lmfor (version 1.6)

updown: Solve a simple equation using a step halving algorithm.

Description

Solves equations of form \(f(x)=0\), for scalar \(x\) \((l<=x<=u)\) using a simple step halving algorithm, where \(f(x)\) is a monotonic continuous function. Initial finite upper and lower bounds for x are required. The algorithm first computes \(f\) for \(x=u\) and \(x=l\). If the sign was different then another call is performed at the midpoint \(x=(u+l)/2\), and the midpoint is taken as a new upper or lower bound, according to the location of sign change. The upper or lower bound are repeatedly updated until the absolute value of f at the midpoint is below a specified criteria.

Usage

updown(l, u, fn, crit = 6)

Arguments

l

The initial lower bound

u

The initial upper bound

fn

R-function for \(f(x)\)

crit

The convergence criteria (Maximum accepted value of f at the solution is \(10^{-\code{crit}}\)).

Value

A scalar giving the value of \(x\) at the solution. If the sign did not change between l and u, NA is returned.

Warning

May lead to infinite loop for non-continuous functions. Works only with monotonic functions.

Examples

# NOT RUN {
## Compute the median of Weibull distibution
fn<-function(x) pweibull(x,5,15)-0.5
updown(1,50,fn)
# }