2 * We try to find an optimal triangle grid
9 #include <gsl/gsl_errno.h>
10 #include <gsl/gsl_multimin.h>
15 static const char *input_file, *output_file;
16 static char *output_file_tmp;
18 static void compute_vertex_areas(const Vertices vertices, double areas[N]);
19 static double best_energy= DBL_MAX;
21 enum printing_instance { pr_cost, pr_size, pr__max };
23 static void addcost(double *energy, double tweight, double tcost, int pr);
24 #define COST(weight, compute) addcost(&energy, (weight), (compute), printing)
25 static int printing_check(enum printing_instance);
26 static void printing_init(void);
28 /*---------- main energy computation and subroutines ----------*/
30 static double compute_energy(const Vertices vertices) {
31 double vertex_areas[N], energy;
34 compute_vertex_areas(vertices,vertex_areas);
37 printing= printing_check(pr_cost);
39 if (printing) printf("cost > energy |");
41 COST(1e2, edgewise_vertex_displacement_cost(vertices));
42 // COST(1e0, graph_layout_cost(vertices,vertex_areas));
43 COST(1e4, noncircular_rim_cost(vertices));
45 if (printing) printf("| total %# e |", energy);
47 if (energy < best_energy) {
51 if (printing) printf(" BEST");
53 best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out");
54 r= fwrite(vertices,sizeof(Vertices),1,best_f); if (r!=1) diee("fwrite");
55 if (fclose(best_f)) diee("fclose new best");
56 if (rename(output_file_tmp,output_file)) diee("rename install new best");
68 static void addcost(double *energy, double tweight, double tcost, int pr) {
69 double tenergy= tweight * tcost;
70 if (pr) printf(" %# e > %# e |", tcost, tenergy);
74 static void compute_vertex_areas(const Vertices vertices, double areas[N]) {
75 int v0,v1,v2, e1,e2, k;
86 double e1v[D3], e2v[D3], av[D3];
88 e1v[k]= vertices[v1][k] - vertices[v0][k];
89 e2v[k]= vertices[v2][k] - vertices[v0][k];
95 areas[v0]= total / count;
99 /*---------- use of GSL ----------*/
101 /* We want to do multidimensional minimisation.
103 * We don't think there are any local minima. Or at least, if there
104 * are, the local minimum which will be found from the starting
105 * state is the one we want.
107 * We don't want to try to provide a derivative of the cost
108 * function. That's too tedious (and anyway the polynomial
109 * approximation to our our cost function sometimes has high degree
110 * in the inputs which means the quadratic model implied by most of
111 * the gradient descent minimisers is not ideal).
113 * This eliminates most of the algorithms. Nelder and Mead's
114 * simplex algorithm is still available and we will try that.
116 * In our application we are searching for the optimal locations of
117 * N actualvertices in D3 (3) dimensions - ie, we are searching for
118 * the optimal metapoint in an N*D3-dimensional space.
120 * So eg with X=Y=100, the simplex will contain 300 metavertices
121 * each of which is an array of 300 doubles for the actualvertex
122 * coordinates. Hopefully this won't be too slow ...
125 static gsl_multimin_fminimizer *minimiser;
127 static const double stop_epsilon= 1e-4;
129 static double minfunc_f(const gsl_vector *x, void *params) {
130 assert(x->size == DIM);
131 assert(x->stride == 1);
132 return compute_energy((const double(*)[D3])x->data);
135 int main(int argc, const char *const *argv) {
136 gsl_multimin_function multimin_function;
138 Vertices initial, step_size;
140 gsl_vector initial_gsl, step_size_gsl;
143 if (argc!=3 || argv[1][0]=='-' || strncmp(argv[2],"-o",2))
144 { fputs("usage: minimise <input> -o<output\n",stderr); exit(8); }
147 output_file= argv[2]+2;
148 if (asprintf(&output_file_tmp,"%s.new",output_file) <= 0) diee("asprintf");
150 graph_layout_prepare();
153 minimiser= gsl_multimin_fminimizer_alloc
154 (gsl_multimin_fminimizer_nmsimplex, DIM);
155 if (!minimiser) { perror("alloc minimiser"); exit(-1); }
157 multimin_function.f= minfunc_f;
158 multimin_function.n= DIM;
159 multimin_function.params= 0;
161 initial_f= fopen(input_file,"rb"); if (!initial_f) diee("fopen initial");
162 errno= 0; r= fread(initial,sizeof(initial),1,initial_f);
163 if (r!=1) diee("fread");
166 initial_gsl.size= DIM;
167 initial_gsl.stride= 1;
168 initial_gsl.block= 0;
169 initial_gsl.owner= 0;
170 step_size_gsl= initial_gsl;
172 initial_gsl.data= &initial[0][0];
173 step_size_gsl.data= &step_size[0][0];
176 K step_size[v][k]= 0.03;
178 // FOR_RIM_VERTEX(vx,vy,v)
179 // step_size[v][3] *= 0.1;
181 GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
182 &initial_gsl, &step_size_gsl) );
185 GA( gsl_multimin_fminimizer_iterate(minimiser) );
187 size= gsl_multimin_fminimizer_size(minimiser);
188 r= gsl_multimin_test_size(size, stop_epsilon);
190 if (printing_check(pr_size))
191 printf("%*s size %# e, r=%d\n", 135,"", size, r);
194 if (r==GSL_SUCCESS) break;
195 assert(r==GSL_CONTINUE);
200 /*---------- Edgewise vertex displacement ----------*/
218 * Let delta = 180deg - angle RMS
223 * Giving energy contribution:
231 * (The dimensions of this are those of F_vd.)
233 * We calculate delta as atan2(|AxB|, A.B)
234 * where A = RM, B = MS
236 * In practice to avoid division by zero we'll add epsilon to d and
237 * |AxB| and the huge energy ought then to be sufficient for the
238 * model to avoid being close to R=S.
241 double edgewise_vertex_displacement_cost(const Vertices vertices) {
242 static const double axb_epsilon= 1e-6;
244 int pi,e,qi,ri,si, k;
245 double m[D3], a[D3], b[D3], axb[D3];
246 double total_cost= 0;
249 ri= EDGE_END2(pi,(e+1)%V6); if (ri<0) continue;
250 si= EDGE_END2(pi,(e+5)%V6); if (si<0) continue;
252 K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5;
253 K a[k]= -vertices[ri][k] + m[k];
254 K b[k]= -m[k] + vertices[si][k];
258 double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
259 double cost= delta * delta;
265 /*---------- noncircular rim cost ----------*/
267 double noncircular_rim_cost(const Vertices vertices) {
271 FOR_RIM_VERTEX(vy,vx,v) {
273 /* By symmetry, nearest point on circle is the one with
274 * the same angle subtended at the z axis. */
275 oncircle[0]= vertices[v][0];
276 oncircle[1]= vertices[v][1];
278 double mult= 1.0/ magnD(oncircle);
281 double d2= hypotD2(vertices[v], oncircle);
287 /*---------- printing rate limit ----------*/
289 static volatile unsigned print_todo;
290 static sigset_t print_alarmset;
292 static int printing_check(enum printing_instance which) {
293 static int skipped[pr__max];
295 unsigned bits= 1u << which;
298 if (!(print_todo & bits)) {
303 sigprocmask(SIG_BLOCK,&print_alarmset,0);
305 sigprocmask(SIG_UNBLOCK,&print_alarmset,0);
308 if (sk) printf("[%4d] ",sk);
315 static void alarmhandler(int ignored) {
319 static void printing_init(void) {
321 struct itimerval itv;
323 sigemptyset(&print_alarmset);
324 sigaddset(&print_alarmset,SIGALRM);
326 sa.sa_handler= alarmhandler;
327 sa.sa_mask= print_alarmset;
328 sa.sa_flags= SA_RESTART;
329 if (sigaction(SIGALRM,&sa,0)) diee("sigaction ALRM");
331 itv.it_interval.tv_sec= 0;
332 itv.it_interval.tv_usec= 200000;
333 itv.it_value= itv.it_interval;
335 if (setitimer(ITIMER_REAL,&itv,0)) diee("setitimer REAL");