CosmoMC: Rombint failed to converge

[Xin Wang]

Hi Antony,

In order to impose constraints on cosmic relic neutrinos' total mass, I assign a non-zero prior to the parameter f_{\nu}. However I get some feedback repeatedly, i.e.

Warning: Rombint failed to converge;
integral, error, tol: 18758.6992612042 -6.890126438285904E-007
1.000000000000000E-007

Here the tolerance is 1e-7, which is only used in DeltaTime function, in the phrase of
atol = tol/1000/exp(AccuracyBoost-1)

I'm wondering how does this warning affect the constraints on massive neutrino masses? Can we fix this problem simply by increasing the atol given by the abovementioned phrase?

Thanks in advance!

[Antony Lewis]

What cosmological parameters give this warning? It should be fine with neutrino masses, at least within normal bounds. Though it is probably harmless anyway as you are very close to convergence.

[Xin Wang]

What cosmological parameters give this warning? It should be fine with neutrino masses, at least within normal bounds. Though it is probably harmless anyway as you are very close to convergence.

Thanks, Antony! I suspect that the involved cosmological parameter should be fnu. I tried with the data sets of WMAP7, WMAP7+BAO(sdss+WiggleZ), WMAP7+MPK (LRG DR7), and if the prior of fnu is non-zero, that pieces of warning kept flashing on the screen. Some of them shows three order of magnitude discrepancy between error and tol, e.g.
Warning: Rombint failed to converge;
integral, error, tol: 18708.8406740630 -8.580504189961147E-004
1.000000000000000E-007
Is this level of convergence still harmless to the constraints on neutrino masses?

I use the latest version (Jan. 2012) of CosmoMC and the prior of fnu is
param[fnu] = 0 0 0.02154 0.0003 0.0003

Moreover, I notice that this warning starts to emerge at the very beginning of the chains, e.g. num_metropolis around 200, using the basic Metropolis sampling algorithm.

Because the tolerance level in every piece of warning is 1e-7, which only corresponds to function DeltaTime(a1,a2, in_tol), with in_tol omitted,

Code: Select all

        function DeltaTime(a1,a2, in_tol)
        implicit none
        real(dl) DeltaTime, atol
        real(dl), intent(IN) :: a1,a2
        real(dl), optional, intent(in) :: in_tol
        real(dl) dtauda, rombint !diff of tau w.CP%r.t a and integration
        external dtauda, rombint

        if (present(in_tol)) then
         atol = in_tol
        else
         atol = tol/1000/exp(AccuracyBoost-1)
        end if
        DeltaTime=rombint(dtauda,a1,a2,atol)
      
        end function DeltaTime

This omission happens in the subroutine GaugeInterface_Init,

Code: Select all

         do nu_i=1, CP%Nu_Mass_eigenstates
            a_mass =  1.e-1_dl/nu_masses(nu_i)/lAccuracyBoost 
            !if (HighAccuracyDefault) a_mass=a_mass/4
            time=DeltaTime(0._dl,nu_q(1)*a_mass)
            nu_tau_notmassless(1, nu_i) = time
            do j=2,nqmax
             !times when each momentum mode becomes signficantly nonrelativistic
             time= time + DeltaTime(nu_q(j-1)*a_mass,nu_q(j)*a_mass, 0.01_dl)
             nu_tau_notmassless(j, nu_i) = time
            end do
            
            a_nonrel =  2.d0/nu_masses(nu_i)*AccuracyBoost
            nu_tau_nonrelativistic(nu_i) =DeltaTime(0._dl,a_nonrel) 
            a_massive =  17.d0/nu_masses(nu_i)*AccuracyBoost 
            nu_tau_massive(nu_i) =nu_tau_nonrelativistic(nu_i) + DeltaTime(a_nonrel,a_massive) 
            
         end do 

I will be greatly grateful if you could share some fundamental ideas behind the codes of dtauda, DeltaTime, GaugeInterface_Init. Thanks so much!

[Antony Lewis]

The latest neutrino handling is described in the appendix of 1201.3654. Deltatime is just the amount of conformal time between two scale factors.

Might be an issue (bug?) with very light masses which only become non-relativistic in the future? If you can produce a camb .ini file with some specfic set of parameters that give the problem I'll have a look at it.

[Xin Wang]

The latest neutrino handling is described in the appendix of 1201.3654. Deltatime is just the amount of conformal time between two scale factors.

Might be an issue (bug?) with very light masses which only become non-relativistic in the future? If you can produce a camb .ini file with some specfic set of parameters that give the problem I'll have a look at it.

Thank you for telling me to try with CAMB. I think I've already obtained a few hints. It seems to have little things to do with neutrinos having very light masses, since this piece of warning never appears even for omnuh2 as low as 3e-6 (corresponding to \Sigma m_{\nu}\sim3\times10^{-4}eV). According to 1+z_{nr}\sim1890(m_{\nu}/1eV) (Takada et al. 2006), this sort of neutrino is far from being non-relativistic today.

Rather, this "problem" might be concerned with the fact that the value of omnuh2 cannot be smaller than the tolerance level. The .ini file attached below gives the same warning as
Warning: Rombint failed to converge;
integral, error, tol: 19433.4059916783 -3.463242010948164E-006
9.512294245007141E-008

Do we have to impose a non-zero lower limit, say 7e-4 on omnuh2 (as you did in 1201.3654), if we use CosmoMC to constrain the sum of neutrino masses? Anyway this limit is to some extent justified by the combination of solar and atmospheric oscillation experiments. I'm eager to learn your idea. Thanks!

The .ini file is as follows,

Code: Select all

#Parameters for CAMB

#output_root is prefixed to output file names
output_root = fnu_Rombint

#What to do
get_scalar_cls = T
get_vector_cls = F
get_tensor_cls = F
get_transfer   = F

#if do_lensing then scalar_output_file contains additional columns of l^4 C_l^{pp} and l^3 C_l^{pT}
#where p is the projected potential. Output lensed CMB Cls (without tensors) are in lensed_output_file below.
do_lensing     = F

# 0: linear, 1: non-linear matter power (HALOFIT), 2: non-linear CMB lensing (HALOFIT)
do_nonlinear = 2

#Maximum multipole and k*eta. 
#  Note that C_ls near l_max are inaccurate (about 5%), go to 50 more than you need
#  Lensed power spectra are computed to l_max_scalar-100 
#  To get accurate lensed BB need to have l_max_scalar>2000, k_eta_max_scalar > 10000
#  Otherwise k_eta_max_scalar=2*l_max_scalar usually suffices, or don't set to use default
l_max_scalar      = 2200
#k_eta_max_scalar  = 4000

#  Tensor settings should be less than or equal to the above
l_max_tensor      = 1500
k_eta_max_tensor  = 3000

#Main cosmological parameters, neutrino masses are assumed degenerate
# If use_phyical set phyiscal densities in baryone, CDM and neutrinos + Omega_k
use_physical   = T
ombh2          = 0.0223
omch2          = 0.105
omnuh2         = 1e-7
omk            = 0
hubble         = 70.1
#effective equation of state parameter for dark energy, assumed constant
w              = -1
#constant comoving sound speed of the dark energy (1=quintessence)
cs2_lam        = 1

#if use_physical = F set parameters as here
#omega_baryon   = 0.0462
#omega_cdm      = 0.2538
#omega_lambda   = 0.7
#omega_neutrino = 0

temp_cmb           = 2.726
helium_fraction    = 0.24
# massless_neutrinos is the effective number (for QED + non-instantaneous decoupling)
# fractional part of the number is used to increase the neutrino temperature, e.g.
# 2.99 correponds to 2 neutrinos with a much higher temperature, 3.04 correponds to
# 3 neutrinos with a slightly higher temperature. 3.046 is consistent with CosmoMC.
massless_neutrinos = 0
massive_neutrinos  = 3

#Neutrino mass splittings
nu_mass_eigenstates = 1
#nu_mass_degeneracies = 0 sets nu_mass_degeneracies = massive_neutrinos
#otherwise should be an array
#e.g. for 3 neutrinos with 2 non-degenerate eigenstates, nu_mass_degeneracies = 2 1
nu_mass_degeneracies = 0  
#Fraction of total omega_nu h^2 accounted for by each eigenstate, eg. 0.5 0.5
nu_mass_fractions = 1

#Initial power spectrum, amplitude, spectral index and running. Pivot k in Mpc^{-1}.
initial_power_num         = 1
pivot_scalar              = 0.05
pivot_tensor              = 0.05

scalar_amp(1)             = 21.76059e-10
scalar_spectral_index(1)  = 0.960

scalar_nrun(1)            = 0
tensor_spectral_index(1)  = 0
#ratio is that of the initial tens/scal power spectrum amplitudes
initial_ratio(1)          = 1
#note vector modes use the scalar settings above


#Reionization, ignored unless reionization = T, re_redshift measures where x_e=0.5
reionization         = T

re_use_optical_depth = T
re_optical_depth     = 0.09
#If re_use_optical_depth = F then use following, otherwise ignored
re_redshift          = 11
#width of reionization transition. CMBFAST model was similar to re_delta_redshift~0.5.
re_delta_redshift    = 1.5
#re_ionization_frac=-1 sets to become fully ionized using YHe to get helium contribution
#Otherwise x_e varies from 0 to re_ionization_frac
re_ionization_frac   = -1


#RECFAST 1.5 recombination parameters;
RECFAST_fudge = 1.14
RECFAST_fudge_He = 0.86
RECFAST_Heswitch = 6
RECFAST_Hswitch  = T

#Initial scalar perturbation mode (adiabatic=1, CDM iso=2, Baryon iso=3, 
# neutrino density iso =4, neutrino velocity iso = 5) 
initial_condition   = 1
#If above is zero, use modes in the following (totally correlated) proportions
#Note: we assume all modes have the same initial power spectrum
initial_vector = -1 0 0 0 0

#For vector modes: 0 for regular (neutrino vorticity mode), 1 for magnetic
vector_mode = 0

#Normalization
COBE_normalize = F
##CMB_outputscale scales the output Cls
#To get MuK^2 set realistic initial amplitude (e.g. scalar_amp(1) = 2.3e-9 above) and
#otherwise for dimensionless transfer functions set scalar_amp(1)=1 and use
#CMB_outputscale = 1
CMB_outputscale = 7.4311e12

#Transfer function settings, transfer_kmax=0.5 is enough for sigma_8
#transfer_k_per_logint=0 sets sensible non-even sampling; 
#transfer_k_per_logint=5 samples fixed spacing in log-k
#transfer_interp_matterpower =T produces matter power in regular interpolated grid in log k; 
# use transfer_interp_matterpower =F to output calculated values (e.g. for later interpolation)
transfer_high_precision = T
transfer_kmax           = 2
transfer_k_per_logint   = 0
transfer_num_redshifts  = 1
transfer_interp_matterpower = T
transfer_redshift(1)    = 0
transfer_filename(1)    = transfer_out.dat
#Matter power spectrum output against k/h in units of h^{-3} Mpc^3
transfer_matterpower(1) = matterpower.dat

transfer_redshift(2)    = 1
transfer_filename(2)    = transfer_out_z1.dat
transfer_matterpower(2) = matterpower_z1.dat
transfer_redshift(3)    = 3
transfer_filename(3)    = z3_transfer_out.dat
transfer_matterpower(3) = z3_matterpower.dat


#Output files not produced if blank. make camb_fits to use use the FITS setting.
scalar_output_file = scalCls.dat
vector_output_file = vecCls.dat
tensor_output_file = tensCls.dat
total_output_file  = totCls.dat
lensed_output_file = lensedCls.dat
lensed_total_output_file  =lensedtotCls.dat
lens_potential_output_file = lenspotentialCls.dat
FITS_filename      = scalCls.fits


#Bispectrum parameters if required; primordial is currently only local model (fnl=1)
#lensing is fairly quick, primordial takes several minutes on quad core
do_lensing_bispectrum = F
do_primordial_bispectrum = F

#1 for just temperature, 2 with E
bispectrum_nfields = 1
#set slice non-zero to output slice b_{bispectrum_slice_base_L L L+delta}
bispectrum_slice_base_L = 0
bispectrum_ndelta=3
bispectrum_delta(1)=0
bispectrum_delta(2)=2
bispectrum_delta(3)=4
#bispectrum_do_fisher estimates errors and correlations between bispectra
#note you need to compile with LAPACK and FISHER defined to use get the Fisher info
bispectrum_do_fisher= F
#Noise is in muK^2, e.g. 2e-4 roughly for Planck temperature
bispectrum_fisher_noise=0
bispectrum_fisher_noise_pol=0
bispectrum_fisher_fwhm_arcmin=7
#Filename if you want to write full reduced bispectrum (at sampled values of l_1)
bispectrum_full_output_file=
bispectrum_full_output_sparse=F
#Export alpha_l(r), beta_l(r) for local non-Gaussianity
bispectrum_export_alpha_beta=F

##Optional parameters to control the computation speed,accuracy and feedback

#If feedback_level > 0 print out useful information computed about the model
feedback_level = 1

# 1: curved correlation function, 2: flat correlation function, 3: inaccurate harmonic method
lensing_method = 1
accurate_BB = F


#massive_nu_approx: 0 - integrate distribution function
#                   1 - switch to series in velocity weight once non-relativistic
massive_nu_approx = 1

#Whether you are bothered about polarization. 
accurate_polarization   = T

#Whether you are bothered about percent accuracy on EE from reionization
accurate_reionization   = T

#whether or not to include neutrinos in the tensor evolution equations
do_tensor_neutrinos     = T

#Whether to turn off small-scale late time radiation hierarchies (save time,v. accurate)
do_late_rad_truncation   = T

#Computation parameters
#if number_of_threads=0 assigned automatically
number_of_threads       = 0

#Default scalar accuracy is about 0.3% (except lensed BB) if high_accuracy_default=F
#If high_accuracy_default=T the default taget accuracy is 0.1% at L>600 (with boost parameter=1 below)
#Try accuracy_boost=2, l_accuracy_boost=2 if you want to check stability/even higher accuracy
#Note increasing accuracy_boost parameters is very inefficient if you want higher accuracy,
#but high_accuracy_default is efficient 

high_accuracy_default=T

#Increase accuracy_boost to decrease time steps, use more k values,  etc.
#Decrease to speed up at cost of worse accuracy. Suggest 0.8 to 3.
accuracy_boost          = 1.05

#Larger to keep more terms in the hierarchy evolution. 
l_accuracy_boost        = 1

#Increase to use more C_l values for interpolation.
#Increasing a bit will improve the polarization accuracy at l up to 200 -
#interpolation errors may be up to 3%
#Decrease to speed up non-flat models a bit
l_sample_boost          = 1