```
# NOT RUN {
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: fixed point of cos(.):
uniroot(function(x) cos(x) - x, lower = -pi, upper = pi, tol = 1e-9)$root
str(uniroot(function(x) x*(x^2-1) + .5, lower = -2, upper = 2,
tol = 0.0001))
str(uniroot(function(x) x*(x^2-1) + .5, lower = -2, upper = 2,
tol = 1e-10))
## Find the smallest value x for which exp(x) > 0 (numerically):
r <- uniroot(function(x) 1e80*exp(x) - 1e-300, c(-1000, 0), tol = 1e-15)
str(r, digits.d = 15) # around -745, depending on the platform.
exp(r$root) # = 0, but not for r$root * 0.999...
minexp <- r$root * (1 - 10*.Machine$double.eps)
exp(minexp) # typically denormalized
# }
# NOT RUN {
<!-- % donttest because printed output is so much platform dependent -->
# }
# NOT RUN {
##--- uniroot() with new interval extension + checking features: --------------
f1 <- function(x) (121 - x^2)/(x^2+1)
f2 <- function(x) exp(-x)*(x - 12)
try(uniroot(f1, c(0,10)))
try(uniroot(f2, c(0, 2)))
##--> error: f() .. end points not of opposite sign
## where as 'extendInt="yes"' simply first enlarges the search interval:
u1 <- uniroot(f1, c(0,10),extendInt="yes", trace=1)
u2 <- uniroot(f2, c(0,2), extendInt="yes", trace=2)
stopifnot(all.equal(u1$root, 11, tolerance = 1e-5),
all.equal(u2$root, 12, tolerance = 6e-6))
## The *danger* of interval extension:
## No way to find a zero of a positive function, but
## numerically, f(-|M|) becomes zero :
u3 <- uniroot(exp, c(0,2), extendInt="yes", trace=TRUE)
## Nonsense example (must give an error):
tools::assertCondition( uniroot(function(x) 1, 0:1, extendInt="yes"),
"error", verbose=TRUE)
## Convergence checking :
sinc <- function(x) ifelse(x == 0, 1, sin(x)/x)
curve(sinc, -6,18); abline(h=0,v=0, lty=3, col=adjustcolor("gray", 0.8))
# }
# NOT RUN {
uniroot(sinc, c(0,5), extendInt="yes", maxiter=4) #-> "just" a warning
# }
# NOT RUN {
## now with check.conv=TRUE, must signal a convergence error :
# }
# NOT RUN {
uniroot(sinc, c(0,5), extendInt="yes", maxiter=4, check.conv=TRUE)
# }
# NOT RUN {
### Weibull cumulative hazard (example origin, Ravi Varadhan):
cumhaz <- function(t, a, b) b * (t/b)^a
froot <- function(x, u, a, b) cumhaz(x, a, b) - u
n <- 1000
u <- -log(runif(n))
a <- 1/2
b <- 1
## Find failure times
ru <- sapply(u, function(x)
uniroot(froot, u=x, a=a, b=b, interval= c(1.e-14, 1e04),
extendInt="yes")$root)
ru2 <- sapply(u, function(x)
uniroot(froot, u=x, a=a, b=b, interval= c(0.01, 10),
extendInt="yes")$root)
stopifnot(all.equal(ru, ru2, tolerance = 6e-6))
r1 <- uniroot(froot, u= 0.99, a=a, b=b, interval= c(0.01, 10),
extendInt="up")
stopifnot(all.equal(0.99, cumhaz(r1$root, a=a, b=b)))
## An error if 'extendInt' assumes "wrong zero-crossing direction":
# }
# NOT RUN {
uniroot(froot, u= 0.99, a=a, b=b, interval= c(0.1, 10), extendInt="down")
# }
```

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