pracma (version 0.7.5)

numderiv: Richardson's Numerical Derivative

Description

Richardson's method applied to the computation of the numerical derivative.

Usage

numderiv(f, x0, maxiter = 16, h = 1, ..., accuracy = .Machine$double.eps)
numdiff(f, x, maxiter = 16, h = 1, ..., accuracy = .Machine$double.eps)

Arguments

f

function to be differentiated.

x0, x

point(s) at which the derivative is to be computed.

maxiter

maximum number of iterations.

h

starting step size, should be the default h=1.

accuracy

accuracy with which the function f can be computed.

...

variables to be passed to function f.

Value

• Numeric scalar or vector of approximated derivatives.

Details

Returns the derivative of f at x0 resp. at all points of the vector x.

References

Mathews, J. H., and K. D. Fink (1999). Numerical Methods Using Matlab. Third Edition, Prentice Hall.

See Also

fderiv, complexstep

Examples

# Differentiate an anti-derivative function
f <- function(x) sin(x)*sqrt(1+sin(x))
F <- function(x)
        integrate(f, 0, x, rel.tol = 1e-12)$value
x0 <- 1
dF0 <- numderiv(F, x0, accuracy = 6.5e-15)  #=> 1.141882942715462
f(x0)                                       #   1.141882942715464 true value
# fderiv(F, x0)                             #   1.141882942704476
# numDeriv::grad(F, x0)                     #   1.141882942705797

# Compare over a whole period
x <- seq(0, 2*pi, length.out = 11)
max(abs(numdiff(sin, x) - cos(x)))          #=> 1.61e-15
# max(abs(numDeriv::grad(sin, x) - cos(x))) #   7.70e-12