calculus (version 0.2.0)

laplacian: Numerical and Symbolic Laplacian

Description

Computes the laplacian of functions, expressions and characters.

Usage

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

Arguments

f

function, expression or character array.

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

laplacian array.

Functions

• laplacian: arbitrary coordinate system

• %laplacian%: cartesian coordinates

Examples

# NOT RUN {
# laplacian of a scalar field
f <- 'x^2+y^2+z^2'
laplacian(f, var = c('x','y','z'))
f %laplacian% c('x','y','z')

# laplacian of scalar fields
f <- c('x^2','y^3','z^4')
laplacian(f, var = c('x','y','z'))
f %laplacian% c('x','y','z')

# numerical laplacian of scalar fields
f <- c(function(x,y,z) x^2, function(x,y,z) y^3, function(x,y,z) z^4)
laplacian(f, var = c('x'=1,'y'=1,'z'=1))
f %laplacian% c('x'=1,'y'=1,'z'=1)

# laplacian of array of scalar fields
f1 <- c('x^2','y^3','z^4')
f2 <- c('x','y','z')
a <- matrix(c(f1,f2), nrow = 2, byrow = TRUE)
laplacian(a, var = c('x','y','z'))
a %laplacian% c('x','y','z')

# laplacian in polar coordinates
f <- c('sqrt(r)/10','sqrt(r)')
laplacian(f, var = c('r','phi'), coordinates = 'polar')

# }