Setting precision?

[hezi-zhang]

Hi,

As I need to take derivative of Cl's, I found that there is a lot of noise and the curve is not smooth. Although I tried fitting them, the result seems to depend on how dense the sampling is. So I wonder why there is so much noise on the curves of Cl's and whether I can enhance the precision to get rid of it. If so, how can I change the precision? I saw that there are some precision files, but they contain so much parameters that I can not figure out which to change.

Thank you,
Hezi

[ThomasTram]

Hi Hexi

The two relevant parameters are

l_logstep = 1.12
l_linstep = 40

where I have shown the default values. The Cl's are computed from a cubic spline, so the first derivatives are guaranteed to be continuous (but not smooth).

Cheers,
Thomas

[lesgourg]

Hi Hexi,
The default precision is tuned for the needs of MCMC parameter extraction, which work well with low precision. Taking derivatives with respect to l or with respect to Cosmo parameters (for Fisher , or for gradient methods of minimisation) indeed requires better precision. Please say a bit more on the kind of derivatives you are computing (wrt l or parameters?) and I can provide you a small subset of relevant precision parameters.

[BryanSagredo]

Hello Class team, I'm in similar trouble adjusting the precision parameters.

I'm doing a Fisher forecast using the galaxy power spectrum and I'd like to increase the amount of k-points used for the interpolation (using classy Python wrapper) to take better derivatives wrt cosmological parameters.

Thank you in advance!
Cheers,

Bryan

[lesgourg]

Hi there,
Let me first give below a set of precision parameters that I trust for lowering considerably the noise. It has been used in the paper https://arxiv.org/pdf/1311.1657.pdf which performed a frequentist analysis and had to use a high-precision minimisation algorithm instead of an MCMC. As stated in their Table 1, they found that they should use:

tol_background_integration = 1.e-3 
tol_thermo_integration = 1.e-3
tol_perturb_integration = 1.e-6
reionization optical depth tol = 1.e-5
l_logstep = 1.08 
l_linstep = 25
perturb_sampling_stepsize = 0.04
delta_l_max = 800

But the question of Bryan was more specific. Bryan I think that you should play with two parameters fixed by default to

k_per_decade_for_pk = 10
k_per_decade_for_bao = 70

controlling respectively the sampling in the BAO region and in the rest. You could increase both to a common high number, e.g. 100 or 400...

[lesgourg]

PS in the last post I forgot the _ in

reionization_optical_depth_tol = 1.e-5

[BryanSagredo]

Thank you very much! So far it's working like a charm.

Also, increasing the last two parameters makes the derivatives even more stable.

Cheers,
Bryan