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triangle_group_limit_set
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continue limit curve past degeneration point

This commit is contained in:
Florian Stecker 2018-10-27 14:56:46 -07:00
parent 000d8a53b9
commit e631dee661
3 changed files with 106 additions and 23 deletions
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105
limit_set.c
View File

@ -52,6 +52,8 @@ int show_boxes = 0;
int show_attractors = 0;
int show_reflectors = 0;
int show_limit = 1;
int limit_with_lines = 1;
int use_repelling = 1;
void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s)
{
@ -157,7 +159,7 @@ void drawPolygon(DrawingContext *ctx, int sides, point_t a, point_t b, point_t c
drawSegment(ctx, d, a);
}
void fixedPoints(const char *word, point_t *out)
int fixedPoints(const char *word, point_t *out)
{
gsl_matrix *tmp = ws->stack[10];
gsl_matrix *ev = ws->stack[11];
@ -168,11 +170,13 @@ void fixedPoints(const char *word, point_t *out)
continue;
multiply_right(tmp, gen[word[i]-'a'], ws);
}
eigenvectors(tmp, ev, ws);
int count = real_eigenvectors(tmp, ev, ws);
multiply_left(cob, ev, ws);
LOOP(i) out[i].x = gsl_matrix_get(ev, 0, i) / gsl_matrix_get(ev, 2, i);
LOOP(i) out[i].y = gsl_matrix_get(ev, 1, i) / gsl_matrix_get(ev, 2, i);
return count;
}
void drawAttractorConnection(DrawingContext *ctx, const char *word1, const char *word2)
@ -233,6 +237,8 @@ int computeLimitCurve()
int p = 5, q = 5, r = 5;
int k = 2, l = 2, m = 2;
int column = use_repelling ? 2 : 0;
generate_triangle_group(group, n_group_elements, p, q, r);
// do first in the Fuchsian case to get the angles
@ -243,14 +249,16 @@ int computeLimitCurve()
multiply(matrices[group[i].parent->id], gen[group[i].letter], matrices[i]);
diagonalize_symmetric_form(cartan, cob, ws);
multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
if(!eigenvectors(coxeter, coxeter_fixedpoints, ws))
int ev_count_fuchsian = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
if(ev_count_fuchsian != 3)
return 0;
for(int i = 0; i < n_group_elements; i++) {
multiply_many(ws, fixedpoints, 3, cob, matrices[i], coxeter_fixedpoints);
limit_curve[3*i+2] = atan2(
gsl_matrix_get(fixedpoints, 0, 0)/gsl_matrix_get(fixedpoints, 2, 0),
gsl_matrix_get(fixedpoints, 1, 0)/gsl_matrix_get(fixedpoints, 2, 0));
gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column),
gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column));
}
// now to it again to calculate x and y coordinates
@ -262,14 +270,18 @@ int computeLimitCurve()
gsl_matrix_memcpy(cob, cartan); // is this a good choice of basis
// gsl_matrix_set_identity(cob);
multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
if(!eigenvectors(coxeter, coxeter_fixedpoints, ws))
int ev_count = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
if(ev_count == 1)
column = 0;
if(ev_count == 0)
return 0;
for(int i = 0; i < n_group_elements; i++) {
multiply_many(ws, fixedpoints, 3, cob, matrices[i], coxeter_fixedpoints);
limit_curve[3*i] = gsl_matrix_get(fixedpoints, 0, 0)/gsl_matrix_get(fixedpoints, 2, 0);
limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, 0)/gsl_matrix_get(fixedpoints, 2, 0);
limit_curve[3*i] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
}
qsort(limit_curve, n_group_elements, 3*sizeof(double), compareAngle);
@ -281,14 +293,12 @@ void drawBoxes(DrawingContext *ctx)
{
cairo_t *C = ctx->cairo;
/*
cairo_set_source_rgb(C, 1, 0, 0);
drawBoxStd(ctx, "c", 'C');
drawBoxStd(ctx, "", 'B');
drawBoxStd(ctx, "a", 'A');
drawBoxStd(ctx, "", 'C');
drawBoxStd(ctx, "b", 'B');
*/
cairo_set_source_rgb(C, 0, 0, 0);
drawBoxStd(ctx, "ca", 'A');
@ -297,9 +307,6 @@ void drawBoxes(DrawingContext *ctx)
drawBoxStd(ctx, "acac", 'C');
drawBoxStd(ctx, "aca", 'A');
drawBoxStd(ctx, "ac", 'C');
cairo_set_source_rgb(C, 1, 0, 1);
/*
drawBoxStd(ctx, "aca cb", 'B');
drawBoxStd(ctx, "aca cbc", 'C');
@ -307,14 +314,31 @@ void drawBoxes(DrawingContext *ctx)
drawBoxStd(ctx, "aca bcbc", 'C');
drawBoxStd(ctx, "aca bcb", 'B');
drawBoxStd(ctx, "aca bc", 'C');
drawBoxStd(ctx, "caca cb", 'B');
drawBoxStd(ctx, "caca cbc", 'C');
drawBoxStd(ctx, "caca cbcb", 'B');
drawBoxStd(ctx, "caca bcbc", 'C');
drawBoxStd(ctx, "caca bcb", 'B');
drawBoxStd(ctx, "caca bc", 'C');
*/
cairo_set_source_rgb(C, 1, 0, 1);
drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "ca bcb", 'B');
drawBoxStd(ctx, "ca bcbc", 'C');
drawBoxStd(ctx, "ca cbcb", 'B');
drawBoxStd(ctx, "ca cbc", 'C');
drawBoxStd(ctx, "ca cb", 'B');
cairo_set_source_rgb(C, 0, 1, 0);
// drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "cabc ba", 'A');
drawBoxStd(ctx, "cabc bab", 'B');
drawBoxStd(ctx, "cabc baba", 'A');
drawBoxStd(ctx, "cabc abab", 'B');
drawBoxStd(ctx, "cabc aba", 'A');
drawBoxStd(ctx, "cabc ab", 'B');
}
void drawReflectors(DrawingContext *ctx)
@ -373,7 +397,9 @@ void draw(DrawingContext *ctx)
if(limit_curve_valid) {
if(show_limit) {
int last_inside = 0;
cairo_save(C);
int previous_inside = 0;
for(int i = 0; i < n_group_elements; i++) {
double x = limit_curve[3*i];
double y = limit_curve[3*i+1];
@ -381,19 +407,30 @@ void draw(DrawingContext *ctx)
cairo_user_to_device(C, &x, &y);
if(-x < ctx->width && x < 3*ctx->width && -y < ctx->height && y < 3*ctx->height) {
if(!last_inside) {
cairo_move_to(C, limit_curve[3*i], limit_curve[3*i+1]);
if(limit_with_lines) {
if(!previous_inside)
cairo_move_to(C, limit_curve[3*i], limit_curve[3*i+1]);
else
cairo_line_to(C, limit_curve[3*i], limit_curve[3*i+1]);
} else {
cairo_line_to(C, limit_curve[3*i], limit_curve[3*i+1]);
cairo_move_to(C, limit_curve[3*i], limit_curve[3*i+1]);
cairo_close_path(C);
}
last_inside = 1;
previous_inside = 1;
} else {
last_inside = 0;
previous_inside = 0;
}
}
if(!limit_with_lines) { // draw dots instead of lines
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(C, 3.0/ctx->scalefactor);
}
cairo_set_source_rgb(C, 0, 0, 0);
cairo_stroke(C);
cairo_restore(C);
}
if(show_boxes)
@ -411,7 +448,7 @@ void draw(DrawingContext *ctx)
cairo_move_to(C, 15, 30);
cairo_set_source_rgb(C, 0, 0, 0);
char buf[100];
sprintf(buf, "t = %.8f", parameter);
sprintf(buf, "t = exp(%.8f) = %.8f", log(parameter), parameter);
cairo_show_text(C, buf);
cairo_surface_flush(cairo_get_target(C));
@ -419,7 +456,7 @@ void draw(DrawingContext *ctx)
void setup()
{
n_group_elements = 100000;
n_group_elements = 50000;
limit_curve = malloc(3*n_group_elements*sizeof(double));
group = malloc(n_group_elements*sizeof(groupelement_t));
ws = workspace_alloc(3);
@ -490,14 +527,30 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
printf("Key pressed: %ld\n", key);
switch(key) {
case '<':
case XK_Down:
parameter /= exp(0.002);
limit_curve_valid = computeLimitCurve();
break;
case '>':
case XK_Up:
parameter *= exp(0.002);
limit_curve_valid = computeLimitCurve();
break;
case XK_Left:
parameter /= exp(0.0001);
limit_curve_valid = computeLimitCurve();
break;
case XK_Right:
parameter *= exp(0.0001);
limit_curve_valid = computeLimitCurve();
break;
case XK_Page_Down:
parameter /= exp(0.2);
limit_curve_valid = computeLimitCurve();
break;
case XK_Page_Up:
parameter *= exp(0.2);
limit_curve_valid = computeLimitCurve();
break;
case ' ':
parameter = 2.890053638;
limit_curve_valid = computeLimitCurve();
@ -523,12 +576,18 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
case 'r':
show_reflectors = !show_reflectors;
break;
case 'L':
limit_with_lines = !limit_with_lines;
break;
case 'l':
show_limit = !show_limit;
break;
case 'p':
print(info->context);
break;
case 'f':
use_repelling = !use_repelling;
limit_curve_valid = computeLimitCurve();
}
return STATUS_REDRAW;

23
linalg.c
View File

@ -190,6 +190,29 @@ int eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
return 1;
}
// only fills in the real eigenvectors and returns their count
int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
{
gsl_matrix_memcpy(ws->stack[0], g);
gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
int r = gsl_eigen_nonsymmv(ws->stack[0], ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
ERROR(r, "gsl_eigen_nonsymmv failed!\n");
gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
int real = 0;
for(int i = 0; i < ws->n; i++) {
if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) == 0) {// real
for(int j = 0; j < ws->n; j++)
gsl_matrix_set(evec_real, j, real, GSL_REAL(gsl_matrix_complex_get(ws->evec_complex, j, i)));
real++;
}
}
return real;
}
void eigensystem_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws)
{
gsl_matrix_memcpy(ws->stack[0], g);

1
linalg.h
View File

@ -42,6 +42,7 @@ int jordan_calc(gsl_matrix *g, double *mu, workspace_t *ws);
double trace(gsl_matrix *g);
double determinant(gsl_matrix *g, workspace_t *ws);
int eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws);
int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws);