compute complex max slope
This commit is contained in:
Florian Stecker
parent
244784794d
commit
0763056ccb
4
Makefile
4
Makefile
@ -1,8 +1,8 @@
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HEADERS=mat.h coxeter.h enumerate.h generators.h qext.h
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SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
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#SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
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SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
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#SPECIAL_OPTIONS=
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@ -9,6 +9,7 @@
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#include <math.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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/*
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Elements up to length 0: 1
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@ -134,15 +135,50 @@ int main(int argc, char *argv[])
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struct tracedata *traces;
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int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);
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mps_context *solver = mps_context_new();
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mps_monomial_poly *poly = mps_monomial_poly_new(solver, 3);
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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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double ev_real[3], ev_imag[3], ev_abs2[3];
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double max_slope = 0;
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int max_slope_id = 0;
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LOOP(i, nuniq) {
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printf("%d %f %f %f %f\n",
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traces[i].id,
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solve_characteristic_polynomial_d(solver, poly,
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gaussian_sqrt5_real(traces[i].tr),
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gaussian_sqrt5_imag(traces[i].tr),
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gaussian_sqrt5_real(traces[i].trinv),
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gaussian_sqrt5_imag(traces[i].trinv));
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gaussian_sqrt5_imag(traces[i].trinv),
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ev_real, ev_imag);
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LOOP(j, 3) ev_abs2[j] = ev_real[j]*ev_real[j] + ev_imag[j]*ev_imag[j];
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if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
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SWAP(double, ev_abs2[0], ev_abs2[1]);
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if(fabs(ev_abs2[1]) < fabs(ev_abs2[2]))
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SWAP(double, ev_abs2[1], ev_abs2[2]);
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if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
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SWAP(double, ev_abs2[0], ev_abs2[1]);
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if(log(ev_abs2[0]) < 1e-3) // we regard this as a finite order element
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continue;
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double slope = - log(ev_abs2[0]) / log(ev_abs2[2]);
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if(slope > max_slope) {
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max_slope = slope;
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max_slope_id = traces[i].id;
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}
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printf("%d %f %f %f\n",
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traces[i].id, log(ev_abs2[0]), log(ev_abs2[1]), log(ev_abs2[2]));
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}
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coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);
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gmp_printf("q = %Qd + i*%Qd\tElements: %d\tTraces: %d\tMaximal slope: %f at %s\n", qreal, qimag, n, nuniq, max_slope, buf);
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mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
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mps_context_free(solver);
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enumerate_tracedata_clear(traces, nuniq);
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LOOP(i, 3) mat_clear(gen[i]);
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coxeter_clear(group);
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49
enumerate.c
49
enumerate.c
@ -120,3 +120,52 @@ void enumerate_tracedata_clear(struct tracedata *traces, int n)
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}
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free(traces);
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}
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// returns squares of absolute values
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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)
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{
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// mpq_t coeff1, coeff2, zero;
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cplx_t *roots;
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double radii[3];
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double *radii_p[3];
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mps_boolean errors;
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int result = 0;
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/*
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mpq_inits(coeff1, coeff2, zero, NULL);
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mpq_set(coeff1, trinv);
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mpq_sub(coeff2, zero, tr);
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*/
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mps_monomial_poly_set_coefficient_d(solv, poly, 0, -1, 0);
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mps_monomial_poly_set_coefficient_d(solv, poly, 1, trinv_real, trinv_imag);
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mps_monomial_poly_set_coefficient_d(solv, poly, 2, -tr_real, -tr_imag);
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// mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
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// mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
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mps_monomial_poly_set_coefficient_d(solv, poly, 3, 1, 0);
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mps_context_set_input_poly(solv, (mps_polynomial*)poly);
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mps_mpsolve(solv);
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roots = cplx_valloc(3);
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for(int i = 0; i < 3; i++)
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radii_p[i] = &(radii[i]);
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mps_context_get_roots_d(solv, &roots, radii_p);
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errors = mps_context_has_errors(solv);
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if(errors) {
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result = 1;
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} else {
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for(int i = 0; i < 3; i++) {
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eigenvalues_real[i] = cplx_Re(roots[i]);
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eigenvalues_imag[i] = cplx_Im(roots[i]);
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// if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
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// result = 2;
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}
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}
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cplx_vfree(roots);
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// mpq_clears(coeff1, coeff2, zero, NULL);
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return result;
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}
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@ -4,6 +4,8 @@
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#include "mat.h"
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#include "coxeter.h"
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#include <mps/mps.h>
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struct tracedata {
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int id;
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NUMBER tr;
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@ -15,4 +17,6 @@ int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **
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void enumerate_tracedata_clear(struct tracedata *traces, int n);
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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);
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#endif
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