void adjoint44(Mat4 *out, const Mat4 *in)
{
Mat4 A;
Vec4 tempv;
copy44( &A, in );
mxv_neg( tempv.elt, A.row[0].elt, 4 );
cross4( &(out->row[0]), &(A.row[1]), &(A.row[2]), &(A.row[3]));
cross4( &(out->row[1]), &(tempv), &(A.row[2]), &(A.row[3]));
cross4( &(out->row[2]), &(A.row[0]), &(A.row[1]), &(A.row[3]));
cross4( &(out->row[3]), &(tempv), &(A.row[1]), &(A.row[2]));
}
Graph::Graph(const int *cartan,
const std::vector<Word>& gens, //namesake
const std::vector<Word>& v_cogens,
const std::vector<Word>& e_gens,
const std::vector<Word>& f_gens,
const Vect& weights)
{
//define symmetry group relations
std::vector<Word> words = words_from_cartan(cartan);
{
const Logging::fake_ostream& os = logger.debug();
os << "relations =";
for (int w=0; w<6; ++w) {
Word& word = words[w];
os << "\n ";
for (unsigned i=0; i<word.size(); ++i) {
os << word[i];
}
}
os |0;
}
//check vertex stabilizer generators
{
const Logging::fake_ostream& os = logger.debug();
os << "v_cogens =";
for (unsigned w=0; w<v_cogens.size(); ++w) {
const Word& jenn = v_cogens[w]; //namesake
os << "\n ";
for (unsigned t=0; t<jenn.size(); ++t) {
int j = jenn[t];
os << j;
Assert (0<=j and j<4,
"generator out of range: letter w["
<< w << "][" << t << "] = " << j );
}
}
os |0;
}
//check edge generators
{
const Logging::fake_ostream& os = logger.debug();
os << "e_gens =";
for (unsigned w=0; w<e_gens.size(); ++w) {
const Word& edge = e_gens[w];
os << "\n ";
for (unsigned t=0; t<edge.size(); ++t) {
int j = edge[t];
os << j;
Assert (0<=j and j<4,
"generator out of range: letter w["
<< w << "][" << t << "] = " << j );
}
}
os |0;
}
//check face generators
{
const Logging::fake_ostream& os = logger.debug();
os << "f_gens =";
for (unsigned w=0; w<f_gens.size(); ++w) {
const Word& face = f_gens[w];
os << "\n ";
for (unsigned t=0; t<face.size(); ++t) {
int j = face[t];
os << j;
Assert (0<=j and j<4,
"generator out of range: letter w["
<< w << "][" << t << "] = " << j );
}
}
os |0;
}
//build symmetry group
Group group(words);
logger.debug() << "group.ord = " << group.ord |0;
//build subgroup
std::vector<int> subgroup; subgroup.push_back(0);
std::set<int> in_subgroup; in_subgroup.insert(0);
for (unsigned g=0; g<subgroup.size(); ++g) {
int g0 = subgroup[g];
for (unsigned j=0; j<gens.size(); ++j) {
int g1 = group.left(g0,gens[j]);
if (in_subgroup.find(g1) != in_subgroup.end()) continue;
subgroup.push_back(g1);
in_subgroup.insert(g1);
}
}
logger.debug() << "subgroup.ord = " << subgroup.size() |0;
//build cosets and count ord
std::map<int,int> coset; //maps group elements to cosets
ord = 0; //used as coset number
for (unsigned g=0; g<subgroup.size(); ++g) {
int g0 = subgroup[g];
if (coset.find(g0) != coset.end()) continue;
int c0 = ord++;
coset[g0] = c0;
std::vector<int> members(1, g0);
std::vector<int> others(0);
for (unsigned i=0; i<members.size(); ++i) {
int g1 = members[i];
for (unsigned w=0; w<v_cogens.size(); ++w) {
int g2 = group.left(g1, v_cogens[w]);
if (coset.find(g2) != coset.end()) continue;
coset[g2] = c0;
members.push_back(g2);
}
}
}
logger.info() << "cosets table built: " << " ord = " << ord |0;
//build edge lists
std::vector<std::set<int> > neigh(ord);
for (unsigned g=0; g<subgroup.size(); ++g) {
int g0 = subgroup[g];
int c0 = coset[g0];
for (unsigned w=0; w<e_gens.size(); ++w) {
int g1 = group.left(g0, e_gens[w]);
Assert (in_subgroup.find(g1) != in_subgroup.end(),
"edge leaves subgroup");
int c1 = coset[g1];
if (c0 != c1) neigh[c0].insert(c1);
}
}
// make symmetric
for (int c0=0; c0<ord; ++c0) {
const std::set<int>& n = neigh[c0];
for (std::set<int>::iterator c1=n.begin(); c1!=n.end(); ++c1) {
neigh[*c1].insert(c0);
}
}
// build edge table
adj.resize(ord);
for (int c=0; c<ord; ++c) {
adj[c].insert(adj[c].begin(), neigh[c].begin(), neigh[c].end());
}
neigh.clear();
deg = adj[0].size();
logger.info() << "edge table built: deg = " << deg |0;
//define faces
for (unsigned g=0; g<f_gens.size(); ++g) {
const Word& face = f_gens[g];
logger.debug() << "defining faces on " << face |0;
Logging::IndentBlock block;
//define basic face in group
Ring basic(1,0);
// g = 0;
int g0 = 0;
for (unsigned c=0; true; ++c) {
g0 = group.left(g0, face[c%face.size()]);
if (c >= face.size() and g0 == 0) break;
if (in_subgroup.find(g0) != in_subgroup.end() and g0 != basic.back()) {
basic.push_back(g0);
}
}
for (unsigned c=0; c<basic.size(); ++c) {
logger.debug() << " corner: " << basic[c] |0;
}
logger.debug() << "sides/face (free) = " << basic.size() |0;
//build orbit of basic face
std::vector<Ring> faces_g; faces_g.push_back(basic);
FaceRecognizer recognized; recognized(basic);
for (unsigned i=0; i<faces_g.size(); ++i) {
const Ring f = faces_g[i];
for (unsigned j=0; j<gens.size(); ++j) {
//right action of group on faces
Ring f_j(f.size());
for (unsigned c=0; c<f.size(); ++c) {
f_j[c] = group.right(f[c],gens[j]);
}
//add face
if (not recognized(f_j)) {
faces_g.push_back(f_j);
//logger.debug() << "new face: " << f_j |0;
} else {
//logger.debug() << "old face: " << f_j|0;
}
}
}
//hom face down to quotient graph
recognized.clear();
for (unsigned f=0; f<faces_g.size(); ++f) {
const Ring face_g = faces_g[f];
Ring face;
face.push_back(coset[face_g[0]]);
for (unsigned i=1; i<face_g.size(); ++i) {
int c = coset[face_g[i]];
if (c != face.back() and c != face[0]) {
face.push_back(c);
}
}
if (face.size() < 3) continue;
if (not recognized(face)) {
faces.push_back(face);
}
}
}
ord_f = faces.size();
logger.info() << "faces defined: order = " << ord_f |0;
//define vertex coset
std::vector<Word> vertex_coset;
for (unsigned g=0; g<subgroup.size(); ++g) {
int g0 = subgroup[g];
if (coset[g0]==0) vertex_coset.push_back(group.parse(g0));
}
//build geometry
std::vector<Mat> gen_reps(gens.size());
points.resize(ord);
build_geom(cartan, vertex_coset, gens, v_cogens, weights,
gen_reps, points[0]);
std::vector<int> pointed(ord,0);
pointed[0] = true;
logger.debug() << "geometry built" |0;
//build point sets
std::vector<int> reached(1,0);
std::set<int> is_reached;
is_reached.insert(0);
for (unsigned g=0; g<subgroup.size(); ++g) {
int g0 = reached[g];
for (unsigned j=0; j<gens.size(); ++j) {
int g1 = group.right(g0,gens[j]);
if (is_reached.find(g1) == is_reached.end()) {
if (not pointed[coset[g1]]) {
vect_mult(gen_reps[j], points[coset[g0]],
points[coset[g1]]);
pointed[coset[g1]] = true;
}
reached.push_back(g1);
is_reached.insert(g1);
}
}
}
logger.debug() << "point set built." |0;
//build face normals
normals.resize(ord_f);
for (int f=0; f<ord_f; ++f) {
Ring& face = faces[f];
Vect &a = points[face[0]];
Vect &b = points[face[1]];
Vect &c = points[face[2]];
Vect &n = normals[f];
cross4(a,b,c, n);
normalize(n);
/*
Assert1(fabs(inner(a,n)) < 1e-6,
"bad normal: <n,a> = " << fabs(inner(a,n)));
Assert1(fabs(inner(b,n)) < 1e-6,
"bad normal: <n,b> = " << fabs(inner(b,n)));
Assert1(fabs(inner(c,n)) < 1e-6,
"bad normal: <n,b> = " << fabs(inner(c,n)));
*/
}
logger.debug() << "face normals built." |0;
}
