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% vararray of characters or a function returning a numeric array.
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.
list of additional parameters passed to f.
coordinate system to use. One of: cartesian, polar, spherical, cylindrical, parabolic, parabolic-cylindrical or a vector of scale factors for each varibale.
degree of accuracy for numerical derivatives.
finite differences stepsize for numerical derivatives. It is based on the precision of the machine by default.
array.
The function is basically a wrapper for gradient with drop=FALSE.
f %jacobian% var: binary operator with default parameters.
Guidotti E (2022). "calculus: High-Dimensional Numerical and Symbolic Calculus in R." Journal of Statistical Software, 104(5), 1-37. doi:10.18637/jss.v104.i05
Other differential operators:
curl(),
derivative(),
divergence(),
gradient(),
hessian(),
laplacian()
### symbolic Jacobian
jacobian("x*y*z", var = c("x", "y", "z"))
#> [,1] [,2] [,3]
#> [1,] "y * z" "x * z" "x * y"
### 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))
#> [,1] [,2] [,3]
#> [1,] 6 3 2
### vectorized interface
f <- function(x) x[1]*x[2]*x[3]
jacobian(f = f, var = c(1, 2, 3))
#> [,1] [,2] [,3]
#> [1,] 6 3 2
### symbolic vector-valued functions
f <- c("y*sin(x)", "x*cos(y)")
jacobian(f = f, var = c("x","y"))
#> [,1] [,2]
#> [1,] "y * cos(x)" "sin(x)"
#> [2,] "cos(y)" "-(x * sin(y))"
### numerical vector-valued functions
f <- function(x) c(sum(x), prod(x))
jacobian(f = f, var = c(0,0,0))
#> [,1] [,2] [,3]
#> [1,] 1 1 1
#> [2,] 0 0 0
### binary operator
"x*y^2" %jacobian% c(x=1, y=3)
#> [,1] [,2]
#> [1,] 9 6