compute complex max slope

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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@ -1,8 +1,8 @@
HEADERS=mat.h coxeter.h enumerate.h generators.h qext.h HEADERS=mat.h coxeter.h enumerate.h generators.h qext.h
SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT #SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
#SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline #SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL #SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
#SPECIAL_OPTIONS= #SPECIAL_OPTIONS=

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@ -9,6 +9,7 @@
#include <math.h> #include <math.h>
#define LOOP(i,n) for(int i = 0; i < (n); i++) #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 Elements up to length 0: 1
@ -134,15 +135,50 @@ int main(int argc, char *argv[])
struct tracedata *traces; struct tracedata *traces;
int nuniq = enumerate_coxeter_group_traces(group, gen, &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) { LOOP(i, nuniq) {
printf("%d %f %f %f %f\n", solve_characteristic_polynomial_d(solver, poly,
traces[i].id, gaussian_sqrt5_real(traces[i].tr),
gaussian_sqrt5_real(traces[i].tr), gaussian_sqrt5_imag(traces[i].tr),
gaussian_sqrt5_imag(traces[i].tr), gaussian_sqrt5_real(traces[i].trinv),
gaussian_sqrt5_real(traces[i].trinv), gaussian_sqrt5_imag(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); enumerate_tracedata_clear(traces, nuniq);
LOOP(i, 3) mat_clear(gen[i]); LOOP(i, 3) mat_clear(gen[i]);
coxeter_clear(group); coxeter_clear(group);

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@ -120,3 +120,52 @@ void enumerate_tracedata_clear(struct tracedata *traces, int n)
} }
free(traces); free(traces);
} }
// returns squares of absolute values
int solve_characteristic_polynomial_d(mps_context *solv, mps_monomial_poly *poly, double tr_real, double tr_imag, double trinv_real, double trinv_imag, double *eigenvalues_real, double *eigenvalues_imag)
{
// mpq_t coeff1, coeff2, zero;
cplx_t *roots;
double radii[3];
double *radii_p[3];
mps_boolean errors;
int result = 0;
/*
mpq_inits(coeff1, coeff2, zero, NULL);
mpq_set(coeff1, trinv);
mpq_sub(coeff2, zero, tr);
*/
mps_monomial_poly_set_coefficient_d(solv, poly, 0, -1, 0);
mps_monomial_poly_set_coefficient_d(solv, poly, 1, trinv_real, trinv_imag);
mps_monomial_poly_set_coefficient_d(solv, poly, 2, -tr_real, -tr_imag);
// mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
// mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
mps_monomial_poly_set_coefficient_d(solv, poly, 3, 1, 0);
mps_context_set_input_poly(solv, (mps_polynomial*)poly);
mps_mpsolve(solv);
roots = cplx_valloc(3);
for(int i = 0; i < 3; i++)
radii_p[i] = &(radii[i]);
mps_context_get_roots_d(solv, &roots, radii_p);
errors = mps_context_has_errors(solv);
if(errors) {
result = 1;
} else {
for(int i = 0; i < 3; i++) {
eigenvalues_real[i] = cplx_Re(roots[i]);
eigenvalues_imag[i] = cplx_Im(roots[i]);
// if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
// result = 2;
}
}
cplx_vfree(roots);
// mpq_clears(coeff1, coeff2, zero, NULL);
return result;
}

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@ -4,6 +4,8 @@
#include "mat.h" #include "mat.h"
#include "coxeter.h" #include "coxeter.h"
#include <mps/mps.h>
struct tracedata { struct tracedata {
int id; int id;
NUMBER tr; NUMBER tr;
@ -15,4 +17,6 @@ int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **
void enumerate_tracedata_clear(struct tracedata *traces, int n); void enumerate_tracedata_clear(struct tracedata *traces, int n);
int solve_characteristic_polynomial_d(mps_context *solv, mps_monomial_poly *poly, double tr_real, double tr_imag, double trinv_real, double trinv_imag, double *eigenvalues_real, double *eigenvalues_imag);
#endif #endif