#include "common.h"
#include "minimise.h"
#include "mgraph.h"
+#include "parallel.h"
-#include <gsl/gsl_errno.h>
-#include <gsl/gsl_multimin.h>
+double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6];
-#include <signal.h>
-#include <sys/time.h>
+static double best_energy= DBL_MAX;
-static const char *input_file, *output_file;
-static char *output_file_tmp;
+static void addcost(double *energy, double tweight, double tcost, int pr);
-static void compute_vertex_areas(const Vertices vertices, double areas[N]);
-static double best_energy= DBL_MAX;
+/*---------- main energy computation, weights, etc. ----------*/
+
+typedef double CostComputation(const Vertices vertices, int section);
+typedef void PreComputation(const Vertices vertices, int section);
+
+typedef struct {
+ double weight;
+ CostComputation *fn;
+} CostContribution;
+
+#define NPRECOMPS ((sizeof(precomps)/sizeof(precomps[0])))
+#define NCOSTS ((sizeof(costs)/sizeof(costs[0])))
+#define COST(weight, compute) { (weight),(compute) },
+
+static PreComputation *const precomps[]= {
+ compute_edge_lengths,
+ compute_vertex_areas
+};
+
+static const CostContribution costs[]= {
+
+#if XBITS==3
+#define STOP_EPSILON 1e-6
+ COST( 3e3, line_bending_cost)
+ COST( 3e3, edge_length_variation_cost)
+ COST( 0.4e3, rim_proximity_cost)
+ COST( 1e6, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.7)
+// COST( 1e1, small_triangles_cost)
+ COST( 1e12, noncircular_rim_cost)
+#endif
+
+#if XBITS==4
+#define STOP_EPSILON 1e-6
+ COST( 3e5, line_bending_cost)
+ COST( 10e2, edge_length_variation_cost)
+ COST( 9.0e1, rim_proximity_cost) // 5e1 is too much
+ // 2.5e1 is too little
+ // 0.2e1 grows compared to previous ?
+ // 0.6e0 shrinks compared to previous ?
+
+ COST( 1e12, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.3)
+ COST( 1e18, noncircular_rim_cost)
+#endif
+
+#if XBITS==5
+#define STOP_EPSILON 1e-6
+ COST( 3e5, line_bending_cost)
+ COST( 10e2, edge_length_variation_cost)
+ COST( 9.0e1, rim_proximity_cost) // 5e1 is too much
+ // 2.5e1 is too little
+ // 0.2e1 grows compared to previous ?
+ // 0.6e0 shrinks compared to previous ?
+
+ COST( 1e12, edge_angle_cost)
+ #define EDGE_ANGLE_COST_CIRCCIRCRAT (0.5/1.3)
+ COST( 1e18, noncircular_rim_cost)
+#endif
+
+};
+
+const double edge_angle_cost_circcircrat= EDGE_ANGLE_COST_CIRCCIRCRAT;
+
+void energy_init(void) {
+ stop_epsilon= STOP_EPSILON;
+}
-enum printing_instance { pr_cost, pr_size, pr__max };
+/*---------- energy computation machinery ----------*/
-static void addcost(double *energy, double tweight, double tcost, int pr);
-#define COST(weight, compute) addcost(&energy, (weight), (compute), printing)
-static int printing_check(enum printing_instance);
-static void printing_init(void);
+void compute_energy_separately(const struct Vertices *vs,
+ int section, void *energies_v, void *totals_v) {
+ double *energies= energies_v;
+ int ci;
+
+ for (ci=0; ci<NPRECOMPS; ci++) {
+ costs[ci].fn(vs->a, section);
+ inparallel_barrier();
+ }
+ for (ci=0; ci<NCOSTS; ci++)
+ energies[ci]= costs[ci].fn(vs->a, section);
+}
-/*---------- main energy computation and subroutines ----------*/
+void compute_energy_combine(const struct Vertices *vertices,
+ int section, void *energies_v, void *totals_v) {
+ int ci;
+ double *energies= energies_v;
+ double *totals= totals_v;
-static double compute_energy(const Vertices vertices) {
- double vertex_areas[N], energy;
- int printing;
+ for (ci=0; ci<NCOSTS; ci++)
+ totals[ci] += energies[ci];
+}
- compute_vertex_areas(vertices,vertex_areas);
- energy= 0;
+double compute_energy(const struct Vertices *vs) {
+ static int bests_unprinted;
+
+ double totals[NCOSTS], energy;
+ int ci, printing;
+
+ printing= printing_check(pr_cost,0);
- printing= printing_check(pr_cost);
+ if (printing) printf("%15lld c>e |", evaluations);
- if (printing) printf("cost > energy |");
+ for (ci=0; ci<NCOSTS; ci++)
+ totals[ci]= 0;
- COST(1e2, edgewise_vertex_displacement_cost(vertices));
- COST(1e2, graph_layout_cost(vertices,vertex_areas));
-// COST(1e4, noncircular_rim_cost(vertices));
+ inparallel(vs,
+ compute_energy_separately,
+ compute_energy_combine,
+ sizeof(totals) /* really, size of energies */,
+ totals);
+
+ energy= 0;
+ for (ci=0; ci<NCOSTS; ci++)
+ addcost(&energy, costs[ci].weight, totals[ci], printing);
if (printing) printf("| total %# e |", energy);
FILE *best_f;
int r;
- if (printing) printf(" BEST");
+ if (printing) {
+ printf(" BEST");
+ if (bests_unprinted) printf(" [%4d]",bests_unprinted);
+ bests_unprinted= 0;
+ } else {
+ bests_unprinted++;
+ }
- best_f= fopen(output_file_tmp,"wb"); if (!best_f) diee("fopen new out");
- r= fwrite(vertices,sizeof(Vertices),1,best_f); if (r!=1) diee("fwrite");
+ best_f= fopen(best_file_tmp,"wb"); if (!best_f) diee("fopen new out");
+ r= fwrite(vs->a,sizeof(vs->a),1,best_f); if (r!=1) diee("fwrite");
if (fclose(best_f)) diee("fclose new best");
- if (rename(output_file_tmp,output_file)) diee("rename install new best");
+ if (rename(best_file_tmp,best_file)) diee("rename install new best");
best_energy= energy;
}
flushoutput();
}
+ evaluations++;
return energy;
}
static void addcost(double *energy, double tweight, double tcost, int pr) {
double tenergy= tweight * tcost;
- if (pr) printf(" %# e > %# e |", tcost, tenergy);
+ if (pr) printf(" %# e x %g > %# e* |", tcost, tweight, tenergy);
*energy += tenergy;
}
-static void compute_vertex_areas(const Vertices vertices, double areas[N]) {
- int v0,v1,v2, e1,e2, k;
+/*---------- Precomputations ----------*/
- FOR_VERTEX(v0) {
- double total= 0.0;
+void compute_edge_lengths(const Vertices vertices, int section) {
+ int v1,e,v2;
+
+ FOR_EDGE(v1,e,v2, OUTER)
+ edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
+}
+
+void compute_vertex_areas(const Vertices vertices, int section) {
+ int v0,v1,v2, e1,e2;
+// int k;
+
+ FOR_VERTEX(v0, OUTER) {
+ double total= 0.0, edges_total=0;
int count= 0;
FOR_VEDGE(v0,e1,v1) {
v2= EDGE_END2(v0,e2);
if (v2<0) continue;
- double e1v[D3], e2v[D3], av[D3];
- K {
- e1v[k]= vertices[v1][k] - vertices[v0][k];
- e2v[k]= vertices[v2][k] - vertices[v0][k];
- }
- xprod(av, e1v, e2v);
- total += magnD(av);
+ edges_total += edge_lengths[v0][e1];
+
+// double e1v[D3], e2v[D3], av[D3];
+// K {
+// e1v[k]= vertices[v1][k] - vertices[v0][k];
+// e2v[k]= vertices[v2][k] - vertices[v0][k];
+// }
+// xprod(av, e1v, e2v);
+// total += magnD(av);
+
count++;
}
- areas[v0]= total / count;
+ vertex_areas[v0]= total / count;
+ vertex_mean_edge_lengths[v0]= edges_total / count;
}
}
-/*---------- use of GSL ----------*/
+/*---------- Edgewise vertex displacement ----------*/
- /* We want to do multidimensional minimisation.
+ /*
+ * Definition:
*
- * We don't think there are any local minima. Or at least, if there
- * are, the local minimum which will be found from the starting
- * state is the one we want.
+ * At each vertex Q, in each direction e:
*
- * We don't want to try to provide a derivative of the cost
- * function. That's too tedious (and anyway the polynomial
- * approximation to our our cost function sometimes has high degree
- * in the inputs which means the quadratic model implied by most of
- * the gradient descent minimisers is not ideal).
+ * e
+ * Q ----->----- R
+ * _,-'\__/
+ * _,-' delta
+ * P '
*
- * This eliminates most of the algorithms. Nelder and Mead's
- * simplex algorithm is still available and we will try that.
+ * r
+ * cost = delta (we use r=3)
+ * Q,e
*
- * In our application we are searching for the optimal locations of
- * N actualvertices in D3 (3) dimensions - ie, we are searching for
- * the optimal metapoint in an N*D3-dimensional space.
*
- * So eg with X=Y=100, the simplex will contain 300 metavertices
- * each of which is an array of 300 doubles for the actualvertex
- * coordinates. Hopefully this won't be too slow ...
+ * Calculation:
+ *
+ * Let vector A = PQ
+ * B = QR
+ *
+ * -1 A . B
+ * delta = tan -------
+ * | A x B |
+ *
+ * which is always in the range 0..pi because the denominator
+ * is nonnegative. We add epsilon to |AxB| to avoid division
+ * by zero.
+ *
+ * r
+ * cost = delta
+ * Q,e
*/
-static gsl_multimin_fminimizer *minimiser;
+double line_bending_cost(const Vertices vertices, int section) {
+ static const double axb_epsilon= 1e-6;
+ static const double exponent_r= 4;
-static const double stop_epsilon= 1e-6;
+ int pi,e,qi,ri, k;
+ double a[D3], b[D3], axb[D3];
+ double total_cost= 0;
-static double minfunc_f(const gsl_vector *x, void *params) {
- assert(x->size == DIM);
- assert(x->stride == 1);
- return compute_energy((const double(*)[D3])x->data);
-}
+ FOR_EDGE(qi,e,ri, OUTER) {
+ pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
-int main(int argc, const char *const *argv) {
- gsl_multimin_function multimin_function;
- double size;
- Vertices initial, step_size;
- FILE *initial_f;
- gsl_vector initial_gsl, step_size_gsl;
- int r, v, k;
+//if (!(qi&XMASK)) fprintf(stderr,"%02x-%02x-%02x (%d)\n",pi,qi,ri,e);
- if (argc!=3 || argv[1][0]=='-' || strncmp(argv[2],"-o",2))
- { fputs("usage: minimise <input> -o<output\n",stderr); exit(8); }
+ K a[k]= -vertices[pi][k] + vertices[qi][k];
+ K b[k]= -vertices[qi][k] + vertices[ri][k];
- input_file= argv[1];
- output_file= argv[2]+2;
- if (asprintf(&output_file_tmp,"%s.new",output_file) <= 0) diee("asprintf");
+ xprod(axb,a,b);
- graph_layout_prepare();
- printing_init();
-
- minimiser= gsl_multimin_fminimizer_alloc
- (gsl_multimin_fminimizer_nmsimplex, DIM);
- if (!minimiser) { perror("alloc minimiser"); exit(-1); }
+ double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
+ double cost= pow(delta,exponent_r);
- multimin_function.f= minfunc_f;
- multimin_function.n= DIM;
- multimin_function.params= 0;
+ total_cost += cost;
+ }
+ return total_cost;
+}
- initial_f= fopen(input_file,"rb"); if (!initial_f) diee("fopen initial");
- errno= 0; r= fread(initial,sizeof(initial),1,initial_f);
- if (r!=1) diee("fread");
- fclose(initial_f);
+/*---------- edge length variation ----------*/
- initial_gsl.size= DIM;
- initial_gsl.stride= 1;
- initial_gsl.block= 0;
- initial_gsl.owner= 0;
- step_size_gsl= initial_gsl;
+ /*
+ * Definition:
+ *
+ * See the diagram above.
+ * r
+ * cost = ( |PQ| - |QR| )
+ * Q,e
+ */
- initial_gsl.data= &initial[0][0];
- step_size_gsl.data= &step_size[0][0];
+double edge_length_variation_cost(const Vertices vertices, int section) {
+ double diff, cost= 0, exponent_r= 2;
+ int q, e,r, eback;
- FOR_VERTEX(v)
- K step_size[v][k]= 0.03;
-//int vx,vy;
-// FOR_RIM_VERTEX(vx,vy,v)
-// step_size[v][3] *= 0.1;
+ FOR_EDGE(q,e,r, OUTER) {
+ eback= edge_reverse(q,e);
+ diff= edge_lengths[q][e] - edge_lengths[q][eback];
+ cost += pow(diff,exponent_r);
+ }
+ return cost;
+}
- GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
- &initial_gsl, &step_size_gsl) );
+/*---------- rim proximity cost ----------*/
+
+static void find_nearest_oncircle(double oncircle[D3], const double p[D3]) {
+ /* By symmetry, nearest point on circle is the one with
+ * the same angle subtended at the z axis. */
+ oncircle[0]= p[0];
+ oncircle[1]= p[1];
+ oncircle[2]= 0;
+ double mult= 1.0/ magnD(oncircle);
+ oncircle[0] *= mult;
+ oncircle[1] *= mult;
+}
- for (;;) {
- GA( gsl_multimin_fminimizer_iterate(minimiser) );
+double rim_proximity_cost(const Vertices vertices, int section) {
+ double oncircle[3], cost=0;
+ int v;
- size= gsl_multimin_fminimizer_size(minimiser);
- r= gsl_multimin_test_size(size, stop_epsilon);
+ FOR_VERTEX(v, OUTER) {
+ int y= v >> YSHIFT;
+ int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
+ if (nominal_edge_distance==0) continue;
- if (printing_check(pr_size))
- printf("%*s size %# e, r=%d\n", 135,"", size, r);
- flushoutput();
+ find_nearest_oncircle(oncircle, vertices[v]);
- if (r==GSL_SUCCESS) break;
- assert(r==GSL_CONTINUE);
+ cost +=
+ vertex_mean_edge_lengths[v] *
+ (nominal_edge_distance*nominal_edge_distance) /
+ (hypotD2(vertices[v], oncircle) + 1e-6);
}
- return 0;
+ return cost;
}
-/*---------- Edgewise vertex displacement ----------*/
+/*---------- noncircular rim cost ----------*/
+
+double noncircular_rim_cost(const Vertices vertices, int section) {
+ int vy,vx,v;
+ double cost= 0.0;
+ double oncircle[3];
+
+ FOR_RIM_VERTEX(vy,vx,v, OUTER) {
+ find_nearest_oncircle(oncircle, vertices[v]);
+
+ double d2= hypotD2(vertices[v], oncircle);
+ cost += d2*d2;
+ }
+ return cost;
+}
+
+/*---------- overly sharp edge cost ----------*/
/*
- *
- *
*
* Q `-_
- * / | `-_
- * / | `-.
- * / M - - - - - S
- * / ' | _,-'
- * / ' | _,-'
- * / ' , P '
- * / ',-'
- * /,-'
+ * / | `-_ P'Q' ------ S'
+ * / | `-. _,' `. .
+ * / | S _,' : .
+ * / | _,-' _,' :r .r
+ * / | _,-' R' ' `. .
+ * / , P ' ` . r : .
+ * / ,-' ` . :
+ * /,-' ` C'
* /'
* R
*
- * Let delta = 180deg - angle RMS
*
- * Let l = |PQ|
- * d = |RS|
*
- * Giving energy contribution:
- *
- * 3
- * l delta
- * E = F . --------
- * vd, edge PQ vd d
- *
- *
- * (The dimensions of this are those of F_vd.)
+ * Let delta = angle between two triangles' normals
*
- * We calculate delta as atan2(|AxB|, A.B)
- * where A = PQ, B = QR
+ * Giving energy contribution:
*
- * In practice to avoid division by zero we'll add epsilon to d and
- * |AxB| and the huge energy ought then to be sufficient for the
- * model to avoid being close to R=S.
+ * 2
+ * E = F . delta
+ * vd, edge PQ vd
*/
-double edgewise_vertex_displacement_cost(const Vertices vertices) {
- static const double axb_epsilon= 1e-6;
+double edge_angle_cost(const Vertices vertices, int section) {
+ double pq1[D3], rp[D3], ps[D3], rp_2d[D3], ps_2d[D3], rs_2d[D3];
+ double a,b,c,s,r;
+ const double minradius_base= 0.2;
- int pi,e,qi,ri, k; //,si
- double a[D3], b[D3], axb[D3]; //m[D3],
+ int pi,e,qi,ri,si, k;
+// double our_epsilon=1e-6;
double total_cost= 0;
- FOR_EDGE(qi,e,ri) {
- pi= EDGE_END2(qi,(e+3)%V6); if (pi<0) continue;
+ FOR_EDGE(pi,e,qi, OUTER) {
+// if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
-// K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5;
- K a[k]= -vertices[pi][k] + vertices[qi][k];
- K b[k]= -vertices[qi][k] + vertices[ri][k];
+ si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
+ ri= EDGE_END2(pi,(e +1)%V6); if (ri<0) continue;
- xprod(axb,a,b);
-
- double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
- double cost= pow(delta,3);
+ K {
+ pq1[k]= -vertices[pi][k] + vertices[qi][k];
+ rp[k]= -vertices[ri][k] + vertices[pi][k];
+ ps[k]= -vertices[pi][k] + vertices[si][k];
+ }
- if (!e && !(qi & YMASK))
- cost *= 10;
+ normalise(pq1,1,1e-6);
+ xprod(rp_2d, rp,pq1); /* projects RP into plane normal to PQ */
+ xprod(ps_2d, ps,pq1); /* likewise PS */
+ K rs_2d[k]= rp_2d[k] + ps_2d[k];
+ /* radius of circumcircle of R'P'S' from Wikipedia
+ * `Circumscribed circle' */
+ a= magnD(rp_2d);
+ b= magnD(ps_2d);
+ c= magnD(rs_2d);
+ s= 0.5*(a+b+c);
+ r= a*b*c / sqrt((a+b+c)*(a-b+c)*(b-c+a)*(c-a+b) + 1e-6);
+
+ double minradius= minradius_base + edge_angle_cost_circcircrat*(a+b);
+ double deficit= minradius - r;
+ if (deficit < 0) continue;
+ double cost= deficit*deficit;
total_cost += cost;
}
- return total_cost;
-}
-/*---------- noncircular rim cost ----------*/
-
-double noncircular_rim_cost(const Vertices vertices) {
- int vy,vx,v;
- double cost= 0.0;
-
- FOR_RIM_VERTEX(vy,vx,v) {
- double oncircle[3];
- /* By symmetry, nearest point on circle is the one with
- * the same angle subtended at the z axis. */
- oncircle[0]= vertices[v][0];
- oncircle[1]= vertices[v][1];
- oncircle[2]= 0;
- double mult= 1.0/ magnD(oncircle);
- oncircle[0] *= mult;
- oncircle[1] *= mult;
- double d2= hypotD2(vertices[v], oncircle);
- cost += d2*d2;
- }
- return cost;
+ return total_cost;
}
-/*---------- printing rate limit ----------*/
-
-static volatile unsigned print_todo;
-static sigset_t print_alarmset;
-
-static int printing_check(enum printing_instance which) {
- static int skipped[pr__max];
-
- unsigned bits= 1u << which;
- int sk;
-
- if (!(print_todo & bits)) {
- skipped[which]++;
- return 0;;
- }
-
- sigprocmask(SIG_BLOCK,&print_alarmset,0);
- print_todo &= ~bits;
- sigprocmask(SIG_UNBLOCK,&print_alarmset,0);
+/*---------- small triangles cost ----------*/
- sk= skipped[which];
- if (sk) printf("[%4d] ",sk);
- else printf(" ");
- skipped[which]= 0;
+ /*
+ *
+ * Q `-_
+ * / | `-_
+ * / | `-.
+ * / | S
+ * / | _,-'
+ * / | _,-'
+ * / , P '
+ * / ,-'
+ * /,-'
+ * /'
+ * R
+ *
+ * Let delta = angle between two triangles' normals
+ *
+ * Giving energy contribution:
+ *
+ * 2
+ * E = F . delta
+ * vd, edge PQ vd
+ */
- return 1;
-}
+double small_triangles_cost(const Vertices vertices, int section) {
+ double pq[D3], ps[D3];
+ double x[D3];
+ int pi,e,qi,si, k;
+// double our_epsilon=1e-6;
+ double total_cost= 0;
-static void alarmhandler(int ignored) {
- print_todo= ~0u;
-}
+ FOR_EDGE(pi,e,qi, OUTER) {
+// if (!(RIM_VERTEX_P(pi) || RIM_VERTEX_P(qi))) continue;
-static void printing_init(void) {
- struct sigaction sa;
- struct itimerval itv;
+ si= EDGE_END2(pi,(e+V6-1)%V6); if (si<0) continue;
- sigemptyset(&print_alarmset);
- sigaddset(&print_alarmset,SIGALRM);
+ K {
+ pq[k]= vertices[qi][k] - vertices[pi][k];
+ ps[k]= vertices[si][k] - vertices[pi][k];
+ }
+ xprod(x, pq,ps);
- sa.sa_handler= alarmhandler;
- sa.sa_mask= print_alarmset;
- sa.sa_flags= SA_RESTART;
- if (sigaction(SIGALRM,&sa,0)) diee("sigaction ALRM");
-
- itv.it_interval.tv_sec= 0;
- itv.it_interval.tv_usec= 200000;
- itv.it_value= itv.it_interval;
+ double cost= 1/(magnD2(x) + 0.01);
- if (setitimer(ITIMER_REAL,&itv,0)) diee("setitimer REAL");
+//double cost= pow(magnD(spqxpqr), 3);
+//assert(dot>=-1 && dot <=1);
+//double cost= 1-dot;
+ total_cost += cost;
+ }
- raise(SIGALRM);
+ return total_cost;
}
~ian / moebius2.git / blobdiff