rcosmo (version 1.1.2)

covPwSp: Covariance estimate via power spectra

Description

This function provides a covariance estimate using the values of the estimated power spectra.

Usage

covPwSp(PowerSpectra, Ns)

Arguments

PowerSpectra

A data frame which first column lists values of multipole moments and the second column gives the corresponding values of CMB power spectra.

Ns

A number of points in which the covariance estimate is computed on the interval [-1,1]

Value

A data frame which first column is 1-d grid starting at -1+1/Ns and finishing at 1 with the step 2/Ns. The second column is the values of estimated covariances on this grid.

References

Formula (2.1) in Baran A., Terdik G. Power spectrum estimation of spherical random fields based on covariances. Annales Mathematicae et Informaticae 44 (2015) pp. 15<U+2013>22.

Power Spectra data are from Planck Legacy Archive http://pla.esac.esa.int/pla/#cosmology

Examples

# NOT RUN {
## Download the power spectrum first
# N <- 20000
# COM_PowerSpectra <- downloadCMBPS(link=1)
#
# Cov_est <- covPwSp(COM_PowerSpectra[,1:2], N)
# plot(Cov_est, type="l")

## Plot the covariance estimate as a function of angular distances
# plot(acos(Cov_est[,1]), Cov_est[,2], type ="l",
#      xlab ="angular distance", ylab ="Estimated Covariance")

# }