A Rust crate for scientific processes
This crate is designed to help any mathematical or scientific processes for the Rust community. It compiles many useful concepts and items that are key in scientific applications, such as Bessel functions, statistical analysis, physical constants, etc...
The aim is to provide classical functions in pure Rust, for ease of operability.
As of the creation of this readme, I am working on this project alone which means a few things:
The schedule of the development of the crate is not clear, as I am for now writing this as a side project. I plan on adding many useful functions from a physics point of view, but will expand as I go. For now, my long term objectives are: Astrophysics, Thermodynamics, Quantum mechanics, Electromagnetism.
And hopefully more when this is done (statistics, integration tool, calculus, ...).
The Rust library doesn't provide some functions that are quite common in scientific processes, and this crate attempts to provide as many as it can. Euler's Gamma and Beta function, Newton's binomial, factorial, the error functions (erf, erfc, erfi), ...
```rust // These functions can be found in the math crate use scilib::math::basic::*;
let g = gamma(3.2); let b = beta(-1.2, 2.5);
// The erf function can compute Complex numbers (erfc, erfi as well) let c = Complex::from(-0.1, 0.7); let e = erf(c); ```
This crate provides functionalities for coordinate systems, such as Cartesian and Spherical, with many standard operations and conversions.
```rust // They are found in the coordinate crate use scilib::coordinate::*;
let car = cartesian::Cartesian::from(2.0, 1, 0.25); let sph = spherical::Spherical::fromdegree(1.2, 30, 60.2); let cyl = spherical::Cylindrical::fromdegree(1.2, 30, -2.55); ```
This crate provides basic functionalities for complex numbers, mainly to support its other goals. The implementation uses f64 for both the real and imaginary parts, to ensure precision in the computations.
Basic operations have been implemented to facilitate their use, and should be pretty easy to manipulate.
```rust // They are found in the complex crate use scilib::math::complex::Complex;
let c1 = Complex::from(2, 3.5); let c2 = Complex::from(-1.2, 4) * 2; println!("{}", c1 + c2); ```
More functionalities are on their way, they will be added as they are needed for other domains.
Essential in many maths and physics domain, bessel function are solutions of Bessel's differential equation (Wiki page). This crate provides functions for both real and complex numbers, and for integer or real function order.
All functions are implemented: - J: First kind - Y: Second Kind - I: Modified first kind - K: Modified second kind - H1: Hankel first kind - H2: Hankel second kind - j: Spherical first kind - y: Spherical second kind - h1: Spherical hankel first kind - h2: Spherical hankel second kind
```rust // Found in the math crate use scilib::math::bessel;
// All functions support complex numbers, and real orders let resj = bessel::jf(-1.2, -2.3); // J function; works for any input and order let resy = bessel::y(3.5, 1); // Y function; computes the limit for integer order let resi = bessel::i(7.2, 2.25); // I function; similar to J let resk = bessel::k(-1.1, 0.5); // K function; computes the limit for integer order let res1 = bessel::hankelfirst(2, -2); // Hankel first kind let res2 = bessel::hankelsecond(1, -1.32); // Hankel first kind let ressj = bessel::sj(4.4, 2); // Spherical first kind let ressy = bessel::sy(-1.54, 3); // Spherical second kind let ressj = bessel::shfirst(2.11, 4); // Spherical hankel first kind let ressj = bessel::shsecond(0.253, 0); // Spherical hankel second kind ```
Values are compared to known results (thanks, WolframAlpha), and the results are within small margins of error.
Thanks to Neven for adding the Spherical versions.
Support to conduct both fast Fourier transform (fft) and the inverse fast Fourier transform (ifft) is available. Computations are
done using Bluestein's algorithm. Convolution is also possible,
with any two vector sizes.
```rust // Found in the fourier crate use scilib::signal::*
// Computing values of the sinus
let r = range::linear(0.0, 10.0, 15);
let s: Vec
let res = fft(&s); let res2 = ifft(&res); let res3 = convolve(&r, &s); ```
Useful polynomials will be implemented to facilitate their uses to everyone; as it stands, both the Legendre (Plm(x)) and Laguerre (Llm(x)) polynomials have been implemented, where -l <= m <= l.
```rust // They are found in the polynomial crate use scilib::math::polynomial::*;
// Legendre and Laguerre support derivative (and negative m) let leg = Legendre::new(2, 1); // l=2, m=1 let lag = Laguerre::new(3, -2); // l=3, m=-2
// Standard support for Bernoulli and Euler (numbers and polynomials) let ber = Bernoulli::new(3); // n=3 let eul = Euler::new(5); // n=5 ```
Both the radial wave function Rnl(r) and the spherical harmonics Ylm(theta, phi) have been added to the quantum section. The Ylm is also valid for acoustics as well.
```rust // Found in the quantum crate use scilib::quantum::*;
// Computing Ylm for l=3, m=1, theta = 0.2 and phi = -0.3 let sph = spherical_harmonics(3, 1, 0.2, -0.3);
// Computing the Rnl for n=4, l=2 let rad = radial_wavefunction(4, 2, 1.3e-12); ```