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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
#[cfg(feature = "with_mumps")]
use super::ComplexSolverMUMPS;
use super::{ComplexCooMatrix, ComplexSolverKLU, ComplexSolverUMFPACK, Genie, LinSolParams, StatsLinSol};
use crate::StrError;
use russell_lab::ComplexVector;
/// Defines a unified interface for complex linear system solvers
pub trait ComplexLinSolTrait: Send {
/// Performs the factorization (and analysis/initialization if needed)
///
/// # Input
///
/// * `mat` -- The sparse matrix (COO, CSC, or CSR).
/// * `params` -- configuration parameters; None => use default
///
/// # Notes
///
/// 1. The structure of the matrix (nrow, ncol, nnz, sym) must be
/// exactly the same among multiple calls to `factorize`. The values may differ
/// from call to call, nonetheless.
/// 2. The first call to `factorize` will define the structure which must be
/// kept the same for the next calls.
/// 3. If the structure of the matrix needs to be changed, the solver must
/// be "dropped" and a new solver allocated.
fn factorize(&mut self, mat: &ComplexCooMatrix, params: Option<LinSolParams>) -> Result<(), StrError>;
/// Computes the solution of the linear system
///
/// Solves the linear system:
///
/// ```text
/// A · x = rhs
/// (m,n) (n) (m)
/// ```
///
/// # Output
///
/// * `x` -- the vector of unknown values with dimension equal to mat.ncol
///
/// # Input
///
/// * `mat` -- the coefficient matrix A.
/// * `rhs` -- the right-hand side vector with know values an dimension equal to mat.ncol
/// * `verbose` -- shows messages
///
/// **Warning:** the matrix must be same one used in `factorize`.
fn solve(&mut self, x: &mut ComplexVector, rhs: &ComplexVector, verbose: bool) -> Result<(), StrError>;
/// Updates the stats structure (should be called after solve)
fn update_stats(&self, stats: &mut StatsLinSol);
/// Returns the nanoseconds spent on initialize
fn get_ns_init(&self) -> u128;
/// Returns the nanoseconds spent on factorize
fn get_ns_fact(&self) -> u128;
/// Returns the nanoseconds spent on solve
fn get_ns_solve(&self) -> u128;
}
/// Unifies the access to linear system solvers
pub struct ComplexLinSolver<'a> {
/// Holds the actual implementation
pub actual: Box<dyn Send + ComplexLinSolTrait + 'a>,
}
impl<'a> ComplexLinSolver<'a> {
/// Allocates a new instance
///
/// # Input
///
/// * `genie` -- the actual implementation that does all the magic
pub fn new(genie: Genie) -> Result<Self, StrError> {
#[cfg(feature = "with_mumps")]
let actual: Box<dyn Send + ComplexLinSolTrait> = match genie {
Genie::Klu => Box::new(ComplexSolverKLU::new()?),
Genie::Mumps => Box::new(ComplexSolverMUMPS::new()?),
Genie::Umfpack => Box::new(ComplexSolverUMFPACK::new()?),
};
#[cfg(not(feature = "with_mumps"))]
let actual: Box<dyn Send + ComplexLinSolTrait> = match genie {
Genie::Klu => Box::new(ComplexSolverKLU::new()?),
Genie::Mumps => return Err("MUMPS solver is not available"),
Genie::Umfpack => Box::new(ComplexSolverUMFPACK::new()?),
};
Ok(ComplexLinSolver { actual })
}
/// Computes the solution of a complex linear system
///
/// Solves the linear system:
///
/// ```text
/// A · x = rhs
/// (m,n) (n) (m)
/// ```
///
/// # Output
///
/// * `x` -- the vector of unknown values with dimension equal to mat.ncol
///
/// # Input
///
/// * `genie` -- the actual implementation that does all the magic
/// * `mat` -- the matrix representing the sparse coefficient matrix A (see Notes below)
/// * `rhs` -- the right-hand side vector with know values an dimension equal to coo.nrow
/// * `verbose` -- shows messages
///
/// # Notes
///
/// 1. For symmetric matrices, `MUMPS` requires [crate::Sym::YesLower]
/// 2. For symmetric matrices, `UMFPACK` requires [crate::Sym::YesFull]
/// 4. This function calls the actual implementation (genie) via the functions `factorize`, and `solve`.
/// 5. This function is best for a **single-use**, whereas the actual
/// solver should be considered for a recurrent use (e.g., inside a loop).
pub fn compute(
genie: Genie,
x: &mut ComplexVector,
mat: &ComplexCooMatrix,
rhs: &ComplexVector,
params: Option<LinSolParams>,
) -> Result<Self, StrError> {
let mut solver = ComplexLinSolver::new(genie)?;
solver.actual.factorize(mat, params)?;
let verbose = if let Some(p) = params { p.verbose } else { false };
solver.actual.solve(x, rhs, verbose)?;
Ok(solver)
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#[cfg(test)]
mod tests {
use super::ComplexLinSolver;
use crate::{Genie, Samples};
use russell_lab::{complex_vec_approx_eq, cpx, Complex64, ComplexVector};
#[cfg(feature = "with_mumps")]
use serial_test::serial;
#[test]
fn complex_lin_solver_compute_works_klu() {
let (coo, _, _, _) = Samples::complex_symmetric_3x3_full();
let mut x = ComplexVector::new(3);
let rhs = ComplexVector::from(&[cpx!(-3.0, 3.0), cpx!(2.0, -2.0), cpx!(9.0, 7.0)]);
ComplexLinSolver::compute(Genie::Klu, &mut x, &coo, &rhs, None).unwrap();
let x_correct = &[cpx!(1.0, 1.0), cpx!(2.0, -2.0), cpx!(3.0, 3.0)];
complex_vec_approx_eq(&x, x_correct, 1e-15);
}
#[test]
#[serial]
#[cfg(feature = "with_mumps")]
fn complex_lin_solver_compute_works_mumps() {
let (coo, _, _, _) = Samples::complex_symmetric_3x3_lower();
let mut x = ComplexVector::new(3);
let rhs = ComplexVector::from(&[cpx!(-3.0, 3.0), cpx!(2.0, -2.0), cpx!(9.0, 7.0)]);
ComplexLinSolver::compute(Genie::Mumps, &mut x, &coo, &rhs, None).unwrap();
let x_correct = &[cpx!(1.0, 1.0), cpx!(2.0, -2.0), cpx!(3.0, 3.0)];
complex_vec_approx_eq(&x, x_correct, 1e-15);
}
#[test]
fn complex_lin_solver_compute_works_umfpack() {
let (coo, _, _, _) = Samples::complex_symmetric_3x3_full();
let mut x = ComplexVector::new(3);
let rhs = ComplexVector::from(&[cpx!(-3.0, 3.0), cpx!(2.0, -2.0), cpx!(9.0, 7.0)]);
ComplexLinSolver::compute(Genie::Umfpack, &mut x, &coo, &rhs, None).unwrap();
let x_correct = &[cpx!(1.0, 1.0), cpx!(2.0, -2.0), cpx!(3.0, 3.0)];
complex_vec_approx_eq(&x, x_correct, 1e-15);
}
}