fixedPoint: Fixed Point Algorithm Infrastructure

In wahani/saeRobustTools: Robust Small Area Estimation

Fixed Point Algorithm Infrastructure

Description

A fixed-point function supplied by the user is iteratively evaluated. addAverageDamp can be used to add average damping to the function - this may have a positive effect on the speed of convergence.

Usage

fixedPoint(fun, x0, convCrit)

addAverageDamp(fun)

addConstraintMin(fun, value)

addConstraintMax(fun, value)

convCritAbsolute(tolerance = 1e-06)

convCritRelative(tolerance = 1e-06)

addMaxIter(fun, maxIter)

addCounter(fun)

addHistory(fun)

addStorage(fun)

newtonRaphson(funList, ...)

newtonRaphsonFunction(funList)

Arguments

fun	the function to be evaluated in the algorithm
x0	starting value
convCrit	a function returning a logical scalar. Is called with two arguments; the first is the value from iteration n; the second is the value from iteration n-1
value	(numeric)
tolerance	a numeric value > 0
maxIter	maximum number of iterations
funList	(list) the functions to be evaluated in the algorithm. First element is typically the score function, second is the derivative of the score.
...	arguments passed to fixedPoint

Details

addAverageDamp adds average damping to an arbitrary fixed point function.

addConstraintMin takes care that values are not below a minimum value.

addConstraintMax takes care that values are not larger than maximum value.

convCritAbsolute absolute difference as convergence criterion.

convCritRelative relative (to previous iteration) absolute difference as convergence criterion. If value is smaller than 1, absolute difference is used.

addMaxIter can be used to modify convergence criterion functions.

addCounter can be used to count the number of calls of a function.

addHistory can be used to save a history of results of a function. The history is stored as a matrix, so this works best if the return value of fun is numeric.

addStorage will add a storage to a function. The storage is a list in which each result is stored. The function will coerce the return value into a numeric.

newtonRaphson finds zeroes of a function. The user can supply the function and its first derivative. Note that the Newton Raphson Algorithm is a special case of a fixed point algorithm thus it is implemented using fixedPoint and is only a convenience.

Examples

## Not run: 
vignette("fixedPoint", "saeRobust")

## End(Not run)

wahani/saeRobustTools documentation built on March 16, 2024, 11:29 a.m.