265 lines
7.1 KiB
C
265 lines
7.1 KiB
C
#include "coxeter.h"
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#include "linalg.h"
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#include "mat.h"
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#include "enumerate_triangle_group.h"
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
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#define DEBUG(msg, ...)
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struct result {
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int id;
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int count;
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mpq_t tr;
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mpq_t trinv;
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double x;
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double y;
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};
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static int compare_result(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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d = mpq_cmp((*a)->tr,(*b)->tr);
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if(d == 0) {
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d = mpq_cmp((*a)->trinv, (*b)->trinv);
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}
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return d;
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}
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static int compare_result_with_id(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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d = mpq_cmp((*a)->tr,(*b)->tr);
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if(d == 0) {
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d = mpq_cmp((*a)->trinv, (*b)->trinv);
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if(d == 0) {
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d = (*b)->id - (*a)->id;
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}
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}
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return d;
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}
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static int compare_result_by_slope(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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double slopea = (*a)->x / (*a)->y;
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double slopeb = (*b)->x / (*b)->y;
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return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
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}
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int main(int argc, char *argv[])
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{
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mpq_t s, q, t, tmp;
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double sapprox, tapprox, qapprox, tqfactor;
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mat *matrices;
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group_t *group;
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int index;
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mps_context *solver;
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int acc = 100;
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int n, nuniq, nmax;
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int retval;
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double evs[3];
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double max_slope;
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char buf[100];
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char buf2[100];
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struct result *invariants;
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struct result **distinct_invariants;
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if(argc < 4) {
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fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]);
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exit(1);
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}
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nmax = atoi(argv[1]);
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DEBUG("Allocate\n");
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mpq_inits(s, q, t, tmp, NULL);
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matrices = malloc(nmax*sizeof(mat));
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for(int i = 0; i < nmax; i++)
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mat_init(matrices[i], 3);
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invariants = malloc(nmax*sizeof(struct result));
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distinct_invariants = malloc(nmax*sizeof(struct result));
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for(int i = 0; i < nmax; i++) {
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mpq_init(invariants[i].tr);
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mpq_init(invariants[i].trinv);
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distinct_invariants[i] = &invariants[i];
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}
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solver = mps_context_new();
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mps_context_set_output_prec(solver, 20); // relative precision
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mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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DEBUG("Approximate parameters\n");
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// get approximate s and q values
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sapprox = atof(argv[2]);
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qapprox = atof(argv[3]);
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// tapprox = atof(argv[3]);
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// tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
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// qapprox = tapprox/tqfactor;
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, sapprox, i);
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if(fabs(mpq_get_d(t)-sapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(s, tmp);
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}
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mpq_canonicalize(s);
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, qapprox, i);
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if(fabs(mpq_get_d(t)-qapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(q, tmp);
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}
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mpq_canonicalize(q);
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tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);
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// group
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// order of the triangle reflection generators: a, b, c
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// order of the rotation orders: bc, ac, ab
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DEBUG("Generate group\n");
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group = coxeter_init_triangle(4, 3, 3, nmax);
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DEBUG("Compute matrices\n");
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enumerate(group, matrices, 4, 3, 3, s, q);
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n = 0;
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DEBUG("Compute traces\n");
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for(int i = 0; i < nmax; i++) {
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if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
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continue;
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invariants[i].id = i;
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mat_trace(invariants[i].tr, matrices[i]);
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mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
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distinct_invariants[n++] = &invariants[i];
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}
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DEBUG("Get unique traces\n");
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qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
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nuniq = 0;
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for(int i = 0; i < n; i++) {
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if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0) {
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distinct_invariants[nuniq] = distinct_invariants[i];
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distinct_invariants[nuniq]->count = 1;
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nuniq++;
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} else {
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distinct_invariants[nuniq-1]->count++;
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int oldlength = group->elements[distinct_invariants[nuniq-1]->id].length;
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int newlength = group->elements[distinct_invariants[i]->id].length;
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if(newlength < oldlength)
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distinct_invariants[nuniq-1]->id = distinct_invariants[i]->id;
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}
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// gmp_printf("%d %d %s\n", i, nuniq-1, print_word(&group->elements[i], buf));
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}
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max_slope = 0;
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int max_slope_index;
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DEBUG("Solve characteristic polynomials\n");
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for(int i = 0; i < nuniq; i++) {
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retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
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if(retval == 1) {
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fprintf(stderr, "Error! Could not solve polynomial.\n");
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continue;
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} else if(retval == 2) {
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continue;
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}
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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if(fabs(evs[1]) < fabs(evs[2]))
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SWAP(double, evs[1], evs[2]);
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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double x = log(fabs(evs[0]));
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double y = -log(fabs(evs[2]));
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distinct_invariants[i]->x = x;
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distinct_invariants[i]->y = y;
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if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
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max_slope_index = distinct_invariants[i] - invariants;
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max_slope = y/x;
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}
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}
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qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);
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gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
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// printf("- 0 0 - - - - 0.5\n");
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int cumulative = 0;
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double slope;
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for(int i = 0; i < nuniq; i++) {
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slope = distinct_invariants[i]->y/distinct_invariants[i]->x;
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mpq_set_si(tmp, 1, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
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continue;
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}
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mpq_set_si(tmp, 0, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
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continue;
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}
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mpq_set_si(tmp, -1, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
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continue;
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}
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mpq_set_si(tmp, 3, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
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continue;
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}
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cumulative += distinct_invariants[i]->count;
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gmp_printf("%d %d %d %Qd %Qd %f %f %f %f %f %s\n",
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distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
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distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
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log(fabs(mpq_get_d(distinct_invariants[i]->tr))), log(fabs(mpq_get_d(distinct_invariants[i]->trinv))),
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distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
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print_word(&group->elements[distinct_invariants[i]->id], buf)
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);
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}
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// printf("- 0 %d - - - - 2.0\n", cumulative);
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DEBUG("Clean up\n");
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for(int i = 0; i < nmax; i++) {
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mpq_clear(invariants[i].tr);
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mpq_clear(invariants[i].trinv);
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}
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free(invariants);
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free(distinct_invariants);
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for(int i = 0; i < nmax; i++)
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mat_clear(matrices[i]);
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free(matrices);
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coxeter_clear(group);
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mpq_clears(s, q, t, tmp, NULL);
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mps_context_free(solver);
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}
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