#include "triangle.h"
#include "linalg.h"

#define MAX_ELEMENTS 20000

void initialize_triangle_generators(gsl_matrix **gen, double a1, double a2, double a3, double s)
{
  for(int i = 0; i < 3; i++)
    gsl_matrix_set_identity(gen[i]);

  gsl_matrix_set(gen[0], 0, 0, -1);
  gsl_matrix_set(gen[0], 1, 0, 2*s*cos(M_PI*a1));
  gsl_matrix_set(gen[0], 2, 0, 2/s*cos(M_PI*a2));

  gsl_matrix_set(gen[1], 0, 1, 2/s*cos(M_PI*a1));
  gsl_matrix_set(gen[1], 1, 1, -1);
  gsl_matrix_set(gen[1], 2, 1, 2*s*cos(M_PI*a3));

  gsl_matrix_set(gen[2], 0, 2, 2*s*cos(M_PI*a2));
  gsl_matrix_set(gen[2], 1, 2, 2/s*cos(M_PI*a3));
  gsl_matrix_set(gen[2], 2, 2, -1);
}

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;
}

int main(int argc, char *argv[])
{
  groupelement_t *group;
  workspace_t *ws;
  gsl_matrix **matrices;
  gsl_matrix *gen[3];
  gsl_matrix *tmp, *tmp2, *coxeter;
  double mu[2];
  char buf[100];

  if(argc < 2) {
    fprintf(stderr, "Too few arguments!\n");
    return 1;
  }

  // allocate stuff
  group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
  ws = workspace_alloc(3);
  matrices = malloc(MAX_ELEMENTS*sizeof(gsl_matrix*));
  for(int i = 0; i < MAX_ELEMENTS; i++)
    matrices[i] = gsl_matrix_alloc(3, 3);
  for(int i = 0; i < 3; i++)
    gen[i] = gsl_matrix_alloc(3, 3);
  tmp = gsl_matrix_alloc(3, 3);
  tmp2 = gsl_matrix_alloc(3, 3);
  coxeter = gsl_matrix_alloc(3, 3);

  // the real action
  generate_triangle_group(group, MAX_ELEMENTS, 5, 9, 7);
  //  initialize_triangle_generators(gen, 1.0/5, 1.0/5, 1.0/5, 1.0); // Fuchsian
  initialize_triangle_generators(gen, 3.0/5.0, 3.0/5.0, 3.0/5.0, atof(argv[1]));

  gsl_matrix_set_identity(matrices[0]);
  for(int i = 1; i < MAX_ELEMENTS; i++)
    multiply(matrices[group[i].parent->id], gen[group[i].letter], matrices[i]);

  for(int i = 0; i < MAX_ELEMENTS; i++) {
    cartan_calc(matrices[i], mu, ws);
    printf("%d %f %f 0x0000ff %s\n", group[i].length, mu[0], mu[1], print_word(&group[i], buf));
    //invert(matrices[i], tmp, ws);
    //printf("%d %f %f %f 0x0000ff\n", group[i].length, determinant(matrices[i], ws)*trace(matrices[i]), determinant(matrices[i], ws)*trace(tmp), determinant(matrices[i], ws));
  }

  /*
  for(int p = 0; p < 6; p++) {
    groupelement_t *cur = &group[0];
    while(1) {
      if(!(cur = cur->adj[p%3]))
	break;

      cartan_calc(matrices[cur->id], mu, ws);
      printf("%d %f %f 0xff0000\n", group[cur->id].length, mu[0], mu[1]);

      if(!(cur = cur->adj[(p+p/3+1)%3]))
	break;

      cartan_calc(matrices[cur->id], mu, ws);
      printf("%d %f %f 0xff0000\n", group[cur->id].length, mu[0], mu[1]);

      if(!(cur = cur->adj[(p-p/3+2)%3]))
	break;

      cartan_calc(matrices[cur->id], mu, ws);
      printf("%d %f %f 0xff0000\n", group[cur->id].length, mu[0], mu[1]);
      //      invert(matrices[cur->id], tmp, ws);
      //      printf("%d %f %f %f 0xff0000\n", group[cur->id].length, determinant(matrices[cur->id], ws)*trace(matrices[cur->id]), determinant(matrices[cur->id], ws)*trace(tmp), determinant(matrices[cur->id], ws));
    }
  }
  */

  // free stuff
  for(int i = 0; i < MAX_ELEMENTS; i++)
    gsl_matrix_free(matrices[i]);
  for(int i = 0; i < 3; i++)
    gsl_matrix_free(gen[i]);
  gsl_matrix_free(tmp);
  gsl_matrix_free(tmp2);
  gsl_matrix_free(coxeter);
  free(matrices);
  free(group);
  workspace_free(ws);

  return 0;
}