/// Solve multiple systems w/ each column of the Matrix a single RHS
MatrixType *p_solve(const MatrixType& B) const
{
VectorType b(B.communicator(), B.localRows());
VectorType X(B.communicator(), B.localRows());
MatrixType *result(new MatrixType(B.communicator(), B.localRows(), B.localCols(), Dense));
int ilo, ihi;
X.localIndexRange(ilo, ihi);
int nloc(X.localSize());
std::vector<IdxType> iidx;
iidx.reserve(nloc);
for (IdxType i = ilo; i < ihi; ++i) { iidx.push_back(i); }
std::vector<IdxType> jidx(nloc);
std::vector<TheType> locX(nloc);
for (int j = 0; j < B.cols(); ++j) {
column(B, j, b);
X.zero();
X.ready();
if (j == 0) {
this->solve(b, X);
} else {
this->resolve(b, X);
}
std::fill(jidx.begin(), jidx.end(), j);
X.getElements(nloc, &iidx[0], &locX[0]);
result->setElements(nloc, &iidx[0], &jidx[0], &locX[0]);
}
result->ready();
return result;
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node, LocalMatOps>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
Ppattern_ = Ppattern;
const RCP<const Map> uniqueMap = Ppattern_->getDomainMap();
const RCP<const Map> nonUniqueMap = Ppattern_->getColMap();
RCP<const Import> importer = ImportFactory::Build(uniqueMap, nonUniqueMap);
const size_t NSDim = Bc.getNumVectors();
X_ = MultiVectorFactory::Build(nonUniqueMap, NSDim);
X_->doImport(Bc, *importer, Xpetra::INSERT);
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
Teuchos::SerialDenseVector<LO,SC> BcRow(NSDim, false);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false);
for (size_t j = 0; j < nnz; j++) {
for (size_t k = 0; k < NSDim; k++)
BcRow[k] = X_->getData(k)[indices[j]];
Teuchos::setCol(BcRow, (LO)j, locX);
}
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false);
Teuchos::BLAS<LO,SC> blas;
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
Teuchos::ScalarTraits<SC>::one(), locX.values(), locX.stride(),
locX.values(), locX.stride(), Teuchos::ScalarTraits<SC>::zero(),
XXtInv_[i].values(), XXtInv_[i].stride());
Teuchos::LAPACK<LO,SC> lapack;
LO info, lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
lapack.GETRF(NSDim, NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), &info);
lapack.GETRI(NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
const size_t NSDim = Bc.getNumVectors();
Ppattern_ = Ppattern;
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
RCP<const Import> importer = Ppattern_->getImporter();
X_ = MultiVectorFactory::Build(Ppattern_->getColMap(), NSDim);
if (!importer.is_null())
X_->doImport(Bc, *importer, Xpetra::INSERT);
else
*X_ = Bc;
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
SC zero = Teuchos::ScalarTraits<SC>::zero();
SC one = Teuchos::ScalarTraits<SC>::one();
Teuchos::BLAS <LO,SC> blas;
Teuchos::LAPACK<LO,SC> lapack;
LO lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false/*zeroOut*/);
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
if (NSDim == 1) {
SC d = zero;
for (size_t j = 0; j < nnz; j++)
d += Xval[0][indices[j]] * Xval[0][indices[j]];
XXtInv(0,0) = one/d;
} else {
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false/*zeroOut*/);
for (size_t j = 0; j < nnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][indices[j]];
// XXtInv_ = (locX*locX^T)^{-1}
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
one, locX.values(), locX.stride(),
locX.values(), locX.stride(),
zero, XXtInv.values(), XXtInv.stride());
LO info;
// Compute LU factorization using partial pivoting with row exchanges
lapack.GETRF(NSDim, NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), &info);
// Use the computed factorization to compute the inverse
lapack.GETRI(NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Apply(const Matrix& P, Matrix& Projected) const {
// We check only row maps. Column may be different.
TEUCHOS_TEST_FOR_EXCEPTION(!P.getRowMap()->isSameAs(*Projected.getRowMap()), Exceptions::Incompatible,
"Row maps are incompatible");
const size_t NSDim = X_->getNumVectors();
const size_t numRows = P.getNodeNumRows();
const Map& colMap = *P.getColMap();
const Map& PColMap = *Projected.getColMap();
Projected.resumeFill();
Teuchos::ArrayView<const LO> indices, pindices;
Teuchos::ArrayView<const SC> values, pvalues;
Teuchos::Array<SC> valuesAll(colMap.getNodeNumElements()), newValues;
LO invalid = Teuchos::OrdinalTraits<LO>::invalid();
LO oneLO = Teuchos::OrdinalTraits<LO>::one();
SC zero = Teuchos::ScalarTraits<SC> ::zero();
SC one = Teuchos::ScalarTraits<SC> ::one();
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
for (size_t i = 0; i < numRows; i++) {
P .getLocalRowView(i, indices, values);
Projected.getLocalRowView(i, pindices, pvalues);
size_t nnz = indices.size(); // number of nonzeros in the supplied matrix
size_t pnnz = pindices.size(); // number of nonzeros in the constrained matrix
newValues.resize(pnnz);
// Step 1: fix stencil
// Projected *must* already have the correct stencil
// Step 2: copy correct stencil values
// The algorithm is very similar to the one used in the calculation of
// Frobenius dot product, see src/Transfers/Energy-Minimization/Solvers/MueLu_CGSolver_def.hpp
// NOTE: using extra array allows us to skip the search among indices
for (size_t j = 0; j < nnz; j++)
valuesAll[indices[j]] = values[j];
for (size_t j = 0; j < pnnz; j++) {
LO ind = colMap.getLocalElement(PColMap.getGlobalElement(pindices[j])); // FIXME: we could do that before the full loop just once
if (ind != invalid)
// index indices[j] is part of template, copy corresponding value
newValues[j] = valuesAll[ind];
else
newValues[j] = zero;
}
for (size_t j = 0; j < nnz; j++)
valuesAll[indices[j]] = zero;
// Step 3: project to the space
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, pnnz, false);
for (size_t j = 0; j < pnnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][pindices[j]];
Teuchos::SerialDenseVector<LO,SC> val(pnnz, false), val1(NSDim, false), val2(NSDim, false);
for (size_t j = 0; j < pnnz; j++)
val[j] = newValues[j];
Teuchos::BLAS<LO,SC> blas;
// val1 = locX * val;
blas.GEMV(Teuchos::NO_TRANS, NSDim, pnnz,
one, locX.values(), locX.stride(),
val.values(), oneLO,
zero, val1.values(), oneLO);
// val2 = XXtInv * val1
blas.GEMV(Teuchos::NO_TRANS, NSDim, NSDim,
one, XXtInv.values(), XXtInv.stride(),
val1.values(), oneLO,
zero, val2.values(), oneLO);
// val = X^T * val2
blas.GEMV(Teuchos::CONJ_TRANS, NSDim, pnnz,
one, locX.values(), locX.stride(),
val2.values(), oneLO,
zero, val.values(), oneLO);
for (size_t j = 0; j < pnnz; j++)
newValues[j] -= val[j];
Projected.replaceLocalValues(i, pindices, newValues);
}
Projected.fillComplete(Projected.getDomainMap(), Projected.getRangeMap()); //FIXME: maps needed?
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node, LocalMatOps>::Apply(const Matrix& P, Matrix& Projected) const {
const size_t NSDim = X_->getNumVectors();
const size_t numRows = P.getNodeNumRows();
Projected.resumeFill();
Teuchos::SerialDenseVector<LO,SC> BcRow(NSDim, false);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices, pindices;
Teuchos::ArrayView<const SC> values, pvalues;
P .getLocalRowView(i, indices, values);
Projected.getLocalRowView(i, pindices, pvalues);
size_t nnz = pindices.size(); // number of nonzeros in the constrained matrix
size_t nnz1 = indices.size(); // number of nonzeros in the supplied matrix
Teuchos::Array<SC> newValues(nnz, Teuchos::ScalarTraits<SC>::zero());
// step 1: fix stencil
// Projected already has the correct stencil
// step 2: copy correct stencil values
for (size_t j = 0; j < nnz1; j++) {
// this might be accelerated if we know smth about ordering
size_t k = 0;
for (; k < nnz; k++)
if (pindices[k] == indices[j])
break;
if (k != nnz) {
// index indices[j] is part of template, copy corresponding value
newValues[k] = values[j];
}
}
// step 3: project to the space
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false);
for (size_t j = 0; j < nnz; j++) {
for (size_t k = 0; k < NSDim; k++)
BcRow[k] = X_->getData(k)[pindices[j]];
Teuchos::setCol(BcRow, (LO)j, locX);
}
Teuchos::SerialDenseVector<LO,SC> val(nnz, false), val1(NSDim, false), val2(NSDim, false);
for (size_t j = 0; j < nnz; j++)
val[j] = newValues[j];
Teuchos::BLAS<LO,SC> blas;
blas.GEMV(Teuchos::NO_TRANS, NSDim, nnz, Teuchos::ScalarTraits<SC>::one(), locX.values(),
locX.stride(), val.values(), (LO)1, Teuchos::ScalarTraits<SC>::zero(), val1.values(), (LO)1);
blas.GEMV(Teuchos::NO_TRANS, NSDim, NSDim, Teuchos::ScalarTraits<SC>::one(), XXtInv_[i].values(),
XXtInv_[i].stride(), val1.values(), (LO)1, Teuchos::ScalarTraits<SC>::zero(), val2.values(), (LO)1);
blas.GEMV(Teuchos::CONJ_TRANS, NSDim, nnz, Teuchos::ScalarTraits<SC>::one(), locX.values(),
locX.stride(), val2.values(), (LO)1, Teuchos::ScalarTraits<SC>::zero(), val.values(), (LO)1);
for (size_t j = 0; j < nnz; j++)
newValues[j] -= val[j];
Projected.replaceLocalValues(i, pindices, newValues);
}
Projected.fillComplete(Projected.getDomainMap(), Projected.getRangeMap()); //FIXME: maps needed?
}