRS_to_J2000.dot({vector}), {tie1}, 1e-15)
def test_reverse_frame_tie():
compare(framelib.ICRS_to_J2000.T.dot({vector}), {tie2}, 1e-15)
""")
for i, jd in enumerate(date_floats):
jcentury = (jd - T0) / 36525.0
arguments = novas.fund_args(jcentury)
output(
locals(), """\
def test_fundamental_arguments_date{i}():
compare(nutationlib.fundamental_arguments({jcentury!r}),
array({arguments}), 0.000000002 * arcsecond)
""")
for i, jd in enumerate(date_floats):
psi, eps = nutation_module.iau2000a(jd, 0.0)
psi *= 1e7 / ASEC2RAD
eps *= 1e7 / ASEC2RAD
output(
locals(), """\
def test_iau2000a_date{i}():
compare(nutationlib.iau2000a({jd!r}),
array([{psi!r}, {eps!r}]), 0.001)
""")
for i, jd in enumerate(date_floats):
psi, eps = nutation_module.iau2000b(jd, 0.0)
psi *= 1e7 / ASEC2RAD
eps *= 1e7 / ASEC2RAD
output(
locals(), """\
def test_iau2000b_date{i}():
compare(nutationlib.iau2000b({jd!r}),
array([{psi!r}, {eps!r}]), 0.001)
""")
for i, args in enumerate([
(-4712, 1, 1, 0.0),
(-4712, 3, 1, 0.0),
(-4712, 12, 31, 0.5),
(-241, 3, 25, 19.0),
(530, 9, 27, 23.5),
(1976, 3, 7, 12.5),
(2000, 1, 1, 0.0),
]):
jd = novas.julian_date(*args)
output(
locals(), """\
def test_julian_date_function_date{i}():
compare(timelib.julian_date{args}, {jd!r}, 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.mean_obliq(jd)
output(
locals(), """\
def test_mean_obliquity_date{i}():
compare(nutationlib.mean_obliquity({jd!r}),
{angle!r}, 0.0) # arcseconds
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = nutation_function(jd, vector)
output(
locals(), """\
def test_nutation_date{i}(ts):
matrix = nutationlib.compute_nutation(ts.tdb_jd({jd!r}))
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-14)
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = novas.precession(T0, vector, jd)
output(
locals(), """\
def test_precession_date{i}():
matrix = precessionlib.compute_precession({jd!r})
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-15)
""")
for i, jd in enumerate(date_floats):
result1 = novas.sidereal_time(jd, 0.0, 0.0, False, True)
result2 = novas.sidereal_time(jd, 0.0, 99.9, False, True)
output(
locals(), """\
def test_sidereal_time_on_date{i}():
jd = load.timescale(delta_t=0.0).tt_jd({jd!r})
compare(earthlib.sidereal_time(jd), {result1!r}, 1e-13)
def test_sidereal_time_with_nonzero_delta_t_on_date{i}():
jd = load.timescale(delta_t=99.9).tt_jd({jd!r} + 99.9 * one_second)
compare(earthlib.sidereal_time(jd), {result2!r}, 1e-13)
""")
p, v = novas.starvectors(
novas.make_cat_entry('POLARIS', 'HIP', 0, 2.530301028, 89.264109444,
44.22, -11.75, 7.56, -17.4))
output(
locals(), """\
def test_star_vector():
star = starlib.Star(ra_hours=2.530301028, dec_degrees=89.264109444,
ra_mas_per_year=44.22, dec_mas_per_year=-11.75,
parallax_mas=7.56, radial_km_per_s=-17.4)
star.au_km = OLD_AU_KM
star._compute_vectors()
compare(star._position_au,
{p!r},
1e3 * meter)
compare(star._velocity_au_per_d,
{v!r},
1e-3 * meter) # TODO: was 1e-6 before switch to modern au
""")
atp = product([-5, -1, 15, 89.95], [10, 25], [1010, 1013.25])
for i, (angle, temperature, pressure) in enumerate(atp):
location = novas.make_on_surface(0.0, 0.0, 0, temperature, pressure)
r = novas.refract(location, 90 - angle, 2)
output(
locals(), """\
def test_refraction{i}():
r = earthlib.refraction({angle}, {temperature}, {pressure})
compare(r, {r!r}, 1e-9 * arcsecond)
""")
northpole = novas.make_on_surface(90.0, 0.0, 0.0, 10.0, 1010.0)
for i, angle in enumerate([-90, -2, -1, 0, 1, 3, 9, 90]):
alt, az = altaz_maneuver(T0, northpole, 0.0, angle, ref=2)
output(
locals(), """\
def test_refract{i}():
alt = earthlib.refract({angle!r}, 10.0, 1010.0)
compare(alt, {alt!r}, 1e-9 * arcsecond)
""")
usno = novas.make_on_surface(38.9215, -77.0669, 92.0, 10.0, 1010.0)
ra = 12.34
for i, (tt, dec) in enumerate(product(date_floats, [56.78, -67.89])):
alt, az = altaz_maneuver(tt, usno, ra, dec, ref=0)
output(
locals(), """\
def test_from_altaz_{i}(earth):
jd = load.timescale(delta_t=0.0).tt_jd({tt!r})
usno = earth + Topos(
'38.9215 N', '77.0669 W', elevation_m=92.0)
a = usno.at(jd).from_altaz(alt_degrees={alt!r}, az_degrees={az!r})
ra, dec, distance = a.radec(epoch=jd)
compare(ra.hours, {ra!r}, 1e-9 * arcsecond)
compare(dec.degrees, {dec!r}, 1e-9 * arcsecond)
""")
for i, (tt, delta_t) in enumerate(zip(date_floats, delta_t_floats)):
jd_low = xp = yp = 0.0
vector = [1.1, 1.2, 1.3]
ut1 = tt - delta_t * one_second
result = novas.ter2cel(ut1, jd_low, delta_t, xp, yp, vector)
output(
locals(), """\
def test_ITRF_to_GCRS_conversion_on_date{i}():
jd = load.timescale(delta_t={delta_t!r}).tt_jd({tt!r})
position = positionlib.ITRF_to_GCRS(jd, {vector!r})
compare(position, {result!r}, 1e-13)
""")
for i, jd_tdb in enumerate(date_floats):
result = novas.tdb2tt(jd_tdb)[1]
output(
locals(), """\
def test_tdb_minus_tt_on_date{i}():
result = timelib.tdb_minus_tt({jd_tdb!r})
compare(result, {result!r}, 1e-16)
""")
def test_tdb2tt(jd_float_or_vector):
jd_tdb = jd_float_or_vector
u = c.tdb2tt(jd_tdb)[1]
v = timelib.tdb_minus_tt(jd_tdb)
epsilon_seconds = 1e-16 # 11 or 12 digits of agreement; why not more?
eq(u, v, epsilon_seconds)
def output_subroutine_tests(dates):
date_floats = [d for d in dates if not isinstance(d, list)]
delta_t_floats = [+39.707, +57.1136, +63.8285, +66.7846]
def shorter_cal_date(jd):
y, m, d, h = novas.cal_date(jd)
return y, m, d + h / 24.0 - 0.5
for i, jd in enumerate(date_floats):
cal_date = call(shorter_cal_date, jd)
output(locals(), """\
def test_calendar_date_{i}():
compare(timelib.calendar_date({jd!r}), array({cal_date}), 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.era(jd)
output(locals(), """\
def test_earth_rotation_angle_date{i}():
compare(earthlib.earth_rotation_angle({jd!r}) * 360.0, {angle},
0.000001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
angles = novas.e_tilt(jd)
output(locals(), """\
def test_earth_tilt_date{i}():
compare(nutationlib.earth_tilt(JulianDate(tdb={jd!r})),
array({angles}), 0.00001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
terms = novas.ee_ct(jd, 0.0, 0)
output(locals(), """\
def test_equation_of_the_equinoxes_complimentary_terms_date{i}():
compare(nutationlib.equation_of_the_equinoxes_complimentary_terms({jd!r}),
array({terms}), 0.0000000000000001 * arcsecond)
""")
vector = (1.1, 1.2, 1.3)
tie1 = novas.frame_tie(vector, 0)
tie2 = novas.frame_tie(vector, -1)
output(locals(), """\
def test_forward_frame_tie():
compare(framelib.ICRS_to_J2000.dot({vector}), {tie1}, 1e-15)
def test_reverse_frame_tie():
compare(framelib.ICRS_to_J2000.T.dot({vector}), {tie2}, 1e-15)
""")
for i, jd in enumerate(date_floats):
jcentury = (jd - T0) / 36525.0
arguments = novas.fund_args(jcentury)
output(locals(), """\
def test_fundamental_arguments_date{i}():
compare(nutationlib.fundamental_arguments({jcentury!r}),
array({arguments}), 0.000000002 * arcsecond)
""")
for i, jd in enumerate(date_floats):
psi, eps = nutation_module.iau2000a(jd, 0.0)
psi *= 1e7 / ASEC2RAD
eps *= 1e7 / ASEC2RAD
output(locals(), """\
def test_iau2000a_date{i}():
compare(nutationlib.iau2000a({jd!r}),
array([{psi}, {eps}]), 0.001)
""")
for i, args in enumerate([
(-4712, 1, 1, 0.0),
(-4712, 3, 1, 0.0),
(-4712, 12, 31, 0.5),
(-241, 3, 25, 19.0),
(530, 9, 27, 23.5),
(1976, 3, 7, 12.5),
(2000, 1, 1, 0.0),
]):
jd = novas.julian_date(*args)
output(locals(), """\
def test_julian_date_function_date{i}():
compare(timelib.julian_date{args}, {jd!r}, 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.mean_obliq(jd)
output(locals(), """\
def test_mean_obliquity_date{i}():
compare(nutationlib.mean_obliquity({jd!r}),
{angle!r}, 0.0) # arcseconds
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = nutation_function(jd, vector)
output(locals(), """\
def test_nutation_date{i}():
matrix = nutationlib.compute_nutation(JulianDate(tdb={jd!r}))
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-14)
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = novas.precession(T0, vector, jd)
output(locals(), """\
def test_precession_date{i}():
matrix = precessionlib.compute_precession({jd!r})
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-15)
""")
for i, jd in enumerate(date_floats):
result1 = novas.sidereal_time(jd, 0.0, 0.0, False, True)
result2 = novas.sidereal_time(jd, 0.0, 99.9, False, True)
output(locals(), """\
def test_sidereal_time_on_date{i}():
jd = JulianDate(tt={jd!r})
compare(earthlib.sidereal_time(jd), {result1!r}, 1e-13)
def test_sidereal_time_with_nonzero_delta_t_on_date{i}():
jd = JulianDate(tt={jd!r} + 99.9 * one_second, delta_t=99.9)
compare(earthlib.sidereal_time(jd), {result2!r}, 1e-13)
""")
p, v = novas.starvectors(novas.make_cat_entry(
'POLARIS', 'HIP', 0, 2.530301028, 89.264109444,
44.22, -11.75, 7.56, -17.4))
output(locals(), """\
def test_star_vector():
star = starlib.Star(ra_hours=2.530301028, dec_degrees=89.264109444,
ra_mas_per_year=44.22, dec_mas_per_year=-11.75,
parallax_mas=7.56, radial_km_per_s=-17.4)
star.au_km = de405.jplephemeris.AU
star._compute_vectors()
compare(star._position_au,
{p!r},
1e3 * meter)
compare(star._velocity_au_per_d,
{v!r},
1e-3 * meter) # TODO: was 1e-6 before switch to modern au
""")
atp = product([-5, -1, 15, 89.95], [10, 25], [1010, 1013.25])
for i, (angle, temperature, pressure) in enumerate(atp):
location = novas.make_on_surface(0.0, 0.0, 0, temperature, pressure)
r = novas.refract(location, 90 - angle, 2)
output(locals(), """\
def test_refraction{i}():
r = earthlib.refraction({angle}, {temperature}, {pressure})
compare(r, {r}, 0.001 * arcsecond)
""")
northpole = novas.make_on_surface(90.0, 0.0, 0.0, 10.0, 1010.0)
for i, angle in enumerate([-90, -2, -1, 0, 1, 3, 9, 90]):
alt, az = altaz_maneuver(T0, northpole, 0.0, angle, ref=2)
output(locals(), """\
def test_refract{i}():
alt = earthlib.refract({angle!r}, 10.0, 1010.0)
compare(alt, {alt!r}, 0.000000001 * arcsecond)
""")
usno = novas.make_on_surface(38.9215, -77.0669, 92.0, 10.0, 1010.0)
ra = 12.34
for i, (tt, dec) in enumerate(product(date_floats, [56.78, -67.89])):
alt, az = altaz_maneuver(tt, usno, ra, dec, ref=0)
output(locals(), """\
def test_from_altaz_{i}():
jd = JulianDate(tt={tt!r})
usno = de405.earth.topos(
'38.9215 N', '77.0669 W', elevation_m=92.0)
a = usno(jd).from_altaz(alt_degrees={alt!r}, az_degrees={az!r})
ra, dec, distance = a.radec(epoch=jd)
compare(ra.hours, {ra!r}, 0.000000001 * arcsecond)
compare(dec.degrees, {dec!r}, 0.000000001 * arcsecond)
""")
for i, (tt, delta_t) in enumerate(zip(date_floats, delta_t_floats)):
jd_low = xp = yp = 0.0
vector = [1.1, 1.2, 1.3]
ut1 = tt - delta_t * one_second
result = novas.ter2cel(ut1, jd_low, delta_t, xp, yp, vector)
output(locals(), """\
def test_ITRF_to_GCRS_conversion_on_date{i}():
jd = JulianDate(tt={tt!r}, delta_t={delta_t!r})
position = positionlib.ITRF_to_GCRS(jd, {vector!r})
compare(position, {result!r}, 1e-13)
""")
for i, jd_tdb in enumerate(date_floats):
result = novas.tdb2tt(jd_tdb)[1]
output(locals(), """\
def test_tdb_minus_tt_on_date{i}():
result = timelib.tdb_minus_tt({jd_tdb!r})
compare(result, {result!r}, 1e-16)
""")
def jdTDB(self, jd_utc):
jd_tt = self.jdTT(jd_utc)
_, tdb_tt = novas.tdb2tt(jd_tt)
jd_tdb = jd_tt + tdb_tt / (24.0 * 60 * 60)
return jd_tdb
def output_subroutine_tests(dates):
date_floats = [d for d in dates if not isinstance(d, list)]
delta_t_floats = [+39.707, +57.1136, +63.8285, +66.7846]
def shorter_cal_date(jd):
y, m, d, h = novas.cal_date(jd)
return y, m, d + h / 24.0 - 0.5
for i, jd in enumerate(date_floats):
cal_date = call(shorter_cal_date, jd)
output(locals(), """\
def test_calendar_date_{i}():
compare(timelib.calendar_date({jd!r}), array({cal_date}), 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.era(jd)
output(locals(), """\
def test_earth_rotation_angle_date{i}():
compare(earthlib.earth_rotation_angle({jd!r}), {angle},
0.000001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
angles = novas.e_tilt(jd)
output(locals(), """\
def test_earth_tilt_date{i}():
compare(nutationlib.earth_tilt(JulianDate(tdb={jd!r})),
array({angles}), 0.00001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
terms = novas.ee_ct(jd, 0.0, 0)
output(locals(), """\
def test_equation_of_the_equinoxes_complimentary_terms_date{i}():
compare(nutationlib.equation_of_the_equinoxes_complimentary_terms({jd!r}),
array({terms}), 0.0000000000000001 * arcsecond)
""")
vector = (1.1, 1.2, 1.3)
tie1 = novas.frame_tie(vector, 0)
tie2 = novas.frame_tie(vector, -1)
output(locals(), """\
def test_forward_frame_tie():
compare(framelib.ICRS_to_J2000.dot({vector}), {tie1}, 1e-15)
def test_reverse_frame_tie():
compare(framelib.ICRS_to_J2000.T.dot({vector}), {tie2}, 1e-15)
""")
for i, jd in enumerate(date_floats):
jcentury = (jd - T0) / 36525.0
arguments = novas.fund_args(jcentury)
output(locals(), """\
def test_fundamental_arguments_date{i}():
compare(nutationlib.fundamental_arguments({jcentury!r}),
array({arguments}), 0.000000001 * arcsecond)
""")
for i, jd in enumerate(date_floats):
psi, eps = nutation_module.iau2000a(jd, 0.0)
psi *= 1e7 / ASEC2RAD
eps *= 1e7 / ASEC2RAD
output(locals(), """\
def test_iau2000a_date{i}():
compare(nutationlib.iau2000a({jd!r}),
array([{psi}, {eps}]), 0.001)
""")
for i, args in enumerate([
(-4712, 1, 1, 0.0),
(-4712, 3, 1, 0.0),
(-4712, 12, 31, 0.5),
(-241, 3, 25, 19.0),
(530, 9, 27, 23.5),
(1976, 3, 7, 12.5),
(2000, 1, 1, 0.0),
]):
jd = novas.julian_date(*args)
output(locals(), """\
def test_julian_date_function_date{i}():
compare(timelib.julian_date{args}, {jd!r}, 0.0)
""")
for i, jd in enumerate(date_floats):
angle = novas.mean_obliq(jd)
output(locals(), """\
def test_mean_obliquity_date{i}():
compare(nutationlib.mean_obliquity({jd!r}),
{angle!r}, 0.0) # arcseconds
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = nutation_function(jd, vector)
output(locals(), """\
def test_nutation_date{i}():
matrix = nutationlib.compute_nutation(JulianDate(tdb={jd!r}))
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-14)
""")
for i, jd in enumerate(date_floats):
vector = [1.1, 1.2, 1.3]
result = novas.precession(T0, vector, jd)
output(locals(), """\
def test_precession_date{i}():
matrix = precessionlib.compute_precession({jd!r})
result = einsum('ij...,j...->i...', matrix, [1.1, 1.2, 1.3])
compare({result},
result, 1e-15)
""")
for i, jd in enumerate(date_floats):
result1 = novas.sidereal_time(jd, 0.0, 0.0, False, True)
result2 = novas.sidereal_time(jd, 0.0, 99.9, False, True)
output(locals(), """\
def test_sidereal_time_on_date{i}():
jd = JulianDate(tt={jd!r})
compare(earthlib.sidereal_time(jd), {result1!r}, 1e-13)
def test_sidereal_time_with_nonzero_delta_t_on_date{i}():
jd = JulianDate(tt={jd!r} + 99.9 * one_second, delta_t=99.9)
compare(earthlib.sidereal_time(jd), {result2!r}, 1e-13)
""")
p, v = novas.starvectors(novas.make_cat_entry(
'POLARIS', 'HIP', 0, 2.530301028, 89.264109444,
44.22, -11.75, 7.56, -17.4))
output(locals(), """\
def test_star_vector():
star = starlib.Star(ra_hours=2.530301028, dec_degrees=89.264109444,
ra_mas_per_year=44.22, dec_mas_per_year=-11.75,
parallax_mas=7.56, radial_km_per_s=-17.4)
compare(star._position,
{p},
1e3 * meter)
compare(star._velocity,
{v},
1e-6 * meter)
""")
for i, (tt, delta_t) in enumerate(zip(date_floats, delta_t_floats)):
jd_low = xp = yp = 0.0
vector = [1.1, 1.2, 1.3]
ut1 = tt - delta_t * one_second
result = novas.ter2cel(ut1, jd_low, delta_t, xp, yp, vector)
output(locals(), """\
def test_ITRF_to_GCRS_conversion_on_date{i}():
jd = JulianDate(tt={tt!r}, delta_t={delta_t!r})
position = positionlib.ITRF_to_GCRS(jd, {vector!r})
compare(position, {result!r}, 1e-13)
""")
for i, jd_tdb in enumerate(date_floats):
result = novas.tdb2tt(jd_tdb)[1]
output(locals(), """\
def test_tdb_minus_tt_on_date{i}():
result = timelib.tdb_minus_tt({jd_tdb!r})
compare(result, {result!r}, 1e-16)
""")