def lnprob(p, data, bins):
# unpack parameters
incl = p[0]
PA = p[1]
offx = p[2]
offy = p[3]
sbs = p[4:]
# priors
# enforce positive surface brightnesses
if (np.any(sbs) < 0.):
return -np.inf
# enforce monotonicity
if (np.array_equal(np.sort(sbs), sbs[::-1]) == False):
return -np.inf
# geometry common sense
if (incl < 0. or incl > 90. or PA < 0. or PA > 180.):
return -np.inf
# unpack data
u, v, dreal, dimag, dwgt = data
uvsamples = u, v
# generate model visibilities
pars = incl, PA, np.array([offx, offy]), sbs
mvis = discreteModel(pars, uvsamples, bins)
# compute a chi2 value
chi2 = np.sum(dwgt*(dreal-mvis.real)**2 + dwgt*(dimag-mvis.imag)**2)
# return a log-likelihood value
return -0.5*chi2
offy = -0.2
SB = (sig/cb)**0.7 * np.exp(-(cb/sig)**2.5) # fullA distribution; where
# flux=0.12, sig=0.6, i=50,
# PA = 70., offs=[-0.3, -0.2]
int_SB = np.trapz(2.*np.pi*SB*cb, cb) # a check on the total flux
SB *= flux / int_SB
itheta = incl, PA, np.array([offx, offy]), SB
# FT and sample it for each configuration
ldata = np.load('DATA/base/dummy.c1.sim.alma.cycle3.3.vis.npz')
lu = ldata['u']
lv = ldata['v']
lvis = ldata['Vis']
lrms = 0.035e-3
lo_vis = discreteModel(itheta, [lu, lv], bins)
hdata = np.load('DATA/base/dummy.c2.sim.alma.cycle3.6.vis.npz')
hu = hdata['u']
hv = hdata['v']
hvis = hdata['Vis']
hrms = 0.020e-3
hi_vis = discreteModel(itheta, [hu, hv], bins)
# add (white) noise to the model visibilities; record noise in weights
lnoise = np.random.normal(loc=0., scale=lrms*np.sqrt(len(lu)), size=len(lu))
#lo_vis.real += lnoise
#lo_vis.imag += lnoise
lo_wgt = np.ones_like(lu)/(lrms*np.sqrt(len(lu)))**2
# load the "data" (w/ and w/o noise) data = np.load(filename+'.vis.npz') u = data['u'] v = data['v'] rho = np.sqrt(u**2 + v**2) ivis = data['nf_Vis'] vis = data['Vis'] wgt = data['Wgt'] # binned models for the data ltheta = incl, PA, np.array([offx, offy]), lSB lvis = discreteModel(ltheta, [u, v], lbins) vtheta = incl, PA, np.array([offx, offy]), vSB vvis = discreteModel(vtheta, [u, v], vbins) xtheta = incl, PA, np.array([offx, offy]), xSB xvis = discreteModel(xtheta, [u, v], xbins) # plot them and the residuals (real only, since symmetric for now) plt.figure(figsize=(7, 10)) plt.clf() gs = gridspec.GridSpec(3, 1, height_ratios=[1, 1, 1])
imag = data['Im'] wgt = 10000.*data['Wt'] # deproject incl = 0. PA = 0. offset = np.array([0., 0.]) indata = u, v, real, imag dvis = deprojectVis(indata, incl=incl, PA=PA, offset=offset) drho, dreal, dimag = dvis # initial guess visibilities ftheta = incl, PA, offset, guess_sb uvsamples = u, v fmodelvis = discreteModel(ftheta, uvsamples, bins) mindata = u, v, fmodelvis.real, fmodelvis.imag fvis = deprojectVis(mindata, incl=incl, PA=PA, offset=offset) frho, freal, fimag = fvis # truth ttheta = incl, PA, offset, SBtruth bins_true = rin, rtruth tmodelvis = discreteModel(ttheta, uvsamples, bins_true) mindata = u, v, tmodelvis.real, tmodelvis.imag tvis = deprojectVis(mindata, incl=incl, PA=PA, offset=offset) trho, treal, timag = tvis plt.axis([0, 2000., -0.025, 0.15]) plt.plot(drho, dreal, '.y', alpha=0.01) # loop through initialized walkers
