1 | /* matrix.c |
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2 | * Matrix building and solving routines |
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3 | * Copyright (C) 1993-2003,2010 Olly Betts |
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4 | * |
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5 | * This program is free software; you can redistribute it and/or modify |
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6 | * it under the terms of the GNU General Public License as published by |
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7 | * the Free Software Foundation; either version 2 of the License, or |
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8 | * (at your option) any later version. |
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9 | * |
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10 | * This program is distributed in the hope that it will be useful, |
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11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 | * GNU General Public License for more details. |
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14 | * |
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15 | * You should have received a copy of the GNU General Public License |
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16 | * along with this program; if not, write to the Free Software |
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17 | * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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18 | */ |
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19 | |
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20 | /*#define SOR 1*/ |
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21 | |
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22 | #if 0 |
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23 | # define DEBUG_INVALID 1 |
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24 | #endif |
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25 | |
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26 | #ifdef HAVE_CONFIG_H |
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27 | # include <config.h> |
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28 | #endif |
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29 | |
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30 | #include "debug.h" |
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31 | #include "cavern.h" |
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32 | #include "filename.h" |
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33 | #include "message.h" |
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34 | #include "netbits.h" |
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35 | #include "matrix.h" |
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36 | #include "out.h" |
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37 | |
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38 | #undef PRINT_MATRICES |
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39 | #define PRINT_MATRICES 0 |
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40 | |
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41 | #undef DEBUG_MATRIX_BUILD |
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42 | #define DEBUG_MATRIX_BUILD 0 |
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43 | |
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44 | #undef DEBUG_MATRIX |
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45 | #define DEBUG_MATRIX 0 |
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46 | |
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47 | #if PRINT_MATRICES |
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48 | static void print_matrix(real *M, real *B, long n); |
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49 | #endif |
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50 | |
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51 | static void choleski(real *M, real *B, long n); |
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52 | |
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53 | #ifdef SOR |
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54 | static void sor(real *M, real *B, long n); |
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55 | #endif |
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56 | |
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57 | /* for M(row, col) col must be <= row, so Y <= X */ |
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58 | # define M(X, Y) ((real *)M)[((((OSSIZE_T)(X)) * ((X) + 1)) >> 1) + (Y)] |
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59 | /* +(Y>X?0*printf("row<col (line %d)\n",__LINE__):0) */ |
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60 | /*#define M_(X, Y) ((real *)M)[((((OSSIZE_T)(Y)) * ((Y) + 1)) >> 1) + (X)]*/ |
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61 | |
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62 | static int find_stn_in_tab(node *stn); |
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63 | static int add_stn_to_tab(node *stn); |
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64 | static void build_matrix(node *list); |
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65 | |
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66 | static long n_stn_tab; |
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67 | |
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68 | static pos **stn_tab; |
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69 | |
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70 | extern void |
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71 | solve_matrix(node *list) |
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72 | { |
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73 | node *stn; |
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74 | long n = 0; |
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75 | FOR_EACH_STN(stn, list) { |
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76 | if (!fixed(stn)) n++; |
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77 | } |
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78 | if (n == 0) return; |
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79 | |
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80 | /* we just need n to be a reasonable estimate >= the number |
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81 | * of stations left after reduction. If memory is |
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82 | * plentiful, we can be crass. |
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83 | */ |
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84 | stn_tab = osmalloc((OSSIZE_T)(n * ossizeof(pos*))); |
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85 | n_stn_tab = 0; |
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86 | |
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87 | FOR_EACH_STN(stn, list) { |
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88 | if (!fixed(stn)) add_stn_to_tab(stn); |
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89 | } |
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90 | |
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91 | if (n_stn_tab < n) { |
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92 | /* release unused entries in stn_tab */ |
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93 | stn_tab = osrealloc(stn_tab, n_stn_tab * ossizeof(pos*)); |
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94 | } |
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95 | |
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96 | build_matrix(list); |
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97 | #if DEBUG_MATRIX |
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98 | FOR_EACH_STN(stn, list) { |
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99 | printf("(%8.2f, %8.2f, %8.2f ) ", POS(stn, 0), POS(stn, 1), POS(stn, 2)); |
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100 | print_prefix(stn->name); |
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101 | putnl(); |
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102 | } |
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103 | #endif |
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104 | |
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105 | osfree(stn_tab); |
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106 | } |
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107 | |
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108 | #ifdef NO_COVARIANCES |
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109 | # define FACTOR 1 |
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110 | #else |
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111 | # define FACTOR 3 |
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112 | #endif |
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113 | |
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114 | static void |
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115 | build_matrix(node *list) |
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116 | { |
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117 | real *M; |
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118 | real *B; |
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119 | int dim; |
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120 | |
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121 | if (n_stn_tab == 0) { |
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122 | if (!fQuiet) |
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123 | puts(msg(/*Network solved by reduction - no simultaneous equations to solve.*/74)); |
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124 | return; |
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125 | } |
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126 | /* (OSSIZE_T) cast may be needed if n_stn_tab>=181 */ |
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127 | M = osmalloc((OSSIZE_T)((((OSSIZE_T)n_stn_tab * FACTOR * (n_stn_tab * FACTOR + 1)) >> 1)) * ossizeof(real)); |
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128 | B = osmalloc((OSSIZE_T)(n_stn_tab * FACTOR * ossizeof(real))); |
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129 | |
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130 | if (!fQuiet) { |
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131 | putnl(); |
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132 | if (n_stn_tab == 1) |
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133 | puts(msg(/*Solving one equation*/78)); |
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134 | else { |
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135 | printf(msg(/*Solving %d simultaneous equations*/75), n_stn_tab); |
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136 | putnl(); |
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137 | } |
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138 | } |
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139 | |
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140 | #ifdef NO_COVARIANCES |
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141 | dim = 2; |
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142 | #else |
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143 | dim = 0; /* fudge next loop for now */ |
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144 | #endif |
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145 | for ( ; dim >= 0; dim--) { |
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146 | char buf[256]; |
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147 | node *stn; |
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148 | int row; |
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149 | |
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150 | sprintf(buf, msg(/*Solving to find %c coordinates*/76), (char)('x'+dim)); |
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151 | out_current_action(buf); |
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152 | |
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153 | /* Initialise M and B to zero - zeroing "linearly" will minimise |
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154 | * paging when the matrix is large */ |
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155 | { |
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156 | int end = n_stn_tab * FACTOR; |
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157 | for (row = 0; row < end; row++) B[row] = (real)0.0; |
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158 | end = ((OSSIZE_T)n_stn_tab * FACTOR * (n_stn_tab * FACTOR + 1)) >> 1; |
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159 | for (row = 0; row < end; row++) M[row] = (real)0.0; |
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160 | } |
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161 | |
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162 | /* Construct matrix - Go thru' stn list & add all forward legs between |
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163 | * two unfixed stations to M (so each leg goes on exactly once). |
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164 | * |
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165 | * All legs between two fixed stations can be ignored here. |
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166 | * |
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167 | * All legs between a fixed and an unfixed station are then considered |
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168 | * from the unfixed end (if we consider them from the fixed end we'd |
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169 | * need to somehow detect when we're at a fixed point cut line and work |
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170 | * out which side we're dealing with at this time. */ |
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171 | FOR_EACH_STN(stn, list) { |
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172 | #ifdef NO_COVARIANCES |
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173 | real e; |
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174 | #else |
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175 | svar e; |
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176 | delta a; |
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177 | #endif |
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178 | int f, t; |
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179 | int dirn; |
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180 | #if DEBUG_MATRIX_BUILD |
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181 | print_prefix(stn->name); |
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182 | printf(" used: %d colour %ld\n", |
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183 | (!!stn->leg[2]) << 2 | (!!stn -> leg[1]) << 1 | (!!stn->leg[0]), |
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184 | stn->colour); |
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185 | |
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186 | for (dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) { |
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187 | #ifdef NO_COVARIANCES |
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188 | printf("Leg %d, vx=%f, reverse=%d, to ", dirn, |
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189 | stn->leg[dirn]->v[0], stn->leg[dirn]->l.reverse); |
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190 | #else |
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191 | printf("Leg %d, vx=%f, reverse=%d, to ", dirn, |
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192 | stn->leg[dirn]->v[0][0], stn->leg[dirn]->l.reverse); |
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193 | #endif |
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194 | print_prefix(stn->leg[dirn]->l.to->name); |
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195 | putnl(); |
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196 | } |
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197 | putnl(); |
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198 | #endif /* DEBUG_MATRIX_BUILD */ |
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199 | |
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200 | if (!fixed(stn)) { |
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201 | f = find_stn_in_tab(stn); |
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202 | for (dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) { |
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203 | linkfor *leg = stn->leg[dirn]; |
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204 | node *to = leg->l.to; |
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205 | if (fixed(to)) { |
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206 | bool fRev = !data_here(leg); |
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207 | if (fRev) leg = reverse_leg(leg); |
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208 | /* Ignore equated nodes */ |
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209 | #ifdef NO_COVARIANCES |
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210 | e = leg->v[dim]; |
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211 | if (e != (real)0.0) { |
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212 | e = ((real)1.0) / e; |
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213 | M(f,f) += e; |
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214 | B[f] += e * POS(to, dim); |
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215 | if (fRev) { |
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216 | B[f] += leg->d[dim]; |
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217 | } else { |
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218 | B[f] -= leg->d[dim]; |
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219 | } |
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220 | } |
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221 | #else |
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222 | if (invert_svar(&e, &leg->v)) { |
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223 | delta b; |
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224 | int i; |
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225 | if (fRev) { |
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226 | adddd(&a, &POSD(to), &leg->d); |
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227 | } else { |
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228 | subdd(&a, &POSD(to), &leg->d); |
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229 | } |
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230 | mulsd(&b, &e, &a); |
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231 | for (i = 0; i < 3; i++) { |
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232 | M(f * FACTOR + i, f * FACTOR + i) += e[i]; |
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233 | B[f * FACTOR + i] += b[i]; |
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234 | } |
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235 | M(f * FACTOR + 1, f * FACTOR) += e[3]; |
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236 | M(f * FACTOR + 2, f * FACTOR) += e[4]; |
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237 | M(f * FACTOR + 2, f * FACTOR + 1) += e[5]; |
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238 | } |
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239 | #endif |
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240 | } else if (data_here(leg)) { |
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241 | /* forward leg, unfixed -> unfixed */ |
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242 | t = find_stn_in_tab(to); |
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243 | #if DEBUG_MATRIX |
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244 | printf("Leg %d to %d, var %f, delta %f\n", f, t, e, |
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245 | leg->d[dim]); |
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246 | #endif |
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247 | /* Ignore equated nodes & lollipops */ |
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248 | #ifdef NO_COVARIANCES |
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249 | e = leg->v[dim]; |
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250 | if (t != f && e != (real)0.0) { |
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251 | real a; |
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252 | e = ((real)1.0) / e; |
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253 | M(f,f) += e; |
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254 | M(t,t) += e; |
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255 | if (f < t) M(t,f) -= e; else M(f,t) -= e; |
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256 | a = e * leg->d[dim]; |
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257 | B[f] -= a; |
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258 | B[t] += a; |
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259 | } |
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260 | #else |
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261 | if (t != f && invert_svar(&e, &leg->v)) { |
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262 | int i; |
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263 | mulsd(&a, &e, &leg->d); |
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264 | for (i = 0; i < 3; i++) { |
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265 | M(f * FACTOR + i, f * FACTOR + i) += e[i]; |
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266 | M(t * FACTOR + i, t * FACTOR + i) += e[i]; |
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267 | if (f < t) |
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268 | M(t * FACTOR + i, f * FACTOR + i) -= e[i]; |
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269 | else |
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270 | M(f * FACTOR + i, t * FACTOR + i) -= e[i]; |
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271 | B[f * FACTOR + i] -= a[i]; |
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272 | B[t * FACTOR + i] += a[i]; |
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273 | } |
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274 | M(f * FACTOR + 1, f * FACTOR) += e[3]; |
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275 | M(t * FACTOR + 1, t * FACTOR) += e[3]; |
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276 | M(f * FACTOR + 2, f * FACTOR) += e[4]; |
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277 | M(t * FACTOR + 2, t * FACTOR) += e[4]; |
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278 | M(f * FACTOR + 2, f * FACTOR + 1) += e[5]; |
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279 | M(t * FACTOR + 2, t * FACTOR + 1) += e[5]; |
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280 | if (f < t) { |
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281 | M(t * FACTOR + 1, f * FACTOR) -= e[3]; |
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282 | M(t * FACTOR, f * FACTOR + 1) -= e[3]; |
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283 | M(t * FACTOR + 2, f * FACTOR) -= e[4]; |
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284 | M(t * FACTOR, f * FACTOR + 2) -= e[4]; |
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285 | M(t * FACTOR + 2, f * FACTOR + 1) -= e[5]; |
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286 | M(t * FACTOR + 1, f * FACTOR + 2) -= e[5]; |
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287 | } else { |
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288 | M(f * FACTOR + 1, t * FACTOR) -= e[3]; |
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289 | M(f * FACTOR, t * FACTOR + 1) -= e[3]; |
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290 | M(f * FACTOR + 2, t * FACTOR) -= e[4]; |
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291 | M(f * FACTOR, t * FACTOR + 2) -= e[4]; |
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292 | M(f * FACTOR + 2, t * FACTOR + 1) -= e[5]; |
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293 | M(f * FACTOR + 1, t * FACTOR + 2) -= e[5]; |
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294 | } |
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295 | } |
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296 | #endif |
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297 | } |
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298 | } |
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299 | } |
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300 | } |
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301 | |
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302 | #if PRINT_MATRICES |
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303 | print_matrix(M, B, n_stn_tab * FACTOR); /* 'ave a look! */ |
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304 | #endif |
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305 | |
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306 | #ifdef SOR |
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307 | /* defined in network.c, may be altered by -z<letters> on command line */ |
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308 | if (optimize & BITA('i')) |
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309 | sor(M, B, n_stn_tab * FACTOR); |
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310 | else |
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311 | #endif |
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312 | choleski(M, B, n_stn_tab * FACTOR); |
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313 | |
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314 | { |
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315 | int m; |
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316 | for (m = (int)(n_stn_tab - 1); m >= 0; m--) { |
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317 | #ifdef NO_COVARIANCES |
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318 | stn_tab[m]->p[dim] = B[m]; |
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319 | if (dim == 0) { |
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320 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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321 | "setting station coordinates didn't mark pos as fixed"); |
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322 | } |
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323 | #else |
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324 | int i; |
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325 | for (i = 0; i < 3; i++) { |
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326 | stn_tab[m]->p[i] = B[m * FACTOR + i]; |
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327 | } |
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328 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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329 | "setting station coordinates didn't mark pos as fixed"); |
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330 | #endif |
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331 | } |
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332 | #if EXPLICIT_FIXED_FLAG |
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333 | for (m = n_stn_tab - 1; m >= 0; m--) fixpos(stn_tab[m]); |
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334 | #endif |
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335 | } |
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336 | } |
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337 | osfree(B); |
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338 | osfree(M); |
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339 | } |
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340 | |
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341 | static int |
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342 | find_stn_in_tab(node *stn) |
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343 | { |
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344 | int i = 0; |
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345 | pos *p = stn->name->pos; |
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346 | while (stn_tab[i] != p) |
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347 | if (++i == n_stn_tab) { |
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348 | #if DEBUG_INVALID |
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349 | fputs("Station ", stderr); |
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350 | fprint_prefix(stderr, stn->name); |
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351 | fputs(" not in table\n\n", stderr); |
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352 | #endif |
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353 | #if 0 |
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354 | print_prefix(stn->name); |
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355 | printf(" used: %d colour %d\n", |
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356 | (!!stn->leg[2])<<2 | (!!stn->leg[1])<<1 | (!!stn->leg[0]), |
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357 | stn->colour); |
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358 | #endif |
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359 | fatalerror(/*Bug in program detected! Please report this to the authors*/11); |
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360 | } |
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361 | return i; |
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362 | } |
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363 | |
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364 | static int |
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365 | add_stn_to_tab(node *stn) |
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366 | { |
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367 | int i; |
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368 | pos *p = stn->name->pos; |
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369 | for (i = 0; i < n_stn_tab; i++) { |
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370 | if (stn_tab[i] == p) return i; |
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371 | } |
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372 | stn_tab[n_stn_tab++] = p; |
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373 | return i; |
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374 | } |
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375 | |
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376 | /* Solve MX=B for X by Choleski factorisation - modified Choleski actually |
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377 | * since we factor into LDL' while Choleski is just LL' |
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378 | */ |
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379 | /* Note M must be symmetric positive definite */ |
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380 | /* routine is entitled to scribble on M and B if it wishes */ |
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381 | static void |
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382 | choleski(real *M, real *B, long n) |
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383 | { |
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384 | int i, j, k; |
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385 | #ifndef NO_PERCENTAGE |
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386 | unsigned long flopsTot, flops = 0, temp = 0; |
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387 | #define do_percent(N) BLK(flops += (N); printf("%d%%\r", (int)((100.0 * flops) / flopsTot));) |
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388 | |
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389 | /* calc as double so we don't overflow a unsigned long with intermediate results */ |
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390 | flopsTot = (unsigned long)(n * (2.0 * n * n + 9.0 * n - 5.0) / 6.0); |
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391 | /* 3*n*(n-1)/2 + n*(n-1)*(n-2)/3 + n*(n-1)/2 + n + n*(n-1)/2; */ |
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392 | /* n*(9*n-5 + 2*n*n )/6 ; */ |
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393 | #endif |
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394 | |
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395 | for (j = 1; j < n; j++) { |
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396 | real V; |
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397 | for (i = 0; i < j; i++) { |
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398 | V = (real)0.0; |
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399 | for (k = 0; k < i; k++) V += M(i,k) * M(j,k) * M(k,k); |
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400 | M(j,i) = (M(j,i) - V) / M(i,i); |
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401 | } |
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402 | V = (real)0.0; |
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403 | for (k = 0; k < j; k++) V += M(j,k) * M(j,k) * M(k,k); |
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404 | M(j,j) -= V; /* may be best to add M() last for numerical reasons too */ |
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405 | |
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406 | #ifndef NO_PERCENTAGE |
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407 | if (fPercent) { |
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408 | temp += ((unsigned long)j + j) + 1ul; /* avoid multiplies */ |
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409 | do_percent(temp); |
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410 | } |
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411 | #endif |
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412 | } |
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413 | |
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414 | /* Multiply x by L inverse */ |
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415 | for (i = 0; i < n - 1; i++) { |
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416 | for (j = i + 1; j < n; j++) { |
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417 | B[j] -= M(j,i) * B[i]; |
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418 | } |
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419 | } |
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420 | |
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421 | #ifndef NO_PERCENTAGE |
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422 | if (fPercent) { |
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423 | temp = (unsigned long)n * (n - 1ul) / 2ul; /* needed again lower down */ |
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424 | do_percent(temp); |
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425 | } |
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426 | #endif |
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427 | |
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428 | /* Multiply x by D inverse */ |
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429 | for (i = 0; i < n; i++) { |
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430 | B[i] /= M(i,i); |
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431 | } |
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432 | |
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433 | #ifndef NO_PERCENTAGE |
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434 | if (fPercent) do_percent((unsigned long)n); |
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435 | #endif |
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436 | |
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437 | /* Multiply x by (L transpose) inverse */ |
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438 | for (i = (int)(n - 1); i > 0; i--) { |
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439 | for (j = i - 1; j >= 0; j--) { |
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440 | B[j] -= M(i,j) * B[i]; |
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441 | } |
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442 | } |
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443 | |
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444 | #ifndef NO_PERCENTAGE |
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445 | if (fPercent) do_percent(temp); |
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446 | # undef do_percent |
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447 | #endif |
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448 | |
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449 | /* printf("\n%ld/%ld\n\n",flops,flopsTot); */ |
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450 | } |
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451 | |
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452 | #ifdef SOR |
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453 | /* factor to use for SOR (must have 1 <= SOR_factor < 2) */ |
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454 | #define SOR_factor 1.93 /* 1.95 */ |
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455 | |
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456 | /* Solve MX=B for X by SOR of Gauss-Siedel */ |
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457 | /* routine is entitled to scribble on M and B if it wishes */ |
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458 | static void |
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459 | sor(real *M, real *B, long n) |
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460 | { |
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461 | real t, x, delta, threshold, t2; |
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462 | int row, col; |
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463 | real *X; |
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464 | long it = 0; |
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465 | |
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466 | X = osmalloc(n * ossizeof(real)); |
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467 | |
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468 | threshold = 0.00001; |
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469 | |
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470 | printf("reciprocating diagonal\n"); /* TRANSLATE */ |
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471 | |
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472 | /* munge diagonal so we can multiply rather than divide */ |
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473 | for (row = n - 1; row >= 0; row--) { |
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474 | M(row,row) = 1 / M(row,row); |
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475 | X[row] = 0; |
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476 | } |
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477 | |
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478 | printf("starting iteration\n"); /* TRANSLATE */ |
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479 | |
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480 | do { |
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481 | /*printf("*");*/ |
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482 | it++; |
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483 | t = 0.0; |
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484 | for (row = 0; row < n; row++) { |
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485 | x = B[row]; |
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486 | for (col = 0; col < row; col++) x -= M(row,col) * X[col]; |
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487 | for (col++; col < n; col++) x -= M(col,row) * X[col]; |
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488 | x *= M(row,row); |
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489 | delta = (x - X[row]) * SOR_factor; |
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490 | X[row] += delta; |
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491 | t2 = fabs(delta); |
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492 | if (t2 > t) t = t2; |
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493 | } |
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494 | printf("% 6d: %8.6f\n", it, t); |
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495 | } while (t >= threshold && it < 100000); |
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496 | |
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497 | if (t >= threshold) { |
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498 | fprintf(stderr, "*not* converged after %ld iterations\n", it); |
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499 | BUG("iteration stinks"); |
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500 | } |
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501 | |
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502 | printf("%ld iterations\n", it); /* TRANSLATE */ |
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503 | |
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504 | #if 0 |
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505 | putnl(); |
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506 | for (row = n - 1; row >= 0; row--) { |
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507 | t = 0.0; |
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508 | for (col = 0; col < row; col++) t += M(row, col) * X[col]; |
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509 | t += X[row] / M(row, row); |
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510 | for (col = row + 1; col < n; col++) |
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511 | t += M(col, row) * X[col]; |
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512 | printf("[ %f %f ]\n", t, B[row]); |
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513 | } |
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514 | #endif |
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515 | |
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516 | for (row = n - 1; row >= 0; row--) B[row] = X[row]; |
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517 | |
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518 | osfree(X); |
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519 | printf("\ndone\n"); /* TRANSLATE */ |
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520 | } |
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521 | #endif |
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522 | |
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523 | #if PRINT_MATRICES |
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524 | static void |
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525 | print_matrix(real *M, real *B, long n) |
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526 | { |
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527 | long row, col; |
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528 | printf("Matrix, M and vector, B:\n"); |
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529 | for (row = 0; row < n; row++) { |
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530 | for (col = 0; col <= row; col++) printf("%6.2f\t", M(row, col)); |
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531 | for (; col <= n; col++) printf(" \t"); |
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532 | printf("\t%6.2f\n", B[row]); |
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533 | } |
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534 | putnl(); |
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535 | return; |
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536 | } |
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537 | #endif |
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