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", side=NULL, method.args=list(), ...) # S3 method for default
jacobian(func, x, method="Richardson", side=NULL,
method.args=list(), ...)
a function with a real (vector) result.
a real or real vector argument to func, indicating the point at which the gradient is to be calculated.
one of "Richardson"
, "simple"
, or
"complex"
indicating the method to use for the approximation.
arguments passed to method. See grad
.
(Arguments not specified remain with their default values.)
any additional arguments passed to func
.
WARNING: None of these should have names matching other arguments of this function.
an indication of whether one-sided derivatives should be
attempted (see details in function grad
).
A real m by n matrix.
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 method.args=list(eps=1e-4, d=0.0001,
zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2, show.details=FALSE)
is set as the default.
If method is "simple", the calculation is done using a simple epsilon
difference.
For method "simple" method.args=list(eps=1e-4)
is the
default. Only eps
is used by this method.
If method is "complex", the calculation is done using the complex step
derivative approach. See addition comments in grad
before
choosing this method.
For method "complex", method.args
is ignored.
The algorithm uses an eps
of .Machine$double.eps
which cannot
(and should not) be modified.
# NOT RUN {
func2 <- function(x) c(sin(x), cos(x))
x <- (0:1)*2*pi
jacobian(func2, x)
jacobian(func2, x, "complex")
# }
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