Struct rstat::UnitSimplex

pub struct UnitSimplex(_);

Utility for sampling from a unit \(K\)-simplex.

Methods

impl UnitSimplex

pub fn new(n: usize) -> UnitSimplex

Construct a \(K = n + 1\) probability simplex.

pub fn centre(&self) -> SimplexVector

Compute the central point of the simplex \(x_i = 1 / K\).

Examples

use rstat::UnitSimplex;

let s = UnitSimplex::new(2).centre();

for i in 0..3 {
    assert_eq!(s[i], 1.0 / 3.0);
}

pub fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> SimplexVector

Draws a uniformly random point on the simplex.

This algorithm works as follows:

1. Draw \(K\) independent points, \(x_i \in [0, 1]\), uniformly at random.
2. Apply the transformation \(z_i = -\ln{x_i}\).
3. Compute the sum \(s = \sum_i x_i\).
4. Return the vector of values \(z_i / s\).

Examples

use rand::thread_rng;
use rstat::UnitSimplex;

let s = UnitSimplex::new(2).sample(&mut thread_rng());

assert!((s.iter().sum::<f64>() - 1.0).abs() < 1e-7);

Trait Implementations

impl Clone for UnitSimplex

fn clone(&self) -> UnitSimplex

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for UnitSimplex

impl Debug for UnitSimplex

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.