LanczosEigenSolver.cpp

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/*
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or
 * (at your option) any later version.
 *
 * Written (W) 2013 Soumyajit De
 */

#include <shogun/lib/common.h>

#ifdef HAVE_LAPACK
#ifdef HAVE_EIGEN3

#include <shogun/base/Parameter.h>
#include <shogun/mathematics/lapack.h>
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/linalg/linop/LinearOperator.h>
#include <shogun/mathematics/linalg/linsolver/IterativeSolverIterator.h>
#include <shogun/mathematics/linalg/eigsolver/LanczosEigenSolver.h>
#include <vector>
#include <shogun/lib/SGVector.h>

using namespace Eigen;

namespace shogun
{

CLanczosEigenSolver::CLanczosEigenSolver()
    : CEigenSolver()
{
    init();
}

CLanczosEigenSolver::CLanczosEigenSolver(
    CLinearOperator<float64_t>* linear_operator)
    : CEigenSolver(linear_operator)
{
    init();
}

void CLanczosEigenSolver::init()
{
    m_max_iteration_limit=1000;
    m_relative_tolerence=1E-6;
    m_absolute_tolerence=1E-6;

    SG_ADD(&m_max_iteration_limit, "max_iteration_limit",
        "Maximum number of iteration for the solver", MS_NOT_AVAILABLE);

    SG_ADD(&m_relative_tolerence, "relative_tolerence",
        "Relative tolerence of solver", MS_NOT_AVAILABLE);

    SG_ADD(&m_absolute_tolerence, "absolute_tolerence",
        "Absolute tolerence of solver", MS_NOT_AVAILABLE);
}

CLanczosEigenSolver::~CLanczosEigenSolver()
{
}

void CLanczosEigenSolver::compute()
{
    SG_DEBUG("Entering\n");

    if (m_is_computed_min && m_is_computed_max)
    {
        SG_DEBUG("Minimum/maximum eigenvalues are already computed, exiting\n");
        return;
    }

    REQUIRE(m_linear_operator, "Operator is NULL!\n");

    // vector v_0
    VectorXd v=VectorXd::Zero(m_linear_operator->get_dimension());

    // vector v_i, for i=1 this is random valued with norm 1
    SGVector<float64_t> v_(v.rows());
    Map<VectorXd> v_i(v_.vector, v_.vlen);
    v_i=VectorXd::Random(v_.vlen);
    v_i/=v_i.norm();

    // the iterator for this iterative solver
    IterativeSolverIterator<float64_t> it(v_i, m_max_iteration_limit,
        m_relative_tolerence, m_absolute_tolerence);

    // the diagonal for Lanczos T-matrix (tridiagonal)
    std::vector<float64_t> alpha;

    // the subdiagonal for Lanczos T-matrix (tridiagonal)
    std::vector<float64_t> beta;

    float64_t beta_i=0.0;
    SGVector<float64_t> w_(v_.vlen);

    // CG iteration begins
    for (it.begin(v_i); !it.end(v_i); ++it)
    {
        SG_DEBUG("CG iteration %d, residual norm %f\n",
                it.get_iter_info().iteration_count,
                it.get_iter_info().residual_norm);

        // apply linear operator to the direction vector
        w_=m_linear_operator->apply(v_);
        Map<VectorXd> w_i(w_.vector, w_.vlen);

        // compute v^{T}Av, if zero, failure
        float64_t alpha_i=w_i.dot(v_i);
        if (alpha_i==0.0)
            break;

        // update w_i, v_(i-1) and find beta
        w_i-=alpha_i*v_i+beta_i*v;
        beta_i=w_i.norm();
        v=v_i;
        v_i=w_i/beta_i;

        // prepate Lanczos T-matrix from alpha and beta
        alpha.push_back(alpha_i);
        beta.push_back(beta_i);
    }

    // solve Lanczos T-matrix to get the eigenvalues
    int32_t M=0;
    SGVector<float64_t> w(alpha.size());
    int32_t info=0;

    // keeping copies of the diagonal and subdiagonal
    // because subsequent call to dstemr destroys it
    std::vector<float64_t> alpha_orig=alpha;
    std::vector<float64_t> beta_orig=beta;

    if (!m_is_computed_min)
    {
        // computing min eigenvalue
        wrap_dstemr('N', 'I', alpha.size(), &alpha[0], &beta[0],
            0.0, 0.0, 1, 1, &M, w.vector, NULL, 1, 1, NULL, 0.0, &info);

        if (info==0)
        {
            SG_INFO("Iteration took %ld times, residual norm=%.20lf\n",
            it.get_iter_info().iteration_count, it.get_iter_info().residual_norm);

            m_min_eigenvalue=w[0];
            m_is_computed_min=true;
        }
        else
            SG_WARNING("Some error occured while computing eigenvalues!\n");
    }

    if (!m_is_computed_max)
    {
        // computing max eigenvalue
        wrap_dstemr('N', 'I', alpha_orig.size(), &alpha_orig[0], &beta_orig[0],
            0.0, 0.0, w.vlen, w.vlen, &M, w.vector, NULL, 1, 1, NULL, 0.0, &info);

        if (info==0)
        {
            SG_INFO("Iteration took %ld times, residual norm=%.20lf\n",
            it.get_iter_info().iteration_count, it.get_iter_info().residual_norm);
            m_max_eigenvalue=w[0];
            m_is_computed_max=true;
        }
        else
            SG_WARNING("Some error occured while computing eigenvalues!\n");
    }

    SG_DEBUG("Leaving\n");
}

}
#endif // HAVE_EIGEN3
#endif // HAVE_LAPACK