diffsol 0.1.9

A library for solving ordinary differential equations (ODEs) in Rust.
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

use crate::{
    ode_solver::problem::OdeSolverSolution, scalar::scale, DenseMatrix, OdeBuilder, OdeEquations,
    OdeSolverProblem, Vector,
};
use nalgebra::ComplexField;
use num_traits::{One, Zero};
use std::ops::MulAssign;

// exponential decay problem with algebraic constraint
// dy/dt = -ay
// 0 = z - y
// remove warning about unused mut
#[allow(unused_mut)]
fn exponential_decay_with_algebraic<M: DenseMatrix>(
    x: &M::V,
    p: &M::V,
    _t: M::T,
    mut y: &mut M::V,
) {
    y.copy_from(x);
    y.mul_assign(scale(-p[0]));
    let nstates = y.len();
    y[nstates - 1] = x[nstates - 1] - x[nstates - 2];
}

#[allow(unused_mut)]
fn exponential_decay_with_algebraic_sens<M: DenseMatrix>(
    x: &M::V,
    _p: &M::V,
    _t: M::T,
    v: &M::V,
    mut y: &mut M::V,
) {
    y.copy_from(x);
    y.mul_assign(scale(-v[0]));
    let nstates = y.len();
    y[nstates - 1] = M::T::zero();
}

// Jv = [[-av, 0], [-1, 1]]v = [-av, -v[0] + v[1]]
#[allow(unused_mut)]
fn exponential_decay_with_algebraic_jacobian<M: DenseMatrix>(
    _x: &M::V,
    p: &M::V,
    _t: M::T,
    v: &M::V,
    mut y: &mut M::V,
) {
    y.copy_from(v);
    y.mul_assign(scale(-p[0]));
    let nstates = y.len();
    y[nstates - 1] = v[nstates - 1] - v[nstates - 2];
}

// y = Mx + beta * y = | 1 0 | | x[0] | + beta | y[0] |
//                     | 0 0 | | x[1] |         | y[1] |
fn exponential_decay_with_algebraic_mass<M: DenseMatrix>(
    x: &M::V,
    _p: &M::V,
    _t: M::T,
    beta: M::T,
    y: &mut M::V,
) {
    let nstates = y.len();
    let yn = beta * y[nstates - 1];
    y.axpy(M::T::one(), x, beta);
    y[nstates - 1] = yn;
}

fn exponential_decay_with_algebraic_mass_sens<M: DenseMatrix>(
    _x: &M::V,
    _p: &M::V,
    _t: M::T,
    _v: &M::V,
    y: &mut M::V,
) {
    y.fill(M::T::zero());
}

fn exponential_decay_with_algebraic_init<M: DenseMatrix>(_p: &M::V, _t: M::T) -> M::V {
    M::V::from_vec(vec![1.0.into(), 1.0.into(), 0.0.into()])
}

fn exponential_decay_with_algebraic_init_sens<M: DenseMatrix>(
    _p: &M::V,
    _t: M::T,
    _v: &M::V,
    y: &mut M::V,
) {
    y.fill(M::T::zero());
}

pub fn exponential_decay_with_algebraic_problem<M: DenseMatrix + 'static>(
    use_coloring: bool,
) -> (
    OdeSolverProblem<impl OdeEquations<M = M, V = M::V, T = M::T>>,
    OdeSolverSolution<M::V>,
) {
    let p = M::V::from_vec(vec![0.1.into()]);
    let problem = OdeBuilder::new()
        .p([0.1])
        .use_coloring(use_coloring)
        .build_ode_with_mass(
            exponential_decay_with_algebraic::<M>,
            exponential_decay_with_algebraic_jacobian::<M>,
            exponential_decay_with_algebraic_mass::<M>,
            exponential_decay_with_algebraic_init::<M>,
        )
        .unwrap();

    let mut soln = OdeSolverSolution::default();
    for i in 0..10 {
        let t = M::T::from(i as f64 / 10.0);
        let y0 = M::V::from_vec(vec![1.0.into(), 1.0.into(), 1.0.into()]);
        let y: M::V = y0 * scale(M::T::exp(-p[0] * t));
        soln.push(y, t);
    }
    (problem, soln)
}

pub fn exponential_decay_with_algebraic_problem_sens<M: DenseMatrix + 'static>(
    use_coloring: bool,
) -> (
    OdeSolverProblem<impl OdeEquations<M = M, V = M::V, T = M::T>>,
    OdeSolverSolution<M::V>,
) {
    let p = M::V::from_vec(vec![0.1.into()]);
    let problem = OdeBuilder::new()
        .p([0.1])
        .use_coloring(use_coloring)
        .sensitivities_error_control(true)
        .build_ode_with_mass_and_sens(
            exponential_decay_with_algebraic::<M>,
            exponential_decay_with_algebraic_jacobian::<M>,
            exponential_decay_with_algebraic_sens::<M>,
            exponential_decay_with_algebraic_mass::<M>,
            exponential_decay_with_algebraic_mass_sens::<M>,
            exponential_decay_with_algebraic_init::<M>,
            exponential_decay_with_algebraic_init_sens::<M>,
        )
        .unwrap();

    let mut soln = OdeSolverSolution::default();
    for i in 0..10 {
        let t = M::T::from(i as f64 / 10.0);
        let y0 = M::V::from_vec(vec![1.0.into(), 1.0.into(), 1.0.into()]);
        let y: M::V = y0.clone() * scale(M::T::exp(-p[0] * t));
        let yp = y0 * scale(-t * M::T::exp(-p[0] * t));
        soln.push_sens(y, t, &[yp]);
    }
    (problem, soln)
}