CAMB Power spectrum factorization

 Posts: 5
 Joined: February 19 2021
 Affiliation: University of Turin
CAMB Power spectrum factorization
Hello everybody,
I've a question regarding the factorization that CAMB use when is calculating the angular power spectrum (Cl).
What is the correct factorization with these "counts" set to "True"?
pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = True
For instance I know that the correct factorization for the case:
pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = False
is: Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j])
Thanks in advance.
I've a question regarding the factorization that CAMB use when is calculating the angular power spectrum (Cl).
What is the correct factorization with these "counts" set to "True"?
pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = True
For instance I know that the correct factorization for the case:
pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = False
is: Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j])
Thanks in advance.

 Posts: 1685
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: CAMB Power spectrum factorization
CAMB doesn't calculate it using a factorization, it calculates a single source term include the various sources adding them, then calculate the C_l. counts_lensing includes magnification bias.

 Posts: 5
 Joined: February 19 2021
 Affiliation: University of Turin
Re: CAMB Power spectrum factorization
Yes, that is for sure, but my question was:
If I want to do the reverse and reobtain the value that CAMB gives me in this particular set of parameters what is the correct factorization to use?
Like I said I know that the correct factorization to reobtain the (density,redshift) case is the one that I written before, but I'm not sure about the (density,redshift,lensing) case.
Thanks in advance.
If I want to do the reverse and reobtain the value that CAMB gives me in this particular set of parameters what is the correct factorization to use?
Like I said I know that the correct factorization to reobtain the (density,redshift) case is the one that I written before, but I'm not sure about the (density,redshift,lensing) case.
Thanks in advance.

 Posts: 1685
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: CAMB Power spectrum factorization
You'd just have to add the auto and all the crosses for the magnification bias term.

 Posts: 5
 Joined: February 19 2021
 Affiliation: University of Turin
Re: CAMB Power spectrum factorization
Thanks!
I've tried to use:
Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (si*sj)*(Cl_ss[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j]) + (bi*sj + bj*si)*(Cl_bs[i,j]) + (fi*sj + fj*si)*(Cl_sf[i,j])
but it seems to be incorrect and does not recreate the one calculated by CAMB, so I do not know what term I'm missing.
I've tried to use:
Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (si*sj)*(Cl_ss[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j]) + (bi*sj + bj*si)*(Cl_bs[i,j]) + (fi*sj + fj*si)*(Cl_sf[i,j])
but it seems to be incorrect and does not recreate the one calculated by CAMB, so I do not know what term I'm missing.