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#include <iostream>
#include <type_traits>
#include <random>
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/HermEigsSolver.h>
#include <Spectra/MatOp/DenseHermMatProd.h>
#include <Spectra/MatOp/SparseHermMatProd.h>
#include "catch.hpp"
using namespace Spectra;
using Matrix = Eigen::MatrixXcd;
using Vector = Eigen::VectorXcd;
using SpMatrix = Eigen::SparseMatrix<std::complex<double>>;
using RealMatrix = Eigen::MatrixXd;
using RealVector = Eigen::VectorXd;
// Generate data for testing
Matrix gen_dense_data(int n)
{
const Matrix mat = Matrix::Random(n, n);
return mat + mat.adjoint();
}
SpMatrix gen_sparse_data(int n, double prob = 0.5)
{
// Eigen solver only uses the lower triangular part of mat,
// so we don't need to make mat an Hermitian matrix here,
// but diagonal elements must have a zero imaginary part
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)
{
double re = distr(gen) - 0.5;
double im = (i == j) ? 0.0 : (distr(gen) - 0.5);
mat.insert(i, j) = std::complex<double>(re, im);
}
}
}
return mat;
}
template <typename MatType, typename Solver>
void run_test(const MatType& mat, Solver& eigs, SortRule selection)
{
eigs.init();
int nconv = eigs.compute(selection);
int niter = eigs.num_iterations();
int nops = eigs.num_operations();
INFO("nconv = " << nconv);
INFO("niter = " << niter);
INFO("nops = " << nops);
REQUIRE(eigs.info() == CompInfo::Successful);
RealVector 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)
{
constexpr bool is_dense = std::is_same<MatType, Matrix>::value;
using DenseOp = DenseHermMatProd<std::complex<double>>;
using SparseOp = SparseHermMatProd<std::complex<double>>;
using OpType = typename std::conditional<is_dense, DenseOp, SparseOp>::type;
OpType op(mat);
HermEigsSolver<OpType> eigs(op, k, m);
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);
}
SECTION("Smallest Value")
{
run_test(mat, eigs, SortRule::SmallestAlge);
}
SECTION("Both Ends")
{
run_test(mat, eigs, SortRule::BothEnds);
}
}
TEST_CASE("Eigensolver of Hermitian matrix [10x10]", "[eigs_herm]")
{
std::srand(123);
const Matrix A = gen_dense_data(10);
int k = 3;
int m = 6;
run_test_sets(A, k, m);
}
TEST_CASE("Eigensolver of Hermitian matrix [100x100]", "[eigs_herm]")
{
std::srand(123);
const Matrix A = gen_dense_data(100);
int k = 10;
int m = 20;
run_test_sets(A, k, m);
}
TEST_CASE("Eigensolver of Hermitian matrix [1000x1000]", "[eigs_herm]")
{
std::srand(123);
const Matrix A = gen_dense_data(1000);
int k = 20;
int m = 50;
run_test_sets(A, k, m);
}
TEST_CASE("Eigensolver of sparse Hermitian matrix [10x10]", "[eigs_herm]")
{
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;
run_test_sets(A, k, m);
}
TEST_CASE("Eigensolver of sparse Hermitian matrix [100x100]", "[eigs_herm]")
{
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;
run_test_sets(A, k, m);
}
TEST_CASE("Eigensolver of sparse Hermitian matrix [1000x1000]", "[eigs_herm]")
{
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;
run_test_sets(A, k, m);
}
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