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[pull] master from TheAlgorithms:master #207

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Merged
pull merged 1 commit into AlgorithmAndLeetCode:master from TheAlgorithms:master
Oct 26, 2025
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1 change: 1 addition & 0 deletions DIRECTORY.md
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Original file line number Diff line number Diff line change
Expand Up @@ -174,6 +174,7 @@
* Optimization
* [Adam](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/optimization/adam.rs)
* [Gradient Descent](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/optimization/gradient_descent.rs)
* [Momentum](https://github.com/TheAlgorithms/Rust/blob/master/src/machine_learning/optimization/momentum.rs)
* Math
* [Abs](https://github.com/TheAlgorithms/Rust/blob/master/src/math/abs.rs)
* [Aliquot Sum](https://github.com/TheAlgorithms/Rust/blob/master/src/math/aliquot_sum.rs)
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1 change: 1 addition & 0 deletions src/machine_learning/optimization/mod.rs
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mod adam;
mod gradient_descent;
mod momentum;

pub use self::adam::Adam;
pub use self::gradient_descent::gradient_descent;
144 changes: 144 additions & 0 deletions src/machine_learning/optimization/momentum.rs
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/// Momentum Optimization
///
/// Momentum is an extension of gradient descent that accelerates convergence by accumulating
/// a velocity vector in directions of persistent reduction in the objective function.
/// This helps the optimizer navigate ravines and avoid getting stuck in local minima.
///
/// The algorithm maintains a velocity vector that accumulates exponentially decaying moving
/// averages of past gradients. This allows the optimizer to build up speed in consistent
/// directions while dampening oscillations.
///
/// The update equations are:
/// velocity_{k+1} = beta * velocity_k + gradient_of_function(x_k)
/// x_{k+1} = x_k - learning_rate * velocity_{k+1}
///
/// where beta (typically 0.9) controls how much past gradients influence the current update.
///
/// # Arguments
///
/// * `derivative_fn` - The function that calculates the gradient of the objective function at a given point.
/// * `x` - The initial parameter vector to be optimized.
/// * `learning_rate` - Step size for each iteration.
/// * `beta` - Momentum coefficient (typically 0.9). Higher values give more weight to past gradients.
/// * `num_iterations` - The number of iterations to run the optimization.
///
/// # Returns
///
/// A reference to the optimized parameter vector `x`.
#[allow(dead_code)]
pub fn momentum(
derivative: impl Fn(&[f64]) -> Vec<f64>,
x: &mut Vec<f64>,
learning_rate: f64,
beta: f64,
num_iterations: i32,
) -> &mut Vec<f64> {
// Initialize velocity vector to zero
let mut velocity: Vec<f64> = vec![0.0; x.len()];

for _ in 0..num_iterations {
let gradient = derivative(x);

// Update velocity and parameters
for ((x_k, vel), grad) in x.iter_mut().zip(velocity.iter_mut()).zip(gradient.iter()) {
*vel = beta * *vel + grad;
*x_k -= learning_rate * *vel;
}
}
x
}

#[cfg(test)]
mod test {
use super::*;

#[test]
fn test_momentum_optimized() {
fn derivative_of_square(params: &[f64]) -> Vec<f64> {
params.iter().map(|x| 2.0 * x).collect()
}

let mut x: Vec<f64> = vec![5.0, 6.0];
let learning_rate: f64 = 0.01;
let beta: f64 = 0.9;
let num_iterations: i32 = 1000;

let minimized_vector = momentum(
derivative_of_square,
&mut x,
learning_rate,
beta,
num_iterations,
);

let test_vector = [0.0, 0.0];
let tolerance = 1e-6;

for (minimized_value, test_value) in minimized_vector.iter().zip(test_vector.iter()) {
assert!((minimized_value - test_value).abs() < tolerance);
}
}

#[test]
fn test_momentum_unoptimized() {
fn derivative_of_square(params: &[f64]) -> Vec<f64> {
params.iter().map(|x| 2.0 * x).collect()
}

let mut x: Vec<f64> = vec![5.0, 6.0];
let learning_rate: f64 = 0.01;
let beta: f64 = 0.9;
let num_iterations: i32 = 10;

let minimized_vector = momentum(
derivative_of_square,
&mut x,
learning_rate,
beta,
num_iterations,
);

let test_vector = [0.0, 0.0];
let tolerance = 1e-6;

for (minimized_value, test_value) in minimized_vector.iter().zip(test_vector.iter()) {
assert!((minimized_value - test_value).abs() >= tolerance);
}
}

#[test]
fn test_momentum_faster_than_gd() {
fn derivative_of_square(params: &[f64]) -> Vec<f64> {
params.iter().map(|x| 2.0 * x).collect()
}

// Test that momentum converges faster than gradient descent
let mut x_momentum: Vec<f64> = vec![5.0, 6.0];
let mut x_gd: Vec<f64> = vec![5.0, 6.0];
let learning_rate: f64 = 0.01;
let beta: f64 = 0.9;
let num_iterations: i32 = 50;

momentum(
derivative_of_square,
&mut x_momentum,
learning_rate,
beta,
num_iterations,
);

// Gradient descent from your original implementation
for _ in 0..num_iterations {
let gradient = derivative_of_square(&x_gd);
for (x_k, grad) in x_gd.iter_mut().zip(gradient.iter()) {
*x_k -= learning_rate * grad;
}
}

// Momentum should be closer to zero
let momentum_distance: f64 = x_momentum.iter().map(|x| x * x).sum();
let gd_distance: f64 = x_gd.iter().map(|x| x * x).sum();

assert!(momentum_distance < gd_distance);
}
}

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