PrepareHatFunction: Builds the hat function for a given Lipschitz constant

In ranlip: Generation of Random Vectors with User-Defined Density

Description

Function for Building the hat function using Lipschitz constant

Usage

  ranlip.PrepareHatFunction(num, numfine, Lip, dist)

Arguments

num	The number of subdivisions in each variable to partition the Domain D into hyperrectangles D|k. On each D|k, the hat function will have a constant value h|k
numfine	The number of subdivisions in the finer partition in each variable. Each D|k is subdivided into (numfine-1)^dim smaller hyperrectangles, in order to improve the quality of the overstimate h|k. nunmfine should be a power of 2 for numerical efficiency reason ( if not, it will be automatically changed to a power of 2 larger than the supplied value) numdine can be 2, in which case the fine partition is not used
Lip	Lipschitz constant supplied
dist	The distribution function p(x) where x is the array of size dim.

Value

output

No return value. Generates and stores internally the hat function.

Author(s)

Gleb Beliakov, Daniela L. Calderon, Deakin University

Examples

    dim<-2
	left<-c(-1,-1,0)
	right<-c(1,1,5)

	ranlip.Init(dim, left, right)
	

	num <- 10
	numfine <- 2
	Lip <- 1



	Fn <- function(x,dim){
		r<-x[1]*x[1]+x[2]*x[2]
		r<-sqrt(r)
		out <- exp(-( (x[1]+0.2)^2+(x[2]+0.1)^2)/1.1 )*exp(-sqrt(r))
		return(out)
	}


	ranlip.PrepareHatFunction(num, numfine, Lip, Fn);
	ranlip.RandomVec(Fn)	
	r<-ranlip.RandomVec( Fn)
	print(r)
	r<-ranlip.RandomVec( Fn)
	print(r)
	
 	ranlip.FreeMem()

                

ranlip documentation built on June 24, 2021, 9:08 a.m.