def plot_img_pos(pars, pix_scale=1., threshold=0.8, fits_file=None, img_xobs=None, img_yobs=None, d=None):
xsrcA, ysrcA, sigsrcA, xlens, ylens, blens, qlens, plens = pars
fig_dir = 'Figures/lensed_quasar/'
sa = (0, 100) # search area is 2000 pixels to 5000 pixels
# Define source positions as a Guassian surface brightness profile
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
X1['A'] = pymc.Uniform('X1A', 0., 100., value=xsrcA)
Y1['A'] = pymc.Uniform('Y1A', 0., 100., value=ysrcA)
Q1['A'] = pymc.Uniform('Q1A', 0.2, 1., value=1.)
P1['A'] = pymc.Uniform('P1A', -180., 180., value=0.)
S1['A'] = pymc.Uniform('N1A', 0., 6., value=sigsrcA)
srcs['A'] = SBObjects.Gauss('', {'x': X1['A'], 'y': Y1['A'], 'q': Q1['A'],'pa': P1['A'], 'sigma': S1['A']})
# Define lens mass model
LX = pymc.Uniform('lx', 0., 100., value=xlens)
LY = pymc.Uniform('ly', 0., 100., value=ylens)
LB = pymc.Uniform('lb', 0., 100., value=blens)
LQ = pymc.Uniform('lq', 0.2, 1., value=qlens)
LP = pymc.Uniform('lp', -180., 180., value=plens)
XB = pymc.Uniform('xb', -0.2, 0.2, value=0.)
XP = pymc.Uniform('xp', -180., 180., value=0.)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
shear = MassModels.ExtShear('',{'x':LX,'y':LY,'b':XB,'pa':XP})
lenses = [lens]
x, y = np.meshgrid(np.arange(sa[0], sa[1], pix_scale), np.arange(sa[0], sa[1], pix_scale))
image_plane, image_coords_pred = {}, {}
for name in ['A']:
x_src, y_src = pylens.getDeflections(lenses, [x, y], d=d[name])
image_plane[name] = srcs[name].pixeval(x_src, y_src)
plt.figure()
plt.imshow(image_plane[name], interpolation='nearest', origin='lower')
plt.xlabel('%dx - %d pixels' % (pix_scale, sa[0]))
plt.ylabel('%dy - %d pixels' % (pix_scale, sa[0]))
plt.savefig(os.path.join(ROOT_DIR, fig_dir, 'image_plane%s.png' % name))
image_coords_pred[name] = np.add(np.multiply(np.where(image_plane[name] > threshold), pix_scale)[::-1], sa[0])
lnlike, img_xpred_compare, img_ypred_compare = calc_lnlike(image_coords_pred[name], img_xobs[name], img_yobs[name])
print(img_xpred_compare, img_xobs[name], lnlike)
print(img_ypred_compare, img_yobs[name], lnlike)
colors = (col for col in ['#1f77b4', '#2ca02c', '#9467bd', '#17becf', '#e377c2'])
fig = plt.figure('image_and_position')
plot_image(fits_file, figname='image_and_position', vmax=10.)
plt.xlim(sa[0], sa[1])
plt.ylim(sa[0], sa[1])
for name in ['A']:
plt.scatter(image_coords_pred[name][0], image_coords_pred[name][1], marker='.', alpha=0.3, c=next(colors))
plt.savefig(os.path.join(ROOT_DIR, fig_dir, 'image_with_predicted_image_plane.png'))
def get_quasar_img_pos(pix_scale=1., threshold=0.8, fits_file=None, img_xobs=None, img_yobs=None, d=None):
fig_dir = 'Figures/lensed_quasar/'
sa = (0, 100) # search area is 2000 pixels to 5000 pixels
# Define source positions as a Guassian surface brightness profile
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
X1['A'] = pymc.Uniform('X1A', 0., 100., value=52.)
Y1['A'] = pymc.Uniform('Y1A', 0., 100., value=48.)
Q1['A'] = pymc.Uniform('Q1A', 1., 1., value=1.)
P1['A'] = pymc.Uniform('P1A', 0., 0., value=0.)
S1['A'] = pymc.Uniform('N1A', 0., 6., value=1.2)
srcs['A'] = SBObjects.Gauss('', {'x': X1['A'], 'y': Y1['A'], 'q': Q1['A'],'pa': P1['A'], 'sigma': S1['A']})
pars = [X1['A'], Y1['A'], S1['A']] # List of parameters
cov = [0.1, 0.1, 1.5] # List of initial `scatter' for emcee
# Define lens mass model
LX = pymc.Uniform('lx', 0., 100., value=49.)
LY = pymc.Uniform('ly', 0., 100., value=50.)
LB = pymc.Uniform('lb', 10., 40., value=20.)
LQ = pymc.Uniform('lq', 0.2, 1., value=0.8)
LP = pymc.Uniform('lp', -180., 180., value=85.)
XB = pymc.Uniform('xb', -0.2, 0.2, value=0.)
XP = pymc.Uniform('xp', -180., 180., value=0.)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
# shear = MassModels.ExtShear('', {'x': LX, 'y': LY, 'b': XB, 'pa': XP})
lenses = [lens]
pars += [LX, LY, LB, LQ, LP]
cov += [0.2, 0.2, 0.2, 0.05, 10.]
cov = np.array(cov)
# Get grid of x and y points
x, y = np.meshgrid(np.arange(sa[0], sa[1], pix_scale), np.arange(sa[0], sa[1], pix_scale))
# MCMC setup
nwalkers = 100
nsteps = 1000
# Define likelihood function
@pymc.observed
def logL(value=0., tmp=pars):
for key in srcs:
srcs[key].setPars()
for lens in lenses:
lens.setPars()
lnlike = {}
for name in ['A']:
# Calculate deflections
x_src, y_src = pylens.getDeflections(lenses, [x, y], d[name])
# Get list of predicted image coordinates
image_plane = srcs[name].pixeval(x_src, y_src)
image_coords_pred = np.add(np.multiply(np.where(image_plane > threshold), pix_scale)[::-1], sa[0]) # Only if brightness > threshold
if not image_coords_pred.size: # If it's an empty list
return -1e30
img_xpred, img_ypred = image_coords_pred
# Map each observed image to the single closest predicted image
pred_arg = []
for xo, yo in zip(img_xobs[name], img_yobs[name]):
xdist = np.abs(img_xpred - xo) # pixel distance between xobs and xpredicted
ydist = np.abs(img_ypred - yo)
dist = xdist**2 + ydist**2
pred_arg.append(np.argmin(dist)) # The index of the pred_img that the given observed image is closest to
pred_arg = np.array(pred_arg)
# these pred images are the ones that are being compared with the list of the obs images
img_xpred_compare = np.array([img_xpred[i] for i in pred_arg])
img_ypred_compare = np.array([img_ypred[i] for i in pred_arg])
lnlike[name] = -0.5 * (np.sum((img_xpred_compare - img_xobs[name]) ** 2 + (img_ypred_compare - img_yobs[name]) ** 2))
print(name, img_xpred_compare, lnlike[name], float(srcs[name].x), float(srcs[name].y), float(srcs[name].sigma), float(lens.x), float(lens.y), float(lens.b), float(lens.q), float(lens.pa))
print(name, img_ypred_compare, lnlike[name], float(srcs[name].x), float(srcs[name].y), float(srcs[name].sigma), float(lens.x), float(lens.y), float(lens.b), float(lens.q), float(lens.pa))
return sum(lnlike.values())
# Run MCMC
sampler = myEmcee.Emcee(pars+[logL], cov, nwalkers=nwalkers, nthreads=44)
sampler.sample(nsteps)
# Plot chains
result = sampler.result()
posterior, samples, _, best = result
print best
import pylab
for j in range(nwalkers):
pylab.plot(posterior[:, j])
for i in range(len(pars)):
pylab.figure()
for j in range(nwalkers):
pylab.plot(samples[:, j, i])
# Trim initial samples (ie the burn-in) and concatenate chains
burn = 200
samples = samples[burn:].reshape(((nsteps-burn) * nwalkers, len(pars)))
# Get best fit parameters
samples_exp = samples.copy()
samples_exp[:, 2] = np.exp(samples_exp[:, 2])
best_fits = list(map(lambda v: (v[1]), zip(*np.percentile(samples_exp, [16, 50, 84], axis=0))))
print('bestfits')
print(best_fits)
# Plot parameter contours and mcmc chains
param_names = ['$xA_{src}$', '$yA_{src}$', '$\sigma A_{src}$']
param_names += ['$x_{lens}$', '$y_{lens}$', '$b_{lens}$', '$q_{lens}$', '$pa_{lens}$']
c = ChainConsumer()
c.add_chain(samples, parameters=param_names)
c.configure(summary=True, cloud=True)
fig = c.plotter.plot()
fig.savefig(os.path.join(ROOT_DIR, fig_dir, 'source_pos_parameter_contours.png'), transparent=False)
fig = c.plotter.plot_walks(convolve=100)
fig.savefig(os.path.join(ROOT_DIR, fig_dir, 'source_pos_mcmc_walks.png'), transparent=False)
b = best
print(b)
plot_img_pos(pars=b, pix_scale=pix_scale, threshold=threshold, fits_file=fits_file, img_xobs=img_xobs, img_yobs=img_yobs, d=d)
def plot_img_pos(pars,
pix_scale=1.,
threshold=0.8,
fits_file=None,
img_xobs=None,
img_yobs=None,
d=None,
fig_dir=None):
names = img_xobs.keys()
sa = (2000, 4500) # search area is 2000 pixels to 5000 pixels
xsrc, ysrc, sigsrc = {}, {}, {}
for i, name in enumerate(names):
xsrc[name], ysrc[name], sigsrc[name] = pars[3 * i:3 * (i + 1)]
xlens, ylens, blens, qlens, plens = pars[-5:]
# Define source positions as a Guassian surface brightness profile
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
for name in names:
X1[name] = pymc.Uniform('X1%s' % name, 0., 5000., value=xsrc[name])
Y1[name] = pymc.Uniform('Y1%s' % name, 0., 5000., value=ysrc[name])
Q1[name] = pymc.Uniform('Q1%s' % name, 0.2, 1., value=1.)
P1[name] = pymc.Uniform('P1%s' % name, -180., 180., value=0.)
S1[name] = pymc.Uniform('N1%s' % name, 0., 10000., value=sigsrc[name])
srcs[name] = SBObjects.Gauss(
'', {
'x': X1[name],
'y': Y1[name],
'q': Q1[name],
'pa': P1[name],
'sigma': S1[name]
})
# Define lens mass model
LX = pymc.Uniform('lx', 0., 5000., value=xlens)
LY = pymc.Uniform('ly', 0., 5000., value=ylens)
LB = pymc.Uniform('lb', 0., 5000., value=blens)
LQ = pymc.Uniform('lq', 0.2, 1., value=qlens)
LP = pymc.Uniform('lp', -180., 180., value=plens)
XB = pymc.Uniform('xb', -0.2, 0.2, value=0.)
XP = pymc.Uniform('xp', -180., 180., value=0.)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
shear = MassModels.ExtShear('', {'x': LX, 'y': LY, 'b': XB, 'pa': XP})
lenses = [lens]
x, y = np.meshgrid(np.arange(sa[0], sa[1], pix_scale),
np.arange(sa[0], sa[1], pix_scale))
image_plane, image_coords_pred = {}, {}
for name in names:
x_src, y_src = pylens.getDeflections(lenses, [x, y], d=d[name])
image_plane[name] = srcs[name].pixeval(x_src, y_src)
plt.figure()
plt.imshow(image_plane[name], interpolation='nearest', origin='lower')
plt.xlabel('%dx - %d pixels' % (pix_scale, sa[0]))
plt.ylabel('%dy - %d pixels' % (pix_scale, sa[0]))
plt.savefig(os.path.join(ROOT_DIR, fig_dir,
'image_plane%s.png' % name))
image_indexes_pred = np.where(image_plane[name] > threshold)
image_coords_pred[name] = np.array(
[x[image_indexes_pred], y[image_indexes_pred]])
print(name, image_coords_pred[name])
colors = (col for col in
['#1f77b4', '#2ca02c', '#9467bd', '#17becf', '#e377c2', 'lime'])
markers = (marker for marker in ['x', 'o', '*', '+', 'v', 'D'])
fig = plt.figure('image_and_position', figsize=(13, 13))
plot_image(fits_file, figname='image_and_position')
plt.xlim(sa[0], sa[1])
plt.ylim(sa[0], sa[1])
for name in names:
plt.scatter(img_xobs[name],
img_yobs[name],
marker=next(markers),
c='white',
label="%s obs" % name,
alpha=0.8)
plt.scatter(image_coords_pred[name][0],
image_coords_pred[name][1],
marker='.',
alpha=0.5,
c=next(colors),
label=name)
plt.legend(loc='upper right')
plt.savefig(
os.path.join(ROOT_DIR, fig_dir,
'image_with_predicted_image_plane.png'))
def macs0451_multiple_sources():
fig_dir = os.path.join(ROOT_DIR, 'Figures/penalise1MACS0451_multiple_sis_model_log')
if not os.path.exists(fig_dir):
os.makedirs(fig_dir)
fits_file = '/home/djm241/PycharmProjects/StrongLensing/data/MACS0451/MACS0451_F110W.fits'
if not os.path.isfile(fits_file):
fits_file = '/Users/danmuth/PycharmProjects/StrongLensing/data/MACS0451/MACS0451_F110W.fits'
sa = (2000, 4500)
pix_scale = 10.
img_name = ''
z_lens = 0.43
img_xobs, img_yobs, d, init = OrderedDict(), OrderedDict(), OrderedDict(), OrderedDict()
img_xobs['A'] = np.array([2375.942110, 2378.5, 2379.816610, 2381.299088, 2384, 2385.927991, 2389.555816, 2457.694760, 2450.744242, 2442.833333, 2437.857924, 2433.064587, 2427.166666, 2424.099866, 2418.5, 2416.444081, 2462])
img_yobs['A'] = np.array([3038.016677, 3024, 3012.367933, 2999.365293, 2983.5, 2970.435199, 2955.945319, 2737.545077, 2752.305849, 2766.166666, 2782.058508, 2795.293450, 2811.166666, 2823.079067, 2837.5, 2846.943113, 2728])
d['A'] = scale_einstein_radius(z_lens=z_lens, z_src=2.013)
init['A'] = {'xsrc': 3.49212756e+03, 'ysrc': 3.08381379e+03, 'sigsrc': 8.06085547e+00}
img_xobs['B'] = np.array([3276.693717, 3261.382557, 3427.351819, 3417.043471, 3497.163625, 3486.371962])
img_yobs['B'] = np.array([3482.795501, 3482.854177, 2592.719350, 2590.191799, 3075.107748, 3069.305065])
d['B'] = scale_einstein_radius(z_lens=z_lens, z_src=1.405)
init['B'] = {'xsrc': 3.00192697e+03, 'ysrc': 2.96770223e+03, 'sigsrc': 2.17208719e+00}
img_xobs['11'] = np.array([3557.178601, 3548.271886, 3541.407488])
img_yobs['11'] = np.array([3363.943860, 3375.285957, 3385.515024])
d['11'] = scale_einstein_radius(z_lens=z_lens, z_src=2.06)
init['11'] = {'xsrc': 3034, 'ysrc': 3053, 'sigsrc': 3.}
img_xobs['31'] = np.array([2933.063074, 2943.400421, 2890.687234, 2878.906523])
img_yobs['31'] = np.array([3393.715824, 3398.196336, 3044.431729, 3042.460964])
d['31'] = scale_einstein_radius(z_lens=z_lens, z_src=1.904)
init['31'] = {'xsrc': 3034, 'ysrc': 3053, 'sigsrc': 3.}
img_xobs['41'] = np.array([3222.796159, 3227.700108])
img_yobs['41'] = np.array([3550.903781, 3542.180780])
d['41'] = scale_einstein_radius(z_lens=z_lens, z_src=1.810)
init['41'] = {'xsrc': 3034, 'ysrc': 3053, 'sigsrc': 3.}
img_xobs['C'] = np.array([3799.999263, 3794.5, 3863.057095, 3861.1])
img_yobs['C'] = np.array([3358.972702, 3367.9, 3059.195359, 3069.9])
d['C'] = scale_einstein_radius(z_lens=z_lens, z_src=2.0)
init['C'] = {'xsrc': 3034, 'ysrc': 3053, 'sigsrc': 3.}
names = img_xobs.keys()
# Define source positions as a Guassian surface brightness profile
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
pars, cov = [], []
for name in names:
X1[name] = pymc.Uniform('X1%s' % name, 2300., 3900., value=init[name]['xsrc'])
Y1[name] = pymc.Uniform('Y1%s' % name, 2300., 3900., value=init[name]['ysrc'])
Q1[name] = pymc.Uniform('Q1%s' % name, 1., 1., value=1.)
P1[name] = pymc.Uniform('P1%s' % name, 0., 0., value=0.)
S1[name] = pymc.Uniform('N1%s' % name, 0., 10., value=init[name]['sigsrc'])
srcs[name] = SBObjects.Gauss('', {'x': X1[name], 'y': Y1[name], 'q': Q1[name],'pa': P1[name], 'sigma': S1[name]})
pars += [X1[name], Y1[name], S1[name]] # List of parameters
cov += [400., 400., 1.5] # List of initial `scatter' for emcee
# Define overall lens SIE mass model
LX = pymc.Uniform('lx', 3100., 3500., value=3.29213154e+03)
LY = pymc.Uniform('ly', 2850., 3150., value=3.04899548e+03)
LB = pymc.Uniform('lb', 100., 3000., value=2.56554040e+02)
LQ = pymc.Uniform('lq', 0.01, 1., value=1.24379589e-01)
LP = pymc.Uniform('lp', -180., 180., value=5.67806821e+00)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
lenses = [lens]
pars = [LX, LY, LB, LQ, LP]
cov = [400., 400., 400., 0.3, 50.]
# Define individual lens models for each major light source that are in the same section on the color magnitude plot
masses_pos = [(2965.5288, 1933.9563), (2049.9021, 2192.387), (3141.9883, 2217.7527), (4607.7075, 2167.5984), (3549.3555, 2162.8872), (2068.0742, 2216.7585), (4268.5576, 2319.8298), (4663.2427, 2328.0593), (3323.5115, 2425.0659), (2221.5608, 2512.1736), (2950.5073, 2629.0552), (2981.6868, 2652.0073), (2033.7075, 2788.6877), (1949.4614, 2728.1226), (4241.4492, 2750.6653), (3361.4163, 2940.6357), (3173.2246, 2941.2471), (4516.8184, 2908.7585), (3382.9978, 2781.5076), (2898.4788, 2840.1252), (1942.7456, 2877.2471), (2899.8923, 2899.4895), (4041.6626, 2880.5015), (4162.7109, 2886.1875), (3989.6919, 2935.3879), (3303.6855, 2938.9148), (3968.1621, 2968.2993), (4613.0122, 2897.4099), (4649.1987, 2862.4167), (3261.9656, 2921.2605), (3386.9814, 2911.084), (3414.7791, 2936.4338), (2298.7419, 2965.8403), (3427.4221, 3072.7476), (3227.8262, 3095.5388), (3275.3184, 3263.1567), (4284.9653, 3240.2017), (3227.1746, 3250.7136), (2487.8906, 3230.6677), (2559.6587, 3186.9429), (2017.4875, 3195.2239), (2740.4167, 3208.8381), (3146.053, 3237.4194), (2401.4067, 3203.291), (2808.7485, 3427.9224), (4322.1392, 3317.6938), (3397.1904, 3356.5364), (3074.5276, 3448.4421), (3954.7253, 3590.8535), (3116.0625, 3523.1008), (2640.4075, 3624.4426), (3082.8025, 3548.231), (4583.7495, 3697.9534), (2768.9014, 3617.7961), (2639.042, 3615.2815), (2255.7852, 3900.9021), (2476.9795, 4028.5874)]
masses_flux = np.array([378.1141, 1527.1989999999998, 773.9109, 294.5334, 275.1775, 346.9561, 780.823, 201.5256, 244.387, 391.2144, 954.7488, 273.3743, 2777.741, 636.8357, 317.5356, 2693.8559999999998, 3436.873, 1680.48, 219.1088, 591.2639, 624.871, 590.7428, 695.0563, 485.1097, 901.0128, 947.5237, 939.0687, 290.4246, 226.5177, 717.8644, 325.5481, 285.941, 266.1354, 232.6961, 257.5104, 1943.4389999999999, 957.1483, 1277.3110000000001, 821.7504, 362.3544, 343.2694, 381.5304, 260.1786, 306.7749, 1675.8770000000002, 442.8735, 549.5866, 910.3147, 979.7011, 389.7068, 707.3599, 433.32599999999996, 1193.312, 204.4583, 218.7119, 451.3262, 333.3452])
masses_flux = masses_flux/200.
print(masses_flux)
flux_dependent_b = True
if flux_dependent_b:
# ------> b_sis = slope * flux ** 8 + intercept <-------- #
slope = pymc.Uniform('slope', 0., 1000., value=1.53454884e+01)
intercept = pymc.Uniform('intercept', -100., 1000., value=-7.22002250e-02)
# n = pymc.Uniform('n', 0., 10., value=4.)
pars += [slope, intercept]
cov += [5., 5.]
cov = np.array(cov)
for (lx, ly), flux in zip(masses_pos, masses_flux):
LX = pymc.Uniform('lx', 1000., 5000., value=lx)
LY = pymc.Uniform('ly', 1000., 5000., value=ly)
LB = slope * np.log(flux) + intercept
lens = MassModels.SIS('', {'x': LX, 'y': LY, 'b': LB})
lenses += [lens]
else:
for lx, ly in masses_pos:
LX = pymc.Uniform('lx', 1000., 5000., value=lx)
LY = pymc.Uniform('ly', 1000., 5000., value=ly)
LB = pymc.Uniform('lb', 0., 2000., value=50.)
lens = MassModels.SIS('', {'x': LX, 'y': LY, 'b': LB})
lenses += [lens]
pars += [LB]
cov += [30.]
cov = np.array(cov)
nwalkers = 200
nsteps = 500
burn = 100
best_lens = [ 3.29213154e+03, 3.04899548e+03, 2.56554040e+02,
1.24379589e-01, 5.67806821e+00, 1.53454884e+01,
-7.22002250e-02]
# plot_source_and_pred_lens_positions(best_lens, img_xobs, img_yobs, d, fig_dir, threshold=0.01, plotimage=True, fits_file=fits_file, mass_pos=masses_pos, flux_dependent_b=flux_dependent_b, masses_flux=masses_flux, sa=sa, pix_scale=pix_scale)
run_mcmc(img_xobs, img_yobs, fig_dir, d, lenses, srcs, pars, cov, nwalkers=nwalkers, nsteps=nsteps, burn=burn, fits_file=fits_file, img_name=img_name, mass_pos=masses_pos, flux_dependent_b=flux_dependent_b, masses_flux=masses_flux, threshold=0.01, sa=sa, pix_scale=pix_scale)
def plot_source_and_pred_lens_positions(pars, img_xobs, img_yobs, d, fig_dir, threshold=0.01, plotimage=False, fits_file=None, mass_pos=None, flux_dependent_b=False, masses_flux=None, sa=(2000, 4500), pix_scale=10.):
if plotimage:
fig = plt.figure('image_and_position', figsize=(13, 13))
plot_image(fits_file, figname='image_and_position')
names = img_xobs.keys()
xsrc, ysrc, sigsrc = {}, {}, {}
for i, name in enumerate(names):
xsrc[name], ysrc[name], sigsrc[name] = pars[3 * i: 3 * (i + 1)]
xlens, ylens, blens, qlens, plens = pars[-7:-2]
# Define source positions as a Guassian surface brightness profile
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
for name in names:
X1[name] = pymc.Uniform('X1%s' % name, 0., 5000., value=xsrc[name])
Y1[name] = pymc.Uniform('Y1%s' % name, 0., 5000., value=ysrc[name])
Q1[name] = pymc.Uniform('Q1%s' % name, 0.2, 1., value=1.)
P1[name] = pymc.Uniform('P1%s' % name, -180., 180., value=0.)
S1[name] = pymc.Uniform('N1%s' % name, 0., 10000., value=sigsrc[name])
srcs[name] = SBObjects.Gauss('', {'x': X1[name], 'y': Y1[name], 'q': Q1[name],'pa': P1[name], 'sigma': S1[name]})
# Define lens mass model
LX = pymc.Uniform('lx', 0., 5000., value=xlens)
LY = pymc.Uniform('ly', 0., 5000., value=ylens)
LB = pymc.Uniform('lb', 0., 5000., value=blens)
LQ = pymc.Uniform('lq', 0., 1., value=qlens)
LP = pymc.Uniform('lp', -180., 180., value=plens)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
lenses = [lens]
if flux_dependent_b:
for (lx, ly), flux in zip(mass_pos, masses_flux):
slope, intercept = pars[-2:]
LX = pymc.Uniform('lx', 0., 5000., value=lx)
LY = pymc.Uniform('ly', 0., 5000., value=ly)
LB = slope * np.log(flux) + intercept
lens = MassModels.SIS('', {'x': LX, 'y': LY, 'b': LB})
lenses += [lens]
print('lens einstein radius', lens.b)
else:
for b, (lx, ly) in zip(pars[-2:], mass_pos):
LX = pymc.Uniform('lx', 0., 5000., value=lx)
LY = pymc.Uniform('ly', 0., 5000., value=ly)
LB = pymc.Uniform('lb', 0., 5000., value=b)
lens = MassModels.SIS('', {'x': LX, 'y': LY, 'b': LB})
lenses += [lens]
print('lens einstein radius', lens.b)
colors = (col for col in ['#1f77b4', '#2ca02c', '#9467bd', '#17becf', '#e377c2', '#ADFF2F'])
markers = (marker for marker in ['x', 'o', '*', '+', 'v', 'D'])
x_src, y_src = {}, {}
image_plane, image_coords_pred = {}, {}
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
x, y = np.meshgrid(np.arange(sa[0], sa[1], pix_scale), np.arange(sa[0], sa[1], pix_scale))
plt.xlim(sa[0], sa[1])
plt.ylim(sa[0], sa[1])
for name in names:
plt.figure('image_and_position')
col = next(colors)
plt.scatter(img_xobs[name], img_yobs[name], marker=next(markers), c='white', label="%s obs" % name, alpha=0.8)
plt.scatter(x_src[name], y_src[name], marker='.', alpha=0.5, c=col, label="%s pred src" % name)
# Get Image plane
x_src_all, y_src_all = pylens.getDeflections(lenses, [x, y], d=d[name])
image_plane[name] = srcs[name].pixeval(x_src_all, y_src_all)
image_indexes_pred = np.where(image_plane[name] > threshold)
image_coords_pred[name] = np.array([x[image_indexes_pred], y[image_indexes_pred]])
image_plane_norm = (image_plane[name] - image_plane[name].min())/(image_plane[name].max() - image_plane[name].min())
rgba = np.zeros((len(image_coords_pred[name][0]), 4))
rgba[:, 0:3] = list(int(col[i:i+2], 16)/256. for i in (1, 3, 5))
rgba[:, 3] = 0.8 * np.array(image_plane_norm[image_indexes_pred])
plt.scatter(image_coords_pred[name][0], image_coords_pred[name][1], marker='x', color=rgba, label="%s pred img" % name)
plt.figure(name)
plt.title(name)
plt.imshow(image_plane[name], interpolation='nearest', origin='lower')
print(x_src, y_src)
plt.figure('image_and_position')
plt.legend(loc='upper right')
plt.savefig(os.path.join(fig_dir, 'image_with_contours_and_images.png'))
def plot_source_and_pred_lens_positions(pars, img_xobs, img_yobs, d, fig_dir, threshold=0.01, plotimage=False, fits_file=None):
if plotimage:
fig = plt.figure(figsize=(13, 13))
plot_image(fits_file, fig)
names = img_xobs.keys()
try:
xlens, ylens, blens, qlens, plens = pars
bshear, pshear = 0., 0.
except ValueError: # includes shear
xlens, ylens, blens, qlens, plens, bshear, pshear = pars
# Define lens mass model
LX = pymc.Uniform('lx', 0., 5000., value=xlens)
LY = pymc.Uniform('ly', 0., 5000., value=ylens)
LB = pymc.Uniform('lb', 0., 5000., value=blens)
LQ = pymc.Uniform('lq', 0.2, 1., value=qlens)
LP = pymc.Uniform('lp', -180., 180., value=plens)
XB = pymc.Uniform('xb', -200., 200., value=bshear)
XP = pymc.Uniform('xp', -180., 180., value=pshear)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
lenses = [lens]
if len(pars) == 7:
shear = MassModels.ExtShear('',{'x':LX,'y':LY,'b':XB,'pa':XP})
lenses += [shear]
colors = (col for col in ['#1f77b4', '#2ca02c', '#9467bd', '#17becf', '#e377c2', 'lime'])
markers = (marker for marker in ['x', 'o', '*', '+', 'v', 'D'])
x_src, y_src = {}, {}
image_plane, image_coords_pred = {}, {}
X1, Y1, Q1, P1, S1, srcs = {}, {}, {}, {}, {}, {}
print(float(lens.x), float(lens.y), float(lens.b), float(lens.q), float(lens.pa))
sa = (2000, 4500)
pix_scale = 10.
x, y = np.meshgrid(np.arange(sa[0], sa[1], pix_scale), np.arange(sa[0], sa[1], pix_scale))
plt.xlim(sa[0], sa[1])
plt.ylim(sa[0], sa[1])
for name in names:
x_src[name], y_src[name] = pylens.getDeflections(lenses, [img_xobs[name], img_yobs[name]], d[name])
xs = np.median(x_src[name])
ys = np.median(y_src[name])
lnlike = -0.5 * (x_src[name].var() + y_src[name].var())
print(float(lens.x), float(lens.y), float(lens.b), float(lens.q), float(lens.pa))
print(name, xs, ys, lnlike)
col = next(colors)
plt.scatter(img_xobs[name], img_yobs[name], marker=next(markers), c='white', label="%s obs" % name, alpha=0.8)
plt.scatter(x_src[name], y_src[name], marker='.', alpha=0.5, c=col, label="%s pred src" % name)
# CALC IMG POS
# Assume gaussian surface brightness at (xs, ys)
X1[name] = pymc.Uniform('X1%s' % name, 0., 5000., value=xs)
Y1[name] = pymc.Uniform('Y1%s' % name, 0., 5000., value=ys)
Q1[name] = pymc.Uniform('Q1%s' % name, 0.2, 1., value=1.)
P1[name] = pymc.Uniform('P1%s' % name, -180., 180., value=0.)
S1[name] = pymc.Uniform('N1%s' % name, 0., 10000., value=6.)
srcs[name] = SBObjects.Gauss('', {'x': X1[name], 'y': Y1[name], 'q': Q1[name], 'pa': P1[name], 'sigma': S1[name]})
# Get Image plane
x_src_all, y_src_all = pylens.getDeflections(lenses, [x, y], d=d[name])
image_plane[name] = srcs[name].pixeval(x_src_all, y_src_all)
image_indexes_pred = np.where(image_plane[name] > threshold)
image_coords_pred[name] = np.array([x[image_indexes_pred], y[image_indexes_pred]])
plt.scatter(image_coords_pred[name][0], image_coords_pred[name][1], marker='x', alpha=0.5, c=col, label="%s pred img" % name)
print(x_src, y_src)
plt.legend(loc='upper right')
plt.savefig(os.path.join(fig_dir, 'image_with_contours_and_images.png'))
def macs0451_multiple_sources():
fig_dir = os.path.join(ROOT_DIR, 'Figures/MACS0451_min_src_pos_var_getlenspy_with_shear/')
if not os.path.exists(fig_dir):
os.makedirs(fig_dir)
fits_file = '/home/djm241/PycharmProjects/StrongLensing/data/MACS0451/MACS0451_F110W.fits'
if not os.path.isfile(fits_file):
fits_file = '/Users/danmuth/PycharmProjects/StrongLensing/data/MACS0451/MACS0451_F110W.fits'
img_name = '_multiple_sources'
z_lens = 0.43
img_xobs, img_yobs, d = OrderedDict(), OrderedDict(), OrderedDict()
img_xobs['A'] = np.array([2375.942110, 2378.5, 2379.816610, 2381.299088, 2384, 2385.927991, 2389.555816, 2457.694760, 2450.744242, 2442.833333, 2437.857924, 2433.064587, 2427.166666, 2424.099866, 2418.5, 2416.444081, 2462])
img_yobs['A'] = np.array([3038.016677, 3024, 3012.367933, 2999.365293, 2983.5, 2970.435199, 2955.945319, 2737.545077, 2752.305849, 2766.166666, 2782.058508, 2795.293450, 2811.166666, 2823.079067, 2837.5, 2846.943113, 2728])
d['A'] = scale_einstein_radius(z_lens=z_lens, z_src=2.013)
img_xobs['B'] = np.array([3276.693717, 3261.382557, 3427.351819, 3417.043471, 3497.163625, 3486.371962])
img_yobs['B'] = np.array([3482.795501, 3482.854177, 2592.719350, 2590.191799, 3075.107748, 3069.305065])
d['B'] = scale_einstein_radius(z_lens=z_lens, z_src=1.405)
img_xobs['11'] = np.array([3557.178601, 3548.271886, 3541.407488])
img_yobs['11'] = np.array([3363.943860, 3375.285957, 3385.515024])
d['11'] = scale_einstein_radius(z_lens=z_lens, z_src=2.06)
img_xobs['31'] = np.array([2933.063074, 2943.400421, 2890.687234, 2878.906523])
img_yobs['31'] = np.array([3393.715824, 3398.196336, 3044.431729, 3042.460964])
d['31'] = scale_einstein_radius(z_lens=z_lens, z_src=1.904)
img_xobs['41'] = np.array([3222.796159, 3227.700108])
img_yobs['41'] = np.array([3550.903781, 3542.180780])
d['41'] = scale_einstein_radius(z_lens=z_lens, z_src=1.810)
img_xobs['C'] = np.array([3799.999263, 3794.5, 3863.057095, 3861.1])
img_yobs['C'] = np.array([3358.972702, 3367.9, 3059.195359, 3069.9])
d['C'] = scale_einstein_radius(z_lens=z_lens, z_src=2.0)
# Define lens mass model
LX = pymc.Uniform('lx', 2400., 4000., value=3.13876545e+03)
LY = pymc.Uniform('ly', 2000., 3700., value=2.97884105e+03)
LB = pymc.Uniform('lb', 10., 2000., value=1.50779124e+03)
LQ = pymc.Uniform('lq', 0.2, 1., value=4.90424861e-01)
LP = pymc.Uniform('lp', -180., 180., value=1.04010643e+02)
XB = pymc.Uniform('xb', -200., 200., value=0.)
XP = pymc.Uniform('xp', -180., 180., value=0.)
lens = MassModels.SIE('', {'x': LX, 'y': LY, 'b': LB, 'q': LQ, 'pa': LP})
shear = MassModels.ExtShear('', {'x': LX, 'y': LY, 'b': XB, 'pa': XP})
lenses = [lens]
pars = [LX, LY, LB, LQ, LP]
cov = [400., 400., 400., 0.3, 50.]
lenses += [shear]
pars += [XB, XP]
cov += [40., 30.]
cov = np.array(cov)
nwalkers = 500
nsteps = 30000
burn = 500
best_lens = [ 3.21895080e+03, 3.03726175e+03, 6.67192222e+02, 2.26586238e-01, 5.91357933e+00]
# plot_source_and_pred_lens_positions(best_lens, img_xobs, img_yobs, d, fig_dir, threshold=0.01, plotimage=True, fits_file=fits_file)
run_mcmc(img_xobs, img_yobs, fig_dir, d, lenses, pars, cov, nwalkers=nwalkers, nsteps=nsteps, burn=burn, fits_file=fits_file, img_name=img_name)
