Function roots::find_root_newton_raphson

pub fn find_root_newton_raphson<F, Func, Deriv>(
    start: F, 
    f: Func, 
    d: Deriv, 
    convergency: &mut dyn Convergency<F>
) -> Result<F, SearchError> where
    F: FloatType,
    Func: Fn(F) -> F,
    Deriv: Fn(F) -> F, 

Find a root of the function f(x) = 0 using the Newton-Raphson method.

Pro

• Simple
• Fast convergency for well-behaved functions
• No need for initial bracketing

Contra

• Needs derivative function
• Impossible to predict which root will be found when many roots exist
• Unstable convergency for non-trivial functions
• Cannot continue when derivative is zero

Failures

ZeroDerivative

The stationary point of the function is encountered. Algorithm cannot continue.

NoConvergency

Algorithm cannot find a root within the given number of iterations.

Examples

use roots::SimpleConvergency;
use roots::find_root_newton_raphson;

let f = |x| { 1f64*x*x - 1f64 };
let d = |x| { 2f64*x };
let mut convergency = SimpleConvergency { eps:1e-15f64, max_iter:30 };

let root1 = find_root_newton_raphson(10f64, &f, &d, &mut convergency);
// Returns approximately Ok(1);

let root2 = find_root_newton_raphson(-10f64, &f, &d, &mut 1e-15f64);
// Returns approximately Ok(-1);