kryst 4.0.4

Krylov subspace and preconditioned iterative solvers for dense and sparse linear systems, with shared and distributed memory parallelism.
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
153
154
155
156
157
158
159

#![cfg(all(feature = "complex", feature = "backend-faer"))]

use kryst::algebra::prelude::*;
use kryst::config::options::PcOptions;
use kryst::context::pc_context::PcType;
use kryst::core::traits::MatVec;
use kryst::matrix::sparse::CsrMatrix;
use kryst::preconditioner::sor::{MatSorType, SorPc};
use kryst::preconditioner::{ApproxInvKind, ApproxInvParams, SpaiCsr};
use kryst::preconditioner::{PcSide, Preconditioner};
use kryst::utils::diagnostics::PcDiagnostics;

#[test]
fn pc_diagnostics_reports_complex_capability_mode() {
    let sor = PcDiagnostics::from_options(Some(PcType::Sor), Some(&PcOptions::default()));
    let ilutp = PcDiagnostics::from_options(Some(PcType::Ilutp), Some(&PcOptions::default()));
    let ilu0 = PcDiagnostics::from_options(Some(PcType::Ilu0), Some(&PcOptions::default()));
    let ainv =
        PcDiagnostics::from_options(Some(PcType::ApproxInverse), Some(&PcOptions::default()));

    assert_eq!(sor.complex_support, "native_complex");
    assert_eq!(ilu0.complex_support, "native_complex");
    assert_eq!(ilutp.complex_support, "projected_complex");
    assert_eq!(ainv.complex_support, "native_complex");
}

#[test]
fn sor_native_complex_preserves_imaginary_coupling() {
    let a = CsrMatrix::from_csr(
        2,
        2,
        vec![0, 1, 3],
        vec![0, 0, 1],
        vec![
            S::from_parts(2.0, 0.0),
            S::from_parts(1.0, 2.0),
            S::from_parts(3.0, 0.0),
        ],
    );
    let mut pc = SorPc::new(1.0, 1, MatSorType::APPLY_LOWER, 0.0);
    pc.setup(&a).expect("setup");

    let rhs = vec![S::from_real(1.0), S::from_real(1.0)];
    let mut out = vec![S::zero(); 2];
    pc.apply(PcSide::Left, &rhs, &mut out).expect("apply");

    assert!(
        out[1].imag().abs() > 1e-12,
        "expected imaginary coupling, got {out:?}"
    );
}

#[test]
fn ilu_csr_native_complex_beats_split_baseline_on_coupled_system() {
    use kryst::preconditioner::Preconditioner as _;
    use kryst::preconditioner::ilu_csr::{IluCsr, IluCsrConfig, IluKind};

    let a = CsrMatrix::from_csr(
        2,
        2,
        vec![0, 2, 4],
        vec![0, 1, 0, 1],
        vec![
            S::from_parts(4.0, 0.0),
            S::from_parts(0.0, 1.0),
            S::from_parts(0.0, 1.0),
            S::from_parts(3.0, 0.0),
        ],
    );
    let mut pc = IluCsr::new_with_config(IluCsrConfig {
        kind: IluKind::Ilu0,
        ..IluCsrConfig::default()
    });
    pc.setup(&a).expect("setup complex ilu_csr");

    let rhs = vec![S::from_parts(1.0, -1.5), S::from_parts(-0.75, 2.0)];
    let mut native = vec![S::zero(); 2];
    pc.apply(PcSide::Left, &rhs, &mut native)
        .expect("native apply");

    // degraded baseline: split solve on real and imaginary parts with same real factors
    let mut real_part = vec![S::zero(); 2];
    let mut imag_part = vec![S::zero(); 2];
    let xr = vec![S::from_real(rhs[0].real()), S::from_real(rhs[1].real())];
    let xi = vec![S::from_real(rhs[0].imag()), S::from_real(rhs[1].imag())];
    pc.apply_op(kryst::preconditioner::Op::NoTrans, &xr, &mut real_part)
        .expect("split real");
    pc.apply_op(kryst::preconditioner::Op::NoTrans, &xi, &mut imag_part)
        .expect("split imag");
    let split = vec![
        S::from_parts(real_part[0].real(), imag_part[0].real()),
        S::from_parts(real_part[1].real(), imag_part[1].real()),
    ];

    let residual_norm = |z: &Vec<S>| {
        let mut az = vec![S::zero(); 2];
        MatVec::matvec(&a, z, &mut az);
        az.iter()
            .zip(rhs.iter())
            .map(|(l, r)| (*l - *r).abs())
            .fold(0.0f64, f64::max)
    };

    let rn = residual_norm(&native);
    let rs = residual_norm(&split);
    assert!(
        rn < rs * 0.2,
        "native residual {rn} not better than split {rs}"
    );
}

#[test]
fn approxinv_spai_complex_setup_apply_residual_acceptance() {
    let a = CsrMatrix::from_csr(
        3,
        3,
        vec![0, 3, 6, 9],
        vec![0, 1, 2, 0, 1, 2, 0, 1, 2],
        vec![
            S::from_parts(4.0, 0.2),
            S::from_parts(-1.0, 0.4),
            S::from_parts(0.5, -0.2),
            S::from_parts(-1.2, -0.3),
            S::from_parts(3.8, 0.1),
            S::from_parts(-0.7, 0.25),
            S::from_parts(0.4, 0.15),
            S::from_parts(-0.9, -0.35),
            S::from_parts(3.2, -0.1),
        ],
    );
    let rhs = vec![
        S::from_parts(1.0, -0.5),
        S::from_parts(-0.25, 0.75),
        S::from_parts(0.5, 0.25),
    ];

    let mut pc = SpaiCsr::new_with_params(ApproxInvParams {
        kind: ApproxInvKind::SPAI,
        levels: 1,
        max_per_col: 3,
        drop_tol: 1e-6,
        ..ApproxInvParams::default()
    });
    pc.setup(&a).expect("spai complex setup");
    assert!(pc.complex_setup_used_native());

    let mut out = vec![S::zero(); rhs.len()];
    pc.apply(PcSide::Left, &rhs, &mut out)
        .expect("spai complex apply");

    let mut az = vec![S::zero(); rhs.len()];
    MatVec::matvec(&a, &out, &mut az);
    let rn = az
        .iter()
        .zip(rhs.iter())
        .map(|(l, r)| (*l - *r).abs())
        .fold(0.0f64, f64::max);
    assert!(rn.is_finite() && rn < 3.0, "SPAI residual too large: {rn}");
}