uniroot
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.
Setting extendInt
to a non"no"
string, means searching
for the correct interval = c(lower,upper)
if sign(f(x))
does not satisfy the requirements at the interval end points; see the
‘Details’ section.
 Keywords
 optimize
Usage
uniroot(f, interval, ..., lower = min(interval), upper = max(interval), f.lower = f(lower, ...), f.upper = f(upper, ...), extendInt = c("no", "yes", "downX", "upX"), check.conv = FALSE, tol = .Machine$double.eps^0.25, maxiter = 1000, trace = 0)
Arguments
 f
 the function for which the root is sought.
 interval
 a vector containing the endpoints of the interval to be searched for the root.
 ...
 additional named or unnamed arguments to be passed
to
f
 lower, upper
 the lower and upper end points of the interval to be searched.
 f.lower, f.upper
 the same as
f(upper)
andf(lower)
, respectively. Passing these values from the caller where they are often known is more economical as soon asf()
contains nontrivial computations.  extendInt
 character string specifying if the interval
c(lower,upper)
should be extended or directly produce an error whenf()
does not have differing signs at the endpoints. The default,"no"
, keeps the search interval and hence produces an error. Can be abbreviated.  check.conv
 logical indicating whether a convergence warning of the
underlying
uniroot
should be caught as an error and if nonconvergence inmaxiter
iterations should be an error instead of a warning.  tol
 the desired accuracy (convergence tolerance).
 maxiter
 the maximum number of iterations.
 trace
 integer number; if positive, tracing information is produced. Higher values giving more details.
Details
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), for extendInt="no"
, the default. Otherwise, if
extendInt="yes"
, the interval is extended on both sides, in
search of a sign change, i.e., until the search interval $[l,u]$
satisfies $f(l) * f(u) <= 0$.<="" p="">
If it is known how $f$ changes sign at the root
$x0$, that is, if the function is increasing or decreasing there,
extendInt
can (and typically should) be specified as
"upX"
(for “upward crossing”) or "downX"
,
respectively. Equivalently, define $S:= +/ 1$, to
require $S = sign(f(x0 +
eps))$ at the solution. In that case, the search interval $[l,u]$
possibly is extended to be such that $
S * f(l) <= 0$="" and="" $s="" *="" f(u)="">= 0$.
uniroot()
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.
The argument passed to f
has special semantics and used to be
shared between calls. The function should not copy it.
Value

A list with at least 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
.)Further components may be added in future: component init.it
was added in R 3.1.0.
Source
Based on ‘zeroin.c’ in http://www.netlib.org/c/brent.shar.
References
Brent, R. (1973) Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: PrenticeHall.
See Also
polyroot
for all complex roots of a polynomial;
optimize
, nlm
.
Examples
library(stats)
## uniroot() with new interval extension + checking features: 
f1 < function(x) (121  x^2)/(x^2+1)
f2 < function(x) exp(x)*(x  12)
try(uniroot(f1, c(0,10)))
try(uniroot(f2, c(0, 2)))
##> error: f() .. end points not of opposite sign
## where as 'extendInt="yes"' simply first enlarges the search interval:
u1 < uniroot(f1, c(0,10),extendInt="yes", trace=1)
u2 < uniroot(f2, c(0,2), extendInt="yes", trace=2)
stopifnot(all.equal(u1$root, 11, tolerance = 1e5),
all.equal(u2$root, 12, tolerance = 6e6))
## The *danger* of interval extension:
## No way to find a zero of a positive function, but
## numerically, f(M) becomes zero :
u3 < uniroot(exp, c(0,2), extendInt="yes", trace=TRUE)
## Nonsense example (must give an error):
tools::assertCondition( uniroot(function(x) 1, 0:1, extendInt="yes"),
"error", verbose=TRUE)
## Convergence checking :
sinc < function(x) ifelse(x == 0, 1, sin(x)/x)
curve(sinc, 6,18); abline(h=0,v=0, lty=3, col=adjustcolor("gray", 0.8))
uniroot(sinc, c(0,5), extendInt="yes", maxiter=4) #> "just" a warning
## now with check.conv=TRUE, must signal a convergence error :
uniroot(sinc, c(0,5), extendInt="yes", maxiter=4, check.conv=TRUE)
### Weibull cumulative hazard (example origin, Ravi Varadhan):
cumhaz < function(t, a, b) b * (t/b)^a
froot < function(x, u, a, b) cumhaz(x, a, b)  u
n < 1000
u < log(runif(n))
a < 1/2
b < 1
## Find failure times
ru < sapply(u, function(x)
uniroot(froot, u=x, a=a, b=b, interval= c(1.e14, 1e04),
extendInt="yes")$root)
ru2 < sapply(u, function(x)
uniroot(froot, u=x, a=a, b=b, interval= c(0.01, 10),
extendInt="yes")$root)
stopifnot(all.equal(ru, ru2, tolerance = 6e6))
r1 < uniroot(froot, u= 0.99, a=a, b=b, interval= c(0.01, 10),
extendInt="up")
stopifnot(all.equal(0.99, cumhaz(r1$root, a=a, b=b)))
## An error if 'extendInt' assumes "wrong zerocrossing direction":
uniroot(froot, u= 0.99, a=a, b=b, interval= c(0.1, 10), extendInt="down")