matrix<int> graph<V,E>::incidence_matrix()
{
matrix<int> incidence(this->vertices.size(),this->edges.size());
for(int i=0,a,b; i<this->edges.size(); i++)
{
for(a=0;this->vertices[a].ID!=this->edges[i].IDstart;a++);
for(b=0;this->vertices[b].ID!=this->edges[i].IDend;b++);
incidence(a,i) = -1;
incidence(b,i) = +1;
}
return incidence;
}
bool LineSegment::isIncident(const cv::Point3d &vp, double ANGLE_EPSILON) const
{
cv::Point3d l = lineThroughPoints(middle, vp);
normalizeZ(l);
double d = incidence(l, from) / (norm12(l) * norm12(middle - from));
return abs(asin(d)) <= ANGLE_EPSILON;
}
int NuTo::Structure::ElementsCreate(int rInterpolationTypeId, const Eigen::MatrixXi& rNodeNumbers)
{
std::vector<int> newElementIds;
// go through the elements
for (int iNode = 0; iNode < rNodeNumbers.cols(); ++iNode)
{
auto column = rNodeNumbers.col(iNode);
std::vector<int> incidence(column.data(), column.data() + column.size());
int newElementId = ElementCreate(rInterpolationTypeId, incidence);
newElementIds.push_back(newElementId);
}
bool showTime = mShowTime;
mShowTime = false;
// create element group containing the new elements
int newElementGroup = GroupCreate(eGroupId::Elements);
for (int newElementId : newElementIds)
GroupAddElement(newElementGroup, newElementId);
mShowTime = showTime;
return newElementGroup;
}
void Homology::findCompatibleBasisPair(int master, std::vector<int> dim)
{
if(!this->isHomologyComputed(dim)) this->findHomologyBasis(dim);
if(!this->isCohomologyComputed(dim)) this->findCohomologyBasis(dim);
for(unsigned int idim = 0 ; idim < dim.size(); idim++) {
int d = dim.at(idim);
if(d < 1 || d > 2) continue;
int n = this->betti(d);
if(n < 2) continue;
if((int)_chains[d].size() != n || (int)_cochains[d].size() != n) {
Msg::Warning("Cannot produce compatible %d-(co)homology bases.", d);
Msg::Debug("%d basis %d-chains and %d basis %d-cochains.",
(int)_chains[d].size(), d, (int)_cochains[d].size(), d);
continue;
}
fullMatrix<double> m(n,n);
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
if(master==0) m(i,j) = incidence(*_cochains[d].at(i), *_chains[d].at(j));
else m(i,j) = incidence(*_chains[d].at(i), *_cochains[d].at(j));
}
}
int det = m.determinant();
if(abs(det) != 1 || !m.invertInPlace()) {
Msg::Warning("Cannot produce compatible %d-(co)homology bases.", d);
Msg::Debug("Incidence matrix: ");
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
Msg::Debug("(%d, %d) = %d", i, j, m(i,j));
continue;
}
std::vector<Chain<int>*> newBasis(n);
if(master==0) {
for(int i = 0; i < n; i++) {
newBasis.at(i) = new Chain<int>();
for(int j = 0; j < n; j++) {
*newBasis.at(i) += (int)m(i,j)*(*_cochains[d].at(j));
}
}
for(int i = 0; i < n; i++) {
newBasis.at(i)->setName(_cochains[d].at(i)->getName());
delete _cochains[d].at(i);
_cochains[d].at(i) = newBasis.at(i);
}
}
else {
for(int i = 0; i < n; i++) {
newBasis.at(i) = new Chain<int>();
for(int j = 0; j < n; j++) {
*newBasis.at(i) += (int)m(i,j)*(*_chains[d].at(j));
}
}
for(int i = 0; i < n; i++) {
newBasis.at(i)->setName(_chains[d].at(i)->getName());
delete _chains[d].at(i);
_chains[d].at(i) = newBasis.at(i);
}
}
}
}
