generate beautiful pictures of the complex Anosov set
This commit is contained in:
Florian Stecker
parent
729d1a10b7
commit
429f0890d6
242
complex_anosov.c
242
complex_anosov.c
@ -8,35 +8,39 @@
|
||||
#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, ...)
|
||||
|
||||
/*
|
||||
Elements up to length 0: 1
|
||||
Elements up to length 1: 4
|
||||
Elements up to length 2: 10
|
||||
Elements up to length 3: 22
|
||||
Elements up to length 4: 46
|
||||
Elements up to length 5: 91
|
||||
Elements up to length 6: 175
|
||||
Elements up to length 7: 334
|
||||
Elements up to length 8: 634
|
||||
Elements up to length 9: 1198
|
||||
Elements up to length 10: 2260
|
||||
Elements up to length 11: 4261
|
||||
Elements up to length 12: 8029
|
||||
Elements up to length 13: 15124
|
||||
Elements up to length 14: 28486
|
||||
Elements up to length 15: 53650
|
||||
Elements up to length 16: 101038
|
||||
Elements up to length 17: 190279
|
||||
Elements up to length 18: 358339
|
||||
Elements up to length 19: 674830
|
||||
Elements up to length 20: 1270846
|
||||
Elements up to length 21: 2393266
|
||||
Elements up to length 22: 4507012
|
||||
Elements up to length 23: 8487625
|
||||
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)
|
||||
@ -82,9 +86,56 @@ static double gaussian_sqrt5_imag(NUMBER x)
|
||||
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_TRACES,
|
||||
MODE_EIGENVALUES,
|
||||
MODE_SUMMARY,
|
||||
MODE_TRACE_IDS
|
||||
};
|
||||
@ -94,10 +145,13 @@ 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], "traces") == 0)
|
||||
mode = MODE_TRACES;
|
||||
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)
|
||||
@ -106,72 +160,78 @@ int main(int argc, char *argv[])
|
||||
mode = MODE_HELP;
|
||||
|
||||
if(mode == MODE_HELP) {
|
||||
fprintf(stderr, "Usage: %s <help|traces|summary|trace_ids> [arguments]\n", argv[0]);
|
||||
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 traces <n> <qreal> <qimag> enumerate group and output unique trace/trace inverse pairs\n", argv[0]);
|
||||
fprintf(stderr, "%s summary <n> <qreal> <qimag> only output max slope etc.\n", argv[0]);
|
||||
fprintf(stderr, "%s trace_ids <n> <qreal> <qimag> list of ids of unique traces\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 < 5) {
|
||||
if(argc < 8) {
|
||||
fprintf(stderr, "Not enough arguments!\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
int n = atoi(argv[2]);
|
||||
int nlist, nuniq;
|
||||
|
||||
mpq_t qreal, qimag;
|
||||
mpq_inits(qreal, qimag, NULL);
|
||||
mpq_set_str(qreal, argv[3], 10);
|
||||
mpq_set_str(qimag, argv[4], 10);
|
||||
// mpq_set_si(qreal, 50, 10);
|
||||
// mpq_set_si(qimag, 1, 10);
|
||||
mpq_canonicalize(qreal);
|
||||
mpq_canonicalize(qimag);
|
||||
|
||||
/*
|
||||
int length = 0;
|
||||
LOOP(i, n) {
|
||||
if(group->elements[i].length > length) {
|
||||
printf("Elements up to length %d: %d\n", length, i);
|
||||
length = group->elements[i].length;
|
||||
}
|
||||
}
|
||||
return 0;
|
||||
*/
|
||||
|
||||
/*
|
||||
LOOP(i, n) {
|
||||
groupelement_t *cur = &group->elements[i];
|
||||
groupelement_t *other;
|
||||
|
||||
cur->conjugacy_class = cur; // start with itself and reduce if possible
|
||||
|
||||
LOOP(j, 3) {
|
||||
if(cur->left[j] && cur->left[j]->right[j]) {
|
||||
other = cur->left[j]->right[j];
|
||||
if(other->id < cur->id)
|
||||
cur->conjugacy_class = other->conjugacy_class;
|
||||
}
|
||||
if(cur->right[j] && cur->right[j]->left[j]) {
|
||||
other = cur->right[j]->left[j];
|
||||
if(other->id < cur->id)
|
||||
cur->conjugacy_class = other->conjugacy_class;
|
||||
}
|
||||
}
|
||||
}
|
||||
*/
|
||||
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, 2, 2, 2, qreal, qimag);
|
||||
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;
|
||||
int nuniq = enumerate_coxeter_group_traces(group, gen, &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
|
||||
@ -198,7 +258,14 @@ int main(int argc, char *argv[])
|
||||
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
|
||||
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]);
|
||||
@ -207,28 +274,31 @@ int main(int argc, char *argv[])
|
||||
max_slope_id = traces[i].id;
|
||||
}
|
||||
|
||||
if(mode == MODE_TRACES) {
|
||||
if(mode == MODE_EIGENVALUES) {
|
||||
printf("%d %f %f %f\n",
|
||||
traces[i].id, log(ev_abs2[0]), log(ev_abs2[1]), log(ev_abs2[2]));
|
||||
} else if(mode == MODE_TRACE_IDS) {
|
||||
printf("%d\n", traces[i].id);
|
||||
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 %f %s\n", mpq_get_d(qreal), mpq_get_d(qimag), n, nuniq, max_slope, buf);
|
||||
} else {
|
||||
gmp_fprintf(stderr, "q = %Qd + i*%Qd\tElements: %d\tTraces: %d\tMaximal slope: %f at %s\n", qreal, qimag, n, nuniq, max_slope, buf);
|
||||
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);
|
||||
}
|
||||
|
||||
mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
|
||||
// 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(qreal, qimag, NULL);
|
||||
mpq_clears(treal, timag, NULL);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
9
compute_picture.sh
Executable file
9
compute_picture.sh
Executable file
@ -0,0 +1,9 @@
|
||||
#!/bin/bash
|
||||
|
||||
for i in $(seq -50 50); do
|
||||
for j in $(seq 0 50); do
|
||||
if [ $i -ne 0 ] || [ $j -ne 0 ]; then
|
||||
IDLIST=output/idlist_13 ./complex_anosov summary 15124 1 1 1 $i/50 $j/50
|
||||
fi
|
||||
done
|
||||
done
|
||||
118
enumerate.c
118
enumerate.c
@ -3,25 +3,84 @@
|
||||
#include <stdlib.h>
|
||||
|
||||
#define LOOP(i,n) for(int i = 0; i < (n); i++)
|
||||
// #define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
|
||||
#define INFO(msg, ...)
|
||||
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices)
|
||||
static int compare_int(const void *a, const void *b)
|
||||
{
|
||||
TYPE t = GETTYPE(gen[0]->x[0]);
|
||||
const int *aa = a;
|
||||
const int *bb = b;
|
||||
return (*aa > *bb) - (*aa < *bb);
|
||||
}
|
||||
|
||||
static int index_in_list(const int *list, int n, int key)
|
||||
{
|
||||
int *ptr = bsearch(&key, list, n, sizeof(int), compare_int);
|
||||
if(ptr)
|
||||
return ptr - list;
|
||||
else
|
||||
return -1;
|
||||
}
|
||||
|
||||
// idlist is assumed to be sorted and symmetric
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist)
|
||||
{
|
||||
TYPE type = GETTYPE(gen[0]->x[0]);
|
||||
mat_workspace *ws;
|
||||
|
||||
ws = mat_workspace_init(3, t);
|
||||
// mark elements which we need to compute
|
||||
int ncompute = 0;
|
||||
LOOP(i, group->size) group->elements[i].need_to_compute = 0;
|
||||
LOOP(i, nlist) {
|
||||
groupelement_t *cur = &group->elements[idlist[i]];
|
||||
while(cur && cur->need_to_compute == 0) {
|
||||
cur->need_to_compute = 1;
|
||||
ncompute++;
|
||||
cur = cur->parent;
|
||||
}
|
||||
}
|
||||
INFO("need to compute %d elements for %d elements in list\n", ncompute, nlist);
|
||||
|
||||
mat_identity(matrices[0]);
|
||||
for(int i = 1; i < group->size; i++) {
|
||||
if(!group->elements[i].inverse)
|
||||
continue;
|
||||
// compute them depth first
|
||||
int maxlen = group->elements[group->size-1].length;
|
||||
|
||||
int parent = group->elements[i].parent->id;
|
||||
int letter = group->elements[i].letter;
|
||||
groupelement_t **stack = malloc((maxlen+1)*sizeof(groupelement_t));
|
||||
int *letter_stack = malloc((maxlen+1)*sizeof(int));
|
||||
mat *matrix_stack = malloc((maxlen+1)*sizeof(mat));
|
||||
int level = 0;
|
||||
|
||||
mat_multiply(ws, matrices[i], matrices[parent], gen[letter]);
|
||||
LOOP(i, maxlen+1) mat_init(matrix_stack[i], 3, type);
|
||||
ws = mat_workspace_init(3, type);
|
||||
|
||||
stack[0] = &group->elements[0];
|
||||
mat_identity(matrix_stack[0]);
|
||||
letter_stack[0] = 0;
|
||||
|
||||
while(level >= 0) {
|
||||
int letter = letter_stack[level];
|
||||
groupelement_t *next = stack[level]->left[letter];
|
||||
if(next && next->length > level && next->need_to_compute) {
|
||||
mat_multiply(ws, matrix_stack[level+1], gen[letter], matrix_stack[level]);
|
||||
int id = next->id;
|
||||
int listid = index_in_list(idlist, nlist, id);
|
||||
if(listid != -1)
|
||||
mat_copy(matrices[listid], matrix_stack[level+1]);
|
||||
next->need_to_compute = 0;
|
||||
stack[level+1] = next;
|
||||
letter_stack[level+1] = 0;
|
||||
level++;
|
||||
} else {
|
||||
letter = ++letter_stack[level];
|
||||
while(letter >= group->rank) { // done with this level, go back down
|
||||
level--;
|
||||
if(level < 0)
|
||||
break;
|
||||
letter = ++letter_stack[level];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
LOOP(i, maxlen+1) mat_clear(matrix_stack[i]);
|
||||
mat_workspace_clear(ws);
|
||||
}
|
||||
|
||||
@ -48,35 +107,33 @@ static int compare_tracedata_id(const void *a, const void *b)
|
||||
return ida > idb ? 1 : ida < idb ? -1 : 0;
|
||||
}
|
||||
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out)
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique)
|
||||
{
|
||||
TYPE t = GETTYPE(gen[0]->x[0]);
|
||||
int n = group->size;
|
||||
int nuniq;
|
||||
|
||||
mat *matrices = malloc(n*sizeof(mat));
|
||||
struct tracedata *traces = malloc(n*sizeof(struct tracedata));
|
||||
struct tracedata **distinct_traces = malloc(n*sizeof(struct tracedata*));
|
||||
mat *matrices = malloc(nlist*sizeof(mat));
|
||||
struct tracedata *traces = malloc(nlist*sizeof(struct tracedata));
|
||||
struct tracedata **distinct_traces = malloc(nlist*sizeof(struct tracedata*));
|
||||
|
||||
LOOP(i, n) mat_init(matrices[i], 3, t);
|
||||
enumerate_coxeter_group(group, gen, matrices);
|
||||
LOOP(i, nlist) mat_init(matrices[i], 3, t);
|
||||
enumerate_coxeter_group(group, gen, matrices, idlist, nlist);
|
||||
|
||||
LOOP(i, n) {
|
||||
LOOP(i, nlist) {
|
||||
INIT(traces[i].tr, t);
|
||||
INIT(traces[i].trinv, t);
|
||||
}
|
||||
LOOP(i, n) {
|
||||
if(!group->elements[i].inverse)
|
||||
continue;
|
||||
int inv_id_in_list = index_in_list(idlist, nlist, group->elements[idlist[i]].inverse->id);
|
||||
mat_trace(traces[i].tr, matrices[i]);
|
||||
mat_trace(traces[i].trinv, matrices[group->elements[i].inverse->id]);
|
||||
traces[i].id = i;
|
||||
mat_trace(traces[i].trinv, matrices[inv_id_in_list]);
|
||||
traces[i].id = idlist[i];
|
||||
distinct_traces[i] = &traces[i];
|
||||
}
|
||||
|
||||
qsort(distinct_traces, n, sizeof(struct tracedata*), compare_tracedata);
|
||||
if(unique) {
|
||||
qsort(distinct_traces, nlist, sizeof(struct tracedata*), compare_tracedata);
|
||||
|
||||
int nuniq = 0;
|
||||
LOOP(i, n) {
|
||||
nuniq = 0;
|
||||
LOOP(i, nlist) {
|
||||
if(i == 0 || compare_tracedata(&distinct_traces[i], &distinct_traces[nuniq-1]) != 0) {
|
||||
distinct_traces[nuniq] = distinct_traces[i];
|
||||
nuniq++;
|
||||
@ -87,6 +144,9 @@ int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **
|
||||
distinct_traces[nuniq-1]->id = distinct_traces[i]->id;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
nuniq = nlist;
|
||||
}
|
||||
|
||||
qsort(distinct_traces, nuniq, sizeof(struct tracedata*), compare_tracedata_id);
|
||||
|
||||
@ -99,8 +159,8 @@ int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **
|
||||
unique_traces[i].id = distinct_traces[i]->id;
|
||||
}
|
||||
|
||||
LOOP(i, n) mat_clear(matrices[i]);
|
||||
LOOP(i, n) {
|
||||
LOOP(i, nlist) mat_clear(matrices[i]);
|
||||
LOOP(i, nlist) {
|
||||
CLEAR(traces[i].tr);
|
||||
CLEAR(traces[i].trinv);
|
||||
}
|
||||
|
||||
@ -12,8 +12,8 @@ struct tracedata {
|
||||
NUMBER trinv;
|
||||
};
|
||||
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices);
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out);
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist);
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique);
|
||||
|
||||
void enumerate_tracedata_clear(struct tracedata *traces, int n);
|
||||
|
||||
|
||||
62
generators.c
62
generators.c
@ -3,39 +3,39 @@
|
||||
|
||||
#define LOOP(i,n) for(int i = 0; i < (n); i++)
|
||||
|
||||
void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER q)
|
||||
void generators_triangle_reflection_generic(mat *gen, NUMBER sqrho1, NUMBER sqrho2, NUMBER sqrho3, NUMBER t)
|
||||
{
|
||||
NUMBER tmp;
|
||||
NUMBER qinv;
|
||||
TYPE t = GETTYPE(rho1);
|
||||
NUMBER tinv;
|
||||
TYPE type = GETTYPE(sqrho1);
|
||||
|
||||
INIT(tmp, t);
|
||||
INIT(qinv, t);
|
||||
INV(qinv, q);
|
||||
INIT(tmp, type);
|
||||
INIT(tinv, type);
|
||||
INV(tinv, t);
|
||||
|
||||
LOOP(i, 3) {
|
||||
mat_init(gen[i], 3, t);
|
||||
mat_init(gen[i], 3, type);
|
||||
mat_zero(gen[i]);
|
||||
LOOP(j, 3) {
|
||||
SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
|
||||
}
|
||||
}
|
||||
|
||||
MUL(tmp, q, rho1);
|
||||
MUL(tmp, t, sqrho1);
|
||||
NEG(*mat_ref(gen[2], 1, 2), tmp);
|
||||
MUL(tmp, q, rho2);
|
||||
NEG(*mat_ref(gen[0], 2, 0), tmp);
|
||||
MUL(tmp, q, rho3);
|
||||
NEG(*mat_ref(gen[1], 0, 1), tmp);
|
||||
NEG(*mat_ref(gen[0], 2, 0), sqrho2);
|
||||
NEG(*mat_ref(gen[1], 0, 1), sqrho3);
|
||||
|
||||
NEG(*mat_ref(gen[1], 2, 1), qinv);
|
||||
NEG(*mat_ref(gen[2], 0, 2), qinv);
|
||||
NEG(*mat_ref(gen[0], 1, 0), qinv);
|
||||
MUL(tmp, tinv, sqrho1);
|
||||
NEG(*mat_ref(gen[1], 2, 1), tmp);
|
||||
NEG(*mat_ref(gen[2], 0, 2), sqrho2);
|
||||
NEG(*mat_ref(gen[0], 1, 0), sqrho3);
|
||||
|
||||
CLEAR(tmp);
|
||||
CLEAR(qinv);
|
||||
CLEAR(tinv);
|
||||
}
|
||||
|
||||
// warning: this is not compatible anymore!
|
||||
int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t t)
|
||||
{
|
||||
int p[3] = {p1, p2, p3};
|
||||
@ -107,23 +107,23 @@ int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, i
|
||||
|
||||
int q[3] = {q1, q2, q3};
|
||||
|
||||
NUMBER rho[3];
|
||||
LOOP(i, 3) INIT(rho[i], QT_GAUSS_SQRT5);
|
||||
NUMBER sqrho[3];
|
||||
LOOP(i, 3) INIT(sqrho[i], QT_GAUSS_SQRT5);
|
||||
|
||||
// compute rho1, rho2, rho3
|
||||
// compute sqrho1, sqrho2, sqrho3
|
||||
LOOP(i, 3) {
|
||||
if(q[i] == 1) {
|
||||
// 4cos(pi/5)^2 = 3/2 + 1/2*sqrt(5)
|
||||
mpq_set_si(rho[i]->a[0], 3, 2);
|
||||
mpq_set_si(rho[i]->a[1], 7, 12);
|
||||
mpq_set_si(rho[i]->a[2], 0, 1);
|
||||
mpq_set_si(rho[i]->a[3], -1, 24);
|
||||
// 2cos(pi/5) = 1/2 + 1/2*sqrt(5) = 1/2 + 7/12 a - 1/24 a^3
|
||||
mpq_set_si(sqrho[i]->a[0], 1, 2);
|
||||
mpq_set_si(sqrho[i]->a[1], 7, 12);
|
||||
mpq_set_si(sqrho[i]->a[2], 0, 1);
|
||||
mpq_set_si(sqrho[i]->a[3], -1, 24);
|
||||
} else if(q[i] == 2) {
|
||||
// 4cos(pi/5)^2 = 3/2 - 1/2*sqrt(5)
|
||||
mpq_set_si(rho[i]->a[0], 3, 2);
|
||||
mpq_set_si(rho[i]->a[1], -7, 12);
|
||||
mpq_set_si(rho[i]->a[2], 0, 1);
|
||||
mpq_set_si(rho[i]->a[3], 1, 24);
|
||||
// 2cos(pi/5) = -1/2 + 1/2*sqrt(5)
|
||||
mpq_set_si(sqrho[i]->a[0], -1, 2);
|
||||
mpq_set_si(sqrho[i]->a[1], 7, 12);
|
||||
mpq_set_si(sqrho[i]->a[2], 0, 1);
|
||||
mpq_set_si(sqrho[i]->a[3], -1, 24);
|
||||
} else {
|
||||
return 0;
|
||||
}
|
||||
@ -138,9 +138,9 @@ int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, i
|
||||
mpq_set_si(param->a[3], 1, 12);
|
||||
mpq_mul(param->a[3], param->a[3], timag);
|
||||
|
||||
generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);
|
||||
generators_triangle_reflection_generic(gen, sqrho[0], sqrho[1], sqrho[2], param);
|
||||
|
||||
LOOP(i, 3) CLEAR(rho[i]);
|
||||
LOOP(i, 3) CLEAR(sqrho[i]);
|
||||
CLEAR(param);
|
||||
|
||||
return 1;
|
||||
|
||||
67
make_picture.py
Executable file
67
make_picture.py
Executable file
@ -0,0 +1,67 @@
|
||||
#!/usr/bin/python
|
||||
|
||||
import sys
|
||||
import math
|
||||
|
||||
def sharpen(x):
|
||||
alpha = 1
|
||||
y = abs(2*x-1)**alpha # between 0 and 1
|
||||
if x > 0.499 and x < 0.501:
|
||||
return 0.5
|
||||
elif x > 0.5:
|
||||
return (y+1)/2
|
||||
else:
|
||||
return (1-y)/2
|
||||
|
||||
f = open(sys.argv[1])
|
||||
lines = [x.split() for x in f]
|
||||
f.close()
|
||||
|
||||
res1 = int(sys.argv[2]) # 400 pixel per unit
|
||||
res2 = int(sys.argv[3]) # 50 pixel in picture (acutally one quadrant)
|
||||
|
||||
data = {(round(float(l[0])*res1), round(float(l[1])*res1)) : float(l[5]) for l in lines}
|
||||
data[(0,0)] = 2.0
|
||||
|
||||
print("P3")
|
||||
print("1000 1000")
|
||||
print("255")
|
||||
|
||||
for i in range (-500,500):
|
||||
for j in range(-500,500):
|
||||
x = j/500*res2
|
||||
y = i/500*res2
|
||||
|
||||
if y < 0:
|
||||
y = -y
|
||||
|
||||
x0 = math.floor(x)
|
||||
y0 = math.floor(y)
|
||||
x1 = math.ceil(x)
|
||||
y1 = math.ceil(y)
|
||||
tx = sharpen(x-x0)
|
||||
ty = sharpen(y-y0)
|
||||
|
||||
if not (x0,y0) in data or not (x0,y1) in data or not (x1,y0) in data or not (x1,y1) in data:
|
||||
value = 0
|
||||
else:
|
||||
value = 0.0
|
||||
value += data[(x0,y0)]*(1-tx)*(1-ty)
|
||||
value += data[(x0,y1)]*(1-tx)*ty
|
||||
value += data[(x1,y0)]*tx*(1-ty)
|
||||
value += data[(x1,y1)]*tx*ty
|
||||
value -= 1
|
||||
|
||||
value = 0 if value < 0 else 1 if value > 1 else value
|
||||
|
||||
r = round(255*math.sqrt(value))
|
||||
g = round(255*(value)**3)
|
||||
b = round(255*math.sin(2*math.pi*(value)))
|
||||
|
||||
r = 0 if r < 0 else 255 if r > 255 else r
|
||||
g = 0 if g < 0 else 255 if g > 255 else g
|
||||
b = 0 if b < 0 else 255 if b > 255 else b
|
||||
|
||||
print("%d %d %d" % (r,g,b))
|
||||
|
||||
#print(data)
|
||||
Loading…
Reference in New Issue
Block a user