covCMB: Sample covariance function
In rcosmo: Cosmic Microwave Background Data Analysis

Description Usage Arguments Value References Examples

This function provides an empirical covariance function for data in a CMBDataFrame or data.frame. It assumes that data are from a stationary spherical random field and the covariance depends only on a geodesic distance between locations. Output is a binned covariance.

covCMB(
  cmbdf,
  num.bins = 10,
  sample.size,
  max.dist = pi,
  breaks,
  equiareal = TRUE,
  calc.max.dist = FALSE
)

`cmbdf`	is a `CMBDataFrame` or `data.frame`
`num.bins`	specifies the number of bins
`sample.size`	optionally specify the size of a simple random sample to take before calculating covariance. This may be useful if the full covariance computation is too slow.
`max.dist`	an optional number between 0 and pi specifying the maximum geodesic distance to use for calculating covariance. Only used if `breaks` are unspecified.
`breaks`	optionally specify the breaks manually using a vector giving the break points between cells. This vector has length `num.bins` since the last break point is taken as `max.dist`. If `equiareal = TRUE` then these breaks should be cos(r_i) where r_i are radii. If `equiareal = FALSE` then these breaks should be r_i.
`equiareal`	if TRUE then the bins have equal spherical area. If false then the bins have equal annular widths. Default is TRUE.
`calc.max.dist`	if TRUE then the `max.dist` will be calculated from the locations in cmbdf. Otherwise either `max.dist` must be specified or max.dist will default to pi.

An object of the class CMBCovariance that is a modification of variog from the package geoR with variogram values replaced by covariances.

The attribute "breaks" contains the break points used to create bins. The result has num.bins + 1 values since the first value, the sample variance, is not counted as a bin.

u: a vector with distances.
v: a vector with estimated covariance values at distances given in u.
n: number of pairs in each bin
sd: standard deviation of the values in each bin
bins.lim: limits defining the interval spanned by each bin
ind.bin: a logical vector indicating whether the number of pairs in each bin is greater or equal to the value in the argument pairs.min
var.mark: variance of the data
beta.ols: parameters of the mean part of the model fitted by ordinary least squares
output.type: echoes the option argument
max.dist: maximum distance between pairs allowed in the covariance calculations
n.data: number of data
direction: direction for which the covariance was computed
call: the function call

geoR package, variog, variogramCMB, corrCMB

## Download the map first
# downloadCMBMap(foreground = "smica", nside = 1024)
# df <- CMBDataFrame("CMB_map_smica1024.fits")
# cmbdf <- sampleCMB(df, sample.size = 100000)
# Cov <- covCMB(cmbdf, max.dist = 0.03, num.bins = 10)
# Cov