Internal helper functions for generating interpolation grids for speed up in package RobExtremes
Description
These functions are used internally to generate interpolation grids, for Lagrange multipliers or LDEstimators in package RobExtremes, to be stored in the respective ‘sysdata.rda’ file.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  .getPsi(param, fct, L2Fam , type)
.is.na.Psi(param, fct, nam = "shape")
.modify.xi.PFam.call(xi, PFam)
.RMXE.xi(xi, PFam)
.MBRE.xi(xi, PFam)
.OMSE.xi(xi, PFam)
.getLMGrid(xiGrid = getShapeGrid(), PFam = GParetoFamily(scale=1,shape=2),
optFct = .RMXE.xi, GridFileName="LMGrid.Rdata", withPrint = FALSE,
len = 13)
.svInt(optF = .RMXE.th, xiGrid = getShapeGrid(700, cutoff.at.0=0.005),
PFam = GParetoFamily(shape=1,scale=2), radius = 0.5, upper = 1e4,
lower = 1e4, OptOrIter = "iterate", maxiter = 150,
tol = .Machine$double.eps^0.5, loRad = 0, upRad = Inf, loRad0 = 1e3,
loRad.s = 0.2, up.Rad.s = 1, withStartLM = TRUE, len = 13, namFzus = "")
.generateInterpGridSn(xiGrid = getShapeGrid(500, cutoff.at.0=0.005),
PFam = GParetoFamily(), withPrint = TRUE)

Arguments
param 
object of class 
fct 
list of functions containing the interpolators. 
L2Fam 
an object of class 
nam 
character; name of the shape parameter. 
type 
type of the optimality: one of ".OMSE" for maxMSE, ".RMXE" for rmx, and ".MBRE" for MBRE. 
xi 
numeric of length 1; shape value. 
PFam 
an object of class 
xiGrid 
numeric; grid of shape values. 
optFct, optF 
function with arguments 
GridFileName 
character; if 
withPrint 
logical of length 1: shall current shape value be printed out? 
radius 
[for OMSE]: positive numeric of length 1: the radius of the neighborhood for which the LM's are to be computed; defaults to 0.5. 
loRad 
the lower end point of the interval to be searched in the inner optimization (for the least favorable situation to the userguessed radius). 
upRad 
the upper end point of the interval to be searched in the inner optimization (for the least favorable situation to the userguessed radius). 
loRad.s 
the lower end point of the interval
to be searched in the outer optimization
(for the userguessed radius); if 
upRad.s 
the upper end point of the interval to be searched in the
outer optimization (for the userguessed radius); if

upper 
upper bound for the optimal clipping bound. 
lower 
lower bound for the optimal clipping bound. 
OptOrIter 
character; which method to be used for determining Lagrange
multipliers 
loRad0 
for numerical reasons: the effective lower bound for the zero search;
internally set to 
withStartLM 
logical of length 1: shall the LM's of the preceding grid value serve as starting value for the next grid value? 
len 
integer; number of Lagrange multipliers to be calibrated. 
namFzus 
character; infix for the name of the ‘.csv’File to which the results are written; used to split the work on xigrids into chunks. 
Details
.getpsi
reads the respective interpolating function
from an object from ‘sysdata.rda’ and generates a respective
HampelIC
object by a call to generateIC
.
.is.na.Psi
checks whether the shape parameter already lies
beyond the range for which inter/extrapolation is admitted
(and, correspondingly, returns TRUE
if one has to compute the
IC completely anew.).
.MBRE.xi
computes the Lagrange multipliers for the MBRE estimator,
.OMSE.xi
for the OMSE estimator at radius r=0.5
,
and .RMXE.xi
the RMXE estimator.
.svInt
is a short form for ROptEst:::.generateInterpGrid
for LM interpolation.
Value
.getpsi 
an IC. 
.is.na.Psi 
logical of length 1. 
.modify.xi.PFam.call 
A call to evaluate the parametric family at the new parameter value. 
.MBRE.xi 
A list with items 
.OMSE.xi 
as 
.RMXE.xi 
as 
.getLMGrid 
A list with items 
.generateInterpGridSn 

.svInt 

Note
These functions are only meant for the developers of package RobExtremes
(or respective packages).
They can be used to speed up things by interpolation.
Our use case is a speed up for further scaleshape families (or enhance
existing speedups) such that the respective grids are stored in
the ‘sysdata.rda’ file of this package and can be used in
(exported) new particular methods for functional Sn
.
Special attention has to be paid for Rversions pre and post R2.16.
So if interpolation functions are desired for both alternatives, one
has to run ROptEst:::.recomputeInterpolators
once on each
version.
See Also
interpolateSn