fdHess: Finite difference Hessian

Description

Evaluate an approximate Hessian and gradient of a scalar function using finite differences.

Usage

fdHess(pars, fun, ...,
       .relStep = .Machine$double.eps^(1/3), minAbsPar = 0)

Value

A list with components

mean: the value of function fun evaluated at the parameter values pars
gradient: an approximate gradient (of length length(pars)).
Hessian: a matrix whose upper triangle contains an approximate Hessian.

Arguments

pars: the numeric values of the parameters at which to evaluate the function fun and its derivatives.
fun: a function depending on the parameters pars that returns a numeric scalar.
...: Optional additional arguments to fun
.relStep: The relative step size to use in the finite differences. It defaults to the cube root of .Machine$double.eps
minAbsPar: The minimum magnitude of a parameter value that is considered non-zero. It defaults to zero meaning that any non-zero value will be considered different from zero.

Author

José Pinheiro and Douglas Bates bates@stat.wisc.edu

Details

This function uses a second-order response surface design known as a “Koschal design” to determine the parameter values at which the function is evaluated.

Examples

Run this code

(fdH <- fdHess(c(12.3, 2.34), function(x) x[1]*(1-exp(-0.4*x[2]))))
stopifnot(length(fdH$ mean) == 1,
          length(fdH$ gradient) == 2,
          identical(dim(fdH$ Hessian), c(2L, 2L)))

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