bisect: Bisection Method

In ppham27/setsim: Software tool for the visualization of confidence regions in statistical models

Description

This function finds the approximate roots of a numeric function by bisection algorithm. The root-finding method is one-dimensional.

Usage

bisect(fn, a, b, tol = 1e-05, error = 1e-04, decimal = 5, input, VZ, c_value)

Arguments

fn	a numeric function defined by the user. An object which is not a numeric function will not be allowed.
a	numeric value of the lower end point of the interval to be searched.
b	numeric value of the upper end point of the interval to be searched.
tol	tolerance to stop bisection algorithm. The default value is 0.00001.
error	significance of the approximate root. The default value is 0.0001.
decimal	the number of decimal places to round off for the approximate root.
input	a list of response variable, design(X) matrix, maximum likelihood estimators for the parameters and maximized log likelihood value. This argument must be ignored if confidence region visualization algorithm is not used.
VZ	a matrix product by multiplying the matrix square root of a covariance matrix for the maximum likelihood estimator and random vector generated from a standard multivariate normal distribution. This argument must be ignored if confidence region visualization algorithm is not used.
c_value	the critical values to visualize confidence regions. This argument must be ignored if confidence region visualization algorithm is not used.

Details

The function requires at least one root to process. Check nroots if a roots exists.

Value

the approximate root by bisection algorithm. The error of approximation, number of decimal places and other requirements can be adjusted by user to produce a different root.

Warning

If this function is not used for confidence region visualization algorithm, the numeric function to be calculated must include {...} in its argument. This is due to the last three arguments of this function.

See Also

nroots for finding the lower and upper end point of the interval containing a root.

Examples

y <- function(x,...){x^2-4}
bisect(y,a=-5,b=0,error=0.1,decimal=5)
bisect(y,a=-5,b=0,error=0.0001,decimal=5)

f <- function(x,...){sin(x)}
x <- seq(-50,50,length=100)
roots <- nroots(f,x)
n <- roots$n
range <- roots$range
sol <- 0
for (i in 1:n){
	sol[i] <- bisect(f,a=range[i,1],b=range[i,2])}
sol

ppham27/setsim documentation built on May 25, 2019, 11:25 a.m.