source: git/src/matrix.c @ 298e2f3

stereo-2025
Last change on this file since 298e2f3 was 4a59b4f, checked in by Olly Betts <olly@…>, 12 months ago

Fix matrix solving with EXPLICIT_FIXED_FLAG enabled
  • Property mode set to 100644
File size: 12.3 KB
Line 
1/* matrix.c
2 * Matrix building and solving routines
3 * Copyright (C) 1993-2003,2010,2013 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
60static void build_matrix(node *list);
61
62static long n_stn_tab;
63
64static pos **stn_tab;
65
66extern void
67solve_matrix(node *list)
68{
69   node *stn;
70   long n = 0;
71   FOR_EACH_STN(stn, list) {
72      if (!fixed(stn))
73          n++;
74   }
75   if (n == 0) return;
76
77   /* We need to allocate stn_tab with one entry per unfixed cluster of equated
78    * stations, but it's much simpler to count the number of unfixed nodes.
79    * This will over-count stations with more than 3 legs and equated stations
80    * but in a typical survey that's a small minority of stations.
81    */
82   stn_tab = osmalloc((OSSIZE_T)(n * ossizeof(pos*)));
83   n_stn_tab = 0;
84
85   /* We store the stn_tab index in stn->colour for quick and easy lookup in
86    * build_matrix().
87    */
88   FOR_EACH_STN(stn, list) {
89      if (!fixed(stn)) {
90          int i;
91          pos *p = stn->name->pos;
92          for (i = 0; i < n_stn_tab; i++) {
93              if (stn_tab[i] == p)
94                  break;
95          }
96          if (i == n_stn_tab)
97              stn_tab[n_stn_tab++] = p;
98          stn->colour = i;
99      } else {
100          stn->colour = -1;
101      }
102   }
103
104   build_matrix(list);
105#if DEBUG_MATRIX
106   FOR_EACH_STN(stn, list) {
107      printf("(%8.2f, %8.2f, %8.2f ) ", POS(stn, 0), POS(stn, 1), POS(stn, 2));
108      print_prefix(stn->name);
109      putnl();
110   }
111#endif
112
113   osfree(stn_tab);
114}
115
116#ifdef NO_COVARIANCES
117# define FACTOR 1
118#else
119# define FACTOR 3
120#endif
121
122static void
123build_matrix(node *list)
124{
125   SVX_ASSERT(n_stn_tab > 0);
126   /* (OSSIZE_T) cast may be needed if n_stn_tab>=181 */
127   real *M = osmalloc((OSSIZE_T)((((OSSIZE_T)n_stn_tab * FACTOR * (n_stn_tab * FACTOR + 1)) >> 1)) * ossizeof(real));
128   real *B = osmalloc((OSSIZE_T)(n_stn_tab * FACTOR * ossizeof(real)));
129
130   if (!fQuiet) {
131      if (n_stn_tab == 1)
132         out_current_action(msg(/*Solving one equation*/78));
133      else
134         out_current_action1(msg(/*Solving %d simultaneous equations*/75), n_stn_tab);
135   }
136
137#ifdef NO_COVARIANCES
138   int dim = 2;
139#else
140   int dim = 0; /* fudge next loop for now */
141#endif
142   for ( ; dim >= 0; dim--) {
143      node *stn;
144      int row;
145
146      /* Initialise M and B to zero - zeroing "linearly" will minimise
147       * paging when the matrix is large */
148      {
149         int end = n_stn_tab * FACTOR;
150         for (row = 0; row < end; row++) B[row] = (real)0.0;
151         end = ((OSSIZE_T)n_stn_tab * FACTOR * (n_stn_tab * FACTOR + 1)) >> 1;
152         for (row = 0; row < end; row++) M[row] = (real)0.0;
153      }
154
155      /* Construct matrix by going through the stn list.
156       *
157       * All legs between two fixed stations can be ignored here.
158       *
159       * Other legs we want to add exactly once to M.  To achieve this we
160       * wan to:
161       *
162       * - add forward legs between two unfixed stations,
163       *
164       * - add legs from unfixed stations to fixed stations (we do them from
165       *   the unfixed end so we don't need to detect when we're at a fixed
166       *   point cut line and determine which side we're currently dealing
167       *   with).
168       *
169       * To implement this, we only look at legs from unfixed stations and add
170       * a leg if to a fixed station, or to an unfixed station and it's a
171       * forward leg.
172       */
173      FOR_EACH_STN(stn, list) {
174#ifdef NO_COVARIANCES
175         real e;
176#else
177         svar e;
178         delta a;
179#endif
180#if DEBUG_MATRIX_BUILD
181         print_prefix(stn->name);
182         printf(" used: %d colour %ld\n",
183                (!!stn->leg[2]) << 2 | (!!stn -> leg[1]) << 1 | (!!stn->leg[0]),
184                stn->colour);
185
186         for (int dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) {
187#ifdef NO_COVARIANCES
188            printf("Leg %d, vx=%f, reverse=%d, to ", dirn,
189                   stn->leg[dirn]->v[0], stn->leg[dirn]->l.reverse);
190#else
191            printf("Leg %d, vx=%f, reverse=%d, to ", dirn,
192                   stn->leg[dirn]->v[0][0], stn->leg[dirn]->l.reverse);
193#endif
194            print_prefix(stn->leg[dirn]->l.to->name);
195            putnl();
196         }
197         putnl();
198#endif /* DEBUG_MATRIX_BUILD */
199
200         if (!fixed(stn)) {
201            int f = stn->colour;
202            for (int dirn = 0; dirn <= 2 && stn->leg[dirn]; dirn++) {
203               linkfor *leg = stn->leg[dirn];
204               node *to = leg->l.to;
205               if (fixed(to)) {
206                  bool fRev = !data_here(leg);
207                  if (fRev) leg = reverse_leg(leg);
208                  /* Ignore equated nodes */
209#ifdef NO_COVARIANCES
210                  e = leg->v[dim];
211                  if (e != (real)0.0) {
212                     e = ((real)1.0) / e;
213                     M(f,f) += e;
214                     B[f] += e * POS(to, dim);
215                     if (fRev) {
216                        B[f] += leg->d[dim];
217                     } else {
218                        B[f] -= leg->d[dim];
219                     }
220                  }
221#else
222                  if (invert_svar(&e, &leg->v)) {
223                     if (fRev) {
224                        adddd(&a, &POSD(to), &leg->d);
225                     } else {
226                        subdd(&a, &POSD(to), &leg->d);
227                     }
228                     delta b;
229                     mulsd(&b, &e, &a);
230                     for (int i = 0; i < 3; i++) {
231                        M(f * FACTOR + i, f * FACTOR + i) += e[i];
232                        B[f * FACTOR + i] += b[i];
233                     }
234                     M(f * FACTOR + 1, f * FACTOR) += e[3];
235                     M(f * FACTOR + 2, f * FACTOR) += e[4];
236                     M(f * FACTOR + 2, f * FACTOR + 1) += e[5];
237                  }
238#endif
239               } else if (data_here(leg)) {
240                  /* forward leg, unfixed -> unfixed */
241                  int t = to->colour;
242#if DEBUG_MATRIX
243                  printf("Leg %d to %d, var %f, delta %f\n", f, t, e,
244                         leg->d[dim]);
245#endif
246                  /* Ignore equated nodes & lollipops */
247#ifdef NO_COVARIANCES
248                  e = leg->v[dim];
249                  if (t != f && e != (real)0.0) {
250                     e = ((real)1.0) / e;
251                     M(f,f) += e;
252                     M(t,t) += e;
253                     if (f < t) M(t,f) -= e; else M(f,t) -= e;
254                     real a = e * leg->d[dim];
255                     B[f] -= a;
256                     B[t] += a;
257                  }
258#else
259                  if (t != f && invert_svar(&e, &leg->v)) {
260                     mulsd(&a, &e, &leg->d);
261                     for (int i = 0; i < 3; i++) {
262                        M(f * FACTOR + i, f * FACTOR + i) += e[i];
263                        M(t * FACTOR + i, t * FACTOR + i) += e[i];
264                        if (f < t)
265                           M(t * FACTOR + i, f * FACTOR + i) -= e[i];
266                        else
267                           M(f * FACTOR + i, t * FACTOR + i) -= e[i];
268                        B[f * FACTOR + i] -= a[i];
269                        B[t * FACTOR + i] += a[i];
270                     }
271                     M(f * FACTOR + 1, f * FACTOR) += e[3];
272                     M(t * FACTOR + 1, t * FACTOR) += e[3];
273                     M(f * FACTOR + 2, f * FACTOR) += e[4];
274                     M(t * FACTOR + 2, t * FACTOR) += e[4];
275                     M(f * FACTOR + 2, f * FACTOR + 1) += e[5];
276                     M(t * FACTOR + 2, t * FACTOR + 1) += e[5];
277                     if (f < t) {
278                        M(t * FACTOR + 1, f * FACTOR) -= e[3];
279                        M(t * FACTOR, f * FACTOR + 1) -= e[3];
280                        M(t * FACTOR + 2, f * FACTOR) -= e[4];
281                        M(t * FACTOR, f * FACTOR + 2) -= e[4];
282                        M(t * FACTOR + 2, f * FACTOR + 1) -= e[5];
283                        M(t * FACTOR + 1, f * FACTOR + 2) -= e[5];
284                     } else {
285                        M(f * FACTOR + 1, t * FACTOR) -= e[3];
286                        M(f * FACTOR, t * FACTOR + 1) -= e[3];
287                        M(f * FACTOR + 2, t * FACTOR) -= e[4];
288                        M(f * FACTOR, t * FACTOR + 2) -= e[4];
289                        M(f * FACTOR + 2, t * FACTOR + 1) -= e[5];
290                        M(f * FACTOR + 1, t * FACTOR + 2) -= e[5];
291                     }
292                  }
293#endif
294               }
295            }
296         }
297      }
298
299#if PRINT_MATRICES
300      print_matrix(M, B, n_stn_tab * FACTOR); /* 'ave a look! */
301#endif
302
303#ifdef SOR
304      /* defined in network.c, may be altered by -z<letters> on command line */
305      if (optimize & BITA('i'))
306         sor(M, B, n_stn_tab * FACTOR);
307      else
308#endif
309         choleski(M, B, n_stn_tab * FACTOR);
310
311      {
312         for (int m = (int)(n_stn_tab - 1); m >= 0; m--) {
313#ifdef NO_COVARIANCES
314            stn_tab[m]->p[dim] = B[m];
315# if !EXPLICIT_FIXED_FLAG
316            if (dim == 0) {
317               SVX_ASSERT2(pos_fixed(stn_tab[m]),
318                       "setting station coordinates didn't mark pos as fixed");
319            }
320# endif
321#else
322            for (int i = 0; i < 3; i++) {
323               stn_tab[m]->p[i] = B[m * FACTOR + i];
324            }
325# if !EXPLICIT_FIXED_FLAG
326            SVX_ASSERT2(pos_fixed(stn_tab[m]),
327                    "setting station coordinates didn't mark pos as fixed");
328# endif
329#endif
330#if EXPLICIT_FIXED_FLAG && !defined NO_COVARIANCES
331            fixpos(stn_tab[m]);
332#endif
333         }
334      }
335   }
336#if EXPLICIT_FIXED_FLAG && defined NO_COVARIANCES
337   for (int m = n_stn_tab - 1; m >= 0; m--) fixpos(stn_tab[m]);
338#endif
339   osfree(B);
340   osfree(M);
341}
342
343/* Solve MX=B for X by Choleski factorisation - modified Choleski actually
344 * since we factor into LDL' while Choleski is just LL'
345 */
346/* Note M must be symmetric positive definite */
347/* routine is entitled to scribble on M and B if it wishes */
348static void
349choleski(real *M, real *B, long n)
350{
351   for (int j = 1; j < n; j++) {
352      real V;
353      for (int i = 0; i < j; i++) {
354         V = (real)0.0;
355         for (int k = 0; k < i; k++) V += M(i,k) * M(j,k) * M(k,k);
356         M(j,i) = (M(j,i) - V) / M(i,i);
357      }
358      V = (real)0.0;
359      for (int k = 0; k < j; k++) V += M(j,k) * M(j,k) * M(k,k);
360      M(j,j) -= V; /* may be best to add M() last for numerical reasons too */
361   }
362
363   /* Multiply x by L inverse */
364   for (int i = 0; i < n - 1; i++) {
365      for (int j = i + 1; j < n; j++) {
366         B[j] -= M(j,i) * B[i];
367      }
368   }
369
370   /* Multiply x by D inverse */
371   for (int i = 0; i < n; i++) {
372      B[i] /= M(i,i);
373   }
374
375   /* Multiply x by (L transpose) inverse */
376   for (int i = (int)(n - 1); i > 0; i--) {
377      for (int j = i - 1; j >= 0; j--) {
378         B[j] -= M(i,j) * B[i];
379      }
380   }
381
382   /* printf("\n%ld/%ld\n\n",flops,flopsTot); */
383}
384
385#ifdef SOR
386/* factor to use for SOR (must have 1 <= SOR_factor < 2) */
387#define SOR_factor 1.93 /* 1.95 */
388
389/* Solve MX=B for X by SOR of Gauss-Siedel */
390/* routine is entitled to scribble on M and B if it wishes */
391static void
392sor(real *M, real *B, long n)
393{
394   long it = 0;
395
396   real *X = osmalloc(n * ossizeof(real));
397
398   const real threshold = 0.00001;
399
400   printf("reciprocating diagonal\n"); /* TRANSLATE */
401
402   /* munge diagonal so we can multiply rather than divide */
403   for (int row = n - 1; row >= 0; row--) {
404      M(row,row) = 1 / M(row,row);
405      X[row] = 0;
406   }
407
408   printf("starting iteration\n"); /* TRANSLATE */
409
410   real t;
411   do {
412      /*printf("*");*/
413      it++;
414      t = 0.0;
415      for (int row = 0; row < n; row++) {
416         real x = B[row];
417         int col;
418         for (col = 0; col < row; col++) x -= M(row,col) * X[col];
419         for (col++; col < n; col++) x -= M(col,row) * X[col];
420         x *= M(row,row);
421         real sor_delta = (x - X[row]) * SOR_factor;
422         X[row] += sor_delta;
423         real t2 = fabs(sor_delta);
424         if (t2 > t) t = t2;
425      }
426      printf("% 6ld: %8.6f\n", it, t);
427   } while (t >= threshold && it < 100000);
428
429   if (t >= threshold) {
430      fprintf(stderr, "*not* converged after %ld iterations\n", it);
431      BUG("iteration stinks");
432   }
433
434   printf("%ld iterations\n", it); /* TRANSLATE */
435
436#if 0
437   putnl();
438   for (int row = n - 1; row >= 0; row--) {
439      t = 0.0;
440      for (int col = 0; col < row; col++) t += M(row, col) * X[col];
441      t += X[row] / M(row, row);
442      for (col = row + 1; col < n; col++)
443         t += M(col, row) * X[col];
444      printf("[ %f %f ]\n", t, B[row]);
445   }
446#endif
447
448   for (int row = n - 1; row >= 0; row--) B[row] = X[row];
449
450   osfree(X);
451   printf("\ndone\n"); /* TRANSLATE */
452}
453#endif
454
455#if PRINT_MATRICES
456static void
457print_matrix(real *M, real *B, long n)
458{
459   printf("Matrix, M and vector, B:\n");
460   for (long row = 0; row < n; row++) {
461      long col;
462      for (col = 0; col <= row; col++) printf("%6.2f\t", M(row, col));
463      for (; col <= n; col++) printf(" \t");
464      printf("\t%6.2f\n", B[row]);
465   }
466   putnl();
467   return;
468}
469#endif
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