[815] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // $Id: G4ErrorSymMatrix.cc,v 1.3 2007/06/21 15:04:10 gunter Exp $ |
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[850] | 27 | // GEANT4 tag $Name: HEAD $ |
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[815] | 28 | // |
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| 29 | // ------------------------------------------------------------ |
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| 30 | // GEANT 4 class implementation file |
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| 31 | // ------------------------------------------------------------ |
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| 32 | |
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| 33 | #include "globals.hh" |
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| 34 | #include <iostream> |
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| 35 | #include <cmath> |
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| 36 | |
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| 37 | #include "G4ErrorSymMatrix.hh" |
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| 38 | #include "G4ErrorMatrix.hh" |
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| 39 | |
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| 40 | // Simple operation for all elements |
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| 41 | |
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| 42 | #define SIMPLE_UOP(OPER) \ |
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| 43 | G4ErrorMatrixIter a=m.begin(); \ |
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| 44 | G4ErrorMatrixIter e=m.begin()+num_size(); \ |
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| 45 | for(;a<e; a++) (*a) OPER t; |
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| 46 | |
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| 47 | #define SIMPLE_BOP(OPER) \ |
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| 48 | G4ErrorMatrixIter a=m.begin(); \ |
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| 49 | G4ErrorMatrixConstIter b=m2.m.begin(); \ |
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| 50 | G4ErrorMatrixConstIter e=m.begin()+num_size(); \ |
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| 51 | for(;a<e; a++, b++) (*a) OPER (*b); |
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| 52 | |
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| 53 | #define SIMPLE_TOP(OPER) \ |
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| 54 | G4ErrorMatrixConstIter a=m1.m.begin(); \ |
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| 55 | G4ErrorMatrixConstIter b=m2.m.begin(); \ |
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| 56 | G4ErrorMatrixIter t=mret.m.begin(); \ |
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| 57 | G4ErrorMatrixConstIter e=m1.m.begin()+m1.num_size(); \ |
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| 58 | for( ;a<e; a++, b++, t++) (*t) = (*a) OPER (*b); |
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| 59 | |
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| 60 | #define CHK_DIM_2(r1,r2,c1,c2,fun) \ |
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| 61 | if (r1!=r2 || c1!=c2) { \ |
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| 62 | G4ErrorMatrix::error("Range error in Matrix function " #fun "(1)."); \ |
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| 63 | } |
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| 64 | |
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| 65 | #define CHK_DIM_1(c1,r2,fun) \ |
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| 66 | if (c1!=r2) { \ |
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| 67 | G4ErrorMatrix::error("Range error in Matrix function " #fun "(2)."); \ |
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| 68 | } |
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| 69 | |
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| 70 | // Constructors. (Default constructors are inlined and in .icc file) |
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| 71 | |
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| 72 | G4ErrorSymMatrix::G4ErrorSymMatrix(G4int p) |
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| 73 | : m(p*(p+1)/2), nrow(p) |
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| 74 | { |
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| 75 | size = nrow * (nrow+1) / 2; |
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| 76 | m.assign(size,0); |
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| 77 | } |
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| 78 | |
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| 79 | G4ErrorSymMatrix::G4ErrorSymMatrix(G4int p, G4int init) |
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| 80 | : m(p*(p+1)/2), nrow(p) |
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| 81 | { |
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| 82 | size = nrow * (nrow+1) / 2; |
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| 83 | |
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| 84 | m.assign(size,0); |
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| 85 | switch(init) |
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| 86 | { |
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| 87 | case 0: |
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| 88 | break; |
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| 89 | |
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| 90 | case 1: |
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| 91 | { |
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| 92 | G4ErrorMatrixIter a = m.begin(); |
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| 93 | for(G4int i=1;i<=nrow;i++) |
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| 94 | { |
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| 95 | *a = 1.0; |
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| 96 | a += (i+1); |
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| 97 | } |
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| 98 | break; |
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| 99 | } |
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| 100 | default: |
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| 101 | G4ErrorMatrix::error("G4ErrorSymMatrix: initialization must be 0 or 1."); |
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| 102 | } |
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| 103 | } |
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| 104 | |
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| 105 | // |
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| 106 | // Destructor |
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| 107 | // |
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| 108 | |
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| 109 | G4ErrorSymMatrix::~G4ErrorSymMatrix() |
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| 110 | { |
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| 111 | } |
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| 112 | |
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| 113 | G4ErrorSymMatrix::G4ErrorSymMatrix(const G4ErrorSymMatrix &m1) |
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| 114 | : m(m1.size), nrow(m1.nrow), size(m1.size) |
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| 115 | { |
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| 116 | m = m1.m; |
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| 117 | } |
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| 118 | |
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| 119 | // |
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| 120 | // |
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| 121 | // Sub matrix |
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| 122 | // |
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| 123 | // |
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| 124 | |
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| 125 | G4ErrorSymMatrix G4ErrorSymMatrix::sub(G4int min_row, G4int max_row) const |
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| 126 | { |
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| 127 | G4ErrorSymMatrix mret(max_row-min_row+1); |
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| 128 | if(max_row > num_row()) |
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| 129 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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| 130 | G4ErrorMatrixIter a = mret.m.begin(); |
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| 131 | G4ErrorMatrixConstIter b1 = m.begin() + (min_row+2)*(min_row-1)/2; |
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| 132 | for(G4int irow=1; irow<=mret.num_row(); irow++) |
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| 133 | { |
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| 134 | G4ErrorMatrixConstIter b = b1; |
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| 135 | for(G4int icol=1; icol<=irow; icol++) |
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| 136 | { |
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| 137 | *(a++) = *(b++); |
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| 138 | } |
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| 139 | b1 += irow+min_row-1; |
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| 140 | } |
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| 141 | return mret; |
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| 142 | } |
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| 143 | |
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| 144 | G4ErrorSymMatrix G4ErrorSymMatrix::sub(G4int min_row, G4int max_row) |
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| 145 | { |
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| 146 | G4ErrorSymMatrix mret(max_row-min_row+1); |
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| 147 | if(max_row > num_row()) |
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| 148 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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| 149 | G4ErrorMatrixIter a = mret.m.begin(); |
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| 150 | G4ErrorMatrixIter b1 = m.begin() + (min_row+2)*(min_row-1)/2; |
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| 151 | for(G4int irow=1; irow<=mret.num_row(); irow++) |
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| 152 | { |
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| 153 | G4ErrorMatrixIter b = b1; |
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| 154 | for(G4int icol=1; icol<=irow; icol++) |
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| 155 | { |
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| 156 | *(a++) = *(b++); |
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| 157 | } |
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| 158 | b1 += irow+min_row-1; |
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| 159 | } |
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| 160 | return mret; |
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| 161 | } |
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| 162 | |
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| 163 | void G4ErrorSymMatrix::sub(G4int row,const G4ErrorSymMatrix &m1) |
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| 164 | { |
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| 165 | if(row <1 || row+m1.num_row()-1 > num_row() ) |
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| 166 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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| 167 | G4ErrorMatrixConstIter a = m1.m.begin(); |
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| 168 | G4ErrorMatrixIter b1 = m.begin() + (row+2)*(row-1)/2; |
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| 169 | for(G4int irow=1; irow<=m1.num_row(); irow++) |
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| 170 | { |
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| 171 | G4ErrorMatrixIter b = b1; |
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| 172 | for(G4int icol=1; icol<=irow; icol++) |
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| 173 | { |
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| 174 | *(b++) = *(a++); |
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| 175 | } |
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| 176 | b1 += irow+row-1; |
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| 177 | } |
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| 178 | } |
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| 179 | |
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| 180 | // |
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| 181 | // Direct sum of two matricies |
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| 182 | // |
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| 183 | |
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| 184 | G4ErrorSymMatrix dsum(const G4ErrorSymMatrix &m1, |
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| 185 | const G4ErrorSymMatrix &m2) |
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| 186 | { |
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| 187 | G4ErrorSymMatrix mret(m1.num_row() + m2.num_row(), 0); |
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| 188 | mret.sub(1,m1); |
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| 189 | mret.sub(m1.num_row()+1,m2); |
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| 190 | return mret; |
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| 191 | } |
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| 192 | |
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| 193 | /* ----------------------------------------------------------------------- |
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| 194 | This section contains support routines for matrix.h. This section contains |
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| 195 | The two argument functions +,-. They call the copy constructor and +=,-=. |
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| 196 | ----------------------------------------------------------------------- */ |
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| 197 | |
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| 198 | G4ErrorSymMatrix G4ErrorSymMatrix::operator- () const |
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| 199 | { |
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| 200 | G4ErrorSymMatrix m2(nrow); |
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| 201 | G4ErrorMatrixConstIter a=m.begin(); |
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| 202 | G4ErrorMatrixIter b=m2.m.begin(); |
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| 203 | G4ErrorMatrixConstIter e=m.begin()+num_size(); |
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| 204 | for(;a<e; a++, b++) { (*b) = -(*a); } |
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| 205 | return m2; |
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| 206 | } |
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| 207 | |
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| 208 | G4ErrorMatrix operator+(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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| 209 | { |
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| 210 | G4ErrorMatrix mret(m1); |
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| 211 | CHK_DIM_2(m1.num_row(),m2.num_row(), m1.num_col(),m2.num_col(),+); |
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| 212 | mret += m2; |
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| 213 | return mret; |
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| 214 | } |
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| 215 | |
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| 216 | G4ErrorMatrix operator+(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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| 217 | { |
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| 218 | G4ErrorMatrix mret(m2); |
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| 219 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),+); |
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| 220 | mret += m1; |
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| 221 | return mret; |
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| 222 | } |
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| 223 | |
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| 224 | G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &m1, |
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| 225 | const G4ErrorSymMatrix &m2) |
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| 226 | { |
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| 227 | G4ErrorSymMatrix mret(m1.nrow); |
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| 228 | CHK_DIM_1(m1.nrow, m2.nrow,+); |
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| 229 | SIMPLE_TOP(+) |
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| 230 | return mret; |
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| 231 | } |
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| 232 | |
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| 233 | // |
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| 234 | // operator - |
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| 235 | // |
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| 236 | |
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| 237 | G4ErrorMatrix operator-(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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| 238 | { |
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| 239 | G4ErrorMatrix mret(m1); |
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| 240 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),-); |
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| 241 | mret -= m2; |
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| 242 | return mret; |
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| 243 | } |
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| 244 | |
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| 245 | G4ErrorMatrix operator-(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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| 246 | { |
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| 247 | G4ErrorMatrix mret(m1); |
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| 248 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),-); |
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| 249 | mret -= m2; |
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| 250 | return mret; |
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| 251 | } |
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| 252 | |
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| 253 | G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &m1, |
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| 254 | const G4ErrorSymMatrix &m2) |
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| 255 | { |
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| 256 | G4ErrorSymMatrix mret(m1.num_row()); |
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| 257 | CHK_DIM_1(m1.num_row(),m2.num_row(),-); |
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| 258 | SIMPLE_TOP(-) |
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| 259 | return mret; |
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| 260 | } |
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| 261 | |
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| 262 | /* ----------------------------------------------------------------------- |
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| 263 | This section contains support routines for matrix.h. This file contains |
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| 264 | The two argument functions *,/. They call copy constructor and then /=,*=. |
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| 265 | ----------------------------------------------------------------------- */ |
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| 266 | |
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| 267 | G4ErrorSymMatrix operator/(const G4ErrorSymMatrix &m1,G4double t) |
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| 268 | { |
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| 269 | G4ErrorSymMatrix mret(m1); |
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| 270 | mret /= t; |
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| 271 | return mret; |
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| 272 | } |
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| 273 | |
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| 274 | G4ErrorSymMatrix operator*(const G4ErrorSymMatrix &m1,G4double t) |
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| 275 | { |
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| 276 | G4ErrorSymMatrix mret(m1); |
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| 277 | mret *= t; |
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| 278 | return mret; |
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| 279 | } |
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| 280 | |
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| 281 | G4ErrorSymMatrix operator*(G4double t,const G4ErrorSymMatrix &m1) |
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| 282 | { |
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| 283 | G4ErrorSymMatrix mret(m1); |
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| 284 | mret *= t; |
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| 285 | return mret; |
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| 286 | } |
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| 287 | |
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| 288 | G4ErrorMatrix operator*(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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| 289 | { |
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| 290 | G4ErrorMatrix mret(m1.num_row(),m2.num_col()); |
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| 291 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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| 292 | G4ErrorMatrixConstIter mit1, mit2, sp,snp; //mit2=0 |
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| 293 | G4double temp; |
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| 294 | G4ErrorMatrixIter mir=mret.m.begin(); |
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| 295 | G4int step,stept; |
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| 296 | for(mit1=m1.m.begin(); |
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| 297 | mit1<m1.m.begin()+m1.num_row()*m1.num_col(); mit1 = mit2) |
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| 298 | { |
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| 299 | for(step=1,snp=m2.m.begin();step<=m2.num_row();) |
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| 300 | { |
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| 301 | mit2=mit1; |
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| 302 | sp=snp; |
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| 303 | snp+=step; |
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| 304 | temp=0; |
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| 305 | while(sp<snp) |
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| 306 | { |
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| 307 | temp+=*(sp++)*(*(mit2++)); |
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| 308 | } |
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| 309 | sp+=step-1; |
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| 310 | for(stept=++step;stept<=m2.num_row();stept++) |
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| 311 | { |
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| 312 | temp+=*sp*(*(mit2++)); |
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| 313 | sp+=stept; |
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| 314 | } |
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| 315 | *(mir++)=temp; |
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| 316 | } |
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| 317 | } |
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| 318 | return mret; |
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| 319 | } |
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| 320 | |
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| 321 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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| 322 | { |
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| 323 | G4ErrorMatrix mret(m1.num_row(),m2.num_col()); |
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| 324 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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| 325 | G4int step,stept; |
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| 326 | G4ErrorMatrixConstIter mit1,mit2,sp,snp; |
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| 327 | G4double temp; |
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| 328 | G4ErrorMatrixIter mir=mret.m.begin(); |
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| 329 | for(step=1,snp=m1.m.begin();step<=m1.num_row();snp+=step++) |
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| 330 | { |
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| 331 | for(mit1=m2.m.begin();mit1<m2.m.begin()+m2.num_col();mit1++) |
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| 332 | { |
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| 333 | mit2=mit1; |
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| 334 | sp=snp; |
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| 335 | temp=0; |
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| 336 | while(sp<snp+step) |
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| 337 | { |
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| 338 | temp+=*mit2*(*(sp++)); |
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| 339 | mit2+=m2.num_col(); |
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| 340 | } |
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| 341 | sp+=step-1; |
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| 342 | for(stept=step+1;stept<=m1.num_row();stept++) |
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| 343 | { |
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| 344 | temp+=*mit2*(*sp); |
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| 345 | mit2+=m2.num_col(); |
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| 346 | sp+=stept; |
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| 347 | } |
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| 348 | *(mir++)=temp; |
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| 349 | } |
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| 350 | } |
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| 351 | return mret; |
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| 352 | } |
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| 353 | |
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| 354 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, const G4ErrorSymMatrix &m2) |
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| 355 | { |
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| 356 | G4ErrorMatrix mret(m1.num_row(),m1.num_row()); |
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| 357 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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| 358 | G4int step1,stept1,step2,stept2; |
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| 359 | G4ErrorMatrixConstIter snp1,sp1,snp2,sp2; |
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| 360 | G4double temp; |
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| 361 | G4ErrorMatrixIter mr = mret.m.begin(); |
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| 362 | for(step1=1,snp1=m1.m.begin();step1<=m1.num_row();snp1+=step1++) |
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| 363 | { |
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| 364 | for(step2=1,snp2=m2.m.begin();step2<=m2.num_row();) |
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| 365 | { |
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| 366 | sp1=snp1; |
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| 367 | sp2=snp2; |
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| 368 | snp2+=step2; |
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| 369 | temp=0; |
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| 370 | if(step1<step2) |
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| 371 | { |
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| 372 | while(sp1<snp1+step1) |
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| 373 | { temp+=(*(sp1++))*(*(sp2++)); } |
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| 374 | sp1+=step1-1; |
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| 375 | for(stept1=step1+1;stept1!=step2+1;sp1+=stept1++) |
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| 376 | { temp+=(*sp1)*(*(sp2++)); } |
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| 377 | sp2+=step2-1; |
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| 378 | for(stept2=++step2;stept2<=m2.num_row();sp1+=stept1++,sp2+=stept2++) |
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| 379 | { temp+=(*sp1)*(*sp2); } |
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| 380 | } |
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| 381 | else |
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| 382 | { |
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| 383 | while(sp2<snp2) |
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| 384 | { temp+=(*(sp1++))*(*(sp2++)); } |
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| 385 | sp2+=step2-1; |
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| 386 | for(stept2=++step2;stept2!=step1+1;sp2+=stept2++) |
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| 387 | { temp+=(*(sp1++))*(*sp2); } |
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| 388 | sp1+=step1-1; |
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| 389 | for(stept1=step1+1;stept1<=m1.num_row();sp1+=stept1++,sp2+=stept2++) |
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| 390 | { temp+=(*sp1)*(*sp2); } |
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| 391 | } |
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| 392 | *(mr++)=temp; |
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| 393 | } |
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| 394 | } |
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| 395 | return mret; |
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| 396 | } |
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| 397 | |
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| 398 | /* ----------------------------------------------------------------------- |
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| 399 | This section contains the assignment and inplace operators =,+=,-=,*=,/=. |
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| 400 | ----------------------------------------------------------------------- */ |
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| 401 | |
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| 402 | G4ErrorMatrix & G4ErrorMatrix::operator+=(const G4ErrorSymMatrix &m2) |
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| 403 | { |
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| 404 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=); |
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| 405 | G4int n = num_col(); |
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| 406 | G4ErrorMatrixConstIter sjk = m2.m.begin(); |
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| 407 | G4ErrorMatrixIter m1j = m.begin(); |
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| 408 | G4ErrorMatrixIter mj = m.begin(); |
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| 409 | // j >= k |
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| 410 | for(G4int j=1;j<=num_row();j++) |
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| 411 | { |
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| 412 | G4ErrorMatrixIter mjk = mj; |
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| 413 | G4ErrorMatrixIter mkj = m1j; |
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| 414 | for(G4int k=1;k<=j;k++) |
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| 415 | { |
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| 416 | *(mjk++) += *sjk; |
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| 417 | if(j!=k) *mkj += *sjk; |
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| 418 | sjk++; |
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| 419 | mkj += n; |
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| 420 | } |
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| 421 | mj += n; |
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| 422 | m1j++; |
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| 423 | } |
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| 424 | return (*this); |
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| 425 | } |
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| 426 | |
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| 427 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator+=(const G4ErrorSymMatrix &m2) |
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| 428 | { |
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| 429 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=); |
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| 430 | SIMPLE_BOP(+=) |
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| 431 | return (*this); |
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| 432 | } |
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| 433 | |
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| 434 | G4ErrorMatrix & G4ErrorMatrix::operator-=(const G4ErrorSymMatrix &m2) |
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| 435 | { |
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| 436 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=); |
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| 437 | G4int n = num_col(); |
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| 438 | G4ErrorMatrixConstIter sjk = m2.m.begin(); |
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| 439 | G4ErrorMatrixIter m1j = m.begin(); |
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| 440 | G4ErrorMatrixIter mj = m.begin(); |
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| 441 | // j >= k |
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| 442 | for(G4int j=1;j<=num_row();j++) |
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| 443 | { |
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| 444 | G4ErrorMatrixIter mjk = mj; |
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| 445 | G4ErrorMatrixIter mkj = m1j; |
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| 446 | for(G4int k=1;k<=j;k++) |
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| 447 | { |
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| 448 | *(mjk++) -= *sjk; |
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| 449 | if(j!=k) *mkj -= *sjk; |
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| 450 | sjk++; |
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| 451 | mkj += n; |
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| 452 | } |
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| 453 | mj += n; |
---|
| 454 | m1j++; |
---|
| 455 | } |
---|
| 456 | return (*this); |
---|
| 457 | } |
---|
| 458 | |
---|
| 459 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator-=(const G4ErrorSymMatrix &m2) |
---|
| 460 | { |
---|
| 461 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=); |
---|
| 462 | SIMPLE_BOP(-=) |
---|
| 463 | return (*this); |
---|
| 464 | } |
---|
| 465 | |
---|
| 466 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator/=(G4double t) |
---|
| 467 | { |
---|
| 468 | SIMPLE_UOP(/=) |
---|
| 469 | return (*this); |
---|
| 470 | } |
---|
| 471 | |
---|
| 472 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator*=(G4double t) |
---|
| 473 | { |
---|
| 474 | SIMPLE_UOP(*=) |
---|
| 475 | return (*this); |
---|
| 476 | } |
---|
| 477 | |
---|
| 478 | G4ErrorMatrix & G4ErrorMatrix::operator=(const G4ErrorSymMatrix &m1) |
---|
| 479 | { |
---|
| 480 | if(m1.nrow*m1.nrow != size) |
---|
| 481 | { |
---|
| 482 | size = m1.nrow * m1.nrow; |
---|
| 483 | m.resize(size); |
---|
| 484 | } |
---|
| 485 | nrow = m1.nrow; |
---|
| 486 | ncol = m1.nrow; |
---|
| 487 | G4int n = ncol; |
---|
| 488 | G4ErrorMatrixConstIter sjk = m1.m.begin(); |
---|
| 489 | G4ErrorMatrixIter m1j = m.begin(); |
---|
| 490 | G4ErrorMatrixIter mj = m.begin(); |
---|
| 491 | // j >= k |
---|
| 492 | for(G4int j=1;j<=num_row();j++) |
---|
| 493 | { |
---|
| 494 | G4ErrorMatrixIter mjk = mj; |
---|
| 495 | G4ErrorMatrixIter mkj = m1j; |
---|
| 496 | for(G4int k=1;k<=j;k++) |
---|
| 497 | { |
---|
| 498 | *(mjk++) = *sjk; |
---|
| 499 | if(j!=k) *mkj = *sjk; |
---|
| 500 | sjk++; |
---|
| 501 | mkj += n; |
---|
| 502 | } |
---|
| 503 | mj += n; |
---|
| 504 | m1j++; |
---|
| 505 | } |
---|
| 506 | return (*this); |
---|
| 507 | } |
---|
| 508 | |
---|
| 509 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator=(const G4ErrorSymMatrix &m1) |
---|
| 510 | { |
---|
| 511 | if(m1.nrow != nrow) |
---|
| 512 | { |
---|
| 513 | nrow = m1.nrow; |
---|
| 514 | size = m1.size; |
---|
| 515 | m.resize(size); |
---|
| 516 | } |
---|
| 517 | m = m1.m; |
---|
| 518 | return (*this); |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | // Print the Matrix. |
---|
| 522 | |
---|
| 523 | std::ostream& operator<<(std::ostream &s, const G4ErrorSymMatrix &q) |
---|
| 524 | { |
---|
| 525 | s << G4endl; |
---|
| 526 | |
---|
| 527 | // Fixed format needs 3 extra characters for field, |
---|
| 528 | // while scientific needs 7 |
---|
| 529 | |
---|
| 530 | G4int width; |
---|
| 531 | if(s.flags() & std::ios::fixed) |
---|
| 532 | { |
---|
| 533 | width = s.precision()+3; |
---|
| 534 | } |
---|
| 535 | else |
---|
| 536 | { |
---|
| 537 | width = s.precision()+7; |
---|
| 538 | } |
---|
| 539 | for(G4int irow = 1; irow<= q.num_row(); irow++) |
---|
| 540 | { |
---|
| 541 | for(G4int icol = 1; icol <= q.num_col(); icol++) |
---|
| 542 | { |
---|
| 543 | s.width(width); |
---|
| 544 | s << q(irow,icol) << " "; |
---|
| 545 | } |
---|
| 546 | s << G4endl; |
---|
| 547 | } |
---|
| 548 | return s; |
---|
| 549 | } |
---|
| 550 | |
---|
| 551 | G4ErrorSymMatrix G4ErrorSymMatrix:: |
---|
| 552 | apply(G4double (*f)(G4double, G4int, G4int)) const |
---|
| 553 | { |
---|
| 554 | G4ErrorSymMatrix mret(num_row()); |
---|
| 555 | G4ErrorMatrixConstIter a = m.begin(); |
---|
| 556 | G4ErrorMatrixIter b = mret.m.begin(); |
---|
| 557 | for(G4int ir=1;ir<=num_row();ir++) |
---|
| 558 | { |
---|
| 559 | for(G4int ic=1;ic<=ir;ic++) |
---|
| 560 | { |
---|
| 561 | *(b++) = (*f)(*(a++), ir, ic); |
---|
| 562 | } |
---|
| 563 | } |
---|
| 564 | return mret; |
---|
| 565 | } |
---|
| 566 | |
---|
| 567 | void G4ErrorSymMatrix::assign (const G4ErrorMatrix &m1) |
---|
| 568 | { |
---|
| 569 | if(m1.nrow != nrow) |
---|
| 570 | { |
---|
| 571 | nrow = m1.nrow; |
---|
| 572 | size = nrow * (nrow+1) / 2; |
---|
| 573 | m.resize(size); |
---|
| 574 | } |
---|
| 575 | G4ErrorMatrixConstIter a = m1.m.begin(); |
---|
| 576 | G4ErrorMatrixIter b = m.begin(); |
---|
| 577 | for(G4int r=1;r<=nrow;r++) |
---|
| 578 | { |
---|
| 579 | G4ErrorMatrixConstIter d = a; |
---|
| 580 | for(G4int c=1;c<=r;c++) |
---|
| 581 | { |
---|
| 582 | *(b++) = *(d++); |
---|
| 583 | } |
---|
| 584 | a += nrow; |
---|
| 585 | } |
---|
| 586 | } |
---|
| 587 | |
---|
| 588 | G4ErrorSymMatrix G4ErrorSymMatrix::similarity(const G4ErrorMatrix &m1) const |
---|
| 589 | { |
---|
| 590 | G4ErrorSymMatrix mret(m1.num_row()); |
---|
| 591 | G4ErrorMatrix temp = m1*(*this); |
---|
| 592 | |
---|
| 593 | // If m1*(*this) has correct dimensions, then so will the m1.T multiplication. |
---|
| 594 | // So there is no need to check dimensions again. |
---|
| 595 | |
---|
| 596 | G4int n = m1.num_col(); |
---|
| 597 | G4ErrorMatrixIter mr = mret.m.begin(); |
---|
| 598 | G4ErrorMatrixIter tempr1 = temp.m.begin(); |
---|
| 599 | for(G4int r=1;r<=mret.num_row();r++) |
---|
| 600 | { |
---|
| 601 | G4ErrorMatrixConstIter m1c1 = m1.m.begin(); |
---|
| 602 | for(G4int c=1;c<=r;c++) |
---|
| 603 | { |
---|
| 604 | G4double tmp = 0.0; |
---|
| 605 | G4ErrorMatrixIter tempri = tempr1; |
---|
| 606 | G4ErrorMatrixConstIter m1ci = m1c1; |
---|
| 607 | for(G4int i=1;i<=m1.num_col();i++) |
---|
| 608 | { |
---|
| 609 | tmp+=(*(tempri++))*(*(m1ci++)); |
---|
| 610 | } |
---|
| 611 | *(mr++) = tmp; |
---|
| 612 | m1c1 += n; |
---|
| 613 | } |
---|
| 614 | tempr1 += n; |
---|
| 615 | } |
---|
| 616 | return mret; |
---|
| 617 | } |
---|
| 618 | |
---|
| 619 | G4ErrorSymMatrix G4ErrorSymMatrix::similarity(const G4ErrorSymMatrix &m1) const |
---|
| 620 | { |
---|
| 621 | G4ErrorSymMatrix mret(m1.num_row()); |
---|
| 622 | G4ErrorMatrix temp = m1*(*this); |
---|
| 623 | G4int n = m1.num_col(); |
---|
| 624 | G4ErrorMatrixIter mr = mret.m.begin(); |
---|
| 625 | G4ErrorMatrixIter tempr1 = temp.m.begin(); |
---|
| 626 | for(G4int r=1;r<=mret.num_row();r++) |
---|
| 627 | { |
---|
| 628 | G4ErrorMatrixConstIter m1c1 = m1.m.begin(); |
---|
| 629 | G4int c; |
---|
| 630 | for(c=1;c<=r;c++) |
---|
| 631 | { |
---|
| 632 | G4double tmp = 0.0; |
---|
| 633 | G4ErrorMatrixIter tempri = tempr1; |
---|
| 634 | G4ErrorMatrixConstIter m1ci = m1c1; |
---|
| 635 | G4int i; |
---|
| 636 | for(i=1;i<c;i++) |
---|
| 637 | { |
---|
| 638 | tmp+=(*(tempri++))*(*(m1ci++)); |
---|
| 639 | } |
---|
| 640 | for(i=c;i<=m1.num_col();i++) |
---|
| 641 | { |
---|
| 642 | tmp+=(*(tempri++))*(*(m1ci)); |
---|
| 643 | m1ci += i; |
---|
| 644 | } |
---|
| 645 | *(mr++) = tmp; |
---|
| 646 | m1c1 += c; |
---|
| 647 | } |
---|
| 648 | tempr1 += n; |
---|
| 649 | } |
---|
| 650 | return mret; |
---|
| 651 | } |
---|
| 652 | |
---|
| 653 | G4ErrorSymMatrix G4ErrorSymMatrix::similarityT(const G4ErrorMatrix &m1) const |
---|
| 654 | { |
---|
| 655 | G4ErrorSymMatrix mret(m1.num_col()); |
---|
| 656 | G4ErrorMatrix temp = (*this)*m1; |
---|
| 657 | G4int n = m1.num_col(); |
---|
| 658 | G4ErrorMatrixIter mrc = mret.m.begin(); |
---|
| 659 | G4ErrorMatrixIter temp1r = temp.m.begin(); |
---|
| 660 | for(G4int r=1;r<=mret.num_row();r++) |
---|
| 661 | { |
---|
| 662 | G4ErrorMatrixConstIter m11c = m1.m.begin(); |
---|
| 663 | for(G4int c=1;c<=r;c++) |
---|
| 664 | { |
---|
| 665 | G4double tmp = 0.0; |
---|
| 666 | G4ErrorMatrixIter tempir = temp1r; |
---|
| 667 | G4ErrorMatrixConstIter m1ic = m11c; |
---|
| 668 | for(G4int i=1;i<=m1.num_row();i++) |
---|
| 669 | { |
---|
| 670 | tmp+=(*(tempir))*(*(m1ic)); |
---|
| 671 | tempir += n; |
---|
| 672 | m1ic += n; |
---|
| 673 | } |
---|
| 674 | *(mrc++) = tmp; |
---|
| 675 | m11c++; |
---|
| 676 | } |
---|
| 677 | temp1r++; |
---|
| 678 | } |
---|
| 679 | return mret; |
---|
| 680 | } |
---|
| 681 | |
---|
| 682 | void G4ErrorSymMatrix::invert(G4int &ifail) |
---|
| 683 | { |
---|
| 684 | ifail = 0; |
---|
| 685 | |
---|
| 686 | switch(nrow) |
---|
| 687 | { |
---|
| 688 | case 3: |
---|
| 689 | { |
---|
| 690 | G4double det, temp; |
---|
| 691 | G4double t1, t2, t3; |
---|
| 692 | G4double c11,c12,c13,c22,c23,c33; |
---|
| 693 | c11 = (*(m.begin()+2)) * (*(m.begin()+5)) |
---|
| 694 | - (*(m.begin()+4)) * (*(m.begin()+4)); |
---|
| 695 | c12 = (*(m.begin()+4)) * (*(m.begin()+3)) |
---|
| 696 | - (*(m.begin()+1)) * (*(m.begin()+5)); |
---|
| 697 | c13 = (*(m.begin()+1)) * (*(m.begin()+4)) |
---|
| 698 | - (*(m.begin()+2)) * (*(m.begin()+3)); |
---|
| 699 | c22 = (*(m.begin()+5)) * (*m.begin()) |
---|
| 700 | - (*(m.begin()+3)) * (*(m.begin()+3)); |
---|
| 701 | c23 = (*(m.begin()+3)) * (*(m.begin()+1)) |
---|
| 702 | - (*(m.begin()+4)) * (*m.begin()); |
---|
| 703 | c33 = (*m.begin()) * (*(m.begin()+2)) |
---|
| 704 | - (*(m.begin()+1)) * (*(m.begin()+1)); |
---|
| 705 | t1 = std::fabs(*m.begin()); |
---|
| 706 | t2 = std::fabs(*(m.begin()+1)); |
---|
| 707 | t3 = std::fabs(*(m.begin()+3)); |
---|
| 708 | if (t1 >= t2) |
---|
| 709 | { |
---|
| 710 | if (t3 >= t1) |
---|
| 711 | { |
---|
| 712 | temp = *(m.begin()+3); |
---|
| 713 | det = c23*c12-c22*c13; |
---|
| 714 | } |
---|
| 715 | else |
---|
| 716 | { |
---|
| 717 | temp = *m.begin(); |
---|
| 718 | det = c22*c33-c23*c23; |
---|
| 719 | } |
---|
| 720 | } |
---|
| 721 | else if (t3 >= t2) |
---|
| 722 | { |
---|
| 723 | temp = *(m.begin()+3); |
---|
| 724 | det = c23*c12-c22*c13; |
---|
| 725 | } |
---|
| 726 | else |
---|
| 727 | { |
---|
| 728 | temp = *(m.begin()+1); |
---|
| 729 | det = c13*c23-c12*c33; |
---|
| 730 | } |
---|
| 731 | if (det==0) |
---|
| 732 | { |
---|
| 733 | ifail = 1; |
---|
| 734 | return; |
---|
| 735 | } |
---|
| 736 | { |
---|
| 737 | G4double s = temp/det; |
---|
| 738 | G4ErrorMatrixIter mm = m.begin(); |
---|
| 739 | *(mm++) = s*c11; |
---|
| 740 | *(mm++) = s*c12; |
---|
| 741 | *(mm++) = s*c22; |
---|
| 742 | *(mm++) = s*c13; |
---|
| 743 | *(mm++) = s*c23; |
---|
| 744 | *(mm) = s*c33; |
---|
| 745 | } |
---|
| 746 | } |
---|
| 747 | break; |
---|
| 748 | case 2: |
---|
| 749 | { |
---|
| 750 | G4double det, temp, s; |
---|
| 751 | det = (*m.begin())*(*(m.begin()+2)) - (*(m.begin()+1))*(*(m.begin()+1)); |
---|
| 752 | if (det==0) |
---|
| 753 | { |
---|
| 754 | ifail = 1; |
---|
| 755 | return; |
---|
| 756 | } |
---|
| 757 | s = 1.0/det; |
---|
| 758 | *(m.begin()+1) *= -s; |
---|
| 759 | temp = s*(*(m.begin()+2)); |
---|
| 760 | *(m.begin()+2) = s*(*m.begin()); |
---|
| 761 | *m.begin() = temp; |
---|
| 762 | break; |
---|
| 763 | } |
---|
| 764 | case 1: |
---|
| 765 | { |
---|
| 766 | if ((*m.begin())==0) |
---|
| 767 | { |
---|
| 768 | ifail = 1; |
---|
| 769 | return; |
---|
| 770 | } |
---|
| 771 | *m.begin() = 1.0/(*m.begin()); |
---|
| 772 | break; |
---|
| 773 | } |
---|
| 774 | case 5: |
---|
| 775 | { |
---|
| 776 | invert5(ifail); |
---|
| 777 | return; |
---|
| 778 | } |
---|
| 779 | case 6: |
---|
| 780 | { |
---|
| 781 | invert6(ifail); |
---|
| 782 | return; |
---|
| 783 | } |
---|
| 784 | case 4: |
---|
| 785 | { |
---|
| 786 | invert4(ifail); |
---|
| 787 | return; |
---|
| 788 | } |
---|
| 789 | default: |
---|
| 790 | { |
---|
| 791 | invertBunchKaufman(ifail); |
---|
| 792 | return; |
---|
| 793 | } |
---|
| 794 | } |
---|
| 795 | return; // inversion successful |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | G4double G4ErrorSymMatrix::determinant() const |
---|
| 799 | { |
---|
| 800 | static const G4int max_array = 20; |
---|
| 801 | |
---|
| 802 | // ir must point to an array which is ***1 longer than*** nrow |
---|
| 803 | |
---|
| 804 | static std::vector<G4int> ir_vec (max_array+1); |
---|
| 805 | if (ir_vec.size() <= static_cast<unsigned int>(nrow)) |
---|
| 806 | { |
---|
| 807 | ir_vec.resize(nrow+1); |
---|
| 808 | } |
---|
| 809 | G4int * ir = &ir_vec[0]; |
---|
| 810 | |
---|
| 811 | G4double det; |
---|
| 812 | G4ErrorMatrix mt(*this); |
---|
| 813 | G4int i = mt.dfact_matrix(det, ir); |
---|
| 814 | if(i==0) { return det; } |
---|
| 815 | return 0.0; |
---|
| 816 | } |
---|
| 817 | |
---|
| 818 | G4double G4ErrorSymMatrix::trace() const |
---|
| 819 | { |
---|
| 820 | G4double t = 0.0; |
---|
| 821 | for (G4int i=0; i<nrow; i++) |
---|
| 822 | { t += *(m.begin() + (i+3)*i/2); } |
---|
| 823 | return t; |
---|
| 824 | } |
---|
| 825 | |
---|
| 826 | void G4ErrorSymMatrix::invertBunchKaufman(G4int &ifail) |
---|
| 827 | { |
---|
| 828 | // Bunch-Kaufman diagonal pivoting method |
---|
| 829 | // It is decribed in J.R. Bunch, L. Kaufman (1977). |
---|
| 830 | // "Some Stable Methods for Calculating Inertia and Solving Symmetric |
---|
| 831 | // Linear Systems", Math. Comp. 31, p. 162-179. or in Gene H. Golub, |
---|
| 832 | // Charles F. van Loan, "Matrix Computations" (the second edition |
---|
| 833 | // has a bug.) and implemented in "lapack" |
---|
| 834 | // Mario Stanke, 09/97 |
---|
| 835 | |
---|
| 836 | G4int i, j, k, s; |
---|
| 837 | G4int pivrow; |
---|
| 838 | |
---|
| 839 | // Establish the two working-space arrays needed: x and piv are |
---|
| 840 | // used as pointers to arrays of doubles and ints respectively, each |
---|
| 841 | // of length nrow. We do not want to reallocate each time through |
---|
| 842 | // unless the size needs to grow. We do not want to leak memory, even |
---|
| 843 | // by having a new without a delete that is only done once. |
---|
| 844 | |
---|
| 845 | static const G4int max_array = 25; |
---|
| 846 | static std::vector<G4double> xvec (max_array); |
---|
| 847 | static std::vector<G4int> pivv (max_array); |
---|
| 848 | typedef std::vector<G4int>::iterator pivIter; |
---|
| 849 | if (xvec.size() < static_cast<unsigned int>(nrow)) xvec.resize(nrow); |
---|
| 850 | if (pivv.size() < static_cast<unsigned int>(nrow)) pivv.resize(nrow); |
---|
| 851 | // Note - resize should do nothing if the size is already larger than nrow, |
---|
| 852 | // but on VC++ there are indications that it does so we check. |
---|
| 853 | // Note - the data elements in a vector are guaranteed to be contiguous, |
---|
| 854 | // so x[i] and piv[i] are optimally fast. |
---|
| 855 | G4ErrorMatrixIter x = xvec.begin(); |
---|
| 856 | // x[i] is used as helper storage, needs to have at least size nrow. |
---|
| 857 | pivIter piv = pivv.begin(); |
---|
| 858 | // piv[i] is used to store details of exchanges |
---|
| 859 | |
---|
| 860 | G4double temp1, temp2; |
---|
| 861 | G4ErrorMatrixIter ip, mjj, iq; |
---|
| 862 | G4double lambda, sigma; |
---|
| 863 | const G4double alpha = .6404; // = (1+sqrt(17))/8 |
---|
| 864 | const G4double epsilon = 32*DBL_EPSILON; |
---|
| 865 | // whenever a sum of two doubles is below or equal to epsilon |
---|
| 866 | // it is set to zero. |
---|
| 867 | // this constant could be set to zero but then the algorithm |
---|
| 868 | // doesn't neccessarily detect that a matrix is singular |
---|
| 869 | |
---|
| 870 | for (i = 0; i < nrow; i++) |
---|
| 871 | { |
---|
| 872 | piv[i] = i+1; |
---|
| 873 | } |
---|
| 874 | |
---|
| 875 | ifail = 0; |
---|
| 876 | |
---|
| 877 | // compute the factorization P*A*P^T = L * D * L^T |
---|
| 878 | // L is unit lower triangular, D is direct sum of 1x1 and 2x2 matrices |
---|
| 879 | // L and D^-1 are stored in A = *this, P is stored in piv[] |
---|
| 880 | |
---|
| 881 | for (j=1; j < nrow; j+=s) // main loop over columns |
---|
| 882 | { |
---|
| 883 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
| 884 | lambda = 0; // compute lambda = max of A(j+1:n,j) |
---|
| 885 | pivrow = j+1; |
---|
| 886 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 887 | for (i=j+1; i <= nrow ; ip += i++) |
---|
| 888 | { |
---|
| 889 | if (std::fabs(*ip) > lambda) |
---|
| 890 | { |
---|
| 891 | lambda = std::fabs(*ip); |
---|
| 892 | pivrow = i; |
---|
| 893 | } |
---|
| 894 | } |
---|
| 895 | if (lambda == 0 ) |
---|
| 896 | { |
---|
| 897 | if (*mjj == 0) |
---|
| 898 | { |
---|
| 899 | ifail = 1; |
---|
| 900 | return; |
---|
| 901 | } |
---|
| 902 | s=1; |
---|
| 903 | *mjj = 1./ *mjj; |
---|
| 904 | } |
---|
| 905 | else |
---|
| 906 | { |
---|
| 907 | if (std::fabs(*mjj) >= lambda*alpha) |
---|
| 908 | { |
---|
| 909 | s=1; |
---|
| 910 | pivrow=j; |
---|
| 911 | } |
---|
| 912 | else |
---|
| 913 | { |
---|
| 914 | sigma = 0; // compute sigma = max A(pivrow, j:pivrow-1) |
---|
| 915 | ip = m.begin() + pivrow*(pivrow-1)/2+j-1; |
---|
| 916 | for (k=j; k < pivrow; k++) |
---|
| 917 | { |
---|
| 918 | if (std::fabs(*ip) > sigma) |
---|
| 919 | sigma = std::fabs(*ip); |
---|
| 920 | ip++; |
---|
| 921 | } |
---|
| 922 | if (sigma * std::fabs(*mjj) >= alpha * lambda * lambda) |
---|
| 923 | { |
---|
| 924 | s=1; |
---|
| 925 | pivrow = j; |
---|
| 926 | } |
---|
| 927 | else if (std::fabs(*(m.begin()+pivrow*(pivrow-1)/2+pivrow-1)) |
---|
| 928 | >= alpha * sigma) |
---|
| 929 | { s=1; } |
---|
| 930 | else |
---|
| 931 | { s=2; } |
---|
| 932 | } |
---|
| 933 | if (pivrow == j) // no permutation neccessary |
---|
| 934 | { |
---|
| 935 | piv[j-1] = pivrow; |
---|
| 936 | if (*mjj == 0) |
---|
| 937 | { |
---|
| 938 | ifail=1; |
---|
| 939 | return; |
---|
| 940 | } |
---|
| 941 | temp2 = *mjj = 1./ *mjj; // invert D(j,j) |
---|
| 942 | |
---|
| 943 | // update A(j+1:n, j+1,n) |
---|
| 944 | for (i=j+1; i <= nrow; i++) |
---|
| 945 | { |
---|
| 946 | temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2; |
---|
| 947 | ip = m.begin()+i*(i-1)/2+j; |
---|
| 948 | for (k=j+1; k<=i; k++) |
---|
| 949 | { |
---|
| 950 | *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1); |
---|
| 951 | if (std::fabs(*ip) <= epsilon) |
---|
| 952 | { *ip=0; } |
---|
| 953 | ip++; |
---|
| 954 | } |
---|
| 955 | } |
---|
| 956 | // update L |
---|
| 957 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 958 | for (i=j+1; i <= nrow; ip += i++) |
---|
| 959 | { |
---|
| 960 | *ip *= temp2; |
---|
| 961 | } |
---|
| 962 | } |
---|
| 963 | else if (s==1) // 1x1 pivot |
---|
| 964 | { |
---|
| 965 | piv[j-1] = pivrow; |
---|
| 966 | |
---|
| 967 | // interchange rows and columns j and pivrow in |
---|
| 968 | // submatrix (j:n,j:n) |
---|
| 969 | ip = m.begin() + pivrow*(pivrow-1)/2 + j; |
---|
| 970 | for (i=j+1; i < pivrow; i++, ip++) |
---|
| 971 | { |
---|
| 972 | temp1 = *(m.begin() + i*(i-1)/2 + j-1); |
---|
| 973 | *(m.begin() + i*(i-1)/2 + j-1)= *ip; |
---|
| 974 | *ip = temp1; |
---|
| 975 | } |
---|
| 976 | temp1 = *mjj; |
---|
| 977 | *mjj = *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1); |
---|
| 978 | *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1) = temp1; |
---|
| 979 | ip = m.begin() + (pivrow+1)*pivrow/2 + j-1; |
---|
| 980 | iq = ip + pivrow-j; |
---|
| 981 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
| 982 | { |
---|
| 983 | temp1 = *iq; |
---|
| 984 | *iq = *ip; |
---|
| 985 | *ip = temp1; |
---|
| 986 | } |
---|
| 987 | |
---|
| 988 | if (*mjj == 0) |
---|
| 989 | { |
---|
| 990 | ifail = 1; |
---|
| 991 | return; |
---|
| 992 | } |
---|
| 993 | temp2 = *mjj = 1./ *mjj; // invert D(j,j) |
---|
| 994 | |
---|
| 995 | // update A(j+1:n, j+1:n) |
---|
| 996 | for (i = j+1; i <= nrow; i++) |
---|
| 997 | { |
---|
| 998 | temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2; |
---|
| 999 | ip = m.begin()+i*(i-1)/2+j; |
---|
| 1000 | for (k=j+1; k<=i; k++) |
---|
| 1001 | { |
---|
| 1002 | *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1); |
---|
| 1003 | if (std::fabs(*ip) <= epsilon) |
---|
| 1004 | { *ip=0; } |
---|
| 1005 | ip++; |
---|
| 1006 | } |
---|
| 1007 | } |
---|
| 1008 | // update L |
---|
| 1009 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 1010 | for (i=j+1; i<=nrow; ip += i++) |
---|
| 1011 | { |
---|
| 1012 | *ip *= temp2; |
---|
| 1013 | } |
---|
| 1014 | } |
---|
| 1015 | else // s=2, ie use a 2x2 pivot |
---|
| 1016 | { |
---|
| 1017 | piv[j-1] = -pivrow; |
---|
| 1018 | piv[j] = 0; // that means this is the second row of a 2x2 pivot |
---|
| 1019 | |
---|
| 1020 | if (j+1 != pivrow) |
---|
| 1021 | { |
---|
| 1022 | // interchange rows and columns j+1 and pivrow in |
---|
| 1023 | // submatrix (j:n,j:n) |
---|
| 1024 | ip = m.begin() + pivrow*(pivrow-1)/2 + j+1; |
---|
| 1025 | for (i=j+2; i < pivrow; i++, ip++) |
---|
| 1026 | { |
---|
| 1027 | temp1 = *(m.begin() + i*(i-1)/2 + j); |
---|
| 1028 | *(m.begin() + i*(i-1)/2 + j) = *ip; |
---|
| 1029 | *ip = temp1; |
---|
| 1030 | } |
---|
| 1031 | temp1 = *(mjj + j + 1); |
---|
| 1032 | *(mjj + j + 1) = |
---|
| 1033 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1); |
---|
| 1034 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1; |
---|
| 1035 | temp1 = *(mjj + j); |
---|
| 1036 | *(mjj + j) = *(m.begin() + pivrow*(pivrow-1)/2 + j-1); |
---|
| 1037 | *(m.begin() + pivrow*(pivrow-1)/2 + j-1) = temp1; |
---|
| 1038 | ip = m.begin() + (pivrow+1)*pivrow/2 + j; |
---|
| 1039 | iq = ip + pivrow-(j+1); |
---|
| 1040 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
| 1041 | { |
---|
| 1042 | temp1 = *iq; |
---|
| 1043 | *iq = *ip; |
---|
| 1044 | *ip = temp1; |
---|
| 1045 | } |
---|
| 1046 | } |
---|
| 1047 | // invert D(j:j+1,j:j+1) |
---|
| 1048 | temp2 = *mjj * *(mjj + j + 1) - *(mjj + j) * *(mjj + j); |
---|
| 1049 | if (temp2 == 0) |
---|
| 1050 | { |
---|
| 1051 | G4cerr |
---|
| 1052 | << "G4ErrorSymMatrix::bunch_invert: error in pivot choice" |
---|
| 1053 | << G4endl; |
---|
| 1054 | } |
---|
| 1055 | temp2 = 1. / temp2; |
---|
| 1056 | |
---|
| 1057 | // this quotient is guaranteed to exist by the choice |
---|
| 1058 | // of the pivot |
---|
| 1059 | |
---|
| 1060 | temp1 = *mjj; |
---|
| 1061 | *mjj = *(mjj + j + 1) * temp2; |
---|
| 1062 | *(mjj + j + 1) = temp1 * temp2; |
---|
| 1063 | *(mjj + j) = - *(mjj + j) * temp2; |
---|
| 1064 | |
---|
| 1065 | if (j < nrow-1) // otherwise do nothing |
---|
| 1066 | { |
---|
| 1067 | // update A(j+2:n, j+2:n) |
---|
| 1068 | for (i=j+2; i <= nrow ; i++) |
---|
| 1069 | { |
---|
| 1070 | ip = m.begin() + i*(i-1)/2 + j-1; |
---|
| 1071 | temp1 = *ip * *mjj + *(ip + 1) * *(mjj + j); |
---|
| 1072 | if (std::fabs(temp1 ) <= epsilon) |
---|
| 1073 | { temp1 = 0; } |
---|
| 1074 | temp2 = *ip * *(mjj + j) + *(ip + 1) * *(mjj + j + 1); |
---|
| 1075 | if (std::fabs(temp2 ) <= epsilon) |
---|
| 1076 | { temp2 = 0; } |
---|
| 1077 | for (k = j+2; k <= i ; k++) |
---|
| 1078 | { |
---|
| 1079 | ip = m.begin() + i*(i-1)/2 + k-1; |
---|
| 1080 | iq = m.begin() + k*(k-1)/2 + j-1; |
---|
| 1081 | *ip -= temp1 * *iq + temp2 * *(iq+1); |
---|
| 1082 | if (std::fabs(*ip) <= epsilon) |
---|
| 1083 | { *ip = 0; } |
---|
| 1084 | } |
---|
| 1085 | } |
---|
| 1086 | // update L |
---|
| 1087 | for (i=j+2; i <= nrow ; i++) |
---|
| 1088 | { |
---|
| 1089 | ip = m.begin() + i*(i-1)/2 + j-1; |
---|
| 1090 | temp1 = *ip * *mjj + *(ip+1) * *(mjj + j); |
---|
| 1091 | if (std::fabs(temp1) <= epsilon) |
---|
| 1092 | { temp1 = 0; } |
---|
| 1093 | *(ip+1) = *ip * *(mjj + j) + *(ip+1) * *(mjj + j + 1); |
---|
| 1094 | if (std::fabs(*(ip+1)) <= epsilon) |
---|
| 1095 | { *(ip+1) = 0; } |
---|
| 1096 | *ip = temp1; |
---|
| 1097 | } |
---|
| 1098 | } |
---|
| 1099 | } |
---|
| 1100 | } |
---|
| 1101 | } // end of main loop over columns |
---|
| 1102 | |
---|
| 1103 | if (j == nrow) // the the last pivot is 1x1 |
---|
| 1104 | { |
---|
| 1105 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
| 1106 | if (*mjj == 0) |
---|
| 1107 | { |
---|
| 1108 | ifail = 1; |
---|
| 1109 | return; |
---|
| 1110 | } |
---|
| 1111 | else |
---|
| 1112 | { |
---|
| 1113 | *mjj = 1. / *mjj; |
---|
| 1114 | } |
---|
| 1115 | } // end of last pivot code |
---|
| 1116 | |
---|
| 1117 | // computing the inverse from the factorization |
---|
| 1118 | |
---|
| 1119 | for (j = nrow ; j >= 1 ; j -= s) // loop over columns |
---|
| 1120 | { |
---|
| 1121 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
| 1122 | if (piv[j-1] > 0) // 1x1 pivot, compute column j of inverse |
---|
| 1123 | { |
---|
| 1124 | s = 1; |
---|
| 1125 | if (j < nrow) |
---|
| 1126 | { |
---|
| 1127 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 1128 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
| 1129 | { |
---|
| 1130 | x[i] = *ip; |
---|
| 1131 | } |
---|
| 1132 | for (i=j+1; i<=nrow ; i++) |
---|
| 1133 | { |
---|
| 1134 | temp2=0; |
---|
| 1135 | ip = m.begin() + i*(i-1)/2 + j; |
---|
| 1136 | for (k=0; k <= i-j-1; k++) |
---|
| 1137 | { temp2 += *ip++ * x[k]; } |
---|
| 1138 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
| 1139 | { temp2 += *ip * x[k]; } |
---|
| 1140 | *(m.begin()+ i*(i-1)/2 + j-1) = -temp2; |
---|
| 1141 | } |
---|
| 1142 | temp2 = 0; |
---|
| 1143 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 1144 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
| 1145 | { temp2 += x[k] * *ip; } |
---|
| 1146 | *mjj -= temp2; |
---|
| 1147 | } |
---|
| 1148 | } |
---|
| 1149 | else //2x2 pivot, compute columns j and j-1 of the inverse |
---|
| 1150 | { |
---|
| 1151 | if (piv[j-1] != 0) |
---|
| 1152 | { G4cerr << "error in piv" << piv[j-1] << G4endl; } |
---|
| 1153 | s=2; |
---|
| 1154 | if (j < nrow) |
---|
| 1155 | { |
---|
| 1156 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 1157 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
| 1158 | { |
---|
| 1159 | x[i] = *ip; |
---|
| 1160 | } |
---|
| 1161 | for (i=j+1; i<=nrow ; i++) |
---|
| 1162 | { |
---|
| 1163 | temp2 = 0; |
---|
| 1164 | ip = m.begin() + i*(i-1)/2 + j; |
---|
| 1165 | for (k=0; k <= i-j-1; k++) |
---|
| 1166 | { temp2 += *ip++ * x[k]; } |
---|
| 1167 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
| 1168 | { temp2 += *ip * x[k]; } |
---|
| 1169 | *(m.begin()+ i*(i-1)/2 + j-1) = -temp2; |
---|
| 1170 | } |
---|
| 1171 | temp2 = 0; |
---|
| 1172 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
| 1173 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
| 1174 | { temp2 += x[k] * *ip; } |
---|
| 1175 | *mjj -= temp2; |
---|
| 1176 | temp2 = 0; |
---|
| 1177 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
| 1178 | for (i=j+1; i <= nrow; ip += i++) |
---|
| 1179 | { temp2 += *ip * *(ip+1); } |
---|
| 1180 | *(mjj-1) -= temp2; |
---|
| 1181 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
| 1182 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
| 1183 | { |
---|
| 1184 | x[i] = *ip; |
---|
| 1185 | } |
---|
| 1186 | for (i=j+1; i <= nrow ; i++) |
---|
| 1187 | { |
---|
| 1188 | temp2 = 0; |
---|
| 1189 | ip = m.begin() + i*(i-1)/2 + j; |
---|
| 1190 | for (k=0; k <= i-j-1; k++) |
---|
| 1191 | { temp2 += *ip++ * x[k]; } |
---|
| 1192 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
| 1193 | { temp2 += *ip * x[k]; } |
---|
| 1194 | *(m.begin()+ i*(i-1)/2 + j-2)= -temp2; |
---|
| 1195 | } |
---|
| 1196 | temp2 = 0; |
---|
| 1197 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
| 1198 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
| 1199 | { temp2 += x[k] * *ip; } |
---|
| 1200 | *(mjj-j) -= temp2; |
---|
| 1201 | } |
---|
| 1202 | } |
---|
| 1203 | |
---|
| 1204 | // interchange rows and columns j and piv[j-1] |
---|
| 1205 | // or rows and columns j and -piv[j-2] |
---|
| 1206 | |
---|
| 1207 | pivrow = (piv[j-1]==0)? -piv[j-2] : piv[j-1]; |
---|
| 1208 | ip = m.begin() + pivrow*(pivrow-1)/2 + j; |
---|
| 1209 | for (i=j+1;i < pivrow; i++, ip++) |
---|
| 1210 | { |
---|
| 1211 | temp1 = *(m.begin() + i*(i-1)/2 + j-1); |
---|
| 1212 | *(m.begin() + i*(i-1)/2 + j-1) = *ip; |
---|
| 1213 | *ip = temp1; |
---|
| 1214 | } |
---|
| 1215 | temp1 = *mjj; |
---|
| 1216 | *mjj = *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1); |
---|
| 1217 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1; |
---|
| 1218 | if (s==2) |
---|
| 1219 | { |
---|
| 1220 | temp1 = *(mjj-1); |
---|
| 1221 | *(mjj-1) = *( m.begin() + pivrow*(pivrow-1)/2 + j-2); |
---|
| 1222 | *( m.begin() + pivrow*(pivrow-1)/2 + j-2) = temp1; |
---|
| 1223 | } |
---|
| 1224 | |
---|
| 1225 | ip = m.begin() + (pivrow+1)*pivrow/2 + j-1; // &A(i,j) |
---|
| 1226 | iq = ip + pivrow-j; |
---|
| 1227 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
| 1228 | { |
---|
| 1229 | temp1 = *iq; |
---|
| 1230 | *iq = *ip; |
---|
| 1231 | *ip = temp1; |
---|
| 1232 | } |
---|
| 1233 | } // end of loop over columns (in computing inverse from factorization) |
---|
| 1234 | |
---|
| 1235 | return; // inversion successful |
---|
| 1236 | } |
---|
| 1237 | |
---|
| 1238 | G4double G4ErrorSymMatrix::posDefFraction5x5 = 1.0; |
---|
| 1239 | G4double G4ErrorSymMatrix::posDefFraction6x6 = 1.0; |
---|
| 1240 | G4double G4ErrorSymMatrix::adjustment5x5 = 0.0; |
---|
| 1241 | G4double G4ErrorSymMatrix::adjustment6x6 = 0.0; |
---|
| 1242 | const G4double G4ErrorSymMatrix::CHOLESKY_THRESHOLD_5x5 = .5; |
---|
| 1243 | const G4double G4ErrorSymMatrix::CHOLESKY_THRESHOLD_6x6 = .2; |
---|
| 1244 | const G4double G4ErrorSymMatrix::CHOLESKY_CREEP_5x5 = .005; |
---|
| 1245 | const G4double G4ErrorSymMatrix::CHOLESKY_CREEP_6x6 = .002; |
---|
| 1246 | |
---|
| 1247 | // Aij are indices for a 6x6 symmetric matrix. |
---|
| 1248 | // The indices for 5x5 or 4x4 symmetric matrices are the same, |
---|
| 1249 | // ignoring all combinations with an index which is inapplicable. |
---|
| 1250 | |
---|
| 1251 | #define A00 0 |
---|
| 1252 | #define A01 1 |
---|
| 1253 | #define A02 3 |
---|
| 1254 | #define A03 6 |
---|
| 1255 | #define A04 10 |
---|
| 1256 | #define A05 15 |
---|
| 1257 | |
---|
| 1258 | #define A10 1 |
---|
| 1259 | #define A11 2 |
---|
| 1260 | #define A12 4 |
---|
| 1261 | #define A13 7 |
---|
| 1262 | #define A14 11 |
---|
| 1263 | #define A15 16 |
---|
| 1264 | |
---|
| 1265 | #define A20 3 |
---|
| 1266 | #define A21 4 |
---|
| 1267 | #define A22 5 |
---|
| 1268 | #define A23 8 |
---|
| 1269 | #define A24 12 |
---|
| 1270 | #define A25 17 |
---|
| 1271 | |
---|
| 1272 | #define A30 6 |
---|
| 1273 | #define A31 7 |
---|
| 1274 | #define A32 8 |
---|
| 1275 | #define A33 9 |
---|
| 1276 | #define A34 13 |
---|
| 1277 | #define A35 18 |
---|
| 1278 | |
---|
| 1279 | #define A40 10 |
---|
| 1280 | #define A41 11 |
---|
| 1281 | #define A42 12 |
---|
| 1282 | #define A43 13 |
---|
| 1283 | #define A44 14 |
---|
| 1284 | #define A45 19 |
---|
| 1285 | |
---|
| 1286 | #define A50 15 |
---|
| 1287 | #define A51 16 |
---|
| 1288 | #define A52 17 |
---|
| 1289 | #define A53 18 |
---|
| 1290 | #define A54 19 |
---|
| 1291 | #define A55 20 |
---|
| 1292 | |
---|
| 1293 | void G4ErrorSymMatrix::invert5(G4int & ifail) |
---|
| 1294 | { |
---|
| 1295 | if (posDefFraction5x5 >= CHOLESKY_THRESHOLD_5x5) |
---|
| 1296 | { |
---|
| 1297 | invertCholesky5(ifail); |
---|
| 1298 | posDefFraction5x5 = .9*posDefFraction5x5 + .1*(1-ifail); |
---|
| 1299 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
| 1300 | { |
---|
| 1301 | invertHaywood5(ifail); |
---|
| 1302 | } |
---|
| 1303 | } |
---|
| 1304 | else |
---|
| 1305 | { |
---|
| 1306 | if (posDefFraction5x5 + adjustment5x5 >= CHOLESKY_THRESHOLD_5x5) |
---|
| 1307 | { |
---|
| 1308 | invertCholesky5(ifail); |
---|
| 1309 | posDefFraction5x5 = .9*posDefFraction5x5 + .1*(1-ifail); |
---|
| 1310 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
| 1311 | { |
---|
| 1312 | invertHaywood5(ifail); |
---|
| 1313 | adjustment5x5 = 0; |
---|
| 1314 | } |
---|
| 1315 | } |
---|
| 1316 | else |
---|
| 1317 | { |
---|
| 1318 | invertHaywood5(ifail); |
---|
| 1319 | adjustment5x5 += CHOLESKY_CREEP_5x5; |
---|
| 1320 | } |
---|
| 1321 | } |
---|
| 1322 | return; |
---|
| 1323 | } |
---|
| 1324 | |
---|
| 1325 | void G4ErrorSymMatrix::invert6(G4int & ifail) |
---|
| 1326 | { |
---|
| 1327 | if (posDefFraction6x6 >= CHOLESKY_THRESHOLD_6x6) |
---|
| 1328 | { |
---|
| 1329 | invertCholesky6(ifail); |
---|
| 1330 | posDefFraction6x6 = .9*posDefFraction6x6 + .1*(1-ifail); |
---|
| 1331 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
| 1332 | { |
---|
| 1333 | invertHaywood6(ifail); |
---|
| 1334 | } |
---|
| 1335 | } |
---|
| 1336 | else |
---|
| 1337 | { |
---|
| 1338 | if (posDefFraction6x6 + adjustment6x6 >= CHOLESKY_THRESHOLD_6x6) |
---|
| 1339 | { |
---|
| 1340 | invertCholesky6(ifail); |
---|
| 1341 | posDefFraction6x6 = .9*posDefFraction6x6 + .1*(1-ifail); |
---|
| 1342 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
| 1343 | { |
---|
| 1344 | invertHaywood6(ifail); |
---|
| 1345 | adjustment6x6 = 0; |
---|
| 1346 | } |
---|
| 1347 | } |
---|
| 1348 | else |
---|
| 1349 | { |
---|
| 1350 | invertHaywood6(ifail); |
---|
| 1351 | adjustment6x6 += CHOLESKY_CREEP_6x6; |
---|
| 1352 | } |
---|
| 1353 | } |
---|
| 1354 | return; |
---|
| 1355 | } |
---|
| 1356 | |
---|
| 1357 | void G4ErrorSymMatrix::invertHaywood5 (G4int & ifail) |
---|
| 1358 | { |
---|
| 1359 | ifail = 0; |
---|
| 1360 | |
---|
| 1361 | // Find all NECESSARY 2x2 dets: (25 of them) |
---|
| 1362 | |
---|
| 1363 | G4double Det2_23_01 = m[A20]*m[A31] - m[A21]*m[A30]; |
---|
| 1364 | G4double Det2_23_02 = m[A20]*m[A32] - m[A22]*m[A30]; |
---|
| 1365 | G4double Det2_23_03 = m[A20]*m[A33] - m[A23]*m[A30]; |
---|
| 1366 | G4double Det2_23_12 = m[A21]*m[A32] - m[A22]*m[A31]; |
---|
| 1367 | G4double Det2_23_13 = m[A21]*m[A33] - m[A23]*m[A31]; |
---|
| 1368 | G4double Det2_23_23 = m[A22]*m[A33] - m[A23]*m[A32]; |
---|
| 1369 | G4double Det2_24_01 = m[A20]*m[A41] - m[A21]*m[A40]; |
---|
| 1370 | G4double Det2_24_02 = m[A20]*m[A42] - m[A22]*m[A40]; |
---|
| 1371 | G4double Det2_24_03 = m[A20]*m[A43] - m[A23]*m[A40]; |
---|
| 1372 | G4double Det2_24_04 = m[A20]*m[A44] - m[A24]*m[A40]; |
---|
| 1373 | G4double Det2_24_12 = m[A21]*m[A42] - m[A22]*m[A41]; |
---|
| 1374 | G4double Det2_24_13 = m[A21]*m[A43] - m[A23]*m[A41]; |
---|
| 1375 | G4double Det2_24_14 = m[A21]*m[A44] - m[A24]*m[A41]; |
---|
| 1376 | G4double Det2_24_23 = m[A22]*m[A43] - m[A23]*m[A42]; |
---|
| 1377 | G4double Det2_24_24 = m[A22]*m[A44] - m[A24]*m[A42]; |
---|
| 1378 | G4double Det2_34_01 = m[A30]*m[A41] - m[A31]*m[A40]; |
---|
| 1379 | G4double Det2_34_02 = m[A30]*m[A42] - m[A32]*m[A40]; |
---|
| 1380 | G4double Det2_34_03 = m[A30]*m[A43] - m[A33]*m[A40]; |
---|
| 1381 | G4double Det2_34_04 = m[A30]*m[A44] - m[A34]*m[A40]; |
---|
| 1382 | G4double Det2_34_12 = m[A31]*m[A42] - m[A32]*m[A41]; |
---|
| 1383 | G4double Det2_34_13 = m[A31]*m[A43] - m[A33]*m[A41]; |
---|
| 1384 | G4double Det2_34_14 = m[A31]*m[A44] - m[A34]*m[A41]; |
---|
| 1385 | G4double Det2_34_23 = m[A32]*m[A43] - m[A33]*m[A42]; |
---|
| 1386 | G4double Det2_34_24 = m[A32]*m[A44] - m[A34]*m[A42]; |
---|
| 1387 | G4double Det2_34_34 = m[A33]*m[A44] - m[A34]*m[A43]; |
---|
| 1388 | |
---|
| 1389 | // Find all NECESSARY 3x3 dets: (30 of them) |
---|
| 1390 | |
---|
| 1391 | G4double Det3_123_012 = m[A10]*Det2_23_12 - m[A11]*Det2_23_02 |
---|
| 1392 | + m[A12]*Det2_23_01; |
---|
| 1393 | G4double Det3_123_013 = m[A10]*Det2_23_13 - m[A11]*Det2_23_03 |
---|
| 1394 | + m[A13]*Det2_23_01; |
---|
| 1395 | G4double Det3_123_023 = m[A10]*Det2_23_23 - m[A12]*Det2_23_03 |
---|
| 1396 | + m[A13]*Det2_23_02; |
---|
| 1397 | G4double Det3_123_123 = m[A11]*Det2_23_23 - m[A12]*Det2_23_13 |
---|
| 1398 | + m[A13]*Det2_23_12; |
---|
| 1399 | G4double Det3_124_012 = m[A10]*Det2_24_12 - m[A11]*Det2_24_02 |
---|
| 1400 | + m[A12]*Det2_24_01; |
---|
| 1401 | G4double Det3_124_013 = m[A10]*Det2_24_13 - m[A11]*Det2_24_03 |
---|
| 1402 | + m[A13]*Det2_24_01; |
---|
| 1403 | G4double Det3_124_014 = m[A10]*Det2_24_14 - m[A11]*Det2_24_04 |
---|
| 1404 | + m[A14]*Det2_24_01; |
---|
| 1405 | G4double Det3_124_023 = m[A10]*Det2_24_23 - m[A12]*Det2_24_03 |
---|
| 1406 | + m[A13]*Det2_24_02; |
---|
| 1407 | G4double Det3_124_024 = m[A10]*Det2_24_24 - m[A12]*Det2_24_04 |
---|
| 1408 | + m[A14]*Det2_24_02; |
---|
| 1409 | G4double Det3_124_123 = m[A11]*Det2_24_23 - m[A12]*Det2_24_13 |
---|
| 1410 | + m[A13]*Det2_24_12; |
---|
| 1411 | G4double Det3_124_124 = m[A11]*Det2_24_24 - m[A12]*Det2_24_14 |
---|
| 1412 | + m[A14]*Det2_24_12; |
---|
| 1413 | G4double Det3_134_012 = m[A10]*Det2_34_12 - m[A11]*Det2_34_02 |
---|
| 1414 | + m[A12]*Det2_34_01; |
---|
| 1415 | G4double Det3_134_013 = m[A10]*Det2_34_13 - m[A11]*Det2_34_03 |
---|
| 1416 | + m[A13]*Det2_34_01; |
---|
| 1417 | G4double Det3_134_014 = m[A10]*Det2_34_14 - m[A11]*Det2_34_04 |
---|
| 1418 | + m[A14]*Det2_34_01; |
---|
| 1419 | G4double Det3_134_023 = m[A10]*Det2_34_23 - m[A12]*Det2_34_03 |
---|
| 1420 | + m[A13]*Det2_34_02; |
---|
| 1421 | G4double Det3_134_024 = m[A10]*Det2_34_24 - m[A12]*Det2_34_04 |
---|
| 1422 | + m[A14]*Det2_34_02; |
---|
| 1423 | G4double Det3_134_034 = m[A10]*Det2_34_34 - m[A13]*Det2_34_04 |
---|
| 1424 | + m[A14]*Det2_34_03; |
---|
| 1425 | G4double Det3_134_123 = m[A11]*Det2_34_23 - m[A12]*Det2_34_13 |
---|
| 1426 | + m[A13]*Det2_34_12; |
---|
| 1427 | G4double Det3_134_124 = m[A11]*Det2_34_24 - m[A12]*Det2_34_14 |
---|
| 1428 | + m[A14]*Det2_34_12; |
---|
| 1429 | G4double Det3_134_134 = m[A11]*Det2_34_34 - m[A13]*Det2_34_14 |
---|
| 1430 | + m[A14]*Det2_34_13; |
---|
| 1431 | G4double Det3_234_012 = m[A20]*Det2_34_12 - m[A21]*Det2_34_02 |
---|
| 1432 | + m[A22]*Det2_34_01; |
---|
| 1433 | G4double Det3_234_013 = m[A20]*Det2_34_13 - m[A21]*Det2_34_03 |
---|
| 1434 | + m[A23]*Det2_34_01; |
---|
| 1435 | G4double Det3_234_014 = m[A20]*Det2_34_14 - m[A21]*Det2_34_04 |
---|
| 1436 | + m[A24]*Det2_34_01; |
---|
| 1437 | G4double Det3_234_023 = m[A20]*Det2_34_23 - m[A22]*Det2_34_03 |
---|
| 1438 | + m[A23]*Det2_34_02; |
---|
| 1439 | G4double Det3_234_024 = m[A20]*Det2_34_24 - m[A22]*Det2_34_04 |
---|
| 1440 | + m[A24]*Det2_34_02; |
---|
| 1441 | G4double Det3_234_034 = m[A20]*Det2_34_34 - m[A23]*Det2_34_04 |
---|
| 1442 | + m[A24]*Det2_34_03; |
---|
| 1443 | G4double Det3_234_123 = m[A21]*Det2_34_23 - m[A22]*Det2_34_13 |
---|
| 1444 | + m[A23]*Det2_34_12; |
---|
| 1445 | G4double Det3_234_124 = m[A21]*Det2_34_24 - m[A22]*Det2_34_14 |
---|
| 1446 | + m[A24]*Det2_34_12; |
---|
| 1447 | G4double Det3_234_134 = m[A21]*Det2_34_34 - m[A23]*Det2_34_14 |
---|
| 1448 | + m[A24]*Det2_34_13; |
---|
| 1449 | G4double Det3_234_234 = m[A22]*Det2_34_34 - m[A23]*Det2_34_24 |
---|
| 1450 | + m[A24]*Det2_34_23; |
---|
| 1451 | |
---|
| 1452 | // Find all NECESSARY 4x4 dets: (15 of them) |
---|
| 1453 | |
---|
| 1454 | G4double Det4_0123_0123 = m[A00]*Det3_123_123 - m[A01]*Det3_123_023 |
---|
| 1455 | + m[A02]*Det3_123_013 - m[A03]*Det3_123_012; |
---|
| 1456 | G4double Det4_0124_0123 = m[A00]*Det3_124_123 - m[A01]*Det3_124_023 |
---|
| 1457 | + m[A02]*Det3_124_013 - m[A03]*Det3_124_012; |
---|
| 1458 | G4double Det4_0124_0124 = m[A00]*Det3_124_124 - m[A01]*Det3_124_024 |
---|
| 1459 | + m[A02]*Det3_124_014 - m[A04]*Det3_124_012; |
---|
| 1460 | G4double Det4_0134_0123 = m[A00]*Det3_134_123 - m[A01]*Det3_134_023 |
---|
| 1461 | + m[A02]*Det3_134_013 - m[A03]*Det3_134_012; |
---|
| 1462 | G4double Det4_0134_0124 = m[A00]*Det3_134_124 - m[A01]*Det3_134_024 |
---|
| 1463 | + m[A02]*Det3_134_014 - m[A04]*Det3_134_012; |
---|
| 1464 | G4double Det4_0134_0134 = m[A00]*Det3_134_134 - m[A01]*Det3_134_034 |
---|
| 1465 | + m[A03]*Det3_134_014 - m[A04]*Det3_134_013; |
---|
| 1466 | G4double Det4_0234_0123 = m[A00]*Det3_234_123 - m[A01]*Det3_234_023 |
---|
| 1467 | + m[A02]*Det3_234_013 - m[A03]*Det3_234_012; |
---|
| 1468 | G4double Det4_0234_0124 = m[A00]*Det3_234_124 - m[A01]*Det3_234_024 |
---|
| 1469 | + m[A02]*Det3_234_014 - m[A04]*Det3_234_012; |
---|
| 1470 | G4double Det4_0234_0134 = m[A00]*Det3_234_134 - m[A01]*Det3_234_034 |
---|
| 1471 | + m[A03]*Det3_234_014 - m[A04]*Det3_234_013; |
---|
| 1472 | G4double Det4_0234_0234 = m[A00]*Det3_234_234 - m[A02]*Det3_234_034 |
---|
| 1473 | + m[A03]*Det3_234_024 - m[A04]*Det3_234_023; |
---|
| 1474 | G4double Det4_1234_0123 = m[A10]*Det3_234_123 - m[A11]*Det3_234_023 |
---|
| 1475 | + m[A12]*Det3_234_013 - m[A13]*Det3_234_012; |
---|
| 1476 | G4double Det4_1234_0124 = m[A10]*Det3_234_124 - m[A11]*Det3_234_024 |
---|
| 1477 | + m[A12]*Det3_234_014 - m[A14]*Det3_234_012; |
---|
| 1478 | G4double Det4_1234_0134 = m[A10]*Det3_234_134 - m[A11]*Det3_234_034 |
---|
| 1479 | + m[A13]*Det3_234_014 - m[A14]*Det3_234_013; |
---|
| 1480 | G4double Det4_1234_0234 = m[A10]*Det3_234_234 - m[A12]*Det3_234_034 |
---|
| 1481 | + m[A13]*Det3_234_024 - m[A14]*Det3_234_023; |
---|
| 1482 | G4double Det4_1234_1234 = m[A11]*Det3_234_234 - m[A12]*Det3_234_134 |
---|
| 1483 | + m[A13]*Det3_234_124 - m[A14]*Det3_234_123; |
---|
| 1484 | |
---|
| 1485 | // Find the 5x5 det: |
---|
| 1486 | |
---|
| 1487 | G4double det = m[A00]*Det4_1234_1234 |
---|
| 1488 | - m[A01]*Det4_1234_0234 |
---|
| 1489 | + m[A02]*Det4_1234_0134 |
---|
| 1490 | - m[A03]*Det4_1234_0124 |
---|
| 1491 | + m[A04]*Det4_1234_0123; |
---|
| 1492 | |
---|
| 1493 | if ( det == 0 ) |
---|
| 1494 | { |
---|
| 1495 | ifail = 1; |
---|
| 1496 | return; |
---|
| 1497 | } |
---|
| 1498 | |
---|
| 1499 | G4double oneOverDet = 1.0/det; |
---|
| 1500 | G4double mn1OverDet = - oneOverDet; |
---|
| 1501 | |
---|
| 1502 | m[A00] = Det4_1234_1234 * oneOverDet; |
---|
| 1503 | m[A01] = Det4_1234_0234 * mn1OverDet; |
---|
| 1504 | m[A02] = Det4_1234_0134 * oneOverDet; |
---|
| 1505 | m[A03] = Det4_1234_0124 * mn1OverDet; |
---|
| 1506 | m[A04] = Det4_1234_0123 * oneOverDet; |
---|
| 1507 | |
---|
| 1508 | m[A11] = Det4_0234_0234 * oneOverDet; |
---|
| 1509 | m[A12] = Det4_0234_0134 * mn1OverDet; |
---|
| 1510 | m[A13] = Det4_0234_0124 * oneOverDet; |
---|
| 1511 | m[A14] = Det4_0234_0123 * mn1OverDet; |
---|
| 1512 | |
---|
| 1513 | m[A22] = Det4_0134_0134 * oneOverDet; |
---|
| 1514 | m[A23] = Det4_0134_0124 * mn1OverDet; |
---|
| 1515 | m[A24] = Det4_0134_0123 * oneOverDet; |
---|
| 1516 | |
---|
| 1517 | m[A33] = Det4_0124_0124 * oneOverDet; |
---|
| 1518 | m[A34] = Det4_0124_0123 * mn1OverDet; |
---|
| 1519 | |
---|
| 1520 | m[A44] = Det4_0123_0123 * oneOverDet; |
---|
| 1521 | |
---|
| 1522 | return; |
---|
| 1523 | } |
---|
| 1524 | |
---|
| 1525 | void G4ErrorSymMatrix::invertHaywood6 (G4int & ifail) |
---|
| 1526 | { |
---|
| 1527 | ifail = 0; |
---|
| 1528 | |
---|
| 1529 | // Find all NECESSARY 2x2 dets: (39 of them) |
---|
| 1530 | |
---|
| 1531 | G4double Det2_34_01 = m[A30]*m[A41] - m[A31]*m[A40]; |
---|
| 1532 | G4double Det2_34_02 = m[A30]*m[A42] - m[A32]*m[A40]; |
---|
| 1533 | G4double Det2_34_03 = m[A30]*m[A43] - m[A33]*m[A40]; |
---|
| 1534 | G4double Det2_34_04 = m[A30]*m[A44] - m[A34]*m[A40]; |
---|
| 1535 | G4double Det2_34_12 = m[A31]*m[A42] - m[A32]*m[A41]; |
---|
| 1536 | G4double Det2_34_13 = m[A31]*m[A43] - m[A33]*m[A41]; |
---|
| 1537 | G4double Det2_34_14 = m[A31]*m[A44] - m[A34]*m[A41]; |
---|
| 1538 | G4double Det2_34_23 = m[A32]*m[A43] - m[A33]*m[A42]; |
---|
| 1539 | G4double Det2_34_24 = m[A32]*m[A44] - m[A34]*m[A42]; |
---|
| 1540 | G4double Det2_34_34 = m[A33]*m[A44] - m[A34]*m[A43]; |
---|
| 1541 | G4double Det2_35_01 = m[A30]*m[A51] - m[A31]*m[A50]; |
---|
| 1542 | G4double Det2_35_02 = m[A30]*m[A52] - m[A32]*m[A50]; |
---|
| 1543 | G4double Det2_35_03 = m[A30]*m[A53] - m[A33]*m[A50]; |
---|
| 1544 | G4double Det2_35_04 = m[A30]*m[A54] - m[A34]*m[A50]; |
---|
| 1545 | G4double Det2_35_05 = m[A30]*m[A55] - m[A35]*m[A50]; |
---|
| 1546 | G4double Det2_35_12 = m[A31]*m[A52] - m[A32]*m[A51]; |
---|
| 1547 | G4double Det2_35_13 = m[A31]*m[A53] - m[A33]*m[A51]; |
---|
| 1548 | G4double Det2_35_14 = m[A31]*m[A54] - m[A34]*m[A51]; |
---|
| 1549 | G4double Det2_35_15 = m[A31]*m[A55] - m[A35]*m[A51]; |
---|
| 1550 | G4double Det2_35_23 = m[A32]*m[A53] - m[A33]*m[A52]; |
---|
| 1551 | G4double Det2_35_24 = m[A32]*m[A54] - m[A34]*m[A52]; |
---|
| 1552 | G4double Det2_35_25 = m[A32]*m[A55] - m[A35]*m[A52]; |
---|
| 1553 | G4double Det2_35_34 = m[A33]*m[A54] - m[A34]*m[A53]; |
---|
| 1554 | G4double Det2_35_35 = m[A33]*m[A55] - m[A35]*m[A53]; |
---|
| 1555 | G4double Det2_45_01 = m[A40]*m[A51] - m[A41]*m[A50]; |
---|
| 1556 | G4double Det2_45_02 = m[A40]*m[A52] - m[A42]*m[A50]; |
---|
| 1557 | G4double Det2_45_03 = m[A40]*m[A53] - m[A43]*m[A50]; |
---|
| 1558 | G4double Det2_45_04 = m[A40]*m[A54] - m[A44]*m[A50]; |
---|
| 1559 | G4double Det2_45_05 = m[A40]*m[A55] - m[A45]*m[A50]; |
---|
| 1560 | G4double Det2_45_12 = m[A41]*m[A52] - m[A42]*m[A51]; |
---|
| 1561 | G4double Det2_45_13 = m[A41]*m[A53] - m[A43]*m[A51]; |
---|
| 1562 | G4double Det2_45_14 = m[A41]*m[A54] - m[A44]*m[A51]; |
---|
| 1563 | G4double Det2_45_15 = m[A41]*m[A55] - m[A45]*m[A51]; |
---|
| 1564 | G4double Det2_45_23 = m[A42]*m[A53] - m[A43]*m[A52]; |
---|
| 1565 | G4double Det2_45_24 = m[A42]*m[A54] - m[A44]*m[A52]; |
---|
| 1566 | G4double Det2_45_25 = m[A42]*m[A55] - m[A45]*m[A52]; |
---|
| 1567 | G4double Det2_45_34 = m[A43]*m[A54] - m[A44]*m[A53]; |
---|
| 1568 | G4double Det2_45_35 = m[A43]*m[A55] - m[A45]*m[A53]; |
---|
| 1569 | G4double Det2_45_45 = m[A44]*m[A55] - m[A45]*m[A54]; |
---|
| 1570 | |
---|
| 1571 | // Find all NECESSARY 3x3 dets: (65 of them) |
---|
| 1572 | |
---|
| 1573 | G4double Det3_234_012 = m[A20]*Det2_34_12 - m[A21]*Det2_34_02 |
---|
| 1574 | + m[A22]*Det2_34_01; |
---|
| 1575 | G4double Det3_234_013 = m[A20]*Det2_34_13 - m[A21]*Det2_34_03 |
---|
| 1576 | + m[A23]*Det2_34_01; |
---|
| 1577 | G4double Det3_234_014 = m[A20]*Det2_34_14 - m[A21]*Det2_34_04 |
---|
| 1578 | + m[A24]*Det2_34_01; |
---|
| 1579 | G4double Det3_234_023 = m[A20]*Det2_34_23 - m[A22]*Det2_34_03 |
---|
| 1580 | + m[A23]*Det2_34_02; |
---|
| 1581 | G4double Det3_234_024 = m[A20]*Det2_34_24 - m[A22]*Det2_34_04 |
---|
| 1582 | + m[A24]*Det2_34_02; |
---|
| 1583 | G4double Det3_234_034 = m[A20]*Det2_34_34 - m[A23]*Det2_34_04 |
---|
| 1584 | + m[A24]*Det2_34_03; |
---|
| 1585 | G4double Det3_234_123 = m[A21]*Det2_34_23 - m[A22]*Det2_34_13 |
---|
| 1586 | + m[A23]*Det2_34_12; |
---|
| 1587 | G4double Det3_234_124 = m[A21]*Det2_34_24 - m[A22]*Det2_34_14 |
---|
| 1588 | + m[A24]*Det2_34_12; |
---|
| 1589 | G4double Det3_234_134 = m[A21]*Det2_34_34 - m[A23]*Det2_34_14 |
---|
| 1590 | + m[A24]*Det2_34_13; |
---|
| 1591 | G4double Det3_234_234 = m[A22]*Det2_34_34 - m[A23]*Det2_34_24 |
---|
| 1592 | + m[A24]*Det2_34_23; |
---|
| 1593 | G4double Det3_235_012 = m[A20]*Det2_35_12 - m[A21]*Det2_35_02 |
---|
| 1594 | + m[A22]*Det2_35_01; |
---|
| 1595 | G4double Det3_235_013 = m[A20]*Det2_35_13 - m[A21]*Det2_35_03 |
---|
| 1596 | + m[A23]*Det2_35_01; |
---|
| 1597 | G4double Det3_235_014 = m[A20]*Det2_35_14 - m[A21]*Det2_35_04 |
---|
| 1598 | + m[A24]*Det2_35_01; |
---|
| 1599 | G4double Det3_235_015 = m[A20]*Det2_35_15 - m[A21]*Det2_35_05 |
---|
| 1600 | + m[A25]*Det2_35_01; |
---|
| 1601 | G4double Det3_235_023 = m[A20]*Det2_35_23 - m[A22]*Det2_35_03 |
---|
| 1602 | + m[A23]*Det2_35_02; |
---|
| 1603 | G4double Det3_235_024 = m[A20]*Det2_35_24 - m[A22]*Det2_35_04 |
---|
| 1604 | + m[A24]*Det2_35_02; |
---|
| 1605 | G4double Det3_235_025 = m[A20]*Det2_35_25 - m[A22]*Det2_35_05 |
---|
| 1606 | + m[A25]*Det2_35_02; |
---|
| 1607 | G4double Det3_235_034 = m[A20]*Det2_35_34 - m[A23]*Det2_35_04 |
---|
| 1608 | + m[A24]*Det2_35_03; |
---|
| 1609 | G4double Det3_235_035 = m[A20]*Det2_35_35 - m[A23]*Det2_35_05 |
---|
| 1610 | + m[A25]*Det2_35_03; |
---|
| 1611 | G4double Det3_235_123 = m[A21]*Det2_35_23 - m[A22]*Det2_35_13 |
---|
| 1612 | + m[A23]*Det2_35_12; |
---|
| 1613 | G4double Det3_235_124 = m[A21]*Det2_35_24 - m[A22]*Det2_35_14 |
---|
| 1614 | + m[A24]*Det2_35_12; |
---|
| 1615 | G4double Det3_235_125 = m[A21]*Det2_35_25 - m[A22]*Det2_35_15 |
---|
| 1616 | + m[A25]*Det2_35_12; |
---|
| 1617 | G4double Det3_235_134 = m[A21]*Det2_35_34 - m[A23]*Det2_35_14 |
---|
| 1618 | + m[A24]*Det2_35_13; |
---|
| 1619 | G4double Det3_235_135 = m[A21]*Det2_35_35 - m[A23]*Det2_35_15 |
---|
| 1620 | + m[A25]*Det2_35_13; |
---|
| 1621 | G4double Det3_235_234 = m[A22]*Det2_35_34 - m[A23]*Det2_35_24 |
---|
| 1622 | + m[A24]*Det2_35_23; |
---|
| 1623 | G4double Det3_235_235 = m[A22]*Det2_35_35 - m[A23]*Det2_35_25 |
---|
| 1624 | + m[A25]*Det2_35_23; |
---|
| 1625 | G4double Det3_245_012 = m[A20]*Det2_45_12 - m[A21]*Det2_45_02 |
---|
| 1626 | + m[A22]*Det2_45_01; |
---|
| 1627 | G4double Det3_245_013 = m[A20]*Det2_45_13 - m[A21]*Det2_45_03 |
---|
| 1628 | + m[A23]*Det2_45_01; |
---|
| 1629 | G4double Det3_245_014 = m[A20]*Det2_45_14 - m[A21]*Det2_45_04 |
---|
| 1630 | + m[A24]*Det2_45_01; |
---|
| 1631 | G4double Det3_245_015 = m[A20]*Det2_45_15 - m[A21]*Det2_45_05 |
---|
| 1632 | + m[A25]*Det2_45_01; |
---|
| 1633 | G4double Det3_245_023 = m[A20]*Det2_45_23 - m[A22]*Det2_45_03 |
---|
| 1634 | + m[A23]*Det2_45_02; |
---|
| 1635 | G4double Det3_245_024 = m[A20]*Det2_45_24 - m[A22]*Det2_45_04 |
---|
| 1636 | + m[A24]*Det2_45_02; |
---|
| 1637 | G4double Det3_245_025 = m[A20]*Det2_45_25 - m[A22]*Det2_45_05 |
---|
| 1638 | + m[A25]*Det2_45_02; |
---|
| 1639 | G4double Det3_245_034 = m[A20]*Det2_45_34 - m[A23]*Det2_45_04 |
---|
| 1640 | + m[A24]*Det2_45_03; |
---|
| 1641 | G4double Det3_245_035 = m[A20]*Det2_45_35 - m[A23]*Det2_45_05 |
---|
| 1642 | + m[A25]*Det2_45_03; |
---|
| 1643 | G4double Det3_245_045 = m[A20]*Det2_45_45 - m[A24]*Det2_45_05 |
---|
| 1644 | + m[A25]*Det2_45_04; |
---|
| 1645 | G4double Det3_245_123 = m[A21]*Det2_45_23 - m[A22]*Det2_45_13 |
---|
| 1646 | + m[A23]*Det2_45_12; |
---|
| 1647 | G4double Det3_245_124 = m[A21]*Det2_45_24 - m[A22]*Det2_45_14 |
---|
| 1648 | + m[A24]*Det2_45_12; |
---|
| 1649 | G4double Det3_245_125 = m[A21]*Det2_45_25 - m[A22]*Det2_45_15 |
---|
| 1650 | + m[A25]*Det2_45_12; |
---|
| 1651 | G4double Det3_245_134 = m[A21]*Det2_45_34 - m[A23]*Det2_45_14 |
---|
| 1652 | + m[A24]*Det2_45_13; |
---|
| 1653 | G4double Det3_245_135 = m[A21]*Det2_45_35 - m[A23]*Det2_45_15 |
---|
| 1654 | + m[A25]*Det2_45_13; |
---|
| 1655 | G4double Det3_245_145 = m[A21]*Det2_45_45 - m[A24]*Det2_45_15 |
---|
| 1656 | + m[A25]*Det2_45_14; |
---|
| 1657 | G4double Det3_245_234 = m[A22]*Det2_45_34 - m[A23]*Det2_45_24 |
---|
| 1658 | + m[A24]*Det2_45_23; |
---|
| 1659 | G4double Det3_245_235 = m[A22]*Det2_45_35 - m[A23]*Det2_45_25 |
---|
| 1660 | + m[A25]*Det2_45_23; |
---|
| 1661 | G4double Det3_245_245 = m[A22]*Det2_45_45 - m[A24]*Det2_45_25 |
---|
| 1662 | + m[A25]*Det2_45_24; |
---|
| 1663 | G4double Det3_345_012 = m[A30]*Det2_45_12 - m[A31]*Det2_45_02 |
---|
| 1664 | + m[A32]*Det2_45_01; |
---|
| 1665 | G4double Det3_345_013 = m[A30]*Det2_45_13 - m[A31]*Det2_45_03 |
---|
| 1666 | + m[A33]*Det2_45_01; |
---|
| 1667 | G4double Det3_345_014 = m[A30]*Det2_45_14 - m[A31]*Det2_45_04 |
---|
| 1668 | + m[A34]*Det2_45_01; |
---|
| 1669 | G4double Det3_345_015 = m[A30]*Det2_45_15 - m[A31]*Det2_45_05 |
---|
| 1670 | + m[A35]*Det2_45_01; |
---|
| 1671 | G4double Det3_345_023 = m[A30]*Det2_45_23 - m[A32]*Det2_45_03 |
---|
| 1672 | + m[A33]*Det2_45_02; |
---|
| 1673 | G4double Det3_345_024 = m[A30]*Det2_45_24 - m[A32]*Det2_45_04 |
---|
| 1674 | + m[A34]*Det2_45_02; |
---|
| 1675 | G4double Det3_345_025 = m[A30]*Det2_45_25 - m[A32]*Det2_45_05 |
---|
| 1676 | + m[A35]*Det2_45_02; |
---|
| 1677 | G4double Det3_345_034 = m[A30]*Det2_45_34 - m[A33]*Det2_45_04 |
---|
| 1678 | + m[A34]*Det2_45_03; |
---|
| 1679 | G4double Det3_345_035 = m[A30]*Det2_45_35 - m[A33]*Det2_45_05 |
---|
| 1680 | + m[A35]*Det2_45_03; |
---|
| 1681 | G4double Det3_345_045 = m[A30]*Det2_45_45 - m[A34]*Det2_45_05 |
---|
| 1682 | + m[A35]*Det2_45_04; |
---|
| 1683 | G4double Det3_345_123 = m[A31]*Det2_45_23 - m[A32]*Det2_45_13 |
---|
| 1684 | + m[A33]*Det2_45_12; |
---|
| 1685 | G4double Det3_345_124 = m[A31]*Det2_45_24 - m[A32]*Det2_45_14 |
---|
| 1686 | + m[A34]*Det2_45_12; |
---|
| 1687 | G4double Det3_345_125 = m[A31]*Det2_45_25 - m[A32]*Det2_45_15 |
---|
| 1688 | + m[A35]*Det2_45_12; |
---|
| 1689 | G4double Det3_345_134 = m[A31]*Det2_45_34 - m[A33]*Det2_45_14 |
---|
| 1690 | + m[A34]*Det2_45_13; |
---|
| 1691 | G4double Det3_345_135 = m[A31]*Det2_45_35 - m[A33]*Det2_45_15 |
---|
| 1692 | + m[A35]*Det2_45_13; |
---|
| 1693 | G4double Det3_345_145 = m[A31]*Det2_45_45 - m[A34]*Det2_45_15 |
---|
| 1694 | + m[A35]*Det2_45_14; |
---|
| 1695 | G4double Det3_345_234 = m[A32]*Det2_45_34 - m[A33]*Det2_45_24 |
---|
| 1696 | + m[A34]*Det2_45_23; |
---|
| 1697 | G4double Det3_345_235 = m[A32]*Det2_45_35 - m[A33]*Det2_45_25 |
---|
| 1698 | + m[A35]*Det2_45_23; |
---|
| 1699 | G4double Det3_345_245 = m[A32]*Det2_45_45 - m[A34]*Det2_45_25 |
---|
| 1700 | + m[A35]*Det2_45_24; |
---|
| 1701 | G4double Det3_345_345 = m[A33]*Det2_45_45 - m[A34]*Det2_45_35 |
---|
| 1702 | + m[A35]*Det2_45_34; |
---|
| 1703 | |
---|
| 1704 | // Find all NECESSARY 4x4 dets: (55 of them) |
---|
| 1705 | |
---|
| 1706 | G4double Det4_1234_0123 = m[A10]*Det3_234_123 - m[A11]*Det3_234_023 |
---|
| 1707 | + m[A12]*Det3_234_013 - m[A13]*Det3_234_012; |
---|
| 1708 | G4double Det4_1234_0124 = m[A10]*Det3_234_124 - m[A11]*Det3_234_024 |
---|
| 1709 | + m[A12]*Det3_234_014 - m[A14]*Det3_234_012; |
---|
| 1710 | G4double Det4_1234_0134 = m[A10]*Det3_234_134 - m[A11]*Det3_234_034 |
---|
| 1711 | + m[A13]*Det3_234_014 - m[A14]*Det3_234_013; |
---|
| 1712 | G4double Det4_1234_0234 = m[A10]*Det3_234_234 - m[A12]*Det3_234_034 |
---|
| 1713 | + m[A13]*Det3_234_024 - m[A14]*Det3_234_023; |
---|
| 1714 | G4double Det4_1234_1234 = m[A11]*Det3_234_234 - m[A12]*Det3_234_134 |
---|
| 1715 | + m[A13]*Det3_234_124 - m[A14]*Det3_234_123; |
---|
| 1716 | G4double Det4_1235_0123 = m[A10]*Det3_235_123 - m[A11]*Det3_235_023 |
---|
| 1717 | + m[A12]*Det3_235_013 - m[A13]*Det3_235_012; |
---|
| 1718 | G4double Det4_1235_0124 = m[A10]*Det3_235_124 - m[A11]*Det3_235_024 |
---|
| 1719 | + m[A12]*Det3_235_014 - m[A14]*Det3_235_012; |
---|
| 1720 | G4double Det4_1235_0125 = m[A10]*Det3_235_125 - m[A11]*Det3_235_025 |
---|
| 1721 | + m[A12]*Det3_235_015 - m[A15]*Det3_235_012; |
---|
| 1722 | G4double Det4_1235_0134 = m[A10]*Det3_235_134 - m[A11]*Det3_235_034 |
---|
| 1723 | + m[A13]*Det3_235_014 - m[A14]*Det3_235_013; |
---|
| 1724 | G4double Det4_1235_0135 = m[A10]*Det3_235_135 - m[A11]*Det3_235_035 |
---|
| 1725 | + m[A13]*Det3_235_015 - m[A15]*Det3_235_013; |
---|
| 1726 | G4double Det4_1235_0234 = m[A10]*Det3_235_234 - m[A12]*Det3_235_034 |
---|
| 1727 | + m[A13]*Det3_235_024 - m[A14]*Det3_235_023; |
---|
| 1728 | G4double Det4_1235_0235 = m[A10]*Det3_235_235 - m[A12]*Det3_235_035 |
---|
| 1729 | + m[A13]*Det3_235_025 - m[A15]*Det3_235_023; |
---|
| 1730 | G4double Det4_1235_1234 = m[A11]*Det3_235_234 - m[A12]*Det3_235_134 |
---|
| 1731 | + m[A13]*Det3_235_124 - m[A14]*Det3_235_123; |
---|
| 1732 | G4double Det4_1235_1235 = m[A11]*Det3_235_235 - m[A12]*Det3_235_135 |
---|
| 1733 | + m[A13]*Det3_235_125 - m[A15]*Det3_235_123; |
---|
| 1734 | G4double Det4_1245_0123 = m[A10]*Det3_245_123 - m[A11]*Det3_245_023 |
---|
| 1735 | + m[A12]*Det3_245_013 - m[A13]*Det3_245_012; |
---|
| 1736 | G4double Det4_1245_0124 = m[A10]*Det3_245_124 - m[A11]*Det3_245_024 |
---|
| 1737 | + m[A12]*Det3_245_014 - m[A14]*Det3_245_012; |
---|
| 1738 | G4double Det4_1245_0125 = m[A10]*Det3_245_125 - m[A11]*Det3_245_025 |
---|
| 1739 | + m[A12]*Det3_245_015 - m[A15]*Det3_245_012; |
---|
| 1740 | G4double Det4_1245_0134 = m[A10]*Det3_245_134 - m[A11]*Det3_245_034 |
---|
| 1741 | + m[A13]*Det3_245_014 - m[A14]*Det3_245_013; |
---|
| 1742 | G4double Det4_1245_0135 = m[A10]*Det3_245_135 - m[A11]*Det3_245_035 |
---|
| 1743 | + m[A13]*Det3_245_015 - m[A15]*Det3_245_013; |
---|
| 1744 | G4double Det4_1245_0145 = m[A10]*Det3_245_145 - m[A11]*Det3_245_045 |
---|
| 1745 | + m[A14]*Det3_245_015 - m[A15]*Det3_245_014; |
---|
| 1746 | G4double Det4_1245_0234 = m[A10]*Det3_245_234 - m[A12]*Det3_245_034 |
---|
| 1747 | + m[A13]*Det3_245_024 - m[A14]*Det3_245_023; |
---|
| 1748 | G4double Det4_1245_0235 = m[A10]*Det3_245_235 - m[A12]*Det3_245_035 |
---|
| 1749 | + m[A13]*Det3_245_025 - m[A15]*Det3_245_023; |
---|
| 1750 | G4double Det4_1245_0245 = m[A10]*Det3_245_245 - m[A12]*Det3_245_045 |
---|
| 1751 | + m[A14]*Det3_245_025 - m[A15]*Det3_245_024; |
---|
| 1752 | G4double Det4_1245_1234 = m[A11]*Det3_245_234 - m[A12]*Det3_245_134 |
---|
| 1753 | + m[A13]*Det3_245_124 - m[A14]*Det3_245_123; |
---|
| 1754 | G4double Det4_1245_1235 = m[A11]*Det3_245_235 - m[A12]*Det3_245_135 |
---|
| 1755 | + m[A13]*Det3_245_125 - m[A15]*Det3_245_123; |
---|
| 1756 | G4double Det4_1245_1245 = m[A11]*Det3_245_245 - m[A12]*Det3_245_145 |
---|
| 1757 | + m[A14]*Det3_245_125 - m[A15]*Det3_245_124; |
---|
| 1758 | G4double Det4_1345_0123 = m[A10]*Det3_345_123 - m[A11]*Det3_345_023 |
---|
| 1759 | + m[A12]*Det3_345_013 - m[A13]*Det3_345_012; |
---|
| 1760 | G4double Det4_1345_0124 = m[A10]*Det3_345_124 - m[A11]*Det3_345_024 |
---|
| 1761 | + m[A12]*Det3_345_014 - m[A14]*Det3_345_012; |
---|
| 1762 | G4double Det4_1345_0125 = m[A10]*Det3_345_125 - m[A11]*Det3_345_025 |
---|
| 1763 | + m[A12]*Det3_345_015 - m[A15]*Det3_345_012; |
---|
| 1764 | G4double Det4_1345_0134 = m[A10]*Det3_345_134 - m[A11]*Det3_345_034 |
---|
| 1765 | + m[A13]*Det3_345_014 - m[A14]*Det3_345_013; |
---|
| 1766 | G4double Det4_1345_0135 = m[A10]*Det3_345_135 - m[A11]*Det3_345_035 |
---|
| 1767 | + m[A13]*Det3_345_015 - m[A15]*Det3_345_013; |
---|
| 1768 | G4double Det4_1345_0145 = m[A10]*Det3_345_145 - m[A11]*Det3_345_045 |
---|
| 1769 | + m[A14]*Det3_345_015 - m[A15]*Det3_345_014; |
---|
| 1770 | G4double Det4_1345_0234 = m[A10]*Det3_345_234 - m[A12]*Det3_345_034 |
---|
| 1771 | + m[A13]*Det3_345_024 - m[A14]*Det3_345_023; |
---|
| 1772 | G4double Det4_1345_0235 = m[A10]*Det3_345_235 - m[A12]*Det3_345_035 |
---|
| 1773 | + m[A13]*Det3_345_025 - m[A15]*Det3_345_023; |
---|
| 1774 | G4double Det4_1345_0245 = m[A10]*Det3_345_245 - m[A12]*Det3_345_045 |
---|
| 1775 | + m[A14]*Det3_345_025 - m[A15]*Det3_345_024; |
---|
| 1776 | G4double Det4_1345_0345 = m[A10]*Det3_345_345 - m[A13]*Det3_345_045 |
---|
| 1777 | + m[A14]*Det3_345_035 - m[A15]*Det3_345_034; |
---|
| 1778 | G4double Det4_1345_1234 = m[A11]*Det3_345_234 - m[A12]*Det3_345_134 |
---|
| 1779 | + m[A13]*Det3_345_124 - m[A14]*Det3_345_123; |
---|
| 1780 | G4double Det4_1345_1235 = m[A11]*Det3_345_235 - m[A12]*Det3_345_135 |
---|
| 1781 | + m[A13]*Det3_345_125 - m[A15]*Det3_345_123; |
---|
| 1782 | G4double Det4_1345_1245 = m[A11]*Det3_345_245 - m[A12]*Det3_345_145 |
---|
| 1783 | + m[A14]*Det3_345_125 - m[A15]*Det3_345_124; |
---|
| 1784 | G4double Det4_1345_1345 = m[A11]*Det3_345_345 - m[A13]*Det3_345_145 |
---|
| 1785 | + m[A14]*Det3_345_135 - m[A15]*Det3_345_134; |
---|
| 1786 | G4double Det4_2345_0123 = m[A20]*Det3_345_123 - m[A21]*Det3_345_023 |
---|
| 1787 | + m[A22]*Det3_345_013 - m[A23]*Det3_345_012; |
---|
| 1788 | G4double Det4_2345_0124 = m[A20]*Det3_345_124 - m[A21]*Det3_345_024 |
---|
| 1789 | + m[A22]*Det3_345_014 - m[A24]*Det3_345_012; |
---|
| 1790 | G4double Det4_2345_0125 = m[A20]*Det3_345_125 - m[A21]*Det3_345_025 |
---|
| 1791 | + m[A22]*Det3_345_015 - m[A25]*Det3_345_012; |
---|
| 1792 | G4double Det4_2345_0134 = m[A20]*Det3_345_134 - m[A21]*Det3_345_034 |
---|
| 1793 | + m[A23]*Det3_345_014 - m[A24]*Det3_345_013; |
---|
| 1794 | G4double Det4_2345_0135 = m[A20]*Det3_345_135 - m[A21]*Det3_345_035 |
---|
| 1795 | + m[A23]*Det3_345_015 - m[A25]*Det3_345_013; |
---|
| 1796 | G4double Det4_2345_0145 = m[A20]*Det3_345_145 - m[A21]*Det3_345_045 |
---|
| 1797 | + m[A24]*Det3_345_015 - m[A25]*Det3_345_014; |
---|
| 1798 | G4double Det4_2345_0234 = m[A20]*Det3_345_234 - m[A22]*Det3_345_034 |
---|
| 1799 | + m[A23]*Det3_345_024 - m[A24]*Det3_345_023; |
---|
| 1800 | G4double Det4_2345_0235 = m[A20]*Det3_345_235 - m[A22]*Det3_345_035 |
---|
| 1801 | + m[A23]*Det3_345_025 - m[A25]*Det3_345_023; |
---|
| 1802 | G4double Det4_2345_0245 = m[A20]*Det3_345_245 - m[A22]*Det3_345_045 |
---|
| 1803 | + m[A24]*Det3_345_025 - m[A25]*Det3_345_024; |
---|
| 1804 | G4double Det4_2345_0345 = m[A20]*Det3_345_345 - m[A23]*Det3_345_045 |
---|
| 1805 | + m[A24]*Det3_345_035 - m[A25]*Det3_345_034; |
---|
| 1806 | G4double Det4_2345_1234 = m[A21]*Det3_345_234 - m[A22]*Det3_345_134 |
---|
| 1807 | + m[A23]*Det3_345_124 - m[A24]*Det3_345_123; |
---|
| 1808 | G4double Det4_2345_1235 = m[A21]*Det3_345_235 - m[A22]*Det3_345_135 |
---|
| 1809 | + m[A23]*Det3_345_125 - m[A25]*Det3_345_123; |
---|
| 1810 | G4double Det4_2345_1245 = m[A21]*Det3_345_245 - m[A22]*Det3_345_145 |
---|
| 1811 | + m[A24]*Det3_345_125 - m[A25]*Det3_345_124; |
---|
| 1812 | G4double Det4_2345_1345 = m[A21]*Det3_345_345 - m[A23]*Det3_345_145 |
---|
| 1813 | + m[A24]*Det3_345_135 - m[A25]*Det3_345_134; |
---|
| 1814 | G4double Det4_2345_2345 = m[A22]*Det3_345_345 - m[A23]*Det3_345_245 |
---|
| 1815 | + m[A24]*Det3_345_235 - m[A25]*Det3_345_234; |
---|
| 1816 | |
---|
| 1817 | // Find all NECESSARY 5x5 dets: (19 of them) |
---|
| 1818 | |
---|
| 1819 | G4double Det5_01234_01234 = m[A00]*Det4_1234_1234 - m[A01]*Det4_1234_0234 |
---|
| 1820 | + m[A02]*Det4_1234_0134 - m[A03]*Det4_1234_0124 + m[A04]*Det4_1234_0123; |
---|
| 1821 | G4double Det5_01235_01234 = m[A00]*Det4_1235_1234 - m[A01]*Det4_1235_0234 |
---|
| 1822 | + m[A02]*Det4_1235_0134 - m[A03]*Det4_1235_0124 + m[A04]*Det4_1235_0123; |
---|
| 1823 | G4double Det5_01235_01235 = m[A00]*Det4_1235_1235 - m[A01]*Det4_1235_0235 |
---|
| 1824 | + m[A02]*Det4_1235_0135 - m[A03]*Det4_1235_0125 + m[A05]*Det4_1235_0123; |
---|
| 1825 | G4double Det5_01245_01234 = m[A00]*Det4_1245_1234 - m[A01]*Det4_1245_0234 |
---|
| 1826 | + m[A02]*Det4_1245_0134 - m[A03]*Det4_1245_0124 + m[A04]*Det4_1245_0123; |
---|
| 1827 | G4double Det5_01245_01235 = m[A00]*Det4_1245_1235 - m[A01]*Det4_1245_0235 |
---|
| 1828 | + m[A02]*Det4_1245_0135 - m[A03]*Det4_1245_0125 + m[A05]*Det4_1245_0123; |
---|
| 1829 | G4double Det5_01245_01245 = m[A00]*Det4_1245_1245 - m[A01]*Det4_1245_0245 |
---|
| 1830 | + m[A02]*Det4_1245_0145 - m[A04]*Det4_1245_0125 + m[A05]*Det4_1245_0124; |
---|
| 1831 | G4double Det5_01345_01234 = m[A00]*Det4_1345_1234 - m[A01]*Det4_1345_0234 |
---|
| 1832 | + m[A02]*Det4_1345_0134 - m[A03]*Det4_1345_0124 + m[A04]*Det4_1345_0123; |
---|
| 1833 | G4double Det5_01345_01235 = m[A00]*Det4_1345_1235 - m[A01]*Det4_1345_0235 |
---|
| 1834 | + m[A02]*Det4_1345_0135 - m[A03]*Det4_1345_0125 + m[A05]*Det4_1345_0123; |
---|
| 1835 | G4double Det5_01345_01245 = m[A00]*Det4_1345_1245 - m[A01]*Det4_1345_0245 |
---|
| 1836 | + m[A02]*Det4_1345_0145 - m[A04]*Det4_1345_0125 + m[A05]*Det4_1345_0124; |
---|
| 1837 | G4double Det5_01345_01345 = m[A00]*Det4_1345_1345 - m[A01]*Det4_1345_0345 |
---|
| 1838 | + m[A03]*Det4_1345_0145 - m[A04]*Det4_1345_0135 + m[A05]*Det4_1345_0134; |
---|
| 1839 | G4double Det5_02345_01234 = m[A00]*Det4_2345_1234 - m[A01]*Det4_2345_0234 |
---|
| 1840 | + m[A02]*Det4_2345_0134 - m[A03]*Det4_2345_0124 + m[A04]*Det4_2345_0123; |
---|
| 1841 | G4double Det5_02345_01235 = m[A00]*Det4_2345_1235 - m[A01]*Det4_2345_0235 |
---|
| 1842 | + m[A02]*Det4_2345_0135 - m[A03]*Det4_2345_0125 + m[A05]*Det4_2345_0123; |
---|
| 1843 | G4double Det5_02345_01245 = m[A00]*Det4_2345_1245 - m[A01]*Det4_2345_0245 |
---|
| 1844 | + m[A02]*Det4_2345_0145 - m[A04]*Det4_2345_0125 + m[A05]*Det4_2345_0124; |
---|
| 1845 | G4double Det5_02345_01345 = m[A00]*Det4_2345_1345 - m[A01]*Det4_2345_0345 |
---|
| 1846 | + m[A03]*Det4_2345_0145 - m[A04]*Det4_2345_0135 + m[A05]*Det4_2345_0134; |
---|
| 1847 | G4double Det5_02345_02345 = m[A00]*Det4_2345_2345 - m[A02]*Det4_2345_0345 |
---|
| 1848 | + m[A03]*Det4_2345_0245 - m[A04]*Det4_2345_0235 + m[A05]*Det4_2345_0234; |
---|
| 1849 | G4double Det5_12345_01234 = m[A10]*Det4_2345_1234 - m[A11]*Det4_2345_0234 |
---|
| 1850 | + m[A12]*Det4_2345_0134 - m[A13]*Det4_2345_0124 + m[A14]*Det4_2345_0123; |
---|
| 1851 | G4double Det5_12345_01235 = m[A10]*Det4_2345_1235 - m[A11]*Det4_2345_0235 |
---|
| 1852 | + m[A12]*Det4_2345_0135 - m[A13]*Det4_2345_0125 + m[A15]*Det4_2345_0123; |
---|
| 1853 | G4double Det5_12345_01245 = m[A10]*Det4_2345_1245 - m[A11]*Det4_2345_0245 |
---|
| 1854 | + m[A12]*Det4_2345_0145 - m[A14]*Det4_2345_0125 + m[A15]*Det4_2345_0124; |
---|
| 1855 | G4double Det5_12345_01345 = m[A10]*Det4_2345_1345 - m[A11]*Det4_2345_0345 |
---|
| 1856 | + m[A13]*Det4_2345_0145 - m[A14]*Det4_2345_0135 + m[A15]*Det4_2345_0134; |
---|
| 1857 | G4double Det5_12345_02345 = m[A10]*Det4_2345_2345 - m[A12]*Det4_2345_0345 |
---|
| 1858 | + m[A13]*Det4_2345_0245 - m[A14]*Det4_2345_0235 + m[A15]*Det4_2345_0234; |
---|
| 1859 | G4double Det5_12345_12345 = m[A11]*Det4_2345_2345 - m[A12]*Det4_2345_1345 |
---|
| 1860 | + m[A13]*Det4_2345_1245 - m[A14]*Det4_2345_1235 + m[A15]*Det4_2345_1234; |
---|
| 1861 | |
---|
| 1862 | // Find the determinant |
---|
| 1863 | |
---|
| 1864 | G4double det = m[A00]*Det5_12345_12345 |
---|
| 1865 | - m[A01]*Det5_12345_02345 |
---|
| 1866 | + m[A02]*Det5_12345_01345 |
---|
| 1867 | - m[A03]*Det5_12345_01245 |
---|
| 1868 | + m[A04]*Det5_12345_01235 |
---|
| 1869 | - m[A05]*Det5_12345_01234; |
---|
| 1870 | |
---|
| 1871 | if ( det == 0 ) |
---|
| 1872 | { |
---|
| 1873 | ifail = 1; |
---|
| 1874 | return; |
---|
| 1875 | } |
---|
| 1876 | |
---|
| 1877 | G4double oneOverDet = 1.0/det; |
---|
| 1878 | G4double mn1OverDet = - oneOverDet; |
---|
| 1879 | |
---|
| 1880 | m[A00] = Det5_12345_12345*oneOverDet; |
---|
| 1881 | m[A01] = Det5_12345_02345*mn1OverDet; |
---|
| 1882 | m[A02] = Det5_12345_01345*oneOverDet; |
---|
| 1883 | m[A03] = Det5_12345_01245*mn1OverDet; |
---|
| 1884 | m[A04] = Det5_12345_01235*oneOverDet; |
---|
| 1885 | m[A05] = Det5_12345_01234*mn1OverDet; |
---|
| 1886 | |
---|
| 1887 | m[A11] = Det5_02345_02345*oneOverDet; |
---|
| 1888 | m[A12] = Det5_02345_01345*mn1OverDet; |
---|
| 1889 | m[A13] = Det5_02345_01245*oneOverDet; |
---|
| 1890 | m[A14] = Det5_02345_01235*mn1OverDet; |
---|
| 1891 | m[A15] = Det5_02345_01234*oneOverDet; |
---|
| 1892 | |
---|
| 1893 | m[A22] = Det5_01345_01345*oneOverDet; |
---|
| 1894 | m[A23] = Det5_01345_01245*mn1OverDet; |
---|
| 1895 | m[A24] = Det5_01345_01235*oneOverDet; |
---|
| 1896 | m[A25] = Det5_01345_01234*mn1OverDet; |
---|
| 1897 | |
---|
| 1898 | m[A33] = Det5_01245_01245*oneOverDet; |
---|
| 1899 | m[A34] = Det5_01245_01235*mn1OverDet; |
---|
| 1900 | m[A35] = Det5_01245_01234*oneOverDet; |
---|
| 1901 | |
---|
| 1902 | m[A44] = Det5_01235_01235*oneOverDet; |
---|
| 1903 | m[A45] = Det5_01235_01234*mn1OverDet; |
---|
| 1904 | |
---|
| 1905 | m[A55] = Det5_01234_01234*oneOverDet; |
---|
| 1906 | |
---|
| 1907 | return; |
---|
| 1908 | } |
---|
| 1909 | |
---|
| 1910 | void G4ErrorSymMatrix::invertCholesky5 (G4int & ifail) |
---|
| 1911 | { |
---|
| 1912 | |
---|
| 1913 | // Invert by |
---|
| 1914 | // |
---|
| 1915 | // a) decomposing M = G*G^T with G lower triangular |
---|
| 1916 | // (if M is not positive definite this will fail, leaving this unchanged) |
---|
| 1917 | // b) inverting G to form H |
---|
| 1918 | // c) multiplying H^T * H to get M^-1. |
---|
| 1919 | // |
---|
| 1920 | // If the matrix is pos. def. it is inverted and 1 is returned. |
---|
| 1921 | // If the matrix is not pos. def. it remains unaltered and 0 is returned. |
---|
| 1922 | |
---|
| 1923 | G4double h10; // below-diagonal elements of H |
---|
| 1924 | G4double h20, h21; |
---|
| 1925 | G4double h30, h31, h32; |
---|
| 1926 | G4double h40, h41, h42, h43; |
---|
| 1927 | |
---|
| 1928 | G4double h00, h11, h22, h33, h44; // 1/diagonal elements of G = |
---|
| 1929 | // diagonal elements of H |
---|
| 1930 | |
---|
| 1931 | G4double g10; // below-diagonal elements of G |
---|
| 1932 | G4double g20, g21; |
---|
| 1933 | G4double g30, g31, g32; |
---|
| 1934 | G4double g40, g41, g42, g43; |
---|
| 1935 | |
---|
| 1936 | ifail = 1; // We start by assuing we won't succeed... |
---|
| 1937 | |
---|
| 1938 | // Form G -- compute diagonal members of H directly rather than of G |
---|
| 1939 | //------- |
---|
| 1940 | |
---|
| 1941 | // Scale first column by 1/sqrt(A00) |
---|
| 1942 | |
---|
| 1943 | h00 = m[A00]; |
---|
| 1944 | if (h00 <= 0) { return; } |
---|
| 1945 | h00 = 1.0 / std::sqrt(h00); |
---|
| 1946 | |
---|
| 1947 | g10 = m[A10] * h00; |
---|
| 1948 | g20 = m[A20] * h00; |
---|
| 1949 | g30 = m[A30] * h00; |
---|
| 1950 | g40 = m[A40] * h00; |
---|
| 1951 | |
---|
| 1952 | // Form G11 (actually, just h11) |
---|
| 1953 | |
---|
| 1954 | h11 = m[A11] - (g10 * g10); |
---|
| 1955 | if (h11 <= 0) { return; } |
---|
| 1956 | h11 = 1.0 / std::sqrt(h11); |
---|
| 1957 | |
---|
| 1958 | // Subtract inter-column column dot products from rest of column 1 and |
---|
| 1959 | // scale to get column 1 of G |
---|
| 1960 | |
---|
| 1961 | g21 = (m[A21] - (g10 * g20)) * h11; |
---|
| 1962 | g31 = (m[A31] - (g10 * g30)) * h11; |
---|
| 1963 | g41 = (m[A41] - (g10 * g40)) * h11; |
---|
| 1964 | |
---|
| 1965 | // Form G22 (actually, just h22) |
---|
| 1966 | |
---|
| 1967 | h22 = m[A22] - (g20 * g20) - (g21 * g21); |
---|
| 1968 | if (h22 <= 0) { return; } |
---|
| 1969 | h22 = 1.0 / std::sqrt(h22); |
---|
| 1970 | |
---|
| 1971 | // Subtract inter-column column dot products from rest of column 2 and |
---|
| 1972 | // scale to get column 2 of G |
---|
| 1973 | |
---|
| 1974 | g32 = (m[A32] - (g20 * g30) - (g21 * g31)) * h22; |
---|
| 1975 | g42 = (m[A42] - (g20 * g40) - (g21 * g41)) * h22; |
---|
| 1976 | |
---|
| 1977 | // Form G33 (actually, just h33) |
---|
| 1978 | |
---|
| 1979 | h33 = m[A33] - (g30 * g30) - (g31 * g31) - (g32 * g32); |
---|
| 1980 | if (h33 <= 0) { return; } |
---|
| 1981 | h33 = 1.0 / std::sqrt(h33); |
---|
| 1982 | |
---|
| 1983 | // Subtract inter-column column dot product from A43 and scale to get G43 |
---|
| 1984 | |
---|
| 1985 | g43 = (m[A43] - (g30 * g40) - (g31 * g41) - (g32 * g42)) * h33; |
---|
| 1986 | |
---|
| 1987 | // Finally form h44 - if this is possible inversion succeeds |
---|
| 1988 | |
---|
| 1989 | h44 = m[A44] - (g40 * g40) - (g41 * g41) - (g42 * g42) - (g43 * g43); |
---|
| 1990 | if (h44 <= 0) { return; } |
---|
| 1991 | h44 = 1.0 / std::sqrt(h44); |
---|
| 1992 | |
---|
| 1993 | // Form H = 1/G -- diagonal members of H are already correct |
---|
| 1994 | //------------- |
---|
| 1995 | |
---|
| 1996 | // The order here is dictated by speed considerations |
---|
| 1997 | |
---|
| 1998 | h43 = -h33 * g43 * h44; |
---|
| 1999 | h32 = -h22 * g32 * h33; |
---|
| 2000 | h42 = -h22 * (g32 * h43 + g42 * h44); |
---|
| 2001 | h21 = -h11 * g21 * h22; |
---|
| 2002 | h31 = -h11 * (g21 * h32 + g31 * h33); |
---|
| 2003 | h41 = -h11 * (g21 * h42 + g31 * h43 + g41 * h44); |
---|
| 2004 | h10 = -h00 * g10 * h11; |
---|
| 2005 | h20 = -h00 * (g10 * h21 + g20 * h22); |
---|
| 2006 | h30 = -h00 * (g10 * h31 + g20 * h32 + g30 * h33); |
---|
| 2007 | h40 = -h00 * (g10 * h41 + g20 * h42 + g30 * h43 + g40 * h44); |
---|
| 2008 | |
---|
| 2009 | // Change this to its inverse = H^T*H |
---|
| 2010 | //------------------------------------ |
---|
| 2011 | |
---|
| 2012 | m[A00] = h00 * h00 + h10 * h10 + h20 * h20 + h30 * h30 + h40 * h40; |
---|
| 2013 | m[A01] = h10 * h11 + h20 * h21 + h30 * h31 + h40 * h41; |
---|
| 2014 | m[A11] = h11 * h11 + h21 * h21 + h31 * h31 + h41 * h41; |
---|
| 2015 | m[A02] = h20 * h22 + h30 * h32 + h40 * h42; |
---|
| 2016 | m[A12] = h21 * h22 + h31 * h32 + h41 * h42; |
---|
| 2017 | m[A22] = h22 * h22 + h32 * h32 + h42 * h42; |
---|
| 2018 | m[A03] = h30 * h33 + h40 * h43; |
---|
| 2019 | m[A13] = h31 * h33 + h41 * h43; |
---|
| 2020 | m[A23] = h32 * h33 + h42 * h43; |
---|
| 2021 | m[A33] = h33 * h33 + h43 * h43; |
---|
| 2022 | m[A04] = h40 * h44; |
---|
| 2023 | m[A14] = h41 * h44; |
---|
| 2024 | m[A24] = h42 * h44; |
---|
| 2025 | m[A34] = h43 * h44; |
---|
| 2026 | m[A44] = h44 * h44; |
---|
| 2027 | |
---|
| 2028 | ifail = 0; |
---|
| 2029 | return; |
---|
| 2030 | } |
---|
| 2031 | |
---|
| 2032 | void G4ErrorSymMatrix::invertCholesky6 (G4int & ifail) |
---|
| 2033 | { |
---|
| 2034 | // Invert by |
---|
| 2035 | // |
---|
| 2036 | // a) decomposing M = G*G^T with G lower triangular |
---|
| 2037 | // (if M is not positive definite this will fail, leaving this unchanged) |
---|
| 2038 | // b) inverting G to form H |
---|
| 2039 | // c) multiplying H^T * H to get M^-1. |
---|
| 2040 | // |
---|
| 2041 | // If the matrix is pos. def. it is inverted and 1 is returned. |
---|
| 2042 | // If the matrix is not pos. def. it remains unaltered and 0 is returned. |
---|
| 2043 | |
---|
| 2044 | G4double h10; // below-diagonal elements of H |
---|
| 2045 | G4double h20, h21; |
---|
| 2046 | G4double h30, h31, h32; |
---|
| 2047 | G4double h40, h41, h42, h43; |
---|
| 2048 | G4double h50, h51, h52, h53, h54; |
---|
| 2049 | |
---|
| 2050 | G4double h00, h11, h22, h33, h44, h55; // 1/diagonal elements of G = |
---|
| 2051 | // diagonal elements of H |
---|
| 2052 | |
---|
| 2053 | G4double g10; // below-diagonal elements of G |
---|
| 2054 | G4double g20, g21; |
---|
| 2055 | G4double g30, g31, g32; |
---|
| 2056 | G4double g40, g41, g42, g43; |
---|
| 2057 | G4double g50, g51, g52, g53, g54; |
---|
| 2058 | |
---|
| 2059 | ifail = 1; // We start by assuing we won't succeed... |
---|
| 2060 | |
---|
| 2061 | // Form G -- compute diagonal members of H directly rather than of G |
---|
| 2062 | //------- |
---|
| 2063 | |
---|
| 2064 | // Scale first column by 1/sqrt(A00) |
---|
| 2065 | |
---|
| 2066 | h00 = m[A00]; |
---|
| 2067 | if (h00 <= 0) { return; } |
---|
| 2068 | h00 = 1.0 / std::sqrt(h00); |
---|
| 2069 | |
---|
| 2070 | g10 = m[A10] * h00; |
---|
| 2071 | g20 = m[A20] * h00; |
---|
| 2072 | g30 = m[A30] * h00; |
---|
| 2073 | g40 = m[A40] * h00; |
---|
| 2074 | g50 = m[A50] * h00; |
---|
| 2075 | |
---|
| 2076 | // Form G11 (actually, just h11) |
---|
| 2077 | |
---|
| 2078 | h11 = m[A11] - (g10 * g10); |
---|
| 2079 | if (h11 <= 0) { return; } |
---|
| 2080 | h11 = 1.0 / std::sqrt(h11); |
---|
| 2081 | |
---|
| 2082 | // Subtract inter-column column dot products from rest of column 1 and |
---|
| 2083 | // scale to get column 1 of G |
---|
| 2084 | |
---|
| 2085 | g21 = (m[A21] - (g10 * g20)) * h11; |
---|
| 2086 | g31 = (m[A31] - (g10 * g30)) * h11; |
---|
| 2087 | g41 = (m[A41] - (g10 * g40)) * h11; |
---|
| 2088 | g51 = (m[A51] - (g10 * g50)) * h11; |
---|
| 2089 | |
---|
| 2090 | // Form G22 (actually, just h22) |
---|
| 2091 | |
---|
| 2092 | h22 = m[A22] - (g20 * g20) - (g21 * g21); |
---|
| 2093 | if (h22 <= 0) { return; } |
---|
| 2094 | h22 = 1.0 / std::sqrt(h22); |
---|
| 2095 | |
---|
| 2096 | // Subtract inter-column column dot products from rest of column 2 and |
---|
| 2097 | // scale to get column 2 of G |
---|
| 2098 | |
---|
| 2099 | g32 = (m[A32] - (g20 * g30) - (g21 * g31)) * h22; |
---|
| 2100 | g42 = (m[A42] - (g20 * g40) - (g21 * g41)) * h22; |
---|
| 2101 | g52 = (m[A52] - (g20 * g50) - (g21 * g51)) * h22; |
---|
| 2102 | |
---|
| 2103 | // Form G33 (actually, just h33) |
---|
| 2104 | |
---|
| 2105 | h33 = m[A33] - (g30 * g30) - (g31 * g31) - (g32 * g32); |
---|
| 2106 | if (h33 <= 0) { return; } |
---|
| 2107 | h33 = 1.0 / std::sqrt(h33); |
---|
| 2108 | |
---|
| 2109 | // Subtract inter-column column dot products from rest of column 3 and |
---|
| 2110 | // scale to get column 3 of G |
---|
| 2111 | |
---|
| 2112 | g43 = (m[A43] - (g30 * g40) - (g31 * g41) - (g32 * g42)) * h33; |
---|
| 2113 | g53 = (m[A53] - (g30 * g50) - (g31 * g51) - (g32 * g52)) * h33; |
---|
| 2114 | |
---|
| 2115 | // Form G44 (actually, just h44) |
---|
| 2116 | |
---|
| 2117 | h44 = m[A44] - (g40 * g40) - (g41 * g41) - (g42 * g42) - (g43 * g43); |
---|
| 2118 | if (h44 <= 0) { return; } |
---|
| 2119 | h44 = 1.0 / std::sqrt(h44); |
---|
| 2120 | |
---|
| 2121 | // Subtract inter-column column dot product from M54 and scale to get G54 |
---|
| 2122 | |
---|
| 2123 | g54 = (m[A54] - (g40 * g50) - (g41 * g51) - (g42 * g52) - (g43 * g53)) * h44; |
---|
| 2124 | |
---|
| 2125 | // Finally form h55 - if this is possible inversion succeeds |
---|
| 2126 | |
---|
| 2127 | h55 = m[A55] - (g50*g50) - (g51*g51) - (g52*g52) - (g53*g53) - (g54*g54); |
---|
| 2128 | if (h55 <= 0) { return; } |
---|
| 2129 | h55 = 1.0 / std::sqrt(h55); |
---|
| 2130 | |
---|
| 2131 | // Form H = 1/G -- diagonal members of H are already correct |
---|
| 2132 | //------------- |
---|
| 2133 | |
---|
| 2134 | // The order here is dictated by speed considerations |
---|
| 2135 | |
---|
| 2136 | h54 = -h44 * g54 * h55; |
---|
| 2137 | h43 = -h33 * g43 * h44; |
---|
| 2138 | h53 = -h33 * (g43 * h54 + g53 * h55); |
---|
| 2139 | h32 = -h22 * g32 * h33; |
---|
| 2140 | h42 = -h22 * (g32 * h43 + g42 * h44); |
---|
| 2141 | h52 = -h22 * (g32 * h53 + g42 * h54 + g52 * h55); |
---|
| 2142 | h21 = -h11 * g21 * h22; |
---|
| 2143 | h31 = -h11 * (g21 * h32 + g31 * h33); |
---|
| 2144 | h41 = -h11 * (g21 * h42 + g31 * h43 + g41 * h44); |
---|
| 2145 | h51 = -h11 * (g21 * h52 + g31 * h53 + g41 * h54 + g51 * h55); |
---|
| 2146 | h10 = -h00 * g10 * h11; |
---|
| 2147 | h20 = -h00 * (g10 * h21 + g20 * h22); |
---|
| 2148 | h30 = -h00 * (g10 * h31 + g20 * h32 + g30 * h33); |
---|
| 2149 | h40 = -h00 * (g10 * h41 + g20 * h42 + g30 * h43 + g40 * h44); |
---|
| 2150 | h50 = -h00 * (g10 * h51 + g20 * h52 + g30 * h53 + g40 * h54 + g50 * h55); |
---|
| 2151 | |
---|
| 2152 | // Change this to its inverse = H^T*H |
---|
| 2153 | //------------------------------------ |
---|
| 2154 | |
---|
| 2155 | m[A00] = h00 * h00 + h10 * h10 + h20 * h20 + h30 * h30 + h40 * h40 + h50*h50; |
---|
| 2156 | m[A01] = h10 * h11 + h20 * h21 + h30 * h31 + h40 * h41 + h50 * h51; |
---|
| 2157 | m[A11] = h11 * h11 + h21 * h21 + h31 * h31 + h41 * h41 + h51 * h51; |
---|
| 2158 | m[A02] = h20 * h22 + h30 * h32 + h40 * h42 + h50 * h52; |
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| 2159 | m[A12] = h21 * h22 + h31 * h32 + h41 * h42 + h51 * h52; |
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| 2160 | m[A22] = h22 * h22 + h32 * h32 + h42 * h42 + h52 * h52; |
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| 2161 | m[A03] = h30 * h33 + h40 * h43 + h50 * h53; |
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| 2162 | m[A13] = h31 * h33 + h41 * h43 + h51 * h53; |
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| 2163 | m[A23] = h32 * h33 + h42 * h43 + h52 * h53; |
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| 2164 | m[A33] = h33 * h33 + h43 * h43 + h53 * h53; |
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| 2165 | m[A04] = h40 * h44 + h50 * h54; |
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| 2166 | m[A14] = h41 * h44 + h51 * h54; |
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| 2167 | m[A24] = h42 * h44 + h52 * h54; |
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| 2168 | m[A34] = h43 * h44 + h53 * h54; |
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| 2169 | m[A44] = h44 * h44 + h54 * h54; |
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| 2170 | m[A05] = h50 * h55; |
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| 2171 | m[A15] = h51 * h55; |
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| 2172 | m[A25] = h52 * h55; |
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| 2173 | m[A35] = h53 * h55; |
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| 2174 | m[A45] = h54 * h55; |
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| 2175 | m[A55] = h55 * h55; |
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| 2176 | |
---|
| 2177 | ifail = 0; |
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| 2178 | return; |
---|
| 2179 | } |
---|
| 2180 | |
---|
| 2181 | void G4ErrorSymMatrix::invert4 (G4int & ifail) |
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| 2182 | { |
---|
| 2183 | ifail = 0; |
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| 2184 | |
---|
| 2185 | // Find all NECESSARY 2x2 dets: (14 of them) |
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| 2186 | |
---|
| 2187 | G4double Det2_12_01 = m[A10]*m[A21] - m[A11]*m[A20]; |
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| 2188 | G4double Det2_12_02 = m[A10]*m[A22] - m[A12]*m[A20]; |
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| 2189 | G4double Det2_12_12 = m[A11]*m[A22] - m[A12]*m[A21]; |
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| 2190 | G4double Det2_13_01 = m[A10]*m[A31] - m[A11]*m[A30]; |
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| 2191 | G4double Det2_13_02 = m[A10]*m[A32] - m[A12]*m[A30]; |
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| 2192 | G4double Det2_13_03 = m[A10]*m[A33] - m[A13]*m[A30]; |
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| 2193 | G4double Det2_13_12 = m[A11]*m[A32] - m[A12]*m[A31]; |
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| 2194 | G4double Det2_13_13 = m[A11]*m[A33] - m[A13]*m[A31]; |
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| 2195 | G4double Det2_23_01 = m[A20]*m[A31] - m[A21]*m[A30]; |
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| 2196 | G4double Det2_23_02 = m[A20]*m[A32] - m[A22]*m[A30]; |
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| 2197 | G4double Det2_23_03 = m[A20]*m[A33] - m[A23]*m[A30]; |
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| 2198 | G4double Det2_23_12 = m[A21]*m[A32] - m[A22]*m[A31]; |
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| 2199 | G4double Det2_23_13 = m[A21]*m[A33] - m[A23]*m[A31]; |
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| 2200 | G4double Det2_23_23 = m[A22]*m[A33] - m[A23]*m[A32]; |
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| 2201 | |
---|
| 2202 | // Find all NECESSARY 3x3 dets: (10 of them) |
---|
| 2203 | |
---|
| 2204 | G4double Det3_012_012 = m[A00]*Det2_12_12 - m[A01]*Det2_12_02 |
---|
| 2205 | + m[A02]*Det2_12_01; |
---|
| 2206 | G4double Det3_013_012 = m[A00]*Det2_13_12 - m[A01]*Det2_13_02 |
---|
| 2207 | + m[A02]*Det2_13_01; |
---|
| 2208 | G4double Det3_013_013 = m[A00]*Det2_13_13 - m[A01]*Det2_13_03 |
---|
| 2209 | + m[A03]*Det2_13_01; |
---|
| 2210 | G4double Det3_023_012 = m[A00]*Det2_23_12 - m[A01]*Det2_23_02 |
---|
| 2211 | + m[A02]*Det2_23_01; |
---|
| 2212 | G4double Det3_023_013 = m[A00]*Det2_23_13 - m[A01]*Det2_23_03 |
---|
| 2213 | + m[A03]*Det2_23_01; |
---|
| 2214 | G4double Det3_023_023 = m[A00]*Det2_23_23 - m[A02]*Det2_23_03 |
---|
| 2215 | + m[A03]*Det2_23_02; |
---|
| 2216 | G4double Det3_123_012 = m[A10]*Det2_23_12 - m[A11]*Det2_23_02 |
---|
| 2217 | + m[A12]*Det2_23_01; |
---|
| 2218 | G4double Det3_123_013 = m[A10]*Det2_23_13 - m[A11]*Det2_23_03 |
---|
| 2219 | + m[A13]*Det2_23_01; |
---|
| 2220 | G4double Det3_123_023 = m[A10]*Det2_23_23 - m[A12]*Det2_23_03 |
---|
| 2221 | + m[A13]*Det2_23_02; |
---|
| 2222 | G4double Det3_123_123 = m[A11]*Det2_23_23 - m[A12]*Det2_23_13 |
---|
| 2223 | + m[A13]*Det2_23_12; |
---|
| 2224 | |
---|
| 2225 | // Find the 4x4 det: |
---|
| 2226 | |
---|
| 2227 | G4double det = m[A00]*Det3_123_123 |
---|
| 2228 | - m[A01]*Det3_123_023 |
---|
| 2229 | + m[A02]*Det3_123_013 |
---|
| 2230 | - m[A03]*Det3_123_012; |
---|
| 2231 | |
---|
| 2232 | if ( det == 0 ) |
---|
| 2233 | { |
---|
| 2234 | ifail = 1; |
---|
| 2235 | return; |
---|
| 2236 | } |
---|
| 2237 | |
---|
| 2238 | G4double oneOverDet = 1.0/det; |
---|
| 2239 | G4double mn1OverDet = - oneOverDet; |
---|
| 2240 | |
---|
| 2241 | m[A00] = Det3_123_123 * oneOverDet; |
---|
| 2242 | m[A01] = Det3_123_023 * mn1OverDet; |
---|
| 2243 | m[A02] = Det3_123_013 * oneOverDet; |
---|
| 2244 | m[A03] = Det3_123_012 * mn1OverDet; |
---|
| 2245 | |
---|
| 2246 | |
---|
| 2247 | m[A11] = Det3_023_023 * oneOverDet; |
---|
| 2248 | m[A12] = Det3_023_013 * mn1OverDet; |
---|
| 2249 | m[A13] = Det3_023_012 * oneOverDet; |
---|
| 2250 | |
---|
| 2251 | m[A22] = Det3_013_013 * oneOverDet; |
---|
| 2252 | m[A23] = Det3_013_012 * mn1OverDet; |
---|
| 2253 | |
---|
| 2254 | m[A33] = Det3_012_012 * oneOverDet; |
---|
| 2255 | |
---|
| 2256 | return; |
---|
| 2257 | } |
---|
| 2258 | |
---|
| 2259 | void G4ErrorSymMatrix::invertHaywood4 (G4int & ifail) |
---|
| 2260 | { |
---|
| 2261 | invert4(ifail); // For the 4x4 case, the method we use for invert is already |
---|
| 2262 | // the Haywood method. |
---|
| 2263 | } |
---|
| 2264 | |
---|