The function UnirootAll searches the interval from lower to upper
for several roots (i.e., zero's) of a function f with respect to
its first argument.
UnirootAll(f, interval, lower = min(interval), upper = max(interval),
tol = .Machine$double.eps^0.5, maxiter = 1000, n = 100, ...)a vector with the roots found in the interval
the function for which the root is sought.
a vector containing the end-points of the interval to be searched for the root.
the lower end point of the interval to be searched.
the upper end point of the interval to be searched.
the desired accuracy (convergence tolerance).
the maximum number of iterations.
number of subintervals in which the root is sought.
additional named or unnamed arguments to be passed to f
(but beware of partial matching to other arguments).
Karline Soetaert <karline.soetaert@nioz.nl>
f will be called as f(x, ...) for a numeric value of x.
Run demo(Jacobandroots) for an example of the use of UnirootAll
for steady-state analysis.
See also second example of gradient
This example is discussed in the book by Soetaert and Herman (2009).
uniroot for more information about input.
## =======================================================================
## Mathematical examples
## =======================================================================
# a well-behaved case...
fun <- function (x) cos(2*x)^3
curve(fun(x), 0, 10,main = "UnirootAll")
All <- UnirootAll(fun, c(0, 10))
points(All, y = rep(0, length(All)), pch = 16, cex = 2)
# a difficult case...
f <- function (x) 1/cos(1+x^2)
AA <- UnirootAll(f, c(-5, 5))
curve(f(x), -5, 5, n = 500, main = "UnirootAll")
points(AA, rep(0, length(AA)), col = "red", pch = 16)
f(AA) # !!!
## =======================================================================
## Vectorisation:
## =======================================================================
# from R-help Digest, Vol 130, Issue 27
# https://stat.ethz.ch/pipermail/r-help/2013-December/364799.html
integrand1 <- function(x) 1/x*dnorm(x)
integrand2 <- function(x) 1/(2*x-50)*dnorm(x)
integrand3 <- function(x, C) 1/(x+C)
res <- function(C) {
integrate(integrand1, lower = 1, upper = 50)$value +
integrate(integrand2, lower = 50, upper = 100)$value -
integrate(integrand3, C = C, lower = 1, upper = 100)$value
}
# uniroot passes one value at a time to the function, so res can be used as such
uniroot(res, c(1, 1000))
# Need to vectorise the function to use UnirootAll:
res <- Vectorize(res)
UnirootAll(res, c(1,1000))
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