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compute complex max slope

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This commit is contained in:
Florian Stecker
2022-06-14 15:41:43 +02:00
parent 244784794d
commit 0763056ccb
4 changed files with 97 additions and 8 deletions
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48
complex_anosov.c
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@@ -9,6 +9,7 @@
#include <math.h>
#define LOOP(i,n) for(int i = 0; i < (n); i++)
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
/*
Elements up to length 0: 1
@@ -134,15 +135,50 @@ int main(int argc, char *argv[])
struct tracedata *traces;
int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);
mps_context *solver = mps_context_new();
mps_monomial_poly *poly = mps_monomial_poly_new(solver, 3);
mps_context_set_output_prec(solver, 20); // relative precision
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
double ev_real[3], ev_imag[3], ev_abs2[3];
double max_slope = 0;
int max_slope_id = 0;
LOOP(i, nuniq) {
printf("%d %f %f %f %f\n",
traces[i].id,
gaussian_sqrt5_real(traces[i].tr),
gaussian_sqrt5_imag(traces[i].tr),
gaussian_sqrt5_real(traces[i].trinv),
gaussian_sqrt5_imag(traces[i].trinv));
solve_characteristic_polynomial_d(solver, poly,
gaussian_sqrt5_real(traces[i].tr),
gaussian_sqrt5_imag(traces[i].tr),
gaussian_sqrt5_real(traces[i].trinv),
gaussian_sqrt5_imag(traces[i].trinv),
ev_real, ev_imag);
LOOP(j, 3) ev_abs2[j] = ev_real[j]*ev_real[j] + ev_imag[j]*ev_imag[j];
if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
SWAP(double, ev_abs2[0], ev_abs2[1]);
if(fabs(ev_abs2[1]) < fabs(ev_abs2[2]))
SWAP(double, ev_abs2[1], ev_abs2[2]);
if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
SWAP(double, ev_abs2[0], ev_abs2[1]);
if(log(ev_abs2[0]) < 1e-3) // we regard this as a finite order element
continue;
double slope = - log(ev_abs2[0]) / log(ev_abs2[2]);
if(slope > max_slope) {
max_slope = slope;
max_slope_id = traces[i].id;
}
printf("%d %f %f %f\n",
traces[i].id, log(ev_abs2[0]), log(ev_abs2[1]), log(ev_abs2[2]));
}
coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);
gmp_printf("q = %Qd + i*%Qd\tElements: %d\tTraces: %d\tMaximal slope: %f at %s\n", qreal, qimag, n, nuniq, max_slope, buf);
mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
mps_context_free(solver);
enumerate_tracedata_clear(traces, nuniq);
LOOP(i, 3) mat_clear(gen[i]);
coxeter_clear(group);