JDSymEigsBase.h

// Copyright (C) 2020 Netherlands eScience Center <J.Wehner@esciencecenter.nl>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
#ifndef SPECTRA_JD_SYM_EIGS_BASE_H
#define SPECTRA_JD_SYM_EIGS_BASE_H
 
#include <Eigen/Core>
#include <vector>     // std::vector
#include <cmath>      // std::abs, std::pow
#include <algorithm>  // std::min
#include <stdexcept>  // std::invalid_argument
#include <iostream>
 
#include "Util/SelectionRule.h"
#include "Util/CompInfo.h"
#include "LinAlg/SearchSpace.h"
#include "LinAlg/RitzPairs.h"
 
namespace Spectra {

template <typename Derived, typename OpType>
class JDSymEigsBase
{
protected:
    using Index = Eigen::Index;
    using Scalar = typename OpType::Scalar;
    using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
 
    const OpType& m_matrix_operator;  // object to conduct matrix operation,
                                      // e.g. matrix-vector product
    Index niter_ = 0;
    const Index m_number_eigenvalues;  // number of eigenvalues requested
    Index m_max_search_space_size;
    Index m_initial_search_space_size;
    Index m_correction_size;             // how many correction vectors are added in each iteration
    RitzPairs<Scalar> m_ritz_pairs;      // Ritz eigen pair structure
    SearchSpace<Scalar> m_search_space;  // search space
 
private:
    CompInfo m_info = CompInfo::NotComputed;  // status of the computation
 
    void check_argument() const
    {
        if (m_number_eigenvalues < 1 || m_number_eigenvalues > m_matrix_operator.cols() - 1)
            throw std::invalid_argument("nev must satisfy 1 <= nev <= n - 1, n is the size of matrix");
    }
 
    void initialize()
    {
        // TODO better input validation and checks
        if (m_matrix_operator.cols() < m_max_search_space_size)
        {
            m_max_search_space_size = m_matrix_operator.cols();
        }
        if (m_matrix_operator.cols() < m_initial_search_space_size + m_correction_size)
        {
            m_initial_search_space_size = m_matrix_operator.cols() / 3;
            m_correction_size = m_matrix_operator.cols() / 3;
        }
    }
 
public:
    JDSymEigsBase(OpType& op, Index nev, Index nvec_init, Index nvec_max) :
        m_matrix_operator(op),
        m_number_eigenvalues(nev),
        m_max_search_space_size(nvec_max < op.rows() ? nvec_max : 10 * m_number_eigenvalues),
        m_initial_search_space_size(nvec_init < op.rows() ? nvec_init : 2 * m_number_eigenvalues),
        m_correction_size(m_number_eigenvalues)
    {
        check_argument();
        initialize();
    }
 
    JDSymEigsBase(OpType& op, Index nev) :
        JDSymEigsBase(op, nev, 2 * nev, 10 * nev) {}

    void set_max_search_space_size(Index max_search_space_size)
    {
        m_max_search_space_size = max_search_space_size;
    }

    void set_correction_size(Index correction_size)
    {
        m_correction_size = correction_size;
    }

    void set_initial_search_space_size(Index initial_search_space_size)
    {
        m_initial_search_space_size = initial_search_space_size;
    }

    virtual ~JDSymEigsBase() {}

    CompInfo info() const { return m_info; }

    Index num_iterations() const { return niter_; }
 
    Vector eigenvalues() const { return m_ritz_pairs.ritz_values().head(m_number_eigenvalues); }
 
    Matrix eigenvectors() const { return m_ritz_pairs.ritz_vectors().leftCols(m_number_eigenvalues); }
 
    Index compute(SortRule selection = SortRule::LargestMagn, Index maxit = 100,
                  Scalar tol = 100 * Eigen::NumTraits<Scalar>::dummy_precision())
    {
        Derived& derived = static_cast<Derived&>(*this);
        Matrix intial_space = derived.setup_initial_search_space(selection);
        return compute_with_guess(intial_space, selection, maxit, tol);
    }
 
    Index compute_with_guess(const Eigen::Ref<const Matrix>& initial_space,
                             SortRule selection = SortRule::LargestMagn,
                             Index maxit = 100,
                             Scalar tol = 100 * Eigen::NumTraits<Scalar>::dummy_precision())
 
    {
        m_search_space.initialize_search_space(initial_space);
        niter_ = 0;
        for (niter_ = 0; niter_ < maxit; niter_++)
        {
            bool do_restart = (m_search_space.size() > m_max_search_space_size);
 
            if (do_restart)
            {
                m_search_space.restart(m_ritz_pairs, m_initial_search_space_size);
            }
 
            m_search_space.update_operator_basis_product(m_matrix_operator);
 
            Eigen::ComputationInfo small_problem_info = m_ritz_pairs.compute_eigen_pairs(m_search_space);
            if (small_problem_info != Eigen::ComputationInfo::Success)
            {
                m_info = CompInfo::NumericalIssue;
                break;
            }
            m_ritz_pairs.sort(selection);
 
            bool converged = m_ritz_pairs.check_convergence(tol, m_number_eigenvalues);
            if (converged)
            {
                m_info = CompInfo::Successful;
                break;
            }
            else if (niter_ == maxit - 1)
            {
                m_info = CompInfo::NotConverging;
                break;
            }
            Derived& derived = static_cast<Derived&>(*this);
            Matrix corr_vect = derived.calculate_correction_vector();
 
            m_search_space.extend_basis(corr_vect);
        }
        return (m_ritz_pairs.converged_eigenvalues()).template cast<Index>().head(m_number_eigenvalues).sum();
    }
};
 
}  // namespace Spectra
 
#endif  // SPECTRA_JD_SYM_EIGS_BASE_H