Module peroxide::numerical::root

Root Finding

Implemented Algorithms

• Bisection
• False Position (Regula Falsi)
• Secant
• Newton

Low-level API

Members

• RootState
  • P(f64) : For point-like initial guess
  • I(f64, f64) : For interval-like initial guess
• RootFind : Algorithms for root finding
  • Bisection
  • FalsePosition
  • Newton
  • Secant
• RootError : Error for root finding
  • MismatchedState : Mismatched state and method (ex: Point vs Bisection)
  • TimesUp : No root until self.times
  • NaNRoot : NaN
• RootFinder : Main structure for root finding
  • fn new(RootState, RootFind, f) : Creat RootFinder (times: 100, tol: 1e-10)
  • fn condition_number(&self) -> f64 : Compute condition number
  • fn set_tol(&mut self, f64) -> &mut Self : Set tolerance
  • fn set_times(&mut self, usize) -> &mut Self : Set max iteration times
  • fn update(&mut self) : Update one step
  • fn find_root(&mut self) -> Result<f64, RootError> : Find root

Usage

extern crate peroxide;
use peroxide::fuga::*;

fn main() -> Result<(), RootError> {
    let init = RootState::I(1f64, 4f64);
    let mut rf = RootFinder::<_, AD1>::new(init, Bisection, f)?;
    rf.set_tol(1e-15)       // Default: 1e-10
        .set_times(200);    // Default: 100
    let root = rf.find_root()?;
    root.print();
    Ok(())
}

fn f<T: AD>(x: T) -> T {
    x.sin()
}

High-level API

Members

All output type is Result<f64, RootError>

• bisection(f, interval: (f64, f64), times: usize, tol: f64)
• false_position(f, interval: (f64, f64), times: usize, tol: f64)
• secant(f, initial_guess: (f64, f64), times: usize, tol: f64)
• newton(f, initial_guess: f64, times: usize, tol: f64)

Usage

extern crate peroxide;
use peroxide::fuga::*;

fn main() -> Result<(), RootError> {
    let root = bisection(f, (1f64, 4f64), 100, 1e-15)?;
    root.print();
    Ok(())
}

fn f<T: AD>(x: T) -> T {
    x.sin()
}

Reference

• Walter Gautschi, Numerical Analysis, Springer (2012)

Structs

RootFinder

Structure for Root finding

Enums

RootBool
RootError
RootFind
RootState

Functions

bisection	Bisection method to find root
false_position	False position method to find root
newton	Newton method to find root
secant	Secant method to find root