Newton's method Wikipedia entry
import std.math;
import std.stdio;
double sqr(double a) {
return a*a;
}
double sqr_prime(double a) {
return 2*a;
}
alias Func = double function(double);
alias FuncPrime = double function(double);
double newton_raphson(Func func, FuncPrime func_prime, double A, double initialGuess, int maxIterations = 1_000, double tolerance = 1e-6) {
double x = initialGuess;
for (int i = 0; i < maxIterations; ++i) {
double f_x = func(x) - A;
double f_prime_x = func_prime(x);
if (abs(f_prime_x) < tolerance) {
writeln("Derivative too small, cannot continue.");
break;
}
x = x - f_x / f_prime_x;
if (abs(f_x) < tolerance) {
writeln("\nConverged in ", i, " iterations");
break;
}
}
return x;
}
void main() {
double A = 11_025.0; // Find the square root of 11_025
double result = newton_raphson(&sqr, &sqr_prime, A, A/2.0);
if (isNaN(result)) {
writeln("Newton-Raphson method did not converge.");
} else {
writeln("Square root of ", A, " is approximately ", result);
}
writeln;
}Usage:
git clone https://github.com/miscelleanous-projects/newton-raphson.gitcd d
dub build && dub runuse std::f64;
type Func = fn(f64) -> f64;
type FuncPrime = fn(f64) -> f64;
fn sqr(a: f64) -> f64 {
a * a
}
fn sqr_prime(a: f64) -> f64 {
2.0 * a
}
fn newton_raphson(func: Func, func_prime: FuncPrime, a: f64, initial_guess: f64, max_iterations: usize, tolerance: f64) -> f64 {
let mut x = initial_guess;
for i in 0..max_iterations {
let f_x = func(x) - a;
let f_prime_x = func_prime(x);
if f_prime_x.abs() < tolerance {
eprintln!("Derivative too small, cannot continue.");
break;
}
x = x - f_x / f_prime_x;
if f_x.abs() < tolerance {
eprintln!("\nConverged in {} iterations", i);
break;
}
}
x
}
fn main() {
let a = 11_025.0; // Find the square root of 11025
let result = newton_raphson(sqr, sqr_prime, a, a / 2.0, 1_000, 1e-6);
if result.is_nan() {
eprintln!("Newton-Raphson method did not converge.");
} else {
println!("Square root of {} is approximately {}", a, result);
}
}Usage:
git clone https://github.com/miscelleanous-projects/newton-raphson.gitcd rust
cargo build && cargo runSession sample
Converged in 10 iterations
Square root of 11025 is approximately 105