aa[5, :] = [a5[i] for i in range(3)]
aa[6, :] = [a6[i] for i in range(3)]
aa[7, :] = [a7[i] for i in range(3)]
aa[8, :] = [a8[i] for i in range(3)]
aa[9, :] = [a9[i] for i in range(3)]
aa[10, :] = [a10[i] for i in range(3)]
aa[11, :] = [a11[i] for i in range(3)]
np.savetxt('HD85390_fit.txt', aa, fmt='%.6f')
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, offset, alpha = aa[:, 0]
fit_curve = Model(P1=np.log(P1) / 10,
tau1=tau1 / 100,
k1=k1 / 100,
w1=w1,
e1=e1,
P2=np.log(P2) / 10,
tau2=tau2 / 100,
k2=k2 / 100,
w2=w2,
e2=e2,
offset=offset,
alpha=alpha)
y_fit = fit_curve.get_value(x)
fit_curve2 = Model2(P1=np.log(P1) / 10,
tau1=tau1 / 100,
k1=k1 / 100,
w1=w1,
e1=e1,
P2=np.log(P2) / 10,
tau2=tau2 / 100,
k2=k2 / 100,
tau2=1.,
k2=np.std(y) / 100,
w2=0.,
e2=0.4,
offset1=0.,
offset2=0.)
kwargs = dict(**truth)
kwargs["bounds"] = dict(P1=(7.5, 8.5),
k1=(0, 0.1),
w1=(-2 * np.pi, 2 * np.pi),
e1=(0, 0.8),
tau2=(-50, 50),
k2=(0, 0.2),
w2=(-2 * np.pi, 2 * np.pi),
e2=(0, 0.8))
mean_model = Model(**kwargs)
# mean_model = Model(P1=8., tau1=1., k1=np.std(y)/100, w1=0., e1=0.4,
# P2=100, tau2=1., k2=np.std(y)/100, w2=0., e2=0.4, offset1=0., offset2=0.)
#==============================================================================
# The fit
#==============================================================================
from scipy.optimize import minimize
import celerite
from celerite import terms
# Set up the GP model
# kernel = terms.RealTerm(log_a=np.log(np.var(y)), log_c=-np.log(10.0))
kernel = terms.SHOTerm(log_S0=np.log(2), log_Q=np.log(2), log_omega0=np.log(5))
gp = celerite.GP(kernel, mean=mean_model, fit_mean=True)
self.e2 * np.cos(self.w2))
offset = np.zeros(len(t))
idx = t < 57300
offset[idx] = self.offset1
offset[~idx] = self.offset2
return rv1 + rv2 + offset
mean_model = Model(P1=8.,
tau1=1.,
k1=np.std(y) / 100,
w1=0.,
e1=0.4,
P2=100,
tau2=1.,
k2=np.std(y) / 100,
w2=0.,
e2=0.4,
offset1=0.,
offset2=0.)
#==============================================================================
# The fit
#==============================================================================
import celerite
from celerite import terms
# Set up the GP model
kernel = terms.RealTerm(log_a=np.log(np.var(y)), log_c=-np.log(10.0))
gp = celerite.GP(kernel, mean=mean_model, fit_mean=True)
# plt.rcParams.update({'font.size': 20})
# fig, axes = plt.subplots(figsize=(16, 5))
plt.rcParams.update({'font.size': 24})
fig = plt.figure(figsize=(15, 7))
plt.subplots_adjust(left=left,
bottom=bottom,
right=right,
top=top,
wspace=wspace,
hspace=hspace)
fig.suptitle(r'$\epsilon$ Eridani time series', y=0.95)
axes_1 = plt.subplot(211)
axes_1.axhline(color="gray", ls='--')
fit_curve = Model(P=P, tau=tau, k=k, w0=w0, e0=e0, offset=offset)
plot_x = np.linspace(min(MJD), max(MJD), num=10000)
plot_y = fit_curve.get_value(plot_x)
wrms1 = np.sqrt(
sum(((x - np.mean(x)) / RV_noise)**2) / sum(1 / RV_noise**2))
rms1 = np.var(x)**0.5
plt.errorbar(MJD,
x + 7,
yerr=RV_noise,
fmt="k.",
capsize=0,
alpha=alpha,
label=r'$RV_{HARPS}$')
plt.plot(plot_x, plot_y, 'g-', linewidth=2.0, label='Model')
plt.ylim(-21, 21)
plt.ylabel('RV [m/s]')
aa[10, :] = [a10[i] for i in range(3)]
aa[11, :] = [a11[i] for i in range(3)]
np.savetxt('76920_MCMC_5sets_result.txt', aa, fmt='%.6f')
residual = fit_curve.get_value(np.array(x)) - np.array(y)
chi2 = sum(residual**2 / np.array(yerr)**2)
rms = np.sqrt(np.mean(residual**2))
if 0: # I need to add the offset into the data before plotting
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, m, offset = aa[:, 0]
fit_curve = Model(P1=np.log(P1),
tau1=np.log(tau1),
k1=np.log(k1),
w1=w1,
e1=e1,
P2=np.log(P2),
tau2=np.log(tau2),
k2=np.log(k2),
w2=w2,
e2=e2,
m=m,
offset=offset)
y_fit = fit_curve.get_value(x)
plt.figure()
plt.plot(x, y_fit, 'o', label='MCMC fit')
plt.errorbar(BJD,
RV_HARPS,
yerr=RV_HARPS_err,
fmt=".",
capsize=0,
label='HARPS')
plt.title("RV time series")
return rv1 + offset
truth = dict(P1=8.,
tau1=1.,
k1=np.std(y) / 100,
w1=0.,
e1=0.4,
offset1=0.,
offset2=0.)
kwargs = dict(**truth)
kwargs["bounds"] = dict(P1=(7.5, 8.5),
k1=(0, 0.1),
w1=(-2 * np.pi, 2 * np.pi),
e1=(0, 0.8))
mean_model = Model(**kwargs)
#==============================================================================
# The fit
#==============================================================================
from scipy.optimize import minimize
import celerite
from celerite import terms
# Set up the GP model
# kernel = terms.RealTerm(log_a=np.log(np.var(y)), log_c=-np.log(10.0))
kernel = terms.SHOTerm(log_S0=np.log(2),
log_Q=np.log(20),
log_omega0=np.log(1 / 3000))
gp = celerite.GP(kernel, mean=mean_model, fit_mean=True)
aa[7, :] = [a7[i] for i in range(3)]
aa[8, :] = [a8[i] for i in range(3)]
aa[9, :] = [a9[i] for i in range(3)]
aa[10, :] = [a10[i] for i in range(3)]
np.savetxt('76920_MCMC_6sets_result.txt', aa, fmt='%.6f')
# aa = np.genfromtxt('76920_MCMC_6sets_5MJ_removed_0710/76920_MCMC_6sets_result-5MJ_removed.txt', dtype = None)
aa = np.genfromtxt('76920_MCMC_6sets_result.txt', dtype=None)
P, tau, k, w, e0, off_aat, off_chiron, off_feros, off_mj1, off_mj3, off_fideos = aa[:,
0]
fit_curve = Model(P=np.log(P),
tau=np.log(tau),
k=np.log(k),
w=w,
e0=e0,
off_aat=off_aat / 100,
off_chiron=off_chiron / 100,
off_feros=off_feros / 100,
off_mj1=off_mj1 / 100,
off_mj3=off_mj3 / 100,
off_fideos=off_fideos / 100)
t_fit = np.linspace(min(RV_ALL[:, 0]) - 300,
max(RV_ALL[:, 0] + 300),
num=10001,
endpoint=True)
y_fit = fit_curve.get_value(np.array(t_fit))
residual = fit_curve.get_value(np.array(x)) - np.array(y)
chi2 = sum(residual**2 / np.array(yerr)**2)
rms = np.sqrt(np.mean(residual**2))
yerr = np.array(yerr)
aa[12, :] = [a12[i] for i in range(3)]
aa[13, :] = [a13[i] for i in range(3)]
aa[14, :] = [a14[i] for i in range(3)]
aa[15, :] = [a15[i] for i in range(3)]
np.savetxt('HD85390_fit.txt', aa, fmt='%.6f')
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, P3, tau3, k3, w3, e3, offset = aa[:,
0]
fit_curve = Model(P1=np.log(P1) / 10,
tau1=np.log(tau1),
k1=np.log(k1),
w1=w1,
e1=e1,
P2=np.log(P2) / 10,
tau2=np.log(tau2),
k2=np.log(k2),
w2=w2,
e2=e2,
P3=np.log(P3) / 10,
tau3=np.log(tau3),
k3=np.log(k3),
w3=w3,
e3=e3,
offset=offset)
t_fit = np.linspace(min(x), max(x), num=10001, endpoint=True)
y_fit = fit_curve.get_value(np.array(t_fit))
fig = plt.figure(figsize=(10, 7))
frame1 = fig.add_axes((.15, .3, .8, .6))
frame1.axhline(y=0, color='k', ls='--', alpha=.3)
plt.plot(t_fit, y_fit, alpha=.5)
plt.errorbar(x, y, yerr=yerr, fmt=".k", capsize=0)
zip(*np.percentile(real_samples, [16, 50, 84], axis=0)))
aa = np.zeros((len(guess), 3))
aa[0, :] = [a0[i] for i in range(3)]
aa[1, :] = [a1[i] for i in range(3)]
aa[2, :] = [a2[i] for i in range(3)]
aa[3, :] = [a3[i] for i in range(3)]
aa[4, :] = [a4[i] for i in range(3)]
aa[5, :] = [a5[i] for i in range(3)]
aa[6, :] = [a6[i] for i in range(3)]
np.savetxt('../../output/HD36051/36051_MCMC_result.txt', aa, fmt='%.6f')
P, tau, k, w, e0, offset1, offset2 = aa[:, 0]
fit_curve = Model(P=P,
tau=tau,
k=k,
w=w,
e0=e0,
offset1=offset1,
offset2=offset2)
y_fit = fit_curve.get_value(np.array(x))
plt.figure()
plt.errorbar(x, y, yerr=yerr, fmt=".", capsize=0, label='HARPS')
plt.errorbar(x, y_fit, yerr=yerr, fmt=".", capsize=0, label='MCMC fit')
plt.ylabel("RV [m/s]")
plt.xlabel("MJD")
plt.legend(loc="upper center")
plt.savefig('../../output/HD36051/36051_MCMC_fit.png')
plt.show()
companion = fit_curve.get_value(np.array(x))
def lnlike(theta, x, y, yerr):
P, tau, k, w, e0, offset, alpha = theta
model = Model(P=P, tau=tau, k=k, w=w, e0=e0, offset=offset, alpha=alpha)
return -0.5*(np.sum( ((y-model.get_value(np.array(x)))/yerr)**2. ))
Planet1 = Model2(P1=P1 / 1000,
tau1=tau1 / 1000,
k1=k1 / 100,
w1=w1,
e1=e1,
offset1=offset1)
y1 = Planet1.get_value(t_sample)
plt.plot(t_sample, y1, 'b-.', alpha=.3, label='Planet1')
plt.errorbar(t, xx, yerr=yerr, fmt=".k", capsize=0, label='HARPS RV')
plt.legend()
plt.ylabel("Radial velocity [m/s]")
# Jitter#
Jitter = Model(P1=P1 / 1000,
tau1=tau1 / 1000,
k1=0,
w1=w1,
e1=e1,
offset1=0,
alpha=alpha)
y_jitter = Jitter.get_value(t)
plt.plot(t, y_jitter, 'ro', alpha=.5, label='smoothed jitter')
Fit = Model(P1=P1 / 1000,
tau1=tau1 / 1000,
k1=k1 / 100,
w1=w1,
e1=e1,
offset1=offset1,
alpha=alpha)
y_fit = Fit.get_value(t)
plt.plot(t, y_fit, 'bo', alpha=.5, label='Planet 1 + smoothed jitter')
def lnlike(theta, x, y, yerr):
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, offset, alpha = theta
fit_curve = Model(P1=P1, tau1=tau1, k1=k1, w1=w1, e1=e1,
P2=P2, tau2=tau2, k2=k2, w2=w2, e2=e2, offset=offset, alpha=alpha)
y_fit = fit_curve.get_value(x)
return -0.5*(np.sum( ((y-y_fit)/yerr)**2))
aa[12, :] = [a12[i] for i in range(3)]
aa[13, :] = [a13[i] for i in range(3)]
aa[14, :] = [a14[i] for i in range(3)]
aa[15, :] = [a15[i] for i in range(3)]
np.savetxt('HD85390_fit.txt', aa, fmt='%.6f')
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, P3, tau3, k3, w3, e3, offset = aa[:,
0]
fit_curve = Model(P1=P1 / 100,
tau1=tau1 / 100,
k1=k1 / 100,
w1=w1,
e1=e1,
P2=P2 / 100,
tau2=tau2 / 100,
k2=k2 / 100,
w2=w2,
e2=e2,
P3=P3 / 100,
tau3=tau3 / 100,
k3=k3 / 100,
w3=w3,
e3=e3,
offset=offset)
t_fit = np.linspace(min(x), max(x), num=10001, endpoint=True)
y_fit = fit_curve.get_value(np.array(t_fit))
residual = fit_curve.get_value(x) - y
chi2 = sum(residual**2 / yerr**2)
rms = np.sqrt(np.mean(residual**2))
wrms = np.sqrt(sum((residual / yerr)**2) / sum(1 / yerr**2))
P1, tau1, k1, w1, e1, offset1, offset2, alpha = aa[:,0]
fig = plt.figure(figsize=(10, 7))
frame1 = fig.add_axes((.15,.3,.8,.6))
frame1.axhline(y=0, color='k', ls='--', alpha=.3)
t_sample = np.linspace(min(t), max(t), num=10001, endpoint=True)
# Planet 1 #
Planet1 = Model2(P1=np.log(P1)/10, tau1=tau1/1000, k1=k1/100, w1=w1, e1=e1, offset1=offset1, offset2=offset2)
y1 = Planet1.get_value(t_sample)
plt.plot(t_sample, y1, 'b-.', alpha=.3, label='Planet1')
plt.errorbar(t, xx, yerr=yerr, fmt=".k", capsize=0, label='HARPS RV')
plt.legend()
plt.ylabel("Radial velocity [m/s]")
# Jitter#
Jitter = Model(P1=np.log(P1)/10, tau1=tau1/1000, k1=0, w1=w1, e1=e1, offset1=0, offset2=0, alpha=np.log(alpha))
y_jitter = Jitter.get_value(t)
plt.plot(t, y_jitter, 'ro', alpha=.5, label='smoothed jitter')
Fit = Model(P1=np.log(P1)/10, tau1=tau1/1000, k1=k1/100, w1=w1, e1=e1, offset1=offset1, offset2=offset1, alpha=np.log(alpha))
y_fit = Fit.get_value(t)
plt.plot(t, y_fit, 'bo', alpha=.5, label='Planet 1 + smoothed jitter')
# plt.plot(x[x<57300], alpha*jitter_smooth, 'ro', alpha=.5, label='smoothed jitter')
plt.legend()
plt.ylabel("Radial velocity [m/s]")
residual = y_fit - XX
chi2 = sum(residual**2 / yerr**2)
rms = np.sqrt(np.mean(residual**2))
wrms = np.sqrt(sum((residual/yerr)**2) / sum(1/yerr**2))
#==============================================================================
a0, a1, a2, a3, a4, a5 = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(real_samples, [16, 50, 84], axis=0)))
aa = np.zeros((len(guess), 3))
aa[0, :] = [a0[i] for i in range(3)]
aa[1, :] = [a1[i] for i in range(3)]
aa[2, :] = [a2[i] for i in range(3)]
aa[3, :] = [a3[i] for i in range(3)]
aa[4, :] = [a4[i] for i in range(3)]
aa[5, :] = [a5[i] for i in range(3)]
np.savetxt('../../output/HD103720/103720_MCMC_result.txt', aa, fmt='%.6f')
P, tau, k, w, e0, offset = aa[:, 0]
fit_curve = Model(P=P, tau=tau, k=k, w=w, e0=e0, offset=offset)
t_fit = np.linspace(min(x) - 20, max(x), num=10001, endpoint=True)
y_fit = fit_curve.get_value(np.array(t_fit))
plt.figure()
plt.plot(t_fit, y_fit, label='MCMC fit')
plt.errorbar(x, y, yerr=yerr, fmt=".", capsize=0, label='HARPS')
plt.ylabel("RV [m/s]")
plt.xlabel("MJD")
plt.legend(loc="upper center")
plt.savefig('../../output/HD103720/103720_MCMC_fit.png')
plt.show()
companion = fit_curve.get_value(np.array(x))
residual = np.array(y) - companion
chi2 = sum(residual**2 / np.array(yerr)**2) / (len(x) - len(guess))
def lnlike(theta, x, y, yerr):
P1, tau1, k1, w1, e1, offset1, offset2, alpha = theta
fit_curve = Model(P1=P1, tau1=tau1, k1=k1, w1=w1, e1=e1, offset1=offset1, offset2=offset2, alpha=alpha)
y_fit = fit_curve.get_value(x)
return -0.5*(np.sum( ((y-y_fit)/yerr)**2))
def lnlike(theta, x, y, yerr):
P, tau, k, w, e0, offset = theta
fit_curve = Model(P=P, tau=tau, k=k, w=w, e0=e0, offset=offset)
y_fit = fit_curve.get_value(np.array(x))
return -0.5 * (np.sum(((y - y_fit) / yerr)**2.))
aa[9, :] = [a9[i] for i in range(3)]
aa[10, :] = [a10[i] for i in range(3)]
np.savetxt('HD85390_fit.txt', aa, fmt='%.6f')
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, offset = aa[:, 0]
fig = plt.figure(figsize=(10, 7))
frame1 = fig.add_axes((.15, .3, .8, .6))
frame1.axhline(y=0, color='k', ls='--', alpha=.3)
t_sample = np.linspace(min(x), max(x), num=10001, endpoint=True)
# Planet 1 #
Planet1 = Model(P1=P1 / 100,
tau1=tau1 / 100,
k1=k1 / 100,
w1=w1,
e1=e1,
P2=P2 / 100,
tau2=tau2 / 100,
k2=0,
w2=w2,
e2=e2,
offset=0)
y1 = Planet1.get_value(t_sample)
plt.plot(t_sample, y1, 'b-.', alpha=.3, label='Planet1')
# Planet 2 #
Planet2 = Model(P1=P1 / 100,
tau1=tau1 / 100,
k1=0,
w1=w1,
e1=e1,
P2=P2 / 100,
tau2=tau2 / 100,
aa[5, :] = [a5[i] for i in range(3)]
aa[6, :] = [a6[i] for i in range(3)]
aa[7, :] = [a7[i] for i in range(3)]
aa[8, :] = [a8[i] for i in range(3)]
aa[9, :] = [a9[i] for i in range(3)]
aa[10, :] = [a10[i] for i in range(3)]
aa[11, :] = [a11[i] for i in range(3)]
np.savetxt('HD85390_fit.txt', aa, fmt='%.6f')
P1, tau1, k1, w1, e1, P2, tau2, k2, w2, e2, offset, alpha = aa[:, 0]
fit_curve = Model(P1=np.log(P1) / 10,
tau1=np.log(tau1),
k1=np.log(k1),
w1=w1,
e1=e1,
P2=np.log(P2) / 10,
tau2=np.log(tau2),
k2=np.log(k2),
w2=w2,
e2=e2,
offset=offset,
alpha=alpha)
y_fit = fit_curve.get_value(x)
fit_curve2 = Model2(P1=np.log(P1) / 10,
tau1=np.log(tau1),
k1=np.log(k1),
w1=w1,
e1=e1,
P2=np.log(P2) / 10,
tau2=np.log(tau2),
k2=np.log(k2),
