[421b7d2] | 1 | /* matrix.c |
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[d1b1380] | 2 | * Matrix building and solving routines |
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[9965b2b] | 3 | * Copyright (C) 1993-2003,2010 Olly Betts |
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[846746e] | 4 | * |
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[89231c4] | 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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[846746e] | 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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[89231c4] | 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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[846746e] | 14 | * |
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[89231c4] | 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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[ecbc6c18] | 17 | * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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[d1b1380] | 18 | */ |
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| 19 | |
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[2164fa4] | 20 | /*#define SOR 1*/ |
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[702f518] | 21 | |
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[032ed06] | 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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[a420b49] | 26 | #ifdef HAVE_CONFIG_H |
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| 27 | # include <config.h> |
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| 28 | #endif |
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[d1b1380] | 29 | |
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| 30 | #include "debug.h" |
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[a420b49] | 31 | #include "cavern.h" |
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[c082b69] | 32 | #include "filename.h" |
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| 33 | #include "message.h" |
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[d1b1380] | 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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[9965b2b] | 48 | static void print_matrix(real *M, real *B, long n); |
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[d1b1380] | 49 | #endif |
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| 50 | |
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[9965b2b] | 51 | static void choleski(real *M, real *B, long n); |
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[3fde384f] | 52 | |
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[d1b1380] | 53 | #ifdef SOR |
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[9965b2b] | 54 | static void sor(real *M, real *B, long n); |
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[d1b1380] | 55 | #endif |
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| 56 | |
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[a420b49] | 57 | /* for M(row, col) col must be <= row, so Y <= X */ |
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[9965b2b] | 58 | # define M(X, Y) ((real *)M)[((((OSSIZE_T)(X)) * ((X) + 1)) >> 1) + (Y)] |
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[421b7d2] | 59 | /* +(Y>X?0*printf("row<col (line %d)\n",__LINE__):0) */ |
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[9965b2b] | 60 | /*#define M_(X, Y) ((real *)M)[((((OSSIZE_T)(Y)) * ((Y) + 1)) >> 1) + (X)]*/ |
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[d1b1380] | 61 | |
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[a420b49] | 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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[eb18f4d] | 64 | static void build_matrix(node *list); |
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[d1b1380] | 65 | |
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| 66 | static long n_stn_tab; |
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| 67 | |
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[c19f129] | 68 | static pos **stn_tab; |
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[d1b1380] | 69 | |
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[032ed06] | 70 | extern void |
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[d9b5db53] | 71 | solve_matrix(node *list) |
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[032ed06] | 72 | { |
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| 73 | node *stn; |
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[702f518] | 74 | long n = 0; |
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[d9b5db53] | 75 | FOR_EACH_STN(stn, list) { |
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[032ed06] | 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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[66de220] | 84 | stn_tab = osmalloc((OSSIZE_T)(n * ossizeof(pos*))); |
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[4f613e0] | 85 | n_stn_tab = 0; |
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[cb3d1e2] | 86 | |
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[d9b5db53] | 87 | FOR_EACH_STN(stn, list) { |
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[032ed06] | 88 | if (!fixed(stn)) add_stn_to_tab(stn); |
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| 89 | } |
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| 90 | |
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[66de220] | 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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[cb3d1e2] | 95 | |
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[eb18f4d] | 96 | build_matrix(list); |
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[2c9c3ff] | 97 | #if DEBUG_MATRIX |
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[2164fa4] | 98 | FOR_EACH_STN(stn, list) { |
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[2aa930f] | 99 | printf("(%8.2f, %8.2f, %8.2f ) ", POS(stn, 0), POS(stn, 1), POS(stn, 2)); |
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[2164fa4] | 100 | print_prefix(stn->name); |
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[2aa930f] | 101 | putnl(); |
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[2164fa4] | 102 | } |
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[2c9c3ff] | 103 | #endif |
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[4f613e0] | 104 | |
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| 105 | osfree(stn_tab); |
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[032ed06] | 106 | } |
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[d1b1380] | 107 | |
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[3fde384f] | 108 | #ifdef NO_COVARIANCES |
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[702f518] | 109 | # define FACTOR 1 |
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[3fde384f] | 110 | #else |
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[702f518] | 111 | # define FACTOR 3 |
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[3fde384f] | 112 | #endif |
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| 113 | |
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[a420b49] | 114 | static void |
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[eb18f4d] | 115 | build_matrix(node *list) |
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[a420b49] | 116 | { |
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[9965b2b] | 117 | real *M; |
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[dbd68203] | 118 | real *B; |
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[702f518] | 119 | int dim; |
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[dbd68203] | 120 | |
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[eb18f4d] | 121 | if (n_stn_tab == 0) { |
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[5b68ae1] | 122 | if (!fQuiet) |
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| 123 | puts(msg(/*Network solved by reduction - no simultaneous equations to solve.*/74)); |
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[dbd68203] | 124 | return; |
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| 125 | } |
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[eb18f4d] | 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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[dbd68203] | 129 | |
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[647407d] | 130 | if (!fQuiet) { |
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[5b68ae1] | 131 | putnl(); |
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[eb18f4d] | 132 | if (n_stn_tab == 1) |
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[5b68ae1] | 133 | puts(msg(/*Solving one equation*/78)); |
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[647407d] | 134 | else { |
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[5b68ae1] | 135 | printf(msg(/*Solving %d simultaneous equations*/75), n_stn_tab); |
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| 136 | putnl(); |
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[647407d] | 137 | } |
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[dbd68203] | 138 | } |
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| 139 | |
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[3fde384f] | 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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[a420b49] | 145 | for ( ; dim >= 0; dim--) { |
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| 146 | char buf[256]; |
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[2164fa4] | 147 | node *stn; |
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| 148 | int row; |
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| 149 | |
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[a420b49] | 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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[66de220] | 152 | |
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[907fe10] | 153 | /* Initialise M and B to zero - zeroing "linearly" will minimise |
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[421b7d2] | 154 | * paging when the matrix is large */ |
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[66de220] | 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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[dbd68203] | 161 | |
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[907fe10] | 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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[421b7d2] | 164 | * |
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[907fe10] | 165 | * All legs between two fixed stations can be ignored here. |
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[421b7d2] | 166 | * |
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[907fe10] | 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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[d9b5db53] | 171 | FOR_EACH_STN(stn, list) { |
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[2164fa4] | 172 | #ifdef NO_COVARIANCES |
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| 173 | real e; |
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| 174 | #else |
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[dac18d8] | 175 | svar e; |
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[eb18f4d] | 176 | delta a; |
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[2164fa4] | 177 | #endif |
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[b5d3988] | 178 | int f, t; |
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[dbd68203] | 179 | int dirn; |
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[b5d3988] | 180 | #if DEBUG_MATRIX_BUILD |
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[dbd68203] | 181 | print_prefix(stn->name); |
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[b5d3988] | 182 | printf(" used: %d colour %ld\n", |
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[a420b49] | 183 | (!!stn->leg[2]) << 2 | (!!stn -> leg[1]) << 1 | (!!stn->leg[0]), |
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[b5d3988] | 184 | stn->colour); |
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[3fde384f] | 185 | |
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[907fe10] | 186 | for (dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) { |
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[b5d3988] | 187 | #ifdef NO_COVARIANCES |
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[907fe10] | 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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[b5d3988] | 190 | #else |
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[907fe10] | 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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[b5d3988] | 193 | #endif |
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[907fe10] | 194 | print_prefix(stn->leg[dirn]->l.to->name); |
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| 195 | putnl(); |
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| 196 | } |
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[dbd68203] | 197 | putnl(); |
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[d1b1380] | 198 | #endif /* DEBUG_MATRIX_BUILD */ |
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[b5d3988] | 199 | |
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[907fe10] | 200 | if (!fixed(stn)) { |
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[564f471] | 201 | f = find_stn_in_tab(stn); |
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[907fe10] | 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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[3fde384f] | 209 | #ifdef NO_COVARIANCES |
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[907fe10] | 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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[f52dcc7] | 214 | B[f] += e * POS(to, dim); |
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[907fe10] | 215 | if (fRev) { |
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[f52dcc7] | 216 | B[f] += leg->d[dim]; |
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[907fe10] | 217 | } else { |
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[f52dcc7] | 218 | B[f] -= leg->d[dim]; |
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[564f471] | 219 | } |
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[907fe10] | 220 | } |
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[3fde384f] | 221 | #else |
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[907fe10] | 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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[564f471] | 234 | } |
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[907fe10] | 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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[3fde384f] | 239 | #endif |
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[907fe10] | 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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[d1b1380] | 243 | #if DEBUG_MATRIX |
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[907fe10] | 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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[d1b1380] | 246 | #endif |
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[907fe10] | 247 | /* Ignore equated nodes & lollipops */ |
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[3fde384f] | 248 | #ifdef NO_COVARIANCES |
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[907fe10] | 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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[3fde384f] | 260 | #else |
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[907fe10] | 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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[dbd68203] | 294 | } |
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| 295 | } |
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[907fe10] | 296 | #endif |
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[564f471] | 297 | } |
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[907fe10] | 298 | } |
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[dbd68203] | 299 | } |
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[d1b1380] | 300 | } |
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| 301 | |
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| 302 | #if PRINT_MATRICES |
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[eb18f4d] | 303 | print_matrix(M, B, n_stn_tab * FACTOR); /* 'ave a look! */ |
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[d1b1380] | 304 | #endif |
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| 305 | |
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| 306 | #ifdef SOR |
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[032ed06] | 307 | /* defined in network.c, may be altered by -z<letters> on command line */ |
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[a420b49] | 308 | if (optimize & BITA('i')) |
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[eb18f4d] | 309 | sor(M, B, n_stn_tab * FACTOR); |
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[dbd68203] | 310 | else |
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[d1b1380] | 311 | #endif |
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[eb18f4d] | 312 | choleski(M, B, n_stn_tab * FACTOR); |
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[d1b1380] | 313 | |
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[dbd68203] | 314 | { |
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[a420b49] | 315 | int m; |
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[eb18f4d] | 316 | for (m = (int)(n_stn_tab - 1); m >= 0; m--) { |
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[3fde384f] | 317 | #ifdef NO_COVARIANCES |
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[c19f129] | 318 | stn_tab[m]->p[dim] = B[m]; |
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[032ed06] | 319 | if (dim == 0) { |
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[4c07c51] | 320 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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[032ed06] | 321 | "setting station coordinates didn't mark pos as fixed"); |
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| 322 | } |
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[3fde384f] | 323 | #else |
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[702f518] | 324 | int i; |
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| 325 | for (i = 0; i < 3; i++) { |
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[c19f129] | 326 | stn_tab[m]->p[i] = B[m * FACTOR + i]; |
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[702f518] | 327 | } |
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[4c07c51] | 328 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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[032ed06] | 329 | "setting station coordinates didn't mark pos as fixed"); |
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[3fde384f] | 330 | #endif |
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[a420b49] | 331 | } |
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[d1b1380] | 332 | #if EXPLICIT_FIXED_FLAG |
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[eb18f4d] | 333 | for (m = n_stn_tab - 1; m >= 0; m--) fixpos(stn_tab[m]); |
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[d1b1380] | 334 | #endif |
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[dbd68203] | 335 | } |
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| 336 | } |
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| 337 | osfree(B); |
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| 338 | osfree(M); |
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[d1b1380] | 339 | } |
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| 340 | |
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[a420b49] | 341 | static int |
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| 342 | find_stn_in_tab(node *stn) |
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| 343 | { |
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[dbd68203] | 344 | int i = 0; |
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[eb18f4d] | 345 | pos *p = stn->name->pos; |
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| 346 | while (stn_tab[i] != p) |
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[dbd68203] | 347 | if (++i == n_stn_tab) { |
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[d1b1380] | 348 | #if DEBUG_INVALID |
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[a420b49] | 349 | fputs("Station ", stderr); |
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[eb18f4d] | 350 | fprint_prefix(stderr, stn->name); |
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| 351 | fputs(" not in table\n\n", stderr); |
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[d1b1380] | 352 | #endif |
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| 353 | #if 0 |
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[dbd68203] | 354 | print_prefix(stn->name); |
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[b5d3988] | 355 | printf(" used: %d colour %d\n", |
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[dbd68203] | 356 | (!!stn->leg[2])<<2 | (!!stn->leg[1])<<1 | (!!stn->leg[0]), |
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[eb18f4d] | 357 | stn->colour); |
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[d1b1380] | 358 | #endif |
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[a420b49] | 359 | fatalerror(/*Bug in program detected! Please report this to the authors*/11); |
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[dbd68203] | 360 | } |
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| 361 | return i; |
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[d1b1380] | 362 | } |
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| 363 | |
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[a420b49] | 364 | static int |
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| 365 | add_stn_to_tab(node *stn) |
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| 366 | { |
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[dbd68203] | 367 | int i; |
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[eb18f4d] | 368 | pos *p = stn->name->pos; |
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[a420b49] | 369 | for (i = 0; i < n_stn_tab; i++) { |
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[eb18f4d] | 370 | if (stn_tab[i] == p) return i; |
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[dbd68203] | 371 | } |
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[eb18f4d] | 372 | stn_tab[n_stn_tab++] = p; |
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[dbd68203] | 373 | return i; |
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[d1b1380] | 374 | } |
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| 375 | |
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[702f518] | 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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[d1b1380] | 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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[a420b49] | 381 | static void |
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[9965b2b] | 382 | choleski(real *M, real *B, long n) |
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[a420b49] | 383 | { |
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[dbd68203] | 384 | int i, j, k; |
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[d1b1380] | 385 | #ifndef NO_PERCENTAGE |
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[67508f0] | 386 | unsigned long flopsTot, flops = 0, temp = 0; |
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[5b68ae1] | 387 | #define do_percent(N) BLK(flops += (N); printf("%d%%\r", (int)((100.0 * flops) / flopsTot));) |
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[d1b1380] | 388 | |
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[67508f0] | 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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[a420b49] | 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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[f52dcc7] | 393 | #endif |
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[d1b1380] | 394 | |
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[a420b49] | 395 | for (j = 1; j < n; j++) { |
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[3fde384f] | 396 | real V; |
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[a420b49] | 397 | for (i = 0; i < j; i++) { |
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[421b7d2] | 398 | V = (real)0.0; |
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[a420b49] | 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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[dbd68203] | 401 | } |
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| 402 | V = (real)0.0; |
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[a420b49] | 403 | for (k = 0; k < j; k++) V += M(j,k) * M(j,k) * M(k,k); |
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[3fde384f] | 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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[d1b1380] | 406 | #ifndef NO_PERCENTAGE |
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[dbd68203] | 407 | if (fPercent) { |
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[67508f0] | 408 | temp += ((unsigned long)j + j) + 1ul; /* avoid multiplies */ |
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[dbd68203] | 409 | do_percent(temp); |
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| 410 | } |
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[d1b1380] | 411 | #endif |
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[dbd68203] | 412 | } |
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[d1b1380] | 413 | |
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[dbd68203] | 414 | /* Multiply x by L inverse */ |
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[a420b49] | 415 | for (i = 0; i < n - 1; i++) { |
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| 416 | for (j = i + 1; j < n; j++) { |
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[dbd68203] | 417 | B[j] -= M(j,i) * B[i]; |
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[3fde384f] | 418 | } |
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[dbd68203] | 419 | } |
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[d1b1380] | 420 | |
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| 421 | #ifndef NO_PERCENTAGE |
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[dbd68203] | 422 | if (fPercent) { |
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[67508f0] | 423 | temp = (unsigned long)n * (n - 1ul) / 2ul; /* needed again lower down */ |
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[dbd68203] | 424 | do_percent(temp); |
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| 425 | } |
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[d1b1380] | 426 | #endif |
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| 427 | |
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[dbd68203] | 428 | /* Multiply x by D inverse */ |
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[a420b49] | 429 | for (i = 0; i < n; i++) { |
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[dbd68203] | 430 | B[i] /= M(i,i); |
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[3fde384f] | 431 | } |
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| 432 | |
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[d1b1380] | 433 | #ifndef NO_PERCENTAGE |
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[67508f0] | 434 | if (fPercent) do_percent((unsigned long)n); |
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[d1b1380] | 435 | #endif |
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| 436 | |
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[3fde384f] | 437 | /* Multiply x by (L transpose) inverse */ |
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[9f5d1675] | 438 | for (i = (int)(n - 1); i > 0; i--) { |
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[a420b49] | 439 | for (j = i - 1; j >= 0; j--) { |
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[421b7d2] | 440 | B[j] -= M(i,j) * B[i]; |
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[3fde384f] | 441 | } |
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[dbd68203] | 442 | } |
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[d1b1380] | 443 | |
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| 444 | #ifndef NO_PERCENTAGE |
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[dbd68203] | 445 | if (fPercent) do_percent(temp); |
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[d1b1380] | 446 | # undef do_percent |
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| 447 | #endif |
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| 448 | |
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[dbd68203] | 449 | /* printf("\n%ld/%ld\n\n",flops,flopsTot); */ |
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[d1b1380] | 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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[702f518] | 454 | #define SOR_factor 1.93 /* 1.95 */ |
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[d1b1380] | 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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[a420b49] | 458 | static void |
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[9965b2b] | 459 | sor(real *M, real *B, long n) |
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[a420b49] | 460 | { |
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[dbd68203] | 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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[d1b1380] | 465 | |
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[a420b49] | 466 | X = osmalloc(n * ossizeof(real)); |
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[d1b1380] | 467 | |
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[dbd68203] | 468 | threshold = 0.00001; |
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[d1b1380] | 469 | |
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[647407d] | 470 | printf("reciprocating diagonal\n"); /* TRANSLATE */ |
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[d1b1380] | 471 | |
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[3fde384f] | 472 | /* munge diagonal so we can multiply rather than divide */ |
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[a420b49] | 473 | for (row = n - 1; row >= 0; row--) { |
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[dbd68203] | 474 | M(row,row) = 1 / M(row,row); |
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[702f518] | 475 | X[row] = 0; |
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[dbd68203] | 476 | } |
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[d1b1380] | 477 | |
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[647407d] | 478 | printf("starting iteration\n"); /* TRANSLATE */ |
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[d1b1380] | 479 | |
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[dbd68203] | 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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[a420b49] | 484 | for (row = 0; row < n; row++) { |
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[dbd68203] | 485 | x = B[row]; |
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[a420b49] | 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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[dbd68203] | 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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[702f518] | 494 | printf("% 6d: %8.6f\n", it, t); |
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[dbd68203] | 495 | } while (t >= threshold && it < 100000); |
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[d1b1380] | 496 | |
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[dbd68203] | 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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[d1b1380] | 501 | |
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[647407d] | 502 | printf("%ld iterations\n", it); /* TRANSLATE */ |
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[d1b1380] | 503 | |
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| 504 | #if 0 |
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[dbd68203] | 505 | putnl(); |
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[a420b49] | 506 | for (row = n - 1; row >= 0; row--) { |
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[dbd68203] | 507 | t = 0.0; |
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[a420b49] | 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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[b5d3988] | 512 | printf("[ %f %f ]\n", t, B[row]); |
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[dbd68203] | 513 | } |
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[d1b1380] | 514 | #endif |
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| 515 | |
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[a420b49] | 516 | for (row = n - 1; row >= 0; row--) B[row] = X[row]; |
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[d1b1380] | 517 | |
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[dbd68203] | 518 | osfree(X); |
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[647407d] | 519 | printf("\ndone\n"); /* TRANSLATE */ |
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[dbd68203] | 520 | } |
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[d1b1380] | 521 | #endif |
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| 522 | |
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| 523 | #if PRINT_MATRICES |
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[a420b49] | 524 | static void |
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[9965b2b] | 525 | print_matrix(real *M, real *B, long n) |
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[a420b49] | 526 | { |
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[702f518] | 527 | long row, col; |
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[dbd68203] | 528 | printf("Matrix, M and vector, B:\n"); |
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[a420b49] | 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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[dbd68203] | 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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[d1b1380] | 536 | } |
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| 537 | #endif |
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