numDeriv (version 2009.2-1)

jacobian: Gradient of a Vector Valued Function

Description

Calculate the m by n numerical approximation of the gradient of a real m-vector valued function with n-vector argument.

Usage

jacobian(func, x, method="Richardson", method.args=list(), ...) 
    ## S3 method for class 'default':
jacobian(func, x, method="Richardson",
       method.args=list(eps=1e-4, d=0.0001, 
       zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2, show.details=FALSE), ...)

Arguments

func

a function with a real (vector) result.

x

a real or real vector argument to func, indicating the point at which the gradient is to be calculated.

method

one of "Richardson" or "simple" indicating the method to use for the approximation.

method.args

arguments passed to method. See grad. (Arguments not specified remain with their default values.)

...

any additional arguments passed to func.

Value

• A real m by n matrix.

Details

For $f:R^n -> R^m$ calculate the $m x n$ Jacobian $dy/dx$. The function jacobian calculates a numerical approximation of the first derivative of func at the point x. Any additional arguments in ...are also passed to func, but the gradient is not calculated with respect to these additional arguments. If method is "simple", the calculation is done using a simple epsilon difference. For this case, only the methods.args element eps is used. If method is "Richardson", the calculation is done by Richardson's extrapolation. See link{grad} for more details.

See Also

grad, hessian, numericDeriv

Examples

func2 <- function(x) c(sin(x), cos(x))
   x <- (0:1)*2*pi
   jacobian(func2, x)