florian/triangle_reflection_complex
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triangle_reflection_complex/complex_anosov.c
Florian Stecker 429f0890d6 generate beautiful pictures of the complex Anosov set
2022-06-15 12:20:45 +02:00

305 lines
7.8 KiB
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#include "coxeter.h"
#include "enumerate.h"
#include "generators.h"
#include "mat.h"
#include "qext.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.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);
//#define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
#define INFO(msg, ...)
/*
Number of elements
up to length 0: 1
up to length 1: 4
up to length 2: 10
up to length 3: 22
up to length 4: 46
up to length 5: 91
up to length 6: 175
up to length 7: 334
up to length 8: 634
up to length 9: 1198
up to length 10: 2260
up to length 11: 4261
up to length 12: 8029
up to length 13: 15124
up to length 14: 28486
up to length 15: 53650
up to length 16: 101038
up to length 17: 190279
up to length 18: 358339
up to length 19: 674830
up to length 20: 1270846
up to length 21: 2393266
up to length 22: 4507012
up to length 23: 8487625
*/
static double gaussian_sqrt5_real(NUMBER x)
{
double result = 0.0;
mpq_t tmp;
mpq_init(tmp);
// a_0 + sqrt(5)a_1 + 4a_2 + 2sqrt(5)a_3
mpq_set_si(tmp, 4, 1);
mpq_mul(tmp, tmp, x->a[2]);
mpq_add(tmp, tmp, x->a[0]);
result = mpq_get_d(tmp);
mpq_set_si(tmp, 2, 1);
mpq_mul(tmp, tmp, x->a[3]);
mpq_add(tmp, tmp, x->a[1]);
result += mpq_get_d(tmp)*sqrt(5);
mpq_clear(tmp);
return result;
}
static double gaussian_sqrt5_imag(NUMBER x)
{
double result = 0.0;
mpq_t tmp;
mpq_init(tmp);
// a_1 + 2sqrt(5)a_2 + 14a_3
mpq_set_si(tmp, 14, 1);
mpq_mul(tmp, tmp, x->a[3]);
mpq_add(tmp, tmp, x->a[1]);
result = mpq_get_d(tmp);
mpq_set_si(tmp, 2, 1);
mpq_mul(tmp, tmp, x->a[2]);
result += mpq_get_d(tmp)*sqrt(5);
mpq_clear(tmp);
return result;
}
static int read_idlist(const char *filename, int *list)
{
FILE *f = fopen(filename, "r");
if(f == NULL) {
fprintf(stderr, "Could not open %s\n", filename);
exit(1);
}
char *line = NULL;
size_t len = 0;
ssize_t read;
int n = 0;
while ((read = getline(&line, &len, f)) != -1)
list[n++] = atoi(line);
if (line)
free(line);
fclose(f);
return n;
}
static int compare_int(const void *a, const void *b)
{
const int *aa = a;
const int *bb = b;
return (*aa > *bb) - (*aa < *bb);
}
static double runtime()
{
static struct timespec starttime;
static int started = 0;
if(!started) {
clock_gettime(CLOCK_MONOTONIC, &starttime);
started = 1;
}
struct timespec curtime;
double diff;
clock_gettime(CLOCK_MONOTONIC, &curtime);
return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
}
enum mode {
MODE_HELP,
MODE_EIGENVALUES,
MODE_SUMMARY,
MODE_TRACE_IDS
};
int main(int argc, char *argv[])
{
char buf[100];
int mode;
runtime(); // start timer
// parse arguments
if(argc < 2 || strcmp(argv[1], "help") == 0)
mode = MODE_HELP;
else if(strcmp(argv[1], "evs") == 0)
mode = MODE_EIGENVALUES;
else if(strcmp(argv[1], "summary") == 0)
mode = MODE_SUMMARY;
else if(strcmp(argv[1], "trace_ids") == 0)
mode = MODE_TRACE_IDS;
else
mode = MODE_HELP;
if(mode == MODE_HELP) {
fprintf(stderr, "Usage: %s <help|evs|summary|trace_ids> [arguments]\n", argv[0]);
fprintf(stderr, "%s help display this page\n", argv[0]);
fprintf(stderr, "%s evs <n> <q1> <q2> <q3> <treal> <timag> enumerate group and output unique (log) eigenvalue triples\n", argv[0]);
fprintf(stderr, "%s summary <n> <q1> <q2> <q3> <treal> <timag> only output max slope etc.\n", argv[0]);
fprintf(stderr, "%s trace_ids <n> <q1> <q2> <q3> <treal> <timag> list of ids of unique traces\n", argv[0]);
return 0;
}
if(argc < 8) {
fprintf(stderr, "Not enough arguments!\n");
return 0;
}
int n = atoi(argv[2]);
int nlist, nuniq;
int q[3];
mpq_t treal, timag;
q[0] = atoi(argv[3]);
q[1] = atoi(argv[4]);
q[2] = atoi(argv[5]);
mpq_inits(treal, timag, NULL);
mpq_set_str(treal, argv[6], 10);
mpq_set_str(timag, argv[7], 10);
mpq_canonicalize(treal);
mpq_canonicalize(timag);
// enumerate group
INFO("generate group\n");
group_t *group = coxeter_init_triangle(5, 5, 5, n);
// read list of elements we need to compute, or just fill it with all elements
INFO("prepare list\n");
int *idlist = malloc(n*sizeof(int));
char *id_file = getenv("IDLIST");
if(id_file != NULL) {
nlist = read_idlist(id_file, idlist);
// sort and symmetrize the list
qsort(idlist, nlist, sizeof(int), compare_int);
int ninverses = 0;
LOOP(i, nlist) {
int id = idlist[i];
int invid = group->elements[id].inverse->id;
if(!bsearch(&invid, idlist, nlist, sizeof(int), compare_int)) {
idlist[nlist+ninverses] = invid;
ninverses++;
}
}
nlist += ninverses;
qsort(idlist, nlist, sizeof(int), compare_int);
} else {
// just list all elements which have inverses
nlist = 0;
LOOP(i, n) {
if(group->elements[i].inverse)
idlist[nlist++] = i;
}
}
// get generator matrices
INFO("make generators\n");
mat gen[3];
LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
generators_triangle_reflection_group_555_complex(gen, q[0], q[1], q[2], treal, timag);
// compute the traces of all elements in idlist
INFO("enumerate traces\n");
struct tracedata *traces;
nuniq = enumerate_coxeter_group_traces(group, gen, &traces, idlist, nlist, 1);
// compute eigenvalues out of traces
INFO("compute eigenvalues\n");
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) {
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(mode == MODE_TRACE_IDS) {
// we only want to record unordered pairs here
if(CMP(traces[i].tr, traces[i].trinv) >= 0)
printf("%d\n", traces[i].id);
continue;
}
if(log(ev_abs2[0]) < 1e-6) // 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;
}
if(mode == MODE_EIGENVALUES) {
printf("%d %f %f %f\n",
traces[i].id, log(ev_abs2[0])/2, log(ev_abs2[1])/2, log(ev_abs2[2])/2);
}
}
// output summary
coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);
if(mode == MODE_SUMMARY) {
gmp_fprintf(stdout, "%f %f %d %d %d %f %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
} else if(mode == MODE_EIGENVALUES) {
gmp_fprintf(stderr, "q = %.2f + i*%.2f\tn = %d\tnlist = %d\tnuniq = %d\tMaximal slope: %f at %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
} else if(mode == MODE_TRACE_IDS) {
gmp_fprintf(stderr, "q = %.2f + i*%.2f\tElements: %d\tTraces: %d\n", mpq_get_d(treal), mpq_get_d(timag), n, nuniq);
}
// clean up
INFO("clean up\n");
// mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
mps_context_free(solver);
enumerate_tracedata_clear(traces, nuniq);
free(idlist);
LOOP(i, 3) mat_clear(gen[i]);
coxeter_clear(group);
mpq_clears(treal, timag, NULL);
return 0;
}
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