def myloglike(cube, ndim, nparams):
tmp_profs = Profiles(gp.pops, gp.nipol)
off = 0
rho_param = np.array(cube[off:off+gp.nepol])
if gprio.check_nr(rho_param[2:-1]):
print('dn/dr too big!')
return gh.err(0.7)
tmp_rho = phys.rho(gp.xepol, rho_param)
if(gprio.check_rho(tmp_rho)):
print('rho slope error')
return gh.err(1.)
tmp_profs.set_rho(tmp_rho[:gp.nipol])
tmp_profs.set_M(rho_SUM_Mr(gp.xepol, tmp_rho)[:gp.nipol]) # [munit,3D]
# TODO: mass is set at binmax, not rbin!
# implement integration routine working with density function
# based on density parametrization
# to give mass below rbin
# TODO: implement above function as gl_project.rho_INT_Mr()
off += gp.nepol
nuparstore = []
for pop in np.arange(gp.pops)+1:
nu_param = cube[off:off+gp.nepol]
nuparstore.append(nu_param)
tmp_nu = phys.rho(gp.xepol, nu_param) # [1], [pc]
# if gprio.check_nu(tmp_nu):
# print('nu error')
# return err/2.
if gp.bprior and gprio.check_bprior(tmp_rho, tmp_nu):
print('bprior error')
return gh.err(1.5)
tmp_profs.set_nu(pop, tmp_nu[:gp.nipol]) # [munit/pc^3]
off += gp.nepol
beta_param = np.array(cube[off:off+gp.nbeta])
tmp_beta = phys.beta(gp.xipol, beta_param)
if gprio.check_beta(tmp_beta):
print('beta error')
return gh.err(2.)
tmp_profs.set_beta(pop, tmp_beta)
off += gp.nbeta
try:
# beta_param = np.array([0.,0.])
sig, kap = phys.sig_kap_los(gp.xepol, pop, rho_param, nu_param, beta_param)
# sig and kap already are on data radii only, so no extension by 3 bins here
except Exception as detail:
return gh.err(3.)
tmp_profs.set_sig_kap(pop, sig, kap)
# determine log likelihood (*not* reduced chi2)
chi2 = gc.calc_chi2(tmp_profs, nuparstore)
# print('found log likelihood = ', -chi2/2.)
return -chi2/2. # from likelihood L = exp(-\chi^2/2), want log of that
def rho_param_INT_Rho(r0, rhoparam):
# use splines on variable transformed integral
# \Sigma(R) = \int_{r=R}^{R=\infty} \rho(r) d \sqrt(r^2-R^2)
# gh.checknan(rhoparam, 'rho_param_INT_Rho')
xmin = r0[0]/1e4
r0left = np.array([xmin, r0[0]*0.25, r0[0]*0.50, r0[0]*0.75])
r0nu = np.hstack([r0left, r0])
rhonu = phys.rho(r0nu, rhoparam)
Rho = np.zeros(len(r0nu)-gp.nexp)
for i in range(len(r0nu)-gp.nexp):
xnew = np.sqrt(r0nu[i:]**2-r0nu[i]**2) # [lunit]
ynew = 2.*rhonu[i:]
# power-law extension to infinity. TODO: include in Rho[i] below
C = gh.quadinflog(xnew[-gp.nexp:], ynew[-gp.nexp:], xnew[-1], np.inf)
# tcknu = splrep(xnew, ynew, k=3)
# interpolation in real space, not log space
# problem: splint below could give negative values
# reason: for high radii (high i), have a spline that goes negative
# workaround: multiply by const/add const to keep spline positive @ all times
# or set to log (but then integral is not straightforward
# Rho[i] = splint(0., xnew[-1], tcknu) + C
Rho[i] = gh.quadinfloglog(xnew[1:], ynew[1:], xmin, xnew[-1]) + C
gh.checkpositive(Rho, 'Rho in rho_param_INT_Rho')
return Rho[4:] # @r0 (r0nu without r0left)
def physical(r0, prof, pop, tmp_rho, tmp_nu, tmp_beta):
if prof == "rho":
tmp_prof = phys.rho(r0, tmp_rho)
elif prof == 'nr':
tmp_prof = tmp_rho[1:]
elif prof == "nu":
tmp_prof = rho_INT_Rho(r0, phys.rho(r0, tmp_nu))
elif prof == "betastar":
tmp_prof = phys.mapping_beta_star_poly(r0, tmp_beta)
elif prof == "beta":
tmp_prof = phys.beta(r0, tmp_beta)
elif prof == "sig":
tmp_sig, tmp_kap = phys.sig_kap_los(r0, pop, tmp_rho, tmp_nu, tmp_beta)
tmp_prof = tmp_sig
elif prof == "kap":
tmp_sig, tmp_kap = phys.sig_kap_los(r0, pop, tmp_rho, tmp_nu, tmp_beta)
tmp_prof = tmp_kap
return tmp_prof
def ant_sigkaplos2surf(r0, beta_param, rho_param, nu_param):
# TODO: check all values in ()^2 and ()^4 are >=0
minval = 1.e-30
r0nu = introduce_points_in_between(r0)
rhonu = phys.rho(r0nu, rho_param)
nunu = phys.rho(r0nu, nu_param)
betanu = phys.beta(r0nu, beta_param)
# calculate intbeta from beta approx directly
idnu = ant_intbeta(r0nu, beta_param)
# integrate enclosed 3D mass from 3D density
r0tmp = np.hstack([0.,r0nu])
rhoint = 4.*np.pi*r0nu**2*rhonu
# add point to avoid 0.0 in Mrnu(r0nu[0])
rhotmp = np.hstack([0.,rhoint])
tck1 = splrep(r0tmp, rhotmp, k=3, s=0.) # not necessarily monotonic
Mrnu = np.zeros(len(r0nu)) # work in refined model
for i in range(len(r0nu)): # get Mrnu
Mrnu[i] = splint(0., r0nu[i], tck1)
gh.checkpositive(Mrnu, 'Mrnu')
# (sigr2, 3D) * nu/exp(-idnu)
xint = r0nu # [pc]
yint = gp.G1 * Mrnu / r0nu**2 # [1/pc (km/s)^2]
yint *= nunu # [munit/pc^4 (km/s)^2]
yint *= np.exp(idnu) # [munit/pc^4 (km/s)^2]
gh.checkpositive(yint, 'yint sigr2')
# use quadinflog or quadinfloglog here
sigr2nu = np.zeros(len(r0nu))
for i in range(len(r0nu)):
sigr2nu[i] = np.exp(-idnu[i])/nunu[i]*gh.quadinflog(xint, yint, r0nu[i], np.inf)
# project back to LOS values
# sigl2sold = np.zeros(len(r0nu)-gp.nexp)
sigl2s = np.zeros(len(r0nu)-gp.nexp)
dropoffintold = 1.e30
for i in range(len(r0nu)-gp.nexp): # get sig_los^2
xnew = np.sqrt(r0nu[i:]**2-r0nu[i]**2) # [pc]
ynew = 2.*(1-betanu[i]*(r0nu[i]**2)/(r0nu[i:]**2))
ynew *= nunu[i:] * sigr2nu[i:]
gh.checkpositive(ynew, 'ynew in sigl2s') # is hit several times..
# yscale = 10.**(1.-min(np.log10(ynew[1:])))
# ynew *= yscale
# gh.checkpositive(ynew, 'ynew sigl2s')
tcknu = splrep(xnew, ynew, k=1)
# interpolation in real space for int
# power-law approximation from last three bins to infinity
# tckex = splrep(xnew[-3:], np.log(ynew[-3:]),k=1,s=1.0) # fine
# invexp = lambda x: np.exp(splev(x,tckex,der=0))
# C = quad(invexp,xnew[-1],np.inf)[0]
# C = max(0.,gh.quadinflog(xnew[-2:],ynew[-2:],xnew[-1],np.inf))
# sigl2sold[i] = splint(xnew[0], xnew[-1], tcknu) + C
sigl2s[i] = gh.quadinflog(xnew[1:], ynew[1:], xnew[0], np.inf)
# sigl2s[i] /= yscale
# TODO: for last 3 bins, up to factor 2 off
# if min(sigl2s)<0.:
# pdb.set_trace()
gh.checkpositive(sigl2s, 'sigl2s')
# derefine on radii of the input vector
tck = splrep(r0nu[:-gp.nexp], np.log(sigl2s), k=3, s=0.)
sigl2s_out = np.exp(splev(r0, tck))
gh.checkpositive(sigl2s_out, 'sigl2s_out')
if not gp.usekappa:
# print('not using kappa')
return sigl2s_out, np.ones(len(sigl2s_out))
# for the following: enabled calculation of kappa
# TODO: include another set of anisotropy parameters beta_'
# kappa_r^4
kapr4nu = np.ones(len(r0nu)-gp.nexp)
xint = r0nu # [pc]
yint = gp.G1 * Mrnu/r0nu**2 # [1/pc (km/s)^2]
yint *= nunu # [munit/pc^4 (km/s)^2]
yint *= sigr2nu # [munit/pc^4 (km/s)^4
yint *= np.exp(idnu) # [munit/pc^4 (km/s)^4]
gh.checkpositive(yint, 'yint in kappa_r^4')
yscale = 10.**(1.-min(np.log10(yint[1:])))
yint *= yscale
# power-law extrapolation to infinity
C = max(0., gh.quadinflog(xint[-3:], yint[-3:], r0nu[-1], np.inf))
# tckexp = splrep(xint[-3:],np.log(yint[-3:]),k=1,s=0.) # fine, exact interpolation
# invexp = lambda x: np.exp(splev(x,tckexp,der=0))
# C = quad(invexp,r0nu[-1],np.inf)[0]
tcknu = splrep(xint, yint, k=3) # interpolation in real space # TODO:
for i in range(len(r0nu)-gp.nexp):
# integrate from minimal radius to infinity
kapr4nu[i] = 3.*(np.exp(-idnu[i])/nunu[i]) * \
(splint(r0nu[i], r0nu[-1], tcknu) + C) # [(km/s)^4]
kapr4nu /= yscale
gh.checkpositive(kapr4nu, 'kapr4nu in kappa_r^4')
tcke = splrep(r0nu[:-gp.nexp], np.log(kapr4nu), k=3)
kapr4ext = np.exp(splev(r0ext, tcke))
kapr4nu = np.hstack([kapr4nu, kapr4ext])
gh.checkpositive(kapr4nu, 'kapr4nu in extended kappa_r^4')
tckbet = splrep(r0nu, betanu)
dbetanudr = splev(r0nu, tckbet, der=1)
gh.checknan(dbetanudr, 'dbetanudr in kappa_r^4')
# kappa^4_los*surfdensity
kapl4s = np.zeros(len(r0nu)-gp.nexp)
# gpl.start(); gpl.yscale('linear')
for i in range(len(r0nu)-gp.nexp):
xnew = np.sqrt(r0nu[i:]**2-r0nu[i]**2) # [pc]
ynew = g(r0nu[i:], r0nu[i], betanu[i:], dbetanudr[i:]) # [1]
ynew *= nunu[i:] * kapr4nu[i:] # [TODO]
# TODO: ynew could go negative here.. fine?
#gpl.plot(xnew, ynew)
#gh.checkpositive(ynew, 'ynew in kapl4s')
#yscale = 10.**(1.-min(np.log10(ynew[1:])))
#ynew *= yscale
# gpl.plot(xnew,ynew)
C = max(0., gh.quadinflog(xnew[-3:], ynew[-3:], xnew[-1], np.inf))
tcknu = splrep(xnew,ynew) # not s=0.1, this sometimes gives negative entries after int
kapl4s[i] = 2. * (splint(0., xnew[-1], tcknu) + C)
#kapl4s[i] /= yscale
# print('ynew = ',ynew,', kapl4s =', kapl4s[i])
# TODO: sometimes the last value of kapl4s is nan: why?
gh.checkpositive(kapl4s, 'kapl4s in kappa_r^4')
# project kappa4_los as well
# only use middle values to approximate, without errors in center and far
tck = splrep(r0nu[4:-gp.nexp], kapl4s[4:], k=3) # s=0.
kapl4s_out = np.exp(splev(r0, tck))
gh.checkpositive(kapl4s_out, 'kapl4s_out in kappa_r^4')
return sigl2s_out, kapl4s_out
def get_nu(self, pop):
off = nu_offset(pop)
return phys.rho(gp.xipol, self.cube[off:off+gp.nipol])
def geom_loglike(cube, ndim, nparams, gp):
tmp_profs = Profiles(gp.ntracer_pops, gp.nbins)#, gp.nrhonu, gp.nbaryon_pops, gp.nbaryon_params)
#Normalisation constant C for sigz calculation
off = 0
offstep = 1
norm = cube[off]
off += offstep
#Dark Matter rho parameters (rho_C, kz_C, kz_vector, kz_LS)
offstep = gp.nrhonu + 1
rho_DM_params = np.array(cube[off:off+offstep])
rho_DM_C = rho_DM_params[0] #rho_C
kz_rho_DM_allz = rho_DM_params[1:] #kz for rho across all z points [0, bin_centres, LS]
tmp_rho_DM_allz = phys.rho(gp.z_all_pts, kz_rho_DM_allz, rho_DM_C) #outputs rho across all points
tmp_profs.kz_rho_DM_C = kz_rho_DM_allz[0]
tmp_profs.set_prof('kz_rho_DM_vec', kz_rho_DM_allz[1:-1], 0, gp)
tmp_profs.kz_rho_DM_LS = kz_rho_DM_allz[-1]
tmp_profs.rho_DM_C = tmp_rho_DM_allz[0]
tmp_profs.set_prof('rho_DM_vec', tmp_rho_DM_allz[1:-1], 0, gp)
tmp_profs.rho_DM_LS = tmp_rho_DM_allz[-1]
off += offstep
#Baryons
for bary_pop in range(0, gp.nbaryon_pops):
offstep = gp.nbaryon_params
bary_params = np.array(cube[off:off+offstep])
off += offstep
#Tracer params, nu_C, kz_nu_C, kz_nu_vector, kz_nu_LS
for tracer_pop in range(0, gp.ntracer_pops):
offstep = gp.nrhonu + 1
tracer_params = np.array(cube[off:off+offstep])
nu_C = tracer_params[0]
kz_nu_allz = tracer_params[1:] #kz for rho across all z points [0, bin_centres, LS]
tmp_nu_allz = phys.rho(gp.z_all_pts, kz_nu_allz, nu_C) #outputs nu across all z points
tmp_profs.kz_nu_C = kz_nu_allz[0]
tmp_profs.set_prof('kz_nu_vec', kz_nu_allz[1:-1], 0, gp)
tmp_profs.kz_nu_LS = kz_nu_allz[-1]
tmp_profs.nu_C = tmp_nu_allz[0]
tmp_profs.set_prof('nu_vec', tmp_nu_allz[1:-1], tracer_pop, gp)
tmp_profs.nu_LS = tmp_nu_allz[-1]
off += offstep
if off != gp.ndim:
gh.LOG(1,'wrong subscripts in gl_class_cube')
raise Exception('wrong subscripts in gl_class_cube')
#Calculate Sigma (surface density)
Sig_DM_allz = phys.Sig(gp.z_all_pts, tmp_rho_DM_allz)
tmp_profs.Sig_DM_C = Sig_DM_allz[0]
tmp_profs.set_prof('Sig_DM_vec', Sig_DM_allz[1:-1], 0, gp)
tmp_profs.Sig_DM_LS = Sig_DM_allz[-1]
#Calculate sigma (velocity dispersion)
sigz_vecLS = phys.sigz(gp.z_all_pts, Sig_DM_allz, tmp_nu_allz, norm)
tmp_profs.set_prof('sig_vec', sigz_vecLS[0:-1], 0, gp)
tmp_profs.sig_LS = sigz_vecLS[-1]
# determine log likelihood
chi2 = calc_chi2(tmp_profs, gp) #HS currently rewriting calc_chi2
gh.LOG(1, ' log L = ', -chi2/2.)
tmp_profs.chi2 = chi2
return tmp_profs # from likelihood L = exp(-\chi^2/2), want log of that