windAC (version 1.2.10)

secondDerivative: secondDerivative

Description

Computes numeric second derivatives (hessian) of an arbitrary multidimensional function at a particular location.

Usage

secondDerivative(loc, FUN, ..., eps = 1e-07)

Value

Matrix

Arguments

loc

The location (a vector) where the second derivatives of FUN are desired.

FUN

An R function to compute second derivatives for. This must be a function of the form FUN <- function(x, ...)... where x is the parameters of the function (e.g., location loc). FUN must return a single value (scalar), the height of the surface above x, i.e., FUN evaluated at x.

...

Additional agruments to FUN.

eps

Radius argument, see details. Default is 10e-7.

Details

This function uses the "5-point" numeric second derivative method advocated in numerous numerical recipe texts. During computation of the second derivative, FUN will be evaluated at locations within a hyper-elipsoid with cardinal radius 2*loc*(eps)^0.25.

A handy way to use this function is to call an optimization routine like nlminb with FUN, then call this function with the optimized values (solution) and FUN. This will yeild the hessian at the solution rather than the hessian at the previous step of the optimization.

Examples

func <- function(x){-x*x} # second derivative should be -2
secondDerivative(0,func)
secondDerivative(3,func)

func <- function(x){3 + 5*x^2 + 2*x^3} # second derivative should be 10+12x
secondDerivative(0,func)
secondDerivative(2,func)

func <- function(x){x[1]^2 + 5*x[2]^2} # should be rbind(c(2,0),c(0,10))
secondDerivative(c(1,1),func)
secondDerivative(c(4,9),func)