ranlip (version 1.0.1)

ranlip.PrepareHatFunctionAuto: Computation function of building the hat function and an estimated Lipschitz constant

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.

Examples

# NOT RUN {

    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()
	
                
# }