pgs (version 0.4-0)

latscale: Sampling design for planar area prediction

Description

Planar area can be predicted based on sampling by a lattice of figures $u*Lambda+L+F$. The function latscale computes the scaling parameter $u$ such that the prediction coefficient of error is equal to a given value.

Usage

latscale(x,A,shape,CE.n,upper,maxiter=100,tol=.Machine$double.eps^0.25, lower=.Machine$double.eps ^ 0.5,L=3,only.root=TRUE)

Arguments

x

the lattice of figures as a FigLat object. The vector lattice x@vlat must be unit.

A

a (rough) estimate of the mean area.

shape

a (rough) estimate of the shape parameter $B/sqrt(A)$ where $B$ is the mean perimeter.

CE.n

the given value of the prediction coefficient of error.

lower

the lower point of the interval where the scaling parameter is to be searched. Argument of the function uniroot. Default: .Machine$double.eps ^ 0.5.

upper

the upper point of the interval where the scaling parameter is to be searched. Argument of the function uniroot.

maxiter

other argument passed to the function uniroot.

tol

other argument passed to the function uniroot. Default: .Machine$double.eps^0.25.

L

an integer, the criterion for stopping summation of the Epstein Zeta function. Default: 3.

only.root

a Boolean controlling the returned value, see below. Default: TRUE.

Value

If only.root is TRUE, the function returns the numeric value of the scaling parameter $u$. Else, the function returns a list with four components: scale the numeric value of $u$, CE the coefficient of error computed for $u$, iter the number of iterations used, prec an approximate estimated precision for $u$.

Examples

latscale(FigLat(2,RectLat2(),PointPattern(rep(0,2))),A=1,shape=5,CE.n=0.05,upper=2,only.root=FALSE)