double BasisAngle( const Epetra_MultiVector& S, const Epetra_MultiVector& T )
{
//
// Computes the largest acute angle between the two orthogonal basis
//
if (S.NumVectors() != T.NumVectors()) {
return acos( 0.0 );
} else {
int lwork, info = 0;
int m = S.NumVectors(), n = T.NumVectors();
int num_vecs = ( m < n ? m : n );
double U[ 1 ], Vt[ 1 ];
lwork = 3*m*n;
std::vector<double> work( lwork );
std::vector<double> theta( num_vecs );
Epetra_LAPACK lapack;
Epetra_LocalMap localMap( S.NumVectors(), 0, S.Map().Comm() );
Epetra_MultiVector Pvec( localMap, T.NumVectors() );
info = Pvec.Multiply( 'T', 'N', 1.0, S, T, 0.0 );
//
// Perform SVD on S^T*T
//
lapack.GESVD( 'N', 'N', num_vecs, num_vecs, Pvec.Values(), Pvec.Stride(),
&theta[0], U, 1, Vt, 1, &work[0], &lwork, &info );
assert( info == 0 );
return (acos( theta[num_vecs-1] ) );
}
//
// Default return statement, should never be executed.
//
return acos( 0.0 );
}
void IncSVDPOD::incStep(int lup) {
Epetra_LAPACK lapack;
// perform gram-schmidt expansion
// expand() will update bases U_ and V_, factor B_, as well as counters curRank_ and numProc_
this->expand(lup);
// compute the SVD of B
const int lwork = 5*curRank_;
int info;
Epetra_SerialDenseMatrix Uhat(::Copy,B_->A(),B_->LDA(),curRank_,curRank_), Vhat(curRank_,curRank_);
std::vector<double> Shat(curRank_), work(lwork);
// Note: this actually stores Vhat^T (we remedy this below)
lapack.GESVD('O','A',curRank_,curRank_,Uhat.A(),Uhat.LDA(),&Shat[0],Uhat.A(),Uhat.LDA(),Vhat.A(),Vhat.LDA(),&work[0],&lwork,&info);
TEUCHOS_TEST_FOR_EXCEPTION(info!=0,std::logic_error,"RBGen::IncSVDPOD::incStep(): GESVD return info != 0");
// use filter to determine new rank
std::vector<int> keepind = filter_->filter(Shat);
std::vector<int> truncind(curRank_-keepind.size());
{
std::vector<int> allind(curRank_);
for (int i=0; i<curRank_; i++) {
allind[i] = i;
}
set_difference(allind.begin(),allind.end(),keepind.begin(),keepind.end(),truncind.begin());
// Vhat actually contains Vhat^T; correct this here
Epetra_SerialDenseMatrix Ucopy(Uhat), Vcopy(curRank_,curRank_);
std::vector<double> Scopy(Shat);
for (int j=0; j<curRank_; j++) {
for (int i=0; i<curRank_; i++) {
Vcopy(i,j) = Vhat(j,i);
}
}
// put the desired sigmas at the front of Uhat, Vhat
for (unsigned int j=0; j<keepind.size(); j++) {
std::copy(&Ucopy(0,keepind[j]),&Ucopy(curRank_,keepind[j]),&Uhat(0,j));
std::copy(&Vcopy(0,keepind[j]),&Vcopy(curRank_,keepind[j]),&Vhat(0,j));
Shat[j] = Scopy[keepind[j]];
}
for (unsigned int j=0; j<truncind.size(); j++) {
std::copy(&Ucopy(0,truncind[j]),&Ucopy(curRank_,truncind[j]),&Uhat(0,keepind.size()+j));
std::copy(&Vcopy(0,truncind[j]),&Vcopy(curRank_,truncind[j]),&Vhat(0,keepind.size()+j));
Shat[keepind.size()+j] = Scopy[truncind[j]];
}
}
// shrink back down again
// shrink() will update bases U_ and V_, as well as singular values sigma_ and curRank_
this->shrink(truncind.size(),Shat,Uhat,Vhat);
// print out some info
const Epetra_Comm *comm = &A_->Comm();
if (comm->MyPID() == 0 && verbLevel_ >= 2) {
std::cout
<< "------------- IncSVDPOD::incStep() --------------" << std::endl
<< "| Cols Processed: " << numProc_ << std::endl
<< "| Current lup: " << lup << std::endl
<< "| Current ldown: " << truncind.size() << std::endl
<< "| Current rank: " << curRank_ << std::endl
<< "| Current sigmas: " << std::endl;
for (int i=0; i<curRank_; i++) {
std::cout << "| " << sigma_[i] << std::endl;
}
}
}
