*/
#include "common.h"
-#include "bgl.h"
+#include "minimise.h"
#include "mgraph.h"
-#include <gsl/gsl_errno.h>
-#include <gsl/gsl_multimin.h>
+double vertex_areas[N], vertex_mean_edge_lengths[N], edge_lengths[N][V6];
-#define BEST_F "best"
-#define INITIAL_F "initial"
-
-static double edgewise_vertex_displacement_cost(const Vertices vertices);
-static double noncircular_rim_cost(const Vertices vertices);
-
-static void compute_vertex_areas(const Vertices vertices, double areas[N]);
static double best_energy= DBL_MAX;
-static void cost(double *energy, double tweight, double tcost);
-#define COST(weight, compute) cost(&energy, (weight), (compute))
+static void addcost(double *energy, double tweight, double tcost, int pr);
+#define COST(weight, compute) addcost(&energy, (weight), (compute), printing)
+
+void energy_init(void) {
+}
/*---------- main energy computation and subroutines ----------*/
-static double compute_energy(const Vertices vertices) {
- double vertex_areas[N], energy;
+double compute_energy(const struct Vertices *vs) {
+ static int bests_unprinted;
+
+ double energy;
+ int printing;
- compute_vertex_areas(vertices,vertex_areas);
+ compute_edge_lengths(vs->a);
+ compute_vertex_areas(vs->a);
energy= 0;
- printf("cost > energy |");
- COST(1000.0, edgewise_vertex_displacement_cost(vertices));
- COST(1.0, graph_layout_cost(vertices,vertex_areas));
- COST(1e3, noncircular_rim_cost(vertices));
-
- printf("| total %# e |", energy);
+ printing= printing_check(pr_cost,0);
+
+ if (printing) printf("%15lld c>e |", evaluations);
+
+ if (XBITS==3) {
+ COST( 3e2, line_bending_cost(vs->a));
+ COST( 1e3, edge_length_variation_cost(vs->a));
+ COST( 0.2e3, rim_proximity_cost(vs->a));
+ COST( 1e8, noncircular_rim_cost(vs->a));
+ stop_epsilon= 1e-6;
+ } else if (XBITS==4) {
+ COST( 3e2, line_bending_cost(vs->a));
+ COST( 3e3, edge_length_variation_cost(vs->a));
+ COST( 3.8e1, rim_proximity_cost(vs->a)); // 5e1 is too much
+ // 2.5e1 is too little
+ // 0.2e1 grows compared to previous ?
+ // 0.6e0 shrinks compared to previous ?
+ COST( 1e12, noncircular_rim_cost(vs->a));
+ stop_epsilon= 1e-5;
+ } else {
+ abort();
+ }
+
+ if (printing) printf("| total %# e |", energy);
+
if (energy < best_energy) {
FILE *best_f;
int r;
-
- printf(" BEST");
-
- best_f= fopen(BEST_F ".new","wb"); if (!best_f) diee("fopen new best");
- r= fwrite(vertices,sizeof(vertices),1,best_f); if (r!=1) diee("fwrite");
+
+ if (printing) {
+ printf(" BEST");
+ if (bests_unprinted) printf(" [%4d]",bests_unprinted);
+ bests_unprinted= 0;
+ } else {
+ bests_unprinted++;
+ }
+
+ 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(BEST_F ".new", BEST_F)) diee("rename install new best");
+ if (rename(best_file_tmp,best_file)) diee("rename install new best");
+
+ best_energy= energy;
+ }
+ if (printing) {
+ putchar('\n');
+ flushoutput();
}
- putchar('\n');
- flushoutput();
+ evaluations++;
return energy;
-}
+}
-static void cost(double *energy, double tweight, double tcost) {
+static void addcost(double *energy, double tweight, double tcost, int pr) {
double tenergy= tweight * tcost;
- 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 ----------*/
+
+void compute_edge_lengths(const Vertices vertices) {
+ int v1,e,v2;
+
+ FOR_EDGE(v1,e,v2)
+ edge_lengths[v1][e]= hypotD(vertices[v1],vertices[v2]);
+}
+
+void compute_vertex_areas(const Vertices vertices) {
+ int v0,v1,v2, e1,e2;
+// int k;
+
FOR_VERTEX(v0) {
- double total= 0.0;
+ double total= 0.0, edges_total=0;
int count= 0;
-
+
FOR_VEDGE(v0,e1,v1) {
e2= (e1+1) % V6;
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:
+ *
+ * At each vertex Q, in each direction e:
+ *
+ * e
+ * Q ----->----- R
+ * _,-'\__/
+ * _,-' delta
+ * P '
+ *
+ * r
+ * cost = delta (we use r=3)
+ * Q,e
*
- * 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.
*
- * 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).
+ * Calculation:
*
- * This eliminates most of the algorithms. Nelder and Mead's
- * simplex algorithm is still available and we will try that.
+ * Let vector A = PQ
+ * B = QR
*
- * 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 ...
+ * -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) {
+ static const double axb_epsilon= 1e-6;
+ static const double exponent_r= 3;
-static const double stop_epsilon= 1e-4;
+ 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) {
+ 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, vx,vy, k;
-
- if (argc>1) { fputs("takes no arguments\n",stderr); exit(8); }
+ K a[k]= -vertices[pi][k] + vertices[qi][k];
+ K b[k]= -vertices[qi][k] + vertices[ri][k];
- minimiser= gsl_multimin_fminimizer_alloc
- (gsl_multimin_fminimizer_nmsimplex, DIM);
- if (!minimiser) { perror("alloc minimiser"); exit(-1); }
+ xprod(axb,a,b);
- multimin_function.f= minfunc_f;
- multimin_function.n= DIM;
- multimin_function.params= 0;
+ double delta= atan2(magnD(axb) + axb_epsilon, dotprod(a,b));
+ double cost= pow(delta,exponent_r);
- initial_f= fopen(INITIAL_F,"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);
+ if (!e && !(qi & ~XMASK))
+ cost *= 10;
- initial_gsl.size= DIM;
- initial_gsl.stride= 1;
- initial_gsl.block= 0;
- initial_gsl.owner= 0;
- step_size_gsl= initial_gsl;
-
- initial_gsl.data= (double*)initial;
- step_size_gsl.data= (double*)step_size;
-
- FOR_VERTEX(v)
- K step_size[v][k]= 1e-3;
- FOR_RIM_VERTEX(vx,vy,v)
- step_size[v][3] *= 0.1;
+ total_cost += cost;
+ }
+ return total_cost;
+}
- GA( gsl_multimin_fminimizer_set(minimiser, &multimin_function,
- &initial_gsl, &step_size_gsl) );
-
- for (;;) {
- GA( gsl_multimin_fminimizer_iterate(minimiser) );
+/*---------- edge length variation ----------*/
- size= gsl_multimin_fminimizer_size(minimiser);
- r= gsl_multimin_test_size(size, stop_epsilon);
+ /*
+ * Definition:
+ *
+ * See the diagram above.
+ * r
+ * cost = ( |PQ| - |QR| )
+ * Q,e
+ */
- printf("size %# e, r=%d\n", size, r);
- flushoutput();
+double edge_length_variation_cost(const Vertices vertices) {
+ double diff, cost= 0, exponent_r= 2;
+ int q, e,r, eback;
- if (r==GSL_SUCCESS) break;
- assert(r==GSL_CONTINUE);
+ FOR_EDGE(q,e,r) {
+ eback= edge_reverse(q,e);
+ diff= edge_lengths[q][e] - edge_lengths[q][eback];
+ cost += pow(diff,exponent_r);
}
- return 0;
+ return cost;
}
-/*---------- Edgewise vertex displacement ----------*/
+/*---------- 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;
+}
- /*
- *
- *
- *
- * Q `-_
- * / | `-_
- * R' - _ _ _/_ | `-.
- * . / M - - - - - S
- * . / | _,-'
- * . / | _,-'
- * . / , P '
- * . / ,-'
- * . /,-'
- * . /'
- * R
- *
- *
- *
- * Find R', the `expected' location of R, by
- * reflecting S in M (the midpoint of QP).
- *
- * Let 2d = |RR'|
- * b = |PQ|
- * l = |RS|
- *
- * Giving energy contribution:
- *
- * 2
- * b d
- * E = F . ----
- * vd, edge PQ vd 3
- * l
- *
- * (The dimensions of this are those of F_vd.)
- *
- * By symmetry, this calculation gives the same answer with R and S
- * exchanged. Looking at the projection in the RMS plane:
- *
- *
- * S'
- * ,'
- * ,'
- * R' ,' 2d" = |SS'| = |RR'| = 2d
- * `-._ ,'
- * `-._ ,' By congruent triangles,
- * ` M with M' = midpoint of RS,
- * ,' `-._ |MM'| = |RR'|/2 = d
- * ,' `-._
- * ,' ` S So use
- * ,' M' _ , - ' d = |MM'|
- * ,' _ , - '
- * R - '
- *
- * We choose this value for l (rather than |RM|+|MS|, say, or |RM|)
- * because we want this symmetry and because we're happy to punish
- * bending more than uneveness in the metric.
- *
- * In practice to avoid division by zero we'll add epsilon to l^3
- * and the huge energy ought then to be sufficient for the model to
- * avoid being close to R=S.
- */
+double rim_proximity_cost(const Vertices vertices) {
+ double oncircle[3], cost=0;
+ int v;
+
+ FOR_VERTEX(v) {
+ int y= v >> YSHIFT;
+ int nominal_edge_distance= y <= Y/2 ? y : Y-1-y;
+ if (nominal_edge_distance==0) continue;
+
+ find_nearest_oncircle(oncircle, vertices[v]);
-static double edgewise_vertex_displacement_cost(const Vertices vertices) {
- static const double l3_epsilon= 1e-6;
-
- int pi,e,qi,ri,si, k;
- double m[D3], mprime[D3], b, d2, l, sigma_bd2_l3=0;
-
- FOR_EDGE(pi,e,qi) {
- ri= EDGE_END2(pi,(e+1)%V6); if (ri<0) continue;
- si= EDGE_END2(pi,(e+5)%V6); if (si<0) continue;
- /* assert(ri == EDGE_END2(qi,(e+2)%V6)); */
- /* assert(si == EDGE_END2(qi,(e+4)%V6)); */
-
- K m[k]= (vertices[pi][k] + vertices[qi][k]) * 0.5;
- K mprime[k]= (vertices[ri][k] + vertices[si][k]) * 0.5;
- b= hypotD(vertices[pi], vertices[qi]);
- d2= hypotD2(m, mprime);
- l= hypotD(vertices[ri], vertices[si]);
- double l3 = l*l*l + l3_epsilon;
-
- sigma_bd2_l3 += b * d2 / l3;
+ cost +=
+ vertex_mean_edge_lengths[v] *
+ (nominal_edge_distance*nominal_edge_distance) /
+ (hypotD2(vertices[v], oncircle) + 1e-6);
}
- return sigma_bd2_l3;
+ return cost;
}
/*---------- noncircular rim cost ----------*/
-static double noncircular_rim_cost(const Vertices vertices) {
+double noncircular_rim_cost(const Vertices vertices) {
int vy,vx,v;
double cost= 0.0;
-
+ double oncircle[3];
+
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;
+ find_nearest_oncircle(oncircle, vertices[v]);
+
double d2= hypotD2(vertices[v], oncircle);
cost += d2*d2;
}
~ian / moebius2.git / blobdiff