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(), ...)
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 |
method.args |
arguments passed to method. See |
... |
any additional arguments passed to |
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 "Richardson", the calculation is done by
Richardson's extrapolation. See link{grad}
for more details.
For this method methods.args=list(eps=1e-4, d=0.0001,
zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2, show.details=FALSE)
is set as the default.
If method is "simple", the calculation is done using a simple epsilon
difference.
For method "simple" methods.args=list(eps=1e-4)
is the
default. Only eps
is used by this method.
If method is "complex", the calculation is done using the complex step
derivative approach described in Lyness and Moler. This method requires
that the function be able to handle complex valued arguments and return the
appropriate complex valued result, even though the user may only be
interested in the real case. For cases where it can be used, it is faster than Richardson's extrapolation, and
it also provides gradients that are correct to machine precision (16 digits).
For method "complex", methods.args
is ignored.
The algorithm uses an eps
of .Machine$double.eps
which cannot
(and should not) be modified.
A real m by n matrix.
func2 <- function(x) c(sin(x), cos(x)) x <- (0:1)*2*pi jacobian(func2, x) jacobian(func2, x, "complex")