basin 1.10.0

Numerical optimization in pure Rust, with pluggable linear-algebra backends and WASM support.
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

// `!(a > b)` comparisons below are deliberate NaN-preserving ports of PRIMA's
// `~(a > b)` masks (`a <= b` would exclude NaN, changing tie-breaking); keep them.
#![allow(clippy::neg_cmp_op_on_partial_ord)]

//! Return-point filter for COBYLA (PRIMA `selectx`/`savefilt`/`isbetter`).
//!
//! COBYLA is a trust-region method on an L-infinity merit function, but the
//! point it *returns* is chosen from a filter of mutually non-dominated
//! `(f, cstrv)` pairs, so a low-`F` infeasible iterate never shadows a feasible
//! one. `isbetter` is the domination test; `savefilt` inserts a new point
//! (evicting dominated ones, or the worst by merit when full); `selectx` picks
//! the final index by the merit `φ = f + cweight · max(cstrv − ctol, 0)`.

use crate::core::math::Scalar;

fn funcmax<F: Scalar>() -> F {
    // PRIMA FUNCMAX = 2^100 (a large sub-overflow sentinel); CONSTRMAX = FUNCMAX.
    F::from_f64(2f64.powi(100)).unwrap()
}

/// Is `(f1, c1)` strictly better than `(f2, c2)`? `c*` are constraint
/// violations (`≥ 0`); `ctol` is the feasibility tolerance. PRIMA `isbetter`.
pub(crate) fn isbetter<F: Scalar>(f1: F, c1: F, f2: F, c2: F, ctol: F) -> bool {
    let realmax = F::max_value();
    let eps = F::epsilon();
    let ten = F::from_f64(10.0).unwrap();
    let constrmax = funcmax::<F>();
    let mut better = false;
    better = better
        || ((f1.is_nan() || c1.is_nan()) && !(f2.is_nan() || c2.is_nan()));
    better = better || (f1 < f2 && c1 <= c2);
    better = better || (f1 <= f2 && c1 < c2);
    let cref =
        ten * eps.max(ctol.min(F::from_f64(1.0e-2).unwrap() * constrmax));
    better = better
        || (f1 < realmax && c1 <= ctol && (c2 > ctol.max(cref) || c2.is_nan()));
    better
}

/// Insert `(x, f, cstrv)` into the filter unless dominated; evict points
/// it dominates, or the merit-worst point if the filter is full. PRIMA
/// `savefilt`.
#[allow(clippy::too_many_arguments)]
pub(crate) fn savefilt<F: Scalar>(
    x: &[F],
    f: F,
    cstrv: F,
    n: usize,
    ctol: F,
    cweight: F,
    maxfilt: usize,
    nfilt: &mut usize,
    xfilt: &mut Vec<F>,
    ffilt: &mut Vec<F>,
    cfilt: &mut Vec<F>,
) {
    let zero = F::zero();
    let realmax = F::max_value();
    // Return immediately if any filter column is better than X.
    for k in 0..*nfilt {
        if isbetter(ffilt[k], cfilt[k], f, cstrv, ctol) {
            return;
        }
    }
    let count_keep = (0..*nfilt)
        .filter(|&k| !isbetter(f, cstrv, ffilt[k], cfilt[k], ctol))
        .count();
    let kworst = if count_keep == maxfilt {
        // Evict the merit-worst column.
        let phi = |k: usize| {
            let cs = (cfilt[k] - ctol).max(zero);
            if cweight <= zero {
                ffilt[k]
            } else if cweight.is_infinite() {
                cs
            } else {
                ffilt[k].max(-realmax) + cweight * cs
            }
        };
        let phimax = (0..*nfilt).map(phi).fold(F::neg_infinity(), F::max);
        let cref = (0..*nfilt)
            .filter(|&k| phi(k) >= phimax)
            .map(|k| (cfilt[k] - ctol).max(zero))
            .fold(F::neg_infinity(), F::max);
        let fref = (0..*nfilt)
            .filter(|&k| (cfilt[k] - ctol).max(zero) >= cref)
            .map(|k| ffilt[k])
            .fold(F::neg_infinity(), F::max);
        // kworst = first index maximizing cfilt among ffilt >= fref.
        let cmax = (0..*nfilt)
            .filter(|&k| ffilt[k] >= fref)
            .map(|k| cfilt[k])
            .fold(F::neg_infinity(), F::max);
        let kworst = (0..*nfilt)
            .find(|&k| ffilt[k] >= fref && !(cfilt[k] < cmax))
            .unwrap_or(0);
        Some(kworst)
    } else {
        None
    };

    // Compact kept columns, then append the new point.
    let mut new_n = 0usize;
    for k in 0..*nfilt {
        if Some(k) != kworst && !isbetter(f, cstrv, ffilt[k], cfilt[k], ctol) {
            if new_n != k {
                for r in 0..n {
                    xfilt[r + new_n * n] = xfilt[r + k * n];
                }
                ffilt[new_n] = ffilt[k];
                cfilt[new_n] = cfilt[k];
            }
            new_n += 1;
        }
    }
    xfilt.truncate(new_n * n);
    ffilt.truncate(new_n);
    cfilt.truncate(new_n);
    // Most solves retain only a few nondominated points. Grow geometrically,
    // bounded by MAXFILT, instead of allocating the full history at startup.
    let capacity = (new_n + 1).max(4).next_power_of_two().min(maxfilt);
    for (values, width) in
        [(&mut *xfilt, n), (&mut *ffilt, 1), (&mut *cfilt, 1)]
    {
        if values.capacity() < (new_n + 1) * width {
            values.reserve_exact(capacity * width - values.len());
        }
    }
    xfilt.extend_from_slice(x);
    ffilt.push(f);
    cfilt.push(cstrv);
    *nfilt = new_n + 1;
}

/// Select the index of the point to return from the filter, by the merit
/// function `φ = f + cweight · max(cstrv − ctol, 0)`. PRIMA `selectx`.
pub(crate) fn selectx<F: Scalar>(
    ffilt: &[F],
    cfilt: &[F],
    cweight: F,
    ctol: F,
) -> usize {
    let nhist = ffilt.len();
    let zero = F::zero();
    let eps = F::epsilon();
    let two = F::from_f64(2.0).unwrap();
    let realmax = F::max_value();
    let funcmax = funcmax::<F>();
    let constrmax = funcmax;

    // Reference bounds (tiering against the large sentinels).
    let (mut fref, mut cref) = if (0..nhist)
        .any(|k| ffilt[k] < funcmax && cfilt[k] < constrmax)
    {
        (funcmax, constrmax)
    } else if (0..nhist).any(|k| ffilt[k] < realmax && cfilt[k] < constrmax) {
        (realmax, constrmax)
    } else if (0..nhist).any(|k| ffilt[k] < funcmax && cfilt[k] < realmax) {
        (funcmax, realmax)
    } else {
        (realmax, realmax)
    };

    if !(0..nhist).any(|k| ffilt[k] < fref && cfilt[k] < cref) {
        return nhist - 1;
    }

    let cshift = |k: usize| (cfilt[k] - ctol).max(zero);
    let cmin = (0..nhist)
        .filter(|&k| ffilt[k] < fref)
        .map(cshift)
        .fold(F::infinity(), F::min);
    let cref2 = eps.max(two * cmin);
    let phi = |k: usize| {
        if cweight <= zero {
            ffilt[k]
        } else if cweight.is_infinite() {
            cshift(k)
        } else {
            ffilt[k].max(-realmax) + cweight * cshift(k)
        }
    };
    let phimin = (0..nhist)
        .filter(|&k| ffilt[k] < fref && cshift(k) <= cref2)
        .map(phi)
        .fold(F::infinity(), F::min);
    cref = (0..nhist)
        .filter(|&k| ffilt[k] < fref && phi(k) <= phimin)
        .map(cshift)
        .fold(F::infinity(), F::min);
    fref = (0..nhist)
        .filter(|&k| cshift(k) <= cref)
        .map(|k| ffilt[k])
        .fold(F::infinity(), F::min);
    // kopt = first index minimizing cfilt among ffilt <= fref.
    let cmin2 = (0..nhist)
        .filter(|&k| ffilt[k] <= fref)
        .map(|k| cfilt[k])
        .fold(F::infinity(), F::min);
    (0..nhist)
        .find(|&k| ffilt[k] <= fref && !(cfilt[k] > cmin2))
        .unwrap_or(nhist - 1)
}

/// Moderate a value into `[−FUNCMAX, FUNCMAX]`, mapping `NaN` to `FUNCMAX`
/// (PRIMA's `moderatef`/`moderatec` extreme barrier). Keeps the filter free of
/// `NaN`/`+Inf` and lets soft-rejected points (`+Inf` cost) participate sanely.
pub(crate) fn moderatef<F: Scalar>(f: F) -> F {
    let fmax = funcmax::<F>();
    if f.is_nan() {
        fmax
    } else {
        f.min(fmax).max(-fmax)
    }
}

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

    #[derive(Default)]
    struct Filter {
        count: usize,
        x: Vec<f64>,
        f: Vec<f64>,
        c: Vec<f64>,
    }

    impl Filter {
        fn save(&mut self, id: f64, f: f64, c: f64, limit: usize, weight: f64) {
            savefilt(
                &[id, -id],
                f,
                c,
                2,
                0.0,
                weight,
                limit,
                &mut self.count,
                &mut self.x,
                &mut self.f,
                &mut self.c,
            );
            assert_eq!(self.x.len(), 2 * self.count);
            assert_eq!(self.f.len(), self.count);
            assert_eq!(self.c.len(), self.count);
            assert!(self.count <= limit);
            assert!(self.x.capacity() <= 2 * limit);
            assert!(self.f.capacity() <= limit);
            assert!(self.c.capacity() <= limit);
        }
    }

    #[test]
    fn lazy_filter_saturates_evicts_and_compacts() {
        let mut filter = Filter::default();
        filter.save(0.0, 3000.0, 1.0, 2000, 2.0);
        assert!(filter.x.capacity() < 4000);
        for k in 1..2002 {
            filter.save(k as f64, 3000.0 - k as f64, k as f64 + 1.0, 2000, 2.0);
        }
        assert_eq!(filter.count, 2000);
        for k in 0..1999 {
            assert_eq!(&filter.x[2 * k..2 * k + 2], &[k as f64, -(k as f64)]);
        }
        assert_eq!(&filter.x[3998..], &[2001.0, -2001.0]);
        assert_eq!(selectx(&filter.f, &filter.c, 2.0, 0.0), 0);

        filter.save(-1.0, 0.0, 0.0, 2000, 2.0);
        assert_eq!(filter.count, 1);
        assert_eq!(filter.x, [-1.0, 1.0]);
        filter.save(-2.0, 1.0, 0.0, 2000, 2.0);
        assert_eq!(filter.count, 1);
    }

    #[test]
    fn filter_ties_evict_and_select_the_first_matching_point() {
        for weight in [0.0, 1.0, f64::INFINITY] {
            let mut filter = Filter::default();
            for k in 0..4 {
                filter.save(k as f64, 1.0, 1.0, 3, weight);
            }
            assert_eq!(filter.x, [1.0, -1.0, 2.0, -2.0, 3.0, -3.0]);
            assert_eq!(selectx(&filter.f, &filter.c, weight, 0.0), 0);
        }
    }

    #[test]
    fn moderated_nonfinite_values_do_not_hide_a_feasible_point() {
        let sentinel = funcmax::<f64>();
        assert_eq!(moderatef(f64::NAN), sentinel);
        assert_eq!(moderatef(f64::INFINITY), sentinel);
        assert_eq!(moderatef(f64::NEG_INFINITY), -sentinel);
        let mut filter = Filter::default();
        filter.save(0.0, sentinel, sentinel, 3, 1e8);
        filter.save(1.0, -sentinel, 1.0, 3, 1e8);
        filter.save(2.0, 1.0, 0.0, 3, 1e8);
        let best = selectx(&filter.f, &filter.c, 1e8, 0.0);
        assert_eq!(filter.x[2 * best], 2.0);
        assert_eq!(
            selectx(&[sentinel, sentinel], &[sentinel, sentinel], 1e8, 0.0),
            0
        );
        assert_eq!(selectx(&[f64::MAX; 2], &[f64::MAX; 2], 1e8, 0.0), 1);
    }
}