Module gauss_quad::midpoint

Numerical integration using the midpoint rule.

This is one of the simplest integration schemes.

1. Divide the domain into equally sized sections.
2. Find the function value at the midpoint of each section.
3. The section's integral is approximated as a rectangle as wide as the section and as tall as the function value at the midpoint.

extern crate gauss_quad; 
use gauss_quad::{Midpoint}; 

#[macro_use]
extern crate assert_float_eq;

use std::f64::consts::PI;

fn main() {
    
    let eps = 0.001;
    
    let n = 30; 
    let quad = Midpoint::init(n); 
    
    // integrate some functions 
    let two_thirds = quad.integrate(-1.0, 1.0, |x| x * x); 
    assert_float_absolute_eq!(two_thirds, 0.66666, eps); 

    let estimate_sin = quad.integrate(-PI, PI, |x| x.sin()); 
    assert_float_absolute_eq!(estimate_sin, 0.0, eps); 
    
    // some functions need more steps than others  
    let m = 100; 
    let better_quad = Midpoint::init(m); 

    let piecewise = better_quad.integrate(-5.0, 5.0, 
                      |x| if x > 1.0 && x < 2.0 { 
                           (-x * x).exp() 
                      } else { 0.0 });

    assert_float_absolute_eq!(0.135257, piecewise, eps); 
}

Structs

Midpoint

A midpoint rule quadrature scheme.