variogramCMB: Sample variogram
In rcosmo: Cosmic Microwave Background Data Analysis

Description Usage Arguments Value References Examples

This function provides an empirical variogram 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 variogram.

variogramCMB(
  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 variogram. 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 class variog specified in the package geoR.

The attribute "breaks" contains the break points used to create bins. The result has num.bins + 1 values since the first value at distance 0 is not counted as a bin.

u: a vector with distances.
v: a vector with estimated variogram 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 variogram calculations
n.data: number of data
direction: direction for which the variogram was computed
call: the function call

geoR package, variog, covCMB, corrCMB

## Download the map first
# downloadCMBMap(foreground = "smica", nside = 1024)
# df <- CMBDataFrame("CMB_map_smica1024.fits")
# cmbdf <- sampleCMB(df, sample.size = 100000)
# varcmb <- variogramCMB(cmbdf, max.dist = 0.1, num.bins = 30, sample.size=100)
# varcmb