sl: A scientific library

Analysis package

• na
  • diff (numerical differentiation)
  • quad (numerical integration)
  • ode (ordinary differential equations)
  • interpolation (obtain functions from data)

Mathematical functions package

• mf (mathematical functions)
  • sf (special functions)

See Implementation of special functions.

Plotting package

• gx
  • Canvas (a canvas to draw)

Example

```rust extern crate sl;

use sl::na::quad::gauss; use sl::na::ode::euler;

// Calculate ln(x) = integral(1 to x) 1/t dt // by Gaussian quadrature. fn ln(x: f64) -> f64 { return gauss(&|t| 1.0/t, 1.0, x, 10); }

fn main() { // Calculate exp(x) from the ODE y'=y by the Euler method. // We have y'=g(x,y), g(x,y)=y. let g = |_,y| y; let x0 = 0.0; let y0 = 1.0; let h = 0.001; let n = 10000;

let exp = euler(Box::new(g),x0,y0,h,0,n);

for i in 1..6 {
    let x = i as f64;
    println!("{:8.4} |{:8.4} |{:8.4} |{:8.4}",x,ln(x),exp(x),exp(ln(x)));
}

}

// Output: // 1.0000 | 0.0000 | 2.7169 | 1.0000 // 2.0000 | 0.6931 | 7.3817 | 1.9993 // 3.0000 | 1.0986 | 20.0555 | 2.9984 // 4.0000 | 1.3863 | 54.4891 | 3.9972 // 5.0000 | 1.6094 |148.0428 | 4.9960 ```