calculus (version 0.1.0)

hessian: Numerical and Symbolic Hessian

Description

Computes the hessian matrix of functions, expressions and characters.

Usage

hessian(f, var, accuracy = 2, stepsize = NULL,
  coordinates = "cartesian")
f %hessian% var

Arguments

f

function, expression or character.

var

character vector, giving the variable names with respect to which derivatives will be computed. If a named vector is provided, derivatives will be computed at that point.

accuracy

accuracy degree for numerical derivatives.

stepsize

finite differences stepsize for numerical derivatives. Auto-optimized by default.

coordinates

coordinate system to use. One of: cartesian, polar, spherical, cylindrical, parabolic, parabolic-cylindrical or a character vector of scale factors for each varibale.

Value

hessian matrix.

Functions

• hessian: arbitrary coordinate system

• %hessian%: cartesian coordinates

Examples

# NOT RUN {
# hessian with respect to x
hessian(f = "sin(x)", var = "x")
"sin(x)" %hessian% "x"

# hessian with respect to x and evaluate in x = 0
hessian(f = "sin(x)", var = c("x" = 0))
"sin(x)" %hessian% c(x=0)

# hessian with respect to (x,y)
hessian(f = "y*sin(x)", var = c("x","y"))
"y*sin(x)" %hessian% c("x","y")

# hessian in spherical coordinates
hessian('r*theta*phi', var = c('r','theta','phi'), coordinates = 'spherical')

# numerical hessian in spherical coordinates
f <- function(r, theta, phi) r*theta*phi
hessian(f, var = c('r'=1, 'theta'=pi/4, 'phi'=pi/4), coordinates = 'spherical')

# }