## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
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#' @title The Bisection Method
#'
#' @description
#' Use the bisection method to find real roots
#'
#' @param f function to locate a root for
#' @param a the a bound of the search region
#' @param b the b bound of the search region
#' @param tol the error tolerance
#' @param m the maximum number of iterations
#'
#' @details
#'
#' The bisection method functions by repeatedly halving the interval
#' between \code{a} and \code{b} and will return when the
#' interval between them is less than \code{tol}, the error tolerance.
#' However, this implementation also stops if after \code{m}
#' iterations.
#'
#' @return the real root found
#'
#' @family optimz
#'
#' @examples
#' f <- function(x) { x^3 - 2 * x^2 - 159 * x - 540}
#' bisection(f, 0, 10)
#'
#' @export
bisection <- function(f, a, b, tol = 1e-3, m = 100) {
iter <- 0
f.a <- f(a)
f.b <- f(b)
while (abs(b - a) > tol) {
iter <- iter + 1
if (iter > m) {
warning("iterations maximum exceeded")
break
}
xmid <- (a + b) / 2
ymid <- f(xmid)
if (f.a * ymid > 0) {
a <- xmid
f.a <- ymid
} else {
b <- xmid
f.b <- ymid
}
}
## Interpolate a midpoint for return value
root <- (a + b) / 2
return(root)
}
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