6 releases
0.2.2 | Nov 11, 2024 |
---|---|
0.2.1 | Oct 11, 2024 |
0.1.2 | Feb 28, 2022 |
#461 in Math
498 downloads per month
Used in spdcalc
97KB
2K
SLoC
quad-rs
This crate provides an implementation of adaptive Gauss-Kronrod integration. It aims to provide a suite of integration methods including:
- Adaptive integration with high-accuracy
- Native support for complex integrals and paths
- Native support for contour integration in the complex plane
- Native support for integration of vector and scalar valued functions
- Optional storage and return of the integrand at the evaluation points
Overview
A problem to be integrated needs to implement the Integrable
trait. This has one method integrand
, which takes the integration variable as an argument and returns the integrand. The type of the integration variable Input
and the integrand Output
must also be defined.
use quad_rs::Integrable;
struct Problem {}
impl Integrable for Problem {
type Input = f64;
type Output = f64;
fn integrand(
&self,
input: &Self::Input,
) -> Result<Self::Output, quad_rs::EvaluationError<Self::Input>> {
Ok(input.exp())
}
}
To solve the problem an Integrator
is used
use quad_rs::Integrator;
let integrator = Integrator::default()
.with_maximum_iter(1000)
.relative_tolerance(1e-8);
let range = std::ops::Range {
start: (-1f64),
end: 1f64,
};
let solution = integrator.integrate(Problem {}, range).unwrap();
Example - Real Integration
use quad_rs::{Integrable, Integrator};
struct Problem {}
impl Integrable for Problem {
type Input = f64;
type Output = f64;
fn integrand(
&self,
input: &Self::Input,
) -> Result<Self::Output, quad_rs::EvaluationError<Self::Input>> {
Ok(input.exp())
}
}
let integrator = Integrator::default()
.with_maximum_iter(1000)
.relative_tolerance(1e-8);
let range = std::ops::Range {
start: (-1f64),
end: 1f64,
};
let solution = integrator.integrate(Problem {}, range).unwrap();
let analytical_result = std::f64::consts::E - 1. / std::f64::consts::E;
approx::assert_relative_eq!(
solution.result.result.unwrap(),
analytical_result,
max_relative = 1e-10
)
Example - Complex Integration
use quad_rs::{Integrable, Integrator};
use num_complex::Complex;
use std::ops::Range;
struct Problem {}
impl Integrable for Problem {
type Input = Complex<f64>;
type Output = Complex<f64>;
fn integrand(
&self,
input: &Self::Input,
) -> Result<Self::Output, quad_rs::EvaluationError<Self::Input>> {
Ok(input.exp())
}
}
let integrator = Integrator::default()
.with_maximum_iter(1000)
.relative_tolerance(1e-8);
let range = Range {
start: Complex::new(-1f64, -1f64),
end: Complex::new(1f64, 1f64)
};
let solution = integrator.integrate(Problem {}, range).unwrap();
Example - Real to Complex Integration
use quad_rs::{Integrable, Integrator};
use num_complex::Complex;
use std::ops::Range;
struct Problem {}
impl Integrable for Problem {
type Input = f64;
type Output = Complex<f64>;
fn integrand(
&self,
input: &Self::Input,
) -> Result<Self::Output, quad_rs::EvaluationError<Self::Input>> {
Ok(input.exp())
}
}
let integrator = Integrator::default()
.with_maximum_iter(1000)
.relative_tolerance(1e-8);
let range = Range {
start: (-1f64),
end: 1f64,
};
let solution = integrator
.integrate_real_complex(Problem {}, range)
.unwrap();
let result = solution.result.result.unwrap();
let analytical_result = std::f64::consts::E - 1. / std::f64::consts::E;
dbg!(&result, &analytical_result);
Example - Contour Integration
use quad_rs::{Contour, Direction, Integrable, Integrator}
use num_complex::Complex;
let x_range =-5f64..5f64;
let y_range = -5f64..5f64;
let contour = Contour::generate_rectangular(&x_range, &y_range, Direction::Clockwise);
struct Problem {}
impl Integrable for Problem {
type Input = Complex<f64>;
type Output = Complex<f64>;
fn integrand(
&self,
input: &Self::Input,
) -> Result<Self::Output, quad_rs::EvaluationError<Self::Input>> {
Ok(input.exp())
}
}
let integrator = Integrator::default()
.with_maximum_iter(1000)
.relative_tolerance(1e-8);
let solution = integrator.contour_integrate(Problem {}, contour).unwrap();
Dependencies
~7MB
~142K SLoC