fdHess {nlme} | R Documentation

## 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)

### 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.

### Value

A list with components

`mean` | the value of function `fun` evaluated at the parameter values `pars`
`gradient` | an approximate gradient
`Hessian` | a matrix whose upper triangle containst an approximate Hessian.

### Author(s)

Jose Pinheiro jcp@research.bell-labs.com, Douglas Bates bates@stat.wisc.edu

### Examples

    fdHess(c(12.3, 2.34), function(x) x[1]*(1-exp(-0.4*x[2])))

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