Function reikna::integral::nth_integral

pub fn nth_integral(n: u64, f: &Function, c: f64, p: u64) -> Function

Return a Function that estimates the nth integral of f, using a constant of c and a positive precision constant of p.

The integration itself is done by integrate_wp(), see the documentation for integrate_wp() for more information.

The precision value passed to integrate_wp() is calculated with the following formula:

precision = round(|x|) * p

Where p is the precision constant supplied to this function.

Note -- the computational complexity of the resulting function grows exponentially based on the value of n, IE:

nth_integral(1, f, c, p)(x) -> O(1^x)
nth_integral(2, f, c, p)(x) -> O(2^x)
nth_integral(3, f, c, p)(x) -> O(3^x)

where x is the value of x supplied to the resulting function. For this reason it is not recommended to use values of n greater than three or four, as larger values will cause computational complexity to rapidly inflate.

Panics

Panics if p equals zero.

Examples

#[macro_use] extern crate reikna;
use reikna::integral::*;

let f = func!(|x| x * x);
let integral = nth_integral(1, &f, 1.0, DEFAULT_PRECISION);

println!("integral({}) = {}",  0.0, integral( 0.0));
println!("integral({}) = {}",  1.0, integral( 1.0));
println!("integral({}) = {}", -2.0, integral(-2.0));

Outputs:

integral(0.0) = 1.0
integral(1.0) = 1.3333333333333333
integral(-2.0) = -1.6666666666666665