Thickenings
This commit is contained in:
Florian Stecker
commit
53811ef32a
14
Makefile
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14
Makefile
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all: thickenings
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thickenings: thickenings.o coxeter.o
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gcc -g -o thickenings thickenings.o coxeter.o -lgsl -lcblas
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thickenings.o: thickenings.c coxeter.h
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gcc -g -c thickenings.c -std=gnu99
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coxeter.o: coxeter.c coxeter.h
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gcc -g -c coxeter.c -std=gnu99
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clean:
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rm -f thickenings thickenings.o coxeter.o
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242
coxeter.c
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242
coxeter.c
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#include "coxeter.h"
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#include "queue.h"
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#include <memory.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_blas.h>
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static void applyGenerator(int i, double *x, double *y, int rank, double **schlaefliMatrix)
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{
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memcpy(y, x, rank*sizeof(double));
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for(int j = 0; j < rank; j++)
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y[i] -= schlaefliMatrix[i][j]*x[j];
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}
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static int check_equal_sector(gsl_matrix *x1, gsl_matrix *x2, gsl_matrix *yinv, gsl_matrix *schlaefli, gsl_vector *starting, gsl_vector *i1, gsl_vector *i2)
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{
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double scalarProduct;
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int rank = x1->size1;
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// calculate <y^{-1} * x1 * x2 * s, e_i> for all i, or identically the components of schlaefli*y^{-1}*x*s
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gsl_blas_dgemv(CblasNoTrans, 1.0, x2, starting, 0.0, i1);
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gsl_blas_dgemv(CblasNoTrans, 1.0, x1, i1, 0.0, i2);
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gsl_blas_dgemv(CblasNoTrans, 1.0, yinv, i2, 0.0, i1);
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gsl_blas_dgemv(CblasNoTrans, 1.0, schlaefli, i1, 0.0, i2);
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for(int i = 0; i < rank; i++)
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if(gsl_vector_get(i2, i) < 0)
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return 0;
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return 1;
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}
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static void invert(gsl_matrix *x, gsl_matrix *xinv)
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{
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int rank = x->size1;
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gsl_matrix *xLU = gsl_matrix_alloc(rank, rank);
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gsl_permutation *p = gsl_permutation_alloc(rank);
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int s;
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gsl_matrix_memcpy(xLU, x);
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gsl_linalg_LU_decomp(xLU, p, &s);
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gsl_linalg_LU_invert(xLU, p, xinv);
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gsl_permutation_free(p);
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gsl_matrix_free(xLU);
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}
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static void generate_schlaefli_matrix(semisimple_type_t type, gsl_matrix *mat)
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{
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gsl_matrix_set_zero(mat);
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int offset = 0;
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for(int k = 0; k < type.n; k++) {
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if(type.factors[k].series == 'A') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i - j == 1 || i - j == -1)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'B' || type.factors[k].series == 'C') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i == 0 && j == 1 || i == 1 && j == 0)
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gsl_matrix_set(mat, offset + i, offset + j, -sqrt(2.0));
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else if(i - j == 1 || i - j == -1)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'D') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i > 0 && j > 0 && (i - j == 1 || i - j == -1) || i == 0 && j == 2 || i == 2 && j == 0)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'G') {
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ERROR(type.factors[k].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
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gsl_matrix_set(mat, offset + 0, offset + 0, 2.0);
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gsl_matrix_set(mat, offset + 0, offset + 1, -sqrt(3.0));
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gsl_matrix_set(mat, offset + 1, offset + 0, -sqrt(3.0));
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gsl_matrix_set(mat, offset + 1, offset + 1, 2.0);
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} else {
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
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}
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offset += type.factors[k].rank;
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}
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}
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int coxeter_rank(semisimple_type_t type)
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{
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int rank = 0;
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for(int i = 0; i < type.n; i++)
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rank += type.factors[i].rank;
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return rank;
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}
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int coxeter_order(semisimple_type_t type)
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{
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int order = 1;
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for(int i = 0; i < type.n; i++) {
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if(type.factors[i].series == 'A') { // (rank+1)!
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for(int j = 1; j <= type.factors[i].rank + 1; j++)
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order *= j;
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} else if(type.factors[i].series == 'B' || type.factors[i].series == 'C') { // 2^rank * rank!
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for(int j = 1; j <= type.factors[i].rank; j++)
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order *= 2*j;
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} else if(type.factors[i].series == 'D') { // 2^(rank-1) * rank!
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for(int j = 2; j <= type.factors[i].rank; j++)
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order *= 2*j;
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} else if(type.factors[i].series == 'E') {
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if(type.factors[i].rank == 6)
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order *= 51840;
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else if(type.factors[i].rank == 7)
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order *= 2903040;
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else if(type.factors[i].rank == 8)
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order *= 696729600;
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else
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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} else if(type.factors[i].series == 'F') {
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ERROR(type.factors[i].rank != 4, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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order *= 1152;
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} else if(type.factors[i].series == 'G') {
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ERROR(type.factors[i].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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order *= 12;
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} else if(type.factors[i].series == 'H') {
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if(type.factors[i].rank == 2)
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order *= 10;
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else if(type.factors[i].rank == 3)
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order *= 120;
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else if(type.factors[i].rank == 4)
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order *= 14400;
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else
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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} else {
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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}
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}
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return order;
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}
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static void generate_starting_vector(int rank, gsl_matrix *schlaefli, gsl_vector *result)
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{
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gsl_matrix *schlaefliLU = gsl_matrix_alloc(rank, rank);
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gsl_vector *diagonal = gsl_vector_alloc(rank);
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gsl_permutation *p = gsl_permutation_alloc(rank);
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int s;
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for(int i = 0; i < rank; i++)
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gsl_vector_set(diagonal, i, 1.0);
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gsl_matrix_memcpy(schlaefliLU, schlaefli);
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gsl_linalg_LU_decomp(schlaefliLU, p, &s);
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gsl_linalg_LU_solve(schlaefliLU, p, diagonal, result);
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gsl_permutation_free(p);
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gsl_vector_free(diagonal);
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gsl_matrix_free(schlaefliLU);
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}
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void generate_coxeter_graph(semisimple_type_t type, int *result)
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{
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int rank = coxeter_rank(type);
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int order = coxeter_order(type);
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int element_count;
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gsl_matrix *schlaefliMatrix = gsl_matrix_alloc(rank, rank);
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gsl_vector *startingVector = gsl_vector_alloc(rank);
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gsl_matrix *generators = (gsl_matrix*)malloc(rank*sizeof(gsl_matrix));
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double *generators_data = (double*)malloc(rank*rank*rank*sizeof(double));
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gsl_matrix *elements = (gsl_matrix*)malloc(order*sizeof(gsl_matrix));
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double *elements_data = (double*)malloc(rank*rank*order*sizeof(double));
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gsl_matrix *inverses = (gsl_matrix*)malloc(order*sizeof(gsl_matrix));
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double *inverses_data = (double*)malloc(rank*rank*order*sizeof(double));
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gsl_vector *i1 = gsl_vector_alloc(rank);
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gsl_vector *i2 = gsl_vector_alloc(rank);
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gsl_matrix *current_element = gsl_matrix_alloc(rank, rank);
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queue_t queue;
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int current;
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for(int i = 0; i < rank; i++)
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generators[i] = gsl_matrix_view_array(generators_data + i*rank*rank, rank, rank).matrix;
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for(int i = 0; i < order; i++)
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elements[i] = gsl_matrix_view_array(elements_data + i*rank*rank, rank, rank).matrix;
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for(int i = 0; i < order; i++)
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inverses[i] = gsl_matrix_view_array(inverses_data + i*rank*rank, rank, rank).matrix;
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generate_schlaefli_matrix(type, schlaefliMatrix);
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generate_starting_vector(rank, schlaefliMatrix, startingVector);
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for(int i = 0; i < rank; i++) {
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gsl_matrix_set_identity(&generators[i]);
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for(int j = 0; j < rank; j++)
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if(i == j)
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gsl_matrix_set(&generators[i], i, j, -1.0);
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else
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gsl_matrix_set(&generators[i], i, j, -gsl_matrix_get(schlaefliMatrix, i, j));
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// gsl_matrix_fprintf(stdout, &generators[i], "%f");
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// printf("\n");
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}
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queue_init(&queue);
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queue_put(&queue, 0);
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element_count = 1;
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gsl_matrix_set_identity(&elements[0]);
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gsl_matrix_set_identity(&inverses[0]);
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while((current = queue_get(&queue)) != -1) {
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for(int i = 0; i < rank; i++) {
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int j;
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for(j = 0; j < element_count; j++) {
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if(check_equal_sector(&generators[i], &elements[current], &inverses[j], schlaefliMatrix, startingVector, i1, i2)) { // generators[i] * elements[current] = elements[j]
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result[rank*current + i] = j;
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break;
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}
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}
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// if no existing element equals generators[i] * elements[current], create one
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if(j == element_count) {
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ERROR(element_count >= order, "Got more elements than the order of the group should be!\n");
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &generators[i], &elements[current], 0.0, &elements[element_count]);
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invert(&elements[element_count], &inverses[element_count]);
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result[rank*current + i] = element_count;
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queue_put(&queue, element_count);
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element_count++;
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}
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}
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}
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ERROR(element_count != order, "Somethink went wrong building the Coxeter group. Found %d elements, %d expected\n", element_count, order);
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/*
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for(int i = 0; i < order; i++) {
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printf("%d: ", i);
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for(int j = 0; j < rank; j++)
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printf("%d ", result[rank*i + j]);
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printf("\n");
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}
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*/
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gsl_vector_free(startingVector);
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gsl_vector_free(i1);
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gsl_vector_free(i2);
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gsl_matrix_free(schlaefliMatrix);
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gsl_matrix_free(current_element);
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free(generators);
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free(elements);
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free(generators_data);
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free(elements_data);
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}
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18
coxeter.h
Normal file
18
coxeter.h
Normal file
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#ifndef COXETER_H
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#define COXETER_H
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typedef struct {
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char series;
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int rank;
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} simple_type_t;
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typedef struct {
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int n;
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simple_type_t *factors;
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} semisimple_type_t;
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void generate_coxeter_graph(semisimple_type_t type, int *result);
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int coxeter_order(semisimple_type_t type);
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int coxeter_rank(semisimple_type_t type);
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#endif
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41
queue.h
Normal file
41
queue.h
Normal file
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#ifndef QUEUE_H
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#define QUEUE_H
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#include <stdio.h>
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#include <stdlib.h>
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#define QUEUE_SIZE 2000
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#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
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typedef struct {
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unsigned int start;
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unsigned int end;
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int data[QUEUE_SIZE];
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} queue_t;
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static void queue_init(queue_t *q)
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{
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q->start = q->end = 0;
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}
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static void queue_put(queue_t *q, int x)
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{
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q->data[q->end++] = x;
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q->end %= QUEUE_SIZE;
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ERROR(q->start == q->end, "The queue is full! Increase QUEUE_SIZE\n");
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}
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static int queue_get(queue_t *q)
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{
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if(q->start == q->end)
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return -1;
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int result = q->data[q->start++];
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q->start %= QUEUE_SIZE;
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return result;
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}
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#endif
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467
thickenings.c
Normal file
467
thickenings.c
Normal file
@ -0,0 +1,467 @@
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#define _GNU_SOURCE
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#include <stdio.h>
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#include <limits.h>
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#include <stdlib.h>
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#include <malloc.h>
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#include <memory.h>
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#include "coxeter.h"
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#include "queue.h"
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#define DEBUG(msg, ...) do{fprintf(stderr, msg, ##__VA_ARGS__); }while(0)
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|
||||||
|
typedef struct _edgelist {
|
||||||
|
int to;
|
||||||
|
struct _edgelist *next;
|
||||||
|
} edgelist_t;
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
int *word;
|
||||||
|
int wordlength;
|
||||||
|
int *left;
|
||||||
|
int *right;
|
||||||
|
int opposite;
|
||||||
|
edgelist_t *bruhat_lower;
|
||||||
|
edgelist_t *bruhat_higher;
|
||||||
|
int is_hyperplane_reflection; // boolean value
|
||||||
|
} node_t;
|
||||||
|
|
||||||
|
static char *alphabetize(int *word, int len, const char *alphabet, char *buffer)
|
||||||
|
{
|
||||||
|
int i = 0;
|
||||||
|
for(i = 0; i < len; i++)
|
||||||
|
buffer[i] = alphabet[word[i]];
|
||||||
|
buffer[i] = 0;
|
||||||
|
|
||||||
|
return buffer;
|
||||||
|
}
|
||||||
|
|
||||||
|
static int compare_wordlength(const void *a, const void *b, void *gr)
|
||||||
|
{
|
||||||
|
int i = *((int*)a);
|
||||||
|
int j = *((int*)b);
|
||||||
|
node_t *graph = (node_t*)gr;
|
||||||
|
|
||||||
|
return graph[i].wordlength - graph[j].wordlength;
|
||||||
|
}
|
||||||
|
|
||||||
|
int main(int argc, const char *argv[])
|
||||||
|
{
|
||||||
|
queue_t queue;
|
||||||
|
|
||||||
|
// heap stuff
|
||||||
|
node_t *graph, *graph_unsorted;
|
||||||
|
int *graph_data;
|
||||||
|
int *wordlength_order, *reverse_wordlength_order, *seen, *level;
|
||||||
|
int *words;
|
||||||
|
edgelist_t *edgelists;
|
||||||
|
int *left, *right;
|
||||||
|
int *left_invariant, *right_invariant;
|
||||||
|
|
||||||
|
edgelist_t *edge, *previous;
|
||||||
|
int rank, order;
|
||||||
|
semisimple_type_t type;
|
||||||
|
int edgelist_count, hyperplane_count, max_wordlength;
|
||||||
|
int current, head, i, current_level;
|
||||||
|
int is_fat, is_slim;
|
||||||
|
int thickenings_count, fat_count, slim_count, balanced_count;
|
||||||
|
|
||||||
|
char *string_buffer1, *string_buffer2;
|
||||||
|
|
||||||
|
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
|
||||||
|
|
||||||
|
ERROR(argc < 2, "Too few arguments!\n");
|
||||||
|
|
||||||
|
type.n = argc - 1;
|
||||||
|
type.factors = (simple_type_t*)malloc((argc-1)*sizeof(simple_type_t));
|
||||||
|
for(int i = 0; i < argc - 1; i++) {
|
||||||
|
type.factors[i].series = argv[i+1][0];
|
||||||
|
type.factors[i].rank = argv[i+1][1] - '0';
|
||||||
|
ERROR(argv[i+1][0] < 'A' || argv[i+1][0] > 'I' || argv[i+1][1] < '1' || argv[i+1][1] > '9', "Arguments must be Xn with X out of A-I and n out of 0-9\n");
|
||||||
|
}
|
||||||
|
|
||||||
|
rank = coxeter_rank(type);
|
||||||
|
order = coxeter_order(type);
|
||||||
|
|
||||||
|
ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
|
||||||
|
|
||||||
|
DEBUG("The group has rank %d and order %d\n", rank, order);
|
||||||
|
|
||||||
|
graph = (node_t*)malloc(order*sizeof(node_t));
|
||||||
|
graph_unsorted = (node_t*)malloc(order*sizeof(node_t));
|
||||||
|
graph_data = (int*)malloc(order*rank*sizeof(int));
|
||||||
|
wordlength_order = (int*)malloc(order*sizeof(int));
|
||||||
|
reverse_wordlength_order = (int*)malloc(order*sizeof(int));
|
||||||
|
seen = (int*)malloc(order*sizeof(int));
|
||||||
|
level = (int*)malloc(order*sizeof(int));
|
||||||
|
left = (int*)malloc(order*rank*sizeof(int));
|
||||||
|
right = (int*)malloc(order*rank*sizeof(int));
|
||||||
|
left_invariant = (int*)malloc(rank*sizeof(int));
|
||||||
|
right_invariant = (int*)malloc(rank*sizeof(int));
|
||||||
|
|
||||||
|
DEBUG("Generate Cayley graph\n");
|
||||||
|
|
||||||
|
generate_coxeter_graph(type, graph_data);
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
graph_unsorted[i].left = &left[i*rank];
|
||||||
|
graph_unsorted[i].right = &right[i*rank];
|
||||||
|
for(int j = 0; j < rank; j++)
|
||||||
|
graph_unsorted[i].left[j] = graph_data[i*rank + j];
|
||||||
|
graph_unsorted[i].word = 0;
|
||||||
|
graph_unsorted[i].wordlength = INT_MAX;
|
||||||
|
graph_unsorted[i].bruhat_lower = 0;
|
||||||
|
graph_unsorted[i].bruhat_higher = 0;
|
||||||
|
graph_unsorted[i].is_hyperplane_reflection = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Find wordlengths\n");
|
||||||
|
|
||||||
|
graph_unsorted[0].wordlength = 0;
|
||||||
|
queue_init(&queue);
|
||||||
|
queue_put(&queue, 0);
|
||||||
|
while((current = queue_get(&queue)) != -1) {
|
||||||
|
for(int i = 0; i < rank; i++) {
|
||||||
|
int neighbor = graph_unsorted[current].left[i];
|
||||||
|
if(graph_unsorted[neighbor].wordlength > graph_unsorted[current].wordlength + 1) {
|
||||||
|
graph_unsorted[neighbor].wordlength = graph_unsorted[current].wordlength + 1;
|
||||||
|
queue_put(&queue, neighbor);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
max_wordlength = 0;
|
||||||
|
for(int i = 0; i < order; i++)
|
||||||
|
if(graph_unsorted[i].wordlength > max_wordlength)
|
||||||
|
max_wordlength = graph_unsorted[i].wordlength;
|
||||||
|
|
||||||
|
string_buffer1 = (char*)malloc((max_wordlength+1)*sizeof(char));
|
||||||
|
string_buffer2 = (char*)malloc((max_wordlength+1)*sizeof(char));
|
||||||
|
|
||||||
|
DEBUG("Sort by wordlength\n");
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++)
|
||||||
|
wordlength_order[i] = i;
|
||||||
|
qsort_r(wordlength_order, order, sizeof(int), compare_wordlength, graph_unsorted); // so wordlength_order is a map new index -> old index
|
||||||
|
for(int i = 0; i < order; i++)
|
||||||
|
reverse_wordlength_order[wordlength_order[i]] = i; // reverse_wordlength_order is a map old index -> new index
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
graph[i] = graph_unsorted[wordlength_order[i]]; // copy the whole thing
|
||||||
|
for(int j = 0; j < rank; j++)
|
||||||
|
graph[i].left[j] = reverse_wordlength_order[graph[i].left[j]]; // rewrite references
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Find words\n");
|
||||||
|
|
||||||
|
words = (int*)malloc(order*max_wordlength*sizeof(int));
|
||||||
|
memset(words, 0, order*max_wordlength*sizeof(int));
|
||||||
|
graph[0].word = &words[0];
|
||||||
|
queue_init(&queue);
|
||||||
|
queue_put(&queue, 0);
|
||||||
|
while((current = queue_get(&queue)) != -1) {
|
||||||
|
for(int i = 0; i < rank; i++) {
|
||||||
|
int neighbor = graph[current].left[i];
|
||||||
|
if(graph[neighbor].wordlength == graph[current].wordlength + 1 && graph[neighbor].word == 0) {
|
||||||
|
graph[neighbor].word = &words[neighbor*max_wordlength];
|
||||||
|
memcpy(&graph[neighbor].word[1], &graph[current].word[0], graph[current].wordlength*sizeof(int));
|
||||||
|
graph[neighbor].word[0] = i;
|
||||||
|
queue_put(&queue, neighbor);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Generate right edges\n");
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
for(int j = 0; j < rank; j++) {
|
||||||
|
current = graph[0].left[j];
|
||||||
|
for(int k = graph[i].wordlength - 1; k >= 0; k--) { // apply group element from right to left
|
||||||
|
current = graph[current].left[graph[i].word[k]];
|
||||||
|
}
|
||||||
|
graph[i].right[j] = current;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Find opposites\n");
|
||||||
|
|
||||||
|
node_t *longest = &graph[order-1];
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
current = i;
|
||||||
|
for(int k = longest->wordlength - 1; k >= 0; k--)
|
||||||
|
current = graph[current].left[longest->word[k]];
|
||||||
|
graph[i].opposite = current;
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Enumerate hyperplanes\n"); // every right edge is a reflection along a hyperplane; calculate what this reflection does to the identity
|
||||||
|
|
||||||
|
hyperplane_count = 0;
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
for(int j = 0; j < rank; j++) {
|
||||||
|
current = 0;
|
||||||
|
int *word1 = graph[i].word;
|
||||||
|
int word1len = graph[i].wordlength;
|
||||||
|
int *word2 = graph[graph[i].right[j]].word; // want to calculate word2 * word1^{-1}
|
||||||
|
int word2len = graph[graph[i].right[j]].wordlength;
|
||||||
|
for(int k = 0; k < word1len; k++) // apply inverse, i.e. go from left to right
|
||||||
|
current = graph[current].left[word1[k]];
|
||||||
|
for(int k = word2len - 1; k >= 0; k--) // now from right to left
|
||||||
|
current = graph[current].left[word2[k]];
|
||||||
|
if(graph[current].is_hyperplane_reflection == 0) {
|
||||||
|
graph[current].is_hyperplane_reflection = 1;
|
||||||
|
hyperplane_count++;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("We have %d hyperplanes\n", hyperplane_count);
|
||||||
|
DEBUG("Generate folding order\n");
|
||||||
|
|
||||||
|
edgelists = (edgelist_t*)malloc(order*hyperplane_count*sizeof(edgelist_t));
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
if(graph[i].is_hyperplane_reflection) {
|
||||||
|
for(int j = 0; j < order; j++) {
|
||||||
|
|
||||||
|
current = j;
|
||||||
|
for(int k = graph[i].wordlength - 1; k >= 0; k--) // apply hyperplane reflection
|
||||||
|
current = graph[current].left[graph[i].word[k]];
|
||||||
|
|
||||||
|
if(graph[j].wordlength < graph[current].wordlength) { // current has higher bruhat order than j
|
||||||
|
edgelists[edgelist_count].to = j;
|
||||||
|
edgelists[edgelist_count].next = graph[current].bruhat_lower;
|
||||||
|
graph[current].bruhat_lower = &edgelists[edgelist_count];
|
||||||
|
edgelist_count++;
|
||||||
|
} else if(graph[j].wordlength > graph[current].wordlength) { // j has higher bruhat order than current; these are already included from the other side
|
||||||
|
} else {
|
||||||
|
ERROR(1, "Chambers of equal word lengths should not be folded on each other!\n");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Remove redundant edges\n");
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
memset(seen, 0, order*sizeof(int));
|
||||||
|
for(int len = 1; len <= max_wordlength; len++) {
|
||||||
|
// remove all edges originating from i of length len which connect to something already seen using shorter edges
|
||||||
|
edge = graph[i].bruhat_lower;
|
||||||
|
previous = (edgelist_t*)0;
|
||||||
|
while(edge) {
|
||||||
|
if(seen[edge->to] && graph[i].wordlength - graph[edge->to].wordlength == len) {
|
||||||
|
// printf("deleting from %d to %d\n", i, edge->to);
|
||||||
|
if(previous)
|
||||||
|
previous->next = edge->next;
|
||||||
|
else
|
||||||
|
graph[i].bruhat_lower = edge->next;
|
||||||
|
} else {
|
||||||
|
previous = edge;
|
||||||
|
}
|
||||||
|
edge = edge->next;
|
||||||
|
}
|
||||||
|
|
||||||
|
// see which nodes we can reach using only edges up to length len, mark them as seen
|
||||||
|
queue_init(&queue);
|
||||||
|
queue_put(&queue, i);
|
||||||
|
seen[i] = 1;
|
||||||
|
while((current = queue_get(&queue)) != -1) {
|
||||||
|
edge = graph[current].bruhat_lower;
|
||||||
|
while(edge) {
|
||||||
|
if(!seen[edge->to] && graph[current].wordlength - graph[edge->to].wordlength == len) {
|
||||||
|
seen[edge->to] = 1;
|
||||||
|
queue_put(&queue, edge->to);
|
||||||
|
}
|
||||||
|
edge = edge->next;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
DEBUG("Reverse folding order\n");
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
edge = graph[i].bruhat_lower;
|
||||||
|
while(edge) {
|
||||||
|
edgelists[edgelist_count].to = i;
|
||||||
|
edgelists[edgelist_count].next = graph[edge->to].bruhat_higher;
|
||||||
|
graph[edge->to].bruhat_higher = &edgelists[edgelist_count];
|
||||||
|
edgelist_count++;
|
||||||
|
edge = edge->next;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
printf("The group is: \n");
|
||||||
|
for(int i =0; i < order; i++) {
|
||||||
|
if(graph[i].wordlength == 0)
|
||||||
|
printf("1 ");
|
||||||
|
else
|
||||||
|
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
|
||||||
|
}
|
||||||
|
printf("\n");
|
||||||
|
|
||||||
|
DEBUG("Enumerate thickenings\n");
|
||||||
|
DEBUG("\n");
|
||||||
|
|
||||||
|
thickenings_count = fat_count = slim_count = balanced_count = 0;
|
||||||
|
memset(level, 0, order*sizeof(int));
|
||||||
|
current_level = 1;
|
||||||
|
head = order - 1;
|
||||||
|
level[head] = -1;
|
||||||
|
while(current_level > 0) {
|
||||||
|
// calculate transitive closure
|
||||||
|
queue_init(&queue);
|
||||||
|
queue_put(&queue, head);
|
||||||
|
while((current = queue_get(&queue)) != -1) {
|
||||||
|
edge = graph[current].bruhat_lower;
|
||||||
|
while(edge) {
|
||||||
|
if(level[edge->to] == 0) {
|
||||||
|
level[edge->to] = current_level;
|
||||||
|
queue_put(&queue, edge->to);
|
||||||
|
}
|
||||||
|
edge = edge->next;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
is_fat = is_slim = 1;
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
if(level[graph[i].opposite] != 0) {
|
||||||
|
if(level[i] != 0)
|
||||||
|
is_slim = 0;
|
||||||
|
} else {
|
||||||
|
if(level[i] == 0)
|
||||||
|
is_fat = 0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// count
|
||||||
|
thickenings_count++;
|
||||||
|
if(is_fat)
|
||||||
|
fat_count++;
|
||||||
|
if(is_slim)
|
||||||
|
slim_count++;
|
||||||
|
if(is_slim && is_fat)
|
||||||
|
balanced_count++;
|
||||||
|
|
||||||
|
// print out levels
|
||||||
|
if(is_fat && is_slim) {
|
||||||
|
// check for invariances
|
||||||
|
for(int j = 0; j < rank; j++) {
|
||||||
|
left_invariant[j] = 1;
|
||||||
|
right_invariant[j] = 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
for(int j = 0; j < rank; j++) {
|
||||||
|
if(level[i] == 0 && level[graph[i].left[j]] != 0 || level[i] != 0 && level[graph[i].left[j]] == 0)
|
||||||
|
left_invariant[j] = 0;
|
||||||
|
if(level[i] == 0 && level[graph[i].right[j]] != 0 || level[i] != 0 && level[graph[i].right[j]] == 0)
|
||||||
|
right_invariant[j] = 0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
if(level[i] != 0)
|
||||||
|
printf("x");
|
||||||
|
else
|
||||||
|
printf("%d", level[i]);
|
||||||
|
}
|
||||||
|
printf(" left: ");
|
||||||
|
for(int j = 0; j < rank; j++)
|
||||||
|
if(left_invariant[j])
|
||||||
|
printf("%c", alphabet[j]);
|
||||||
|
else
|
||||||
|
printf(" ");
|
||||||
|
printf(" right: ");
|
||||||
|
for(int j = 0; j < rank; j++)
|
||||||
|
if(right_invariant[j])
|
||||||
|
printf("%c", alphabet[j]);
|
||||||
|
else
|
||||||
|
printf(" ");
|
||||||
|
printf("\n");
|
||||||
|
}
|
||||||
|
|
||||||
|
// try to find empty spot to the left of "head"
|
||||||
|
for(i = head - 1; i >= 0; i--)
|
||||||
|
if(level[i] == 0)
|
||||||
|
break;
|
||||||
|
if(i >= 0) {
|
||||||
|
head = i;
|
||||||
|
level[head] = -1;
|
||||||
|
current_level++;
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
|
||||||
|
// if none was found, try to move "head" to the left
|
||||||
|
while(current_level > 0) {
|
||||||
|
for(i = head - 1; i >= 0; i--)
|
||||||
|
if(level[i] == 0 || level[i] >= current_level)
|
||||||
|
break;
|
||||||
|
if(i >= 0) { // if this was successful, just move head
|
||||||
|
level[head] = 0;
|
||||||
|
head = i;
|
||||||
|
level[head] = -1;
|
||||||
|
break;
|
||||||
|
} else { // if moving the head is not possible, take the next head to the right
|
||||||
|
current_level--;
|
||||||
|
level[head] = 0;
|
||||||
|
do {
|
||||||
|
head++;
|
||||||
|
} while(head < order && level[head] != -1);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// clean up
|
||||||
|
for(int i = 0; i < head; i++)
|
||||||
|
if(level[i] >= current_level)
|
||||||
|
level[i] = 0;
|
||||||
|
|
||||||
|
// print out levels
|
||||||
|
/* for(int i = 0; i < order; i++) { */
|
||||||
|
/* if(level[i] == -1) */
|
||||||
|
/* printf("x"); */
|
||||||
|
/* else */
|
||||||
|
/* printf("%d", level[i]); */
|
||||||
|
/* } */
|
||||||
|
/* printf(" %d\n", current_level); */
|
||||||
|
}
|
||||||
|
|
||||||
|
printf("\n");
|
||||||
|
printf("Found %d thickenings, %d fat, %d slim, %d balanced\n", thickenings_count, fat_count, slim_count, balanced_count);
|
||||||
|
|
||||||
|
/*
|
||||||
|
printf("\n");
|
||||||
|
|
||||||
|
for(int i = 0; i < order; i++) {
|
||||||
|
printf("%-6s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
|
||||||
|
|
||||||
|
edge = graph[i].bruhat_higher;
|
||||||
|
while(edge) {
|
||||||
|
printf("-> %-6s ", alphabetize(graph[edge->to].word, graph[edge->to].wordlength, alphabet, string_buffer1));
|
||||||
|
edge = edge->next;
|
||||||
|
}
|
||||||
|
//printf("Bruhat: %6s -> %-6s\n", alphabetize(graph[current].word, graph[current].wordlength, alphabet, string_buffer1), alphabetize(graph[j].word, graph[j].wordlength, alphabet, string_buffer2));
|
||||||
|
|
||||||
|
printf("\n");
|
||||||
|
}
|
||||||
|
printf("\n");
|
||||||
|
*/
|
||||||
|
|
||||||
|
free(edgelists);
|
||||||
|
free(words);
|
||||||
|
free(string_buffer1);
|
||||||
|
free(string_buffer2);
|
||||||
|
free(graph);
|
||||||
|
free(graph_unsorted);
|
||||||
|
free(graph_data);
|
||||||
|
free(wordlength_order);
|
||||||
|
free(reverse_wordlength_order);
|
||||||
|
free(seen);
|
||||||
|
free(level);
|
||||||
|
free(left);
|
||||||
|
free(right);
|
||||||
|
free(left_invariant);
|
||||||
|
free(right_invariant);
|
||||||
|
free(type.factors);
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue
Block a user