eigen.h

强大的C++库

/*!
 * \file
 * \brief Definitions of eigenvalue decomposition functions
 * \author Tony Ottosson
 *
 * -------------------------------------------------------------------------
 *
 * IT++ - C++ library of mathematical, signal processing, speech processing,
 *        and communications classes and functions
 *
 * Copyright (C) 1995-2008  (see AUTHORS file for a list of contributors)
 *
 * 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 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 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 St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * -------------------------------------------------------------------------
 */

#ifndef EIGEN_H
#define EIGEN_H

#include <itpp/base/mat.h>


namespace itpp {

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues and eigenvectors of a symmetric real matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    The eigenvectors are the columns of the matrix V.
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine DSYEV.
  */
  bool eig_sym(const mat &A, vec &d, mat &V);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a symmetric real matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine DSYEV.
  */
  bool eig_sym(const mat &A, vec &d);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a symmetric real matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real and symmetric \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]

    Uses the LAPACK routine DSYEV.
  */
  vec eig_sym(const mat &A);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues and eigenvectors of a hermitian complex matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    The eigenvectors are the columns of the matrix V.
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine ZHEEV.
  */
  bool eig_sym(const cmat &A, vec &d, cmat &V);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a hermitian complex matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine ZHEEV.
  */
  bool eig_sym(const cmat &A, vec &d);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a hermitian complex matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex and hermitian \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]

    Uses the LAPACK routine ZHEEV.
  */
  vec eig_sym(const cmat &A);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues and eigenvectors of a real non-symmetric matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    The eigenvectors are the columns of the matrix V.
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine DGEEV.
  */
  bool eig(const mat &A, cvec &d, cmat &V);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a real non-symmetric matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine DGEEV.
  */
  bool eig(const mat &A, cvec &d);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a real non-symmetric matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the real \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]

    Uses the LAPACK routine DGEEV.
  */
  cvec eig(const mat &A);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    The eigenvectors are the columns of the matrix V.
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine ZGEEV.
  */
  bool eig(const cmat &A, cvec &d, cmat &V);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a complex non-hermitian matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]
    True is returned if the calculation was successful. Otherwise false.

    Uses the LAPACK routine ZGEEV.
  */
  bool eig(const cmat &A, cvec &d);

  /*!
    \ingroup matrixdecomp
    \brief Calculates the eigenvalues of a complex non-hermitian matrix

    The Eigenvalues \f$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})\f$ and the eigenvectors
    \f$\mathbf{v}_i, \: i=0, \ldots, n-1\f$ of the complex \f$n \times n\f$
    matrix \f$\mathbf{A}\f$ satisfies
    \f[
    \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1.
    \f]

    Uses the LAPACK routine ZGEEV.
  */
  cvec eig(const cmat &A);

} // namespace itpp

#endif // #ifndef EIGEN_H