minimaxdesign (version 0.1.5)

CtoA: Inverse Rosenblatt transformation from the unit hypercube to the unit simplex

Description

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

Usage

CtoA(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 simplex \(A_p\).

Examples

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

    pairs(des_simp,xlim=c(0,1),ylim=c(0,1),pch=16)

  
# }