/usr/include/itpp/base/algebra/eigen.h is in libitpp-dev 4.3.1-8.
This file is owned by root:root, with mode 0o644.
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* \file
* \brief Definitions of eigenvalue decomposition functions
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ 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.
*
* IT++ 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 IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#ifndef EIGEN_H
#define EIGEN_H
#include <itpp/base/mat.h>
#include <itpp/itexports.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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT 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.
*/
ITPP_EXPORT cvec eig(const cmat &A);
} // namespace itpp
#endif // #ifndef EIGEN_H
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