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/*
//
// Copyright 1997-2009 Torsten Rohlfing
//
// Copyright 2004-2010 SRI International
//
// This file is part of the Computational Morphometry Toolkit.
//
// http://www.nitrc.org/projects/cmtk/
//
// The Computational Morphometry Toolkit 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.
//
// The Computational Morphometry Toolkit 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 the Computational Morphometry Toolkit. If not, see
// <http://www.gnu.org/licenses/>.
//
// $Revision: 5436 $
//
// $LastChangedDate: 2018-12-10 19:01:20 -0800 (Mon, 10 Dec 2018) $
//
// $LastChangedBy: torstenrohlfing $
//
*/
/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
pseudocode.
See subroutines comments for additional copyrights.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer listed
in this license in the documentation and/or other materials
provided with the distribution.
- Neither the name of the copyright holders nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/
#ifndef _tdevd_h
#define _tdevd_h
#include "ap.h"
#include "blas.h"
#include "rotations.h"
/*************************************************************************
Finding the eigenvalues and eigenvectors of a tridiagonal symmetric matrix
The algorithm finds the eigen pairs of a tridiagonal symmetric matrix by
using an QL/QR algorithm with implicit shifts.
Input parameters:
D - the main diagonal of a tridiagonal matrix.
Array whose index ranges within [0..N-1].
E - the secondary diagonal of a tridiagonal matrix.
Array whose index ranges within [0..N-2].
N - size of matrix A.
ZNeeded - flag controlling whether the eigenvectors are needed or not.
If ZNeeded is equal to:
* 0, the eigenvectors are not needed;
* 1, the eigenvectors of a tridiagonal matrix
are multiplied by the square matrix Z. It is used if the
tridiagonal matrix is obtained by the similarity
transformation of a symmetric matrix;
* 2, the eigenvectors of a tridiagonal matrix replace the
square matrix Z;
* 3, matrix Z contains the first row of the eigenvectors
matrix.
Z - if ZNeeded=1, Z contains the square matrix by which the
eigenvectors are multiplied.
Array whose indexes range within [0..N-1, 0..N-1].
Output parameters:
D - eigenvalues in ascending order.
Array whose index ranges within [0..N-1].
Z - if ZNeeded is equal to:
* 0, Z hasnt changed;
* 1, Z contains the product of a given matrix (from the left)
and the eigenvectors matrix (from the right);
* 2, Z contains the eigenvectors.
* 3, Z contains the first row of the eigenvectors matrix.
If ZNeeded<3, Z is the array whose indexes range within [0..N-1, 0..N-1].
In that case, the eigenvectors are stored in the matrix columns.
If ZNeeded=3, Z is the array whose indexes range within [0..0, 0..N-1].
Result:
True, if the algorithm has converged.
False, if the algorithm hasn't converged.
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
*************************************************************************/
bool smatrixtdevd(ap::real_1d_array& d,
ap::real_1d_array e,
int n,
int zneeded,
ap::real_2d_array& z);
/*************************************************************************
Obsolete 1-based subroutine.
*************************************************************************/
bool tridiagonalevd(ap::real_1d_array& d,
ap::real_1d_array e,
int n,
int zneeded,
ap::real_2d_array& z);
#endif
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