rlumod 1.0.0

Safe, no_std matrix updates and linear solves using the LUmod algorithm
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

// SPDX-FileCopyrightText: 2026 Daisuke Nagao
// SPDX-License-Identifier: MIT

use super::super::*;
use std::format;

#[cfg(all(target_arch = "wasm32", target_os = "unknown"))]
use wasm_bindgen_test::wasm_bindgen_test as test;

const MAX_DIMENSION: usize = 3;
type ModificationCase<'a> = (i32, i32, i32, i32, usize, &'a [f64]);

fn make_identity(l: &mut [f64], u: &mut [f64], dimension: usize) {
    l.fill(0.0);
    u.fill(0.0);
    for index in 0..dimension {
        l[index * MAX_DIMENSION + index] = 1.0;
        let u_row = index * MAX_DIMENSION - index * index.saturating_sub(1) / 2;
        u[u_row] = 1.0;
    }
}

fn expect_factorization(
    l: &[f64],
    u: &[f64],
    expected_matrix: &[f64],
    dimension: usize,
    context: &str,
) {
    assert_eq!(expected_matrix.len(), dimension * dimension);
    for row in 0..dimension {
        for column in 0..dimension {
            let transformed: f64 = (0..dimension)
                .map(|inner| {
                    l[row * MAX_DIMENSION + inner] * expected_matrix[inner * dimension + column]
                })
                .sum();
            let expected = if row <= column {
                u[u_index(row, column, MAX_DIMENSION)]
            } else {
                0.0
            };
            assert!(
                (transformed - expected).abs() <= 1.0e-12,
                "{context}: (L * A)[{row},{column}]={transformed}, U[{row},{column}]={expected}"
            );
        }
    }
}

#[test]
fn multiplies_and_solves_triangular_factors() {
    let mut l = [0.0; MAX_DIMENSION * MAX_DIMENSION];
    let mut u = [0.0; MAX_DIMENSION * (MAX_DIMENSION + 1) / 2];
    make_identity(&mut l, &mut u, 2);
    l[3] = 2.0;
    u[0] = 2.0;
    u[1] = 1.0;
    u[3] = 4.0;
    let mut y = [3.0, 4.0];
    let mut z = [0.0; 2];
    Lprod(1, MAX_DIMENSION as i32, 2, &mut l, &mut y, &mut z);
    assert_eq!((z[0], z[1]), (3.0, 10.0));
    Lprod(2, MAX_DIMENSION as i32, 2, &mut l, &mut y, &mut z);
    assert_eq!((z[0], z[1]), (11.0, 4.0));
    let mut rhs = [5.0, 8.0];
    Usolve(1, MAX_DIMENSION as i32, 2, &mut u, &mut rhs);
    assert!((rhs[0] - 1.5).abs() <= 1.0e-12);
    assert!((rhs[1] - 2.0).abs() <= 1.0e-12);
    let mut transpose_rhs = [4.0, 10.0];
    Usolve(2, MAX_DIMENSION as i32, 2, &mut u, &mut transpose_rhs);
    assert!((transpose_rhs[0] - 2.0).abs() <= 1.0e-12);
    assert!((transpose_rhs[1] - 2.0).abs() <= 1.0e-12);

    let mut singular_u = [0.0; MAX_DIMENSION * (MAX_DIMENSION + 1) / 2];
    let mut singular_rhs = [1.0];
    Usolve(
        1,
        MAX_DIMENSION as i32,
        1,
        &mut singular_u,
        &mut singular_rhs,
    );
    assert!(singular_rhs[0].is_infinite());
}

#[test]
fn exercises_every_factor_modification_mode() {
    let valid_cases: &[ModificationCase<'_>] = &[
        (1, 1, -1, -1, 1, &[2.0]),
        (1, 2, -1, -1, 2, &[1.0, 1.0, 2.0, 3.0]),
        (2, 2, -1, 1, 2, &[1.0, 1.0, 0.0, 2.0]),
        (2, 2, -1, 0, 2, &[1.0, 0.0, 2.0, 1.0]),
        (3, 1, 0, -1, 1, &[2.0]),
        (3, 2, 0, -1, 2, &[2.0, 3.0, 0.0, 1.0]),
        (4, 2, 1, 1, 1, &[1.0]),
        (4, 2, 0, 0, 1, &[1.0]),
    ];
    for &(mode, dimension, row, column, result_dimension, expected) in valid_cases {
        let mut l = [0.0; MAX_DIMENSION * MAX_DIMENSION];
        let mut u = [0.0; MAX_DIMENSION * (MAX_DIMENSION + 1) / 2];
        make_identity(&mut l, &mut u, dimension as usize);
        let mut y = [2.0, 3.0, 4.0];
        let mut z = [1.0, 2.0, 3.0];
        let mut work = [0.0; 3];
        LUmod(
            mode, 3, dimension, row, column, &mut l, &mut u, &mut y, &mut z, &mut work,
        );
        expect_factorization(
            &l,
            &u,
            expected,
            result_dimension,
            &format!("mode {mode}, n {dimension}, row {row}, column {column}"),
        );
    }

    for (mode, dimension, row, column) in [
        (99, 2, -1, -1),
        (1, 0, -1, -1),
        (2, 2, -1, -1),
        (2, 2, -1, 2),
        (3, 2, -1, -1),
        (3, 2, 2, -1),
        (4, 0, 0, 0),
        (4, 2, -1, 0),
        (4, 2, 2, 0),
        (4, 2, 0, -1),
        (4, 2, 0, 2),
    ] {
        let mut l = [0.0; MAX_DIMENSION * MAX_DIMENSION];
        let mut u = [0.0; MAX_DIMENSION * (MAX_DIMENSION + 1) / 2];
        make_identity(&mut l, &mut u, dimension.max(1) as usize);
        let mut y = [2.0, 3.0, 4.0];
        let mut z = [1.0, 2.0, 3.0];
        let mut work = [0.0; 3];
        let before = (l, u, y, z, work);
        LUmod(
            mode, 3, dimension, row, column, &mut l, &mut u, &mut y, &mut z, &mut work,
        );
        assert_eq!(
            (l, u, y, z, work),
            before,
            "mode {mode}, n {dimension}, row {row}, column {column} must be a no-op"
        );
    }
}