Function beta_simd

Source

pub fn beta_simd<F>(a: &ArrayView1<'_, F>, b: &ArrayView1<'_, F>) -> Array1<F>where
    F: Float + SimdUnifiedOps,

Expand description

Compute the Beta function B(a, b) using SIMD operations

The Beta function is defined as: B(a, b) = Γ(a)Γ(b) / Γ(a+b)

This function computes B(a[i], b[i]) for each pair of elements. The Beta function is fundamental in:

Beta distribution (Bayesian priors for probabilities)
Binomial coefficients: C(n,k) = 1/((n+1)·B(n-k+1, k+1))
Statistical hypothesis testing
Machine learning (Dirichlet processes)

§Mathematical Properties

B(a, b) = B(b, a) (symmetric)
B(1, 1) = 1
B(a, 1) = 1/a
B(1, b) = 1/b
B(a, b) = B(a+1, b) + B(a, b+1)

§Arguments

a - First parameter array (must be > 0)
b - Second parameter array (must be > 0, same length as a)

§Returns

Array with B(a[i], b[i]) for each pair

§Example

use scirs2_core::ndarray_ext::elementwise::beta_simd;
use ndarray::{array, ArrayView1};

let a = array![1.0_f64, 2.0, 0.5];
let b = array![1.0_f64, 2.0, 0.5];
let result = beta_simd(&a.view(), &b.view());
assert!((result[0] - 1.0).abs() < 1e-10);       // B(1,1) = 1
assert!((result[1] - 1.0/6.0).abs() < 1e-10);  // B(2,2) = 1/6
assert!((result[2] - std::f64::consts::PI).abs() < 1e-8);  // B(0.5,0.5) = π

§Applications

Beta Distribution: PDF = x^(a-1)(1-x)^(b-1) / B(a,b)
Bayesian Statistics: Prior/posterior for probability parameters
A/B Testing: Conversion rate analysis
Machine Learning: Dirichlet processes, topic modeling

beta_simd