ranlip (version 1.0.1)

ranlip.PrepareHatFunction: Builds the hat function for a given Lipschitz constant

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.

Examples

# NOT RUN {

    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()

                
# }