uniroot {stats}R Documentation

One Dimensional Root (Zero) Finding


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),
        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.
lower the lower end point of the interval to be searched.
upper the upper end point of the interval to be searched.
tol the desired accuracy (convergence tolerance).
maxiter the maximum number of iterations.
... additional arguments to f.


Either interval or both lower and upper must be specified. The function uses Fortran subroutine ‘"zeroin"’ (from Netlib) based on algorithms given in the reference below.

If the algorithm does not converge in maxiter steps, a warning is printed and the current approximation is returned.


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.


Brent, R. (1973) Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.

See Also

polyroot for all complex roots of a polynomial; optimize, nlm.


f <- function (x,a) x - a
str(xmin <- uniroot(f, c(0, 1), tol = 0.0001, a = 1/3))
str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up = 2, tol = 0.0001),
    dig = 10)
str(uniroot(function(x) x*(x^2-1) + .5, low = -2, up =2 , tol = 1e-10 ),
    dig = 10)

## Find the smallest value x for which exp(x) > 0 (numerically):
r <- uniroot(function(x) 1e80*exp(x) -1e-300,,-1000,0, tol=1e-20)
str(r, digits= 15)##> around -745.1332191

exp(r$r)        # = 0, but not for r$r * 0.999...
minexp <- r$r * (1 - .Machine$double.eps)
exp(minexp)     # typically denormalized

[Package stats version 2.2.1 Index]