[421b7d2] | 1 | /* matrix.c |
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[d1b1380] | 2 | * Matrix building and solving routines |
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[a4adf09] | 3 | * Copyright (C) 1993-2003,2010,2013 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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[a4adf09] | 131 | if (n_stn_tab == 1) |
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| 132 | out_current_action(msg(/*Solving one equation*/78)); |
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| 133 | else |
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| 134 | out_current_action1(msg(/*Solving %d simultaneous equations*/75), n_stn_tab); |
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[dbd68203] | 135 | } |
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| 136 | |
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[3fde384f] | 137 | #ifdef NO_COVARIANCES |
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| 138 | dim = 2; |
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| 139 | #else |
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| 140 | dim = 0; /* fudge next loop for now */ |
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| 141 | #endif |
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[a420b49] | 142 | for ( ; dim >= 0; dim--) { |
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[2164fa4] | 143 | node *stn; |
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| 144 | int row; |
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| 145 | |
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[907fe10] | 146 | /* Initialise M and B to zero - zeroing "linearly" will minimise |
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[421b7d2] | 147 | * paging when the matrix is large */ |
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[66de220] | 148 | { |
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| 149 | int end = n_stn_tab * FACTOR; |
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| 150 | for (row = 0; row < end; row++) B[row] = (real)0.0; |
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| 151 | end = ((OSSIZE_T)n_stn_tab * FACTOR * (n_stn_tab * FACTOR + 1)) >> 1; |
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| 152 | for (row = 0; row < end; row++) M[row] = (real)0.0; |
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| 153 | } |
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[dbd68203] | 154 | |
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[907fe10] | 155 | /* Construct matrix - Go thru' stn list & add all forward legs between |
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| 156 | * two unfixed stations to M (so each leg goes on exactly once). |
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[421b7d2] | 157 | * |
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[907fe10] | 158 | * All legs between two fixed stations can be ignored here. |
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[421b7d2] | 159 | * |
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[907fe10] | 160 | * All legs between a fixed and an unfixed station are then considered |
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| 161 | * from the unfixed end (if we consider them from the fixed end we'd |
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| 162 | * need to somehow detect when we're at a fixed point cut line and work |
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| 163 | * out which side we're dealing with at this time. */ |
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[d9b5db53] | 164 | FOR_EACH_STN(stn, list) { |
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[2164fa4] | 165 | #ifdef NO_COVARIANCES |
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| 166 | real e; |
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| 167 | #else |
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[dac18d8] | 168 | svar e; |
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[eb18f4d] | 169 | delta a; |
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[2164fa4] | 170 | #endif |
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[b5d3988] | 171 | int f, t; |
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[dbd68203] | 172 | int dirn; |
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[b5d3988] | 173 | #if DEBUG_MATRIX_BUILD |
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[dbd68203] | 174 | print_prefix(stn->name); |
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[b5d3988] | 175 | printf(" used: %d colour %ld\n", |
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[a420b49] | 176 | (!!stn->leg[2]) << 2 | (!!stn -> leg[1]) << 1 | (!!stn->leg[0]), |
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[b5d3988] | 177 | stn->colour); |
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[3fde384f] | 178 | |
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[907fe10] | 179 | for (dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) { |
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[b5d3988] | 180 | #ifdef NO_COVARIANCES |
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[907fe10] | 181 | printf("Leg %d, vx=%f, reverse=%d, to ", dirn, |
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| 182 | stn->leg[dirn]->v[0], stn->leg[dirn]->l.reverse); |
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[b5d3988] | 183 | #else |
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[907fe10] | 184 | printf("Leg %d, vx=%f, reverse=%d, to ", dirn, |
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| 185 | stn->leg[dirn]->v[0][0], stn->leg[dirn]->l.reverse); |
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[b5d3988] | 186 | #endif |
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[907fe10] | 187 | print_prefix(stn->leg[dirn]->l.to->name); |
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| 188 | putnl(); |
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| 189 | } |
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[dbd68203] | 190 | putnl(); |
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[d1b1380] | 191 | #endif /* DEBUG_MATRIX_BUILD */ |
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[b5d3988] | 192 | |
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[907fe10] | 193 | if (!fixed(stn)) { |
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[564f471] | 194 | f = find_stn_in_tab(stn); |
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[907fe10] | 195 | for (dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) { |
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| 196 | linkfor *leg = stn->leg[dirn]; |
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| 197 | node *to = leg->l.to; |
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| 198 | if (fixed(to)) { |
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| 199 | bool fRev = !data_here(leg); |
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| 200 | if (fRev) leg = reverse_leg(leg); |
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| 201 | /* Ignore equated nodes */ |
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[3fde384f] | 202 | #ifdef NO_COVARIANCES |
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[907fe10] | 203 | e = leg->v[dim]; |
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| 204 | if (e != (real)0.0) { |
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| 205 | e = ((real)1.0) / e; |
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| 206 | M(f,f) += e; |
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[f52dcc7] | 207 | B[f] += e * POS(to, dim); |
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[907fe10] | 208 | if (fRev) { |
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[f52dcc7] | 209 | B[f] += leg->d[dim]; |
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[907fe10] | 210 | } else { |
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[f52dcc7] | 211 | B[f] -= leg->d[dim]; |
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[564f471] | 212 | } |
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[907fe10] | 213 | } |
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[3fde384f] | 214 | #else |
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[907fe10] | 215 | if (invert_svar(&e, &leg->v)) { |
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| 216 | delta b; |
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| 217 | int i; |
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| 218 | if (fRev) { |
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| 219 | adddd(&a, &POSD(to), &leg->d); |
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| 220 | } else { |
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| 221 | subdd(&a, &POSD(to), &leg->d); |
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| 222 | } |
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| 223 | mulsd(&b, &e, &a); |
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| 224 | for (i = 0; i < 3; i++) { |
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| 225 | M(f * FACTOR + i, f * FACTOR + i) += e[i]; |
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| 226 | B[f * FACTOR + i] += b[i]; |
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[564f471] | 227 | } |
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[907fe10] | 228 | M(f * FACTOR + 1, f * FACTOR) += e[3]; |
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| 229 | M(f * FACTOR + 2, f * FACTOR) += e[4]; |
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| 230 | M(f * FACTOR + 2, f * FACTOR + 1) += e[5]; |
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| 231 | } |
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[3fde384f] | 232 | #endif |
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[907fe10] | 233 | } else if (data_here(leg)) { |
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| 234 | /* forward leg, unfixed -> unfixed */ |
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| 235 | t = find_stn_in_tab(to); |
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[d1b1380] | 236 | #if DEBUG_MATRIX |
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[907fe10] | 237 | printf("Leg %d to %d, var %f, delta %f\n", f, t, e, |
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| 238 | leg->d[dim]); |
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[d1b1380] | 239 | #endif |
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[907fe10] | 240 | /* Ignore equated nodes & lollipops */ |
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[3fde384f] | 241 | #ifdef NO_COVARIANCES |
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[907fe10] | 242 | e = leg->v[dim]; |
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| 243 | if (t != f && e != (real)0.0) { |
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| 244 | real a; |
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| 245 | e = ((real)1.0) / e; |
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| 246 | M(f,f) += e; |
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| 247 | M(t,t) += e; |
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| 248 | if (f < t) M(t,f) -= e; else M(f,t) -= e; |
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| 249 | a = e * leg->d[dim]; |
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| 250 | B[f] -= a; |
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| 251 | B[t] += a; |
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| 252 | } |
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[3fde384f] | 253 | #else |
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[907fe10] | 254 | if (t != f && invert_svar(&e, &leg->v)) { |
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| 255 | int i; |
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| 256 | mulsd(&a, &e, &leg->d); |
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| 257 | for (i = 0; i < 3; i++) { |
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| 258 | M(f * FACTOR + i, f * FACTOR + i) += e[i]; |
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| 259 | M(t * FACTOR + i, t * FACTOR + i) += e[i]; |
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| 260 | if (f < t) |
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| 261 | M(t * FACTOR + i, f * FACTOR + i) -= e[i]; |
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| 262 | else |
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| 263 | M(f * FACTOR + i, t * FACTOR + i) -= e[i]; |
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| 264 | B[f * FACTOR + i] -= a[i]; |
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| 265 | B[t * FACTOR + i] += a[i]; |
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| 266 | } |
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| 267 | M(f * FACTOR + 1, f * FACTOR) += e[3]; |
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| 268 | M(t * FACTOR + 1, t * FACTOR) += e[3]; |
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| 269 | M(f * FACTOR + 2, f * FACTOR) += e[4]; |
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| 270 | M(t * FACTOR + 2, t * FACTOR) += e[4]; |
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| 271 | M(f * FACTOR + 2, f * FACTOR + 1) += e[5]; |
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| 272 | M(t * FACTOR + 2, t * FACTOR + 1) += e[5]; |
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| 273 | if (f < t) { |
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| 274 | M(t * FACTOR + 1, f * FACTOR) -= e[3]; |
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| 275 | M(t * FACTOR, f * FACTOR + 1) -= e[3]; |
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| 276 | M(t * FACTOR + 2, f * FACTOR) -= e[4]; |
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| 277 | M(t * FACTOR, f * FACTOR + 2) -= e[4]; |
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| 278 | M(t * FACTOR + 2, f * FACTOR + 1) -= e[5]; |
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| 279 | M(t * FACTOR + 1, f * FACTOR + 2) -= e[5]; |
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| 280 | } else { |
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| 281 | M(f * FACTOR + 1, t * FACTOR) -= e[3]; |
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| 282 | M(f * FACTOR, t * FACTOR + 1) -= e[3]; |
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| 283 | M(f * FACTOR + 2, t * FACTOR) -= e[4]; |
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| 284 | M(f * FACTOR, t * FACTOR + 2) -= e[4]; |
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| 285 | M(f * FACTOR + 2, t * FACTOR + 1) -= e[5]; |
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| 286 | M(f * FACTOR + 1, t * FACTOR + 2) -= e[5]; |
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[dbd68203] | 287 | } |
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| 288 | } |
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[907fe10] | 289 | #endif |
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[564f471] | 290 | } |
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[907fe10] | 291 | } |
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[dbd68203] | 292 | } |
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[d1b1380] | 293 | } |
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| 294 | |
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| 295 | #if PRINT_MATRICES |
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[eb18f4d] | 296 | print_matrix(M, B, n_stn_tab * FACTOR); /* 'ave a look! */ |
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[d1b1380] | 297 | #endif |
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| 298 | |
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| 299 | #ifdef SOR |
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[032ed06] | 300 | /* defined in network.c, may be altered by -z<letters> on command line */ |
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[a420b49] | 301 | if (optimize & BITA('i')) |
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[eb18f4d] | 302 | sor(M, B, n_stn_tab * FACTOR); |
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[dbd68203] | 303 | else |
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[d1b1380] | 304 | #endif |
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[eb18f4d] | 305 | choleski(M, B, n_stn_tab * FACTOR); |
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[d1b1380] | 306 | |
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[dbd68203] | 307 | { |
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[a420b49] | 308 | int m; |
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[eb18f4d] | 309 | for (m = (int)(n_stn_tab - 1); m >= 0; m--) { |
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[3fde384f] | 310 | #ifdef NO_COVARIANCES |
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[c19f129] | 311 | stn_tab[m]->p[dim] = B[m]; |
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[032ed06] | 312 | if (dim == 0) { |
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[4c07c51] | 313 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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[032ed06] | 314 | "setting station coordinates didn't mark pos as fixed"); |
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| 315 | } |
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[3fde384f] | 316 | #else |
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[702f518] | 317 | int i; |
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| 318 | for (i = 0; i < 3; i++) { |
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[c19f129] | 319 | stn_tab[m]->p[i] = B[m * FACTOR + i]; |
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[702f518] | 320 | } |
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[4c07c51] | 321 | SVX_ASSERT2(pos_fixed(stn_tab[m]), |
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[032ed06] | 322 | "setting station coordinates didn't mark pos as fixed"); |
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[3fde384f] | 323 | #endif |
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[a420b49] | 324 | } |
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[d1b1380] | 325 | #if EXPLICIT_FIXED_FLAG |
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[eb18f4d] | 326 | for (m = n_stn_tab - 1; m >= 0; m--) fixpos(stn_tab[m]); |
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[d1b1380] | 327 | #endif |
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[dbd68203] | 328 | } |
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| 329 | } |
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| 330 | osfree(B); |
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| 331 | osfree(M); |
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[d1b1380] | 332 | } |
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| 333 | |
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[a420b49] | 334 | static int |
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| 335 | find_stn_in_tab(node *stn) |
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| 336 | { |
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[dbd68203] | 337 | int i = 0; |
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[eb18f4d] | 338 | pos *p = stn->name->pos; |
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| 339 | while (stn_tab[i] != p) |
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[dbd68203] | 340 | if (++i == n_stn_tab) { |
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[d1b1380] | 341 | #if DEBUG_INVALID |
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[a420b49] | 342 | fputs("Station ", stderr); |
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[eb18f4d] | 343 | fprint_prefix(stderr, stn->name); |
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| 344 | fputs(" not in table\n\n", stderr); |
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[d1b1380] | 345 | #endif |
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| 346 | #if 0 |
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[dbd68203] | 347 | print_prefix(stn->name); |
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[b5d3988] | 348 | printf(" used: %d colour %d\n", |
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[dbd68203] | 349 | (!!stn->leg[2])<<2 | (!!stn->leg[1])<<1 | (!!stn->leg[0]), |
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[eb18f4d] | 350 | stn->colour); |
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[d1b1380] | 351 | #endif |
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[a420b49] | 352 | fatalerror(/*Bug in program detected! Please report this to the authors*/11); |
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[dbd68203] | 353 | } |
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| 354 | return i; |
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[d1b1380] | 355 | } |
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| 356 | |
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[a420b49] | 357 | static int |
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| 358 | add_stn_to_tab(node *stn) |
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| 359 | { |
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[dbd68203] | 360 | int i; |
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[eb18f4d] | 361 | pos *p = stn->name->pos; |
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[a420b49] | 362 | for (i = 0; i < n_stn_tab; i++) { |
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[eb18f4d] | 363 | if (stn_tab[i] == p) return i; |
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[dbd68203] | 364 | } |
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[eb18f4d] | 365 | stn_tab[n_stn_tab++] = p; |
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[dbd68203] | 366 | return i; |
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[d1b1380] | 367 | } |
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| 368 | |
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[702f518] | 369 | /* Solve MX=B for X by Choleski factorisation - modified Choleski actually |
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| 370 | * since we factor into LDL' while Choleski is just LL' |
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| 371 | */ |
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[d1b1380] | 372 | /* Note M must be symmetric positive definite */ |
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| 373 | /* routine is entitled to scribble on M and B if it wishes */ |
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[a420b49] | 374 | static void |
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[9965b2b] | 375 | choleski(real *M, real *B, long n) |
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[a420b49] | 376 | { |
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[dbd68203] | 377 | int i, j, k; |
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[d1b1380] | 378 | |
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[a420b49] | 379 | for (j = 1; j < n; j++) { |
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[3fde384f] | 380 | real V; |
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[a420b49] | 381 | for (i = 0; i < j; i++) { |
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[421b7d2] | 382 | V = (real)0.0; |
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[a420b49] | 383 | for (k = 0; k < i; k++) V += M(i,k) * M(j,k) * M(k,k); |
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| 384 | M(j,i) = (M(j,i) - V) / M(i,i); |
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[dbd68203] | 385 | } |
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| 386 | V = (real)0.0; |
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[a420b49] | 387 | for (k = 0; k < j; k++) V += M(j,k) * M(j,k) * M(k,k); |
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[3fde384f] | 388 | M(j,j) -= V; /* may be best to add M() last for numerical reasons too */ |
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[dbd68203] | 389 | } |
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[d1b1380] | 390 | |
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[dbd68203] | 391 | /* Multiply x by L inverse */ |
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[a420b49] | 392 | for (i = 0; i < n - 1; i++) { |
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| 393 | for (j = i + 1; j < n; j++) { |
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[dbd68203] | 394 | B[j] -= M(j,i) * B[i]; |
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[3fde384f] | 395 | } |
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[dbd68203] | 396 | } |
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[d1b1380] | 397 | |
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[dbd68203] | 398 | /* Multiply x by D inverse */ |
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[a420b49] | 399 | for (i = 0; i < n; i++) { |
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[dbd68203] | 400 | B[i] /= M(i,i); |
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[3fde384f] | 401 | } |
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| 402 | |
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| 403 | /* Multiply x by (L transpose) inverse */ |
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[9f5d1675] | 404 | for (i = (int)(n - 1); i > 0; i--) { |
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[a420b49] | 405 | for (j = i - 1; j >= 0; j--) { |
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[421b7d2] | 406 | B[j] -= M(i,j) * B[i]; |
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[3fde384f] | 407 | } |
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[dbd68203] | 408 | } |
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[d1b1380] | 409 | |
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[dbd68203] | 410 | /* printf("\n%ld/%ld\n\n",flops,flopsTot); */ |
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[d1b1380] | 411 | } |
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| 412 | |
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| 413 | #ifdef SOR |
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| 414 | /* factor to use for SOR (must have 1 <= SOR_factor < 2) */ |
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[702f518] | 415 | #define SOR_factor 1.93 /* 1.95 */ |
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[d1b1380] | 416 | |
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| 417 | /* Solve MX=B for X by SOR of Gauss-Siedel */ |
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| 418 | /* routine is entitled to scribble on M and B if it wishes */ |
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[a420b49] | 419 | static void |
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[9965b2b] | 420 | sor(real *M, real *B, long n) |
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[a420b49] | 421 | { |
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[dbd68203] | 422 | real t, x, delta, threshold, t2; |
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| 423 | int row, col; |
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| 424 | real *X; |
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| 425 | long it = 0; |
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[d1b1380] | 426 | |
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[a420b49] | 427 | X = osmalloc(n * ossizeof(real)); |
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[d1b1380] | 428 | |
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[dbd68203] | 429 | threshold = 0.00001; |
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[d1b1380] | 430 | |
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[647407d] | 431 | printf("reciprocating diagonal\n"); /* TRANSLATE */ |
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[d1b1380] | 432 | |
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[3fde384f] | 433 | /* munge diagonal so we can multiply rather than divide */ |
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[a420b49] | 434 | for (row = n - 1; row >= 0; row--) { |
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[dbd68203] | 435 | M(row,row) = 1 / M(row,row); |
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[702f518] | 436 | X[row] = 0; |
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[dbd68203] | 437 | } |
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[d1b1380] | 438 | |
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[647407d] | 439 | printf("starting iteration\n"); /* TRANSLATE */ |
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[d1b1380] | 440 | |
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[dbd68203] | 441 | do { |
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| 442 | /*printf("*");*/ |
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| 443 | it++; |
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| 444 | t = 0.0; |
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[a420b49] | 445 | for (row = 0; row < n; row++) { |
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[dbd68203] | 446 | x = B[row]; |
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[a420b49] | 447 | for (col = 0; col < row; col++) x -= M(row,col) * X[col]; |
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| 448 | for (col++; col < n; col++) x -= M(col,row) * X[col]; |
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[dbd68203] | 449 | x *= M(row,row); |
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| 450 | delta = (x - X[row]) * SOR_factor; |
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| 451 | X[row] += delta; |
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| 452 | t2 = fabs(delta); |
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| 453 | if (t2 > t) t = t2; |
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| 454 | } |
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[702f518] | 455 | printf("% 6d: %8.6f\n", it, t); |
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[dbd68203] | 456 | } while (t >= threshold && it < 100000); |
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[d1b1380] | 457 | |
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[dbd68203] | 458 | if (t >= threshold) { |
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| 459 | fprintf(stderr, "*not* converged after %ld iterations\n", it); |
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| 460 | BUG("iteration stinks"); |
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| 461 | } |
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[d1b1380] | 462 | |
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[647407d] | 463 | printf("%ld iterations\n", it); /* TRANSLATE */ |
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[d1b1380] | 464 | |
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| 465 | #if 0 |
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[dbd68203] | 466 | putnl(); |
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[a420b49] | 467 | for (row = n - 1; row >= 0; row--) { |
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[dbd68203] | 468 | t = 0.0; |
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[a420b49] | 469 | for (col = 0; col < row; col++) t += M(row, col) * X[col]; |
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| 470 | t += X[row] / M(row, row); |
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| 471 | for (col = row + 1; col < n; col++) |
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| 472 | t += M(col, row) * X[col]; |
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[b5d3988] | 473 | printf("[ %f %f ]\n", t, B[row]); |
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[dbd68203] | 474 | } |
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[d1b1380] | 475 | #endif |
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| 476 | |
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[a420b49] | 477 | for (row = n - 1; row >= 0; row--) B[row] = X[row]; |
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[d1b1380] | 478 | |
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[dbd68203] | 479 | osfree(X); |
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[647407d] | 480 | printf("\ndone\n"); /* TRANSLATE */ |
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[dbd68203] | 481 | } |
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[d1b1380] | 482 | #endif |
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| 483 | |
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| 484 | #if PRINT_MATRICES |
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[a420b49] | 485 | static void |
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[9965b2b] | 486 | print_matrix(real *M, real *B, long n) |
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[a420b49] | 487 | { |
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[702f518] | 488 | long row, col; |
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[dbd68203] | 489 | printf("Matrix, M and vector, B:\n"); |
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[a420b49] | 490 | for (row = 0; row < n; row++) { |
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| 491 | for (col = 0; col <= row; col++) printf("%6.2f\t", M(row, col)); |
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| 492 | for (; col <= n; col++) printf(" \t"); |
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[dbd68203] | 493 | printf("\t%6.2f\n", B[row]); |
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| 494 | } |
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| 495 | putnl(); |
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| 496 | return; |
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[d1b1380] | 497 | } |
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| 498 | #endif |
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