217 lines
4.9 KiB
C++
217 lines
4.9 KiB
C++
/**
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* $Id$
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* ***** BEGIN GPL/BL DUAL LICENSE BLOCK *****
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version. The Blender
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* Foundation also sells licenses for use in proprietary software under
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* the Blender License. See http://www.blender.org/BL/ for information
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* about this.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software Foundation,
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* Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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*
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* The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
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* All rights reserved.
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*
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* The Original Code is: all of this file.
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*
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* Contributor(s): none yet.
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*
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* ***** END GPL/BL DUAL LICENSE BLOCK *****
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*/
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/*
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*
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* Template Numerical Toolkit (TNT): Linear Algebra Module
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*
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* Mathematical and Computational Sciences Division
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* National Institute of Technology,
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* Gaithersburg, MD USA
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*
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*
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* This software was developed at the National Institute of Standards and
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* Technology (NIST) by employees of the Federal Government in the course
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* of their official duties. Pursuant to title 17 Section 105 of the
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* United States Code, this software is not subject to copyright protection
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* and is in the public domain. The Template Numerical Toolkit (TNT) is
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* an experimental system. NIST assumes no responsibility whatsoever for
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* its use by other parties, and makes no guarantees, expressed or implied,
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* about its quality, reliability, or any other characteristic.
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*
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* BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
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* see http://math.nist.gov/tnt for latest updates.
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*
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*/
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// Triangular Solves
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#ifndef TRISLV_H
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#define TRISLV_H
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#include "triang.h"
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namespace TNT
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{
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template <class MaTriX, class VecToR>
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VecToR Lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
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{
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Subscript N = A.num_rows();
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// make sure matrix sizes agree; A must be square
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assert(A.num_cols() == N);
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assert(b.dim() == N);
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VecToR x(N);
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Subscript i;
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for (i=1; i<=N; i++)
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{
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typename MaTriX::element_type tmp=0;
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for (Subscript j=1; j<i; j++)
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tmp = tmp + A(i,j)*x(j);
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x(i) = (b(i) - tmp)/ A(i,i);
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}
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return x;
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}
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template <class MaTriX, class VecToR>
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VecToR Unit_lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
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{
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Subscript N = A.num_rows();
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// make sure matrix sizes agree; A must be square
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assert(A.num_cols() == N);
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assert(b.dim() == N);
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VecToR x(N);
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Subscript i;
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for (i=1; i<=N; i++)
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{
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typename MaTriX::element_type tmp=0;
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for (Subscript j=1; j<i; j++)
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tmp = tmp + A(i,j)*x(j);
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x(i) = b(i) - tmp;
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}
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return x;
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}
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template <class MaTriX, class VecToR>
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VecToR linear_solve(/*const*/ LowerTriangularView<MaTriX> &A,
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/*const*/ VecToR &b)
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{
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return Lower_triangular_solve(A, b);
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}
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template <class MaTriX, class VecToR>
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VecToR linear_solve(/*const*/ UnitLowerTriangularView<MaTriX> &A,
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/*const*/ VecToR &b)
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{
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return Unit_lower_triangular_solve(A, b);
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}
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//********************** Upper triangular section ****************
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template <class MaTriX, class VecToR>
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VecToR Upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
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{
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Subscript N = A.num_rows();
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// make sure matrix sizes agree; A must be square
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assert(A.num_cols() == N);
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assert(b.dim() == N);
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VecToR x(N);
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Subscript i;
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for (i=N; i>=1; i--)
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{
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typename MaTriX::element_type tmp=0;
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for (Subscript j=i+1; j<=N; j++)
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tmp = tmp + A(i,j)*x(j);
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x(i) = (b(i) - tmp)/ A(i,i);
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}
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return x;
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}
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template <class MaTriX, class VecToR>
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VecToR Unit_upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
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{
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Subscript N = A.num_rows();
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// make sure matrix sizes agree; A must be square
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assert(A.num_cols() == N);
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assert(b.dim() == N);
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VecToR x(N);
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Subscript i;
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for (i=N; i>=1; i--)
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{
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typename MaTriX::element_type tmp=0;
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for (Subscript j=i+1; j<i; j++)
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tmp = tmp + A(i,j)*x(j);
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x(i) = b(i) - tmp;
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}
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return x;
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}
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template <class MaTriX, class VecToR>
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VecToR linear_solve(/*const*/ UpperTriangularView<MaTriX> &A,
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/*const*/ VecToR &b)
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{
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return Upper_triangular_solve(A, b);
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}
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template <class MaTriX, class VecToR>
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VecToR linear_solve(/*const*/ UnitUpperTriangularView<MaTriX> &A,
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/*const*/ VecToR &b)
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{
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return Unit_upper_triangular_solve(A, b);
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}
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} // namespace TNT
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#endif // TRISLV_H
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