eigenvalues.h

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/*!
 * 
 *
 * \brief       Algorithms for Eigenvalue decompositions
 * 
 * 
 * 
 *
 * \author      O. Krause
 * \date        2011
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark 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 Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
#ifndef SHARK_LINALG_EIGENVALUES_H
#define SHARK_LINALG_EIGENVALUES_H

#include <shark/LinAlg/Base.h>
#include <shark/LinAlg/BLAS/kernels/syev.hpp>

namespace shark{ namespace blas{

/**
 * \ingroup shark_globals
 * 
 * @{
 */

/*!
 *  \brief Used as frontend for
 *  eigensymm for calculating the eigenvalues and the normalized eigenvectors of a symmetric matrix
 *  'A' using the Givens and Householder reduction. Each time this frontend is called additional
 *  memory is allocated for intermediate results.
 *
 *
 * \param A \f$ n \times n \f$ matrix, which must be symmetric, so only the bottom triangular matrix must contain values.
 * \param eigenVectors \f$ n \times n \f$ matrix with the calculated normalized eigenvectors, each column contains an eigenvector.
 * \param eigenValues n-dimensional vector with the calculated eigenvalues in descending order.
 * \return none.
 *
 * \throw SharkException
 */
template<class MatrixT,class MatrixU,class VectorT>
void eigensymm
(
    matrix_expression<MatrixT, cpu_tag> const& A,
    matrix_expression<MatrixU, cpu_tag>& eigenVectors,
    vector_expression<VectorT, cpu_tag>& eigenValues
)
{
    SIZE_CHECK(A().size2() == A().size1());
    std::size_t n = A().size1();
    
    eigenVectors().resize(n,n);
    eigenVectors().clear();
    eigenValues().resize(n);
    eigenValues().clear();
    // special case n = 1
    if (n == 1) {
        eigenVectors()( 0 ,  0 ) = 1;
        eigenValues()( 0 ) = A()( 0 ,  0 );
        return;
    }

    // copy matrix
    for (std::size_t i = 0; i < n; i++) {
        for (std::size_t j = 0; j <= i; j++) {
            eigenVectors()(i, j) = A()(i, j);
        }
    }
    
    kernels::syev(eigenVectors,eigenValues);
}



/** @}*/
}}
#endif