taktwerk 0.6.0

Fixed-step model execution engine for Linux with its own OPC UA server
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

//! Random samples of a campaign: distributions, uniform and Latin hypercube draws.

use serde::{Deserialize, Serialize};
use taktwerk_core::rng::{Rng, derive};

/// How a sampled value is distributed.
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
#[serde(deny_unknown_fields)]
#[serde(rename_all = "snake_case")]
pub enum Dist {
    /// Uniform on `[a, b]`.
    Uniform([f64; 2]),
    /// `exp` of uniform on `[ln a, ln b]`; `0 < a < b`.
    LogUniform([f64; 2]),
    /// Normal with mean and standard deviation.
    Normal([f64; 2]),
    /// One of these values, equally likely.
    Choice(Vec<toml::Value>),
}

impl Dist {
    /// Check the parameters.
    ///
    /// # Errors
    /// Bounds out of order, a non-positive log bound or deviation, or an empty choice.
    pub fn check(&self) -> Result<(), String> {
        let finite = |v: &[f64]| v.iter().all(|x| x.is_finite());
        match self {
            Self::Uniform([a, b]) if finite(&[*a, *b]) && a <= b => Ok(()),
            Self::LogUniform([a, b]) if finite(&[*a, *b]) && 0.0 < *a && a <= b => Ok(()),
            Self::Normal([m, s]) if finite(&[*m, *s]) && *s >= 0.0 => Ok(()),
            Self::Choice(v) if !v.is_empty() => Ok(()),
            Self::Uniform(_) => Err("uniform = [a, b] needs finite a <= b".into()),
            Self::LogUniform(_) => Err("log_uniform = [a, b] needs 0 < a <= b".into()),
            Self::Normal(_) => Err("normal = [mean, sd] needs a finite mean and sd >= 0".into()),
            Self::Choice(_) => Err("choice needs at least one value".into()),
        }
    }

    /// The value at probability `p` in `[0, 1)`.
    #[must_use]
    #[allow(
        clippy::cast_possible_truncation,
        clippy::cast_sign_loss,
        clippy::cast_precision_loss,
        reason = "an index from a probability"
    )]
    pub fn at(&self, p: f64) -> toml::Value {
        match self {
            Self::Uniform([a, b]) => (a + (b - a) * p).into(),
            Self::LogUniform([a, b]) => (a.ln() + (b.ln() - a.ln()) * p).exp().into(),
            Self::Normal([m, s]) => (m + s * normal_quantile(p)).into(),
            Self::Choice(v) => {
                let i = ((p * v.len() as f64) as usize).min(v.len() - 1);
                v[i].clone()
            }
        }
    }
}

/// How the probabilities are drawn.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Default, Serialize, Deserialize)]
#[serde(rename_all = "snake_case")]
pub enum Method {
    /// Independent uniform probabilities.
    Uniform,
    /// Latin hypercube: each variable's `n` probabilities fall one in each of `n` equal strata,
    /// strata shuffled independently per variable.
    #[default]
    Lhs,
}

/// `n` probabilities in `[0, 1)` for the variable `name` of a campaign seeded `seed`. Each
/// variable draws from its own stream, so adding one leaves the others' draws as they were.
#[must_use]
#[allow(
    clippy::cast_possible_truncation,
    clippy::cast_precision_loss,
    reason = "indices and counts"
)]
pub fn probabilities(method: Method, n: usize, seed: u64, name: &str) -> Vec<f64> {
    let mut rng = Rng::new(derive(seed, &format!("sample {name}")));
    match method {
        Method::Uniform => (0..n).map(|_| rng.uniform()).collect(),
        Method::Lhs => {
            let mut strata: Vec<usize> = (0..n).collect();
            // Fisher-Yates.
            for i in (1..n).rev() {
                let j = (rng.next_u64() % (i as u64 + 1)) as usize;
                strata.swap(i, j);
            }
            strata
                .into_iter()
                .map(|k| (k as f64 + rng.uniform()) / n as f64)
                .collect()
        }
    }
}

/// The standard normal quantile at `p`, by Acklam's rational approximation (relative error
/// below 1.2e-9); infinite at 0 and 1.
#[must_use]
pub fn normal_quantile(p: f64) -> f64 {
    const A: [f64; 6] = [
        -3.969_683_028_665_376e1,
        2.209_460_984_245_205e2,
        -2.759_285_104_469_687e2,
        1.383_577_518_672_69e2,
        -3.066_479_806_614_716e1,
        2.506_628_277_459_239,
    ];
    const B: [f64; 5] = [
        -5.447_609_879_822_406e1,
        1.615_858_368_580_409e2,
        -1.556_989_798_598_866e2,
        6.680_131_188_771_972e1,
        -1.328_068_155_288_572e1,
    ];
    const C: [f64; 6] = [
        -7.784_894_002_430_293e-3,
        -3.223_964_580_411_365e-1,
        -2.400_758_277_161_838,
        -2.549_732_539_343_734,
        4.374_664_141_464_968,
        2.938_163_982_698_783,
    ];
    const D: [f64; 4] = [
        7.784_695_709_041_462e-3,
        3.224_671_290_700_398e-1,
        2.445_134_137_142_996,
        3.754_408_661_907_416,
    ];
    const LOW: f64 = 0.024_25;
    if p <= 0.0 {
        return f64::NEG_INFINITY;
    }
    if p >= 1.0 {
        return f64::INFINITY;
    }
    let tail = |q: f64| {
        (((((C[0] * q + C[1]) * q + C[2]) * q + C[3]) * q + C[4]) * q + C[5])
            / ((((D[0] * q + D[1]) * q + D[2]) * q + D[3]) * q + 1.0)
    };
    if p < LOW {
        tail((-2.0 * p.ln()).sqrt())
    } else if p > 1.0 - LOW {
        -tail((-2.0 * (1.0 - p).ln()).sqrt())
    } else {
        let q = p - 0.5;
        let r = q * q;
        (((((A[0] * r + A[1]) * r + A[2]) * r + A[3]) * r + A[4]) * r + A[5]) * q
            / (((((B[0] * r + B[1]) * r + B[2]) * r + B[3]) * r + B[4]) * r + 1.0)
    }
}

#[cfg(test)]
#[allow(clippy::unwrap_used, reason = "tests")]
mod tests {
    use super::*;

    #[test]
    fn a_latin_hypercube_puts_one_draw_in_each_stratum() {
        let p = probabilities(Method::Lhs, 50, 1, "a");
        let mut strata: Vec<usize> = p.iter().map(|x| (x * 50.0) as usize).collect();
        strata.sort_unstable();
        assert_eq!(strata, (0..50).collect::<Vec<_>>());
        assert_eq!(p, probabilities(Method::Lhs, 50, 1, "a"), "seeded");
        assert_ne!(
            p,
            probabilities(Method::Lhs, 50, 1, "b"),
            "a stream per variable"
        );
        assert_ne!(p, probabilities(Method::Lhs, 50, 2, "a"));
        assert!(
            probabilities(Method::Uniform, 9, 1, "a")
                .iter()
                .all(|x| (0.0..1.0).contains(x))
        );
    }

    #[test]
    fn distributions_map_probabilities() {
        let f = |d: Dist, p| d.at(p).as_float().unwrap();
        assert_eq!(f(Dist::Uniform([2.0, 4.0]), 0.25), 2.5);
        assert!((f(Dist::LogUniform([0.5, 2.0]), 0.5) - 1.0).abs() < 1e-12);
        assert!((f(Dist::Normal([10.0, 2.0]), 0.975) - (10.0 + 2.0 * 1.959_963_985)).abs() < 1e-6);
        assert_eq!(f(Dist::Normal([0.0, 1.0]), 0.5), 0.0);
        let c = Dist::Choice(vec![1.into(), 2.into(), 3.into()]);
        assert_eq!(c.at(0.0), 1.into());
        assert_eq!(c.at(0.999), 3.into());
        assert!(Dist::LogUniform([0.0, 1.0]).check().is_err());
        assert!(Dist::Uniform([2.0, 1.0]).check().is_err());
        assert!(Dist::Choice(vec![]).check().is_err());
        assert!((normal_quantile(0.001) + 3.090_232_306).abs() < 1e-6);
        assert!((normal_quantile(0.999) - 3.090_232_306).abs() < 1e-6);
    }
}