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>::
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
/// \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
}
}