fdHess function

Finite difference Hessian

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

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

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.

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.

Returns

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.

Author(s)

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

Examples

(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)))