scivex-optim 0.1.1

Scivex — Optimization, root finding, and numerical integration
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132

//! Gradient descent with fixed learning rate.

use scivex_core::{Float, Tensor};

use crate::error::Result;

use super::{MinimizeOptions, MinimizeResult};

/// Minimize `f` using gradient descent with a fixed learning rate.
///
/// The gradient is provided by the `grad` closure. For numerical gradients,
/// use [`numerical_gradient`](super::numerical_gradient) to construct one.
///
/// # Examples
///
/// ```
/// # use scivex_core::Tensor;
/// # use scivex_optim::minimize::{gradient_descent, MinimizeOptions};
/// let f = |x: &Tensor<f64>| { let s = x.as_slice(); s[0] * s[0] };
/// let g = |x: &Tensor<f64>| Tensor::from_vec(vec![2.0 * x.as_slice()[0]], vec![1]).unwrap();
/// let x0 = Tensor::from_vec(vec![5.0_f64], vec![1]).unwrap();
/// let result = gradient_descent(f, g, &x0, &MinimizeOptions::default()).unwrap();
/// assert!(result.f_val < 1e-4);
/// ```
pub fn gradient_descent<T, F, G>(
    f: F,
    grad: G,
    x0: &Tensor<T>,
    options: &MinimizeOptions<T>,
) -> Result<MinimizeResult<T>>
where
    T: Float,
    F: Fn(&Tensor<T>) -> T,
    G: Fn(&Tensor<T>) -> Tensor<T>,
{
    let mut x = x0.clone();
    let mut fx = f(&x);
    let mut f_evals = 1usize;
    let mut g_evals = 0usize;

    for i in 0..options.max_iter {
        let g = grad(&x);
        g_evals += 1;

        // Check gradient norm for convergence
        let grad_norm_sq: T = g.as_slice().iter().map(|&v| v * v).sum();
        let grad_norm = grad_norm_sq.sqrt();

        if grad_norm < options.gtol {
            return Ok(MinimizeResult {
                x,
                f_val: fx,
                grad: Some(g),
                iterations: i + 1,
                f_evals,
                g_evals,
                converged: true,
            });
        }

        // x_new = x - lr * grad
        let step = &g * options.learning_rate;
        let x_new = &x - &step;
        let fx_new = f(&x_new);
        f_evals += 1;

        // Check function value change
        let f_change = (fx - fx_new).abs();
        x = x_new;
        fx = fx_new;

        if f_change < options.ftol {
            return Ok(MinimizeResult {
                x,
                f_val: fx,
                grad: Some(g),
                iterations: i + 1,
                f_evals,
                g_evals,
                converged: true,
            });
        }
    }

    let g = grad(&x);
    g_evals += 1;
    Ok(MinimizeResult {
        x,
        f_val: fx,
        grad: Some(g),
        iterations: options.max_iter,
        f_evals,
        g_evals,
        converged: false,
    })
}

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

    #[test]
    fn test_gradient_descent_quadratic() {
        // f(x, y) = x^2 + y^2, grad = (2x, 2y)
        let f = |x: &Tensor<f64>| {
            let s = x.as_slice();
            s[0] * s[0] + s[1] * s[1]
        };
        let grad = |x: &Tensor<f64>| {
            let s = x.as_slice();
            Tensor::from_vec(vec![2.0 * s[0], 2.0 * s[1]], vec![2]).unwrap()
        };

        let x0 = Tensor::from_vec(vec![5.0, 5.0], vec![2]).unwrap();
        let opts = MinimizeOptions {
            learning_rate: 0.1,
            max_iter: 500,
            gtol: 1e-6,
            ..MinimizeOptions::default()
        };

        let result = gradient_descent(f, grad, &x0, &opts).unwrap();
        assert!(
            result.converged,
            "did not converge after {} iters",
            result.iterations
        );
        let s = result.x.as_slice();
        assert!(s[0].abs() < 1e-4, "x = {}", s[0]);
        assert!(s[1].abs() < 1e-4, "y = {}", s[1]);
    }
}