def likelihood(cube, ndim, nparams):
mL = cube[0]
t0 = cube[1]
xS0 = np.array([cube[2], cube[3]])
beta = cube[4]
muL = np.array([cube[5], cube[6]])
muS = np.array([cube[7], cube[8]])
dL = cube[9]
dLdS = cube[10]
imag_base = cube[11]
# Extra parameters
dS = (1.0 * dL) / dLdS
cube[12] = dS
pspl = model.PSPL(mL, t0, xS0, beta, muL, muS, dL, dS, imag_base)
cube[13] = pspl.tE
cube[14] = pspl.thetaE_amp
cube[15] = pspl.piE[0]
cube[16] = pspl.piE[1]
cube[17] = pspl.u0_amp
cube[18] = pspl.muRel[0]
cube[19] = pspl.muRel[1]
lnL_phot = pspl.likely_photometry(t_phot, imag, imag_err)
lnL_ast = pspl.likely_astrometry(t_ast, xpos, ypos, xpos_err, ypos_err)
lnL = lnL_phot.mean() + lnL_ast.mean()
fmt = 'mL={0:4.1f} t0={1:7.1f} xS0=[{2:8.4f}, {3:8.4f}] beta={4:5.2f} '
fmt += 'muL=[{5:6.2f}, {6:6.2f}] muS=[{7:6.2f}, {8:6.2f}] dL={9:5.0f} dS={10:5.0f} '
fmt += 'imag={11:4.1f} lnL={12:12.2e}'
# print fmt.format(mL, t0, xS0[0], xS0[1], beta, muL[0], muL[1], muS[0], muS[1], dL, dS, imag_base, lnL)
return lnL
def test_pspl_parallax_boden1998(t0):
"""
I can get this one to match Figure 6 of Boden et al. 1998.
"""
# Scenarios from Paczynski 1998
raL = 80.89375 # LMC R.A.
decL = -71.74 # LMC Dec. This is the sin \beta = -0.99 where \beta =
mL = 0.1 # msun
xS0 = np.array([0.000, 0.088e-3]) # arcsec
beta = -0.16 # mas same as p=0.4
muS = np.array([-2.0, 1.5])
muL = np.array([0.0, 0.0])
dL = 8e3 # 10 kpc
dS = 50e3 # 50 kpc in LMC
imag = 19.0
# No parallax
pspl_n = model.PSPL(mL, t0, xS0, beta, muL, muS, dL, dS, imag)
print('pspl_n.u0', pspl_n.u0)
print('pspl_n.muS', pspl_n.muS)
print('pspl_n.u0_hat', pspl_n.u0_hat)
print('pspl_n.thetaE_hat', pspl_n.thetaE_hat)
# With parallax
pspl_p = model.PSPL_parallax(raL, decL, mL, t0, xS0, beta, muL, muS, dL,
dS, imag)
#t = np.arange(56000, 58000, 1)
t = np.arange(t0 - 500, t0 + 500, 1)
dt = t - pspl_n.t0
A_n = pspl_n.get_amplification(t)
A_p = pspl_p.get_amplification(t)
xS_n = pspl_n.get_astrometry(t)
xS_p_unlens = pspl_p.get_astrometry_unlensed(t)
xS_p_lensed = pspl_p.get_astrometry(t)
xL_p_unlens = pspl_p.get_lens_astrometry(t)
thetaS = (xS_p_unlens - xL_p_unlens) * 1e3 # mas
u = thetaS / pspl_p.tE
thetaS_lensed = (xS_p_lensed - xL_p_unlens) * 1e3 # mas
shift_n = pspl_n.get_centroid_shift(t) # mas
shift_p = (xS_p_lensed - xS_p_unlens) * 1e3 # mas
shift_n_amp = np.linalg.norm(shift_n, axis=1)
shift_p_amp = np.linalg.norm(shift_p, axis=1)
# Plot the amplification
fig1 = plt.figure(1)
plt.clf()
f1_1 = fig1.add_axes((0.1, 0.3, 0.8, 0.6))
plt.plot(dt, 2.5 * np.log10(A_n), 'b-', label='No parallax')
plt.plot(dt, 2.5 * np.log10(A_p), 'r-', label='Parallax')
plt.legend()
plt.ylabel('2.5 * log(A)')
f1_1.set_xticklabels([])
f2_1 = fig1.add_axes((0.1, 0.1, 0.8, 0.2))
plt.plot(dt,
2.5 * (np.log10(A_p) - np.log10(A_n)),
'k-',
label='Par - No par')
plt.axhline(0, linestyle='--', color='k')
plt.legend()
plt.ylabel('Diff')
plt.xlabel('t - t0 (MJD)')
idx = np.argmin(np.abs(t - t0))
# Plot the positions of everything
fig2 = plt.figure(2)
plt.clf()
plt.plot(xS_n[:, 0],
xS_n[:, 1],
'r--',
mfc='none',
mec='red',
label='No parallax model')
plt.plot(xS_p_unlens[:, 0],
xS_p_unlens[:, 1],
'b--',
mfc='blue',
mec='blue',
label='Parallax model, unlensed')
plt.plot(xS_p_lensed[:, 0],
xS_p_lensed[:, 1],
'b-',
label='Parallax model, lensed')
plt.plot(xL_p_unlens[:, 0],
xL_p_unlens[:, 1],
'g--',
mfc='none',
mec='green',
label='Parallax model, Lens')
plt.plot(xS_n[idx, 0], xS_n[idx, 1], 'rx')
plt.plot(xS_p_unlens[idx, 0], xS_p_unlens[idx, 1], 'bx')
plt.plot(xS_p_lensed[idx, 0], xS_p_lensed[idx, 1], 'bx')
plt.plot(xL_p_unlens[idx, 0], xL_p_unlens[idx, 1], 'gx')
plt.legend()
plt.gca().invert_xaxis()
# lim = 0.05
# plt.xlim(lim, -lim) # arcsec
# plt.ylim(-lim, lim)
# plt.xlim(0.006, -0.006) # arcsec
# plt.ylim(-0.02, 0.02)
plt.xlabel('R.A. (")')
plt.ylabel('Dec. (")')
# Check just the astrometric shift part.
fig3 = plt.figure(3)
plt.clf()
f1_3 = fig3.add_axes((0.2, 0.3, 0.7, 0.6))
plt.plot(dt, shift_n_amp, 'r--', label='No parallax model')
plt.plot(dt, shift_p_amp, 'b--', label='Parallax model')
plt.legend(fontsize=10)
plt.ylabel('Astrometric Shift (mas)')
f1_3.set_xticklabels([])
f2_3 = fig3.add_axes((0.2, 0.1, 0.7, 0.2))
plt.plot(dt, shift_p_amp - shift_n_amp, 'k-', label='Par - No par')
plt.legend()
plt.axhline(0, linestyle='--', color='k')
plt.xlabel('t - t0 (MJD)')
plt.ylabel('Res.')
fig4 = plt.figure(4)
plt.clf()
plt.plot(shift_n[:, 0], shift_n[:, 1], 'r-', label='No parallax')
plt.plot(shift_p[:, 0], shift_p[:, 1], 'b-', label='Parallax')
plt.axhline(0, linestyle='--')
plt.axvline(0, linestyle='--')
plt.gca().invert_xaxis()
plt.legend(loc='upper left')
plt.xlabel('Shift RA (mas)')
plt.ylabel('Shift Dec (mas)')
plt.axis('equal')
plt.figure(5)
plt.clf()
plt.plot(thetaS[:, 0], shift_p[:, 0], 'r-', label='RA')
plt.plot(thetaS[:, 1], shift_p[:, 1], 'b-', label='Dec')
plt.xlabel('thetaS (")')
plt.ylabel('Shift (mas)')
plt.figure(6)
plt.clf()
plt.plot(thetaS[:, 0], thetaS[:, 1], 'r-', label='Unlensed')
plt.plot(thetaS_lensed[:, 0], thetaS_lensed[:, 1], 'b-', label='Lensed')
plt.axvline(0, linestyle='--', color='k')
plt.legend()
plt.xlabel('thetaS_E (")')
plt.ylabel('thetaS_N (")')
print('Einstein radius: ', pspl_n.thetaE_amp, pspl_p.thetaE_amp)
print('Einstein crossing time: ', pspl_n.tE, pspl_n.tE)
return
def test_PSPL(mL, t0, xS0, beta, muS, muL, dL, dS, imag, outdir=''):
pspl = model.PSPL(mL, t0, xS0, beta, muL, muS, dL, dS, imag)
t = np.arange(t0 - 3000, t0 + 3000, 1)
dt = t - pspl.t0
A = pspl.get_amplification(t)
shift = pspl.get_centroid_shift(t)
shift_amp = np.linalg.norm(shift, axis=1)
# Plot the amplification
plt.figure(1)
plt.clf()
plt.plot(dt, 2.5 * np.log10(A), 'k.')
plt.xlabel('t - t0 (MJD)')
plt.ylabel('2.5 * log(A)')
plt.savefig(outdir + 'amp_v_time.png')
# Plot the positions of everything
lens_pos = pspl.xL0 + np.outer(dt / model.days_per_year, pspl.muL) * 1e-3
srce_pos = pspl.xS0 + np.outer(dt / model.days_per_year, pspl.muS) * 1e-3
imag_pos = srce_pos + (shift * 1e-3)
plt.figure(2)
plt.clf()
plt.plot(lens_pos[:, 0], lens_pos[:, 1], 'r--', mfc='none', mec='red')
plt.plot(srce_pos[:, 0], srce_pos[:, 1], 'b--', mfc='none', mec='blue')
plt.plot(imag_pos[:, 0], imag_pos[:, 1], 'b-')
lim = 0.005
plt.xlim(lim, -lim) # arcsec
plt.ylim(-lim, lim)
plt.xlabel('dRA (arcsec)')
plt.ylabel('dDec (arcsec)')
plt.title('Zoomed-in')
plt.savefig(outdir + 'on_sky_zoomed.png')
plt.figure(3)
plt.clf()
plt.plot(lens_pos[:, 0], lens_pos[:, 1], 'r--', mfc='none', mec='red')
plt.plot(srce_pos[:, 0], srce_pos[:, 1], 'b--', mfc='none', mec='blue')
plt.plot(imag_pos[:, 0], imag_pos[:, 1], 'b-')
lim = 0.05
plt.xlim(lim, -lim) # arcsec
plt.ylim(-lim, lim)
plt.xlabel('dRA (arcsec)')
plt.ylabel('dDec (arcsec)')
plt.title('Zoomed-out')
plt.savefig(outdir + 'on_sky.png')
plt.figure(4)
plt.clf()
plt.plot(dt, shift_amp)
plt.xlabel('t - t0 (MJD)')
plt.ylabel('Astrometric Shift (mas)')
plt.savefig(outdir + 'shift_amp_v_t.png')
plt.figure(5)
plt.clf()
plt.plot(shift[:, 0], shift[:, 1])
plt.gca().invert_xaxis()
plt.xlabel('RA Shift (mas)')
plt.ylabel('Dec Shift (mas)')
plt.xlim(1.5, -1.5)
plt.ylim(-0.5, 2.5)
plt.savefig(outdir + 'shift_on_sky.png')
plt.close(6)
f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)
f.subplots_adjust(hspace=0)
ax1.plot(dt / pspl.tE, shift[:, 0] / pspl.thetaE_amp, 'k-')
ax2.plot(dt / pspl.tE, shift[:, 1] / pspl.thetaE_amp, 'k-')
ax3.plot(dt / pspl.tE, shift_amp / pspl.thetaE_amp, 'k-')
ax3.set_xlabel('(t - t0) / tE)')
ax1.set_ylabel(r'dX / $\theta_E$')
ax2.set_ylabel(r'dY / $\theta_E$')
ax3.set_ylabel(r'dT / $\theta_E$')
ax1.set_ylim(-0.4, 0.4)
ax2.set_ylim(-0.4, 0.4)
ax3.set_ylim(0, 0.4)
plt.savefig(outdir + 'shift_v_t.png')
print('Einstein radius: ', pspl.thetaE_amp)
print('Einstein crossing time: ', pspl.tE)
return pspl
def test_pspl_parallax(raL,
decL,
mL,
t0,
xS0,
beta,
muS,
muL,
dL,
dS,
imag,
outdir=''):
# No parallax
pspl_n = model.PSPL(mL, t0, xS0, beta, muL, muS, dL, dS, imag)
print('pspl_n.u0', pspl_n.u0)
print('pspl_n.muS', pspl_n.muS)
print('pspl_n.u0_hat', pspl_n.u0_hat)
print('pspl_n.thetaE_hat', pspl_n.thetaE_hat)
# With parallax
pspl_p = model.PSPL_parallax(raL, decL, mL, t0, xS0, beta, muL, muS, dL,
dS, imag)
t = np.arange(t0 - 500, t0 + 500, 1)
dt = t - pspl_n.t0
A_n = pspl_n.get_amplification(t)
A_p = pspl_p.get_amplification(t)
xS_n = pspl_n.get_astrometry(t)
xS_p_unlens = pspl_p.get_astrometry_unlensed(t)
xS_p_lensed = pspl_p.get_astrometry(t)
# Plot the amplification
fig1 = plt.figure(1)
plt.clf()
f1_1 = fig1.add_axes((0.20, 0.3, 0.75, 0.6))
plt.plot(dt, 2.5 * np.log10(A_n), 'b-', label='No parallax')
plt.plot(dt, 2.5 * np.log10(A_p), 'r-', label='Parallax')
plt.legend(fontsize=10)
plt.ylabel('2.5 * log(A)')
f1_1.set_xticklabels([])
f2_1 = fig1.add_axes((0.20, 0.1, 0.75, 0.2))
plt.plot(dt,
2.5 * (np.log10(A_p) - np.log10(A_n)),
'k-',
label='Par - No par')
plt.axhline(0, linestyle='--', color='k')
plt.legend(fontsize=10)
plt.ylabel('Diff')
plt.xlabel('t - t0 (MJD)')
plt.savefig(outdir + 'amp_v_time.png')
print("save to " + outdir)
# Plot the positions of everything
fig2 = plt.figure(2)
plt.clf()
plt.plot(xS_n[:, 0] * 1e3,
xS_n[:, 1] * 1e3,
'r--',
mfc='none',
mec='red',
label='No parallax model')
plt.plot(xS_p_unlens[:, 0] * 1e3,
xS_p_unlens[:, 1] * 1e3,
'b--',
mfc='none',
mec='blue',
label='Parallax model, unlensed')
plt.plot(xS_p_lensed[:, 0] * 1e3,
xS_p_lensed[:, 1] * 1e3,
'b-',
label='Parallax model, lensed')
plt.legend(fontsize=10)
# plt.gca().invert_xaxis()
# lim = 0.05
# plt.xlim(lim, -lim) # arcsec
# plt.ylim(-lim, lim)
# plt.xlim(0.006, -0.006) # arcsec
# plt.ylim(-0.02, 0.02)
plt.axis('equal')
plt.xlabel('R.A. (mas)')
plt.ylabel('Dec. (mas)')
plt.savefig(outdir + 'on_sky.png')
# Check just the astrometric shift part.
shift_n = pspl_n.get_centroid_shift(t) # mas
shift_p = (xS_p_lensed - xS_p_unlens) * 1e3 # mas
shift_n_amp = np.linalg.norm(shift_n, axis=1)
shift_p_amp = np.linalg.norm(shift_p, axis=1)
fig3 = plt.figure(3)
plt.clf()
f1_3 = fig3.add_axes((0.20, 0.3, 0.75, 0.6))
plt.plot(dt, shift_n_amp, 'r--', label='No parallax model')
plt.plot(dt, shift_p_amp, 'b--', label='Parallax model')
plt.ylabel('Astrometric Shift (mas)')
plt.legend(fontsize=10)
f1_3.set_xticklabels([])
f2_3 = fig3.add_axes((0.20, 0.1, 0.75, 0.2))
plt.plot(dt, shift_p_amp - shift_n_amp, 'k-', label='Par - No par')
plt.legend(fontsize=10)
plt.axhline(0, linestyle='--', color='k')
plt.ylabel('Diff (mas)')
plt.xlabel('t - t0 (MJD)')
plt.savefig(outdir + 'shift_amp_v_t.png')
fig4 = plt.figure(4)
plt.clf()
plt.plot(shift_n[:, 0], shift_n[:, 1], 'r-', label='No parallax')
plt.plot(shift_p[:, 0], shift_p[:, 1], 'b-', label='Parallax')
plt.axhline(0, linestyle='--')
plt.axvline(0, linestyle='--')
plt.gca().invert_xaxis()
plt.legend(fontsize=10)
plt.xlabel('Shift RA (mas)')
plt.ylabel('Shift Dec (mas)')
plt.axis('equal')
plt.savefig(outdir + 'shift_on_sky.png')
print('Einstein radius: ', pspl_n.thetaE_amp, pspl_p.thetaE_amp)
print('Einstein crossing time: ', pspl_n.tE, pspl_n.tE)
return
def test_pspl_fit():
data, p_in = fake_data1()
# model_fitter.multinest_pspl(data, n_live_points=300, saveto='./mnest_pspl/', runcode='aa')
best = model_fitter.get_best_fit('mnest_pspl/', 'aa')
pspl_out = model.PSPL(best['mL'], best['t0'],
np.array([best['xS0_E'],
best['xS0_N']]), best['beta'],
np.array([best['muL_E'], best['muL_N']]),
np.array([best['muS_E'], best['muS_N']]), best['dL'],
best['dS'], best['imag_base'])
pspl_in = model.PSPL(p_in['mL'], p_in['t0'],
np.array([p_in['xS0_E'],
p_in['xS0_N']]), p_in['beta'],
np.array([p_in['muL_E'], p_in['muL_N']]),
np.array([p_in['muS_E'], p_in['muS_N']]), p_in['dL'],
p_in['dS'], p_in['imag_base'])
p_in['tE'] = pspl_in.tE
p_in['thetaE'] = pspl_in.thetaE_amp
p_in['piE_E'] = pspl_in.piE[0]
p_in['piE_N'] = pspl_in.piE[1]
p_in['u0_amp'] = pspl_in.u0_amp
p_in['muRel_E'] = pspl_in.muRel[0]
p_in['muRel_N'] = pspl_in.muRel[1]
model_fitter.plot_posteriors('mnest_pspl/', 'aa', sim_vals=p_in)
imag_out = pspl_out.get_photometry(data['t_phot'])
pos_out = pspl_out.get_astrometry(data['t_ast'])
imag_in = pspl_in.get_photometry(data['t_phot'])
pos_in = pspl_in.get_astrometry(data['t_ast'])
lnL_phot_out = pspl_out.likely_photometry(data['t_phot'], data['imag'],
data['imag_err'])
lnL_ast_out = pspl_out.likely_astrometry(data['t_ast'], data['xpos'],
data['ypos'], data['xpos_err'],
data['ypos_err'])
lnL_out = lnL_phot_out.mean() + lnL_ast_out.mean()
lnL_phot_in = pspl_in.likely_photometry(data['t_phot'], data['imag'],
data['imag_err'])
lnL_ast_in = pspl_in.likely_astrometry(data['t_ast'], data['xpos'],
data['ypos'], data['xpos_err'],
data['ypos_err'])
lnL_in = lnL_phot_in.mean() + lnL_ast_in.mean()
print('lnL for input: ', lnL_in)
print('lnL for output: ', lnL_out)
plt.figure(1)
plt.clf()
plt.errorbar(data['t_phot'], data['imag'], yerr=data['imag_err'], fmt='k.')
plt.plot(data['t_phot'], imag_out, 'r-')
plt.plot(data['t_phot'], imag_in, 'g-')
plt.xlabel('t - t0 (days)')
plt.ylabel('I (mag)')
plt.title('Input Data and Output Model')
plt.figure(2)
plt.clf()
plt.errorbar(data['xpos'],
data['ypos'],
xerr=data['xpos_err'],
yerr=data['ypos_err'],
fmt='k.')
plt.plot(pos_out[:, 0], pos_out[:, 1], 'r-')
plt.plot(pos_in[:, 0], pos_in[:, 1], 'g-')
plt.gca().invert_xaxis()
plt.xlabel('X Pos (")')
plt.ylabel('Y Pos (")')
plt.title('Input Data and Output Model')
plt.figure(3)
plt.clf()
plt.errorbar(data['t_ast'], data['xpos'], yerr=data['xpos_err'], fmt='k.')
plt.plot(data['t_ast'], pos_out[:, 0], 'r-')
plt.plot(data['t_ast'], pos_in[:, 0], 'g-')
plt.xlabel('t - t0 (days)')
plt.ylabel('X Pos (")')
plt.title('Input Data and Output Model')
plt.figure(4)
plt.clf()
plt.errorbar(data['t_ast'], data['ypos'], yerr=data['ypos_err'], fmt='k.')
plt.plot(data['t_ast'], pos_out[:, 1], 'r-')
plt.plot(data['t_ast'], pos_in[:, 1], 'g-')
plt.xlabel('t - t0 (days)')
plt.ylabel('Y Pos (")')
plt.title('Input Data and Output Model')
return
def fake_data1():
# Input parameters
mL_in = 10.0 # msun
t0_in = 57000.00
xS0_in = np.array([0.000, 0.000])
beta_in = -0.4 # Einstein radii
muL_in = np.array([-0.0, -7.0]) # Strong
#muL_in = np.array([-7.0, 0.0]) # Weak
muS_in = np.array([1.5, -0.5]) # mas/yr
dL_in = 4000.0
dS_in = 8000.0
imag_in = 19.0
pspl_in = model.PSPL(mL_in, t0_in, xS0_in, beta_in, muL_in, muS_in, dL_in,
dS_in, imag_in)
# Simulate
# photometric observations every 1 day and
# astrometric observations every 14 days
# for the bulge observing window. Observations missed
# for 125 days out of 365 days for photometry and missed
# for 245 days out of 365 days for astrometry.
t_phot = np.array([], dtype=float)
t_ast = np.array([], dtype=float)
for year_start in np.arange(54000, 60000, 365.25):
phot_win = 240.0
phot_start = (365.25 - phot_win) / 2.0
t_phot_new = np.arange(year_start + phot_start,
year_start + phot_start + phot_win, 1)
t_phot = np.concatenate([t_phot, t_phot_new])
ast_win = 120.0
ast_start = (365.25 - ast_win) / 2.0
t_ast_new = np.arange(year_start + ast_start,
year_start + ast_start + ast_win, 14)
t_ast = np.concatenate([t_ast, t_ast_new])
A = pspl_in.get_amplification(t_phot)
shift = pspl_in.get_centroid_shift(t_ast)
dt_phot = t_phot - pspl_in.t0
dt_ast = t_ast - pspl_in.t0
# Make the photometric observations.
# Assume 0.05 mag photoemtric errors at I=19.
# This means Signal = 400 e- at I=19.
flux0 = 400.0
imag0 = 19.0
# flux_in = flux0 * 10**((imag_in - imag0) / -2.5)
# flux_obs = flux_in * A
# flux_obs_err = flux_obs**0.5
# flux_obs += np.random.randn(len(t_phot)) * flux_obs_err
# imag_obs = -2.5 * np.log10(flux_obs / flux0) + imag0
# imag_obs_err = 1.087 / flux_obs_err
imag_obs = pspl_in.get_photometry(t_phot)
flux_obs = flux0 * 10**((imag_obs - imag0) / -2.5)
flux_obs_err = flux_obs**0.5
flux_obs += np.random.randn(len(t_phot)) * flux_obs_err
imag_obs = -2.5 * np.log10(flux_obs / flux0) + imag0
imag_obs_err = 1.087 / flux_obs_err
# Make the astrometric observations.
# Assume 0.15 milli-arcsec astrometric errors in each direction at all epochs.
lens_pos_in = pspl_in.xL0 + np.outer(dt_ast / model.days_per_year,
pspl_in.muL) * 1e-3
srce_pos_in = pspl_in.xS0 + np.outer(dt_ast / model.days_per_year,
pspl_in.muS) * 1e-3
pos_obs_tmp = pspl_in.get_astrometry(
t_ast) # srce_pos_in + (shift * 1e-3)
pos_obs_err = np.ones((len(t_ast), 2), dtype=float) * 0.15 * 1e-3
pos_obs = pos_obs_tmp + pos_obs_err * np.random.randn(len(t_ast), 2)
plt.figure(1)
plt.clf()
plt.errorbar(t_phot, imag_obs, yerr=imag_obs_err, fmt='k.')
plt.xlabel('t - t0 (days)')
plt.ylabel('I (mag)')
plt.title('Input Data and Model')
plt.figure(2)
plt.clf()
plt.errorbar(pos_obs[:, 0],
pos_obs[:, 1],
xerr=pos_obs_err[:, 0],
yerr=pos_obs_err[:, 1],
fmt='k.')
plt.gca().invert_xaxis()
plt.xlabel('X Pos (")')
plt.ylabel('Y Pos (")')
plt.plot(srce_pos_in[:, 0], srce_pos_in[:, 1], 'k--')
plt.plot(pos_obs_tmp[:, 0], pos_obs_tmp[:, 1], 'r--')
plt.title('Input Data and Model')
plt.figure(3)
plt.clf()
plt.errorbar(t_ast, pos_obs[:, 0], yerr=pos_obs_err[:, 0], fmt='k.')
plt.plot(t_ast, srce_pos_in[:, 0], 'k--')
plt.plot(t_ast, pos_obs_tmp[:, 0], 'r--')
plt.xlabel('t - t0 (days)')
plt.ylabel('X Pos (")')
plt.title('Input Data and Model')
plt.figure(4)
plt.clf()
plt.errorbar(t_ast, pos_obs[:, 1], yerr=pos_obs_err[:, 1], fmt='k.')
plt.plot(t_ast, srce_pos_in[:, 1], 'k--')
plt.plot(t_ast, pos_obs_tmp[:, 1], 'r--')
plt.xlabel('t - t0 (days)')
plt.ylabel('Y Pos (")')
plt.title('Input Data and Model')
data = {}
data['t_phot'] = t_phot
data['imag'] = imag_obs
data['imag_err'] = imag_obs_err
data['t_ast'] = t_ast
data['xpos'] = pos_obs[:, 0]
data['ypos'] = pos_obs[:, 1]
data['xpos_err'] = pos_obs_err[:, 0]
data['ypos_err'] = pos_obs_err[:, 1]
params = {}
params['mL'] = mL_in
params['t0'] = t0_in
params['xS0_E'] = xS0_in[0]
params['xS0_N'] = xS0_in[1]
params['beta'] = beta_in
params['muS_E'] = muS_in[0]
params['muS_N'] = muS_in[1]
params['muL_E'] = muL_in[0]
params['muL_N'] = muL_in[1]
params['dL'] = dL_in
params['dS'] = dS_in
params['imag_base'] = imag_in
return data, params