gradient: Numerical and Symbolic Gradient

Description

Computes the gradient or jacobian of functions, expressions and characters.

Usage

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

Arguments

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

gradient or jacobian array.

Functions

gradient: arbitrary coordinate system
%gradient%: cartesian coordinates

Examples

Run this code

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

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

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

# jacobian with respect to (x,y)
f <- c("y*sin(x)", "x*cos(y)")
gradient(f = f, var = c("x","y"))
f %gradient% c("x","y")

# jacobian with respect to (x,y) and evaluate in (x = 0, y = 0)
f <- c(function(x, y) y*sin(x), function(x, y) x*cos(y))
gradient(f = f, var = c(x=0,y=0))
f %gradient% c(x=0,y=0)

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

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

# }

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