For the computation of the matrix ds-dcb, we compare the recursion dlss method (eq 15 of 'pixel covariance matrix' - M.Tristram) versus the explicite relation (eq 28)
- Full sky, polar, 1 core.
- MC Precision is computed as {$ \displaystyle \frac{diag(S_{analytic})}{std(diag(S_{mc}))} $}
| Nside | dl_ss (15) | explicite (28) | Monte carlo |
| 2 | ~1 sec | ~0.9 sec | ~ 0.6 sec (10% precision on diag(S) ) |
| 4 | ~29 sec | ~24 sec | ~ 9 sec (5 % precision) |
| 8 | ~1000 sec | ~700 sec | ~ 60 sec (2.5% precision) |
| 16 | ~32000 sec | ~24000 sec | ~ 1500 sec (? % precision not calculated) |
- Conclusion : explicit relation is faster (at least in python) than recursion method dlss.
- Monte-carlo is highly competitive ! Number of simulations = 4*npix. Tests should be extended to compare the estimator variance between the MC and the analytical method.
