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 |  |
| 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 |
 |  |  |
- 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 |  |
| xpure + external cmb maps |  |
| xpure generated cl |  |
| mll |  |
- 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} $} is the pixel window function.
| cl noise weighting |  |
| cl No noise weighting |  |
- PCG using wieghted noise map :
We demand the total variance of the map to be {$ \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 |
 |  |
- min value of hit map inside mask : 0.1733
- max value : 1.73
