def lnlike_full(pars, t1, v1, v1_err, t2, v2, v2_err):
K1, K2, P, T0, w, e, dv1, dv2, lnf = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1) + dv1
rv2_pred = -get_rv(T0=T0, P=P, e=e, K1=K2, w=w, t=t2)
inv_sigma2_1 = 1.0/v1_err**2
inv_sigma2_2 = 1.0/(np.exp(lnf)*v2_err**2)
s1 = np.nansum((rv1_pred - v1)**2 * inv_sigma2_1 - np.log(inv_sigma2_1))
s2 = np.nansum((rv2_pred - (v2 - rv2_pred*K1/K2 - dv2))**2 * inv_sigma2_2 - np.log(inv_sigma2_2))
#print(s1)
#print(s2)
return -0.5*(s1+s2)
def lnlike_full(pars, t1, v1, v1_err, t2, v2, v2_err):
K1, K2, P, T0, w, e, dv1, dv2, gamma, lnf, noise1 = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1) + dv1 + gamma
rv2_pred = -get_rv(T0=T0, P=P, e=e, K1=K2, w=w, t=t2)
inv_sigma2_1 = 1.0 / (v1_err**2 + np.exp(noise1)**2)
inv_sigma2_2 = 1.0 / (np.exp(lnf) * v2_err**2)
s1 = np.nansum((rv1_pred - v1)**2 * inv_sigma2_1 - np.log(inv_sigma2_1 /
(2 * np.pi)))
s2 = np.nansum((rv2_pred - (v2 - rv2_pred * K1 / K2 - dv2 - gamma))**2 *
inv_sigma2_2 - np.log(inv_sigma2_2 / (2 * np.pi)))
# s2 = np.nansum((rv2_pred - (v2 - dv2))**2 * inv_sigma2_2 - np.log(inv_sigma2_2/(2*np.pi)))
#print(s1)
#print(s2)
return -0.5 * (s1 + s2)
def fit_partial(T0, P, e, K1, w, t, rv2, rv2_err):
"""
Get MCMC samples for the mass-ratio, velocity shift, and error scaling
for the orbital parameters T0-w (fit by Stefano Meschiari)
"""
# Get the predicted velocity of the primary at each time
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w * np.pi / 180, t=t)
# Initialize MCMC sampler
initial_pars = [0.47, -5.4, -3.6]
ndim = len(initial_pars)
nwalkers = 100
p0 = emcee.utils.sample_ball(initial_pars,
std=[1e-6] * ndim,
size=nwalkers)
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob_partial,
args=(rv2, rv2_err, rv1_pred),
threads=2)
# Run the sampler
pos, lp, state = sampler.run_mcmc(p0, 1000)
# Save the last 500 (we will just have to hope that the sampler sufficiently burns-in in 500 steps. That is true in tests I've done)
samples = sampler.chain[:, 500:, :].reshape((-1, ndim))
return samples
def lnlike_sb1(pars, t1, v1, v1_err):
K1, P, T0, w, e, dv1 = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1) + dv1
inv_sigma2_1 = 1.0/v1_err**2
s1 = np.nansum((rv1_pred - v1)**2 * inv_sigma2_1 - np.log(inv_sigma2_1))
return -0.5*s1
def lnlike_sb1(pars, t1, v1, v1_err):
K1, P, T0, w, e, dv1 = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1) + dv1
inv_sigma2_1 = 1.0 / v1_err**2
s1 = np.nansum((rv1_pred - v1)**2 * inv_sigma2_1 - np.log(inv_sigma2_1))
return -0.5 * s1
def fit_partial(T0, P, e, K1, w, t, rv2, rv2_err):
"""
Get MCMC samples for the mass-ratio, velocity shift, and error scaling
for the orbital parameters T0-w (fit by Stefano Meschiari)
"""
# Get the predicted velocity of the primary at each time
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w*np.pi/180, t=t)
# Initialize MCMC sampler
initial_pars = [0.47, -5.4, -3.6]
ndim = len(initial_pars)
nwalkers = 100
p0 = emcee.utils.sample_ball(initial_pars, std=[1e-6]*ndim, size=nwalkers)
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob_partial, args=(rv2, rv2_err, rv1_pred), threads=2)
# Run the sampler
pos, lp, state = sampler.run_mcmc(p0, 1000)
# Save the last 500 (we will just have to hope that the sampler sufficiently burns-in in 500 steps. That is true in tests I've done)
samples = sampler.chain[:, 500:, :].reshape((-1, ndim))
return samples
def plot(pars, t1, v1, v1_err, t2, v2, v2_err, resids=True):
K1, K2, P, T0, w, e, dv1, dv2, lnf, noise = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1)
rv2_pred = -get_rv(T0=T0, P=P, e=e, K1=K2, w=w, t=t2)
tplot = np.linspace(min(min(t1), min(t2)), max(max(t2), max(t2)), 100)
rv1_plot = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=tplot)
rv2_plot = get_rv(T0=T0, P=P, e=e, K1=-K2, w=w, t=tplot)
inv_sigma2_1 = 1.0/v1_err**2
inv_sigma2_2 = 1.0/(np.exp(lnf)*v2_err**2)
s1 = np.nansum((rv1_pred - (v1-dv1))**2 * inv_sigma2_1 - np.log(inv_sigma2_1))
s2 = np.nansum((rv2_pred - (v2 - rv2_pred*K1/K2 - dv2))**2 * inv_sigma2_2 - np.log(inv_sigma2_2))
def tick_formatter(x, pos):
return "{:.0f}".format(x - 2450000)
MyFormatter = FuncFormatter(tick_formatter)
fig = plt.figure()
if resids:
gs = gridspec.GridSpec(5, 1)
top = plt.subplot(gs[:3])
resid1 = plt.subplot(gs[3], sharex=top)
resid2 = plt.subplot(gs[4], sharex=top)
fig.subplots_adjust(bottom=0.15, left=0.15, hspace=0.0)
top.errorbar(t1, v1-dv1, yerr=np.sqrt(v1_err**2 + np.exp(noise)), fmt='r^', label='Primary')
top.errorbar(t2, v2 - rv2_pred*K1/K2 - dv2, yerr=v2_err*np.exp(lnf/2.), fmt='ko', label='Secondary')
top.plot(tplot, rv1_plot, 'r-', alpha=0.5)
top.plot(tplot, rv2_plot, 'k-', alpha=0.5)
resid1.scatter(t1, v1-dv1 - rv1_pred)
resid1.plot(t1, np.zeros(len(t1)), 'r--')
resid1.set_ylabel('O-C (rv1)')
print('RMS scatter on primary = {:.3f} km/s'.format(np.std(v1-dv1-rv1_pred)))
resid2.scatter(t2, v2 - rv2_pred*K1/K2 - dv2 - rv2_pred)
resid2.plot(t2, np.zeros(len(t2)), 'r--')
resid2.set_ylabel('O-C (rv2)')
print('RMS scatter on secondary = {:.3f} km/s'.format(np.std(v2 - rv2_pred*K1/K2 - dv2 - rv2_pred)))
top.axes.get_xaxis().set_visible(False)
resid1.axes.get_xaxis().set_visible(False)
resid2.set_xlabel('JD - 2450000')
top.set_ylabel('RV (km/s)')
leg = top.legend(loc='best', fancybox=True)
top.xaxis.set_major_formatter(MyFormatter)
axes = [top, resid1, resid2]
else:
ax = fig.add_subplot(111)
ax.errorbar(t1, v1-dv1, yerr=v1_err, fmt='r^', label='Primary')
ax.errorbar(t2, v2 - rv2_pred*K1/K2 - dv2, yerr=v2_err*np.exp(lnf/2.), fmt='ko', label='Secondary')
ax.plot(tplot, rv1_plot, 'r-', alpha=0.5)
ax.plot(tplot, rv2_plot, 'k-', alpha=0.5)
ax.xaxis.set_major_formatter(MyFormatter)
ax.set_xlabel('JD - 2450000')
ax.set_ylabel('RV (km/s)')
leg = ax.legend(loc='best', fancybox=True)
axes = [ax]
# Calculate chi-squared
chi2 = (np.sum((v1-dv1 - rv1_pred)**2 / (v1_err**2 + np.exp(noise))) +
np.sum((v2 - rv2_pred*K1/K2 - dv2 - rv2_pred)**2 / (v2_err**2 * np.exp(lnf))))
N = len(v1) + len(v2)
print('X^2 = {:.2f}\nN = {}'.format(chi2, N))
return fig, axes
def plot(pars, t1, v1, v1_err, t2, v2, v2_err, resids=True):
K1, K2, P, T0, w, e, dv1, dv2, lnf, noise = pars
rv1_pred = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=t1)
rv2_pred = -get_rv(T0=T0, P=P, e=e, K1=K2, w=w, t=t2)
tplot = np.linspace(min(min(t1), min(t2)), max(max(t2), max(t2)), 100)
rv1_plot = get_rv(T0=T0, P=P, e=e, K1=K1, w=w, t=tplot)
rv2_plot = get_rv(T0=T0, P=P, e=e, K1=-K2, w=w, t=tplot)
inv_sigma2_1 = 1.0 / v1_err**2
inv_sigma2_2 = 1.0 / (np.exp(lnf) * v2_err**2)
s1 = np.nansum((rv1_pred - (v1 - dv1))**2 * inv_sigma2_1 -
np.log(inv_sigma2_1))
s2 = np.nansum((rv2_pred -
(v2 - rv2_pred * K1 / K2 - dv2))**2 * inv_sigma2_2 -
np.log(inv_sigma2_2))
def tick_formatter(x, pos):
return "{:.0f}".format(x - 2450000)
MyFormatter = FuncFormatter(tick_formatter)
fig = plt.figure()
if resids:
gs = gridspec.GridSpec(5, 1)
top = plt.subplot(gs[:3])
resid1 = plt.subplot(gs[3], sharex=top)
resid2 = plt.subplot(gs[4], sharex=top)
fig.subplots_adjust(bottom=0.15, left=0.15, hspace=0.0)
top.errorbar(t1,
v1 - dv1,
yerr=np.sqrt(v1_err**2 + np.exp(noise)),
fmt='r^',
label='Primary')
top.errorbar(t2,
v2 - rv2_pred * K1 / K2 - dv2,
yerr=v2_err * np.exp(lnf / 2.),
fmt='ko',
label='Secondary')
top.plot(tplot, rv1_plot, 'r-', alpha=0.5)
top.plot(tplot, rv2_plot, 'k-', alpha=0.5)
resid1.scatter(t1, v1 - dv1 - rv1_pred)
resid1.plot(t1, np.zeros(len(t1)), 'r--')
resid1.set_ylabel('O-C (rv1)')
print('RMS scatter on primary = {:.3f} km/s'.format(
np.std(v1 - dv1 - rv1_pred)))
resid2.scatter(t2, v2 - rv2_pred * K1 / K2 - dv2 - rv2_pred)
resid2.plot(t2, np.zeros(len(t2)), 'r--')
resid2.set_ylabel('O-C (rv2)')
print('RMS scatter on secondary = {:.3f} km/s'.format(
np.std(v2 - rv2_pred * K1 / K2 - dv2 - rv2_pred)))
top.axes.get_xaxis().set_visible(False)
resid1.axes.get_xaxis().set_visible(False)
resid2.set_xlabel('JD - 2450000')
top.set_ylabel('RV (km/s)')
leg = top.legend(loc='best', fancybox=True)
top.xaxis.set_major_formatter(MyFormatter)
axes = [top, resid1, resid2]
else:
ax = fig.add_subplot(111)
ax.errorbar(t1, v1 - dv1, yerr=v1_err, fmt='r^', label='Primary')
ax.errorbar(t2,
v2 - rv2_pred * K1 / K2 - dv2,
yerr=v2_err * np.exp(lnf / 2.),
fmt='ko',
label='Secondary')
ax.plot(tplot, rv1_plot, 'r-', alpha=0.5)
ax.plot(tplot, rv2_plot, 'k-', alpha=0.5)
ax.xaxis.set_major_formatter(MyFormatter)
ax.set_xlabel('JD - 2450000')
ax.set_ylabel('RV (km/s)')
leg = ax.legend(loc='best', fancybox=True)
axes = [ax]
# Calculate chi-squared
chi2 = (np.sum(
(v1 - dv1 - rv1_pred)**2 / (v1_err**2 + np.exp(noise))) + np.sum(
(v2 - rv2_pred * K1 / K2 - dv2 - rv2_pred)**2 /
(v2_err**2 * np.exp(lnf))))
N = len(v1) + len(v2)
print('X^2 = {:.2f}\nN = {}'.format(chi2, N))
return fig, axes