1 unstable release
0.11.0 | Aug 26, 2021 |
---|
#564 in Science
Used in soco
575KB
13K
SLoC
Scientific Computing in Rust
Features
- Initial value problem solving
- Root finding algorithms
- Polynomials
- Polynomial Interpolation
- Scientific Constants
- Special functions/polynomials
- Numeric quadrature
- Numeric differentiation
Explanations of the features can be found here.
Initial Value Problems
There are two adaptive Runge-Kutta methods, two
Adams predictor-correctors, and two adaptive Backwards Differentiation
Formulas implemented. The interface to all of the solvers is the same.
As an example, this code solves y' = y
using the Runge-Kutta-Fehlberg
method.
use bacon_sci::ivp::{RK45, RungeKuttaSolver};
use nalgebra::{VectorN, U1};
fn deriv(_t: f64, y: &[f64], _params: &mut ()) -> Result<VectorN<f64, U1>, String> {
Ok(VectorN::<f64, U1>::from_column_slice(y))
}
fn solve() -> Result<(), String> {
let solver = RK45::new()
.with_dt_min(0.01)?
.with_dt_max(0.1)?
.with_tolerance(1e-4)?
.with_initial_conditions(&[1.0])?
.with_start(0.0)?
.with_end(10.0)?
.build();
let _solution = solver.solve_ivp(deriv, &mut ())?;
Ok(())
}
There is also a solve_ivp
function in bacon_sci::ivp
that tries a fifth-order
predictor-corrector followed by the Runge-Kutta-Fehlberg method followed by
BDF6.
Root Finding Algorithms
bacon_sci::roots
implements the bisection method, Newton's method,
the secant method, Newton's method for polynomials, and Müller's method
for polynomials.
As an example, the following code snippet finds the root of x^3
using
initial guesses of 0.1
and -0.1
.
use bacon_sci::roots::secant;
use nalgebra::{VectorN, U1};
fn cubic(x: &[f64]) -> VectorN<f64, U1> {
VectorN::<f64, U1>::from_iterator(x.iter.map(|x| x.powi(3)))
}
fn solve() -> f64 {
secant((&[-0.1], &[0.1]), cubic, 0.001, 1000).unwrap()
}
Polynomials and Polynomial Interpolation
bacon_sci::polynomial
implements a polynomial struct. bacon_sci::interp
implements
Lagrange interpolation, Hermite interpolation, and cubic spline interpolation.
Scientific Constants
Several scientific constants are defined in bacon_sci::constants
. The data
comes from NIST. The 2018 CODATA complete listing is available as a hashmap.
Special Functions and Polynomials
Currently, bacon_sci::special
allows you to get Legendre polynomials, Hermite polynomials,
Laguerre polynomials, and Chebyshev polynomials.
Numeric Differentiation and Quadrature
bacon_sci::differentiate
allows first- and second-derivative evaluation numerically.
bacon_sci::integrate
implements Tanh-Sinh quadrature, adaptive Simpson's rule,
Romberg integration, and several adaptive Gaussian integration schemes.
Dependencies
~5MB
~96K SLoC