jacobian() R function from [calculus]

Numerical and Symbolic Jacobian

Computes the numerical Jacobian of functions or the symbolic Jacobian of characters

in arbitrary orthogonal coordinate systems.


jacobian(
  f,
  var,
  params = list(),
  coordinates = "cartesian",
  accuracy = 4,
  stepsize = NULL
)

f %jacobian% var

Arguments

f: array of characters or a function returning a numeric array.
var: vector giving the variable names with respect to which the derivatives are to be computed and/or the point where the derivatives are to be evaluated. See derivative.
params: list of additional parameters passed to f.
coordinates: coordinate system to use. One of: cartesian, polar, spherical, cylindrical, parabolic, parabolic-cylindrical or a vector of scale factors for each varibale.
accuracy: degree of accuracy for numerical derivatives.
stepsize: finite differences stepsize for numerical derivatives. It is based on the precision of the machine by default.

Returns

array.

Details

The function is basically a wrapper for gradient with drop=FALSE.

Functions

f %jacobian% var: binary operator with default parameters.

Examples


### symbolic Jacobian 
jacobian("x*y*z", var = c("x", "y", "z"))

### numerical Jacobian in (x=1, y=2, z=3)
f <- function(x, y, z) x*y*z
jacobian(f = f, var = c(x=1, y=2, z=3))

### vectorized interface
f <- function(x) x[1]*x[2]*x[3]
jacobian(f = f, var = c(1, 2, 3))

### symbolic vector-valued functions
f <- c("y*sin(x)", "x*cos(y)")
jacobian(f = f, var = c("x","y"))

### numerical vector-valued functions
f <- function(x) c(sum(x), prod(x))
jacobian(f = f, var = c(0,0,0))

### binary operator
"x*y^2" %jacobian% c(x=1, y=3)

References

Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. tools:::Rd_expr_doi("10.18637/jss.v104.i05")

jacobian function