00001 /* 00002 ------------------------------------------------------------------- 00003 00004 Copyright (C) 2006, 2007, 2008, 2009, Andrew W. Steiner 00005 00006 This file is part of O2scl. 00007 00008 O2scl is free software; you can redistribute it and/or modify 00009 it under the terms of the GNU General Public License as published by 00010 the Free Software Foundation; either version 3 of the License, or 00011 (at your option) any later version. 00012 00013 O2scl is distributed in the hope that it will be useful, 00014 but WITHOUT ANY WARRANTY; without even the implied warranty of 00015 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00016 GNU General Public License for more details. 00017 00018 You should have received a copy of the GNU General Public License 00019 along with O2scl. If not, see <http://www.gnu.org/licenses/>. 00020 00021 ------------------------------------------------------------------- 00022 */ 00023 /* linalg/givens.c 00024 * 00025 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Gerard Jungman, Brian Gough 00026 * 00027 * This program is free software; you can redistribute it and/or modify 00028 * it under the terms of the GNU General Public License as published by 00029 * the Free Software Foundation; either version 3 of the License, or (at 00030 * your option) any later version. 00031 * 00032 * This program is distributed in the hope that it will be useful, but 00033 * WITHOUT ANY WARRANTY; without even the implied warranty of 00034 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00035 * General Public License for more details. 00036 * 00037 * You should have received a copy of the GNU General Public License 00038 * along with this program; if not, write to the Free Software 00039 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 00040 * 02110-1301, USA. 00041 */ 00042 /** \file givens_base.h 00043 \brief File for Givens rotations 00044 */ 00045 00046 #ifdef DOXYGENP 00047 namespace o2scl_linalg { 00048 #endif 00049 00050 /** 00051 \brief Apply a rotation to matrices from the QR decomposition 00052 00053 This performs \f$ Q \rightarrow Q G \f$ and 00054 \f$ R \rightarrow G^{T} R \f$. 00055 */ 00056 template<class mat1_t, class mat2_t> 00057 void apply_givens_qr(size_t M, size_t N, mat1_t &Q, mat2_t &R, 00058 size_t i, size_t j, double c, double s) { 00059 00060 for(size_t k=0;k<M;k++) { 00061 double qki=O2SCL_IX2(Q,k,i); 00062 double qkj=O2SCL_IX2(Q,k,j); 00063 O2SCL_IX2(Q,k,i)=qki*c-qkj*s; 00064 O2SCL_IX2(Q,k,j)=qki*s+qkj*c; 00065 } 00066 for(size_t k=GSL_MIN(i,j);k<N;k++) { 00067 double rik=O2SCL_IX2(R,i,k); 00068 double rjk=O2SCL_IX2(R,j,k); 00069 O2SCL_IX2(R,i,k)=c*rik-s*rjk; 00070 O2SCL_IX2(R,j,k)=s*rik+c*rjk; 00071 } 00072 00073 return; 00074 } 00075 00076 /** 00077 \brief Apply a rotation to matrices from the LQ decomposition 00078 00079 This performs \f$ Q \rightarrow Q G \f$ and 00080 \f$ L \rightarrow L G^{T} \f$. 00081 */ 00082 template<class mat1_t, class mat2_t> 00083 void apply_givens_lq(size_t M, size_t N, mat1_t &Q, mat2_t &L, 00084 size_t i, size_t j, double c, double s) { 00085 00086 for(size_t k=0;k<M;k++) { 00087 double qik=O2SCL_IX2(Q,i,k); 00088 double qjk=O2SCL_IX2(Q,j,k); 00089 O2SCL_IX2(Q,i,k)=qik*c-qjk*s; 00090 O2SCL_IX2(Q,j,k)=qik*s+qjk*c; 00091 } 00092 for(size_t k=GSL_MIN(i,j);k<N;k++) { 00093 double lki=O2SCL_IX2(L,k,i); 00094 double lkj=O2SCL_IX2(L,k,j); 00095 O2SCL_IX2(L,k,i)=c*lki-s*lkj; 00096 O2SCL_IX2(L,k,j)=s*lki+c*lkj; 00097 } 00098 00099 return; 00100 } 00101 00102 /// Apply a rotation to a vector, \f$ v \rightarrow G^{T} v \f$ 00103 template<class vec_t> 00104 void apply_givens_vec(vec_t &v, size_t i, size_t j, 00105 double c, double s) { 00106 double vi=O2SCL_IX(v,i); 00107 double vj=O2SCL_IX(v,j); 00108 O2SCL_IX(v,i)=c*vi-s*vj; 00109 O2SCL_IX(v,j)=s*vi+c*vj; 00110 return; 00111 } 00112 00113 #ifdef DOXYGENP 00114 } 00115 #endif
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