| jacobian {numDeriv} | R Documentation |
Calculate the m by n numerical approximation of the gradient of a real m-vector valued function with n-vector argument.
jacobian(func, x, method="Richardson", method.args=list(), ...)
## Default S3 method:
jacobian(func, x, method="Richardson",
method.args=list(eps=1e-4, d=0.0001, r=4, v=2, show.details=FALSE), ...)
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 aproximation. |
method.args |
arguments passed to method. (Arguments not specified remain with their default values.) |
... |
any additional arguments passed to func. |
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.
A real m by n matrix.
func2 <- function(x) c(sin(x), cos(x)) x <- (0:1)*2*pi jacobian(func2, x)