RustedSciThe 0.4.11

Rust framework for symbolic and numerical computing:BVP ( Newton-Raphson frozen/damped/with collocations ), IVP( BDF, Radau, Backward Euler, LSODE, LSODA, RK45, DoPri), nonlinear equations ( Levenberg, Gavin) and more
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

use super::{
    Lsode2ControllerConfig, Lsode2NativeExecutionConfig, Lsode2ProblemConfig,
    Lsode2ResidualJacobianSource, Lsode2Solver,
};
use crate::symbolic::symbolic_engine::Expr;
use nalgebra::{DMatrix, DVector};

fn nonstiff_scalar_decay_exact_sparse_config() -> Lsode2ProblemConfig {
    // Exact solution: y(t) = exp(-t), y(0)=1
    Lsode2ProblemConfig::new(
        vec![Expr::parse_expression("-y")],
        vec!["y".to_string()],
        "t".to_string(),
        0.0,
        DVector::from_vec(vec![1.0]),
        5.0,
        1.0,
        1.0e-8,
        1.0e-10,
    )
    .with_first_step(Some(0.2))
    .with_native_sparse_faer_backend()
    .with_controller(Lsode2ControllerConfig::adams_only())
    .with_native_execution(Lsode2NativeExecutionConfig::native_solve(200_000, 200_000))
    .with_residual_jacobian_source(Lsode2ResidualJacobianSource::Analytical)
    .with_analytical_callbacks(
        |_t, y: &DVector<f64>| DVector::from_vec(vec![-y[0]]),
        |_t, _y: &DVector<f64>| DMatrix::from_row_slice(1, 1, &[-1.0]),
    )
}

fn nonstiff_two_scale_exact_banded_config() -> Lsode2ProblemConfig {
    // y2' = -2*y2, y2(0)=1 => y2 = exp(-2t)
    // y1' = -y1 + y2, y1(0)=0 => y1 = exp(-t) - exp(-2t)
    Lsode2ProblemConfig::new(
        vec![
            Expr::parse_expression("-y1 + y2"),
            Expr::parse_expression("-2.0*y2"),
        ],
        vec!["y1".to_string(), "y2".to_string()],
        "t".to_string(),
        0.0,
        DVector::from_vec(vec![0.0, 1.0]),
        5.0,
        1.0,
        1.0e-8,
        1.0e-10,
    )
    .with_first_step(Some(0.2))
    .with_native_banded_faithful_backend()
    .with_controller(Lsode2ControllerConfig::adams_only())
    .with_native_execution(Lsode2NativeExecutionConfig::native_solve(200_000, 200_000))
    .with_residual_jacobian_source(Lsode2ResidualJacobianSource::Analytical)
    .with_analytical_callbacks(
        |_t, y: &DVector<f64>| DVector::from_vec(vec![-y[0] + y[1], -2.0 * y[1]]),
        |_t, _y: &DVector<f64>| DMatrix::from_row_slice(2, 2, &[-1.0, 1.0, 0.0, -2.0]),
    )
}

#[test]
fn lsode2_adams_nonstiff_scalar_exact_sparse_matches_closed_form() {
    let mut solver = Lsode2Solver::new(nonstiff_scalar_decay_exact_sparse_config())
        .expect("nonstiff scalar sparse Adams config should build");
    let summary = solver
        .solve_with_summary()
        .expect("nonstiff scalar sparse Adams solve should finish");

    assert!(
        summary.status == "finished_native_faithful"
            || summary.status == "finished_native_faithful_partial",
        "unexpected status for nonstiff scalar sparse Adams run: {}",
        summary.status
    );
    assert_eq!(summary.algorithm.controller_mode, "adams_only");
    assert_eq!(summary.algorithm.preferred_family, "adams");
    assert_eq!(
        summary.algorithm.executed_family,
        Some(summary.algorithm.preferred_family)
    );

    let final_t = summary.final_t.expect("final t should be present");
    assert!(
        final_t >= 4.999,
        "nonstiff scalar sparse Adams run should reach near t_bound, got t={final_t:e}"
    );
    let y_final = summary.final_y.expect("final y should be present")[0];
    let exact = (-final_t).exp();
    assert!(
        (y_final - exact).abs() < 5.0e-7,
        "nonstiff scalar sparse Adams mismatch: got={y_final:e}, exact={exact:e}"
    );

    assert!(
        summary.native_statistics.executed_adams_count > 0,
        "expected native Adams execution evidence in adams_only mode"
    );
}

#[test]
fn lsode2_adams_nonstiff_two_scale_exact_banded_matches_closed_form() {
    let mut solver = Lsode2Solver::new(nonstiff_two_scale_exact_banded_config())
        .expect("nonstiff two-scale banded Adams config should build");
    let summary = solver
        .solve_with_summary()
        .expect("nonstiff two-scale banded Adams solve should finish");

    assert!(
        summary.status == "finished_native_faithful"
            || summary.status == "finished_native_faithful_partial",
        "unexpected status for nonstiff two-scale banded Adams run: {}",
        summary.status
    );
    assert_eq!(summary.algorithm.controller_mode, "adams_only");
    assert_eq!(summary.algorithm.preferred_family, "adams");
    assert_eq!(
        summary.algorithm.executed_family,
        Some(summary.algorithm.preferred_family)
    );

    let final_t = summary.final_t.expect("final t should be present");
    assert!(
        final_t >= 4.999,
        "nonstiff two-scale banded Adams run should reach near t_bound, got t={final_t:e}"
    );
    let y = summary.final_y.expect("final y should be present");
    let y1_exact = (-final_t).exp() - (-2.0 * final_t).exp();
    let y2_exact = (-2.0 * final_t).exp();
    assert!(
        (y[0] - y1_exact).abs() < 2.0e-6,
        "nonstiff two-scale banded y1 mismatch: got={:e}, exact={:e}",
        y[0],
        y1_exact
    );
    assert!(
        (y[1] - y2_exact).abs() < 2.0e-6,
        "nonstiff two-scale banded y2 mismatch: got={:e}, exact={:e}",
        y[1],
        y2_exact
    );

    assert!(
        summary.native_statistics.executed_adams_count > 0,
        "expected native Adams execution evidence in adams_only mode"
    );
}