quad 0.1.2

Quadrature integration
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

//use std::time::Instant;
use crate::constants::*;

pub fn qk_quadrature<const M: usize, F>(
    f: F,
    a: f64,
    b: f64,
    xgk: &[f64; M],
    wgk: &[f64],
    wg: &[f64],
) -> (Vec<f64>, f64, f64)
where
    F: Fn(f64) -> Vec<f64>,
{
    let hlgth: f64 = 0.5 * (b - a);
    let dhlgth: f64 = hlgth.abs();
    let centr: f64 = 0.5 * (b + a);
    let fc = f(centr);
    let dim = fc.len();
    let mut fv1 = Vec::with_capacity(dim * M);
    let mut fv2 = Vec::with_capacity(dim * M);
    let mut resg: Vec<f64> = Vec::with_capacity(dim);
    let mut resk: Vec<f64> = fc.clone();
    let mut resabs = Vec::with_capacity(dim);

    if M % 2 == 1 {
        resg.extend(&fc);
    } else {
        resg.extend(&vec![0.0; dim]);
    }
    for k in 0..dim {
        resk[k] *= wgk[M];
        resabs.push(resk[k].abs());
        if M % 2 == 1 {
            resg[k] *= wg[(M + 1) / 2 - 1];
        }
    }

    for j in 1..M / 2 + 1 {
        let jtw1 = 2 * j - 1;
        let jtw2 = 2 * j;

        let absc1 = hlgth * xgk[jtw1 - 1];
        let absc2 = hlgth * xgk[jtw2 - 1];

        fv1.append(&mut f(centr - absc1));
        fv1.append(&mut f(centr - absc2));
        fv2.append(&mut f(centr + absc1));
        fv2.append(&mut f(centr + absc2));

        let mut fsum1 = fv1[(jtw1 - 1) * dim..jtw1 * dim].to_vec();
        let mut fsum2 = fv1[(jtw2 - 1) * dim..jtw2 * dim].to_vec();

        for k in 0..dim {
            fsum1[k] += fv2[(jtw1 - 1) * dim + k];
            fsum2[k] += fv2[(jtw2 - 1) * dim + k];
        }

        for k in 0..dim {
            resg[k] += wg[j - 1] * fsum2[k];
            resk[k] += wgk[jtw1 - 1] * fsum1[k] + wgk[jtw2 - 1] * fsum2[k];
            resabs[k] += wgk[jtw1 - 1]
                * (fv1[(jtw1 - 1) * dim + k].abs() + fv2[(jtw1 - 1) * dim + k].abs())
                + wgk[jtw2 - 1]
                    * (fv1[(jtw2 - 1) * dim + k].abs() + fv2[(jtw2 - 1) * dim + k].abs());
        }
    }

    if M / 2 != (M + 1) / 2 {
        let jtw1 = M;
        let absc = hlgth * xgk[jtw1 - 1];
        fv1.append(&mut f(centr - absc));
        fv2.append(&mut f(centr + absc));

        let mut fsum = fv1[(jtw1 - 1) * dim..jtw1 * dim].to_vec();

        for k in 0..dim {
            fsum[k] += fv2[(jtw1 - 1) * dim + k];
        }
        for k in 0..dim {
            resk[k] += wgk[jtw1 - 1] * fsum[k];
            resabs[k] +=
                wgk[jtw1 - 1] * (fv1[(jtw1 - 1) * dim + k].abs() + fv2[(jtw1 - 1) * dim + k].abs());
        }
    }

    let mut reskh = resk.clone();

    for k in 0..dim {
        reskh[k] *= 0.5;
    }

    let mut resasc = vec![0.0; dim];
    for k in 0..dim {
        resasc[k] = wgk[M] * (fc[k] - reskh[k]).abs();
    }

    for j in 1..M + 1 {
        for k in 0..dim {
            resasc[k] += wgk[j - 1]
                * ((fv1[(j - 1) * dim + k] - reskh[k]).abs()
                    + (fv2[(j - 1) * dim + k] - reskh[k]).abs());
        }
    }

    let mut result = resk.clone();

    for k in 0..dim {
        result[k] *= hlgth;
        resabs[k] *= dhlgth;
        resasc[k] *= dhlgth;
    }

    let mut abserr = 0.0;
    let mut resabs_scalar = 0.0;
    let mut resasc_scalar = 0.0;

    for k in 0..dim {
        abserr += (((resk[k] - resg[k]) * hlgth).abs()).powi(2);
        resabs_scalar += resabs[k].powi(2);
        resasc_scalar += resasc[k].powi(2);
    }

    abserr = abserr.sqrt();
    resabs_scalar = resabs_scalar.sqrt();
    resasc_scalar = resasc_scalar.sqrt();

    if resasc_scalar != 0.0 && abserr != 0.0 {
        abserr = resasc_scalar * 1.0_f64.min((200.0 * abserr / resasc_scalar).powf(1.5));
    }

    let round_error = 50.0 * EPMACH * resabs_scalar;

    if round_error > UFLOW {
        abserr = abserr.max(round_error);
    }

    (result, abserr, round_error)
}