uniroot.integer: Find the root of a function to the nearest integer

In ssanv: Sample Size Adjusted for Nonadherence or Variability of Input Parameters

Description

Let f be a monotonic function that changes sign within the interval specified. If f(i)=0 for some i within the interval specified (including the ends of the interval), then the root is i. Otherwise if pos.side=TRUE (or FALSE) then uniroot.integer finds the integer i such that f(i) is closest to the sign change and is positive (or negative).

Usage

uniroot.integer(f, interval, lower = min(interval), upper = max(interval), 
    step.power = 6, step.up = TRUE, pos.side = FALSE, print.steps = FALSE, 
    maxiter = 1000, ...)

Arguments

f	function for which a root is needed
interval	an interval giving minimum and maximum allowable values for root
lower	minimum allowable root
upper	maximum allowable root
step.power	initial step size is 2^step.power
step.up	if TRUE steps up from 'lower', if FALSE steps down from 'upper'
pos.side	if TRUE finds integer, i, closest to the root such that f(i) > zero
print.steps	if TRUE, prints iterations
maxiter	maximum number of iterations
...	additional arguments to 'f'.

Details

The algorithm evaluates f(i) iteratively, increasing (or decreasing if step.up=FALSE) i by 2^step.power until either f(i)=0 or f(i) switches sign. If f(i)=0, then stop. If f(i) switches sign, then the change in 'i' is halved each iteration until convergence.

Value

A list with the following elements:

root	the integer on the correct side of the root
f.root	value of f at root
iter	number of times f was evaluated

Note

Unlike uniroot, the function is not automatically evaluated at both extremes. This makes uniroot.integer an efficient method to use when the calculation time of f(i) increases with the value of 'i'. For an example of the importance of this see ss.fromdata.pois.

Author(s)

Michael P. Fay

See Also

uniroot, used by ss.fromdata.neff, ss.fromdata.pois, ss.nonadh

Examples

root.func<-function(i) i - 500.1 
## initial step sizes = 2^2 =4
uniroot.integer(root.func,c(0,Inf),step.power=2)
## more efficient to use bigger initial step sizes = 2^10 =1024
uniroot.integer(root.func,c(0,Inf),step.power=10,print.steps=TRUE)

Example output

$iter
[1] 129

$f.root
[1] -0.1

$root
[1] 500

[1] "x= 0  f(x)= -500.1"
[1] "x= 1024  f(x)= 523.9"
[1] "x= 512  f(x)= 11.9"
[1] "x= 256  f(x)= -244.1"
[1] "x= 384  f(x)= -116.1"
[1] "x= 448  f(x)= -52.1"
[1] "x= 480  f(x)= -20.1"
[1] "x= 496  f(x)= -4.10000000000002"
[1] "x= 504  f(x)= 3.89999999999998"
[1] "x= 500  f(x)= -0.100000000000023"
[1] "x= 502  f(x)= 1.89999999999998"
[1] "x= 501  f(x)= 0.899999999999977"
$iter
[1] 12

$f.root
[1] -0.1

$root
[1] 500

ssanv documentation built on May 2, 2019, 2:44 a.m.