semiflow 0.15.0-beta

no_std Rust PDE solver: evolution equations via Chernoff approximation of operator semigroups (heat, diffusion, Schrodinger)
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

//! Unit tests for `manifold.rs`.
//!
//! Extracted from `manifold.rs` to keep that file under 500 lines.

// Exact float comparisons in tests verify round-trip identity or sentinel values.
#![allow(clippy::float_cmp)]

use super::*;

// --- Torus ---

#[test]
fn torus_scalar_curvature_is_zero() {
    let t = Torus::<f64, 2>::unit();
    assert_eq!(t.scalar_curvature(&[0.3, 0.7]), 0.0);
}

#[test]
fn torus_exp_map_wraps_into_unit_cell() {
    let t = Torus::<f64, 2>::unit();
    let mut out = [0.0f64; 2];
    t.exp_map(&[0.5, 0.5], &[0.8, 0.8], &mut out).unwrap();
    // (0.5 + 0.8) mod 1.0 = 0.3
    assert!((out[0] - 0.3).abs() < 1e-12, "out[0] = {}", out[0]);
    assert!((out[1] - 0.3).abs() < 1e-12, "out[1] = {}", out[1]);
}

#[test]
fn torus_exp_map_identity_at_zero_v() {
    let t = Torus::<f64, 2>::unit();
    let mut out = [0.0f64; 2];
    t.exp_map(&[0.3, 0.7], &[0.0, 0.0], &mut out).unwrap();
    assert!((out[0] - 0.3).abs() < 1e-15);
    assert!((out[1] - 0.7).abs() < 1e-15);
}

#[test]
fn torus_injectivity_radius_is_half_min_period() {
    let t = Torus::<f64, 3>::with_period([0.5, 1.0, 0.7]).unwrap();
    assert!((t.injectivity_radius() - 0.25).abs() < 1e-12);
}

#[test]
fn torus_parallel_transport_is_identity() {
    let t = Torus::<f64, 2>::unit();
    let v = [0.3, -0.7];
    let mut out = [0.0f64; 2];
    t.parallel_transport(&[0.1, 0.2], &[0.4, 0.6], &v, &mut out)
        .unwrap();
    assert!((out[0] - v[0]).abs() < 1e-15);
    assert!((out[1] - v[1]).abs() < 1e-15);
}

#[test]
fn torus_volume_element_log_is_zero() {
    let t = Torus::<f64, 2>::unit();
    assert_eq!(t.volume_element_log(&[0.3, 0.7]), 0.0);
}

#[test]
fn torus_with_period_rejects_non_positive() {
    assert!(Torus::<f64, 2>::with_period([0.5, 0.0]).is_err());
    assert!(Torus::<f64, 2>::with_period([-1.0, 1.0]).is_err());
    assert!(Torus::<f64, 2>::with_period([f64::NAN, 1.0]).is_err());
}

// --- Sphere2 ---

#[test]
fn sphere2_scalar_curvature_unit() {
    let s = Sphere2::<f64>::unit();
    assert!((s.scalar_curvature(&[0.5, 1.0]) - 2.0).abs() < 1e-12);
}

#[test]
fn sphere2_scalar_curvature_radius5() {
    let s = Sphere2::<f64>::with_radius(5.0).unwrap();
    // R = 2 / 25 = 0.08
    assert!((s.scalar_curvature(&[0.5, 1.0]) - 0.08).abs() < 1e-12);
}

#[test]
fn sphere2_exp_map_zero_v_is_identity() {
    let s = Sphere2::<f64>::unit();
    let mut out = [0.0f64; 2];
    s.exp_map(&[0.5, 1.0], &[0.0, 0.0], &mut out).unwrap();
    assert!((out[0] - 0.5).abs() < 1e-12, "theta = {}", out[0]);
    assert!((out[1] - 1.0).abs() < 1e-12, "phi = {}", out[1]);
}

#[test]
fn sphere2_exp_map_north_pole_quarter_great_circle() {
    // exp at north pole (0, 0) with v = (π/2, 0) should reach equator θ = π/2
    let s = Sphere2::<f64>::unit();
    let pi_half = core::f64::consts::FRAC_PI_2;
    let mut out = [0.0f64; 2];
    s.exp_map(&[0.01, 0.0], &[pi_half, 0.0], &mut out).unwrap();
    // Should end up near equator: θ ≈ π/2 + 0.01
    let expected_theta = pi_half + 0.01;
    assert!((out[0] - expected_theta).abs() < 1e-6, "theta={}", out[0]);
}

#[test]
fn sphere2_with_radius_rejects_invalid() {
    assert!(Sphere2::<f64>::with_radius(f64::NAN).is_err());
    assert!(Sphere2::<f64>::with_radius(0.0).is_err());
    assert!(Sphere2::<f64>::with_radius(-1.0).is_err());
}

#[test]
fn sphere2_injectivity_radius() {
    let s = Sphere2::<f64>::unit();
    let pi = core::f64::consts::PI;
    assert!((s.injectivity_radius() - pi).abs() < 1e-12);
}

// --- Hyperbolic2 ---

#[test]
fn hyperbolic2_scalar_curvature_unit() {
    let h = Hyperbolic2::<f64>::unit();
    assert!((h.scalar_curvature(&[0.3, 0.4]) - (-2.0)).abs() < 1e-12);
}

#[test]
fn hyperbolic2_scalar_curvature_scale2() {
    let h = Hyperbolic2::<f64>::with_scale(2.0).unwrap();
    // R = -2 / 4 = -0.5
    assert!((h.scalar_curvature(&[0.1, 0.2]) - (-0.5)).abs() < 1e-12);
}

#[test]
fn hyperbolic2_exp_map_origin_zero_v_is_origin() {
    let h = Hyperbolic2::<f64>::unit();
    let mut out = [0.0f64; 2];
    h.exp_map(&[0.0, 0.0], &[0.0, 0.0], &mut out).unwrap();
    assert!(out[0].abs() < 1e-12);
    assert!(out[1].abs() < 1e-12);
}

#[test]
fn hyperbolic2_exp_map_origin_stays_in_disk() {
    let h = Hyperbolic2::<f64>::unit();
    let mut out = [0.0f64; 2];
    h.exp_map(&[0.0, 0.0], &[0.5, 0.3], &mut out).unwrap();
    let r_sq = out[0] * out[0] + out[1] * out[1];
    assert!(r_sq < 1.0, "result outside disk: r² = {r_sq}");
}

#[test]
fn hyperbolic2_with_scale_rejects_invalid() {
    assert!(Hyperbolic2::<f64>::with_scale(f64::NAN).is_err());
    assert!(Hyperbolic2::<f64>::with_scale(0.0).is_err());
    assert!(Hyperbolic2::<f64>::with_scale(-1.0).is_err());
}

#[test]
fn hyperbolic2_injectivity_radius_is_infinity() {
    let h = Hyperbolic2::<f64>::unit();
    assert!(h.injectivity_radius().is_infinite());
}