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#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/DavidsonSymEigsSolver.h>
#include <Spectra/MatOp/DenseSymMatProd.h>
#include <Spectra/MatOp/SparseSymMatProd.h>
#include "catch.hpp"
using namespace Spectra;
template <typename T>
using Matrix = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>;
template <typename T>
using Vector = Eigen::Matrix<T, Eigen::Dynamic, 1>;
template <typename T>
using SpMatrix = Eigen::SparseMatrix<T>;
// Traits to obtain operation type from matrix type
template <typename MatType>
struct OpTypeTrait
{
using Scalar = typename MatType::Scalar;
using OpType = DenseSymMatProd<Scalar>;
};
template <typename T>
struct OpTypeTrait<SpMatrix<T>>
{
using OpType = SparseSymMatProd<T>;
};
// Generate data for testing
template <typename Matrix>
Matrix gen_sym_data_dense(int n)
{
Matrix mat = 0.03 * Matrix::Random(n, n);
Matrix mat1 = mat + mat.transpose();
for (Eigen::Index i = 0; i < n; i++)
{
mat1(i, i) += i + 1;
}
return mat1;
}
template <typename SpMatrix>
SpMatrix gen_sym_data_sparse(int n)
{
// Eigen solver only uses the lower triangle of mat,
// so we don't need to make mat symmetric here.
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) = 0.1 * (distr(gen) - 0.5);
if (i == j)
{
mat.coeffRef(i, j) = i + 1;
}
}
}
return mat;
}
template <typename MatType>
void run_test(const MatType& mat, int nev, SortRule selection)
{
using OpType = typename OpTypeTrait<MatType>::OpType;
OpType op(mat);
DavidsonSymEigsSolver<OpType> eigs(op, nev);
int nconv = eigs.compute(selection);
int niter = eigs.num_iterations();
REQUIRE(nconv == nev);
INFO("nconv = " << nconv);
INFO("niter = " << niter);
REQUIRE(eigs.info() == CompInfo::Successful);
using T = typename OpType::Scalar;
Vector<T> evals = eigs.eigenvalues();
Matrix<T> evecs = eigs.eigenvectors();
Matrix<T> resid = op * evecs - evecs * evals.asDiagonal();
const T err = resid.array().abs().maxCoeff();
INFO("||AU - UD||_inf = " << err);
REQUIRE(err < 100 * Eigen::NumTraits<T>::dummy_precision());
}
template <typename MatType>
void run_test_set(const MatType& mat, int k)
{
SECTION("Largest Value")
{
run_test<MatType>(mat, k, SortRule::LargestAlge);
}
SECTION("Smallest Value")
{
run_test<MatType>(mat, k, SortRule::SmallestAlge);
}
}
TEMPLATE_TEST_CASE("Davidson Solver of dense symmetric real matrix [1000x1000]", "", double)
{
std::srand(123);
const Matrix<TestType> A = gen_sym_data_dense<Matrix<TestType>>(1000);
int k = 10;
run_test_set<Matrix<TestType>>(A, k);
}
TEMPLATE_TEST_CASE("Davidson Solver of sparse symmetric real matrix [1000x1000]", "", double)
{
std::srand(123);
int k = 10;
const SpMatrix<TestType> A = gen_sym_data_sparse<SpMatrix<TestType>>(1000);
run_test_set<SpMatrix<TestType>>(A, k);
}
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