def scan_dchisq(seeing, target_dchisq, ps, e1=0.):
pixscale = 0.262
psfsigma = seeing / pixscale / 2.35
print('PSF sigma:', psfsigma, 'pixels')
psf = GaussianMixturePSF(1., 0., 0., psfsigma**2, psfsigma**2, 0.)
sig1 = 0.01
psfnorm = 1./(2. * np.sqrt(np.pi) * psfsigma)
detsig1 = sig1 / psfnorm
sz = 50
cd = pixscale / 3600.
wcs = Tan(0., 0., float(sz/2), float(sz/2), -cd, 0., 0., cd,
float(sz), float(sz))
band = 'r'
tim = Image(data=np.zeros((sz,sz)), inverr=np.ones((sz,sz)) / sig1,
psf=psf,
wcs = ConstantFitsWcs(wcs),
photocal = LinearPhotoCal(1., band=band))
re_vals = np.logspace(-1., 0., 50)
all_runs = []
mods = []
for i,re in enumerate(re_vals):
true_src = ExpGalaxy(RaDecPos(0., 0.),
NanoMaggies(**{band: 1.}),
EllipseE(re, e1, 0.))
print('True source:', true_src)
tr = Tractor([tim], [true_src])
tr.freezeParams('images')
true_mod = tr.getModelImage(0)
dchisq_none = np.sum((true_mod * tim.inverr)**2)
scale = np.sqrt(target_dchisq / dchisq_none)
true_src.brightness.setParams([scale])
true_mod = tr.getModelImage(0)
dchisq_none = np.sum((true_mod * tim.inverr)**2)
mods.append(true_mod)
tim.data = true_mod
exp_src = true_src.copy()
psf_src = PointSource(true_src.pos.copy(), true_src.brightness.copy())
simp_src = SimpleGalaxy(true_src.pos.copy(), true_src.brightness.copy())
dchisqs = []
#for src in [psf_src, simp_src, exp_src]:
for src in [psf_src, simp_src]:
src.freezeParam('pos')
#print('Fitting source:', src)
#src.printThawedParams()
tr.catalog[0] = src
tr.optimize_loop()
#print('Fitted:', src)
mod = tr.getModelImage(0)
dchisqs.append(dchisq_none - np.sum(((true_mod - mod) * tim.inverr)**2))
#print('dchisq:', dchisqs[-1])
dchisqs.append(dchisq_none)
all_runs.append([re,] + dchisqs)
all_runs = np.array(all_runs)
re = all_runs[:,0]
dchi_psf = all_runs[:,1]
dchi_simp = all_runs[:,2]
dchi_exp = all_runs[:,3]
dchi_ps = np.maximum(dchi_psf, dchi_simp)
dchi_cut1 = dchi_ps + 3+9
dchi_cut2 = dchi_ps + dchi_psf * 0.02
dchi_cut3 = dchi_ps + dchi_psf * 0.008
plt.clf()
plt.plot(re, dchi_psf, 'k-', label='PSF')
plt.plot(re, dchi_simp, 'b-', label='SIMP')
plt.plot(re, dchi_exp, 'r-', label='EXP')
plt.plot(re, dchi_cut2, 'm--', alpha=0.5, lw=2, label='Cut: 2%')
plt.plot(re, dchi_cut3, 'm:', alpha=0.5, lw=2, label='Cut: 0.08%')
plt.plot(re, dchi_cut1, 'm-', alpha=0.5, lw=2, label='Cut: 12')
plt.xlabel('True r_e (arcsec)')
plt.ylabel('dchisq')
#plt.legend(loc='lower left')
plt.legend(loc='upper right')
tt = 'Seeing = %g arcsec, S/N ~ %i' % (seeing, int(np.round(np.sqrt(target_dchisq))))
if e1 != 0.:
tt += ', Ellipticity %g' % e1
plt.title(tt)
plt.ylim(0.90 * target_dchisq, 1.05 * target_dchisq)
# aspect = 1.2
# ax = plt.axis()
# dre = (ax[1]-ax[0]) / 20 / aspect
# dchi = (ax[3]-ax[2]) / 20
# I = np.linspace(0, len(re_vals)-1, 8).astype(int)
# for mod,re in [(mods[i], re_vals[i]) for i in I]:
# print('extent:', [re-dre, re+dre, ax[2], ax[2]+dchi])
# plt.imshow(mod, interpolation='nearest', origin='lower', aspect='auto',
# extent=[re-dre, re+dre, ax[2], ax[2]+dchi], cmap='gray')
# plt.axis(ax)
ps.savefig()
EllipseE(re, 0., 0.))
tr = Tractor([tim], [true_src])
tr.freezeParams('images')
true_mod = tr.getModelImage(0)
ima = dict(interpolation='nearest', origin='lower',
vmin=-2.*sig1, vmax=5.*sig1, cmap='hot')
this_dchisqs = []
flux_sns = []
for k in range(Nper):
noise = np.random.normal(scale=sig1, size=true_mod.shape)
tim.data = true_mod + noise
if k == 0 and False:
plt.clf()
plt.subplot(1,2,1)
plt.imshow(true_mod, **ima)
plt.subplot(1,2,2)
plt.imshow(tim.data, **ima)
plt.title('S/N %f, r_e %f' % (sn, re))
ps.savefig()
## run one_blob code? Or shortcut?
src = PointSource(RaDecPos(0., 0.),
NanoMaggies(**{band: flux}))
nblob,iblob,Isrcs = 0, 1, np.array([0])
EllipseE(re, 0., 0.))
tr = Tractor([tim], [true_src])
tr.freezeParams('images')
true_mod = tr.getModelImage(0)
ima = dict(interpolation='nearest', origin='lower',
vmin=-2.*sig1, vmax=5.*sig1, cmap='hot')
this_dchisqs = []
flux_sns = []
for k in range(Nper):
noise = np.random.normal(scale=sig1, size=true_mod.shape)
tim.data = true_mod + noise
if k == 0 and False:
plt.clf()
plt.subplot(1,2,1)
plt.imshow(true_mod, **ima)
plt.subplot(1,2,2)
plt.imshow(tim.data, **ima)
plt.title('S/N %f, r_e %f' % (sn, re))
ps.savefig()
## run one_blob code? Or shortcut?
src = PointSource(RaDecPos(0., 0.),
NanoMaggies(**{band: flux}))
nblob,iblob,Isrcs = 0, 1, np.array([0])
def scan_dchisq(seeing, target_dchisq, ps, e1=0.):
pixscale = 0.262
psfsigma = seeing / pixscale / 2.35
print('PSF sigma:', psfsigma, 'pixels')
psf = GaussianMixturePSF(1., 0., 0., psfsigma**2, psfsigma**2, 0.)
sig1 = 0.01
psfnorm = 1./(2. * np.sqrt(np.pi) * psfsigma)
detsig1 = sig1 / psfnorm
sz = 50
cd = pixscale / 3600.
wcs = Tan(0., 0., float(sz/2), float(sz/2), -cd, 0., 0., cd,
float(sz), float(sz))
band = 'r'
tim = Image(data=np.zeros((sz,sz)), inverr=np.ones((sz,sz)) / sig1,
psf=psf,
wcs = ConstantFitsWcs(wcs),
photocal = LinearPhotoCal(1., band=band))
re_vals = np.logspace(-1., 0., 50)
all_runs = []
mods = []
for i,re in enumerate(re_vals):
true_src = ExpGalaxy(RaDecPos(0., 0.),
NanoMaggies(**{band: 1.}),
EllipseE(re, e1, 0.))
print('True source:', true_src)
tr = Tractor([tim], [true_src])
tr.freezeParams('images')
true_mod = tr.getModelImage(0)
dchisq_none = np.sum((true_mod * tim.inverr)**2)
scale = np.sqrt(target_dchisq / dchisq_none)
true_src.brightness.setParams([scale])
true_mod = tr.getModelImage(0)
dchisq_none = np.sum((true_mod * tim.inverr)**2)
mods.append(true_mod)
tim.data = true_mod
exp_src = true_src.copy()
psf_src = PointSource(true_src.pos.copy(), true_src.brightness.copy())
simp_src = SimpleGalaxy(true_src.pos.copy(), true_src.brightness.copy())
dchisqs = []
#for src in [psf_src, simp_src, exp_src]:
for src in [psf_src, simp_src]:
src.freezeParam('pos')
#print('Fitting source:', src)
#src.printThawedParams()
tr.catalog[0] = src
tr.optimize_loop()
#print('Fitted:', src)
mod = tr.getModelImage(0)
dchisqs.append(dchisq_none - np.sum(((true_mod - mod) * tim.inverr)**2))
#print('dchisq:', dchisqs[-1])
dchisqs.append(dchisq_none)
all_runs.append([re,] + dchisqs)
all_runs = np.array(all_runs)
re = all_runs[:,0]
dchi_psf = all_runs[:,1]
dchi_simp = all_runs[:,2]
dchi_exp = all_runs[:,3]
dchi_ps = np.maximum(dchi_psf, dchi_simp)
dchi_cut1 = dchi_ps + 3+9
dchi_cut2 = dchi_ps + dchi_psf * 0.02
dchi_cut3 = dchi_ps + dchi_psf * 0.008
plt.clf()
plt.plot(re, dchi_psf, 'k-', label='PSF')
plt.plot(re, dchi_simp, 'b-', label='SIMP')
plt.plot(re, dchi_exp, 'r-', label='EXP')
plt.plot(re, dchi_cut2, 'm--', alpha=0.5, lw=2, label='Cut: 2%')
plt.plot(re, dchi_cut3, 'm:', alpha=0.5, lw=2, label='Cut: 0.08%')
plt.plot(re, dchi_cut1, 'm-', alpha=0.5, lw=2, label='Cut: 12')
plt.xlabel('True r_e (arcsec)')
plt.ylabel('dchisq')
#plt.legend(loc='lower left')
plt.legend(loc='upper right')
tt = 'Seeing = %g arcsec, S/N ~ %i' % (seeing, int(np.round(np.sqrt(target_dchisq))))
if e1 != 0.:
tt += ', Ellipticity %g' % e1
plt.title(tt)
plt.ylim(0.90 * target_dchisq, 1.05 * target_dchisq)
# aspect = 1.2
# ax = plt.axis()
# dre = (ax[1]-ax[0]) / 20 / aspect
# dchi = (ax[3]-ax[2]) / 20
# I = np.linspace(0, len(re_vals)-1, 8).astype(int)
# for mod,re in [(mods[i], re_vals[i]) for i in I]:
# print('extent:', [re-dre, re+dre, ax[2], ax[2]+dchi])
# plt.imshow(mod, interpolation='nearest', origin='lower', aspect='auto',
# extent=[re-dre, re+dre, ax[2], ax[2]+dchi], cmap='gray')
# plt.axis(ax)
ps.savefig()
EllipseE(10., 0.5, 0.3))
# Get the model
tractor = Tractor([tim], [gal])
mod = tractor.getModelImage(0)
#mog = gal._getAffineProfile(tim, w//2, h//2)
#print('Exp galaxy profile:', str(mog))
# Plot the model
plt.clf()
plt.imshow(mod, interpolation='nearest', origin='lower')
plt.savefig('mod.png')
# Set the tractor Image to the Exp model postage stamp -- this is what we'll try to fit.
tim.data = mod
# Initialize the MoG components
amp = np.array([0.4, 0.3, 0.3])
mean = np.zeros((3,2))
var = np.array([
[0.01,0., 0., 0.01],
[0.1, 0., 0., 0.1 ],
[1., 0., 0., 1.0 ],
])
var *= 64.
var = var.reshape((-1,2,2))
# ~ arcsec -> degrees
var /= 3600.**2
if False:
