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#include <iostream>
#include <type_traits>
#include <random>
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/GenEigsComplexShiftSolver.h>
#include <Spectra/MatOp/DenseGenComplexShiftSolve.h>
#include <Spectra/MatOp/SparseGenComplexShiftSolve.h>
#include "catch.hpp"
using namespace Spectra;
using Matrix = Eigen::MatrixXd;
using Vector = Eigen::VectorXd;
using ComplexMatrix = Eigen::MatrixXcd;
using ComplexVector = Eigen::VectorXcd;
using SpMatrix = Eigen::SparseMatrix<double>;
// Generate random sparse matrix
SpMatrix gen_sparse_data(int n, double prob = 0.5)
{
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 = 100 to reduce running time for failed cases
int nconv = eigs.compute(selection, 100);
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);
}
ComplexVector evals = eigs.eigenvalues();
ComplexMatrix evecs = eigs.eigenvectors();
ComplexMatrix resid = mat * evecs - evecs * evals.asDiagonal();
const double err = resid.array().abs().maxCoeff();
INFO("||AU - UD||_inf = " << err);
INFO("||AU - UD||_2 colwise = " << resid.colwise().norm());
REQUIRE(err == Approx(0.0).margin(1e-8));
}
template <typename MatType>
void run_test_sets(const MatType& A, int k, int m, double sigmar, double sigmai)
{
constexpr bool is_dense = std::is_same<MatType, Matrix>::value;
using DenseOp = DenseGenComplexShiftSolve<double>;
using SparseOp = SparseGenComplexShiftSolve<double>;
using OpType = typename std::conditional<is_dense, DenseOp, SparseOp>::type;
OpType op(A);
GenEigsComplexShiftSolver<OpType> eigs(op, k, m, sigmar, sigmai);
SECTION("Largest Magnitude")
{
run_test(A, eigs, SortRule::LargestMagn);
}
SECTION("Largest Real Part")
{
run_test(A, eigs, SortRule::LargestReal);
}
SECTION("Largest Imaginary Part")
{
run_test(A, eigs, SortRule::LargestImag);
}
SECTION("Smallest Magnitude")
{
run_test(A, eigs, SortRule::SmallestMagn, true);
}
SECTION("Smallest Real Part")
{
run_test(A, eigs, SortRule::SmallestReal);
}
SECTION("Smallest Imaginary Part")
{
run_test(A, eigs, SortRule::SmallestImag, true);
}
}
TEST_CASE("Eigensolver of general real matrix [10x10]", "[eigs_gen]")
{
std::srand(123);
const Matrix A = Eigen::MatrixXd::Random(10, 10);
int k = 3;
int m = 8;
double sigmar = 2.0;
double sigmai = 1.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
TEST_CASE("Eigensolver of general real matrix [100x100]", "[eigs_gen]")
{
std::srand(123);
const Matrix A = Eigen::MatrixXd::Random(100, 100);
int k = 10;
int m = 20;
double sigmar = 20.0;
double sigmai = 10.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
TEST_CASE("Eigensolver of general real matrix [1000x1000]", "[eigs_gen]")
{
std::srand(123);
const Matrix A = Eigen::MatrixXd::Random(1000, 1000);
int k = 20;
int m = 50;
double sigmar = 200.0;
double sigmai = 100.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
TEST_CASE("Eigensolver of sparse real matrix [10x10]", "[eigs_gen]")
{
std::srand(123);
const SpMatrix A = gen_sparse_data(10, 0.5);
int k = 3;
int m = 6;
double sigmar = 2.0;
double sigmai = 1.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
TEST_CASE("Eigensolver of sparse real matrix [100x100]", "[eigs_gen]")
{
std::srand(123);
const SpMatrix A = gen_sparse_data(100, 0.1);
int k = 10;
int m = 30;
double sigmar = 20.0;
double sigmai = 10.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
TEST_CASE("Eigensolver of sparse real matrix [1000x1000]", "[eigs_gen]")
{
std::srand(123);
const SpMatrix A = gen_sparse_data(1000, 0.01);
int k = 20;
int m = 50;
double sigmar = 200.0;
double sigmai = 100.0;
run_test_sets(A, k, m, sigmar, sigmai);
}
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