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
176
177
178
179
180
181
182
183
184
185
|
#include <iostream>
#include <type_traits>
#include <random>
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/SymEigsShiftSolver.h>
#include <Spectra/MatOp/DenseSymShiftSolve.h>
#include <Spectra/MatOp/SparseSymShiftSolve.h>
#include "catch.hpp"
using namespace Spectra;
using Matrix = Eigen::MatrixXd;
using Vector = Eigen::VectorXd;
using SpMatrix = Eigen::SparseMatrix<double>;
// Generate data for testing
Matrix gen_dense_data(int n)
{
const Matrix mat = Eigen::MatrixXd::Random(n, n);
return mat + mat.transpose();
}
SpMatrix gen_sparse_data(int n, double prob = 0.5)
{
// Eigen solver only uses the lower triangle of mat,
// so we don't need to make mat symmetric here.
SpMatrix mat(n, n);
std::default_random_engine gen;
gen.seed(0);
std::uniform_real_distribution<double> distr(0.0, 1.0);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (distr(gen) < prob)
mat.insert(i, j) = distr(gen) - 0.5;
}
}
return mat;
}
template <typename MatType, typename Solver>
void run_test(const MatType& mat, Solver& eigs, SortRule selection, bool allow_fail = false)
{
eigs.init();
// maxit = 500 to reduce running time for failed cases
int nconv = eigs.compute(selection, 500);
int niter = eigs.num_iterations();
int nops = eigs.num_operations();
if (allow_fail && eigs.info() != CompInfo::Successful)
{
WARN("FAILED on this test");
std::cout << "nconv = " << nconv << std::endl;
std::cout << "niter = " << niter << std::endl;
std::cout << "nops = " << nops << std::endl;
return;
}
else
{
INFO("nconv = " << nconv);
INFO("niter = " << niter);
INFO("nops = " << nops);
REQUIRE(eigs.info() == CompInfo::Successful);
}
Vector evals = eigs.eigenvalues();
Matrix evecs = eigs.eigenvectors();
Matrix resid = mat.template selfadjointView<Eigen::Lower>() * evecs - evecs * evals.asDiagonal();
const double err = resid.array().abs().maxCoeff();
INFO("||AU - UD||_inf = " << err);
REQUIRE(err == Approx(0.0).margin(1e-9));
}
template <typename MatType>
void run_test_sets(const MatType& mat, int k, int m, double sigma)
{
constexpr bool is_dense = std::is_same<MatType, Matrix>::value;
using DenseOp = DenseSymShiftSolve<double>;
using SparseOp = SparseSymShiftSolve<double>;
using OpType = typename std::conditional<is_dense, DenseOp, SparseOp>::type;
OpType op(mat);
SymEigsShiftSolver<OpType> eigs(op, k, m, sigma);
SECTION("Largest Magnitude")
{
run_test(mat, eigs, SortRule::LargestMagn);
}
SECTION("Largest Value")
{
run_test(mat, eigs, SortRule::LargestAlge);
}
SECTION("Smallest Magnitude")
{
run_test(mat, eigs, SortRule::SmallestMagn, true);
}
SECTION("Smallest Value")
{
run_test(mat, eigs, SortRule::SmallestAlge);
}
SECTION("Both Ends")
{
run_test(mat, eigs, SortRule::BothEnds);
}
}
TEST_CASE("Eigensolver of symmetric real matrix [10x10]", "[eigs_sym]")
{
std::srand(123);
const Matrix A = gen_dense_data(10);
int k = 3;
int m = 6;
double sigma = 1.0;
run_test_sets(A, k, m, sigma);
}
TEST_CASE("Eigensolver of symmetric real matrix [100x100]", "[eigs_sym]")
{
std::srand(123);
const Matrix A = gen_dense_data(100);
int k = 10;
int m = 20;
double sigma = 10.0;
run_test_sets(A, k, m, sigma);
}
TEST_CASE("Eigensolver of symmetric real matrix [1000x1000]", "[eigs_sym]")
{
std::srand(123);
const Matrix A = gen_dense_data(1000);
int k = 20;
int m = 50;
double sigma = 100.0;
run_test_sets(A, k, m, sigma);
}
TEST_CASE("Eigensolver of sparse symmetric real matrix [10x10]", "[eigs_sym]")
{
std::srand(123);
// Eigen solver only uses the lower triangle
const SpMatrix A = gen_sparse_data(10, 0.5);
int k = 3;
int m = 6;
double sigma = 1.0;
run_test_sets(A, k, m, sigma);
}
TEST_CASE("Eigensolver of sparse symmetric real matrix [100x100]", "[eigs_sym]")
{
std::srand(123);
// Eigen solver only uses the lower triangle
const SpMatrix A = gen_sparse_data(100, 0.1);
int k = 10;
int m = 20;
double sigma = 10.0;
run_test_sets(A, k, m, sigma);
}
TEST_CASE("Eigensolver of sparse symmetric real matrix [1000x1000]", "[eigs_sym]")
{
std::srand(123);
// Eigen solver only uses the lower triangle
const SpMatrix A = gen_sparse_data(1000, 0.01);
int k = 20;
int m = 50;
double sigma = 100.0;
run_test_sets(A, k, m, sigma);
}
|
