florian/triangle_reflection_complex
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fix bugs in sorting and inconsistency with nex coxeter algorithm

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This commit is contained in:
Florian Stecker 2020-08-10 14:00:52 -04:00
parent 9cb2e44867
commit 581a030235
2 changed files with 35 additions and 17 deletions
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51
singular_values.c
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@ -9,6 +9,9 @@
//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__) //#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
#define DEBUG(msg, ...) #define DEBUG(msg, ...)
#define OUTPUT_POINTS
//#define OUTPUT_POINTS
struct result { struct result {
mpq_t tr; mpq_t tr;
mpq_t trinv; mpq_t trinv;
@ -23,7 +26,7 @@ static int compare_result(const void *a_, const void *b_)
d = mpq_cmp((*a)->tr,(*b)->tr); d = mpq_cmp((*a)->tr,(*b)->tr);
if(d == 0) if(d == 0)
mpq_cmp((*a)->trinv, (*b)->trinv); d = mpq_cmp((*a)->trinv, (*b)->trinv);
return d; return d;
} }
@ -356,11 +359,12 @@ int main(int argc, char *argv[])
int index; int index;
mps_context *solver; mps_context *solver;
int acc = 100; int acc = 100;
int n; int n, nuniq, nmax;
int retval; int retval;
double evs[3]; double evs[3];
double max_slope; double max_slope;
int nmax; char buf[100];
char buf2[100];
struct result *invariants; struct result *invariants;
struct result **distinct_invariants; struct result **distinct_invariants;
@ -413,15 +417,18 @@ int main(int argc, char *argv[])
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); 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);
// gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor); #ifdef OUTPUT_POINTS
gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
#endif
// group // group
DEBUG("Generate group\n"); DEBUG("Generate group\n");
group = coxeter_init_triangle(3, 3, 4, nmax); group = coxeter_init_triangle(4, 3, 3, nmax);
DEBUG("Compute matrices\n"); DEBUG("Compute matrices\n");
enumerate(group, matrices, s, q); enumerate(group, matrices, s, q);
n = 0;
DEBUG("Compute traces\n"); DEBUG("Compute traces\n");
for(int i = 0; i < nmax; i++) { for(int i = 0; i < nmax; i++) {
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse) if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
@ -429,21 +436,25 @@ int main(int argc, char *argv[])
mat_trace(invariants[i].tr, matrices[i]); mat_trace(invariants[i].tr, matrices[i]);
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]); mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
distinct_invariants[n++] = &invariants[i];
} }
DEBUG("Get unique traces\n"); DEBUG("Get unique traces\n");
qsort(distinct_invariants, nmax, sizeof(struct result*), compare_result);
n = 0; qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
for(int i = 0; i < nmax; i++) {
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[n-1]) != 0) nuniq = 0;
distinct_invariants[n++] = distinct_invariants[i]; for(int i = 0; i < n; i++) {
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
distinct_invariants[nuniq++] = distinct_invariants[i];
} }
max_slope = 0; max_slope = 0;
int max_slope_index;
DEBUG("Solve characteristic polynomials\n"); DEBUG("Solve characteristic polynomials\n");
for(int i = 0; i < n; i++) { for(int i = 0; i < nuniq; i++) {
retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs); retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
if(retval == 1) { if(retval == 1) {
fprintf(stderr, "Error! Could not solve polynomial.\n"); fprintf(stderr, "Error! Could not solve polynomial.\n");
@ -459,16 +470,22 @@ int main(int argc, char *argv[])
if(fabs(evs[0]) < fabs(evs[1])) if(fabs(evs[0]) < fabs(evs[1]))
SWAP(double, evs[0], evs[1]); SWAP(double, evs[0], evs[1]);
double x = log(evs[0]); double x = log(fabs(evs[0]));
double y = -log(evs[2]); double y = -log(fabs(evs[2]));
if(y/x > max_slope && (x > 0.1 || y > 0.1)) if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
max_slope_index = distinct_invariants[i] - invariants;
max_slope = y/x; max_slope = y/x;
gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
} }
// printf("%.3f %.3f %f\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope); #ifdef OUTPUT_POINTS
gmp_printf("%Qd %Qd %f %f %f %d\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
#endif
}
#ifdef OUTPUT_SUMMARY
fprintf(stdout, "%.3f %.3f %f %s\n", mpq_get_d(s), mpq_get_d(q)*tqfactor, max_slope, print_word(&group->elements[max_slope_index], buf));
#endif
// output_invariants(group, matrices, s, q, solver); // output_invariants(group, matrices, s, q, solver);

3
singular_values.plt
View File

@ -1,7 +1,8 @@
if(!exists("logt")) logt = log(1.78) if(!exists("logt")) logt = log(1.78)
if(!exists("logs")) logs = log(0.5) if(!exists("logs")) logs = log(0.5)
file = sprintf("< ./singular_values 1000 %f %f", exp(logs), exp(logt)) #file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
set zeroaxis set zeroaxis
set samples 1000 set samples 1000