# latscale: Sampling design for planar area prediction In pgs: Precision of Geometric Sampling

## 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

 ```1 2``` ```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 `[email protected]` 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

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

pgs documentation built on May 29, 2017, 5:30 p.m.