fRen: Sample Renyi function

In rcosmo: Cosmic Microwave Background Data Analysis

Description

This function computes values of the sample Renyi function. Returns the estimated values of T(q) for q taking values on a grid. For large data sets could be rather time consuming.

Usage

fRen(
  cmbdf,
  q.min = 1.01,
  q.max = 10,
  N = 20,
  k.box = log2(nside(cmbdf)) - 3,
  intensities = "I"
)

Arguments

cmbdf	A CMBDataFrame.
q.min	Left endpoint of the interval to compute the Renyi function. The default value is 1.01,
q.max	Right endpoint of the interval to compute the Renyi function. The default value is 10
N	Number of points to compute the Renyi function. The default value is 20.
k.box	A dyadic decomposition level in computing the Renyi function, see the references in Details. The default value is log2(nside(cmbdf)) - 3
intensities	A CMBDataFrame column with measured values

Value

Data frame which first column is the sampling grid seq(q.min, q.max, length.out = N) of q values. Another column consists of values of the sample Renyi function T(q) computed on the grid using the k.boxth level dyadic decomposition of the unit ball.

References

(1) Leonenko, N., and Shieh, N. 2013. Rényi function for multifractal random fields. Fractals 21, Article No. 1350009.

(2) http://mathworld.wolfram.com/RenyiEntropy.html

Examples

## Download the map first
# downloadCMBMap(foreground = "smica", nside = 1024)
#
# cmbdf <- CMBDataFrame("CMB_map_smica1024.fits")
# win <- CMBWindow(theta = c(pi/4,pi/2,pi/2), phi = c(0,0,pi/2))
# cmbdf<- window(cmbdf, new.window = win)
# Tq <- fRen(cmbdf)
#
# plot(Tq[,1], Tq[,2], ylab =expression(D[q]), xlab = "q",
# main = "Sample Renyi function", pch = 20, col = "blue")

rcosmo documentation built on Dec. 11, 2021, 9:29 a.m.