void
dft_HardSphereA22_Tpetra_Operator<Scalar,MatrixType>::
apply
(const MV& X, MV& Y, Teuchos::ETransp mode, Scalar alpha, Scalar beta) const
{
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
#endif
Y.elementWiseMultiply(STS::one(), *densityOnDensityMatrix_, X, STS::zero());
}
void
dft_HardSphereA22_Tpetra_Operator<Scalar,MatrixType>::
applyInverse
(const MV& X, MV& Y) const
{
// Our algorithm is:
// Y = D \ X
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
#endif
Y.elementWiseMultiply(STS::one(), *densityOnDensityInverse_, X, STS::zero());
}
void
dft_PolyA11_Tpetra_Operator<Scalar,MatrixType>::
applyInverse
(const MV& X, MV& Y) const
{
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
printf("\n\n\n\ndft_PolyA11_Tpetra_Operator::applyInverse()\n\n\n\n");
#endif
Scalar ONE = STS::one();
Scalar ZERO = STS::zero();
size_t NumVectors = Y.getNumVectors();
size_t numMyElements = ownedMap_->getNodeNumElements();
RCP<MV > Ytmp = rcp(new MV(ownedMap_,NumVectors));
Y=X; // We can safely do this
RCP<MV > curY = Y.offsetViewNonConst(ownedMap_, 0);
RCP<VEC> diagVec = invDiagonal_->offsetViewNonConst(ownedMap_, 0)->getVectorNonConst(0);
curY->elementWiseMultiply(ONE, *diagVec, *curY, ZERO); // Scale Y by the first block diagonal
// Loop over block 1 through numBlocks (indexing 0 to numBlocks-1)
for (LocalOrdinal i=OTLO::zero(); i< numBlocks_-1; i++)
{
// Update views of Y and diagonal blocks
curY = Y.offsetViewNonConst(ownedMap_, (i+1)*numMyElements);
diagVec = invDiagonal_->offsetViewNonConst(ownedMap_, (i+1)*numMyElements)->getVectorNonConst(0);
matrixOperator_[i]->apply(Y, *Ytmp); // Multiply block lower triangular block
curY->update(-ONE, *Ytmp, ONE); // curY = curX - Ytmp (Note that curX is in curY from initial copy Y = X)
curY->elementWiseMultiply(ONE, *diagVec, *curY, ZERO); // Scale Y by the first block diagonal
}
} //end applyInverse
void
dft_PolyA11_Tpetra_Operator<Scalar,MatrixType>::
apply
(const MV& X, MV& Y, Teuchos::ETransp mode, Scalar alpha, Scalar beta) const
{
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
#endif
size_t numMyElements = ownedMap_->getNodeNumElements();
RCP<MV > curY = Y.offsetViewNonConst(ownedMap_, 0);
for (LocalOrdinal i=OTLO::zero(); i< numBlocks_-1; i++) {
curY = Y.offsetViewNonConst(ownedMap_, (i+1)*numMyElements);
matrixOperator_[i]->apply(X, *curY); // This gives a result that is off-diagonal-matrix*X
}
Y.elementWiseMultiply(STS::one(),*diagonal_, X, STS::one()); // Add diagonal contribution
} //end Apply
// Compute Y := alpha Op X + beta Y.
//
// We ignore the cases alpha != 1 and beta != 0 for simplicity.
void
apply (const MV& X,
MV& Y,
Teuchos::ETransp mode = Teuchos::NO_TRANS,
scalar_type alpha = Teuchos::ScalarTraits<scalar_type>::one (),
scalar_type beta = Teuchos::ScalarTraits<scalar_type>::zero ()) const
{
using Teuchos::RCP;
using Teuchos::rcp;
using std::cout;
using std::endl;
typedef Teuchos::ScalarTraits<scalar_type> STS;
RCP<const Teuchos::Comm<int> > comm = opMap_->getComm ();
const int myRank = comm->getRank ();
const int numProcs = comm->getSize ();
if (myRank == 0) {
cout << "MyOp::apply" << endl;
}
// We're writing the Operator subclass, so we are responsible for
// error handling. You can decide how much error checking you
// want to do. Just remember that checking things like Map
// sameness or compatibility are expensive.
TEUCHOS_TEST_FOR_EXCEPTION(
X.getNumVectors () != Y.getNumVectors (), std::invalid_argument,
"X and Y do not have the same numbers of vectors (columns).");
// Let's make sure alpha is 1 and beta is 0...
// This will throw an exception if that is not the case.
TEUCHOS_TEST_FOR_EXCEPTION(
alpha != STS::one() || beta != STS::zero(), std::logic_error,
"MyOp::apply was given alpha != 1 or beta != 0. "
"These cases are not implemented.");
// Get the number of vectors (columns) in X (and Y).
const size_t numVecs = X.getNumVectors ();
// Make a temporary multivector for holding the redistributed
// data. You could also create this in the constructor and reuse
// it across different apply() calls, but you would need to be
// careful to reallocate if it has a different number of vectors
// than X. The number of vectors in X can vary across different
// apply() calls.
RCP<MV> redistData = rcp (new MV (redistMap_, numVecs));
// Redistribute the data.
// This will do all the necessary communication for you.
// All processes now own enough data to do the matvec.
redistData->doImport (X, *importer_, Tpetra::INSERT);
// Get the number of local rows in X, on the calling process.
const local_ordinal_type nlocRows =
static_cast<local_ordinal_type> (X.getLocalLength ());
// Perform the matvec with the data we now locally own.
//
// For each column...
for (size_t c = 0; c < numVecs; ++c) {
// Get a view of the desired column
Teuchos::ArrayRCP<scalar_type> colView = redistData->getDataNonConst (c);
local_ordinal_type offset;
// Y[0,c] = -colView[0] + 2*colView[1] - colView[2] (using local indices)
if (myRank > 0) {
Y.replaceLocalValue (0, c, -colView[0] + 2*colView[1] - colView[2]);
offset = 0;
}
// Y[0,c] = 2*colView[1] - colView[2] (using local indices)
else {
Y.replaceLocalValue (0, c, 2*colView[0] - colView[1]);
offset = 1;
}
// Y[r,c] = -colView[r-offset] + 2*colView[r+1-offset] - colView[r+2-offset]
for (local_ordinal_type r = 1; r < nlocRows - 1; ++r) {
const scalar_type newVal =
-colView[r-offset] + 2*colView[r+1-offset] - colView[r+2-offset];
Y.replaceLocalValue (r, c, newVal);
}
// Y[nlocRows-1,c] = -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset]
// - colView[nlocRows+1-offset]
if (myRank < numProcs - 1) {
const scalar_type newVal =
-colView[nlocRows-1-offset] + 2*colView[nlocRows-offset]
- colView[nlocRows+1-offset];
Y.replaceLocalValue (nlocRows-1, c, newVal);
}
// Y[nlocRows-1,c] = -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset]
else {
const scalar_type newVal =
-colView[nlocRows-1-offset] + 2*colView[nlocRows-offset];
Y.replaceLocalValue (nlocRows-1, c, newVal);
}
}
}
/// \brief Solve AX=B for X with Chebyshev iteration with left
/// diagonal scaling, imitating ML's implementation.
///
/// \pre A must be real-valued and symmetric positive definite.
/// \pre numIters >= 0
/// \pre eigRatio >= 1
/// \pre 0 < lambdaMax
/// \pre All entries of D_inv are positive.
///
/// \param A [in] The matrix A in the linear system to solve.
/// \param B [in] Right-hand side(s) in the linear system to solve.
/// \param X [in] Initial guess(es) for the linear system to solve.
/// \param numIters [in] Number of Chebyshev iterations.
/// \param lambdaMax [in] Estimate of max eigenvalue of D_inv*A.
/// \param lambdaMin [in] Estimate of min eigenvalue of D_inv*A. We
/// only use this to determine if A is the identity matrix.
/// \param eigRatio [in] Estimate of max / min eigenvalue ratio of
/// D_inv*A. We use this along with lambdaMax to compute the
/// Chebyshev coefficients. This need not be the same as
/// lambdaMax/lambdaMin.
/// \param D_inv [in] Vector of diagonal entries of A. It must have
/// the same distribution as b.
void
mlApplyImpl (const MAT& A,
const MV& B,
MV& X,
const int numIters,
const ST lambdaMax,
const ST lambdaMin,
const ST eigRatio,
const V& D_inv)
{
const ST zero = Teuchos::as<ST> (0);
const ST one = Teuchos::as<ST> (1);
const ST two = Teuchos::as<ST> (2);
MV pAux (B.getMap (), B.getNumVectors ()); // Result of A*X
MV dk (B.getMap (), B.getNumVectors ()); // Solution update
MV R (B.getMap (), B.getNumVectors ()); // Not in original ML; need for B - pAux
ST beta = Teuchos::as<ST> (1.1) * lambdaMax;
ST alpha = lambdaMax / eigRatio;
ST delta = (beta - alpha) / two;
ST theta = (beta + alpha) / two;
ST s1 = theta / delta;
ST rhok = one / s1;
// Diagonal: ML replaces entries containing 0 with 1. We
// shouldn't have any entries like that in typical test problems,
// so it's OK not to do that here.
// The (scaled) matrix is the identity: set X = D_inv * B. (If A
// is the identity, then certainly D_inv is too. D_inv comes from
// A, so if D_inv * A is the identity, then we still need to apply
// the "preconditioner" D_inv to B as well, to get X.)
if (lambdaMin == one && lambdaMin == lambdaMax) {
solve (X, D_inv, B);
return;
}
// The next bit of code is a direct translation of code from ML's
// ML_Cheby function, in the "normal point scaling" section, which
// is in lines 7365-7392 of ml_smoother.c.
if (! zeroStartingSolution_) {
// dk = (1/theta) * D_inv * (B - (A*X))
A.apply (X, pAux); // pAux = A * X
R = B;
R.update (-one, pAux, one); // R = B - pAux
dk.elementWiseMultiply (one/theta, D_inv, R, zero); // dk = (1/theta)*D_inv*R
X.update (one, dk, one); // X = X + dk
} else {
dk.elementWiseMultiply (one/theta, D_inv, B, zero); // dk = (1/theta)*D_inv*B
X = dk;
}
ST rhokp1, dtemp1, dtemp2;
for (int k = 0; k < numIters-1; ++k) {
A.apply (X, pAux);
rhokp1 = one / (two*s1 - rhok);
dtemp1 = rhokp1*rhok;
dtemp2 = two*rhokp1/delta;
rhok = rhokp1;
R = B;
R.update (-one, pAux, one); // R = B - pAux
// dk = dtemp1 * dk + dtemp2 * D_inv * (B - pAux)
dk.elementWiseMultiply (dtemp2, D_inv, B, dtemp1);
X.update (one, dk, one); // X = X + dk
}
}
//! Do the transpose or conjugate transpose solve.
void applyTranspose (const MV& X_in, MV& Y_in, const Teuchos::ETransp mode) const
{
typedef Teuchos::ScalarTraits<Scalar> ST;
using Teuchos::null;
TEUCHOS_TEST_FOR_EXCEPTION
(mode != Teuchos::TRANS && mode != Teuchos::CONJ_TRANS, std::logic_error,
"Tpetra::CrsMatrixSolveOp::applyTranspose: mode is neither TRANS nor "
"CONJ_TRANS. Should never get here! Please report this bug to the "
"Tpetra developers.");
const size_t numVectors = X_in.getNumVectors();
Teuchos::RCP<const Import<LocalOrdinal,GlobalOrdinal,Node> > importer =
matrix_->getGraph ()->getImporter ();
Teuchos::RCP<const Export<LocalOrdinal,GlobalOrdinal,Node> > exporter =
matrix_->getGraph ()->getExporter ();
Teuchos::RCP<const MV> X;
// it is okay if X and Y reference the same data, because we can
// perform a triangular solve in-situ. however, we require that
// column access to each is strided.
// set up import/export temporary multivectors
if (importer != null) {
if (importMV_ != null && importMV_->getNumVectors() != numVectors) {
importMV_ = null;
}
if (importMV_ == null) {
importMV_ = Teuchos::rcp( new MV(matrix_->getColMap(),numVectors) );
}
}
if (exporter != null) {
if (exportMV_ != null && exportMV_->getNumVectors() != numVectors) {
exportMV_ = null;
}
if (exportMV_ == null) {
exportMV_ = Teuchos::rcp( new MV(matrix_->getRowMap(),numVectors) );
}
}
// solve(TRANS): DomainMap -> RangeMap
// lclMatSolve_(TRANS): ColMap -> RowMap
// importer: DomainMap -> ColMap
// exporter: RowMap -> RangeMap
//
// solve = importer o lclMatSolve_ o exporter
// Domainmap -> ColMap -> RowMap -> RangeMap
//
// If we have a non-trivial importer, we must import elements that
// are permuted or are on other processes.
if (importer != null) {
importMV_->doImport(X_in,*importer,INSERT);
X = importMV_;
}
else if (X_in.isConstantStride() == false) {
// cannot handle non-constant stride right now
// generate a copy of X_in
X = Teuchos::rcp(new MV(X_in));
}
else {
// just temporary, so this non-owning RCP is okay
X = Teuchos::rcpFromRef (X_in);
}
// If we have a non-trivial exporter, we must export elements that
// are permuted or belong to other processes. We will compute
// solution into the to-be-exported MV; get a view.
if (exporter != null) {
matrix_->template localSolve<Scalar, Scalar> (*X, *exportMV_,
Teuchos::CONJ_TRANS);
// Make sure target is zero: necessary because we are adding
Y_in.putScalar(ST::zero());
Y_in.doExport(*importMV_, *importer, ADD);
}
// otherwise, solve into Y
else {
if (Y_in.isConstantStride() == false) {
// generate a strided copy of Y
MV Y(Y_in);
matrix_->template localSolve<Scalar, Scalar> (*X, Y, Teuchos::CONJ_TRANS);
Y_in = Y;
}
else {
matrix_->template localSolve<Scalar, Scalar> (*X, Y_in, Teuchos::CONJ_TRANS);
}
}
}
//! Do the non-transpose solve.
void applyNonTranspose (const MV& X_in, MV& Y_in) const
{
using Teuchos::NO_TRANS;
using Teuchos::null;
typedef Teuchos::ScalarTraits<Scalar> ST;
// Solve U X = Y or L X = Y
// X belongs to domain map, while Y belongs to range map
const size_t numVectors = X_in.getNumVectors();
Teuchos::RCP<const Import<LocalOrdinal,GlobalOrdinal,Node> > importer =
matrix_->getGraph ()->getImporter ();
Teuchos::RCP<const Export<LocalOrdinal,GlobalOrdinal,Node> > exporter =
matrix_->getGraph ()->getExporter ();
Teuchos::RCP<const MV> X;
// it is okay if X and Y reference the same data, because we can
// perform a triangular solve in-situ. however, we require that
// column access to each is strided.
// set up import/export temporary multivectors
if (importer != null) {
if (importMV_ != null && importMV_->getNumVectors () != numVectors) {
importMV_ = null;
}
if (importMV_ == null) {
importMV_ = Teuchos::rcp (new MV (matrix_->getColMap (), numVectors));
}
}
if (exporter != null) {
if (exportMV_ != null && exportMV_->getNumVectors () != numVectors) {
exportMV_ = null;
}
if (exportMV_ == null) {
exportMV_ = Teuchos::rcp (new MV (matrix_->getRowMap (), numVectors));
}
}
// solve(NO_TRANS): RangeMap -> DomainMap
// lclMatSolve_: RowMap -> ColMap
// importer: DomainMap -> ColMap
// exporter: RowMap -> RangeMap
//
// solve = reverse(exporter) o lclMatSolve_ o reverse(importer)
// RangeMap -> RowMap -> ColMap -> DomainMap
//
// If we have a non-trivial exporter, we must import elements that
// are permuted or are on other processors
if (exporter != null) {
exportMV_->doImport (X_in, *exporter, INSERT);
X = exportMV_;
}
else if (! X_in.isConstantStride ()) {
// cannot handle non-constant stride right now
// generate a copy of X_in
X = Teuchos::rcp (new MV (X_in));
}
else {
// just temporary, so this non-owning RCP is okay
X = Teuchos::rcpFromRef (X_in);
}
// If we have a non-trivial importer, we must export elements that
// are permuted or belong to other processes. We will compute
// solution into the to-be-exported MV.
if (importer != null) {
matrix_->template localSolve<Scalar, Scalar> (*X, *importMV_, NO_TRANS);
// Make sure target is zero: necessary because we are adding.
Y_in.putScalar (ST::zero ());
Y_in.doExport (*importMV_, *importer, ADD);
}
// otherwise, solve into Y
else {
// can't solve into non-strided multivector
if (! Y_in.isConstantStride ()) {
// generate a strided copy of Y
MV Y (Y_in);
matrix_->template localSolve<Scalar, Scalar> (*X, Y, NO_TRANS);
Tpetra::deep_copy (Y_in, Y);
}
else {
matrix_->template localSolve<Scalar, Scalar> (*X, Y_in, NO_TRANS);
}
}
}
//
// Computes Y = alpha Op X + beta Y
// TraceMin will never use alpha ~= 1 or beta ~= 0,
// so we have ignored those options for simplicity.
//
void apply(const MV& X, MV& Y, Teuchos::ETransp mode=Teuchos::NO_TRANS, Scalar alpha=SCT::one(), Scalar beta=SCT::zero()) const
{
//
// Let's make sure alpha is 1 and beta is 0...
// This will throw an exception if that is not the case.
//
TEUCHOS_TEST_FOR_EXCEPTION(alpha != SCT::one() || beta != SCT::zero(),std::invalid_argument,
"MyOp::apply was given alpha != 1 or beta != 0. That's not supposed to happen.");
//
// Get the number of local rows
//
int nlocRows = X.getLocalLength();
//
// Get the number of vectors
//
int numVecs = X.getNumVectors();
//
// Make a multivector for holding the redistributed data
//
RCP<MV> redistData = rcp(new MV(redistMap_, numVecs));
//
// Redistribute the data.
// This will do all the necessary communication for you.
// All processes now own enough data to do the matvec.
//
redistData->doImport(X, *importer_, Tpetra::INSERT);
//
// Perform the matvec with the data we now locally own
//
// For each column...
for(int c=0; c<numVecs; c++)
{
// Get a view of the desired column
Teuchos::ArrayRCP<Scalar> colView = redistData->getDataNonConst(c);
int offset;
// Y[0,c] = -colView[0] + 2*colView[1] - colView[2] (using local indices)
if(myRank_ > 0)
{
Y.replaceLocalValue(0, c, -colView[0] + 2*colView[1] - colView[2]);
offset = 0;
}
// Y[0,c] = 2*colView[1] - colView[2] (using local indices)
else
{
Y.replaceLocalValue(0, c, 2*colView[0] - colView[1]);
offset = 1;
}
// Y[r,c] = -colView[r-offset] + 2*colView[r+1-offset] - colView[r+2-offset]
for(int r=1; r<nlocRows-1; r++)
{
Y.replaceLocalValue(r, c, -colView[r-offset] + 2*colView[r+1-offset] - colView[r+2-offset]);
}
// Y[nlocRows-1,c] = -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset] - colView[nlocRows+1-offset]
if(myRank_ < numProcs_-1)
{
Y.replaceLocalValue(nlocRows-1, c, -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset] - colView[nlocRows+1-offset]);
}
// Y[nlocRows-1,c] = -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset]
else
{
Y.replaceLocalValue(nlocRows-1, c, -colView[nlocRows-1-offset] + 2*colView[nlocRows-offset]);
}
}
}
void
dft_PolyA22_Tpetra_Operator<Scalar,MatrixType>::
apply
(const MV& X, MV& Y, Teuchos::ETransp mode, Scalar alpha, Scalar beta) const
{
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
#endif
Scalar ONE = STS::one();
Scalar ZERO = STS::zero();
if (F_location_ == 1)
{
//F in NE
size_t numCmsElements = cmsMap_->getNodeNumElements();
// Y1 is a view of the first numCms elements of Y
RCP<MV> Y1 = Y.offsetViewNonConst(cmsMap_, 0);
// Y2 is a view of the last numDensity elements of Y
RCP<MV> Y2 = Y.offsetViewNonConst(densityMap_, numCmsElements);
// X1 is a view of the first numCms elements of X
RCP<const MV> X1 = X.offsetView(cmsMap_, 0);
// X2 is a view of the last numDensity elements of X
RCP<const MV> X2 = X.offsetView(densityMap_, numCmsElements);
// First block row
cmsOnDensityMatrixOp_->apply(*X2, *Y1);
cmsOnCmsMatrixOp_->apply(*X1, *tmpCmsVec_);
Y1->update(ONE, *tmpCmsVec_, ONE);
// Second block row
if (hasDensityOnCms_) {
densityOnCmsMatrixOp_->apply(*X1, *Y2);
Y2->elementWiseMultiply(ONE, *densityOnDensityMatrix_, *X2, ONE);
} else {
Y2->elementWiseMultiply(ONE, *densityOnDensityMatrix_, *X2, ZERO);
}
}
else
{
//F in SW
size_t numDensityElements = densityMap_->getNodeNumElements();
// Y1 is a view of the first numDensity elements of Y
RCP<MV> Y1 = Y.offsetViewNonConst(densityMap_, 0);
// Y2 is a view of the last numCms elements of Y
RCP<MV> Y2 = Y.offsetViewNonConst(cmsMap_, numDensityElements);
// X1 is a view of the first numDensity elements of X
RCP<const MV> X1 = X.offsetView(densityMap_, 0);
// X2 is a view of the last numCms elements of X
RCP<const MV> X2 = X.offsetView(cmsMap_, numDensityElements);
// First block row
if (hasDensityOnCms_) {
densityOnCmsMatrixOp_->apply(*X2, *Y1);
Y1->elementWiseMultiply(ONE, *densityOnDensityMatrix_, *X1, ONE);
} else {
Y1->elementWiseMultiply(ONE, *densityOnDensityMatrix_, *X1, ZERO);
}
// Second block row
cmsOnDensityMatrixOp_->apply(*X1, *Y2);
cmsOnCmsMatrixOp_->apply(*X2, *tmpCmsVec_);
Y2->update(ONE, *tmpCmsVec_, ONE);
}
} //end Apply
void
dft_PolyA22_Tpetra_Operator<Scalar,MatrixType>::
applyInverse
(const MV& X, MV& Y) const
{
// The true A22 block is of the form:
// | Dcc F |
// | Ddc Ddd |
// where
// Dcc is Cms on Cms (diagonal),
// F is Cms on Density (fairly dense)
// Ddc is Density on Cms (diagonal with small coefficient values),
// Ddd is Density on Density (diagonal).
//
// We will approximate A22 with:
// | Dcc F |
// | 0 Ddd |
// replacing Ddc with a zero matrix for the applyInverse method only.
// Our algorithm is then:
// Y2 = Ddd \ X2
// Y1 = Dcc \ (X1 - F*Y2)
// Or, if F is in the SW quadrant:
// The true A22 block is of the form:
// | Ddd Ddc |
// | F Dcc |
// where
// Ddd is Density on Density (diagonal),
// Ddc is Density on Cms (diagonal with small coefficient values),
// F is Cms on Density (fairly dense),
// Dcc is Cms on Cms (diagonal).
//
// We will approximate A22 with:
// | Ddd 0 |
// | F Dcc |
// replacing Ddc with a zero matrix for the applyInverse method only.
// Our algorithm is then:
// Y1 = Ddd \ X1
// Y2 = Dcc \ (X2 - F*Y1)
TEUCHOS_TEST_FOR_EXCEPT(Y.getNumVectors()!=X.getNumVectors());
#ifdef KDEBUG
TEUCHOS_TEST_FOR_EXCEPT(!X.getMap()->isSameAs(*getDomainMap()));
TEUCHOS_TEST_FOR_EXCEPT(!Y.getMap()->isSameAs(*getRangeMap()));
printf("\n\n\n\ndft_PolyA22_Tpetra_Operator::applyInverse()\n\n\n\n");
#endif
Scalar ONE = STS::one();
Scalar ZERO = STS::zero();
if (F_location_ == 1)
{
//F in NE
size_t numCmsElements = cmsMap_->getNodeNumElements();
// Y1 is a view of the first numCms elements of Y
RCP<MV > Y1 = Y.offsetViewNonConst(cmsMap_, 0);
// Y2 is a view of the last numDensity elements of Y
RCP<MV > Y2 = Y.offsetViewNonConst(densityMap_, numCmsElements);
// X1 is a view of the first numCms elements of X
RCP<const MV > X1 = X.offsetView(cmsMap_, 0);
// X2 is a view of the last numDensity elements of X
RCP<const MV > X2 = X.offsetView(densityMap_, numCmsElements);
// Second block row: Y2 = DD\X2
Y2->elementWiseMultiply(ONE, *densityOnDensityInverse_, *X2, ZERO);
// First block row: Y1 = CC \ (X1 - CD*Y2)
cmsOnDensityMatrixOp_->apply(*Y2, *tmpCmsVec_);
tmpCmsVec_->update(ONE, *X1, -ONE);
cmsOnCmsInverseOp_->apply(*tmpCmsVec_, *Y1);
}
else
{
//F in SW
size_t numDensityElements = densityMap_->getNodeNumElements();
// Y1 is a view of the first numDensity elements of Y
RCP<MV > Y1 = Y.offsetViewNonConst(densityMap_, 0);
// Y2 is a view of the last numCms elements of Y
RCP<MV > Y2 = Y.offsetViewNonConst(cmsMap_, numDensityElements);
// X1 is a view of the first numDensity elements of X
RCP<const MV > X1 = X.offsetView(densityMap_, 0);
// X2 is a view of the last numCms elements of X
RCP<const MV > X2 = X.offsetView(cmsMap_, numDensityElements);
// First block row: Y1 = DD\X1
Y1->elementWiseMultiply(ONE, *densityOnDensityInverse_, *X1, ZERO);
// Second block row: Y2 = CC \ (X2 - CD*Y1)
cmsOnDensityMatrixOp_->apply(*Y1, *tmpCmsVec_);
tmpCmsVec_->update(ONE, *X2, -ONE);
cmsOnCmsInverseOp_->apply(*tmpCmsVec_, *Y2);
}
} //end applyInverse