Teko_InvLSCStrategy.cpp

// @HEADER
// *****************************************************************************
//      Teko: A package for block and physics based preconditioning
//
// Copyright 2010 NTESS and the Teko contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#include "NS/Teko_InvLSCStrategy.hpp"
 
#include "Thyra_DefaultDiagonalLinearOp.hpp"
#include "Thyra_VectorStdOps.hpp"
 
#include "Teko_ConfigDefs.hpp"
 
#ifdef TEKO_HAVE_EPETRA
#include "Thyra_EpetraThyraWrappers.hpp"
#include "Thyra_get_Epetra_Operator.hpp"
#include "Thyra_EpetraLinearOp.hpp"
#include "Epetra_Vector.h"
#include "Epetra_Map.h"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.h"
#include "EpetraExt_VectorOut.h"
#include "Teko_EpetraHelpers.hpp"
#include "Teko_EpetraOperatorWrapper.hpp"
#endif
 
#include "Teuchos_Time.hpp"
#include "Teuchos_TimeMonitor.hpp"
 
// Teko includes
#include "Teko_Utilities.hpp"
#include "NS/Teko_LSCPreconditionerFactory.hpp"
 
#include "Teko_TpetraHelpers.hpp"
 
#include "Thyra_TpetraLinearOp.hpp"
 
using Teuchos::RCP;
using Teuchos::rcp_const_cast;
using Teuchos::rcp_dynamic_cast;
 
namespace Teko {
namespace NS {

// InvLSCStrategy Implementation
 
// constructors
InvLSCStrategy::InvLSCStrategy()
    : massMatrix_(Teuchos::null),
      invFactoryF_(Teuchos::null),
      invFactoryS_(Teuchos::null),
      eigSolveParam_(5),
      rowZeroingNeeded_(false),
      useFullLDU_(false),
      useMass_(false),
      useLumping_(false),
      useWScaling_(false),
      scaleType_(Diagonal),
      isSymmetric_(true),
      assumeStable_(false) {}
 
InvLSCStrategy::InvLSCStrategy(const Teuchos::RCP<InverseFactory>& factory, bool rzn)
    : massMatrix_(Teuchos::null),
      invFactoryF_(factory),
      invFactoryS_(factory),
      eigSolveParam_(5),
      rowZeroingNeeded_(rzn),
      useFullLDU_(false),
      useMass_(false),
      useLumping_(false),
      useWScaling_(false),
      scaleType_(Diagonal),
      isSymmetric_(true),
      assumeStable_(false) {}
 
InvLSCStrategy::InvLSCStrategy(const Teuchos::RCP<InverseFactory>& invFactF,
                               const Teuchos::RCP<InverseFactory>& invFactS, bool rzn)
    : massMatrix_(Teuchos::null),
      invFactoryF_(invFactF),
      invFactoryS_(invFactS),
      eigSolveParam_(5),
      rowZeroingNeeded_(rzn),
      useFullLDU_(false),
      useMass_(false),
      useLumping_(false),
      useWScaling_(false),
      scaleType_(Diagonal),
      isSymmetric_(true),
      assumeStable_(false) {}
 
InvLSCStrategy::InvLSCStrategy(const Teuchos::RCP<InverseFactory>& factory, LinearOp& mass,
                               bool rzn)
    : massMatrix_(mass),
      invFactoryF_(factory),
      invFactoryS_(factory),
      eigSolveParam_(5),
      rowZeroingNeeded_(rzn),
      useFullLDU_(false),
      useMass_(false),
      useLumping_(false),
      useWScaling_(false),
      scaleType_(Diagonal),
      isSymmetric_(true),
      assumeStable_(false) {}
 
InvLSCStrategy::InvLSCStrategy(const Teuchos::RCP<InverseFactory>& invFactF,
                               const Teuchos::RCP<InverseFactory>& invFactS, LinearOp& mass,
                               bool rzn)
    : massMatrix_(mass),
      invFactoryF_(invFactF),
      invFactoryS_(invFactS),
      eigSolveParam_(5),
      rowZeroingNeeded_(rzn),
      useFullLDU_(false),
      useMass_(false),
      useLumping_(false),
      useWScaling_(false),
      scaleType_(Diagonal),
      isSymmetric_(true),
      assumeStable_(false) {}

 
void InvLSCStrategy::buildState(BlockedLinearOp& A, BlockPreconditionerState& state) const {
  Teko_DEBUG_SCOPE("InvLSCStrategy::buildState", 10);
 
  LSCPrecondState* lscState = dynamic_cast<LSCPrecondState*>(&state);
  TEUCHOS_ASSERT(lscState != 0);
 
  // if neccessary save state information
  if (not lscState->isInitialized()) {
    Teko_DEBUG_EXPR(Teuchos::Time timer(""));
 
    // construct operators
    {
      Teko_DEBUG_SCOPE("LSC::buildState constructing operators", 1);
      Teko_DEBUG_EXPR(timer.start(true));
 
      initializeState(A, lscState);
 
      Teko_DEBUG_EXPR(timer.stop());
      Teko_DEBUG_MSG("LSC::buildState BuildOpsTime = " << timer.totalElapsedTime(), 1);
    }
 
    // Build the inverses
    {
      Teko_DEBUG_SCOPE("LSC::buildState calculating inverses", 1);
      Teko_DEBUG_EXPR(timer.start(true));
 
      computeInverses(A, lscState);
 
      Teko_DEBUG_EXPR(timer.stop());
      Teko_DEBUG_MSG("LSC::buildState BuildInvTime = " << timer.totalElapsedTime(), 1);
    }
  }
}
 
// functions inherited from LSCStrategy
LinearOp InvLSCStrategy::getInvBQBt(const BlockedLinearOp& /* A */,
                                    BlockPreconditionerState& state) const {
  return state.getInverse("invBQBtmC");
}
 
LinearOp InvLSCStrategy::getInvBHBt(const BlockedLinearOp& /* A */,
                                    BlockPreconditionerState& state) const {
  return state.getInverse("invBHBtmC");
}
 
LinearOp InvLSCStrategy::getInvF(const BlockedLinearOp& /* A */,
                                 BlockPreconditionerState& state) const {
  return state.getInverse("invF");
}
 
LinearOp InvLSCStrategy::getOuterStabilization(const BlockedLinearOp& /* A */,
                                               BlockPreconditionerState& state) const {
  LSCPrecondState* lscState = dynamic_cast<LSCPrecondState*>(&state);
  TEUCHOS_ASSERT(lscState != 0);
  TEUCHOS_ASSERT(lscState->isInitialized())
 
  return lscState->aiD_;
}
 
LinearOp InvLSCStrategy::getInvMass(const BlockedLinearOp& /* A */,
                                    BlockPreconditionerState& state) const {
  LSCPrecondState* lscState = dynamic_cast<LSCPrecondState*>(&state);
  TEUCHOS_ASSERT(lscState != 0);
  TEUCHOS_ASSERT(lscState->isInitialized())
 
  return lscState->invMass_;
}
 
LinearOp InvLSCStrategy::getHScaling(const BlockedLinearOp& A,
                                     BlockPreconditionerState& state) const {
  if (hScaling_ != Teuchos::null) return hScaling_;
  return getInvMass(A, state);
}

void InvLSCStrategy::initializeState(const BlockedLinearOp& A, LSCPrecondState* state) const {
  Teko_DEBUG_SCOPE("InvLSCStrategy::initializeState", 10);
 
  const LinearOp F  = getBlock(0, 0, A);
  const LinearOp Bt = getBlock(0, 1, A);
  const LinearOp B  = getBlock(1, 0, A);
  const LinearOp C  = getBlock(1, 1, A);
 
  LinearOp D = B;
  LinearOp G = isSymmetric_ ? Bt : adjoint(D);
 
  bool isStabilized = assumeStable_ ? false : (not isZeroOp(C));
 
  // The logic follows like this
  //    if there is no mass matrix available --> build from F
  //    if there is a mass matrix and the inverse hasn't yet been built
  //       --> build from the mass matrix
  //    otherwise, there is already an invMass_ matrix that is appropriate
  //       --> use that one
  if (massMatrix_ == Teuchos::null) {
    Teko_DEBUG_MSG(
        "LSC::initializeState Build Scaling <F> type \"" << getDiagonalName(scaleType_) << "\"", 1);
    state->invMass_ = getInvDiagonalOp(F, scaleType_);
  } else if (state->invMass_ == Teuchos::null) {
    Teko_DEBUG_MSG(
        "LSC::initializeState Build Scaling <mass> type \"" << getDiagonalName(scaleType_) << "\"",
        1);
    state->invMass_ = getInvDiagonalOp(massMatrix_, scaleType_);
  }
  // else "invMass_" should be set and there is no reason to rebuild it
 
  // compute BQBt
  state->BQBt_ = explicitMultiply(B, state->invMass_, Bt, state->BQBt_);
  Teko_DEBUG_MSG("Computed BQBt", 10);
 
  // if there is no H-Scaling
  if (wScaling_ != Teuchos::null && hScaling_ == Teuchos::null) {
    // from W vector build H operator scaling
    RCP<const Thyra::VectorBase<double> > w = wScaling_->col(0);
    RCP<const Thyra::VectorBase<double> > iQu =
        rcp_dynamic_cast<const Thyra::DiagonalLinearOpBase<double> >(state->invMass_)->getDiag();
    RCP<Thyra::VectorBase<double> > h = Thyra::createMember(iQu->space());
 
    Thyra::put_scalar(0.0, h.ptr());
    Thyra::ele_wise_prod(1.0, *w, *iQu, h.ptr());
    hScaling_ = Teuchos::rcp(new Thyra::DefaultDiagonalLinearOp<double>(h));
  }
 
  LinearOp H = hScaling_;
  if (H == Teuchos::null && not isSymmetric_) H = state->invMass_;
 
  // setup the scaling operator
  if (H == Teuchos::null)
    state->BHBt_ = state->BQBt_;
  else {
    RCP<Teuchos::Time> time =
        Teuchos::TimeMonitor::getNewTimer("InvLSCStrategy::initializeState Build BHBt");
    Teuchos::TimeMonitor timer(*time);
 
    // compute BHBt
    state->BHBt_ = explicitMultiply(D, H, G, state->BHBt_);
  }
 
  // if this is a stable discretization...we are done!
  if (not isStabilized) {
    state->addInverse("BQBtmC", state->BQBt_);
    state->addInverse("BHBtmC", state->BHBt_);
    state->gamma_ = 0.0;
    state->alpha_ = 0.0;
    state->aiD_   = Teuchos::null;
 
    state->setInitialized(true);
 
    return;
  }
 
  // for Epetra_CrsMatrix...zero out certain rows: this ensures spectral radius is correct
  LinearOp modF = F;
  if (!Teko::TpetraHelpers::isTpetraLinearOp(F)) {  // Epetra
#ifdef TEKO_HAVE_EPETRA
    const RCP<const Epetra_Operator> epF = Thyra::get_Epetra_Operator(*F);
    if (epF != Teuchos::null && rowZeroingNeeded_) {
      // try to get a CRS matrix
      const RCP<const Epetra_CrsMatrix> crsF = rcp_dynamic_cast<const Epetra_CrsMatrix>(epF);
 
      // if it is a CRS matrix get rows that need to be zeroed
      if (crsF != Teuchos::null) {
        std::vector<int> zeroIndices;
 
        // get rows in need of zeroing
        Teko::Epetra::identityRowIndices(crsF->RowMap(), *crsF, zeroIndices);
 
        // build an operator that zeros those rows
        modF = Thyra::epetraLinearOp(rcp(new Teko::Epetra::ZeroedOperator(zeroIndices, crsF)));
      }
    }
#else
    throw std::logic_error(
        "InvLSCStrategy::initializeState is trying to use "
        "Epetra code, but TEKO is not built with Epetra!");
#endif
  } else {  // Tpetra
    ST scalar   = 0.0;
    bool transp = false;
    RCP<const Tpetra::CrsMatrix<ST, LO, GO, NT> > crsF =
        Teko::TpetraHelpers::getTpetraCrsMatrix(F, &scalar, &transp);
 
    std::vector<GO> zeroIndices;
 
    // get rows in need of zeroing
    Teko::TpetraHelpers::identityRowIndices(*crsF->getRowMap(), *crsF, zeroIndices);
 
    // build an operator that zeros those rows
    modF = Thyra::tpetraLinearOp<ST, LO, GO, NT>(
        Thyra::tpetraVectorSpace<ST, LO, GO, NT>(crsF->getDomainMap()),
        Thyra::tpetraVectorSpace<ST, LO, GO, NT>(crsF->getRangeMap()),
        rcp(new Teko::TpetraHelpers::ZeroedOperator(zeroIndices, crsF)));
  }
 
  // compute gamma
  Teko_DEBUG_MSG("Calculating gamma", 10);
  LinearOp iQuF = multiply(state->invMass_, modF);
 
  // do 6 power iterations to compute spectral radius: EHSST2007 Eq. 4.28
  Teko::LinearOp stabMatrix;  // this is the pressure stabilization matrix to use
  state->gamma_ = std::fabs(Teko::computeSpectralRad(iQuF, 5e-2, false, eigSolveParam_)) / 3.0;
  Teko_DEBUG_MSG("Calculated gamma", 10);
  if (userPresStabMat_ != Teuchos::null) {
    Teko::LinearOp invDGl  = Teko::getInvDiagonalOp(userPresStabMat_);
    Teko::LinearOp gammaOp = multiply(invDGl, C);
    state->gamma_ *= std::fabs(Teko::computeSpectralRad(gammaOp, 5e-2, false, eigSolveParam_));
    stabMatrix = userPresStabMat_;
  } else
    stabMatrix = C;
 
  // compute alpha scaled inv(D): EHSST2007 Eq. 4.29
  // construct B_idF_Bt and save it for refilling later: This could reuse BQBt graph
  LinearOp invDiagF                    = getInvDiagonalOp(F);
  Teko::ModifiableLinearOp modB_idF_Bt = state->getInverse("BidFBt");
  modB_idF_Bt                          = explicitMultiply(B, invDiagF, Bt, modB_idF_Bt);
  state->addInverse("BidFBt", modB_idF_Bt);
  const LinearOp B_idF_Bt = modB_idF_Bt;
 
  MultiVector vec_D = getDiagonal(B_idF_Bt);  // this memory could be reused
  update(-1.0, getDiagonal(C), 1.0, vec_D);   // vec_D = diag(B*inv(diag(F))*Bt)-diag(C)
  const LinearOp invD = buildInvDiagonal(vec_D, "inv(D)");
 
  Teko_DEBUG_MSG("Calculating alpha", 10);
  const LinearOp BidFBtidD = multiply<double>(B_idF_Bt, invD);
  double num = std::fabs(Teko::computeSpectralRad(BidFBtidD, 5e-2, false, eigSolveParam_));
  Teko_DEBUG_MSG("Calculated alpha", 10);
  state->alpha_ = 1.0 / num;
  state->aiD_   = Thyra::scale(state->alpha_, invD);
 
  // now build B*Q*Bt-gamma*C
  Teko::ModifiableLinearOp BQBtmC = state->getInverse("BQBtmC");
  BQBtmC = explicitAdd(state->BQBt_, scale(-state->gamma_, stabMatrix), BQBtmC);
  state->addInverse("BQBtmC", BQBtmC);
 
  // now build B*H*Bt-gamma*C
  Teko::ModifiableLinearOp BHBtmC = state->getInverse("BHBtmC");
  if (H == Teuchos::null)
    BHBtmC = BQBtmC;
  else {
    BHBtmC = explicitAdd(state->BHBt_, scale(-state->gamma_, stabMatrix), BHBtmC);
  }
  state->addInverse("BHBtmC", BHBtmC);
 
  Teko_DEBUG_MSG_BEGIN(5) DEBUG_STREAM << "LSC Gamma Parameter = " << state->gamma_ << std::endl;
  DEBUG_STREAM << "LSC Alpha Parameter = " << state->alpha_ << std::endl;
  Teko_DEBUG_MSG_END()
 
      state->setInitialized(true);
}

void InvLSCStrategy::computeInverses(const BlockedLinearOp& A, LSCPrecondState* state) const {
  Teko_DEBUG_SCOPE("InvLSCStrategy::computeInverses", 10);
  Teko_DEBUG_EXPR(Teuchos::Time invTimer(""));
 
  const LinearOp F = getBlock(0, 0, A);

 
  // (re)build the inverse of F
  Teko_DEBUG_MSG("LSC::computeInverses Building inv(F)", 1);
  Teko_DEBUG_EXPR(invTimer.start(true));
  InverseLinearOp invF = state->getInverse("invF");
  if (invF == Teuchos::null) {
    invF = buildInverse(*invFactoryF_, F);
    state->addInverse("invF", invF);
  } else {
    rebuildInverse(*invFactoryF_, F, invF);
  }
  Teko_DEBUG_EXPR(invTimer.stop());
  Teko_DEBUG_MSG("LSC::computeInverses GetInvF = " << invTimer.totalElapsedTime(), 1);

 
  // (re)build the inverse of BQBt
  Teko_DEBUG_MSG("LSC::computeInverses Building inv(BQBtmC)", 1);
  Teko_DEBUG_EXPR(invTimer.start(true));
  const LinearOp BQBt     = state->getInverse("BQBtmC");
  InverseLinearOp invBQBt = state->getInverse("invBQBtmC");
  if (invBQBt == Teuchos::null) {
    invBQBt = buildInverse(*invFactoryS_, BQBt);
    state->addInverse("invBQBtmC", invBQBt);
  } else {
    rebuildInverse(*invFactoryS_, BQBt, invBQBt);
  }
  Teko_DEBUG_EXPR(invTimer.stop());
  Teko_DEBUG_MSG("LSC::computeInverses GetInvBQBt = " << invTimer.totalElapsedTime(), 1);

 
  // Compute the inverse of BHBt or just use BQBt
  ModifiableLinearOp invBHBt = state->getInverse("invBHBtmC");
  if (hScaling_ != Teuchos::null || not isSymmetric_) {
    // (re)build the inverse of BHBt
    Teko_DEBUG_MSG("LSC::computeInverses Building inv(BHBtmC)", 1);
    Teko_DEBUG_EXPR(invTimer.start(true));
    const LinearOp BHBt = state->getInverse("BHBtmC");
    if (invBHBt == Teuchos::null) {
      invBHBt = buildInverse(*invFactoryS_, BHBt);
      state->addInverse("invBHBtmC", invBHBt);
    } else {
      rebuildInverse(*invFactoryS_, BHBt, invBHBt);
    }
    Teko_DEBUG_EXPR(invTimer.stop());
    Teko_DEBUG_MSG("LSC::computeInverses GetInvBHBt = " << invTimer.totalElapsedTime(), 1);
  } else if (invBHBt == Teuchos::null) {
    // just use the Q version
    state->addInverse("invBHBtmC", invBQBt);
  }
}

void InvLSCStrategy::initializeFromParameterList(const Teuchos::ParameterList& pl,
                                                 const InverseLibrary& invLib) {
  // get string specifying inverse
  std::string invStr = "", invVStr = "", invPStr = "";
  bool rowZeroing = true;
  bool useLDU     = false;
  scaleType_      = Diagonal;
 
  // "parse" the parameter list
  if (pl.isParameter("Inverse Type")) invStr = pl.get<std::string>("Inverse Type");
  if (pl.isParameter("Inverse Velocity Type"))
    invVStr = pl.get<std::string>("Inverse Velocity Type");
  if (pl.isParameter("Inverse Pressure Type"))
    invPStr = pl.get<std::string>("Inverse Pressure Type");
  if (pl.isParameter("Ignore Boundary Rows")) rowZeroing = pl.get<bool>("Ignore Boundary Rows");
  if (pl.isParameter("Use LDU")) useLDU = pl.get<bool>("Use LDU");
  if (pl.isParameter("Use Mass Scaling")) useMass_ = pl.get<bool>("Use Mass Scaling");
  // if(pl.isParameter("Use Lumping"))
  //    useLumping_ = pl.get<bool>("Use Lumping");
  if (pl.isParameter("Use W-Scaling")) useWScaling_ = pl.get<bool>("Use W-Scaling");
  if (pl.isParameter("Eigen Solver Iterations"))
    eigSolveParam_ = pl.get<int>("Eigen Solver Iterations");
  if (pl.isParameter("Scaling Type")) {
    scaleType_ = getDiagonalType(pl.get<std::string>("Scaling Type"));
    TEUCHOS_TEST_FOR_EXCEPT(scaleType_ == NotDiag);
  }
  if (pl.isParameter("Assume Stable Discretization"))
    assumeStable_ = pl.get<bool>("Assume Stable Discretization");
 
  Teko_DEBUG_MSG_BEGIN(5) DEBUG_STREAM << "LSC Inverse Strategy Parameters: " << std::endl;
  DEBUG_STREAM << "   inv type   = \"" << invStr << "\"" << std::endl;
  DEBUG_STREAM << "   inv v type = \"" << invVStr << "\"" << std::endl;
  DEBUG_STREAM << "   inv p type = \"" << invPStr << "\"" << std::endl;
  DEBUG_STREAM << "   bndry rows = " << rowZeroing << std::endl;
  DEBUG_STREAM << "   use ldu    = " << useLDU << std::endl;
  DEBUG_STREAM << "   use mass    = " << useMass_ << std::endl;
  DEBUG_STREAM << "   use w-scaling    = " << useWScaling_ << std::endl;
  DEBUG_STREAM << "   assume stable    = " << assumeStable_ << std::endl;
  DEBUG_STREAM << "   scale type    = " << getDiagonalName(scaleType_) << std::endl;
  DEBUG_STREAM << "LSC  Inverse Strategy Parameter list: " << std::endl;
  pl.print(DEBUG_STREAM);
  Teko_DEBUG_MSG_END()
 
  // set defaults as needed
#if defined(Teko_ENABLE_Amesos)
      if (invStr == "") invStr = "Amesos";
#elif defined(Teko_ENABLE_Amesos2)
      if (invStr == "") invStr = "Amesos2";
#endif
  if (invVStr == "") invVStr = invStr;
  if (invPStr == "") invPStr = invStr;
 
  // build velocity inverse factory
  invFactoryF_ = invLib.getInverseFactory(invVStr);
  invFactoryS_ = invFactoryF_;  // by default these are the same
  if (invVStr != invPStr)       // if different, build pressure inverse factory
    invFactoryS_ = invLib.getInverseFactory(invPStr);
 
  // set other parameters
  setUseFullLDU(useLDU);
  setRowZeroing(rowZeroing);
 
  if (useMass_) {
    Teuchos::RCP<Teko::RequestHandler> rh = getRequestHandler();
    rh->preRequest<Teko::LinearOp>(Teko::RequestMesg("Velocity Mass Matrix"));
    Teko::LinearOp mass = rh->request<Teko::LinearOp>(Teko::RequestMesg("Velocity Mass Matrix"));
    setMassMatrix(mass);
  }
}

Teuchos::RCP<Teuchos::ParameterList> InvLSCStrategy::getRequestedParameters() const {
  Teuchos::RCP<Teuchos::ParameterList> result;
  Teuchos::RCP<Teuchos::ParameterList> pl = rcp(new Teuchos::ParameterList());
 
  // grab parameters from F solver
  RCP<Teuchos::ParameterList> fList = invFactoryF_->getRequestedParameters();
  if (fList != Teuchos::null) {
    Teuchos::ParameterList::ConstIterator itr;
    for (itr = fList->begin(); itr != fList->end(); ++itr) pl->setEntry(itr->first, itr->second);
    result = pl;
  }
 
  // grab parameters from S solver
  RCP<Teuchos::ParameterList> sList = invFactoryS_->getRequestedParameters();
  if (sList != Teuchos::null) {
    Teuchos::ParameterList::ConstIterator itr;
    for (itr = sList->begin(); itr != sList->end(); ++itr) pl->setEntry(itr->first, itr->second);
    result = pl;
  }
 
  // use the mass matrix
  if (useWScaling_) {
    pl->set<Teko::LinearOp>("W-Scaling Vector", Teuchos::null, "W-Scaling Vector");
    result = pl;
  }
 
  return result;
}

bool InvLSCStrategy::updateRequestedParameters(const Teuchos::ParameterList& pl) {
  Teko_DEBUG_SCOPE("InvLSCStrategy::updateRequestedParameters", 10);
  bool result = true;
 
  // update requested parameters in solvers
  result &= invFactoryF_->updateRequestedParameters(pl);
  result &= invFactoryS_->updateRequestedParameters(pl);
 
  // use W scaling matrix
  if (useWScaling_) {
    Teko::MultiVector wScale = pl.get<Teko::MultiVector>("W-Scaling Vector");
 
    if (wScale == Teuchos::null)
      result &= false;
    else
      setWScaling(wScale);
  }
 
  return result;
}
 
}  // end namespace NS
}  // end namespace Teko