madness (version 0.2.8)

numderiv: Numerical (approximate) Differentiation.

Description

Approximates the derivative of a function at the input by numerical methods.

Usage

numderiv(f, x, eps=1e-8, type=c('forward','central','backward'),...)
# S4 method for ANY,array
numderiv(f, x, eps = 1e-08, type = c("forward", "central", "backward"), ...)
# S4 method for ANY,madness
numderiv(f, x, eps = 1e-08, type = c("forward", "central", "backward"), ...)

Value

A matrix if x is numeric; a madness object if x is a madness object.

Arguments

f

a function, to be evaluated at and near x.

x

array, matrix, or madness object.

eps

the 'epsilon', a small value added or subtracted from x to compute the first differences.

type

the type of first difference, case-insensitive, substrings ok.

...

arguments passed on to f.

Author

Steven E. Pav

Details

For a multivariate-valued function of multivariate data, approximates the derivative at a point via the forward, central, or backward first differences, returning a madness object.

Examples

f <- function(x,h) {
  cos(x + h)
}
x <- array(rnorm(100),dim=c(10,10))
madx <- numderiv(f,x,1e-8,h=pi)