nalgebra/tests/linalg/exp.rs

98 lines
3.1 KiB
Rust

#[cfg(test)]
mod tests {
//https://github.com/scipy/scipy/blob/c1372d8aa90a73d8a52f135529293ff4edb98fc8/scipy/sparse/linalg/tests/test_matfuncs.py
#[test]
fn exp() {
use nalgebra::{Matrix1, Matrix2, Matrix3};
{
let m = Matrix1::new(1.0);
let f = m.exp();
assert_eq!(f, Matrix1::new(1_f64.exp()));
}
{
let m = Matrix2::new(0.0, 1.0, 0.0, 0.0);
assert_eq!(m.exp(), Matrix2::new(1.0, 1.0, 0.0, 1.0));
}
{
let a: f64 = 1.0;
let b: f64 = 2.0;
let c: f64 = 3.0;
let d: f64 = 4.0;
let m = Matrix2::new(a, b, c, d);
let delta = ((a - d).powf(2.0) + 4.0 * b * c).sqrt();
let delta_2 = delta / 2.0;
let ad_2 = (a + d) / 2.0;
let m11 = ad_2.exp() * (delta * delta_2.cosh() + (a - d) * delta_2.sinh());
let m12 = 2.0 * b * ad_2.exp() * delta_2.sinh();
let m21 = 2.0 * c * ad_2.exp() * delta_2.sinh();
let m22 = ad_2.exp() * (delta * delta_2.cosh() + (d - a) * delta_2.sinh());
let f = Matrix2::new(m11, m12, m21, m22) / delta;
assert!((f - m.exp()).iter().all(|v| v.abs() <= 0.00005));
}
{
// https://mathworld.wolfram.com/MatrixExponential.html
use rand::{
distributions::{Distribution, Uniform},
thread_rng,
};
let mut rng = thread_rng();
let dist = Uniform::new(-10.0, 10.0);
loop {
let a: f64 = dist.sample(&mut rng);
let b: f64 = dist.sample(&mut rng);
let c: f64 = dist.sample(&mut rng);
let d: f64 = dist.sample(&mut rng);
let m = Matrix2::new(a, b, c, d);
let delta_sq = (a - d).powf(2.0) + 4.0 * b * c;
if delta_sq < 0.0 {
continue;
}
let delta = delta_sq.sqrt();
let delta_2 = delta / 2.0;
let ad_2 = (a + d) / 2.0;
let m11 = ad_2.exp() * (delta * delta_2.cosh() + (a - d) * delta_2.sinh());
let m12 = 2.0 * b * ad_2.exp() * delta_2.sinh();
let m21 = 2.0 * c * ad_2.exp() * delta_2.sinh();
let m22 = ad_2.exp() * (delta * delta_2.cosh() + (d - a) * delta_2.sinh());
let f = Matrix2::new(m11, m12, m21, m22) / delta;
println!("a: {}", m);
assert!((f - m.exp()).iter().all(|v| v.abs() <= 0.00005));
break;
}
}
{
let m = Matrix3::new(1.0, 3.0, 0.0, 0.0, 1.0, 5.0, 0.0, 0.0, 2.0);
let e1 = 1.0_f64.exp();
let e2 = 2.0_f64.exp();
let f = Matrix3::new(
e1,
3.0 * e1,
15.0 * (e2 - 2.0 * e1),
0.0,
e1,
5.0 * (e2 - e1),
0.0,
0.0,
e2,
);
assert!((f - m.exp()).iter().all(|v| v.abs() <= 0.00005));
}
}
}