xapphire 0.1.0

compute utility
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

use ndarray::prelude::*;
use num::Float;

use crate::lu::solve_lu;
#[cfg(test)]
use crate::util::*;

pub fn solve_cg(
    a: &Array<f64, Ix2>,
    b: &Array<f64, Ix1>,
    x0: &Array<f64, Ix1>,
    eps: f64,
    iter_max: usize,
) -> Result<(Array<f64, Ix1>, usize, f64), &'static str> {
    if a.shape()[0] != a.shape()[1] {
        return Err("expect square matrix");
    }

    let n = a.shape()[0];

    if b.shape()[0] != n {
        return Err("dimension of b not matching a");
    }

    let mut r = b - &a.dot(x0);
    let r0 = r.clone();
    let mut d = r.clone();
    let mut alpha = 0.;
    let mut lambda: f64 = (&d * &r).sum() / (&d * &a.dot(&d)).sum();
    let mut x = x0 + &(lambda * &d);

    let mut it = 1;
    while it <= iter_max {
        let mut r_new = &r - &(a.dot(&d) * lambda);
        alpha = (&r_new * &r_new).sum() / (&r * &r).sum();
        d = &r_new + &(alpha * &d);
        lambda = (&d * &r_new).sum() / (&d * &a.dot(&d)).sum();
        x = x + lambda * &d;
        if (&r_new * &r_new).sum() / (&r0 * &r0).sum() < eps {
            break;
        }
        std::mem::swap(&mut r, &mut r_new);
        it += 1;
    }

    let d: Array<f64, Ix1> = b - &(a.dot(&x));
    let l2 = (&d * &d).sum();

    Ok((x, it, l2))
}

#[test]
fn test_cg_0() {
    let mut a = arr2(&[[4., 1.], [1., 3.]]);

    let orig = a.clone();

    let b = arr1(&[1., 2.]);

    let x0 = arr1(&[2., 1.]);

    let (x, it, res) = solve_cg(&a, &b, &x0, 1e-9, 100).expect("solve_cg");
    dbg!(&x, it, res);
    assert!(arr1_eq(&x, &arr1(&[1. / 11., 7. / 11.])));
}

#[test]
fn test_cg_1() {
    let mut a = arr2(&[[5., 3., 1.], [3., 4., 2.], [1., 2., 3.]]);

    let orig = a.clone();

    let b = arr1(&[41., 47., 32.]);

    let x0 = arr1(&[0., 0., 0.]);

    let (x, it, res) = solve_cg(&a, &b, &x0, 1e-9, 100).expect("solve_cg");
    dbg!(&x, it, res);
    assert!(arr1_eq(&x, &arr1(&[3., 7., 5.])));
}

pub fn solve_cg_precond(
    a: &Array<f64, Ix2>,
    b: &Array<f64, Ix1>,
    x0: &Array<f64, Ix1>,
    precond: &Array<f64, Ix2>,
    eps: f64,
    iter_max: usize,
) -> Result<(Array<f64, Ix1>, usize, f64), &'static str> {
    if a.shape()[0] != a.shape()[1] {
        return Err("expect square matrix");
    }

    let n = a.shape()[0];

    if b.shape()[0] != n {
        return Err("dimension of b not matching a");
    }

    let mut r = b - &a.dot(x0);
    let r0 = r.clone();
    let mut q = solve_lu(&mut precond.clone(), &r0)?;
    let q0 = q.clone();
    let mut d = q.clone();
    let mut alpha = 0.;
    let mut lambda: f64 = (&q * &r).sum() / (&d * &a.dot(&d)).sum();
    let mut x = x0 + &(lambda * &d);

    let mut it = 1;
    while it <= iter_max {
        let mut r_new = &r - &(a.dot(&d) * lambda);
        let mut q_new = solve_lu(&mut precond.clone(), &r_new)?;
        alpha = (&q_new * &r_new).sum() / (&q * &r).sum();
        d = &q_new + &(alpha * &d);
        lambda = (&q_new * &r_new).sum() / (&d * &a.dot(&d)).sum();
        x = x + lambda * &d;
        if (&q_new * &r_new).sum() / (&q0 * &r0).sum() < eps {
            break;
        }
        std::mem::swap(&mut r, &mut r_new);
        std::mem::swap(&mut q, &mut q_new);
        it += 1;
    }

    let d: Array<f64, Ix1> = b - &(a.dot(&x));
    let l2 = (&d * &d).sum();

    Ok((x, it, l2))
}

#[test]
fn test_cg_precond_1() {
    let mut a = arr2(&[[5., 3., 1.], [3., 4., 2.], [1., 2., 3.]]);

    let orig = a.clone();

    let b = arr1(&[41., 47., 32.]);

    let x0 = arr1(&[1., 1., 1.]);

    let mut precond = arr2(&[[5., 0., 0.], [0., 4., 0.], [0., 0., 5.]]);

    let (x, it, res) =
        solve_cg_precond(&a, &b, &x0, &precond, 1e-9, 100).expect("solve_cg_precond");
    dbg!(&x, it, res);
    assert!(arr1_eq_tol(&x, &arr1(&[3., 7., 5.]), 1e-6));
}