List thickenings when found
This commit is contained in:
Florian Stecker
parent
53811ef32a
commit
3f9df34e01
167
thickenings.c
167
thickenings.c
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@ -11,6 +11,8 @@
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#define DEBUG(msg, ...) do{fprintf(stderr, msg, ##__VA_ARGS__); }while(0)
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#define MAX_THICKENINGS 10000
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typedef struct _edgelist {
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int to;
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struct _edgelist *next;
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@ -37,6 +39,32 @@ static char *alphabetize(int *word, int len, const char *alphabet, char *buffer)
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return buffer;
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}
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static void print_balanced_thickening(int rank, int order, const int *thickening, const int *left_invariant, const int *right_invariant, const char *alphabet)
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{
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for(int i = 0; i < order; i++) {
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if(thickening[i])
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printf("x");
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else
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printf("0");
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}
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printf(" left: ");
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for(int j = 0; j < rank; j++)
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if(left_invariant[j])
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printf("%c", alphabet[j]);
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else
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printf(" ");
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printf(" right: ");
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for(int j = 0; j < rank; j++)
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if(right_invariant[j])
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printf("%c", alphabet[j]);
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else
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printf(" ");
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printf("\n");
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}
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static int compare_wordlength(const void *a, const void *b, void *gr)
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{
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int i = *((int*)a);
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@ -67,6 +95,8 @@ int main(int argc, const char *argv[])
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int is_fat, is_slim;
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int thickenings_count, fat_count, slim_count, balanced_count;
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int *balanced_thickenings;
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char *string_buffer1, *string_buffer2;
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const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
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@ -86,7 +116,7 @@ int main(int argc, const char *argv[])
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ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
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DEBUG("The group has rank %d and order %d\n", rank, order);
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// DEBUG("The group has rank %d and order %d\n", rank, order);
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graph = (node_t*)malloc(order*sizeof(node_t));
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graph_unsorted = (node_t*)malloc(order*sizeof(node_t));
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@ -99,8 +129,9 @@ int main(int argc, const char *argv[])
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right = (int*)malloc(order*rank*sizeof(int));
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left_invariant = (int*)malloc(rank*sizeof(int));
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right_invariant = (int*)malloc(rank*sizeof(int));
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balanced_thickenings = (int*)malloc(MAX_THICKENINGS*order*sizeof(int));
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DEBUG("Generate Cayley graph\n");
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// DEBUG("Generate Cayley graph\n");
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generate_coxeter_graph(type, graph_data);
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@ -116,7 +147,7 @@ int main(int argc, const char *argv[])
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graph_unsorted[i].is_hyperplane_reflection = 0;
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}
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DEBUG("Find wordlengths\n");
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// DEBUG("Find wordlengths\n");
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graph_unsorted[0].wordlength = 0;
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queue_init(&queue);
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@ -139,7 +170,7 @@ int main(int argc, const char *argv[])
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string_buffer1 = (char*)malloc((max_wordlength+1)*sizeof(char));
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string_buffer2 = (char*)malloc((max_wordlength+1)*sizeof(char));
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DEBUG("Sort by wordlength\n");
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// DEBUG("Sort by wordlength\n");
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for(int i = 0; i < order; i++)
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wordlength_order[i] = i;
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@ -152,7 +183,7 @@ int main(int argc, const char *argv[])
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graph[i].left[j] = reverse_wordlength_order[graph[i].left[j]]; // rewrite references
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}
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DEBUG("Find words\n");
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// DEBUG("Find words\n");
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words = (int*)malloc(order*max_wordlength*sizeof(int));
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memset(words, 0, order*max_wordlength*sizeof(int));
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@ -171,7 +202,7 @@ int main(int argc, const char *argv[])
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}
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}
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DEBUG("Generate right edges\n");
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// DEBUG("Generate right edges\n");
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for(int i = 0; i < order; i++) {
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for(int j = 0; j < rank; j++) {
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@ -183,7 +214,7 @@ int main(int argc, const char *argv[])
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}
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}
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DEBUG("Find opposites\n");
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// DEBUG("Find opposites\n");
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node_t *longest = &graph[order-1];
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for(int i = 0; i < order; i++) {
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@ -193,7 +224,7 @@ int main(int argc, const char *argv[])
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graph[i].opposite = current;
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}
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DEBUG("Enumerate hyperplanes\n"); // every right edge is a reflection along a hyperplane; calculate what this reflection does to the identity
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// DEBUG("Enumerate hyperplanes\n"); // every right edge is a reflection along a hyperplane; calculate what this reflection does to the identity
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hyperplane_count = 0;
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for(int i = 0; i < order; i++) {
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@ -214,8 +245,8 @@ int main(int argc, const char *argv[])
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}
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}
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DEBUG("We have %d hyperplanes\n", hyperplane_count);
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DEBUG("Generate folding order\n");
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// DEBUG("The Weyl chambers are bounded by %d hyperplanes\n", hyperplane_count);
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// DEBUG("Generate folding order\n");
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edgelists = (edgelist_t*)malloc(order*hyperplane_count*sizeof(edgelist_t));
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for(int i = 0; i < order; i++) {
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@ -239,7 +270,7 @@ int main(int argc, const char *argv[])
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}
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}
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DEBUG("Remove redundant edges\n");
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// DEBUG("Remove redundant edges\n");
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for(int i = 0; i < order; i++) {
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memset(seen, 0, order*sizeof(int));
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@ -277,7 +308,7 @@ int main(int argc, const char *argv[])
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}
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}
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DEBUG("Reverse folding order\n");
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// DEBUG("Reverse folding order\n");
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for(int i = 0; i < order; i++) {
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edge = graph[i].bruhat_lower;
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@ -290,17 +321,21 @@ int main(int argc, const char *argv[])
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}
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}
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printf("The group is: \n");
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for(int i =0; i < order; i++) {
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if(graph[i].wordlength == 0)
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printf("1 ");
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else
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printf("Rank: %d\t\tOrder: %d\t\tHyperplanes: %d\n", rank, order, hyperplane_count);
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printf("\n");
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printf("Group elements: \n");
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for(int i = 0, wl = 0; i < order; i++) {
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if(i == 0) {
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printf("1");
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} else if(graph[i].wordlength > wl) {
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printf("\n%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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wl = graph[i].wordlength;
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} else
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printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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}
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printf("\n");
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printf("\n\n");
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DEBUG("Enumerate thickenings\n");
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DEBUG("\n");
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// DEBUG("Enumerate thickenings\n");
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thickenings_count = fat_count = slim_count = balanced_count = 0;
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memset(level, 0, order*sizeof(int));
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@ -339,51 +374,33 @@ int main(int argc, const char *argv[])
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fat_count++;
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if(is_slim)
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slim_count++;
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if(is_slim && is_fat)
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if(is_slim && is_fat) {
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ERROR(balanced_count >= MAX_THICKENINGS, "Too many balanced thickenings! Increase MAX_THICKENINGS\n");
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memcpy(&balanced_thickenings[balanced_count*order], level, order*sizeof(int));
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balanced_count++;
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}
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// print out levels
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if(is_fat && is_slim) {
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// check for invariances
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for(int j = 0; j < rank; j++) {
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left_invariant[j] = 1;
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right_invariant[j] = 1;
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left_invariant[j] = 1;
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right_invariant[j] = 1;
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}
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for(int i = 0; i < order; i++) {
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for(int j = 0; j < rank; j++) {
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if(level[i] == 0 && level[graph[i].left[j]] != 0 || level[i] != 0 && level[graph[i].left[j]] == 0)
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left_invariant[j] = 0;
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if(level[i] == 0 && level[graph[i].right[j]] != 0 || level[i] != 0 && level[graph[i].right[j]] == 0)
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right_invariant[j] = 0;
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}
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for(int j = 0; j < rank; j++) {
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if(level[i] == 0 && level[graph[i].left[j]] != 0 || level[i] != 0 && level[graph[i].left[j]] == 0)
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left_invariant[j] = 0;
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if(level[i] == 0 && level[graph[i].right[j]] != 0 || level[i] != 0 && level[graph[i].right[j]] == 0)
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right_invariant[j] = 0;
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}
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}
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for(int i = 0; i < order; i++) {
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if(level[i] != 0)
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printf("x");
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else
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printf("%d", level[i]);
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}
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printf(" left: ");
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for(int j = 0; j < rank; j++)
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if(left_invariant[j])
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printf("%c", alphabet[j]);
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else
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printf(" ");
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printf(" right: ");
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for(int j = 0; j < rank; j++)
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if(right_invariant[j])
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printf("%c", alphabet[j]);
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else
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printf(" ");
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printf("\n");
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print_balanced_thickening(rank, order, level, left_invariant, right_invariant, alphabet);
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}
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// try to find empty spot to the left of "head"
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for(i = head - 1; i >= 0; i--)
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if(level[i] == 0)
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break;
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break;
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if(i >= 0) {
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head = i;
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level[head] = -1;
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@ -414,38 +431,41 @@ int main(int argc, const char *argv[])
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for(int i = 0; i < head; i++)
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if(level[i] >= current_level)
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level[i] = 0;
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// print out levels
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/* for(int i = 0; i < order; i++) { */
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/* if(level[i] == -1) */
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/* printf("x"); */
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/* else */
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/* printf("%d", level[i]); */
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/* } */
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/* printf(" %d\n", current_level); */
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}
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printf("\n");
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printf("Found %d thickenings, %d fat, %d slim, %d balanced\n", thickenings_count, fat_count, slim_count, balanced_count);
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printf("Found %d thickenings, %d fat, %d slim, %d balanced\n\n", thickenings_count, fat_count, slim_count, balanced_count);
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/*
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printf("\n");
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for(int i = 0; i < order; i++) {
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printf("%-6s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
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edge = graph[i].bruhat_higher;
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while(edge) {
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printf("-> %-6s ", alphabetize(graph[edge->to].word, graph[edge->to].wordlength, alphabet, string_buffer1));
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edge = edge->next;
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for(int i = 0; i < balanced_count; i++) {
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// figure out invariances
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for(int j = 0; j < rank; j++) {
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left_invariant[j] = 1;
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right_invariant[j] = 1;
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}
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//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));
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int *current_thickening = balanced_thickenings + i*order;
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for(int k = 0; k < order; k++) {
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for(int j = 0; j < rank; j++) {
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if(current_thickening[k] == 0 && current_thickening[graph[k].left[j]] != 0 || current_thickening[k] != 0 && current_thickening[graph[k].left[j]] == 0)
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left_invariant[j] = 0;
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if(current_thickening[k] == 0 && current_thickening[graph[k].right[j]] != 0 || current_thickening[k] != 0 && current_thickening[graph[k].right[j]] == 0)
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right_invariant[j] = 0;
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}
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}
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printf("left: ");
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for(int k = 0; k < rank; k++)
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printf("%c", left_invariant[k] ? alphabet[k] : ' ');
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printf(" right: ");
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for(int k = 0; k < rank; k++)
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printf("%c", right_invariant[k] ? alphabet[k] : ' ');
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printf("\n");
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}
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printf("\n");
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*/
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free(edgelists);
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free(words);
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free(string_buffer1);
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@ -462,6 +482,7 @@ int main(int argc, const char *argv[])
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free(left_invariant);
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free(right_invariant);
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free(type.factors);
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free(balanced_thickenings);
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return 0;
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}
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