def temporal_smearing(self, lobs, zsource, cosmo=None):
""" Temporal smearing due to turbulent scattering
Parameters
----------
lobs : Quantity
Observed wavelength
zsource : float
cosmo : astropy.cosmology, optional
Returns
-------
tau : Quantity
temporal broadening
"""
# Cosmology
if cosmo is None:
from astropy.cosmology import Planck15 as cosmo
D_S = cosmo.angular_diameter_distance(zsource)
D_L = cosmo.angular_diameter_distance(self.zL)
D_LS = cosmo.angular_diameter_distance_z1z2(self.zL, zsource)
# Angular
theta = self.angular_broadening(lobs, zsource, cosmo=cosmo)
# Calculate
tau = D_L * D_S * (theta.to('radian').value)**2 / D_LS / const.c / (
1 + self.zL)
# Return
return tau.to('ms')
def cal_einstein_radius_in_arcsec(z_l,z_s,sigma):
#b_sie = 4*pi * sigma^2/c^2 * D_ls/D_s
c = const.c.value / 1000 #to km/s
v_fac = (sigma/c)**2
d_fac = cosmo.angular_diameter_distance_z1z2(z_l, z_s).value/cosmo.angular_diameter_distance(z_s).value
radian_to_arcsec = 180.0/np.pi*60*60
return 4.0*np.pi*v_fac*d_fac*radian_to_arcsec
def update(val):
zL,zS = slzL.val,slzS.val
xL,yL = slxL.val, slyL.val
ML,eL,PAL = slML.val,sleL.val,slPAL.val
sh,sha = slss.val,slsa.val
xs,ys = slxs.val, slys.val
Fs,ws = slFs.val, slws.val
ns,ars,pas = slns.val,slars.val,slPAs.val
newDd = cosmo.angular_diameter_distance(zL).value
newDs = cosmo.angular_diameter_distance(zS).value
newDds= cosmo.angular_diameter_distance_z1z2(zL,zS).value
newLens = vl.SIELens(zLens,xL,yL,10**ML,eL,PAL)
newShear = vl.ExternalShear(sh,sha)
newSource = vl.SersicSource(zS,True,xs,ys,Fs,ws,ns,ars,pas)
xs,ys = vl.LensRayTrace(xim,yim,[newLens,newShear],newDd,newDs,newDds)
imbg = vl.SourceProfile(xim,yim,newSource,[newLens,newShear])
imlensed = vl.SourceProfile(xs,ys,newSource,[newLens,newShear])
caustics = vl.CausticsSIE(newLens,newDd,newDs,newDds,newShear)
ax.cla()
ax.imshow(imbg,cmap=cmbg,extent=[xim.min(),xim.max(),yim.min(),yim.max()],origin='lower')
ax.imshow(imlensed,cmap=cmlens,extent=[xim.min(),xim.max(),yim.min(),yim.max()],origin='lower')
mu = imlensed.sum()*(xim[0,1]-xim[0,0])**2 / newSource.flux['value']
ax.text(0.9,1.02,'$\\mu$ = {0:.2f}'.format(mu),transform=ax.transAxes)
#for i in range(caustics.shape[0]):
# ax.plot(caustics[i,0,:],caustics[i,1,:],'k-')
for caustic in caustics:
ax.plot(caustic[:,0],caustic[:,1],'k-')
f.canvas.draw_idle()
def create_modelimage(lens,source,xmap,ymap,xemit,yemit,indices,
Dd=None,Ds=None,Dds=None,sourcedatamap=None):
"""
Creates a model lensed image given the objects and map
coordinates specified. Supposed to be common for both
image fitting and visibility fitting, so we don't need
any data here.
Returns:
immap
A 2D array representing the field evaluated at
xmap,ymap with all sources included.
mus:
A numpy array of length N_sources containing the
magnifications of each source (1 if unlensed).
"""
lens = list(np.array([lens]).flatten()) # Ensure lens(es) are a list
source = list(np.array([source]).flatten()) # Ensure source(s) are a list
mus = np.zeros(len(source))
immap, imsrc = np.zeros(xmap.shape), np.zeros(xemit.shape)
# If we didn't get pre-calculated distances, figure them here assuming Planck15
if np.any((Dd is None,Ds is None, Dds is None)):
from astropy.cosmology import Planck15 as cosmo
Dd = cosmo.angular_diameter_distance(lens[0].z).value
Ds = cosmo.angular_diameter_distance(source[0].z).value
Dds= cosmo.angular_diameter_distance_z1z2(lens[0].z,source[0].z).value
# Do the raytracing for this set of lens & shear params
xsrc,ysrc = LensRayTrace(xemit,yemit,lens,Dd,Ds,Dds)
if sourcedatamap is not None: # ... then particular source(s) are specified for this map
for jsrc in sourcedatamap:
if source[jsrc].lensed:
ims = SourceProfile(xsrc,ysrc,source[jsrc],lens)
imsrc += ims
mus[jsrc] = ims.sum()*(xemit[0,1]-xemit[0,0])**2./source[jsrc].flux['value']
else: immap += SourceProfile(xmap,ymap,source[jsrc],lens); mus[jsrc] = 1.
else: # Assume we put all sources in this map/field
for j,src in enumerate(source):
if src.lensed:
ims = SourceProfile(xsrc,ysrc,src,lens)
imsrc += ims
mus[j] = ims.sum()*(xemit[0,1]-xemit[0,0])**2./src.flux['value']
else: immap += SourceProfile(xmap,ymap,src,lens); mus[j] = 1.
# Try to reproduce matlab's antialiasing thing; this uses a 3lobe lanczos low-pass filter
imsrc = Image.fromarray(imsrc)
resize = np.array(imsrc.resize((int(indices[1]-indices[0]),int(indices[3]-indices[2])),Image.ANTIALIAS))
immap[indices[2]:indices[3],indices[0]:indices[1]] += resize
# Flip image to match sky coords (so coordinate convention is +y = N, +x = W, angle is deg E of N)
immap = immap[::-1,:]
# last, correct for pixel size.
immap *= (xmap[0,1]-xmap[0,0])**2.
return immap,mus
def update(val):
zL, zS = slzL.val, slzS.val
xL, yL = slxL.val, slyL.val
ML, eL, PAL = slML.val, sleL.val, slPAL.val
sh, sha = slss.val, slsa.val
xs, ys = slxs.val, slys.val
Fs, ws = slFs.val, slws.val
ns, ars, pas = slns.val, slars.val, slPAs.val
newDd = cosmo.angular_diameter_distance(zL).value
newDs = cosmo.angular_diameter_distance(zS).value
newDds = cosmo.angular_diameter_distance_z1z2(zL, zS).value
newLens = vl.SIELens(zLens, xL, yL, 10**ML, eL, PAL)
newShear = vl.ExternalShear(sh, sha)
newSource = vl.SersicSource(zS, True, xs, ys, Fs, ws, ns, ars, pas)
xs, ys = vl.LensRayTrace(xim, yim, [newLens, newShear], newDd, newDs,
newDds)
imbg = vl.SourceProfile(xim, yim, newSource, [newLens, newShear])
imlensed = vl.SourceProfile(xs, ys, newSource, [newLens, newShear])
caustics = vl.CausticsSIE(newLens, newDd, newDs, newDds, newShear)
ax.cla()
ax.imshow(imbg,
cmap=cmbg,
extent=[xim.min(), xim.max(),
yim.min(), yim.max()],
origin='lower')
ax.imshow(imlensed,
cmap=cmlens,
extent=[xim.min(), xim.max(),
yim.min(), yim.max()],
origin='lower')
mu = imlensed.sum() * (xim[0, 1] - xim[0, 0])**2 / newSource.flux['value']
ax.text(0.9, 1.02, '$\\mu$ = {0:.2f}'.format(mu), transform=ax.transAxes)
#for i in range(caustics.shape[0]):
# ax.plot(caustics[i,0,:],caustics[i,1,:],'k-')
for caustic in caustics:
ax.plot(caustic[:, 0], caustic[:, 1], 'k-')
f.canvas.draw_idle()
def update(val):
zL,zS = slzL.val,slzS.val
xL,yL = slxL.val, slyL.val
ML,eL,PAL = slML.val,sleL.val,slPAL.val
sh,sha = slss.val,slsa.val
newDd = cosmo.angular_diameter_distance(zL).value
newDs = cosmo.angular_diameter_distance(zS).value
newDds= cosmo.angular_diameter_distance_z1z2(zL,zS).value
newLens = vl.SIELens(zLens,xL,yL,10**ML,eL,PAL)
newShear = vl.ExternalShear(sh,sha)
xsource,ysource = vl.LensRayTrace(xim,yim,[newLens,newShear],newDd,newDs,newDds)
caustics = vl.get_caustics([newLens,newShear],newDd,newDs,newDds)
ax.cla()
ax.plot(xsource,ysource,'b-')
for caustic in caustics:
ax.plot(caustic[:,0],caustic[:,1],'k-')
#ax.set_xlim(-0.5,0.5)
#ax.set_ylim(-0.5,0.5)
#for i in range(len(xs)):
# p[i].set_xdata(xs[i])
# p[i].set_ydata(ys[i])
f.canvas.draw_idle()
def angular_broadening(self, lobs, zsource, cosmo=None):
""" Broadening of a point source due to turbulent scattering
Parameters
----------
lobs : Quantity
Observed wavelength
zsource : float
Redshift of radio source
Returns
-------
theta : Quantity
Angular broadening. Radius (half-width at half-max)
"""
if self.regime == 0:
raise ValueError("Need to set rdiff and the regime first!")
if cosmo is None:
from astropy.cosmology import Planck15 as cosmo
# f
if (self.regime == 1) or np.isclose(self.beta, 4.):
f = 1.18
elif (self.regime == 2) and np.isclose(self.beta, 11 / 3.):
f = 1.01
# Distances
D_S = cosmo.angular_diameter_distance(zsource)
D_LS = cosmo.angular_diameter_distance_z1z2(self.zL, zsource)
if self.verbose:
print("D_LS={}, D_S={}".format(D_LS, D_S))
D_LS_D_S = D_LS / D_S
# Evaluate
k = 2 * np.pi / (lobs / (1 + self.zL)
) # Are we sure about this (1+z) factor?!
self.theta = f * D_LS_D_S / (k * self.rdiff) * u.radian
return self.theta.to('arcsec')
xim, yim = np.meshgrid(xim, yim)
zLens, zSource = 0.8, 5.656
xLens, yLens = 0., 0.
MLens, eLens, PALens = 2.87e11, 0.5, 70.
xSource, ySource, FSource = 0.216, 0.24, 0.02 # arcsec, arcsec, Jy
aSource, nSource, arSource, PAsource = 0.1, 0.5, 1.0, 120. - 90 # arcsec,[],[],deg CCW from x-axis
shear, shearangle = 0.12, 120.
Lens = vl.SIELens(zLens, xLens, yLens, MLens, eLens, PALens)
Shear = vl.ExternalShear(shear, shearangle)
Source = vl.SersicSource(zSource, True, xSource, ySource, FSource, aSource,
nSource, arSource, PAsource)
Dd = cosmo.angular_diameter_distance(zLens).value
Ds = cosmo.angular_diameter_distance(zSource).value
Dds = cosmo.angular_diameter_distance_z1z2(zLens, zSource).value
xsource, ysource = vl.LensRayTrace(xim, yim, [Lens, Shear], Dd, Ds, Dds)
imbg = vl.SourceProfile(xim, yim, Source, [Lens, Shear])
imlensed = vl.SourceProfile(xsource, ysource, Source, [Lens, Shear])
caustics = vl.CausticsSIE(Lens, Dd, Ds, Dds, Shear)
f = pl.figure(figsize=(12, 6))
ax = f.add_subplot(111, aspect='equal')
pl.subplots_adjust(right=0.48, top=0.97, bottom=0.03, left=0.05)
cmbg = cm.cool
cmbg._init()
cmbg._lut[0, -1] = 0.
def lens_efficiency(z_lens, z_src):
"""Calculates the efficiency of the lensing system given source and lens redshifts."""
dist_lens_source = cosmo.angular_diameter_distance_z1z2(z_lens,
z_src).value
dist_observer_source = cosmo.angular_diameter_distance(z_src).value
return dist_lens_source / dist_observer_source
def __init__(
self,
mag_zero=25.5,
mag_iso=22.5,
exposure=1610.0,
fwhm_psf=0.18,
pixel_size=0.1,
n_xy=64,
f_sub=0.05,
beta=-1.9,
m_min_calib=1e6 * M_s,
m_max_sub_div_M_hst_calib=0.01,
m_200_min_sub=1e7 * M_s,
m_200_max_sub_div_M_hst=0.01,
M_200_sigma_v_scatter=False,
params_eval=None,
calculate_joint_score=False,
calculate_msub_derivatives=False,
calculate_sub_residuals=False,
draw_host_mass=True,
draw_host_redshift=True,
draw_alignment=True,
roi_size=2.,
):
"""
Class to simulation an observation strong lensing image, with substructure sprinkled in.
:param mag_zero: Zero-point magnitude of observation
:param mag_iso: Magnitude of isotropic sky brightness
:param exposure: Exposure time of observation, in seconds (including gain)
:param fwhm_psf: FWHM of Gaussian PSF, in arcsecs
:param pixel_size: Pixel side size, in arcsecs
:param n_xy: Number of pixels (along x and y) of observation
:param f_sub: Fraction of total contained mass in substructure
:param beta: Slope in the subhaalo mass function
:param m_min_calib: Minimum mass above which subhalo mass fraction is `f_sub`
:param m_max_sub_div_M_hst_calib: Maximum mass below which subhalo mass fraction is `f_sub`,
in units of the host halo mass
:param m_200_min_sub: Lowest mass of subhalos to draw
:param m_200_max_sub_div_M_hst: Maximum mass of subhalos to draw, in units of host halo mass
:param M_200_sigma_v_scatter: Whether to apply lognormal scatter in sigma_v to M_200_host mapping
:param params_eval: Parameters (f_sub, beta) for which p(x,z|params) will be calculated
:param calculate_joint_score: Whether grad_params log p(x,z|params) will be calculated
:param calculate_msub_derivatives: Whether to calculate derivatives of image wrt subhalos masses
:param calculate_residuals: Whether to calculate residual images wrt subhalos
"""
# beta = -2.0 is forbidden!
if np.abs((beta + 2.)) < 1.e-3:
beta = -2.001
# Store input
self.mag_zero = mag_zero
self.mag_iso = mag_iso
self.exposure = exposure
self.fwhm_psf = fwhm_psf
self.pixel_size = pixel_size
self.n_xy = n_xy
self.f_sub = f_sub
self.beta = beta
self.m_min_calib = m_min_calib
self.m_max_sub_div_M_hst_calib = m_max_sub_div_M_hst_calib
self.m_200_min_sub = m_200_min_sub
self.m_200_max_sub_div_M_hst = m_200_max_sub_div_M_hst
self.M_200_sigma_v_scatter = M_200_sigma_v_scatter
self.params_eval = params_eval
self.calculate_joint_score = calculate_joint_score
self.draw_host_mass = draw_host_mass
self.draw_host_redshift = draw_host_redshift
self.draw_alignment = draw_alignment
self.coordinate_limit = pixel_size * n_xy / 2.0
# Draw lens properties consistent with Collett et al [1507.02657]
# Clip lens redshift `z_l` to be less than 1; high-redshift lenses no good for our purposes!
if self.draw_host_redshift:
self.z_l = 2.0
while self.z_l > 1.0:
self.z_l = 10 ** np.random.normal(-0.25, 0.25)
else:
self.z_l = 10.0 ** -0.25
if self.draw_host_mass:
self.sigma_v = np.random.normal(225, 50)
else:
self.sigma_v = 225.0
if self.draw_alignment:
self.theta_x_0 = np.random.normal(0, 0.2)
self.theta_y_0 = np.random.normal(0, 0.2)
else:
self.theta_x_0 = 0.0
self.theta_y_0 = 0.0
q = 1 # For now, hard-code host to be spherical
# Fix the source properties to reasonable mean-ish values
self.theta_s_e = 0.2
self.z_s = 1.5
self.mag_s = 23.0
# Get relevant distances
self.D_l = Planck15.angular_diameter_distance(z=self.z_l).value * Mpc
D_s = Planck15.angular_diameter_distance(z=self.z_s).value * Mpc
D_ls = Planck15.angular_diameter_distance_z1z2(z1=self.z_l, z2=self.z_s).value * Mpc
# Get properties for NFW host DM halo
if draw_host_mass:
self.M_200_hst = self.M_200_sigma_v(self.sigma_v * Kmps, scatter=M_200_sigma_v_scatter)
else:
self.M_200_hst = self.M_200_sigma_v(self.sigma_v * Kmps, scatter=0.0)
c_200_hst = MassProfileNFW.c_200_SCP(self.M_200_hst)
r_s_hst, rho_s_hst = MassProfileNFW.get_r_s_rho_s_NFW(self.M_200_hst, c_200_hst)
# Get properties for SIE host
self.theta_E = MassProfileSIE.theta_E(self.sigma_v * Kmps, D_ls, D_s)
# Don't consider configuration with subhalo fraction > 1!
self.f_sub_realiz = 2.0
while self.f_sub_realiz > 1.0:
# Generate a subhalo population...
ps = SubhaloPopulation(
f_sub=f_sub,
beta=beta,
M_hst=self.M_200_hst,
c_hst=c_200_hst,
m_min=m_200_min_sub,
m_max=m_200_max_sub_div_M_hst * self.M_200_hst,
m_min_calib=m_min_calib,
m_max_calib=m_max_sub_div_M_hst_calib * self.M_200_hst,
theta_s=r_s_hst / self.D_l,
theta_roi=roi_size * self.theta_E,
theta_E=self.theta_E,
params_eval=params_eval,
calculate_joint_score=calculate_joint_score,
)
# ... and grab its properties
self.m_subs = ps.m_sample
self.n_sub_roi = ps.n_sub_roi
self.theta_xs = ps.theta_x_sample
self.theta_ys = ps.theta_y_sample
self.f_sub_realiz = ps.f_sub_realiz
self.n_sub_in_ring = ps.n_sub_in_ring
self.f_sub_in_ring = ps.f_sub_in_ring
self.n_sub_near_ring = ps.n_sub_near_ring
self.f_sub_near_ring = ps.f_sub_near_ring
# Convert magnitude for source and isotropic component to expected counts
self.S_tot = self._mag_to_flux(self.mag_s, self.mag_zero)
self.f_iso = self._mag_to_flux(self.mag_iso, self.mag_zero)
# Set host properties. Host assumed to be at the center of the image.
self.hst_param_dict = {"profile": "SIE", "theta_x_0": 0.0, "theta_y_0": 0.0, "theta_E": self.theta_E, "q": q}
lens_list = [self.hst_param_dict]
# Set subhalo properties
for i_sub, (m, theta_x, theta_y) in enumerate(zip(self.m_subs, self.theta_xs, self.theta_ys)):
c = MassProfileNFW.c_200_SCP(m)
r_s, rho_s = MassProfileNFW.get_r_s_rho_s_NFW(m, c)
sub_param_dict = {"profile": "NFW", "theta_x_0": theta_x, "theta_y_0": theta_y, "M_200": m, "r_s": r_s, "rho_s": rho_s}
lens_list.append(sub_param_dict)
# Set source properties
src_param_dict = {"profile": "Sersic", "theta_x_0": self.theta_x_0, "theta_y_0": self.theta_y_0, "S_tot": self.S_tot, "theta_e": self.theta_s_e, "n_srsc": 1}
# Set observation and global properties
observation_dict = {
"n_x": n_xy,
"n_y": n_xy,
"theta_x_lims": (-self.coordinate_limit, self.coordinate_limit),
"theta_y_lims": (-self.coordinate_limit, self.coordinate_limit),
"exposure": exposure,
"f_iso": self.f_iso,
}
global_dict = {"z_s": self.z_s, "z_l": self.z_l}
# Inititalize lensing class and produce lensed image
lsi = LensingSim(lens_list, [src_param_dict], global_dict, observation_dict)
self.image = lsi.lensed_image()
self.image_poiss = np.random.poisson(self.image) # Poisson fluctuate
self.image_poiss_psf = self._convolve_psf(self.image_poiss, fwhm_psf, pixel_size) # Convolve with PSF
# Augmented data
self.joint_log_probs = ps.joint_log_probs
self.joint_scores = ps.joint_scores
# Optionally, compute derivatives of image wrt each subahlo mass (takes ~1s/subhalo)
if calculate_msub_derivatives:
self._calculate_derivs()
# Optionally, compute derivatives of image wrt each subahlo mass (takes ~1s/subhalo)
if calculate_sub_residuals:
self._calculate_residuals()
def monte_tau(zeval, nrand=100, nHI=0.1, avg_ne=-2.6,
sigma_ne=0.5, cosmo=None, lobs=50*u.cm, turb=None):
""" Generate random draws of tau at a series of redshifts
Parameters
----------
zeval : ndarray
Array of redshifts for evaluation
nrand : int, optional
Number of samples on NHI
avg_ne : float, optional
Average log10 electron density / cm**3
sigma_ne : float, optional
Error in log10 ne
nHI : float, optional
Fiducial value for n_HI; used for DL value
lobs : Quantity
Wavelength for analysis
turb : Turbulence object, optional
Usually defined internally and that is the highly recommended approach
cosmo : astropy.cosmology, optional
Defaults to Planck15
Returns
-------
rand_tau : ndarray (nrand, nz)
Random tau values reported in ms (but without explicit astropy Units)
"""
# Init
ne_param = dict(value=avg_ne, sigma=sigma_ne) # Neeleman+15
dla_fits = load_dla_fits()
if cosmo is None:
from astropy.cosmology import Planck15 as cosmo
# Setup NHI
lgNmax = np.linspace(20.3, 22., 10000)
intfN = _int_dbl_pow(dla_fits['fN']['dpow'], lgNmax=lgNmax)
# Spline
interp_fN = interp1d(intfN/intfN[-1], lgNmax)#, kind='cubic')
# Setup z
zvals = np.linspace(0., 7., 10000)
nz_s = _dla_nz(zvals)
nz_s[0] = 0.
# Turbulence
if turb is None:
turb = _init_dla_turb()
f_ne=turb.ne
zsource = 2.
turb.set_rdiff(lobs)
fiducial_tau = turb.temporal_smearing(lobs, zsource)
# Take out the cosmology
f_D_S = cosmo.angular_diameter_distance(zsource)
f_D_L = cosmo.angular_diameter_distance(turb.zL)
f_D_LS = cosmo.angular_diameter_distance_z1z2(turb.zL, zsource)
fiducial_tau = fiducial_tau / f_D_LS / f_D_L * f_D_S * (1+turb.zL)**3 # ms/Mpc
kpc_cm = (1*u.kpc).to('cm').value
rand_tau = np.zeros((nrand, zeval.size))
# Loop on zeval
for ss,izeval in enumerate(zeval):
avg_nz = _dla_nz(izeval)
rn = np.random.poisson(avg_nz, size=nrand)
ndla = np.sum(rn)
if ndla == 0:
continue
# Get random NHI
rval = np.random.uniform(size=ndla)
rNHI = interp_fN(rval)
DL = 10.**rNHI / nHI / kpc_cm
# Get random z
imin = np.argmin(np.abs(zvals-izeval))
interp_z = interp1d(nz_s[0:imin]/nz_s[imin-1], zvals[0:imin])#, kind='cubic')
rval = np.random.uniform(size=ndla)
rz = interp_z(rval)
# Cosmology
D_S = cosmo.angular_diameter_distance(izeval)
D_L = cosmo.angular_diameter_distance(rz)
D_LS = cosmo.angular_diameter_distance_z1z2(rz, izeval)
# Get random n_e
rne = 10.**(ne_param['value'] + ne_param['sigma']*np.random.normal(size=ndla))
# Calculate (scale)
rtau = fiducial_tau * (D_LS * D_L / D_S) * (rne/f_ne.to('cm**-3').value)**2 / (1+rz)**3
# Generate, fill
taus = np.zeros((nrand, np.max(rn)))
kk = 0
for jj,irn in enumerate(rn):
if irn > 0:
taus[jj,0:irn] = rtau[kk:kk+irn]
kk += irn
# Finish -- add in quadrature
final_tau = np.sqrt(np.sum(taus**2, axis=1))
# Save
rand_tau[:,ss] = final_tau
# Return
return rand_tau
yim = np.arange(-3,3,.03)
xim,yim = np.meshgrid(xim,yim)
zLens,zSource = 0.8,5.656
xLens,yLens = 0.,0.
MLens,eLens,PALens = 2.87e11,0.5,90.
xSource,ySource,FSource,sSource = 0.216,-0.24,0.023,0.074
Lens = vl.SIELens(zLens,xLens,yLens,MLens,eLens,PALens)
Shear= vl.ExternalShear(0.,0.)
lens = [Lens,Shear]
Source = vl.GaussSource(zSource,True,xSource,ySource,FSource,sSource)
Dd = cosmo.angular_diameter_distance(zLens).value
Ds = cosmo.angular_diameter_distance(zSource).value
Dds = cosmo.angular_diameter_distance_z1z2(zLens,zSource).value
caustics = vl.get_caustics(lens,Dd,Ds,Dds)
xsource,ysource = vl.LensRayTrace(xim,yim,lens,Dd,Ds,Dds)
f = pl.figure()
ax = f.add_subplot(111,aspect='equal')
pl.subplots_adjust(bottom=0.25,top=0.98)
ax.plot(xsource,ysource,'b-')
for caustic in caustics:
ax.plot(caustic[:,0],caustic[:,1],'k-')
# Put in a bunch of sliders to control lensing parameters
def plot_images(data,
mcmcresult,
returnimages=False,
plotcombined=False,
plotall=False,
imsize=256,
pixsize=0.2,
taper=0.,
**kwargs):
"""
Create a five-panel figure from data and chains,
showing data, best-fit model, residuals, high-res image, source plane
Inputs:
data:
The visdata object(s) to be imaged. If more than
one is passed, they'll be imaged/differenced separately.
chains:
A result from running LensModelMCMC.
returnimages: bool, optional
If True, will also return a list of numpy arrays
containing the imaged data, interpolated model, and full-res model.
Default is False.
plotcombined: bool, optional, default False
If True, plots only a single row of images, after combining all datasets
in `data' and applying any necessary rescaling/shifting contained in
`mcmcresult'.
plotall: bool, optional, default False
If True, plots each dataset in its own row *and* the combined dataset in
an extra row.
Returns:
If returnimages is False:
f, axarr:
A matplotlib figure and array of Axes objects.
If returnimages is True:
f,axarr,imagelist:
Same as above; imagelist is a list of length (# of datasets),
containing four arrays each, representing the data,
interpolated model, full-resolution model, and source plane.
"""
limits = kwargs.pop('limits', [
-imsize * pixsize / 2., +imsize * pixsize / 2., -imsize * pixsize / 2.,
+imsize * pixsize / 2.
])
cmap = kwargs.pop('cmap', cm.Greys)
mapcontours = kwargs.pop('mapcontours', np.delete(np.arange(-21, 22, 3),
7))
rescontours = kwargs.pop('rescontours',
np.array([-6, -5, -4, -3, -2, 2, 3, 4, 5, 6]))
level = kwargs.pop('level', None)
logmodel = kwargs.pop('logmodel', False)
datasets = list(np.array([data]).flatten())
# shorthand for later
c = copy.deepcopy(mcmcresult['chains'])
# Now all these things are saved separately, don't have to do the BS above
lens = mcmcresult['best-fit']['lens']
source = mcmcresult['best-fit']['source']
scaleamp = mcmcresult['best-fit']['scaleamp'] if 'scaleamp' in mcmcresult[
'best-fit'].keys() else np.ones(len(datasets))
shiftphase = mcmcresult['best-fit'][
'shiftphase'] if 'shiftphase' in mcmcresult['best-fit'].keys(
) else np.zeros((len(datasets), 2))
sourcedatamap = mcmcresult[
'sourcedatamap'] if 'sourcedatamap' in mcmcresult.keys(
) else [None] * len(datasets)
modelcal = mcmcresult['modelcal'] if 'modelcal' in mcmcresult.keys(
) else [False] * len(datasets)
if plotall:
f, axarr = plt.subplots(len(datasets) + 1,
5,
figsize=(14, 4 * (len(datasets) + 1)))
axarr = np.atleast_2d(axarr)
images = [[] for _ in range(len(datasets) + 1)]
if sourcedatamap[0] is not None:
warnings.warn(
"sourcedatamap[0] is not None. Are you sure you want plotall=True?"
)
sourcedatamap.append(None)
f.subplots_adjust(left=0.05, bottom=0.05, top=0.95, right=0.99)
elif plotcombined:
f, axarr = plt.subplots(1, 5, figsize=(14, 4))
axarr = np.atleast_2d(axarr)
images = [[]]
if sourcedatamap[0] is not None:
warnings.warn(
"sourcedatamap[0] is not None, and has been set to None. Are you sure you want plotcombined=True? This could break the source plane plot."
)
sourcedatamap = [None]
f.subplots_adjust(left=0.05, bottom=0.05, top=0.95, right=0.99)
else:
f, axarr = plt.subplots(len(datasets),
5,
figsize=(14, 4 * len(datasets)))
axarr = np.atleast_2d(axarr)
images = [[] for _ in range(len(datasets))] # effing mutable lists.
f.subplots_adjust(left=0.05, bottom=0.05, top=0.95, right=0.99)
plotdata, plotinterp = [], []
for i, dset in enumerate(datasets):
# Get us some coordinates.
xmap,ymap,xemit,yemit,ix = GenerateLensingGrid(datasets,mcmcresult['xmax'],\
mcmcresult['highresbox'],mcmcresult['fieldres'],mcmcresult['emitres'])
# Create model image
immap,_ = create_modelimage(lens,source,xmap,ymap,xemit,yemit,\
ix,sourcedatamap=sourcedatamap[i])
# And interpolate onto uv-coords of dataset
interpdata = fft_interpolate(dset,immap,xmap,ymap,ug=None,\
scaleamp=scaleamp[i],shiftphase=shiftphase[i])
if modelcal[i]:
selfcal, _ = model_cal(dset, interpdata)
else:
selfcal = copy.deepcopy(dset)
plotdata.append(selfcal)
plotinterp.append(interpdata)
if plotall:
plotdata.append(concatvis(plotdata))
plotinterp.append(concatvis(plotinterp))
elif plotcombined:
plotdata = [concatvis(plotdata)]
plotinterp = [concatvis(plotinterp)]
for row in range(axarr.shape[0]):
# Image the data
imdata = uvimageslow(plotdata[row], imsize, pixsize, taper)
# Image the model
immodel = uvimageslow(plotinterp[row], imsize, pixsize, taper)
# And the residuals
imdiff = imdata - immodel
if returnimages:
images[row].append(imdata)
images[row].append(immodel)
# Plot everything up
ext = [
-imsize * pixsize / 2., imsize * pixsize / 2.,
-imsize * pixsize / 2., imsize * pixsize / 2.
]
# Figure out what to use as the noise level; sum of weights if no user-supplied value
if level is None: s = ((plotdata[row].sigma**-2.).sum())**-0.5
else:
try:
s = [e for e in level][i]
except TypeError:
s = float(level)
print("Data - Model rms: {0:0.3e}".format(imdiff.std()))
axarr[row, 0].imshow(imdata,
interpolation='nearest',
extent=ext,
cmap=cmap)
axarr[row, 0].contour(imdata,
extent=ext,
colors='k',
origin='image',
levels=s * mapcontours)
axarr[row, 0].set_xlim(limits[0], limits[1])
axarr[row, 0].set_ylim(limits[2], limits[3])
axarr[row,1].imshow(immodel,interpolation='nearest',extent=ext,cmap=cmap,\
vmin=imdata.min(),vmax=imdata.max())
axarr[row, 1].contour(immodel,
extent=ext,
colors='k',
origin='image',
levels=s * mapcontours)
axarr[row, 1].set_xlim(limits[0], limits[1])
axarr[row, 1].set_ylim(limits[2], limits[3])
axarr[row,2].imshow(imdiff,interpolation='nearest',extent=ext,cmap=cmap,\
vmin=imdata.min(),vmax=imdata.max())
axarr[row, 2].contour(imdiff,
extent=ext,
colors='k',
origin='image',
levels=s * rescontours)
axarr[row, 2].set_xlim(limits[0], limits[1])
axarr[row, 2].set_ylim(limits[2], limits[3])
if np.log10(s) < -6.: sig, unit = 1e9 * s, 'nJy'
elif np.log10(s) < -3.: sig, unit = 1e6 * s, '$\mu$Jy'
elif np.log10(s) < 0.: sig, unit = 1e3 * s, 'mJy'
else: sig, unit = s, 'Jy'
axarr[row, 2].text(0.05,
0.05,
"Data 1$\sigma$ = {0:.1f}{1:s}".format(sig, unit),
transform=axarr[row, 2].transAxes,
bbox=dict(fc='w'))
# For the last two panels, give the apparent emission at higher resolution
# and the intrinsic source plane structure.
# Create model image at higher res, remove unlensed sources
src = [src for src in source if src.lensed]
imemit,_ = create_modelimage(lens,src,xemit,yemit,xemit,yemit,\
[0,xemit.shape[1],0,xemit.shape[0]],sourcedatamap=sourcedatamap[row])
images[row].append(imemit)
xcen = center_of_mass(imemit)[1] * (xemit[0, 1] -
xemit[0, 0]) + xemit.min()
ycen = -center_of_mass(imemit)[0] * (xemit[0, 1] -
xemit[0, 0]) + yemit.max()
dx = 0.5 * (xemit.max() - xemit.min())
dy = 0.5 * (yemit.max() - yemit.min())
if logmodel:
norm = SymLogNorm(
0.01 * imemit.max()
) #imemit = np.log10(imemit); vmin = imemit.min()-2.
else:
norm = None #vmin = imemit.min()
axarr[row,3].imshow(imemit,interpolation='nearest',\
extent=[xemit.min(),xemit.max(),yemit.min(),yemit.max()],cmap=cmap,norm=norm)
axarr[row, 3].set_xlim(xcen - dx, xcen + dx)
axarr[row, 3].set_ylim(ycen - dy, ycen + dy)
# And create source plane using the exact grids the code used during fitting.
imsource = np.zeros(xemit.shape)
for s in src:
imsource += SourceProfile(xemit, yemit, s,
lens) * (xemit[0, 1] - xemit[0, 0])**2.
images[row].append(imsource)
xcen = center_of_mass(imsource)[1] * (xemit[0, 1] -
xemit[0, 0]) + xemit.min()
ycen = -center_of_mass(imemit)[0] * (xemit[0, 1] -
xemit[0, 0]) + yemit.max()
dx = 0.5 * (xemit.max() - xemit.min())
dy = 0.5 * (yemit.max() - yemit.min())
axarr[row, 4].imshow(
imsource,
interpolation='nearest',
extent=[xemit.min(),
xemit.max(),
yemit.min(),
yemit.max()],
cmap=cmap,
norm=SymLogNorm(0.01 * imsource.max()),
origin='lower')
axarr[row, 4].set_xlim(xcen - dx, xcen + dx)
axarr[row, 4].set_ylim(ycen - dy, ycen + dy)
# Need to precalculate distances to get caustics
Dd = Planck15.angular_diameter_distance(lens[0].z).value
Ds = Planck15.angular_diameter_distance(source[0].z).value
Dds = Planck15.angular_diameter_distance_z1z2(lens[0].z,
source[0].z).value
caustics = get_caustics(lens,
Dd,
Ds,
Dds,
highresbox=mcmcresult['highresbox'],
numres=mcmcresult['emitres'])
for caustic in caustics:
axarr[row, 3].plot(caustic[:, 0],
caustic[:, 1],
ls='-',
marker='',
lw=1,
color='r')
axarr[row, 4].plot(caustic[:, 0],
caustic[:, 1],
ls='-',
marker='',
lw=1,
color='r')
s = imdiff.std()
if np.log10(s) < -6.: sig, unit = 1e9 * s, 'nJy'
elif np.log10(s) < -3.: sig, unit = 1e6 * s, '$\mu$Jy'
elif np.log10(s) < 0.: sig, unit = 1e3 * s, 'mJy'
else: sig, unit = s, 'Jy'
# Label some axes and such
axarr[row, 0].set_title(plotdata[row].filename + '\nDirty Image')
axarr[row, 1].set_title('Model Dirty Image')
axarr[row,
2].set_title('Residual Map rms={0:.1f}{1:s}'.format(sig, unit))
if logmodel: axarr[row, 3].set_title('High-res Model (log-scale)')
else: axarr[row, 3].set_title('High-res Model')
axarr[row, 4].set_title('Source Plane Model')
if returnimages: return f, axarr, images
else: return f, axarr