gaussian_quadrature

DIRECTORY.md

@@ -184,6 +184,7 @@
     * [Frizzy Number](https://github.com/TheAlgorithms/Rust/blob/master/src/math/frizzy_number.rs)
     * [Gaussian Elimination](https://github.com/TheAlgorithms/Rust/blob/master/src/math/gaussian_elimination.rs)
     * [Gaussian Error Linear Unit](https://github.com/TheAlgorithms/Rust/blob/master/src/math/gaussian_error_linear_unit.rs)
+    * [Gaussian_quadrature](https://github.com/Rust/blob/new-feature-branch/src/math/gaussian_quadrature.rs)
     * [Gcd Of N Numbers](https://github.com/TheAlgorithms/Rust/blob/master/src/math/gcd_of_n_numbers.rs)
     * [Geometric Series](https://github.com/TheAlgorithms/Rust/blob/master/src/math/geometric_series.rs)
     * [Greatest Common Divisor](https://github.com/TheAlgorithms/Rust/blob/master/src/math/greatest_common_divisor.rs)

src/math/gaussian_quadrature.rs

@@ -0,0 +1,51 @@
+// Gaussian Quadrature Module
+// https://en.wikipedia.org/wiki/Gaussian_quadrature
+
+pub fn gaussian_quadrature(a: f64, b: f64, f: impl Fn(f64) -> f64, order: usize) -> f64 {
+    let (points, weights) = get_gaussian_quadrature_points_weights(order);
+
+    let result: f64 = points
+        .iter()
+        .zip(weights.iter())
+        .map(|(&point, &weight)| {
+            let x_i = 0.5 * ((a + b) + (b - a) * point);
+            weight * f(x_i)
+        })
+        .sum();
+
+    0.5 * (b - a) * result
+}
+
+fn get_gaussian_quadrature_points_weights(num_points: usize) -> (Vec<f64>, Vec<f64>) {
+    // Hardcoded values for Gaussian Quadrature points and weights
+    match num_points {
+        1 => (vec![0.0], vec![2.0]),
+        2 => (vec![-1.0 / 3.0, 1.0 / 3.0], vec![1.0, 1.0]),
+        3 => (
+            vec![-0.7745966692414834, 0.0, 0.7745966692414834],
+            vec![0.5555555555555556, 0.8888888888888888, 0.5555555555555556],
+        ),
+        _ => unimplemented!("Gaussian Quadrature not implemented for this number of points"),
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_gaussian_quadrature_basic() {
+        let a = 0.0;
+        let b = 1.0;
+        let f = |x: f64| x.powi(2);
+        let order = 3;
+        let expected = 1.0 / 3.0;
+        let eps = 0.0001;
+
+        let result = gaussian_quadrature(a, b, f, order);
+        assert!((result - expected).abs() < eps);
+
+        let result_neg = gaussian_quadrature(b, a, f, order);
+        assert!((result_neg + expected).abs() < eps);
+    }
+}

src/math/mod.rs

@@ -30,6 +30,7 @@ mod field;
 mod frizzy_number;
 mod gaussian_elimination;
 mod gaussian_error_linear_unit;
+mod gaussian_quadrature;
 mod gcd_of_n_numbers;
 mod geometric_series;
 mod greatest_common_divisor;
@@ -115,6 +116,7 @@ pub use self::field::{Field, PrimeField};
 pub use self::frizzy_number::get_nth_frizzy;
 pub use self::gaussian_elimination::gaussian_elimination;
 pub use self::gaussian_error_linear_unit::gaussian_error_linear_unit;
+pub use self::gaussian_quadrature::gaussian_quadrature;
 pub use self::gcd_of_n_numbers::gcd;
 pub use self::geometric_series::geometric_series;
 pub use self::greatest_common_divisor::{