int main(int, char**)
{
cout.precision(3);
EigenSolver<MatrixXf> es;
MatrixXf A = MatrixXf::Random(4,4);
es.compute(A, /* computeEigenvectors = */ false);
cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
es.compute(A + MatrixXf::Identity(4,4), false); // re-use es to compute eigenvalues of A+I
cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
return 0;
}
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
{
EigenSolver<MatrixType> eig;
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
VERIFY_RAISES_ASSERT(eig.eigenvalues());
MatrixType a = MatrixType::Random(m.rows(),m.cols());
eig.compute(a, false);
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
}
void computeSimpleStars(StarSet& stars,
SparseOptimizer* optimizer,
EdgeLabeler* labeler,
EdgeCreator* creator,
OptimizableGraph::Vertex* gauge_,
std::string edgeTag,
std::string vertexTag,
int level,
int step,
int backboneIterations,
int starIterations,
double rejectionThreshold,
bool debug){
cerr << "preforming the tree actions" << endl;
HyperDijkstra d(optimizer);
// compute a spanning tree based on the types of edges and vertices in the pool
EdgeTypesCostFunction f(edgeTag, vertexTag, level);
d.shortestPaths(gauge_,
&f,
std::numeric_limits< double >::max(),
1e-6,
false,
std::numeric_limits< double >::max()/2);
HyperDijkstra::computeTree(d.adjacencyMap());
// constructs the stars on the backbone
BackBoneTreeAction bact(optimizer, vertexTag, level, step);
bact.init();
cerr << "free edges size " << bact.freeEdges().size() << endl;
// perform breadth-first visit of the visit tree and create the stars on the backbone
d.visitAdjacencyMap(d.adjacencyMap(),&bact,true);
stars.clear();
for (VertexStarMultimap::iterator it=bact.vertexStarMultiMap().begin();
it!=bact.vertexStarMultiMap().end(); it++){
stars.insert(it->second);
}
cerr << "stars.size: " << stars.size() << endl;
cerr << "size: " << bact.vertexStarMultiMap().size() << endl;
// for each star
// for all vertices in the backbone, select all edges leading/leaving from that vertex
// that are contained in freeEdges.
// mark the corresponding "open" vertices and add them to a multimap (vertex->star)
// select a gauge in the backbone
// push all vertices on the backbone
// compute an initial guess on the backbone
// one round of optimization backbone
// lock all vertices in the backbone
// push all "open" vertices
// for each open vertex,
// compute an initial guess given the backbone
// do some rounds of solveDirect
// if (fail)
// - remove the vertex and the edges in that vertex from the star
// - make the structures consistent
// pop all "open" vertices
// pop all "vertices" in the backbone
// unfix the vertices in the backbone
int starNum=0;
for (StarSet::iterator it=stars.begin(); it!=stars.end(); it++){
Star* s =*it;
HyperGraph::VertexSet backboneVertices = s->_lowLevelVertices;
HyperGraph::EdgeSet backboneEdges = s->_lowLevelEdges;
if (backboneEdges.empty())
continue;
// cerr << "optimizing backbone" << endl;
// one of these should be the gauge, to be simple we select the fisrt one in the backbone
OptimizableGraph::VertexSet gauge;
gauge.insert(*backboneVertices.begin());
s->gauge()=gauge;
s->optimizer()->push(backboneVertices);
s->optimizer()->setFixed(gauge,true);
s->optimizer()->initializeOptimization(backboneEdges);
s->optimizer()->computeInitialGuess();
s->optimizer()->optimize(backboneIterations);
s->optimizer()->setFixed(backboneVertices, true);
// cerr << "assignind edges.vertices not in bbone" << endl;
HyperGraph::EdgeSet otherEdges;
HyperGraph::VertexSet otherVertices;
std::multimap<HyperGraph::Vertex*, HyperGraph::Edge*> vemap;
for (HyperGraph::VertexSet::iterator bit=backboneVertices.begin(); bit!=backboneVertices.end(); bit++){
HyperGraph::Vertex* v=*bit;
for (HyperGraph::EdgeSet::iterator eit=v->edges().begin(); eit!=v->edges().end(); eit++){
OptimizableGraph::Edge* e = (OptimizableGraph::Edge*) *eit;
HyperGraph::EdgeSet::iterator feit=bact.freeEdges().find(e);
if (feit!=bact.freeEdges().end()){ // edge is admissible
otherEdges.insert(e);
bact.freeEdges().erase(feit);
for (size_t i=0; i<e->vertices().size(); i++){
OptimizableGraph::Vertex* ve= (OptimizableGraph::Vertex*)e->vertices()[i];
if (backboneVertices.find(ve)==backboneVertices.end()){
otherVertices.insert(ve);
vemap.insert(make_pair(ve,e));
}
}
}
}
}
// RAINER TODO maybe need a better solution than dynamic casting here??
OptimizationAlgorithmWithHessian* solverWithHessian = dynamic_cast<OptimizationAlgorithmWithHessian*>(s->optimizer()->solver());
if (solverWithHessian) {
s->optimizer()->push(otherVertices);
// cerr << "optimizing vertices out of bbone" << endl;
// cerr << "push" << endl;
// cerr << "init" << endl;
s->optimizer()->initializeOptimization(otherEdges);
// cerr << "guess" << endl;
s->optimizer()->computeInitialGuess();
// cerr << "solver init" << endl;
s->optimizer()->solver()->init();
// cerr << "structure" << endl;
if (!solverWithHessian->buildLinearStructure())
cerr << "FATAL: failure while building linear structure" << endl;
// cerr << "errors" << endl;
s->optimizer()->computeActiveErrors();
// cerr << "system" << endl;
solverWithHessian->updateLinearSystem();
// cerr << "directSolove" << endl;
} else {
cerr << "FATAL: hierarchical thing cannot be used with a solver that does not support the system structure construction" << endl;
}
// // then optimize the vertices one at a time to check if a solution is good
for (HyperGraph::VertexSet::iterator vit=otherVertices.begin(); vit!=otherVertices.end(); vit++){
OptimizableGraph::Vertex* v=(OptimizableGraph::Vertex*)(*vit);
v->solveDirect();
// cerr << " " << d;
// if a solution is found, add a vertex and all the edges in
//othervertices that are pointing to that edge to the star
s->_lowLevelVertices.insert(v);
for (HyperGraph::EdgeSet::iterator eit=v->edges().begin(); eit!=v->edges().end(); eit++){
OptimizableGraph::Edge* e = (OptimizableGraph::Edge*) *eit;
if (otherEdges.find(e)!=otherEdges.end())
s->_lowLevelEdges.insert(e);
}
}
//cerr << endl;
// relax the backbone and optimize it all
// cerr << "relax bbone" << endl;
s->optimizer()->setFixed(backboneVertices, false);
//cerr << "fox gauge bbone" << endl;
s->optimizer()->setFixed(s->gauge(),true);
//cerr << "opt init" << endl;
s->optimizer()->initializeOptimization(s->_lowLevelEdges);
optimizer->computeActiveErrors();
double initialChi = optimizer->activeChi2();
int starOptResult = s->optimizer()->optimize(starIterations);
//cerr << starOptResult << "(" << starIterations << ") " << endl;
double finalchi=-1.;
cerr << "computing star: " << starNum << endl;
int vKept=0, vDropped=0;
if (!starIterations || starOptResult > 0 ){
optimizer->computeActiveErrors();
finalchi = optimizer->activeChi2();
#if 1
s->optimizer()->computeActiveErrors();
// cerr << "system" << endl;
if (solverWithHessian)
solverWithHessian->updateLinearSystem();
HyperGraph::EdgeSet prunedStarEdges = backboneEdges;
HyperGraph::VertexSet prunedStarVertices = backboneVertices;
for (HyperGraph::VertexSet::iterator vit=otherVertices.begin(); vit!=otherVertices.end(); vit++){
//discard the vertices whose error is too big
OptimizableGraph::Vertex* v=(OptimizableGraph::Vertex*)(*vit);
MatrixXd h(v->dimension(), v->dimension());
for (int i=0; i<v->dimension(); i++){
for (int j=0; j<v->dimension(); j++)
h(i,j)=v->hessian(i,j);
}
EigenSolver<Eigen::MatrixXd> esolver;
esolver.compute(h);
VectorXcd ev= esolver.eigenvalues();
double emin = std::numeric_limits<double>::max();
double emax = -std::numeric_limits<double>::max();
for (int i=0; i<ev.size(); i++){
emin = ev(i).real()>emin ? emin : ev(i).real();
emax = ev(i).real()<emax ? emax : ev(i).real();
}
double d=emin/emax;
// cerr << " " << d;
if (d>rejectionThreshold){
// if a solution is found, add a vertex and all the edges in
//othervertices that are pointing to that edge to the star
prunedStarVertices.insert(v);
for (HyperGraph::EdgeSet::iterator eit=v->edges().begin(); eit!=v->edges().end(); eit++){
OptimizableGraph::Edge* e = (OptimizableGraph::Edge*) *eit;
if (otherEdges.find(e)!=otherEdges.end())
prunedStarEdges.insert(e);
}
//cerr << "K( " << v->id() << "," << d << ")" ;
vKept ++;
} else {
vDropped++;
//cerr << "R( " << v->id() << "," << d << ")" ;
}
}
s->_lowLevelEdges=prunedStarEdges;
s->_lowLevelVertices=prunedStarVertices;
#endif
//cerr << "addHedges" << endl;
//now add to the star the hierarchical edges
std::vector<OptimizableGraph::Vertex*> vertices(2);
vertices[0]= (OptimizableGraph::Vertex*) *s->_gauge.begin();
for (HyperGraph::VertexSet::iterator vit=s->_lowLevelVertices.begin(); vit!=s->_lowLevelVertices.end(); vit++){
OptimizableGraph::Vertex* v=(OptimizableGraph::Vertex*)*vit;
vertices[1]=v;
if (v==vertices[0])
continue;
OptimizableGraph::Edge* e=creator->createEdge(vertices);
//rr << "creating edge" << e << Factory::instance()->tag(vertices[0]) << "->" << Factory::instance()->tag(v) <endl;
if (e) {
e->setLevel(level+1);
optimizer->addEdge(e);
s->_starEdges.insert(e);
} else {
cerr << "HERE" << endl;
cerr << "FATAL, cannot create edge" << endl;
}
}
}
cerr << " gauge: " << (*s->_gauge.begin())->id()
<< " kept: " << vKept
<< " dropped: " << vDropped
<< " edges:" << s->_lowLevelEdges.size()
<< " hedges" << s->_starEdges.size()
<< " initial chi " << initialChi
<< " final chi " << finalchi << endl;
if (debug) {
char starLowName[100];
sprintf(starLowName, "star-%04d-low.g2o", starNum);
ofstream starLowStream(starLowName);
optimizer->saveSubset(starLowStream, s->_lowLevelEdges);
}
bool labelOk=false;
if (!starIterations || starOptResult > 0)
labelOk = s->labelStarEdges(0, labeler);
if (labelOk) {
if (debug) {
char starHighName[100];
sprintf(starHighName, "star-%04d-high.g2o", starNum);
ofstream starHighStream(starHighName);
optimizer->saveSubset(starHighStream, s->_starEdges);
}
} else {
cerr << "FAILURE: " << starOptResult << endl;
}
starNum++;
//label each hierarchical edge
s->optimizer()->pop(otherVertices);
s->optimizer()->pop(backboneVertices);
s->optimizer()->setFixed(s->gauge(),false);
}
StarSet stars2;
// now erase the stars that have 0 edges. They r useless
for (StarSet::iterator it=stars.begin(); it!=stars.end(); it++){
Star* s=*it;
if (s->lowLevelEdges().size()==0) {
delete s;
} else
stars2.insert(s);
}
stars=stars2;
}
SGMatrix<float64_t> CUWedge::diagonalize(SGNDArray<float64_t> C, SGMatrix<float64_t> V0,
double eps, int itermax)
{
int d = C.dims[0];
int L = C.dims[2];
SGMatrix<float64_t> V;
if (V0.num_rows == d && V0.num_cols == d)
{
V = V0.clone();
}
else
{
Map<MatrixXd> C0(C.get_matrix(0),d,d);
EigenSolver<MatrixXd> eig;
eig.compute(C0);
// sort eigenvectors
MatrixXd eigenvectors = eig.pseudoEigenvectors();
MatrixXd eigenvalues = eig.pseudoEigenvalueMatrix();
bool swap = false;
do
{
swap = false;
for (int j = 1; j < d; j++)
{
if ( eigenvalues(j,j) > eigenvalues(j-1,j-1) )
{
std::swap(eigenvalues(j,j),eigenvalues(j-1,j-1));
eigenvectors.col(j).swap(eigenvectors.col(j-1));
swap = true;
}
}
} while(swap);
V = SGMatrix<float64_t>::create_identity_matrix(d,1);
Map<MatrixXd> EV(V.matrix, d,d);
EV = eigenvalues.cwiseAbs().cwiseSqrt().inverse() * eigenvectors.transpose();
}
Map<MatrixXd> EV(V.matrix, d,d);
index_t * Cs_dims = SG_MALLOC(index_t, 3);
Cs_dims[0] = d;
Cs_dims[1] = d;
Cs_dims[2] = L;
SGNDArray<float64_t> Cs(Cs_dims,3);
sg_memcpy(Cs.array, C.array, Cs.dims[0]*Cs.dims[1]*Cs.dims[2]*sizeof(float64_t));
MatrixXd Rs(d,L);
std::vector<float64_t> crit;
crit.push_back(0.0);
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Ci(C.get_matrix(l),d,d);
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
Ci = 0.5 * (Ci + Ci.transpose());
Csi = EV * Ci * EV.transpose();
Rs.col(l) = Csi.diagonal();
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum();
}
float64_t iter = 0;
float64_t improve = 10;
while (improve > eps && iter < itermax)
{
MatrixXd B = Rs * Rs.transpose();
MatrixXd C1 = MatrixXd::Zero(d,d);
for (int id = 0; id < d; id++)
{
// rowSums
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
C1.row(id) += Csi.row(id) * Rs(id,l);
}
}
MatrixXd D0 = B.cwiseProduct(B.transpose()) - B.diagonal() * B.diagonal().transpose();
MatrixXd A0 = MatrixXd::Identity(d,d) + (C1.cwiseProduct(B) - B.diagonal().asDiagonal() * C1.transpose()).cwiseQuotient(D0+MatrixXd::Identity(d,d));
EV = A0.inverse() * EV;
Map<MatrixXd> C0(C.get_matrix(0),d,d);
MatrixXd Raux = EV * C0 * EV.transpose();
MatrixXd aux = Raux.diagonal().cwiseAbs().cwiseSqrt().asDiagonal().inverse();
EV = aux * EV;
crit.push_back(0.0);
for (int l = 0; l < L; l++)
{
Map<MatrixXd> Ci(C.get_matrix(l),d,d);
Map<MatrixXd> Csi(Cs.get_matrix(l),d,d);
Csi = EV * Ci * EV.transpose();
Rs.col(l) = Csi.diagonal();
crit.back() += Csi.cwiseAbs2().sum() - Rs.col(l).cwiseAbs2().sum();
}
improve = CMath::abs(crit.back() - crit[iter]);
iter++;
}
if (iter == itermax)
SG_SERROR("Convergence not reached\n")
return V;
}