int main(int argc, char *argv[]) {
MPI_Init(&argc, &argv);
typedef rokko::grid_row_major grid_major;
typedef rokko::matrix_col_major matrix_major;
//typedef rokko::matrix_row_major matrix_major;
rokko::solver solver("scalapack");
solver.initialize(argc, argv);
MPI_Comm comm = MPI_COMM_WORLD;
rokko::grid<grid_major> g(comm);
int myrank = g.myrank;
const int root = 0;
const int dim = 10;
rokko::distributed_matrix<matrix_major> mat(dim, dim, g);
rokko::generate_frank_matrix(mat);
mat.print();
Eigen::MatrixXd global_mat;
rokko::gather(mat, global_mat, root);
if (myrank == root)
std::cout << "global_mat:" << std::endl << global_mat << std::endl;
Eigen::VectorXd w(dim);
rokko::distributed_matrix<matrix_major> Z(dim, dim, g); //, true);
solver.diagonalize(mat, w, Z);
// gather of eigenvectors
Eigen::MatrixXd eigvec_global;
Eigen::MatrixXd eigvec_sorted(dim, dim);
Eigen::VectorXd eigval_sorted(dim);
rokko::gather(Z, eigvec_global, root);
Z.print();
if (myrank == root) {
std::cout << "eigvec:" << std::endl << eigvec_global << std::endl;
}
std::cout.precision(20);
/*
std::cout << "w=" << std::endl;
for (int i=0; i<dim; ++i) {
std::cout << w[i] << " ";
}
std::cout << std::endl;
*/
if (myrank == root) {
rokko::sort_eigenpairs(w, eigvec_global, eigval_sorted, eigvec_sorted);
std::cout << "Computed Eigenvalues= " << eigval_sorted.transpose() << std::endl;
std::cout.precision(3);
std::cout << "Check the orthogonality of Eigenvectors:" << std::endl
<< eigvec_sorted * eigvec_sorted.transpose() << std::endl; // Is it equal to indentity matrix?
//<< eigvec_global.transpose() * eigvec_global << std::endl; // Is it equal to indentity matrix?
std::cout << "residual := A x - lambda x = " << std::endl
<< global_mat * eigvec_sorted.col(1) - eigval_sorted(1) * eigvec_sorted.col(1) << std::endl;
std::cout << "Are all the following values equal to some eigenvalue = " << std::endl
<< (global_mat * eigvec_sorted.col(0)).array() / eigvec_sorted.col(0).array() << std::endl;
//cout << "global_matrix=" << std::endl << global_matrix << std::endl;
}
/*
double time;
if (rank == 0) {
time = end - start;
std::cout << "time=" << time << std::endl;
ofs << "time=" << time << std::endl;
//cout << "iter=" << iter << std::endl;
//ofs << "iter=" << iter << std::endl;
}
*/
solver.finalize();
MPI_Finalize();
return 0;
}
int main(int argc, char *argv[]) {
MPI_Init(&argc, &argv);
//typedef rokko::matrix_row_major matrix_major;
typedef rokko::matrix_col_major matrix_major;
if (argc <= 2) {
std::cerr << "error: " << argv[0] << " solver_name alps_parameter_file_name" << std::endl;
MPI_Abort(MPI_COMM_WORLD, 34);
}
std::string solver_name(argv[1]);
std::ifstream ifs(argv[2]);
alps::Parameters params(ifs);
std::ostream& out = std::cout;
barista::Hamiltonian<> hamiltonian(params);
int dim = hamiltonian.dimension();
rokko::parallel_dense_solver solver(solver_name);
solver.initialize(argc, argv);
MPI_Comm comm = MPI_COMM_WORLD;
rokko::grid g(comm, rokko::grid_col_major);
int myrank = g.get_myrank();
const int root = 0;
rokko::distributed_matrix<matrix_major> mat(dim, dim, g, solver);
hamiltonian.fill(mat);
mat.print();
rokko::localized_matrix<matrix_major> lmat(dim, dim);
rokko::gather(mat, lmat, root);
if (myrank == root)
std::cout << "lmat:" << std::endl << lmat << std::endl;
rokko::localized_vector w(dim);
rokko::distributed_matrix<matrix_major> Z(dim, dim, g, solver);
try {
solver.diagonalize(mat, w, Z);
}
catch (const char *e) {
std::cout << "Exception : " << e << std::endl;
MPI_Abort(MPI_COMM_WORLD, 22);
}
// gather of eigenvectors
rokko::localized_matrix<matrix_major> eigvec_global;
rokko::localized_matrix<matrix_major> eigvec_sorted(dim, dim);
rokko::localized_vector eigval_sorted(dim);
rokko::gather(Z, eigvec_global, root);
Z.print();
if (myrank == root) {
std::cout << "eigvec:" << std::endl << eigvec_global << std::endl;
}
std::cout.precision(20);
/*
std::cout << "w=" << std::endl;
for (int i=0; i<dim; ++i) {
std::cout << w[i] << " ";
}
std::cout << std::endl;
*/
if (myrank == root) {
rokko::sort_eigenpairs(w, eigvec_global, eigval_sorted, eigvec_sorted);
std::cout << "Computed Eigenvalues= " << eigval_sorted.transpose() << std::endl;
std::cout.precision(3);
std::cout << "Check the orthogonality of Eigenvectors:" << std::endl
<< eigvec_sorted * eigvec_sorted.transpose() << std::endl; // Is it equal to indentity matrix?
//<< eigvec_global.transpose() * eigvec_global << std::endl; // Is it equal to indentity matrix?
std::cout << "residual := A x - lambda x = " << std::endl
<< lmat * eigvec_sorted.col(1) - eigval_sorted(1) * eigvec_sorted.col(1) << std::endl;
std::cout << "Are all the following values equal to some eigenvalue = " << std::endl
<< (lmat * eigvec_sorted.col(0)).array() / eigvec_sorted.col(0).array() << std::endl;
//cout << "lmat=" << std::endl << lmat << std::endl;
}
solver.finalize();
MPI_Finalize();
return 0;
}
