def likelihood(cube, ndim, nparams):
lnlikePhot = 0.0
lnlike_nonPhot = 0.0
parnames = Photpars['parnames']
# Photometric params
if MultiDimPriors == True:
params, lnlikePhot = random_photpar_multidim(cube[0],
Photpars['MultiDimPrior_Bins'],
Photpars['MultiDimPrior'][:,0],
Photpars['MultiDimPrior'][:,1],
Photpars['MultiDimPrior'][:, -nPhotpars:])
for i in range(nPhotpars): cube[i] = params[i]
else:
for i in range(nPhotpars):
param, ln_prob_param = random_photpar(cube[i],
Photpars[parnames[i]][:,0],
Photpars[parnames[i]][:,1],
Photpars[parnames[i]][:,2])
cube[i]=param
lnlikePhot += ln_prob_param
idx = nPhotpars
# x Position at t0:
thetaS0x, ln_prob_thetaS0x = random_thetaS0x(cube[idx])
cube[idx] = thetaS0x
idx += 1
lnlike_nonPhot += ln_prob_thetaS0x
# y Position at t0:
thetaS0y, ln_prob_thetaS0y = random_thetaS0y(cube[idx])
cube[idx] = thetaS0y
idx += 1
lnlike_nonPhot += ln_prob_thetaS0y
# Source proper motion (x dimension)
muSx, ln_prob_muSx = random_muSx(cube[idx])
cube[idx] = muSx
idx += 1
lnlike_nonPhot += ln_prob_muSx
# Source proper motion (y dimension)
muSy, ln_prob_muSy = random_muSy(cube[idx])
cube[idx] = muSy
idx += 1
lnlike_nonPhot += ln_prob_muSy
# Source-lens relative proper motion (x dimension)
muRelx, ln_prob_muRelx = random_muRelx(cube[idx])
cube[idx] = muRelx
idx += 1
lnlike_nonPhot += ln_prob_muRelx
# Source-lens relative proper motion (y dimension)
muRely, ln_prob_muRely = random_muRely(cube[idx])
cube[idx] = muRely
idx += 1
lnlike_nonPhot += ln_prob_muRely
t0 = cube[0]
beta = cube[1]
tE = cube[2]
piEN = cube[3]
piEE= cube[4]
#Create astrometric model of source
thetaS_model, thetaE_amp, M, shift, thetaS_nolens = MCMC_LensModel.LensModel_Trial1(tobs, t0, tE,
[thetaS0x, thetaS0y],
[muSx,muSy],
[muRelx, muRely],
beta,
[piEN, piEE])
cube[11] = thetaE_amp
cube[12] = M
thetaSx_model = thetaS_model[:,0]
thetaSy_model = thetaS_model[:,1]
lnlike = lnlikePhot + lnlike_nonPhot + \
MCMC_LensModel.lnLikelihood(thetaSx_model, thetaSx_data, xerr_data) + \
MCMC_LensModel.lnLikelihood(thetaSy_model, thetaSy_data, yerr_data)
# print "Log Likelihood: ", lnlike
return lnlike
def calc_chi2_lens_fit(
root_dir='/Users/jlu/work/microlens/2015_evan/',
analysis_dir='analysis_ob110022_2014_03_22al_MC100_omit_1/',
mnest_run='bf',
target='OB110022',
useMedian=False,
verbose=True):
# Assume this is NIRC2 data.
pixScale = 9.952 # mas / pixel
if target == 'ob120169':
targname = 'ob120169_R'
else:
targname = target
#Plot astrometric observations
pointsFile = root_dir + analysis_dir + 'points_d/' + targname + '.points'
pointsTab = Table.read(pointsFile, format='ascii')
tobs = pointsTab['col1']
xpix = pointsTab['col2']
ypix = pointsTab['col3']
xerr = pointsTab['col4']
yerr = pointsTab['col5']
thetaSx_data = xpix * pixScale
thetaSy_data = ypix * pixScale
xerr_data = xerr * pixScale
yerr_data = yerr * pixScale
# Load Best-Fit Microlensing Model
mnest_dir = 'multiNest/' + mnest_run + '/'
mnest_root = mnest_run
tab = load_mnest_results(root_dir=root_dir + analysis_dir,
mnest_dir=mnest_dir,
mnest_root=mnest_root)
params = tab.keys()
pcnt = len(params)
Masslim = 0.0
# Clean table and only keep valid results.
ind = np.where((tab['Mass'] >= Masslim))[0]
tab = tab[ind]
if not useMedian:
best = np.argmax(tab['logLike'])
maxLike = tab['logLike'][best]
if verbose:
print 'Best-Fit Solution:'
print ' Index = {0:d}'.format(best)
print ' Log(L) = {0:6.2f}'.format(maxLike)
print ' Params:'
for i in range(pcnt):
print ' {0:15s} {1:10.3f}'.format(params[i],
tab[params[i]][best])
t0 = tab['t0'][best]
tE = tab['tE'][best]
thetaS0x = tab['thetaS0x'][best]
thetaS0y = tab['thetaS0y'][best]
muSx = tab['muSx'][best]
muSy = tab['muSy'][best]
muRelx = tab['muRelx'][best]
muRely = tab['muRely'][best]
beta = tab['beta'][best]
piEN = tab['piEN'][best]
piEE = tab['piEE'][best]
if verbose:
print ' muLx = {0:5.2f} mas/yr'.format(muSx - muRelx)
print ' muLy = {0:5.2f} mas/yr'.format(muSy - muRely)
else:
t0 = weighted_quantile(tab['t0'], 0.5, sample_weight=tab['weights'])
tE = weighted_quantile(tab['tE'], 0.5, sample_weight=tab['weights'])
thetaS0x = weighted_quantile(tab['thetaS0x'],
0.5,
sample_weight=tab['weights'])
thetaS0y = weighted_quantile(tab['thetaS0y'],
0.5,
sample_weight=tab['weights'])
muSx = weighted_quantile(tab['muSx'],
0.5,
sample_weight=tab['weights'])
muSy = weighted_quantile(tab['muSy'],
0.5,
sample_weight=tab['weights'])
muRelx = weighted_quantile(tab['muRelx'],
0.5,
sample_weight=tab['weights'])
muRely = weighted_quantile(tab['muRely'],
0.5,
sample_weight=tab['weights'])
beta = weighted_quantile(tab['beta'],
0.5,
sample_weight=tab['weights'])
piEN = weighted_quantile(tab['piEN'],
0.5,
sample_weight=tab['weights'])
piEE = weighted_quantile(tab['piEE'],
0.5,
sample_weight=tab['weights'])
if verbose:
print 'Median Solution:'
print ' Params:'
print ' {0:15s} {1:10.3f}'.format('t0', t0)
print ' {0:15s} {1:10.3f}'.format('tE', tE)
print ' {0:15s} {1:10.3f}'.format('thetaS0x', thetaS0x)
print ' {0:15s} {1:10.3f}'.format('thetaS0y', thetaS0y)
print ' {0:15s} {1:10.3f}'.format('muSx', muSx)
print ' {0:15s} {1:10.3f}'.format('muSy', muSy)
print ' {0:15s} {1:10.3f}'.format('muRelx', muRelx)
print ' {0:15s} {1:10.3f}'.format('muRely', muRely)
print ' {0:15s} {1:10.3f}'.format('beta', beta)
print ' {0:15s} {1:10.3f}'.format('piEN', piEN)
print ' {0:15s} {1:10.3f}'.format('piEE', piEE)
print ' muLx = {0:5.2f} mas/yr'.format(muSx - muRelx)
print ' muLy = {0:5.2f} mas/yr'.format(muSy - muRely)
##########
# Get astrometry for best-fit model. Do this on a fine time grid
# and also at the points of the observations.
##########
tmod = np.arange(t0 - 20.0, t0 + 20.0, 0.01)
model = MCMC_LensModel.LensModel_Trial1(tmod, t0, tE, [thetaS0x, thetaS0y],
[muSx, muSy], [muRelx, muRely],
beta, [piEN, piEE])
model_tobs = MCMC_LensModel.LensModel_Trial1(tobs, t0, tE,
[thetaS0x, thetaS0y],
[muSx, muSy],
[muRelx, muRely], beta,
[piEN, piEE])
thetaS_model = model[0]
thetaE_amp = model[1]
M = model[2]
shift = model[3]
thetaS_nolens = model[4]
thetaS_model_tobs = model_tobs[0]
thetaE_amp_tobs = model_tobs[1]
M_tobs = model_tobs[2]
shift_tobs = model_tobs[3]
thetaS_nolens_tobs = model_tobs[4]
thetaSx_model = thetaS_model[:, 0]
thetaSy_model = thetaS_model[:, 1]
thetaS_nolensx = thetaS_nolens[:, 0]
thetaS_nolensy = thetaS_nolens[:, 1]
shiftx = shift[:, 0]
shifty = shift[:, 1]
thetaSx_model_tobs = thetaS_model_tobs[:, 0]
thetaSy_model_tobs = thetaS_model_tobs[:, 1]
##########
# Calculate Chi-Squared Star for comparison to velocity-only fit.
##########
# Find the model points closest to the data.
dx = thetaSx_data - thetaSx_model_tobs
dy = thetaSy_data - thetaSy_model_tobs
chi2_x = ((dx / xerr_data)**2).sum()
chi2_y = ((dy / yerr_data)**2).sum()
N_dof = (2 * len(dx)) - 9
chi2_tot = chi2_x + chi2_y
chi2_red = chi2_tot / N_dof
if verbose:
print 'Chi-Squared of Lens Model Fit:'
print ' X Chi^2 = {0:5.2f}'.format(chi2_x)
print ' Y Chi^2 = {0:5.2f}'.format(chi2_y)
print ' Total Chi^2 = {0:5.2f} ({1:d} DOF)'.format(chi2_tot, N_dof)
print ' Reduced Chi^2 = {0:5.2f}'.format(chi2_red)
print ''
print ''
return chi2_tot, N_dof, chi2_red
def likelihood(cube, ndim, nparams):
lnlikePhot = 0.0
lnlike_nonPhot = 0.0
parnames = Photpars['parnames']
# Photometric params
if MultiDimPriors == True:
params, lnlikePhot = random_photpar_multidim(
cube[0], Photpars['MultiDimPrior_Bins'],
Photpars['MultiDimPrior'][:, 0], Photpars['MultiDimPrior'][:,
1],
Photpars['MultiDimPrior'][:, -nPhotpars:])
for i in range(nPhotpars):
cube[i] = params[i]
else:
for i in range(nPhotpars):
param, ln_prob_param = random_photpar(
cube[i], Photpars[parnames[i]][:, 0],
Photpars[parnames[i]][:, 1], Photpars[parnames[i]][:, 2])
cube[i] = param
lnlikePhot += ln_prob_param
idx = nPhotpars
# x Position at t0:
thetaS0x, ln_prob_thetaS0x = random_thetaS0x(cube[idx])
cube[idx] = thetaS0x
idx += 1
lnlike_nonPhot += ln_prob_thetaS0x
# y Position at t0:
thetaS0y, ln_prob_thetaS0y = random_thetaS0y(cube[idx])
cube[idx] = thetaS0y
idx += 1
lnlike_nonPhot += ln_prob_thetaS0y
# Source proper motion (x dimension)
muSx, ln_prob_muSx = random_muSx(cube[idx])
cube[idx] = muSx
idx += 1
lnlike_nonPhot += ln_prob_muSx
# Source proper motion (y dimension)
muSy, ln_prob_muSy = random_muSy(cube[idx])
cube[idx] = muSy
idx += 1
lnlike_nonPhot += ln_prob_muSy
# Source-lens relative proper motion (x dimension)
muRelx, ln_prob_muRelx = random_muRelx(cube[idx])
cube[idx] = muRelx
idx += 1
lnlike_nonPhot += ln_prob_muRelx
# Source-lens relative proper motion (y dimension)
muRely, ln_prob_muRely = random_muRely(cube[idx])
cube[idx] = muRely
idx += 1
lnlike_nonPhot += ln_prob_muRely
t0 = cube[0]
beta = cube[1]
tE = cube[2]
piEN = cube[3]
piEE = cube[4]
#Create astrometric model of source
thetaS_model, thetaE_amp, M, shift, thetaS_nolens = MCMC_LensModel.LensModel_Trial1(
tobs, t0, tE, [thetaS0x, thetaS0y], [muSx, muSy], [muRelx, muRely],
beta, [piEN, piEE])
cube[11] = thetaE_amp
cube[12] = M
thetaSx_model = thetaS_model[:, 0]
thetaSy_model = thetaS_model[:, 1]
lnlike = lnlikePhot + lnlike_nonPhot + \
MCMC_LensModel.lnLikelihood(thetaSx_model, thetaSx_data, xerr_data) + \
MCMC_LensModel.lnLikelihood(thetaSy_model, thetaSy_data, yerr_data)
# print "Log Likelihood: ", lnlike
return lnlike
def plot_OB120169(
root_dir='/Users/jlu/work/microlens/OB120169/analysis_2016_09_14/',
analysis_dir='analysis_ob120169_2016_09_14_a4_m22_w4_MC100/',
points_dir='points_d/',
mnest_dir='multiNest/up/',
mnest_root='up'):
target = 'OB120169_R'
display_name = 'OB120169'
#Plot astrometric observations
pointsFile = root_dir + analysis_dir + points_dir + target + '.points'
pointsTab = Table.read(pointsFile, format='ascii')
tobs = pointsTab['col1']
xpix = pointsTab['col2']
ypix = pointsTab['col3']
xerr = pointsTab['col4']
yerr = pointsTab['col5']
pixScale = 9.952
thetaSx_data = xpix * pixScale
thetaSy_data = ypix * pixScale
xerr_data = xerr * pixScale
yerr_data = yerr * pixScale
# Overplot Best-Fit Model
tab = load_mnest_results_OB120169(root_dir=root_dir + analysis_dir,
mnest_dir=mnest_dir,
mnest_root=mnest_root)
params = tab.keys()
pcnt = len(params)
Masslim = 0.0
# Clean table and only keep valid results.
ind = np.where((tab['Mass'] >= Masslim))[0]
tab = tab[ind]
best = np.argmax(tab['logLike'])
maxLike = tab['logLike'][best]
print 'Best-Fit Solution:'
print ' Index = {0:d}'.format(best)
print ' Log(L) = {0:6.2f}'.format(maxLike)
print ' Params:'
for i in range(pcnt):
print ' {0:15s} {1:10.3f}'.format(params[i], tab[params[i]][best])
t0 = tab['t0'][best]
tE = tab['tE'][best]
thetaS0x = tab['thetaS0x'][best]
thetaS0y = tab['thetaS0y'][best]
muSx = tab['muSx'][best]
muSy = tab['muSy'][best]
muRelx = tab['muRelx'][best]
muRely = tab['muRely'][best]
beta = tab['beta'][best]
piEN = tab['piEN'][best]
piEE = tab['piEE'][best]
print ' muLx = {0:5.2f} mas/yr'.format(muSx - muRelx)
print ' muLy = {0:5.2f} mas/yr'.format(muSy - muRely)
##########
# Get astrometry for best-fit model. Do this on a fine time grid
# and also at the points of the observations.
##########
tmod = np.arange(t0 - 20.0, t0 + 20.0, 0.01)
model = MCMC_LensModel.LensModel_Trial1(tmod, t0, tE, [thetaS0x, thetaS0y],
[muSx, muSy], [muRelx, muRely],
beta, [piEN, piEE])
model_tobs = MCMC_LensModel.LensModel_Trial1(tobs, t0, tE,
[thetaS0x, thetaS0y],
[muSx, muSy],
[muRelx, muRely], beta,
[piEN, piEE])
thetaS_model = model[0]
thetaE_amp = model[1]
M = model[2]
shift = model[3]
thetaS_nolens = model[4]
thetaS_model_tobs = model_tobs[0]
thetaE_amp_tobs = model_tobs[1]
M_tobs = model_tobs[2]
shift_tobs = model_tobs[3]
thetaS_nolens_tobs = model_tobs[4]
thetaSx_model = thetaS_model[:, 0]
thetaSy_model = thetaS_model[:, 1]
thetaS_nolensx = thetaS_nolens[:, 0]
thetaS_nolensy = thetaS_nolens[:, 1]
shiftx = shift[:, 0]
shifty = shift[:, 1]
thetaSx_model_tobs = thetaS_model_tobs[:, 0]
thetaSy_model_tobs = thetaS_model_tobs[:, 1]
##########
# Calculate Chi-Squared Stat for comparison to velocity-only fit.
##########
# Find the model points closest to the data.
dx = thetaSx_data - thetaSx_model_tobs
dy = thetaSy_data - thetaSy_model_tobs
chi2_x = ((dx / xerr_data)**2).sum()
chi2_y = ((dy / yerr_data)**2).sum()
N_dof = (2 * len(dx)) - 9
chi2_red = (chi2_x + chi2_y) / N_dof
print 'Chi-Squared of Lens Model Fit:'
print ' X Chi^2 = {0:5.2f}'.format(chi2_x)
print ' Y Chi^2 = {0:5.2f}'.format(chi2_y)
print ' Reduced Chi^2 = {0:5.2f}'.format(chi2_red)
##########
# Plotting
##########
fontsize1 = 18
fontsize2 = 14
py.clf()
fig1 = py.figure(2, figsize=(10, 8))
py.subplots_adjust(left=0.1, top=0.95, hspace=0.3, wspace=0.3)
paxes = py.subplot(2, 2, 1)
originX = np.mean(thetaSx_model)
originY = np.mean(thetaSy_model)
py.plot(tmod - t0, thetaSx_model - originX, 'r-')
py.plot(tmod - t0, thetaS_nolensx - originX, 'r--')
py.errorbar(tobs - t0, thetaSx_data - originX, yerr=xerr_data, fmt='k.')
py.ylabel(r'$\Delta\alpha$ (mas)', fontsize=fontsize1)
py.xlabel('t - t$_{\mathrm{o}}$ (yr)', fontsize=fontsize1)
py.ylim(-4, 12)
py.xlim(-0.5, 6.0)
xticks = np.arange(0, 4.1, 1, dtype=int)
py.xticks(xticks, fontsize=fontsize2)
py.yticks(fontsize=fontsize2)
paxes = py.subplot(2, 2, 2)
py.plot(tmod - t0, thetaSy_model - originY, 'b-')
py.plot(tmod - t0, thetaS_nolensy - originY, 'b--')
py.errorbar(tobs - t0, thetaSy_data - originY, yerr=yerr_data, fmt='k.')
py.ylabel(r'$\Delta\delta$ (mas)', fontsize=fontsize1)
py.xlabel('t - t$_{\mathrm{o}}$ (yr)', fontsize=fontsize1)
py.ylim(-2, 6)
py.xlim(-0.5, 6.0)
py.xticks(xticks, fontsize=fontsize2)
py.yticks(fontsize=fontsize2)
paxes = py.subplot(2, 2, 3)
n = len(tmod)
py.plot(thetaS_nolensx - originX, thetaS_nolensy - originY, 'g--')
py.plot(thetaSx_model - originX, thetaSy_model - originY, 'g-')
py.errorbar(thetaSx_data - originX,
thetaSy_data - originY,
xerr=xerr_data,
yerr=yerr_data,
fmt='k.')
py.ylabel(r'$\Delta\delta$ (mas)', fontsize=fontsize1)
py.xlabel(r'$\Delta\alpha$ (mas)', fontsize=fontsize1)
py.axis('equal')
py.ylim(-5, 7)
py.xlim(-4, 8)
py.xticks(fontsize=fontsize2)
py.yticks(fontsize=fontsize2)
py.xlim(py.xlim()[::-1])
# Make a histogram of the mass using the weights. This creates the
# marginalized 1D posteriors.
paxes = py.subplot(2, 2, 4)
bins = np.arange(0, 30, 0.25)
n, bins, patch = py.hist(tab['Mass'],
normed=True,
histtype='step',
weights=tab['weights'],
bins=bins,
linewidth=1.5)
bin_centers = (bins[:-1] + bins[1:]) / 2
py.xlabel('Mass')
xtitle = r'Lens Mass (M$_{\odot}$)'
py.xlabel(xtitle, fontsize=fontsize1, labelpad=10)
py.xlim(0, 20)
py.ylim(0, 0.2)
py.ylabel('Relative probability', fontsize=fontsize1, labelpad=10)
py.xticks(fontsize=fontsize2)
py.yticks(fontsize=fontsize2)
outdir = root_dir + analysis_dir + mnest_dir + 'plots/'
outfile = outdir + 'plot_OB120169_data_vs_model.png'
fileUtil.mkdir(outdir)
print 'writing plot to file ' + outfile
py.savefig(outfile)
return