minimaxdesign (version 0.1.5)

CtoB: Inverse Rosenblatt transformation from the unit hypercube to the unit ball

Description

CtoB maps points on the unit hypercube in \(p\)-dimensions, \(C_p = [0,1]^p\), to points on the unit simplex in \(p\)-dimensions, \(B_p\).

Usage

CtoB(D, by=ifelse(ncol(D)>2,1e-3,-1), num_proc=parallel:::detectCores())

Arguments

D

An \(N\)-by-\(p\) matrix representing \(N\) points in \(p\)-dimensions.

by

Step-size used for approximating integrals.

num_proc

Number of processors to use.

Value

An \(N\)-by-\(p\) matrix for the inverse-Rosenblatt mapping of \(D\) onto the unit ball \(B_p\).

Examples

# NOT RUN {
  
# }
# NOT RUN {
    # Map the first 100 points of the Sobol' sequence in 3D
    #   onto the unit ball in 3D
    library(randtoolbox)
    des <- sobol(100,3)
    des_ball <- CtoB(des)

    pairs(des_ball,xlim=c(-1,1),ylim=c(-1,1),pch=16)

  
# }