def test_gradients(plot=False):
"""Test the gradients in the `System` class."""
# Limb-darkened star
A = Primary(lmax=3)
A[1] = 0.4
A[2] = 0.26
A[3] = -0.25
A.r_m = 1e11
# Dipole-map hot jupiter
b = Secondary(lmax=2)
b.r = 0.09
b.a = 60
b.inc = 89.943
b.porb = 50
b.prot = 2.49
b.lambda0 = 89.9
b.ecc = 0.3
b.w = 89
b.L = 1.75e-3
b[1, 0] = 0.5
b[2, 1] = 0.1
b[2, 2] = -0.05
# Dipole-map hot jupiter
c = Secondary(lmax=1)
c.r = 0.12
c.a = 80
c.inc = 89.95
c.porb = 100
c.prot = 7.83
c.lambda0 = 85
c.ecc = 0.29
c.w = 87.4
c.L = 1.5e-3
c[1, 0] = 0.4
# Instantiate the system
# We're adding a ton of light travel delay
# and a finite exposure time: this is a
# comprehensive test of the main `starry` features
system = System(A, b, c)
system.exposure_time = 0.02
# Light curves and gradients of this object
object = system
# Let's plot transit, eclipse, and a PPO
for t1, t2, figname in zip([-0.425, 25.1, -2.6], [0.0, 25.75, -2.0], [
"gradients_transit.png", "gradients_eclipse.png",
"gradients_ppo.png"
]):
# Time arrays
time = np.linspace(t1, t2, 500)
time_num = np.linspace(t1, t2, 50)
# Set up the plot
if plot:
fig = pl.figure(figsize=(6, 10))
fig.subplots_adjust(hspace=0, bottom=0.05, top=0.95)
# Run!
system.compute(time, gradient=True)
flux = np.array(object.lightcurve)
grad = dict(object.gradient)
# Numerical flux
system.compute(time_num, gradient=True)
flux_num = np.array(object.lightcurve)
# Plot it
if plot:
ax = pl.subplot2grid((18, 3), (0, 0), rowspan=5, colspan=3)
ax.plot(time, flux, color='C0')
ax.plot(time_num, flux_num, 'o', ms=3, color='C1')
ax.set_yticks([])
ax.set_xticks([])
[i.set_linewidth(0.) for i in ax.spines.values()]
col = 0
row = 0
eps = 1e-8
error_rel = []
for key in grad.keys():
if key.endswith('.y') or key.endswith('.u'):
for i, gradient in enumerate(grad[key]):
if plot:
axg = pl.subplot2grid((18, 3), (5 + row, col),
colspan=1)
axg.plot(time, gradient, lw=1, color='C0')
if key.endswith('.y'):
y0 = eval(key)
y = np.array(y0)
y[i + 1] += eps
exec(key[0] + "[:, :] = y")
system.compute(time)
exec(key[0] + "[:, :] = y0")
else:
u0 = eval(key)
u = np.array(u0)
u[i] += eps
exec(key[0] + "[:] = u")
system.compute(time)
exec(key[0] + "[:] = u0")
numgrad = (object.lightcurve - flux) / eps
error_rel.append(np.max(abs(numgrad - gradient)))
if plot:
axg.plot(time, numgrad, lw=1, alpha=0.5, color='C1')
axg.set_ylabel(r"$%s_%d$" % (key, i), fontsize=5)
axg.margins(None, 0.5)
axg.set_xticks([])
axg.set_yticks([])
[i.set_linewidth(0.) for i in axg.spines.values()]
if row < 12:
row += 1
else:
row = 0
col += 1
else:
if plot:
axg = pl.subplot2grid((18, 3), (5 + row, col), colspan=1)
axg.plot(time, grad[key], lw=1, color='C0')
exec(key + " += eps")
system.compute(time)
exec(key + " -= eps")
numgrad = (object.lightcurve - flux) / eps
error_rel.append(np.max(abs(numgrad - grad[key])))
if plot:
axg.plot(time, numgrad, lw=1, alpha=0.5, color='C1')
axg.margins(None, 0.5)
axg.set_xticks([])
axg.set_yticks([])
axg.set_ylabel(r"$%s$" % key, fontsize=5)
[i.set_linewidth(0.) for i in axg.spines.values()]
if row < 12:
row += 1
else:
row = 0
col += 1
# Generous error tolerance
assert np.all(np.array(error_rel) < 1e-5)
# Save the figure
if plot:
fig.savefig(figname, bbox_inches='tight', dpi=300)
pl.close()
# Limb-darkened star star = Primary() star[1] = 0.4 star[2] = 0.26 star.r_m = 0 # Dipole-map hot jupiter planet = Secondary() planet.r = 0.1 planet.a = 60 planet.inc = 89.5 planet.porb = 50 planet.prot = 2.49 planet.lambda0 = 89.9 planet.ecc = 0.3 planet.w = 89 planet.L = 1e-3 planet[1, 0] = 0.5 # Instantiate the system system = System(star, planet) system.exposure_time = 0 # Set up the plot fig = pl.figure(figsize=(8, 8)) fig.subplots_adjust(hspace=0, bottom=0.05, top=0.95) # Compute the flux during transit and during secondary eclipse titles = ['Transit', 'Secondary Eclipse'] for i, time in enumerate([time_transit, time_secondary]):
def test_light_travel():
"""Run the test."""
# No delay
star = Primary()
star[1] = 0.40
star[2] = 0.26
star.r_m = 0
planet = Secondary()
planet.L = 1e-3
planet.r = 0.1
planet.porb = 10
planet.prot = 10
planet.a = 22
planet[1, 0] = 0.5
system = System(star, planet)
time = np.concatenate(
(np.linspace(0, 0.5, 10000,
endpoint=False), np.linspace(0.5,
4.5,
100,
endpoint=False),
np.linspace(4.5, 5.5, 10000,
endpoint=False), np.linspace(5.5,
9.5,
100,
endpoint=False),
np.linspace(9.5, 10, 10000)))
phase = time / 10.
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
assert transit == 0
assert eclipse == 0.5
# Let's give the system a real length scale now
star.r_m = 6.95700e8
eps = 1e-3
time = np.concatenate(
(np.linspace(0, 0.5, 100000, endpoint=False),
np.linspace(0.5, 5 - eps, 100, endpoint=False),
np.linspace(5 - eps, 5 + eps, 1000000, endpoint=False),
np.linspace(5 + eps, 9.5, 100,
endpoint=False), np.linspace(9.5, 10, 100000)))
phase = time / planet.porb
system.compute(time)
transit = phase[np.argmin(np.abs(planet.X) + (planet.Z < 0))]
eclipse = phase[np.argmin(np.abs(planet.X) + (planet.Z > 0))]
assert transit == 0.999940999409994
assert eclipse == 0.5000590894
# Run some extra tests
c = 299792458.
RSUN = 6.957e8
time = np.concatenate(
(np.linspace(0, 0.5, 100000,
endpoint=False), np.linspace(0.5,
4.5,
100,
endpoint=False),
np.linspace(4.5, 5.5, 100000,
endpoint=False), np.linspace(5.5,
9.5,
100,
endpoint=False),
np.linspace(9.5, 10, 100000)))
phase = time / planet.porb
# Test this on an inclined orbit
planet.inc = 30
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
delay_starry = (0.5 - (transit - eclipse)) * planet.porb * 86400
a = planet.a * star.r_m
delay_analytic = 2 * a / c * np.sin(planet.inc * np.pi / 180)
assert np.abs(1 - delay_starry / delay_analytic) < 0.01
# Test this on an orbit with nonzero Omega
planet.inc = 90
planet.Omega = 90
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
delay_starry = (0.5 - (transit - eclipse)) * planet.porb * 86400
a = planet.a * star.r_m
delay_analytic = 2 * a / c
assert np.abs(1 - delay_starry / delay_analytic) < 0.01
# Compute the light travel time from the secondary
# eclipse to the barycenter for an eccentric orbit.
# First, compute the phase of secondary eclipse
# with no light travel time delay:
planet.inc = 90
planet.Omega = 0
planet.w = 30
planet.ecc = 0.25
star.r_m = 0
system.compute(time)
eclipse0 = phase[np.argmin(planet.Z)]
z0 = planet.Z[np.argmin(planet.Z)]
# Now, compute the phase w/ the delay
star.r_m = 6.95700e8
system.compute(time)
eclipse = phase[np.argmin(planet.Z)]
# Compute the light travel time to the barycenter in days:
travel_time_starry = (eclipse - eclipse0) * planet.porb * 86400
# Compute the analytic light travel time to the barycenter in days:
travel_time_analytic = (0 - z0) * star.r_m / c
assert np.abs(1 - travel_time_starry / travel_time_analytic) < 0.01