eigs_sym.cc

// -*- mode: c++; fill-column: 80; c-basic-offset: 2; indent-tabs-mode: nil -*-
/*
    Copyright (c) 2010 Juan Jose Garcia Ripoll

    Tensor is free software; you can redistribute it and/or modify it
    under the terms of the GNU Library General Public License as published
    by the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Library General Public License for more details.

    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/

//----------------------------------------------------------------------
// ARPACK DRIVER FOR SYMMETRIC REAL EIGENVALUE PROBLEMS
//

#include <linalg.h>
#include <arpack.h>
#include <utils.h>
#include <sys/blas.h>

RTensor
eigs_sym(const RTensor &A, RArpack::EigType t, size_t neig, RTensor *eigenvectors,
         const RTensor::elt_t *initial_guess)
{
    size_t n = A.columns();

    if ((A.rank() != 2) || (A.rows() != n)) {
        std::cerr << "In eigs(): Can only compute eigenvalues of square matrices.";
        myabort();
    }

    if (neig > n || neig == 0) {
        std::cerr << "In eigs(): Can only compute up to " << n << " eigenvalues\n"
                  << "in a matrix that has " << n << " times " << n << " elements.";
        myabort();
    }

    if (n <= 4) {
        /* For small sizes, the ARPACK solver produces wrong results!
         * In any case, for these sizes it is more efficient to do the solving
         * using the full routine.
         */
        RTensor values = eig_sym(A, eigenvectors);
        UIVector ndx = RArpack::sort_values(values, t)(Range(0, neig-1));
        if (eigenvectors) {
            *eigenvectors = (*eigenvectors)(Range(), Range(ndx));
        }
        return re_part(values(Range(ndx)));
    }

    RArpack data(n, t, neig);

    if (initial_guess)
        data.set_start_vector(initial_guess);

    while (data.update() < RArpack::Finished) {
        gemv('N', n, n, RTensor::elt_one(), A.pointer(), n, data.get_x_vector(), 1,
             RTensor::elt_zero(), data.get_y_vector(), 1);
    }
    if (data.get_status() == RArpack::Finished) {
        return data.get_data(eigenvectors);
    } else {
        std::cerr << data.error_message() << '\n';
        myabort();
    }
    return RTensor();
}