1. Final plots
- Bicep correction of masks list
- LiB and Bicep correction of null spectra results and thus correlations in covariance matrix :
2. tensor to scalar ratio error
LiB | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=sigR_allLol_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7BB.png) |
BIC | Comming |
- LiB tensor to scalar error is lower than C2 isotropic optimization (previously NaMaster), Exept for 0.1 muK, where the error is rising.
- Looking at the covariance matrix diagonals, xpure is lower than C2, as expected from the optimization process. But the off diagonal terms in the correlation matrix are actually higher, hence a higher error on the tensor to scalar ratio :
kll diagonals | Xpure correlation matrix | C2 correlation matrix |
![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=Diagklls_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7BB.png) | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=Corrxpure_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7BB.png) | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=Corrnama_FULL_Ns16_Nbins46_Slmaxmul3_fwhmdeg0.5_r0.001_fsky0.7BB.png) |
- proposition :
- The PCG is optimized for variance minimization. And not sigma r (or covariance) minimization ?
- after correction, some simulaiton were null, thus increasing correlations.
3. xpure VS NaMaster
4. LiB :
- PCG at 5 muK
- 3 types of masks bins :
- 10 => [2,10,20,50]
- 20 => [2,20,50]
- 30 => [2,30,50]
- 2 noises entry :
- first one is for the mask apodization
- seconde one is for noise simulation
- m2 = mode 2 xpure (pure BB, standard EE).
4.1 external cmb maps
cross + external cmb maps | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=xqml_comparison10.png) |
xpure + external cmb maps | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=xqml_comparison9.png) |
xpure generated cl | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=xqml_comparison6.png) |
mll | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=LiBcorrsigp_ns512_rs0.001_R0.001_cust_2.10.20.50.501_nb3_muKarcmin5.0.png) |
- notes :
- Simulated spectra from input inpCellfile are sistematically biased in x2pure. Solution : use external maps (generated via healpy/pix). In that case, one must compute spectra up to the lmax used for cmb generated maps (synfast(lmax=...)).
5. BICEP :
- pixwindow must be corrected for the reconstructed spectra at nside 512. Since the xQML analysis is done on a nside=128 map, we multiply the beam spectrum b_\ell by the correcting factor b_\ell \rightarrow b_\ell p_\ell^{128}/p_\ell^{512} , where p_\ell^{nside} is the pixel window function.
cl noise weighting | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=xqmlBIC_comparison5.png) |
cl No noise weighting | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=xqmlBIC_comparison1.png) |
- PCG using wieghted noise map :
We demand the total variance of the map to be \displaystyle \frac{\sigma^2}{n_{pix}} [\mu K\cdot arcmin] = \frac 1 {\sum_i 1/ V_i} which is equal to \displaystyle \frac{\sigma^2}{n_{pix}} if V_i = \sigma^2 (white noise case). Now we demand a weighting of the variance such that V_i = \beta w_i^{-1} with \beta the normalisation factor. Injecting V_i gives \beta = \displaystyle \frac{\sigma^2}{n_{pix}} \sum_i w_i ad finally \displaystyle V_i = \frac{\sigma^2}{ w_i} \frac{\sum_j w_j}{n_{pix}} .
normalized hit map | weighted noise map |
![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=Nhit.png) | ![](https://cmb.lal.in2p3.fr/lalwiki/Xpure/Xqml?action=download&upname=NoiseMap.png) |
- min value of hit map inside mask : 0.1733
- max value : 1.73