source: git/src/matrix.c @ 1339de3

stereo-2025
Last change on this file since 1339de3 was 9814fb7, checked in by Olly Betts <olly@…>, 9 months ago

Simplify setting row numbers

Check the ->name->pos pointers match rather than checking the legs
are equates, which is slightly simpler and slightly more efficient.
  • Property mode set to 100644
File size: 12.2 KB
Line 
1/* matrix.c
2 * Matrix building and solving routines
3 * Copyright (C) 1993-2003,2010,2013,2024 Olly Betts
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 2 of the License, or
8 * (at your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
13 * GNU General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
18 */
19
20/*#define SOR 1*/
21
22#if 0
23# define DEBUG_INVALID 1
24#endif
25
26#include <config.h>
27
28#include "debug.h"
29#include "cavern.h"
30#include "filename.h"
31#include "message.h"
32#include "netbits.h"
33#include "matrix.h"
34#include "out.h"
35
36#undef PRINT_MATRICES
37#define PRINT_MATRICES 0
38
39#undef DEBUG_MATRIX_BUILD
40#define DEBUG_MATRIX_BUILD 0
41
42#undef DEBUG_MATRIX
43#define DEBUG_MATRIX 0
44
45#if PRINT_MATRICES
46static void print_matrix(real *M, real *B, long n);
47#endif
48
49static void choleski(real *M, real *B, long n);
50
51#ifdef SOR
52static void sor(real *M, real *B, long n);
53#endif
54
55/* for M(row, col) col must be <= row, so Y <= X */
56# define M(X, Y) ((real *)M)[((((OSSIZE_T)(X)) * ((X) + 1)) >> 1) + (Y)]
57              /* +(Y>X?0*printf("row<col (line %d)\n",__LINE__):0) */
58/*#define M_(X, Y) ((real *)M)[((((OSSIZE_T)(Y)) * ((Y) + 1)) >> 1) + (X)]*/
59
60#define COLOUR_FIXED -1
61#define COLOUR_TODO -2
62
63static void set_row(node *stn, int row_number) {
64    // We store the matrix row/column index in stn->colour for quick and easy
65    // lookup when copying out the solved station coordinates.
66    stn->colour = row_number;
67    for (int d = 0; d < 3; d++) {
68        linkfor *leg = stn->leg[d];
69        if (!leg) break;
70        node *to = leg->l.to;
71        if (to->colour == COLOUR_TODO && stn->name->pos == to->name->pos) {
72            set_row(to, row_number);
73        }
74    }
75}
76
77#ifdef NO_COVARIANCES
78# define FACTOR 1
79#else
80# define FACTOR 3
81#endif
82
83extern void
84solve_matrix(node *list)
85{
86   node *stn;
87   bool unfixed_stations = false;
88   FOR_EACH_STN(stn, list) {
89      if (!fixed(stn)) {
90          unfixed_stations = true;
91          stn->colour = COLOUR_TODO;
92      } else {
93          stn->colour = COLOUR_FIXED;
94      }
95   }
96   if (!unfixed_stations) {
97       return;
98   }
99
100   // Assign a matrix row/column index to each group of stations with the same
101   // pos.
102   long n = 0;
103   FOR_EACH_STN(stn, list) {
104      if (stn->colour == COLOUR_TODO) {
105          set_row(stn, n++);
106      }
107   }
108   SVX_ASSERT(n > 0);
109
110   // Array to map from row/column index to pos.  We fill this in as we build
111   // the matrix, and use it to know where to copy the solved station
112   // coordinates to.
113   pos **stn_tab = osmalloc((OSSIZE_T)(n * ossizeof(pos*)));
114
115   /* (OSSIZE_T) cast may be needed if n >= 181 */
116   real *M = osmalloc((OSSIZE_T)((((OSSIZE_T)n * FACTOR * (n * FACTOR + 1)) >> 1)) * ossizeof(real));
117   real *B = osmalloc((OSSIZE_T)(n * FACTOR * ossizeof(real)));
118
119   if (!fQuiet) {
120      if (n == 1)
121         out_current_action(msg(/*Solving one equation*/78));
122      else
123         out_current_action1(msg(/*Solving %d simultaneous equations*/75), n);
124   }
125
126#ifdef NO_COVARIANCES
127   int dim = 2;
128#else
129   int dim = 0; /* Collapse loop to a single iteration. */
130#endif
131   for ( ; dim >= 0; dim--) {
132      /* Initialise M and B to zero - zeroing "linearly" will minimise
133       * paging when the matrix is large */
134      {
135         int end = n * FACTOR;
136         for (int row = 0; row < end; row++) B[row] = (real)0.0;
137         end = ((OSSIZE_T)n * FACTOR * (n * FACTOR + 1)) >> 1;
138         for (int row = 0; row < end; row++) M[row] = (real)0.0;
139      }
140
141      /* Construct matrix by going through the stn list.
142       *
143       * All legs between two fixed stations can be ignored here.
144       *
145       * Other legs we want to add exactly once to M.  To achieve this we
146       * want to:
147       *
148       * - add forward legs between two unfixed stations,
149       *
150       * - add legs from unfixed stations to fixed stations (we do them from
151       *   the unfixed end so we don't need to detect when we're at a fixed
152       *   point cut line and determine which side we're currently dealing
153       *   with).
154       *
155       * To implement this, we only look at legs from unfixed stations and add
156       * a leg if to a fixed station, or to an unfixed station and it's a
157       * forward leg.
158       */
159      FOR_EACH_STN(stn, list) {
160         if (dim == 0) {
161             if (stn->colour != COLOUR_FIXED) {
162                 stn_tab[stn->colour] = stn->name->pos;
163             }
164         }
165
166#ifdef NO_COVARIANCES
167         real e;
168#else
169         svar e;
170         delta a;
171#endif
172#if DEBUG_MATRIX_BUILD
173         print_prefix(stn->name);
174         printf(" used: %d colour %ld\n",
175                (!!stn->leg[2]) << 2 | (!!stn -> leg[1]) << 1 | (!!stn->leg[0]),
176                stn->colour);
177
178         for (int dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) {
179            printf("Leg %d, vx=%f, reverse=%d, to ", dirn,
180                   stn->leg[dirn]->v[0], stn->leg[dirn]->l.reverse);
181            print_prefix(stn->leg[dirn]->l.to->name);
182            putnl();
183         }
184         putnl();
185#endif /* DEBUG_MATRIX_BUILD */
186
187         int f = stn->colour;
188         if (f != COLOUR_FIXED) {
189            for (int dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) {
190               linkfor *leg = stn->leg[dirn];
191               node *to = leg->l.to;
192               int t = to->colour;
193               if (t == COLOUR_FIXED) {
194                  bool fRev = !data_here(leg);
195                  if (fRev) leg = reverse_leg(leg);
196                  /* Ignore equated nodes */
197#ifdef NO_COVARIANCES
198                  e = leg->v[dim];
199                  if (e != (real)0.0) {
200                     e = ((real)1.0) / e;
201                     M(f,f) += e;
202                     B[f] += e * POS(to, dim);
203                     if (fRev) {
204                        B[f] += leg->d[dim];
205                     } else {
206                        B[f] -= leg->d[dim];
207                     }
208                  }
209#else
210                  if (invert_svar(&e, &leg->v)) {
211                     if (fRev) {
212                        adddd(&a, &POSD(to), &leg->d);
213                     } else {
214                        subdd(&a, &POSD(to), &leg->d);
215                     }
216                     delta b;
217                     mulsd(&b, &e, &a);
218                     for (int i = 0; i < 3; i++) {
219                        M(f * FACTOR + i, f * FACTOR + i) += e[i];
220                        B[f * FACTOR + i] += b[i];
221                     }
222                     M(f * FACTOR + 1, f * FACTOR) += e[3];
223                     M(f * FACTOR + 2, f * FACTOR) += e[4];
224                     M(f * FACTOR + 2, f * FACTOR + 1) += e[5];
225                  }
226#endif
227               } else if (data_here(leg)) {
228                  /* forward leg, unfixed -> unfixed */
229#if DEBUG_MATRIX
230# ifdef NO_COVARIANCES
231                  printf("Leg %d to %d, var %f, delta %f\n", f, t, e,
232                         leg->d[dim]);
233# else
234                  printf("Leg %d to %d, var (%f, %f, %f; %f, %f, %f), "
235                         "delta %f\n", f, t, e[0], e[1], e[2], e[3], e[4], e[5],
236                         leg->d[dim]);
237# endif
238#endif
239                  /* Ignore equated nodes & lollipops */
240#ifdef NO_COVARIANCES
241                  e = leg->v[dim];
242                  if (t != f && e != (real)0.0) {
243                     e = ((real)1.0) / e;
244                     M(f,f) += e;
245                     M(t,t) += e;
246                     if (f < t) M(t,f) -= e; else M(f,t) -= e;
247                     real a = e * leg->d[dim];
248                     B[f] -= a;
249                     B[t] += a;
250                  }
251#else
252                  if (t != f && invert_svar(&e, &leg->v)) {
253                     mulsd(&a, &e, &leg->d);
254                     for (int i = 0; i < 3; i++) {
255                        M(f * FACTOR + i, f * FACTOR + i) += e[i];
256                        M(t * FACTOR + i, t * FACTOR + i) += e[i];
257                        if (f < t)
258                           M(t * FACTOR + i, f * FACTOR + i) -= e[i];
259                        else
260                           M(f * FACTOR + i, t * FACTOR + i) -= e[i];
261                        B[f * FACTOR + i] -= a[i];
262                        B[t * FACTOR + i] += a[i];
263                     }
264                     M(f * FACTOR + 1, f * FACTOR) += e[3];
265                     M(t * FACTOR + 1, t * FACTOR) += e[3];
266                     M(f * FACTOR + 2, f * FACTOR) += e[4];
267                     M(t * FACTOR + 2, t * FACTOR) += e[4];
268                     M(f * FACTOR + 2, f * FACTOR + 1) += e[5];
269                     M(t * FACTOR + 2, t * FACTOR + 1) += e[5];
270                     if (f < t) {
271                        M(t * FACTOR + 1, f * FACTOR) -= e[3];
272                        M(t * FACTOR, f * FACTOR + 1) -= e[3];
273                        M(t * FACTOR + 2, f * FACTOR) -= e[4];
274                        M(t * FACTOR, f * FACTOR + 2) -= e[4];
275                        M(t * FACTOR + 2, f * FACTOR + 1) -= e[5];
276                        M(t * FACTOR + 1, f * FACTOR + 2) -= e[5];
277                     } else {
278                        M(f * FACTOR + 1, t * FACTOR) -= e[3];
279                        M(f * FACTOR, t * FACTOR + 1) -= e[3];
280                        M(f * FACTOR + 2, t * FACTOR) -= e[4];
281                        M(f * FACTOR, t * FACTOR + 2) -= e[4];
282                        M(f * FACTOR + 2, t * FACTOR + 1) -= e[5];
283                        M(f * FACTOR + 1, t * FACTOR + 2) -= e[5];
284                     }
285                  }
286#endif
287               }
288            }
289         }
290      }
291
292#if PRINT_MATRICES
293      print_matrix(M, B, n * FACTOR); /* 'ave a look! */
294#endif
295
296#ifdef SOR
297      /* defined in network.c, may be altered by -z<letters> on command line */
298      if (optimize & BITA('i'))
299         sor(M, B, n * FACTOR);
300      else
301#endif
302         choleski(M, B, n * FACTOR);
303
304      {
305         for (int m = (int)(n - 1); m >= 0; m--) {
306#ifdef NO_COVARIANCES
307            stn_tab[m]->p[dim] = B[m];
308            if (dim == 0) {
309               SVX_ASSERT2(pos_fixed(stn_tab[m]),
310                       "setting station coordinates didn't mark pos as fixed");
311            }
312#else
313            for (int i = 0; i < 3; i++) {
314               stn_tab[m]->p[i] = B[m * FACTOR + i];
315            }
316            SVX_ASSERT2(pos_fixed(stn_tab[m]),
317                    "setting station coordinates didn't mark pos as fixed");
318#endif
319         }
320      }
321   }
322   osfree(B);
323   osfree(M);
324   osfree(stn_tab);
325
326#if DEBUG_MATRIX
327   FOR_EACH_STN(stn, list) {
328      printf("(%8.2f, %8.2f, %8.2f ) ", POS(stn, 0), POS(stn, 1), POS(stn, 2));
329      print_prefix(stn->name);
330      putnl();
331   }
332#endif
333}
334
335/* Solve MX=B for X by Choleski factorisation - modified Choleski actually
336 * since we factor into LDL' while Choleski is just LL'
337 */
338/* Note M must be symmetric positive definite */
339/* routine is entitled to scribble on M and B if it wishes */
340static void
341choleski(real *M, real *B, long n)
342{
343   for (int j = 1; j < n; j++) {
344      real V;
345      for (int i = 0; i < j; i++) {
346         V = (real)0.0;
347         for (int k = 0; k < i; k++) V += M(i,k) * M(j,k) * M(k,k);
348         M(j,i) = (M(j,i) - V) / M(i,i);
349      }
350      V = (real)0.0;
351      for (int k = 0; k < j; k++) V += M(j,k) * M(j,k) * M(k,k);
352      M(j,j) -= V; /* may be best to add M() last for numerical reasons too */
353   }
354
355   /* Multiply x by L inverse */
356   for (int i = 0; i < n - 1; i++) {
357      for (int j = i + 1; j < n; j++) {
358         B[j] -= M(j,i) * B[i];
359      }
360   }
361
362   /* Multiply x by D inverse */
363   for (int i = 0; i < n; i++) {
364      B[i] /= M(i,i);
365   }
366
367   /* Multiply x by (L transpose) inverse */
368   for (int i = (int)(n - 1); i > 0; i--) {
369      for (int j = i - 1; j >= 0; j--) {
370         B[j] -= M(i,j) * B[i];
371      }
372   }
373
374   /* printf("\n%ld/%ld\n\n",flops,flopsTot); */
375}
376
377#ifdef SOR
378/* factor to use for SOR (must have 1 <= SOR_factor < 2) */
379#define SOR_factor 1.93 /* 1.95 */
380
381/* Solve MX=B for X by SOR of Gauss-Siedel */
382/* routine is entitled to scribble on M and B if it wishes */
383static void
384sor(real *M, real *B, long n)
385{
386   long it = 0;
387
388   real *X = osmalloc(n * ossizeof(real));
389
390   const real threshold = 0.00001;
391
392   printf("reciprocating diagonal\n"); /* TRANSLATE */
393
394   /* munge diagonal so we can multiply rather than divide */
395   for (int row = n - 1; row >= 0; row--) {
396      M(row,row) = 1 / M(row,row);
397      X[row] = 0;
398   }
399
400   printf("starting iteration\n"); /* TRANSLATE */
401
402   real t;
403   do {
404      /*printf("*");*/
405      it++;
406      t = 0.0;
407      for (int row = 0; row < n; row++) {
408         real x = B[row];
409         int col;
410         for (col = 0; col < row; col++) x -= M(row,col) * X[col];
411         for (col++; col < n; col++) x -= M(col,row) * X[col];
412         x *= M(row,row);
413         real sor_delta = (x - X[row]) * SOR_factor;
414         X[row] += sor_delta;
415         real t2 = fabs(sor_delta);
416         if (t2 > t) t = t2;
417      }
418      printf("% 6ld: %8.6f\n", it, t);
419   } while (t >= threshold && it < 100000);
420
421   if (t >= threshold) {
422      fprintf(stderr, "*not* converged after %ld iterations\n", it);
423      BUG("iteration stinks");
424   }
425
426   printf("%ld iterations\n", it); /* TRANSLATE */
427
428#if 0
429   putnl();
430   for (int row = n - 1; row >= 0; row--) {
431      t = 0.0;
432      for (int col = 0; col < row; col++) t += M(row, col) * X[col];
433      t += X[row] / M(row, row);
434      for (col = row + 1; col < n; col++)
435         t += M(col, row) * X[col];
436      printf("[ %f %f ]\n", t, B[row]);
437   }
438#endif
439
440   for (int row = n - 1; row >= 0; row--) B[row] = X[row];
441
442   osfree(X);
443   printf("\ndone\n"); /* TRANSLATE */
444}
445#endif
446
447#if PRINT_MATRICES
448static void
449print_matrix(real *M, real *B, long n)
450{
451   printf("Matrix, M and vector, B:\n");
452   for (long row = 0; row < n; row++) {
453      long col;
454      for (col = 0; col <= row; col++) printf("%6.2f\t", M(row, col));
455      for (; col <= n; col++) printf(" \t");
456      printf("\t%6.2f\n", B[row]);
457   }
458   putnl();
459   return;
460}
461#endif
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