mosaicCalc (version 0.5.1)

numD: Numerical Derivatives

Description

Constructs the numerical derivatives of mathematical expressions

Usage

numD(formula, ..., .hstep = NULL, add.h.control = FALSE)

Value

a function implementing the derivative as a finite-difference approximation

Arguments

formula

a mathematical expression (see examples and plotFun)

...

additional parameters, typically default values for mathematical parameters

.hstep

numerical finite-difference step (default is 1e-6 or 1e-4 for first and second-order derivatives, respectively)

add.h.control

arranges the returned function to have a .hstep argument that can be used to demonstrate convergence and error

Author

Daniel Kaplan ()

Details

Uses a simple finite-difference scheme to evaluate the derivative. The function created will not contain a formula for the derivative. Instead, the original function is stored at the time the derivative is constructed and that original function is re-evaluated at the finitely-spaced points of an interval. If you redefine the original function, that won't affect any derivatives that were already defined from it. Numerical derivatives, particularly high-order ones, are unstable. The finite-difference parameter .hstep is set, by default, to give reasonable results for first- and second-order derivatives. It's tweaked a bit so that taking a second derivative by differentiating a first derivative will give reasonably accurate results. But, if taking a second derivative, much better to do it in one step to preserve numerical accuracy.

Examples

g = numD( a*x^2 + x*y ~ x, a=1)
g(x=2,y=10)
gg = numD( a*x^2 + x*y ~ x&x, a=1)
gg(x=2,y=10)
ggg = numD( a*x^2 + x*y ~ x&y, a=1)
ggg(x=2,y=10)
h = numD( g(x=x,y=y,a=a) ~ y, a=1)
h(x=2,y=10)
f = numD( sin(x)~x, add.h.control=TRUE)
# plotFun( f(3,.hstep=h)~h, hlim=range(.00000001,.000001))
# ladd( panel.abline(cos(3),0))