| uniroot {stats} | R Documentation |
The function uniroot searches the interval from lower
to upper for a root (i.e., zero) of the function f with
respect to its first argument.
uniroot(f, interval, ...,
lower = min(interval), upper = max(interval),
f.lower = f(lower, ...), f.upper = f(upper, ...),
tol = .Machine$double.eps^0.25, maxiter = 1000)
f |
the function for which the root is sought. |
interval |
a vector containing the end-points of the interval to be searched for the root. |
... |
additional named or unnamed arguments to be passed
to |
lower, upper |
the lower and upper end points of the interval to be searched. |
f.lower, f.upper |
the same as |
tol |
the desired accuracy (convergence tolerance). |
maxiter |
the maximum number of iterations. |
Note that arguments after ... must be matched exactly.
Either interval or both lower and upper must be
specified: the upper endpoint must be strictly larger than the lower
endpoint. The function values at the endpoints must be of opposite
signs (or zero).
The function uses Fortran subroutine ‘"zeroin"’ (from Netlib) based on algorithms given in the reference below. They assume a continuous function (which then is known to have at least one root in the interval).
Convergence is declared either if f(x) == 0 or the change in
x for one step of the algorithm is less than tol (plus an
allowance for representation error in x).
If the algorithm does not converge in maxiter steps, a warning
is printed and the current approximation is returned.
f will be called as f(x, ...) for a numeric value
of x.
A list with four components: root and f.root give the
location of the root and the value of the function evaluated at that
point. iter and estim.prec give the number of iterations
used and an approximate estimated precision for root. (If the
root occurs at one of the endpoints, the estimated precision is
NA.)
Based on ‘zeroin.c’ in http://www.netlib.org/c/brent.shar.
Brent, R. (1973) Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.
polyroot for all complex roots of a polynomial;
optimize, nlm.
require(utils) # for str
## some platforms hit zero exactly on the first step:
## if so the estimated precision is 2/3.
f <- function (x,a) x - a
str(xmin <- uniroot(f, c(0, 1), tol = 0.0001, a = 1/3))
## handheld calculator example: fixpoint of cos(.):
rc <- uniroot(function(x) cos(x) - x, lower=-pi, upper=pi, tol = 1e-9)
rc$root
str(uniroot(function(x) x*(x^2-1) + .5, lower = -2, upper = 2,
tol = 0.0001))
str(uniroot(function(x) x*(x^2-1) + .5, lower = -2, upper = 2,
tol = 1e-10 ))
## Find the smallest value x for which exp(x) > 0 (numerically):
r <- uniroot(function(x) 1e80*exp(x)-1e-300, c(-1000,0), tol = 1e-15)
str(r, digits.d = 15) ##> around -745, depending on the platform.
exp(r$root) # = 0, but not for r$root * 0.999...
minexp <- r$root * (1 - 10*.Machine$double.eps)
exp(minexp) # typically denormalized