void PivotMDS::pivotMDSLayout(GraphAttributes& GA)
{
const Graph& G = GA.constGraph();
bool use3D = GA.has(GraphAttributes::threeD) && DIMENSION_COUNT > 2;
const int n = G.numberOfNodes();
// trivial cases
if (n == 0)
return;
if (n == 1) {
node v1 = G.firstNode();
GA.x(v1) = 0.0;
GA.y(v1) = 0.0;
if (use3D)
GA.z(v1) = 0.0;
return;
}
// check whether the graph is a path or not
const node head = getRootedPath(G);
if (head != nullptr) {
doPathLayout(GA, head);
}
else {
Array<Array<double> > pivDistMatrix;
// compute the pivot matrix
getPivotDistanceMatrix(GA, pivDistMatrix);
// center the pivot matrix
centerPivotmatrix(pivDistMatrix);
// init the coordinate matrix
Array<Array<double> > coord(DIMENSION_COUNT);
for (int i = 0; i < coord.size(); i++) {
coord[i].init(n);
}
// init the eigen values array
Array<double> eVals(DIMENSION_COUNT);
singularValueDecomposition(pivDistMatrix, coord, eVals);
// compute the correct aspect ratio
for (int i = 0; i < coord.size(); i++) {
eVals[i] = sqrt(eVals[i]);
for (int j = 0; j < n; j++) {
coord[i][j] *= eVals[i];
}
}
// set the new positions to the graph
int i = 0;
for (node v : G.nodes)
{
GA.x(v) = coord[0][i];
GA.y(v) = coord[1][i];
if (use3D){
GA.z(v) = coord[2][i];//cout << coord[2][i] << "\n";
}
++i;
}
}
}
void LinearSolver::eigen_system( DENS_MAT & eigenvalues, DENS_MAT & eigenvectors, const DENS_MAT * M) /* const */
{
initialize_matrix(); // no inverse needed
const DENS_MAT * Kp = NULL;
const DENS_MAT * Mp =M;
DENS_MAT MM;
DENS_MAT KM;
if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
Kp = &matrixFreeFree_;
if (M) {
DENS_MAT MfreeFixed; // not used
M->row_partition(freeSet_,MM,MfreeFixed);
Mp = &MM;
}
}
else {
if (matrixDense_.nRows() == 0) matrixDense_ =matrixSparse_->dense_copy();
Kp = &matrixDense_;
}
if (!M) {
MM.identity(Kp->nRows());
Mp = &MM;
}
DENS_MAT eVecs, eVals;
eVecs = eigensystem(*Kp,*Mp,eVals);
eigenvalues.reset(nVariables_,1);
eigenvectors.reset(nVariables_,nVariables_);
set<int>::const_iterator itr;
for (int i = 0; i < Kp->nRows(); i++) { // ordering is by energy not node
eigenvalues(i,0) = eVals(i,0);
int j = 0;
for (itr = freeSet_.begin(); itr != freeSet_.end(); itr++,j++) {
int jj = *itr;
eigenvectors(jj,i) = eVecs(j,i); // transpose
}
}
}
