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()
def main():
# Where are the data?
datadir = os.path.join(os.path.dirname(__file__), 'data-decam')
name = 'decam-520206-S16'
imagefn = os.path.join(datadir, '%s-image-sub.fits' % name)
invvarfn = os.path.join(datadir, '%s-invvar-sub.fits' % name)
psfexfn = os.path.join(datadir, '%s-psfex.fits' % name)
catfn = os.path.join(datadir, 'tractor-1816p325-sub.fits')
# Read the image and inverse-variance maps.
image = fitsio.read(imagefn)
invvar = fitsio.read(invvarfn)
# The DECam inverse-variance maps are unfortunately corrupted
# by fpack, causing zeros to become negative. Fix those.
invvar[invvar < np.median(invvar) * 0.1] = 0.
H, W = image.shape
print('Subimage size:', image.shape)
# For the PSF model, we need to know what subimage region this is:
subimage_offset = (35, 1465)
# We also need the calibrated zeropoint.
zeropoint = 24.7787
# What filter was this image taken in? (z)
prim_header = fitsio.read_header(imagefn)
band = prim_header['FILTER'].strip()[0]
print('Band:', band)
# These DECam images were calibrated so that the zeropoints need
# an exposure-time factor, so add that in.
exptime = prim_header['EXPTIME']
zeropoint += 2.5 * np.log10(exptime)
# Read the PsfEx model file
psf = PixelizedPsfEx(psfexfn)
# Instantiate a constant pixelized PSF at the image center
# (of the subimage)
x0, y0 = subimage_offset
psf = psf.constantPsfAt(x0 + W / 2., y0 + H / 2.)
# Load the WCS model from the header
# We convert from the RA---TPV type to RA---SIP
header = fitsio.read_header(imagefn, ext=1)
wcsobj = wcs_pv2sip_hdr(header, stepsize=10)
# We'll just use a rough sky estimate...
skyval = np.median(image)
# Create the Tractor Image (tim).
tim = Image(data=image,
invvar=invvar,
psf=psf,
wcs=ConstantFitsWcs(wcsobj),
sky=ConstantSky(skyval),
photocal=LinearPhotoCal(
NanoMaggies.zeropointToScale(zeropoint), band=band))
# Read the official DECaLS DR3 catalog -- it has only two sources in this subimage.
catalog = fits_table(catfn)
print('Read', len(catalog), 'sources')
print('Source types:', catalog.type)
# Create Tractor sources corresponding to these two catalog
# entries.
# In DECaLS, the "SIMP" type is a round Exponential galaxy with a
# fixed 0.45" radius, but we'll treat it as a general Exp galaxy.
sources = []
for c in catalog:
# Create a "position" object given the catalog RA,Dec
position = RaDecPos(c.ra, c.dec)
# Create a "brightness" object; in the catalog, the fluxes are
# stored in a [ugrizY] array, so pull out the right index
band_index = 'ugrizY'.index(band)
flux = c.decam_flux[band_index]
brightness = NanoMaggies(**{band: flux})
# Depending on the source classification in the catalog, pull
# out different fields for the galaxy shape, and for the
# galaxy type. The DECaLS catalogs, conveniently, store
# galaxy shapes as (radius, e1, e2) ellipses.
if c.type.strip() == 'DEV':
shape = EllipseE(c.shapedev_r, c.shapedev_e1, c.shapedev_e2)
galclass = DevGalaxy
elif c.type.strip() == 'SIMP':
shape = EllipseE(c.shapeexp_r, c.shapeexp_e1, c.shapeexp_e2)
galclass = ExpGalaxy
else:
assert (False)
# Create the tractor galaxy object
source = galclass(position, brightness, shape)
print('Created', source)
sources.append(source)
# Create the Tractor object -- a list of tractor Images and a list of tractor sources.
tractor = Tractor([tim], sources)
# Render the initial model image.
print('Getting initial model...')
mod = tractor.getModelImage(0)
make_plot(tim, mod, 'Initial Scene', 'mod0.png')
# Instantiate a new source at the location of the unmodelled peak.
print('Adding new source...')
# Find the peak very naively...
ipeak = np.argmax((image - mod) * tim.inverr)
iy, ix = np.unravel_index(ipeak, tim.shape)
print('Residual peak at', ix, iy)
# Compute the RA,Dec location of the peak...
radec = tim.getWcs().pixelToPosition(ix, iy)
print('RA,Dec', radec)
# Try modelling it as a point source.
# We'll initialize the brightness arbitrarily to 1 nanomaggy (= mag 22.5)
brightness = NanoMaggies(**{band: 1.})
source = PointSource(radec, brightness)
# Add it to the catalog!
tractor.catalog.append(source)
# Render the new model image with this source added.
mod = tractor.getModelImage(0)
make_plot(tim, mod, 'New Source (Before Fit)', 'mod1.png')
print('Fitting new source...')
# Now we're going to fit for the properties of the new source we
# added.
# We don't want to fit for any of the image calibration properties:
tractor.freezeParam('images')
# And we don't (yet) want to fit the existing sources. The new
# source is index number 2, so freeze everything else in the catalog.
tractor.catalog.freezeAllBut(2)
print('Fitting parameters:')
tractor.printThawedParams()
# Do the actual optimization:
tractor.optimize_loop()
mod = tractor.getModelImage(0)
make_plot(tim, mod, 'New Source Fit', 'mod2.png')
print('Fitting sources simultaneously...')
# Now let's unfreeze all the sources and fit them simultaneously.
tractor.catalog.thawAllParams()
tractor.printThawedParams()
tractor.optimize_loop()
mod = tractor.getModelImage(0)
make_plot(tim, mod, 'Simultaneous Fit', 'mod3.png')
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()
