oxictl 0.1.1

Pure Rust Real-Time Control Systems Framework
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
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314

//! Particle Swarm Optimization (PSO) for minimizing f: R^D → R.
//!
//! Uses LCG-based pseudo-random number generation (no rand crate).
//! Generic over scalar type S implementing ControlScalar.

use crate::core::scalar::ControlScalar;
use core::fmt;

// ---------------------------------------------------------------------------
// Error type
// ---------------------------------------------------------------------------

/// Errors produced by bioinspired optimizers.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum OptimError {
    /// A parameter is out of its valid range.
    InvalidParameter,
    /// The optimizer hit the maximum iteration limit without converging.
    MaxIterReached,
}

impl fmt::Display for OptimError {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match self {
            OptimError::InvalidParameter => write!(f, "invalid optimizer parameter"),
            OptimError::MaxIterReached => write!(f, "maximum iterations reached"),
        }
    }
}

// ---------------------------------------------------------------------------
// LCG helper
// ---------------------------------------------------------------------------

/// Linear Congruential Generator returning a uniform float in [0, 1).
#[inline]
fn lcg_next(state: &mut u64) -> f64 {
    *state = state
        .wrapping_mul(6_364_136_223_846_793_005)
        .wrapping_add(1_442_695_040_888_963_407);
    (*state >> 11) as f64 / (1u64 << 53) as f64
}

// ---------------------------------------------------------------------------
// ParticleSwarm
// ---------------------------------------------------------------------------

/// Particle Swarm Optimizer with `N` particles in `D` dimensions.
///
/// Minimises an objective function `f: R^D → R` using velocity-position
/// updates driven by personal and global bests.
pub struct ParticleSwarm<S, const D: usize, const N: usize> {
    positions: [[S; D]; N],
    velocities: [[S; D]; N],
    pbest_pos: [[S; D]; N],
    pbest_val: [S; N],
    gbest_pos: [S; D],
    gbest_val: S,
    w: S,
    c1: S,
    c2: S,
    bounds_min: [S; D],
    bounds_max: [S; D],
    lcg: u64,
    iteration: usize,
}

impl<S: ControlScalar, const D: usize, const N: usize> ParticleSwarm<S, D, N> {
    /// Create a new PSO instance.
    ///
    /// * `bounds_min` / `bounds_max` — search space bounds (per dimension).
    /// * `w`  — inertia weight; must be in `(0, 1.5)`.
    /// * `c1` — cognitive coefficient (> 0, typically ~2).
    /// * `c2` — social coefficient   (> 0, typically ~2).
    /// * `seed` — LCG seed.
    pub fn new(
        bounds_min: [S; D],
        bounds_max: [S; D],
        w: S,
        c1: S,
        c2: S,
        seed: u64,
    ) -> Result<Self, OptimError> {
        if w <= S::ZERO || w >= S::from_f64(1.5) {
            return Err(OptimError::InvalidParameter);
        }
        if c1 <= S::ZERO || c2 <= S::ZERO {
            return Err(OptimError::InvalidParameter);
        }

        let mut lcg = seed;

        // Initialise positions uniformly in [bounds_min, bounds_max].
        let mut positions = [[S::ZERO; D]; N];
        for particle in positions.iter_mut() {
            for d in 0..D {
                let r = S::from_f64(lcg_next(&mut lcg));
                particle[d] = bounds_min[d] + r * (bounds_max[d] - bounds_min[d]);
            }
        }

        let velocities = [[S::ZERO; D]; N];
        let pbest_pos = positions;
        let pbest_val = [S::infinity(); N];
        let gbest_pos = positions[0];
        let gbest_val = S::infinity();

        Ok(Self {
            positions,
            velocities,
            pbest_pos,
            pbest_val,
            gbest_pos,
            gbest_val,
            w,
            c1,
            c2,
            bounds_min,
            bounds_max,
            lcg,
            iteration: 0,
        })
    }

    /// Perform one PSO iteration.
    ///
    /// Evaluates `f` for every particle, updates personal/global bests,
    /// then integrates the velocity-position equations.
    pub fn step<F: Fn(&[S; D]) -> S>(&mut self, f: &F) -> Result<(), OptimError> {
        for i in 0..N {
            // ---- evaluate ----
            let val = f(&self.positions[i]);

            // ---- update personal best ----
            if val < self.pbest_val[i] {
                self.pbest_val[i] = val;
                self.pbest_pos[i] = self.positions[i];
            }

            // ---- update global best ----
            if val < self.gbest_val {
                self.gbest_val = val;
                self.gbest_pos = self.positions[i];
            }

            // ---- velocity / position update ----
            let r1 = S::from_f64(lcg_next(&mut self.lcg));
            let r2 = S::from_f64(lcg_next(&mut self.lcg));

            for d in 0..D {
                let cognitive = self.c1 * r1 * (self.pbest_pos[i][d] - self.positions[i][d]);
                let social = self.c2 * r2 * (self.gbest_pos[d] - self.positions[i][d]);

                self.velocities[i][d] = self.w * self.velocities[i][d] + cognitive + social;

                let new_pos = self.positions[i][d] + self.velocities[i][d];
                self.positions[i][d] = new_pos.clamp_val(self.bounds_min[d], self.bounds_max[d]);
            }
        }

        self.iteration += 1;
        Ok(())
    }

    /// Run the optimiser for `max_iter` iterations.
    ///
    /// Returns `(best_value, best_position)`.
    pub fn optimize<F: Fn(&[S; D]) -> S>(
        &mut self,
        f: &F,
        max_iter: usize,
    ) -> Result<(S, [S; D]), OptimError> {
        for _ in 0..max_iter {
            self.step(f)?;
        }
        Ok((self.gbest_val, self.gbest_pos))
    }

    /// Returns a reference to the current global-best position.
    #[inline]
    pub fn best_position(&self) -> &[S; D] {
        &self.gbest_pos
    }

    /// Returns the current global-best objective value.
    #[inline]
    pub fn best_value(&self) -> S {
        self.gbest_val
    }

    /// Returns the number of completed iterations.
    #[inline]
    pub fn iteration(&self) -> usize {
        self.iteration
    }
}

// ---------------------------------------------------------------------------
// Tests
// ---------------------------------------------------------------------------

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

    // ---- helper: Rosenbrock (2D) ------------------------------------------
    fn rosenbrock(x: &[f64; 2]) -> f64 {
        let a = 1.0 - x[0];
        let b = x[1] - x[0] * x[0];
        a * a + 100.0 * b * b
    }

    // 1. Minimize f(x) = x^2 (1D) → should converge to 0
    #[test]
    fn pso_minimize_x_squared() {
        let bounds_min = [-5.0_f64];
        let bounds_max = [5.0_f64];
        let mut pso = ParticleSwarm::<f64, 1, 20>::new(bounds_min, bounds_max, 0.7, 2.0, 2.0, 42)
            .expect("valid params");

        let (best_val, _) = pso
            .optimize(&|x: &[f64; 1]| x[0] * x[0], 300)
            .expect("optimize ok");

        assert!(best_val < 0.01, "best_val={best_val}");
    }

    // 2. Minimize f(x,y) = (x-2)^2 + (y+1)^2 → converges to (2, -1)
    #[test]
    fn pso_minimize_2d() {
        let bounds_min = [-5.0_f64; 2];
        let bounds_max = [5.0_f64; 2];
        let mut pso = ParticleSwarm::<f64, 2, 30>::new(bounds_min, bounds_max, 0.7, 2.0, 2.0, 123)
            .expect("valid params");

        let obj = |x: &[f64; 2]| {
            let dx = x[0] - 2.0;
            let dy = x[1] + 1.0;
            dx * dx + dy * dy
        };
        let (_, best_pos) = pso.optimize(&obj, 500).expect("optimize ok");
        assert!((best_pos[0] - 2.0).abs() < 0.1, "x={}", best_pos[0]);
        assert!((best_pos[1] + 1.0).abs() < 0.1, "y={}", best_pos[1]);
    }

    // 3. Invalid inertia weight w=0.0 → InvalidParameter
    #[test]
    fn pso_invalid_w_zero() {
        let result = ParticleSwarm::<f64, 1, 10>::new([-1.0], [1.0], 0.0, 2.0, 2.0, 1);
        assert!(matches!(result, Err(OptimError::InvalidParameter)));
    }

    // 4. Best value must be non-increasing over steps
    #[test]
    fn pso_best_value_decreases() {
        let mut pso = ParticleSwarm::<f64, 2, 20>::new([-5.0; 2], [5.0; 2], 0.7, 2.0, 2.0, 7)
            .expect("valid params");

        let obj = |x: &[f64; 2]| x[0] * x[0] + x[1] * x[1];
        let mut prev = f64::INFINITY;
        for _ in 0..20 {
            pso.step(&obj).expect("step ok");
            let cur = pso.best_value();
            assert!(cur <= prev + 1e-12, "best went up: {prev} → {cur}");
            prev = cur;
        }
    }

    // 5. All particle positions must remain within bounds after many steps
    #[test]
    fn pso_bounds_respected() {
        let lo = [-3.0_f64; 2];
        let hi = [3.0_f64; 2];
        let mut pso =
            ParticleSwarm::<f64, 2, 20>::new(lo, hi, 0.7, 2.0, 2.0, 99).expect("valid params");

        let obj = |x: &[f64; 2]| x[0] * x[0] + x[1] * x[1];
        pso.optimize(&obj, 100).expect("optimize ok");

        // gbest must be inside bounds
        let pos = pso.best_position();
        for d in 0..2 {
            assert!(pos[d] >= lo[d] && pos[d] <= hi[d], "dim {d} out of bounds");
        }
    }

    // 6. Rosenbrock: minimum at (1, 1), value 0
    #[test]
    fn pso_rosenbrock() {
        let bounds_min = [-2.0_f64; 2];
        let bounds_max = [2.0_f64; 2];
        let mut pso = ParticleSwarm::<f64, 2, 40>::new(bounds_min, bounds_max, 0.7, 1.5, 1.5, 314)
            .expect("valid params");

        let (_, best_pos) = pso.optimize(&rosenbrock, 800).expect("optimize ok");
        assert!(
            (best_pos[0] - 1.0).abs() < 0.5 && (best_pos[1] - 1.0).abs() < 0.5,
            "best={best_pos:?}"
        );
    }

    // 7. Same seed → identical results
    #[test]
    fn pso_seed_reproducibility() {
        let make =
            || ParticleSwarm::<f64, 1, 10>::new([-5.0], [5.0], 0.7, 2.0, 2.0, 55).expect("valid");
        let mut a = make();
        let mut b = make();
        let obj = |x: &[f64; 1]| x[0] * x[0];
        let (va, _) = a.optimize(&obj, 50).expect("ok");
        let (vb, _) = b.optimize(&obj, 50).expect("ok");
        assert!((va - vb).abs() < 1e-15, "seeds differ: {va} vs {vb}");
    }
}