simplified graphs
This commit is contained in:
Florian Stecker
parent
4703357f41
commit
8c21410dda
2
Makefile
2
Makefile
@ -1,5 +1,5 @@
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HEADERS=coxeter.h thickenings.h queue.h
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OPTIONS=-O3 -m64 -march=native -flto -funroll-loops -std=gnu99 -pg
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OPTIONS=-O3 -m64 -march=native -flto -funroll-loops -std=gnu99
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all: generate process
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@ -72,7 +72,7 @@ int main(int argc, const char *argv[])
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fwrite(&type.n, sizeof(int), 1, stdout);
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fwrite(type.factors, sizeof(simple_type_t), type.n, stdout);
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long count = enumerate_balanced_thickenings(type, graph, alphabet, stdout);
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long count = enumerate_balanced_thickenings(type, graph, order, alphabet, stdout);
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fprintf(stderr, "\n");
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fprintf(stderr, "Found %ld balanced thickenings\n\n", count);
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257
test.c
Normal file
257
test.c
Normal file
@ -0,0 +1,257 @@
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#include <stdio.h>
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#include <memory.h>
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#include "thickenings.h"
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#include "queue.h"
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#define SWAP(t, a, b) do {t tmp = a; a = b; b = tmp;} while(0)
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int edgelist_contains(edgelist_t *list, int needle) {
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while(list) {
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if(list->to == needle)
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return 1;
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list = list->next;
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}
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return 0;
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}
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edgelist_t *edgelist_add(edgelist_t *list, int new, edgelist_t *storage, int *storage_index)
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{
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edgelist_t *new_link = &storage[*storage_index];
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new_link->next = list;
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new_link->to = new;
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(*storage_index)++;
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return new_link;
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}
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int main(int argc, const char *argv[])
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{
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semisimple_type_t type;
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node_t *graph;
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int *leftbuf, *rightbuf;
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edgelist_t *edgelists;
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edgelist_t *edgelists_simplified;
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int edgelists_simplified_used;
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int *words;
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int rank, order, max_wordlength;
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int *reduced, *group, *simplified;
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int *seen;
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int current;
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edgelist_t *edge, *previous;
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queue_t queue;
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char alphabet[] = "abcdefghijklmnopqrstuvwxyz";
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char buffer[1024], buffer2[1024];
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int ncosets;
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node_t *simplified_graph;
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// left and right invariances as bitmasks
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// int left = ~(1 << (atoi(argv[1]) - atoi(argv[3])));
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// int right = ~(1 << (atoi(argv[1]) - atoi(argv[2])));
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int left = atoi(argv[2]);
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int right = atoi(argv[3]);
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type.n = 1;
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type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
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type.factors[0].series = 'B';
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type.factors[0].rank = atoi(argv[1]);
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rank = coxeter_rank(type);
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order = coxeter_order(type);
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graph = (node_t*)malloc(order*sizeof(node_t));
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leftbuf = (int*)malloc(rank*order*sizeof(int));
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rightbuf = (int*)malloc(rank*order*sizeof(int));
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for(int i = 0; i < order; i++) {
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graph[i].left = &leftbuf[i*rank];
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graph[i].right = &rightbuf[i*rank];
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}
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prepare_graph(type, graph, &edgelists, &words);
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reduced = (int*)malloc(order*sizeof(int));
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group = (int*)malloc(order*sizeof(int));
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simplified = (int*)malloc(order*sizeof(int));
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for(int i = 0; i < order; i++) {
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group[i] = -1;
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reduced[i] = i;
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}
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// step 1: group
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for(int i = 0; i < order; i++) {
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if(group[i] != -1)
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continue;
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queue_init(&queue);
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queue_put(&queue, i);
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while((current = queue_get(&queue)) != -1) {
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if(group[current] != -1)
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continue;
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group[current] = i;
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for(int j = 0; j < rank; j++) {
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if(left & (1 << j))
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queue_put(&queue, graph[current].left[j]);
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if(right & (1 << j))
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queue_put(&queue, graph[current].right[j]);
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}
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}
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}
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// step 2: find minimum
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for(int i = 0; i < order; i++)
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if(graph[i].wordlength < graph[reduced[group[i]]].wordlength)
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reduced[group[i]] = i;
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// step 3: assign minimum to all
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for(int i = 0; i < order; i++)
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reduced[i] = reduced[group[i]];
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// count cosets
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ncosets = 0;
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for(int i = 0; i < order; i++)
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if(reduced[i] == i)
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simplified[i] = ncosets++;
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for(int i = 0; i < order; i++)
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simplified[i] = simplified[reduced[i]];
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fprintf(stderr, "Number of double cosets: %d\n\n", ncosets);
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max_wordlength = coxeter_hyperplanes(type);
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simplified_graph = (node_t*) malloc(ncosets*sizeof(node_t));
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edgelists_simplified = (edgelist_t*) malloc(2*max_wordlength*order*sizeof(edgelist_t));
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seen = (int*) malloc(ncosets*sizeof(int));
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edgelists_simplified_used = 0;
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// copy minima
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current = 0;
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for(int i = 0; i < order; i++)
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if(reduced[i] == i) { // is minimum
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simplified_graph[simplified[i]].word = graph[i].word;
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simplified_graph[simplified[i]].wordlength = graph[i].wordlength;
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simplified_graph[simplified[i]].opposite = simplified[graph[i].opposite];
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simplified_graph[simplified[i]].bruhat_lower = (edgelist_t*)0;
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simplified_graph[simplified[i]].bruhat_higher = (edgelist_t*)0;
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}
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// some output
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for(int i = 0; i < ncosets; i++)
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fprintf(stderr, "%s <=> %s\n", simplified_graph[i].wordlength == 0 ? "1" : alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer), simplified_graph[simplified_graph[i].opposite].wordlength == 0 ? "1" : alphabetize(simplified_graph[simplified_graph[i].opposite].word, simplified_graph[simplified_graph[i].opposite].wordlength, alphabet, buffer2));
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// find order relations
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for(int i = 0; i < order; i++) {
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edge = graph[i].bruhat_lower;
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while(edge) {
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int this = simplified[i];
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int that = simplified[edge->to];
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if(this != that) {
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// found something
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if(!edgelist_contains(simplified_graph[this].bruhat_lower, that))
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simplified_graph[this].bruhat_lower = edgelist_add(simplified_graph[this].bruhat_lower, that, edgelists_simplified, &edgelists_simplified_used);
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// if(!edgelist_contains(simplified_graph[that].bruhat_higher, this))
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// simplified_graph[that].bruhat_higher = edgelist_add(simplified_graph[that].bruhat_higher, this, edgelists_simplified, &edgelists_simplified_used);
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ERROR(simplified_graph[this].wordlength <= simplified_graph[that].wordlength, "The order assumption is being violated!\n");
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}
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edge = edge->next;
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}
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}
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fprintf(stderr, "\nAdded %d edges.\n\n", edgelists_simplified_used);
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// remove redundant edges
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for(int i = 0; i < ncosets; i++) {
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memset(seen, 0, ncosets*sizeof(int));
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queue_init(&queue);
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for(int len = 1; len <= simplified_graph[i].wordlength; len++) {
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edge = simplified_graph[i].bruhat_lower;
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previous = (edgelist_t*)0;
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while(edge) {
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// only look at edges of this length now
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if(simplified_graph[i].wordlength - simplified_graph[edge->to].wordlength != len) {
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// we only consider edges of length len in this pass
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previous = edge;
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} else if(seen[edge->to]) {
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// this edge is redundant, remove it
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// fprintf(stderr, "removing edge from %d to %d\n", i, edge->to);
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if(previous)
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previous->next = edge->next;
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else
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simplified_graph[i].bruhat_lower = edge->next;
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} else {
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// this edge was not redundant, add to seen
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previous = edge;
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seen[edge->to] = 1;
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queue_put(&queue, edge->to);
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}
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edge = edge->next;
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}
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// calculate transitive closure of seen nodes
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while((current = queue_get(&queue)) != -1) {
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edge = simplified_graph[current].bruhat_lower;
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while(edge) {
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if(!seen[edge->to]) {
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seen[edge->to] = 1;
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queue_put(&queue, edge->to);
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}
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edge = edge->next;
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}
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}
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}
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}
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// reverse order
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for(int i = 0; i < ncosets; i++) {
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edge = simplified_graph[i].bruhat_lower;
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while(edge) {
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simplified_graph[edge->to].bruhat_higher =
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edgelist_add(simplified_graph[edge->to].bruhat_higher,
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i, edgelists_simplified, &edgelists_simplified_used);
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edge = edge->next;
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}
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}
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fprintf(stdout, "digraph test123 {\n");
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for(int i = 0; i < ncosets; i++) {
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edge = simplified_graph[i].bruhat_lower;
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while(edge) {
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fprintf(stdout, "%s -> %s;\n",
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alphabetize(simplified_graph[i].word, simplified_graph[i].wordlength, alphabet, buffer),
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alphabetize(simplified_graph[edge->to].word, simplified_graph[edge->to].wordlength, alphabet, buffer2));
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edge = edge->next;
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}
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}
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fprintf(stdout, "}\n");
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long nthickenings = enumerate_balanced_thickenings(type, simplified_graph, ncosets, alphabet, stdout);
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fprintf(stderr, "Found %ld balanced thickenings.\n", nthickenings);
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/* for(int i = 0; i < order; i++)
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printf("%s <= %s\n",
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reduced[i] == 0 ? "1" : alphabetize(graph[reduced[i]].word, graph[reduced[i]].wordlength, alphabet, buffer2),
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i == 0 ? "1" : alphabetize(graph[i].word, graph[i].wordlength, alphabet, buffer)); */
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free(seen);
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free(simplified_graph);
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free(edgelists_simplified);
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free(type.factors);
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free(graph);
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free(edgelists);
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free(words);
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free(reduced);
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free(group);
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free(simplified);
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free(leftbuf);
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free(rightbuf);
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return 0;
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}
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@ -289,6 +289,7 @@ void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists
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typedef struct {
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int rank;
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int order;
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int size; // the size of the graph; this can vary from the order if we take quotients beforehand
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const node_t *graph;
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int printstep;
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const char *alphabet;
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@ -307,7 +308,7 @@ static int transitive_closure(const enumeration_info_t *info, signed char *level
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level[info->graph[head].opposite] = -current_level;
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queue_put(&queue, head);
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for(int i = head + 1; level[i] != HEAD_MARKER && i < info->order; i++) { // everything which is right to the head and empty will not get marked in this or higher levels, so we can mark its opposite
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for(int i = head + 1; level[i] != HEAD_MARKER && i < info->size; i++) { // everything which is right to the head and empty will not get marked in this or higher levels, so we can mark its opposite
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if(level[i] == current_level) {
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is_slim = 0;
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break;
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@ -342,11 +343,11 @@ static inline void output_thickening(const enumeration_info_t *info, signed char
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{
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// if printstep is set accordingly, write state to stderr
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if(is_slim && is_fat && info->printstep > 0 && (count + 1) % info->printstep == 0) {
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print_thickening(info->rank, info->order, level, current_level, info->alphabet, stderr);
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print_thickening(info->rank, info->size, level, current_level, info->alphabet, stderr);
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fprintf(stderr, "\n");
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}
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else if(info->printstep < 0) {
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print_thickening(info->rank, info->order, level, current_level - !is_slim, info->alphabet, stderr);
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print_thickening(info->rank, info->size, level, current_level - !is_slim, info->alphabet, stderr);
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fprintf(stderr, " ");
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if(is_slim) {
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fprintf(stderr, "S");
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@ -378,7 +379,7 @@ static long enumerate_tree(const enumeration_info_t *info, signed char *level, i
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if(is_fat) {
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count++;
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fwrite(level, sizeof(signed char), info->order, info->outfile);
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fwrite(level, sizeof(signed char), info->size, info->outfile);
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} else {
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for(int i = head - 1; i >= 0; i--)
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if(level[i] == 0)
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@ -388,14 +389,14 @@ static long enumerate_tree(const enumeration_info_t *info, signed char *level, i
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// clean up
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level[head] = 0;
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for(int i = 0; i < info->order; i++)
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for(int i = 0; i < info->size; i++)
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if(level[i] >= current_level && level[i] != HEAD_MARKER || level[i] <= -current_level)
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level[i] = 0;
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return count;
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}
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long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const char *alphabet, FILE *outfile)
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long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, int size, const char *alphabet, FILE *outfile)
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{
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// int rank, order;
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signed char *level;
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@ -406,6 +407,7 @@ long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
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info.rank = coxeter_rank(type);
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info.order = coxeter_order(type);
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info.size = size;
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info.graph = graph;
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info.alphabet = (char*)alphabet;
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info.outfile = outfile;
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@ -414,10 +416,16 @@ long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const
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if(getenv("PRINTSTEP"))
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info.printstep = atoi(getenv("PRINTSTEP"));
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level = (signed char*)malloc(info.order*sizeof(int));
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memset(level, 0, info.order*sizeof(int));
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// the algorithm only works if the opposition pairing does not stabilize any element
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// if this happens, there can be no balanced thickenings
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for(int i = 0; i < info.size; i++)
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if(graph[i].opposite == i)
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return 0;
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for(int i = info.order - 1; i >= 0; i--)
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level = (signed char*)malloc(info.size*sizeof(int));
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memset(level, 0, info.size*sizeof(int));
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for(int i = info.size - 1; i >= 0; i--)
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count += enumerate_tree(&info, level, 1, i);
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free(level);
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@ -29,6 +29,6 @@ char *alphabetize(int *word, int len, const char *alphabet, char *buffer);
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void print_thickening(int rank, int order, const signed char *thickening, int level, const char *alphabet, FILE *f);
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static int compare_wordlength(const void *a, const void *b, void *gr);
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void prepare_graph(semisimple_type_t type, node_t *graph, edgelist_t **edgelists_pointer, int **words_pointer);
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long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, const char *alphabet, FILE *outfile);
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long enumerate_balanced_thickenings(semisimple_type_t type, node_t *graph, int size, const char *alphabet, FILE *outfile);
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#endif
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