Library of well known algorithms for numerical root finding.
[](https://opensource.org/licenses/BSD-2-Clause)[](https://travis-ci.com/vorot/roots)[](https://crates.io/crates/roots)
## Features
- Iterative approximation:
- [Newton-Raphson](https://en.wikipedia.org/wiki/Newton%27s_method) method
- [Secant](https://en.wikipedia.org/wiki/Secant_method) method
- [Regula falsi](https://en.wikipedia.org/wiki/False_position_method) method (with Illinois modification)
- [Brent-Dekker](https://en.wikipedia.org/wiki/Brent%27s_method) method
- [Inverse quadratic](https://en.wikipedia.org/wiki/Inverse_quadratic_interpolation) approximation
- Recursive [Sturm's](https://en.wikipedia.org/wiki/Sturm%27s_theorem) method
- Solving polynomial equations
- [Linear](https://en.wikipedia.org/wiki/Linear_equation) equation (editors' choice)
- [Quadratic](https://en.wikipedia.org/wiki/Quadratic_equation) equation
- [Cubic](https://en.wikipedia.org/wiki/Cubic_function) equation
- [Quartic](https://en.wikipedia.org/wiki/Quartic_function) equation
- [Eigenvalues](https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors) method for higher-degree polynomials
## Usage
```rust
extern crate roots;
use roots::Roots;
use roots::find_roots_cubic;
use roots::find_root_brent;
use roots::find_root_secant;
// Find the root of a complex function in the area determined by a simpler polynom
fn find_solution<F>(enormous_function: F, root_area_polynom:(f64,f64,f64,f64)) -> Option<f64>
where F: Fn(f64) -> f64
{
// de-structure polynom coefficients
match root_area_polynom {
(a3,a2,a1,a0) => {
// Find root area by solving the polynom
match find_roots_cubic(a3,a2,a1,a0) {
// Try to find the root by one of iterative methods
Roots::Three(roots) => {
// Three roots found, normal case
find_root_brent(roots[0],roots[2],enormous_function, &mut 1e-8f64).ok()
},
Roots::Two(roots) => {
// Two roots found, High precision required
find_root_brent(roots[0],roots[1],enormous_function,&mut 1e-15f64).ok()
},
Roots::One(roots) => {
// One root found, Low precision is enough
find_root_secant(roots[0]-1f64,roots[0]+1f64,enormous_function,&mut 1e-3f64).ok()
},
_ => None,
}
},
_ => None,
}
}
```