minuit2 0.4.1

Pure Rust port of CERN Minuit2 parameter optimization engine
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

use minuit2::{FCN, FCNGradient, MnHesse, MnMigrad, MnMinimize, MnSimplex};
use std::cell::Cell;

/// Port of ROOT Minuit2 regression intent from `math/minuit2/test/testMinuit2.cxx`:
/// Hessian indexing must follow floating parameters when fixed parameters exist.
#[test]
fn root_hessian_external_indexing_numeric() {
    let f = |p: &[f64]| {
        let (x, y, z) = (p[0], p[1], p[2]);
        x * x + 10.0 * y * y + 100.0 * z * z + 2.0 * x * y + 4.0 * x * z + 8.0 * y * z
    };

    let minimum = MnMigrad::new()
        .add("x", 1.0, 0.1)
        .add("y", 2.0, 0.1)
        .add("z", 3.0, 0.1)
        .fix(0) // break ext/int identity mapping
        .minimize(&f);
    assert!(minimum.is_valid());

    let hesse = MnHesse::new().calculate(&f, &minimum);
    assert!(hesse.is_valid());
    let state = hesse.user_state();
    let cov = state.covariance().expect("Hesse should provide covariance");

    // Only floating parameters should appear in covariance (y, z).
    assert_eq!(cov.nrow(), 2);

    // For fixed x, Hessian(y,z) = [[20, 8], [8, 200]].
    // ROOT Minuit2 user covariance convention is 2 * Hessian^-1.
    // So expected covariance = 2 * [[200, -8], [-8, 20]] / 3936.
    let c00 = 400.0 / 3936.0;
    let c01 = -16.0 / 3936.0;
    let c11 = 40.0 / 3936.0;

    assert!(
        (cov.get(0, 0) - c00).abs() < 5e-4,
        "cov(0,0) expected ~{c00}, got {}",
        cov.get(0, 0)
    );
    assert!(
        (cov.get(0, 1) - c01).abs() < 5e-4,
        "cov(0,1) expected ~{c01}, got {}",
        cov.get(0, 1)
    );
    assert!(
        (cov.get(1, 1) - c11).abs() < 5e-4,
        "cov(1,1) expected ~{c11}, got {}",
        cov.get(1, 1)
    );
}

struct QuadraticGrad;

impl FCN for QuadraticGrad {
    fn value(&self, p: &[f64]) -> f64 {
        let (x, y, z) = (p[0], p[1], p[2]);
        x * x + 10.0 * y * y + 100.0 * z * z + 2.0 * x * y + 4.0 * x * z + 8.0 * y * z
    }
}

impl FCNGradient for QuadraticGrad {
    fn gradient(&self, p: &[f64]) -> Vec<f64> {
        let (x, y, z) = (p[0], p[1], p[2]);
        vec![
            2.0 * x + 2.0 * y + 4.0 * z,
            2.0 * x + 20.0 * y + 8.0 * z,
            4.0 * x + 8.0 * y + 200.0 * z,
        ]
    }
}

/// Same regression objective as above, but minimizing with analytical gradient path.
#[test]
fn root_hessian_external_indexing_with_gradient() {
    let f = QuadraticGrad;
    let minimum = MnMigrad::new()
        .add("x", 1.0, 0.1)
        .add("y", 2.0, 0.1)
        .add("z", 3.0, 0.1)
        .fix(0)
        .minimize_grad(&f);
    assert!(minimum.is_valid());

    let hesse = MnHesse::new().calculate(&f, &minimum);
    let cov = hesse
        .user_state()
        .covariance()
        .expect("Hesse should provide covariance");
    assert_eq!(cov.nrow(), 2);

    // Same expected 2x2 block for (y,z), with ROOT 2*H^-1 convention.
    assert!((cov.get(0, 0) - 400.0 / 3936.0).abs() < 5e-4);
    assert!((cov.get(0, 1) - (-16.0 / 3936.0)).abs() < 5e-4);
    assert!((cov.get(1, 1) - 40.0 / 3936.0).abs() < 5e-4);
}

struct Quadratic2;

impl FCN for Quadratic2 {
    fn value(&self, p: &[f64]) -> f64 {
        let (x, y) = (p[0], p[1]);
        let dx = x - 1.0;
        let dy = y + 2.0;
        dx * dx + 4.0 * dy * dy + 0.3 * x * y
    }
}

struct Rosenbrock2;

impl FCN for Rosenbrock2 {
    fn value(&self, p: &[f64]) -> f64 {
        let (x, y) = (p[0], p[1]);
        let t1 = y - x * x;
        let t2 = 1.0 - x;
        100.0 * t1 * t1 + t2 * t2
    }
}

struct QuadraticNoG2 {
    g2_called: Cell<usize>,
}

impl FCN for QuadraticNoG2 {
    fn value(&self, p: &[f64]) -> f64 {
        let (x, y) = (p[0], p[1]);
        let dx = x - 1.0;
        let dy = y + 2.0;
        dx * dx + dy * dy
    }

    fn has_hessian(&self) -> bool {
        true
    }

    fn hessian(&self, _p: &[f64]) -> Vec<f64> {
        // Packed upper triangle for 2x2 identity-scaled Hessian.
        vec![2.0, 0.0, 2.0]
    }

    fn has_g2(&self) -> bool {
        false
    }

    fn g2(&self, _p: &[f64]) -> Vec<f64> {
        self.g2_called.set(self.g2_called.get() + 1);
        vec![2.0, 2.0]
    }
}

impl FCNGradient for QuadraticNoG2 {
    fn gradient(&self, p: &[f64]) -> Vec<f64> {
        let (x, y) = (p[0], p[1]);
        vec![2.0 * (x - 1.0), 2.0 * (y + 2.0)]
    }
}

/// Regression for ROOT v6-36-08 parity:
/// Simplex uses tolerance directly as EDM target (scaled by Up),
/// not tolerance*1e-3.
#[test]
fn root_simplex_reference_quadratic2() {
    let f = Quadratic2;
    let min = MnSimplex::new()
        .add("x", 0.4, 0.1)
        .add("y", -1.0, 0.1)
        .tolerance(0.1)
        .minimize(&f);

    assert!(min.is_valid());
    let params = min.params();
    assert!((params[0] - 1.15).abs() < 5e-3, "x mismatch: {}", params[0]);
    assert!((params[1] + 2.05).abs() < 5e-3, "y mismatch: {}", params[1]);
    assert!(
        (min.fval() - (-0.67475)).abs() < 5e-4,
        "fval mismatch: {}",
        min.fval()
    );
    assert!(
        (min.edm() - 0.0334887).abs() < 5e-4,
        "edm mismatch: {}",
        min.edm()
    );
}

/// Regression for ROOT v6-36-08 parity:
/// MnMinimize is not "Simplex then Migrad" by default.
/// It runs Migrad first and falls back only if needed, yielding a covariant minimum here.
#[test]
fn root_minimize_reference_rosenbrock2() {
    let f = Rosenbrock2;
    let min = MnMinimize::new()
        .add("x", 0.0, 0.1)
        .add("y", 0.0, 0.1)
        .tolerance(0.1)
        .minimize(&f);

    assert!(min.is_valid());
    assert!(
        min.user_state().has_covariance(),
        "MnMinimize should end with covariance for this workload"
    );
    assert!(
        min.nfcn() > 50,
        "unexpectedly low call count: {}",
        min.nfcn()
    );

    let params = min.params();
    assert!(
        (params[0] - 0.99415).abs() < 0.02,
        "x mismatch: {}",
        params[0]
    );
    assert!(
        (params[1] - 0.98827).abs() < 0.02,
        "y mismatch: {}",
        params[1]
    );
}

/// Port of ROOT test intent `NoG2CallsWhenFCHasNoG2`:
/// if FCN reports no G2 support, G2 must not be called.
#[test]
fn root_no_g2_calls_when_fcn_has_no_g2() {
    let f = QuadraticNoG2 {
        g2_called: Cell::new(0),
    };
    let min = MnMigrad::new()
        .add("x", 0.4, 0.1)
        .add("y", -1.0, 0.1)
        .tolerance(0.1)
        .minimize_grad(&f);

    assert!(min.is_valid());
    assert_eq!(
        f.g2_called.get(),
        0,
        "G2() must not be called when has_g2() reports false"
    );
}