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enumerate-balanced-ideals
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This commit is contained in:
Florian Stecker 2016-08-26 14:56:23 +02:00
parent a17c6fb06e
commit d47c3cb45b
4 changed files with 96 additions and 21 deletions
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2
Makefile
View File

@ -1,5 +1,5 @@
HEADERS=coxeter.h thickenings.h queue.h
OPTIONS=-O0 -g -std=gnu99
OPTIONS=-O3 -g -std=gnu99
all: generate process

12
process.c
View File

@ -95,17 +95,23 @@ int main(int argc, const char *argv[])
// finally do stuff
int counter = 0;
while(fread(level, sizeof(int), order, infile) == order) {
if((counter++) % 100000 == 0)
print_thickening(rank, order, level, 0, 0, 0, alphabet, stdout);
continue;
for(int j = 0; j < rank; j++) {
left_invariant[j] = 1;
right_invariant[j] = 1;
}
for(int j = 0; j < order; j++) {
for(int k = 0; k < rank; k++) {
if(level[j] == 0 && level[graph[j].left[k]] != 0 || level[j] != 0 && level[graph[j].left[k]] == 0)
if(level[j] > 0 && level[graph[j].left[k]] < 0 || level[j] < 0 && level[graph[j].left[k]] > 0)
left_invariant[k] = 0;
if(level[j] == 0 && level[graph[j].right[k]] != 0 || level[j] != 0 && level[graph[j].right[k]] == 0)
if(level[j] > 0 && level[graph[j].right[k]] < 0 || level[j] < 0 && level[graph[j].right[k]] > 0)
right_invariant[k] = 0;
}
}
@ -113,7 +119,7 @@ int main(int argc, const char *argv[])
ngens = 0;
memset(generators, 0, order*sizeof(int));
for(int j = 0; j < order; j++) {
if(level[j] == -1 && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
if(level[j] == 1000 && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
ngens++;
queue_init(&queue);
queue_put(&queue, j);

100
thickenings.c
View File

@ -20,6 +20,33 @@ char *alphabetize(int *word, int len, const char *alphabet, char *buffer)
return buffer;
}
void print_thickening(int rank, int order, const int *thickening, int is_fat, int is_slim, int conflict, const char *alphabet, FILE *f)
{
for(int i = 0; i < order; i++) {
if(thickening[i] == 1000)
fprintf(f, "\e[41mx\e[40m\e[m");
else if(thickening[i] < 0 && thickening[i] > -10)
fprintf(f, "\e[47m\e[30m%d\e[40m\e[m", -thickening[i]);
else if(thickening[i] <= -10)
fprintf(f, "\e[47m\e[30m+\e[40m\e[m");
else if(thickening[i] > 0 && thickening[i] < 10)
fprintf(f, "%d", thickening[i]);
else if(thickening[i] >= 10)
fprintf(f, "+");
else
fprintf(f, " ");
}
if(is_fat)
fprintf(f, " F");
if(is_slim)
fprintf(f, " S");
if(conflict)
fprintf(f, " C");
fprintf(f, "\n");
}
void print_balanced_thickening(int rank, int order, const int *thickening, const int *left_invariant, const int *right_invariant, const char *alphabet, FILE *f)
{
for(int i = 0; i < order; i++) {
@ -288,6 +315,7 @@ void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
int is_fat, is_slim;
int current_level, head, current;
int i;
int conflict;
edgelist_t *edge;
queue_t queue;
@ -303,14 +331,31 @@ void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
memset(level, 0, order*sizeof(int));
current_level = 1;
head = order - 1;
level[head] = -1;
level[head] = 1000;
while(current_level > 0) {
// calculate transitive closure
conflict = 0;
queue_init(&queue);
queue_put(&queue, head);
for(int i = head + 1; level[i] != 1000 && i < order; i++) {
if(level[graph[i].opposite] == 0) {
level[graph[i].opposite] = current_level;
queue_put(&queue, graph[i].opposite);
}
}
while((current = queue_get(&queue)) != -1) {
if(level[current] < 0 || level[graph[current].opposite] > 0) { // conflict, can not be slim
conflict = 1;
break;
}
if(level[graph[current].opposite] == 0)
level[graph[current].opposite] = - current_level;
edge = graph[current].bruhat_lower;
while(edge) {
if(level[edge->to] < 0) {
conflict = 1;
break;
}
if(level[edge->to] == 0) {
level[edge->to] = current_level;
queue_put(&queue, edge->to);
@ -319,8 +364,8 @@ void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
}
}
/*
// we have a thickening, do something with it!
is_fat = is_slim = 1;
for(int i = 0; i < order; i++) {
if(level[graph[i].opposite] != 0) {
@ -344,7 +389,9 @@ void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
fwrite(level, sizeof(int), order, outfile);
balanced_count++;
}
*/
/*
// print out the thickening
if(is_fat && is_slim) {
// check for invariances
@ -362,44 +409,65 @@ void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
}
print_balanced_thickening(rank, order, level, left_invariant, right_invariant, alphabet, stderr);
}
*/
is_fat = 1;
for(int i = 0; i < order; i++) {
if(level[i] == 0)
is_fat = 0;
}
if(is_fat && !conflict) {
// ERROR(balanced_count >= MAX_THICKENINGS, "Too many balanced thickenings! Increase MAX_THICKENINGS\n");
fwrite(level, sizeof(int), order, outfile);
balanced_count++;
}
// print_thickening(rank, order, level, is_fat, !conflict, conflict, alphabet, stderr);
// now find the next one!
// 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;
// try to find empty spot to the left of "head", but only if it is slim, as otherwise there is no point in adding even more
if(!conflict) {
for(i = head - 1; i >= 0; i--)
if(level[i] == 0)
break;
if(i >= 0) {
head = i;
level[head] = 1000;
current_level++;
// print_thickening(rank, order, level, 0, 0, 0, alphabet, stderr);
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)
if(level[i] == 0 || level[i] >= current_level || level[i] <= -current_level)
break;
if(i >= 0) { // if this was successful, just move head
level[head] = 0;
head = i;
level[head] = -1;
level[head] = 1000;
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);
} while(head < order && level[head] != 1000);
}
}
// clean up
for(int i = 0; i < head; i++)
if(level[i] >= current_level)
for(int i = 0; i < order; i++)
if(level[i] >= current_level && level[i] != 1000 || level[i] <= -current_level)
level[i] = 0;
// print_thickening(rank, order, level, 0, 0, 0, alphabet, stderr);
}
fprintf(stderr, "\n");

3
thickenings.h
View File

@ -5,7 +5,7 @@
#define DEBUG(msg, ...) do{fprintf(stderr, msg, ##__VA_ARGS__); }while(0)
#define MAX_THICKENINGS 1000000
#define MAX_THICKENINGS 10000000
typedef struct _edgelist {
int to;
@ -25,6 +25,7 @@ typedef struct {
char *alphabetize(int *word, int len, const char *alphabet, char *buffer);
void print_balanced_thickening(int rank, int order, const int *thickening, const int *left_invariant, const int *right_invariant, const char *alphabet, FILE *f);
void print_thickening(int rank, int order, const int *thickening, int fat, int slim, int conflict, const char *alphabet, FILE *f);
static int compare_wordlength(const void *a, const void *b, void *gr);
void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists_pointer, int **words_pointer);
void enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const char *alphabet, FILE *outfile);