triangle_reflection_complex/singular_values.c
2020-07-27 11:57:02 -04:00

327 lines
7.7 KiB
C

#include "triangle.h"
#include "linalg.h"
#include "mat.h"
#include <gsl/gsl_poly.h>
//#define MAX_ELEMENTS 2800000
//#define MAX_ELEMENTS 720000
#define MAX_ELEMENTS 3000
//#define DRAW_PICTURE 1
void continued_fraction_approximation(mpq_t out, double in, int level)
{
mpq_t tmp;
if(in < 0) {
mpq_init(tmp);
mpq_set_ui(tmp, 0, 1);
continued_fraction_approximation(out, -in, level);
mpq_sub(out, tmp, out);
mpq_clear(tmp);
return;
}
if(level == 0) {
mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
} else {
continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
mpq_init(tmp);
mpq_set_ui(tmp, 1, 1);
mpq_div(out, tmp, out); // out -> 1/out
mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
mpq_add(out, out, tmp);
mpq_clear(tmp);
}
}
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
{
mpq_t tmp;
mpq_init(tmp);
mpq_set_si(out, a, 1);
mpq_mul(out, out, in);
mpq_set_si(tmp, b, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, c, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, d, 1);
mpq_add(out, out, tmp);
mpq_mul(out, out, in);
mpq_set_si(tmp, e, 1);
mpq_add(out, out, tmp);
mpq_clear(tmp);
}
void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t q)
{
mat r1,r2,r3;
mpq_t rho1, rho2, rho3;
mpq_t b1,c1,a2,c2,a3,b3;
mpq_t sinv;
mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mat_init(r1, 3);
mat_init(r2, 3);
mat_init(r3, 3);
mpq_set_ui(sinv, 1, 1);
mpq_div(sinv, sinv, s);
quartic(rho1, s, 0, 0, 1, -1, 1);
quartic(rho2, s, 0, 0, 1, -1, 1);
quartic(rho3, s, 0, 0, 1, 0, 1);
mpq_mul(c1, rho2, q);
mpq_mul(a2, rho3, q);
mpq_mul(b3, rho1, q);
mpq_set_ui(b1, 1, 1);
mpq_set_ui(c2, 1, 1);
mpq_set_ui(a3, 1, 1);
mpq_div(b1, b1, q);
mpq_div(c2, c2, q);
mpq_div(a3, a3, q);
// actually, we want minus everything
mat_zero(r1);
mat_zero(r2);
mat_zero(r3);
mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
mpq_set(*mat_ref(r1, 1, 0), b1);
mpq_set(*mat_ref(r1, 2, 0), c1);
mpq_set(*mat_ref(r2, 0, 1), a2);
mpq_set(*mat_ref(r2, 2, 1), c2);
mpq_set(*mat_ref(r3, 0, 2), a3);
mpq_set(*mat_ref(r3, 1, 2), b3);
mat_zero(gen[0]);
mat_zero(gen[1]);
mat_zero(gen[2]);
mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
mat_set(gen[0], 1, 1, sinv);
mat_set(gen[0], 2, 2, s);
mat_set(gen[1], 0, 0, s);
mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
mat_set(gen[1], 2, 2, sinv);
mat_set(gen[2], 0, 0, sinv);
mat_set(gen[2], 1, 1, s);
mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
mat_multiply(ws, gen[0], r2, gen[0]);
mat_multiply(ws, gen[0], gen[0], r3);
mat_multiply(ws, gen[1], r3, gen[1]);
mat_multiply(ws, gen[1], gen[1], r1);
mat_multiply(ws, gen[2], r1, gen[2]);
mat_multiply(ws, gen[2], gen[2], r2);
mat_pseudoinverse(ws, gen[3], gen[0]);
mat_pseudoinverse(ws, gen[4], gen[1]);
mat_pseudoinverse(ws, gen[5], gen[2]);
/*
mat_print(r1);
mat_print(r2);
mat_print(r3);
mat_print(gen[0]);
mat_print(gen[1]);
mat_print(gen[2]);
mat_print(gen[3]);
mat_print(gen[4]);
mat_print(gen[5]);
*/
mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
mat_clear(r1);
mat_clear(r2);
mat_clear(r3);
}
char *print_word(groupelement_t *g, char *str)
{
int i = g->length - 1;
str[g->length] = 0;
while(g->parent) {
str[i--] = 'a' + g->letter;
g = g->parent;
}
return str;
}
void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
{
mat_workspace *ws;
mat tmp;
mat gen[6];
char buf[100], buf2[100], buf3[100];
// allocate stuff
ws = mat_workspace_init(3);
for(int i = 0; i < 6; i++)
mat_init(gen[i], 3);
mat_init(tmp, 3);
initialize_triangle_generators(ws, gen, s, t);
mat_identity(matrices[0]);
for(int i = 1; i < MAX_ELEMENTS; i++) {
if(group[i].length % 2 != 0)
continue;
if(!group[i].inverse)
continue;
int parent = group[i].parent->id;
int grandparent = group[i].parent->parent->id;
int letter;
if(group[parent].letter == 1 && group[i].letter == 2)
letter = 0; // p = bc
else if(group[parent].letter == 2 && group[i].letter == 0)
letter = 1; // q = ca
else if(group[parent].letter == 0 && group[i].letter == 1)
letter = 2; // r = ab
if(group[parent].letter == 2 && group[i].letter == 1)
letter = 3; // p^{-1} = cb
else if(group[parent].letter == 0 && group[i].letter == 2)
letter = 4; // q^{-1} = ac
else if(group[parent].letter == 1 && group[i].letter == 0)
letter = 5; // r^{-1} = ba
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
}
// free stuff
for(int i = 0; i < 6; i++)
mat_clear(gen[i]);
mat_clear(tmp);
mat_workspace_clear(ws);
}
void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t q)
{
mpq_t tr, trinv;
char buf[100];
mpq_inits(tr, trinv, NULL);
for(int i = 0; i < MAX_ELEMENTS; i++) {
if(group[i].length % 2 != 0 || !group[i].inverse)
continue;
mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group[i].inverse->id]);
gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
}
mpq_clears(tr, trinv, NULL);
}
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
{
double max = 0;
double slope;
mpq_t tr, trinv;
char buf[100];
mpq_inits(tr, trinv, NULL);
for(int i = 0; i < MAX_ELEMENTS; i++) {
if(group[i].length % 2 != 0 || !group[i].inverse)
continue;
mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group[i].inverse->id]);
slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
if(slope > max)
{
*index = i;
max = slope;
}
}
mpq_clears(tr, trinv, NULL);
return max;
}
int main(int argc, char *argv[])
{
mpq_t s, q, t, tmp;
double sapprox, tapprox, qapprox, tqfactor;
mat *matrices;
groupelement_t *group;
int index;
mpq_inits(s, q, t, tmp, NULL);
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
matrices = malloc(MAX_ELEMENTS*sizeof(mat));
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_init(matrices[i], 3);
int acc = 100;
sapprox = atof(argv[1]);
tapprox = atof(argv[2]);
tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
qapprox = tapprox/tqfactor;
for(int i = 0; ; i++) {
continued_fraction_approximation(tmp, sapprox, i);
// gmp_fprintf(stdout, "%Qd\n", tmp);
if(fabs(mpq_get_d(t)-sapprox) < 1e-10 || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
break;
mpq_set(s, tmp);
}
mpq_canonicalize(s);
for(int i = 0; ; i++) {
continued_fraction_approximation(tmp, qapprox, i);
// gmp_fprintf(stdout, "%Qd\n", tmp);
if(fabs(mpq_get_d(t)-qapprox) < 1e-10 || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
break;
mpq_set(q, tmp);
}
mpq_canonicalize(q);
tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);
gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
// for(int i = 0; i < 10; i++) {
// mpq_set_ui(t,100+i,100);
// mpq_canonicalize(t);
enumerate(group, matrices, s, q);
//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
output_invariants(group, matrices, s, q);
// }
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_clear(matrices[i]);
free(matrices);
free(group);
mpq_clears(s, q, t, tmp, NULL);
}