PrepareHatFunctionAuto: Computation function of building the hat function and an...

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

Description

Builds the hat function and automatically computes an estimate to the Lipschitz constant.

Usage

  ranlip.PrepareHatFunctionAuto(num, numfine, minLip, 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
minLip	the lower bound on the value of the computed Lipschitz constant, the default value is 0
dist	The distribution function p(x) where x is the array of size dim.

Value

output

The estimated Lipschitz constant. Stores the hat function internlly.

Author(s)

Gleb Beliakov, Daniela L. Calderon, Deakin University

Examples

    dim<-3
	left<-c(0,0,0)
	right<-c(5,5,5)

	ranlip.Init(dim, left, right);
	

	num <- 10
	numfine <- 2
	MinLip <- 1



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


	Lip<-ranlip.PrepareHatFunctionAuto(num, numfine, MinLip, Fn)
	
	print(Lip)
	ranlip.RandomVec( Fn)
 	ranlip.FreeMem()
	
                

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