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enumerate-balanced-ideals
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use cddlib to try to find a dominant weight for every balanced ideal

This commit is contained in:
Florian Stecker 2019-01-18 11:57:36 +01:00
parent 7fcb9f1056
commit 6c938f751d
1 changed files with 68 additions and 13 deletions
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81
dominant_weights.c
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@ -9,7 +9,7 @@
doublequotient_t *dq;
double *vector;
char buf[1000];
char buf[1000], buf2[1000];
typedef struct {
dd_MatrixPtr M;
@ -29,34 +29,75 @@ static char* alphabetize(weylgroup_element_t *e, char *str)
return str;
}
static char* print_vector(double *v, int rank, char *buf)
{
int written = 0;
for(int i = 0; i < rank; i++) {
written += sprintf(buf+written, "%.4f", v[i]);
if(i != rank -1) {
sprintf(buf+written, ", ");
written += 2;
}
}
return buf;
}
static char* print_vector_ptr(dd_Arow v, int rank, char *buf)
{
int written = 0;
for(int i = 0; i < rank; i++) {
written += sprintf(buf+written, "%.4f", v[i][0]);
if(i != rank -1) {
sprintf(buf+written, ", ");
written += 2;
}
}
return buf;
}
static void balanced_thickening_callback(const bitvec_t *pos, int size, const enumeration_info_t *ei)
{
int bit, funcbit, sign;
dd_rowset ImL, Lbasis;
dd_ErrorType err = dd_NoError;
info_t *info = (info_t*)ei->callback_data;
int rank = weyl_rank(dq->type);
for(int i = 0; i < size; i++) {
bit = i < size/2 ? bv_get_bit(pos, i) : !bv_get_bit(pos, size - 1 - i);
sign = bit ? 1 : -1;
info->M->matrix[i][0][0] = 0.0;
info->M->matrix[i][1][0] = sign*vector[3*i];
info->M->matrix[i][2][0] = sign*vector[3*i+1];
info->M->matrix[i][3][0] = sign*vector[3*i+2];
for(int j = 0; j < rank; j++)
info->M->matrix[i][j+1][0] = sign*vector[rank*i+j];
// printf("0 %.2f %.2f %.2f %d %d\n", sign*vector[3*i], sign*vector[3*i+1], sign*vector[3*i+2], bit, funcbit);
}
for(int i = 0; i < rank; i++) {
info->M->matrix[i+size][0][0] = 0.0;
for(int j = 0; j < rank; j++) {
if(i == j)
info->M->matrix[i+size][j+1][0] = 1.0;
else
info->M->matrix[i+size][j+1][0] = 0.0;
}
}
// dd_WriteMatrix(stdout, info->M);
dd_FindRelativeInterior(info->M, &ImL, &Lbasis, &(info->lps), &err);
if(set_card(Lbasis) != 0)
printf("codim = %ld\n", set_card(Lbasis));
else
printf("weight = (%.4f, %.4f, %.4f)\n", *info->lps->sol[0], *info->lps->sol[1], *info->lps->sol[2]);
printf("weight = (%s)\n", print_vector_ptr(info->lps->sol, rank + 1, buf));
dd_FreeLPSolution(info->lps);
printf("\n");
// printf("\n");
}
static int apply_reflection(double *in, double *out, int rank, int reflection)
@ -95,22 +136,36 @@ int main(int argc, char *argv[])
weylgroup_element_t *group = dq->group;
vector = malloc(weyl_order(type)*weyl_rank(type)*sizeof(double));
vector[0] = 3;
vector[1] = 4;
vector[2] = 3;
for(int i = 0; i < rank; i++)
vector[i] = 0.0;
for(int i = 0; 2*i < rank; i++) {
for(int j = i; j < rank - i; j++) {
vector[j] += rank - 2*i;
}
}
/*
vector[0] = 4.1;
vector[1] = 6.1;
vector[2] = 5.9;
vector[3] = 3.9;
*/
printf("regular element: (%s)\n", print_vector(vector, rank, buf));
for(int i = 0; i < order; i++) {
printf("%s %.2f %.2f %.2f\n", alphabetize(&group[i], buf), vector[3*i], vector[3*i+1], vector[3*i+2]);
printf("%s (%s)\n", alphabetize(&group[i], buf), print_vector(vector + rank*i, rank, buf2));
for(int j = 0; j < rank; j++)
if(group[i].left[j]->wordlength > group[i].wordlength)
apply_reflection(&vector[3*i], &vector[3*group[i].left[j]->index], rank, j);
apply_reflection(&vector[rank*i], &vector[rank*group[i].left[j]->index], rank, j);
}
printf("\n");
dd_set_global_constants();
info.M = dd_CreateMatrix(24, 4);
info.M = dd_CreateMatrix(order+rank, rank+1);
info.M->representation = dd_Inequality;
info.M->numbtype = dd_Real;
info.M->objective = dd_LPmax;