Exemple #1
0
double NOX::StatusTest::NormF::computeNorm(const NOX::Abstract::Group& grp)
{
  if (!grp.isF())
    return -1.0;

  double norm;
  int n = grp.getX().length();

  switch (normType) 
  {
    
  case NOX::Abstract::Vector::TwoNorm:
    norm = grp.getNormF();
    if (scaleType == Scaled)
      norm /= sqrt(1.0 * n);
    break;

  default:
    norm = grp.getF().norm(normType);
    if (scaleType == Scaled)
      norm /= n;
    break;

  }

  return norm;
}
Exemple #2
0
bool NOX::Direction::QuasiNewton::compute(NOX::Abstract::Vector& dir, 
					  NOX::Abstract::Group& soln, 
					  const Solver::Generic& solver)
{
  NOX::Abstract::Group::ReturnType status;
  
  // Compute F at current solution
  status = soln.computeF();
  if (status != NOX::Abstract::Group::Ok) 
    throwError("compute", "Unable to compute F");

  // Compute Jacobian at current solution.
  status = soln.computeJacobian();
  if (status != NOX::Abstract::Group::Ok) 
    throwError("compute", "Unable to compute Jacobian");

  // Compute the gradient at the current solution
  status = soln.computeGradient();
  if (status != NOX::Abstract::Group::Ok) 
    throwError("compute", "Unable to compute gradient");

  // Push the old information onto the memory, but only after at least one previous iteration
  if (solver.getNumIterations() > 0) 
  {
    const NOX::Abstract::Group& oldSoln = solver.getPreviousSolutionGroup();
    if (oldSoln.isGradient())
      memory.add(soln.getX(), oldSoln.getX(), soln.getGradient(), oldSoln.getGradient());
  }

  // *** Calculate the QN direction ***
  
  // d = -g
  dir = soln.getGradient();
  dir.scale(-1.0);

  if (!memory.empty()) 
  {

    int m = memory.size();
    vector<double> alpha(m);
    double beta;
  
    for (int i = m-1; i >= 0; i --)
    {
      alpha[i] = memory[i].rho() * dir.innerProduct( memory[i].s() );
      dir.update(-1.0 * alpha[i], memory[i].y(), 1.0);
    }

    dir.scale( memory[m-1].sdoty() / memory[m-1].ydoty() );

    for (int i = 0; i < m; i ++)
    {
      beta = memory[i].rho() * dir.innerProduct( memory[i].y() );
      dir.update(alpha[i] - beta, memory[i].s(), 1.0);
    }
  }

  return true;
}
double NOX::MeritFunction::SumOfSquares::
computeSlopeWithoutJacobian(const NOX::Abstract::Vector& dir,
                const NOX::Abstract::Group& grp) const
{
  if (Teuchos::is_null(tmpVecPtr))
    tmpVecPtr = grp.getF().clone(NOX::ShapeCopy);

  if (Teuchos::is_null(tmpGrpPtr))
    tmpGrpPtr = grp.clone(NOX::ShapeCopy);


  // Compute the perturbation parameter
  double lambda = 1.0e-6;
  double denominator = dir.norm();

  // Don't divide by zero
  if (denominator == 0.0)
    denominator = 1.0;

  double eta = lambda * (lambda + grp.getX().norm() / denominator);

  // Don't divide by zero
  if (eta == 0.0)
    eta = 1.0e-6;

  // Perturb the solution vector
  tmpVecPtr->update(eta, dir, 1.0, grp.getX(), 0.0);

  // Compute the new F --> F(x + eta * dir)
  tmpGrpPtr->setX(*(tmpVecPtr.get()));
  tmpGrpPtr->computeF();

  // Compute Js = (F(x + eta * dir) - F(x))/eta
  tmpVecPtr->update(-1.0/eta, grp.getF(), 1.0/eta, tmpGrpPtr->getF(), 0.0);

  return(tmpVecPtr->innerProduct(grp.getF()));
}
// **************************************************************************
// *** computeForcingTerm
// **************************************************************************
double NOX::Direction::Utils::InexactNewton::
computeForcingTerm(const NOX::Abstract::Group& soln,
		   const NOX::Abstract::Group& oldsoln, 
		   int niter,
		   const NOX::Solver::Generic& solver,
		   double eta_last)
{
  const std::string indent = "       ";

  if (forcingTermMethod == Constant) {
    if (printing->isPrintType(NOX::Utils::Details)) {
      printing->out() << indent << "CALCULATING FORCING TERM" << std::endl;
      printing->out() << indent << "Method: Constant" << std::endl;
      printing->out() << indent << "Forcing Term: " << eta_k << std::endl;
    }
    if (setTolerance)
      paramsPtr->sublist(directionMethod).sublist("Linear Solver").
	set("Tolerance", eta_k);

    return eta_k;
  }

  // Get linear solver current tolerance. 
  // NOTE: These values are changing at each nonlinear iteration and 
  // must either be updated from the parameter list each time a compute 
  // is called or supplied during the function call!
  double eta_km1 = 0.0;
  if (eta_last < 0.0)
    eta_km1 = paramsPtr->sublist(directionMethod).
      sublist("Linear Solver").get("Tolerance", 0.0);
  else
    eta_km1 = eta_last;

  // Tolerance may have been adjusted in a line search algorithm so we 
  // have to account for this.
  const NOX::Solver::LineSearchBased* solverPtr = 0;
  solverPtr = dynamic_cast<const NOX::Solver::LineSearchBased*>(&solver);
  if (solverPtr != 0) {
    eta_km1 = 1.0 - solverPtr->getStepSize() * (1.0 - eta_km1);
  }

  if (printing->isPrintType(NOX::Utils::Details)) {
    printing->out() << indent << "CALCULATING FORCING TERM" << std::endl;
    printing->out() << indent << "Method: " << method << std::endl;
  }


  if (forcingTermMethod == Type1) {
    
    if (niter == 0) {
      
      eta_k = eta_initial;

    }
    else {

      // Return norm of predicted F

      // do NOT use the following lines!! This does NOT account for 
      // line search step length taken.
      // const double normpredf = 0.0;
      // oldsoln.getNormLastLinearSolveResidual(normpredf);
      
      // Create a new vector to be the predicted RHS
      if (Teuchos::is_null(predRhs)) {
	predRhs = oldsoln.getF().clone(ShapeCopy);
      }
      if (Teuchos::is_null(stepDir)) {
	stepDir = oldsoln.getF().clone(ShapeCopy);
      }
      
      // stepDir = X - oldX (i.e., the step times the direction)
      stepDir->update(1.0, soln.getX(), -1.0, oldsoln.getX(), 0);
      
      // Compute predRhs = Jacobian * step * dir
      if (!(oldsoln.isJacobian())) {
	if (printing->isPrintType(NOX::Utils::Details)) {
	  printing->out() << "WARNING: NOX::InexactNewtonUtils::resetForcingTerm() - "
	       << "Jacobian is out of date! Recomputing Jacobian." << std::endl;
	}
	const_cast<NOX::Abstract::Group&>(oldsoln).computeJacobian();
      }
      oldsoln.applyJacobian(*stepDir, *predRhs);

      // Compute predRhs = RHSVector + predRhs (this is the predicted RHS)
      predRhs->update(1.0, oldsoln.getF(), 1.0);
      
      // Compute the norms
      double normpredf = predRhs->norm();
      double normf = soln.getNormF();
      double normoldf = oldsoln.getNormF();

      if (printing->isPrintType(NOX::Utils::Details)) {
	printing->out() << indent << "Forcing Term Norm: Using L-2 Norm."
			<< std::endl;
      }

      // Compute forcing term
      eta_k = fabs(normf - normpredf) / normoldf;
      
      // Some output
      if (printing->isPrintType(NOX::Utils::Details)) {
	printing->out() << indent << "Residual Norm k-1 =             " 
	     << normoldf << "\n";
	printing->out() << indent << "Residual Norm Linear Model k =  " 
	     << normpredf << "\n";
	printing->out() << indent << "Residual Norm k =               " << normf << "\n";
	printing->out() << indent << "Calculated eta_k (pre-bounds) = " << eta_k << std::endl;
      }
      
      // Impose safeguard and constraints ...
      const double tmp = (1.0 + sqrt(5.0)) / 2.0;
      const double eta_km1_alpha = pow(eta_km1, tmp);
      if (eta_km1_alpha > 0.1) 
	eta_k = NOX_MAX(eta_k, eta_km1_alpha);
      eta_k = NOX_MAX(eta_k, eta_min);
      eta_k = NOX_MIN(eta_max, eta_k);
    }
  }
    
  else if (forcingTermMethod == Type2) {  
    
    if (niter == 0) {
      
      eta_k = eta_initial;
      
    }
    else {

      double normf = soln.getNormF();
      double normoldf = oldsoln.getNormF();
      
      if (printing->isPrintType(NOX::Utils::Details)) {
	printing->out() << indent << "Forcing Term Norm: Using L-2 Norm."
			<< std::endl;
      }

      const double residual_ratio = normf / normoldf;
      
      eta_k = gamma * pow(residual_ratio, alpha);
      
      // Some output
      if (printing->isPrintType(NOX::Utils::Details)) {
	printing->out() << indent << "Residual Norm k-1 =             " 
			<< normoldf << "\n";
	printing->out() << indent << "Residual Norm k =               " 
			<< normf << "\n";
	printing->out() << indent << "Calculated eta_k (pre-bounds) = " 
			<< eta_k << std::endl;
      }
      
      // Impose safeguard and constraints ... 
      const double eta_k_alpha = gamma * pow(eta_km1, alpha);
      if (eta_k_alpha > 0.1) 
	eta_k = NOX_MAX(eta_k, eta_k_alpha);
      eta_k = NOX_MAX(eta_k, eta_min);
      eta_k = NOX_MIN(eta_max, eta_k);
    }
    
  }
  
  // Set the new linear solver tolerance
  if (setTolerance) 
    paramsPtr->sublist(directionMethod).sublist("Linear Solver").
      set("Tolerance", eta_k);

  if (printing->isPrintType(NOX::Utils::Details)) 
    printing->out() << indent << "Forcing Term: " << eta_k << std::endl;
  
  return eta_k;
}
NOX::Abstract::Group::ReturnType
LOCA::Eigensolver::DGGEVStrategy::computeEigenvalues(
         NOX::Abstract::Group& group,
         Teuchos::RCP< std::vector<double> >& evals_r,
         Teuchos::RCP< std::vector<double> >& evals_i,
         Teuchos::RCP< NOX::Abstract::MultiVector >& evecs_r,
         Teuchos::RCP< NOX::Abstract::MultiVector >& evecs_i)
{

  // Get LAPACK group
  LOCA::LAPACK::Group* grp =
    dynamic_cast<LOCA::LAPACK::Group*>(&group);

  bool hasMassMatrix = true;

  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperIteration)) {
    globalData->locaUtils->out()
      << std::endl << globalData->locaUtils->fill(64,'=') << std::endl
      << "LAPACK ";
    if (hasMassMatrix)
      globalData->locaUtils->out() << "DGGEV ";
    else
      globalData->locaUtils->out() << "DGEEV ";
    globalData->locaUtils->out() << "Eigensolver starting."
                 << std::endl << std::endl;;
  }

  // Make sure Jacobian & mass matrices are fresh
  grp->computeJacobian();
  if (hasMassMatrix)
    grp->computeShiftedMatrix(0.0, 1.0);

  // Get data out of group
  NOX::LAPACK::Matrix<double>& jacobianMatrix = grp->getJacobianMatrix();
  NOX::LAPACK::Matrix<double>& massMatrix = grp->getShiftedMatrix();

  // Size of matrix
  int n = jacobianMatrix.numRows();
  int lda = jacobianMatrix.numRows();
  int ldb = massMatrix.numRows();

  // Space to hold right eigenvectors
  double *vr = new double[n*n];

  // Space to hold real and imaginary eigenvalues
  double *alphar = new double[n];
  double *alphai = new double[n];
  double *beta = new double[n];

  // Size of work array, set to -1 to do a workspace query
  int lwork = -1;

  // Initial work "array"
  double work0;

  // Actual work array
  double *work;

  // Return code
  int info;

  // Copy Jacobian matrix since lapack routines overwrite it
  NOX::LAPACK::Matrix<double> J(jacobianMatrix);

  NOX::LAPACK::Matrix<double> M;

  // First do a workspace query
  if (hasMassMatrix) {

    // Copy mass matrix since lapack routines overwrite it
    M = massMatrix;

    DGGEV_F77("N", "V", &n, &J(0,0), &lda, &M(0,0), &ldb, alphar, alphai, beta,
          vr, &n, vr, &n, &work0, &lwork, &info);
  }
  else {
    DGEEV_F77("N", "V", &n, &J(0,0), &lda, alphar, alphai,
          vr, &n, vr, &n, &work0, &lwork, &info);
  }

  // Allocate work array
  lwork = (int) work0;
  work = new double[lwork];

  // Calculate eigenvalues, eigenvectors
  if (hasMassMatrix) {
    DGGEV_F77("N", "V", &n, &J(0,0), &lda, &M(0,0), &ldb, alphar, alphai, beta,
          vr, &n, vr, &n, work, &lwork, &info);
  }
  else {
    DGEEV_F77("N", "V", &n, &J(0,0), &lda, alphar, alphai,
          vr, &n, vr, &n, work, &lwork, &info);
  }

  // Check for success
  if (info != 0)
    return NOX::Abstract::Group::Failed;

  // Compute all of the eigenvalues and eigenvectors before sorting
  std::vector<double> evals_r_tmp(n);
  std::vector<double> evals_i_tmp(n);
  Teuchos::RCP<NOX::Abstract::MultiVector> evecs_r_tmp =
    group.getX().createMultiVector(n, NOX::ShapeCopy);
  Teuchos::RCP<NOX::Abstract::MultiVector>evecs_i_tmp =
    group.getX().createMultiVector(n, NOX::ShapeCopy);
  NOX::LAPACK::Vector* tmpr;
  NOX::LAPACK::Vector* tmpi;
  double rnext;
  double inext;
  bool isComplexEval = false;
  bool isPrevComplexEval = false;
  for (int j=0; j<n; j++) {

    // Compute eigenvalues
    if (hasMassMatrix) {
      evals_r_tmp[j] = alphar[j]/beta[j];
      evals_i_tmp[j] = alphai[j]/beta[j];
    }
    else {
      evals_r_tmp[j] = alphar[j];
      evals_i_tmp[j] = alphai[j];
    }

    // Compute next eigenvalue
    if (!isPrevComplexEval && j < n-1) {
      if (hasMassMatrix) {
    rnext = alphar[j+1]/beta[j+1];
    inext = alphai[j+1]/beta[j+1];
      }
      else {
    rnext = alphar[j+1];
    inext = alphai[j+1];
      }

      // Determine if this eigenvalue is a complex conjugate pair
      if (fabs(evals_r_tmp[j] - rnext) < 1.0e-14*fabs(1.0+evals_r_tmp[j]) &&
      fabs(evals_i_tmp[j] + inext) < 1.0e-14*fabs(1.0+evals_i_tmp[j]))
    isComplexEval = true;
      else
    isComplexEval = false;
    }
    else if (!isPrevComplexEval && j == n-1)
      isComplexEval = false;

    tmpr = dynamic_cast<NOX::LAPACK::Vector*>(&((*evecs_r_tmp)[j]));
    tmpi = dynamic_cast<NOX::LAPACK::Vector*>(&((*evecs_i_tmp)[j]));

    if (isComplexEval)
      for (int i=0; i<n; i++) {
    (*tmpr)(i) =  vr[i+j*n];
    (*tmpi)(i) =  vr[i+(j+1)*n];
      }
    else if (isPrevComplexEval)
      for (int i=0; i<n; i++) {
    (*tmpr)(i) =  vr[i+(j-1)*n];
    (*tmpi)(i) = -vr[i+j*n];
      }
    else
      for (int i=0; i<n; i++) {
    (*tmpr)(i) = vr[i+j*n];
    (*tmpi)(i) = 0.0;;
      }

    if (isPrevComplexEval) {
      isPrevComplexEval = false;
      isComplexEval = false;
    }
    if (isComplexEval) {
      isPrevComplexEval = true;
      isComplexEval = false;
    }

  }

  // Instantiate a sorting strategy
  Teuchos::RCP<LOCA::EigenvalueSort::AbstractStrategy> evalSort =
    globalData->locaFactory->createEigenvalueSortStrategy(topParams,
                              eigenParams);

  // Create permutation array
  std::vector<int> perm(n);

  // Sort eigenvalues
  evalSort->sort(n, &evals_r_tmp[0], &evals_i_tmp[0], &perm);

  // Get first nev entries of perm
  std::vector<int> perm_short(perm.begin(), perm.begin()+nev);

  // Get sorted eigenvalues and eigenvectors
  evals_r = Teuchos::rcp(new std::vector<double>(evals_r_tmp.begin(),
                         evals_r_tmp.begin()+nev));
  evals_i = Teuchos::rcp(new std::vector<double>(evals_i_tmp.begin(),
                         evals_i_tmp.begin()+nev));
  evecs_r = evecs_r_tmp->subCopy(perm_short);
  evecs_i = evecs_i_tmp->subCopy(perm_short);

  // Print out eigenvalues
  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperIteration)) {
    for (int i=0; i<nev; i++)
      globalData->locaUtils->out()
    << "Eigenvalue " << i << " : "
    << globalData->locaUtils->sciformat((*evals_r)[i]) << " "
    << globalData->locaUtils->sciformat((*evals_i)[i]) << " i"
    << std::endl;
  }

  if (globalData->locaUtils->isPrintType(NOX::Utils::StepperIteration))
    globalData->locaUtils->out()
      << "\nLAPACK Eigensolver finished.\n"
      << globalData->locaUtils->fill(64,'=') << "\n" << std::endl;

  delete [] alphar;
  delete [] alphai;
  delete [] beta;
  delete [] vr;
  delete [] work;

  return NOX::Abstract::Group::Ok;
}
bool
NOX::Solver::TensorBased::computeTensorDirection(NOX::Abstract::Group& soln,
                     const NOX::Solver::Generic& solver)
{
  NOX::Abstract::Group::ReturnType dir_status;

  Teuchos::ParameterList& linearParams = paramsPtr->sublist("Direction").
    sublist(paramsPtr->sublist("Direction").
        get("Method","Tensor")).
    sublist("Linear Solver");

  // Compute F at current solution.
  dir_status = soln.computeF();
  if (dir_status != NOX::Abstract::Group::Ok)
    throwError("computeTensorDirection", "Unable to compute F");

  // Compute Jacobian at current solution.
  dir_status = soln.computeJacobian();
  if (dir_status != NOX::Abstract::Group::Ok)
    throwError("computeTensorDirection", "Unable to compute Jacobian");

  // Begin processing for the tensor step, if necessary.
  double sDotS = 0.0;
  int tempVal1 = 0;
  if ((nIter > 0)  &&  (requestedBaseStep == TensorStep))
  {
    // Compute the tensor term s = x_{k-1} - x_k
    *sVecPtr = soln.getX();
    sVecPtr->update(1.0, solver.getPreviousSolutionGroup().getX(), -1.0);
    double normS = sVecPtr->norm();
    sDotS = normS * normS;

    // Form the tensor term a = (F_{k-1} - F_k - J*s) / (s^T s)^2
    soln.applyJacobian(*sVecPtr, *aVecPtr);
    numJvMults++;
    aVecPtr->update(1.0, solver.getPreviousSolutionGroup().getF(), -1.0);
    aVecPtr->update(-1.0, soln.getF(), 1.0);
    if (sDotS != 0)
      aVecPtr->scale(1.0 / (sDotS * sDotS));

    // Save old Newton step as initial guess to second system
    *tmpVecPtr = *newtonVecPtr;
    tmpVecPtr->scale(-1.0);   // Rewrite to avoid this?

    // Compute residual of linear system using initial guess...
    soln.applyJacobian(*tmpVecPtr, *residualVecPtr);
    numJvMults++;
    residualVecPtr->update(1.0, solver.getPreviousSolutionGroup().getF(),-1.0);
    double residualNorm = residualVecPtr->norm();

#if DEBUG_LEVEL > 0
    double tmpVecNorm = tmpVecPtr->norm();
    double residualNormRel = residualNorm /
      solver.getPreviousSolutionGroup().getNormF();
    if (utilsPtr->isPrintType(NOX::Utils::Details))
    {
      utilsPtr->out() << "  Norm of initial guess: " << utilsPtr->sciformat(tmpVecNorm, 6)
       << std::endl;
      utilsPtr->out() << "  initg norm of model residual =   "
       << utilsPtr->sciformat(residualNorm, 6) << " (abs)     "
       << utilsPtr->sciformat(residualNormRel, 6) << " (rel)" << std::endl;
    }
#endif

    // Save some parameters and use them later...
    double tol = linearParams.get("Tolerance", 1e-4);
    double relativeResidual = residualNorm /
      solver.getPreviousSolutionGroup().getNormF();

    // Decide whether to use initial guess...
    bool isInitialGuessGood = false;
#ifdef USE_INITIAL_GUESS_LOGIC
    if (relativeResidual < 1.0)
    {
      if (utilsPtr->isPrintType(NOX::Utils::Details))
    utilsPtr->out() << "  Initial guess is good..." << std::endl;
      isInitialGuessGood = true;
      // RPP - Brett please make sure the line below is correct.
      *tensorVecPtr = *tmpVecPtr;
      double newTol = tol / relativeResidual;
      if (newTol > 0.99)
    newTol = 0.99;  // force at least one iteration
      linearParams.set("Tolerance",  newTol);
      if (utilsPtr->isPrintType(NOX::Utils::Details))
    utilsPtr->out() << "  Setting tolerance to " << utilsPtr->sciformat(newTol,6) << std::endl;
    }
    else
#endif // USE_INITIAL_GUESS_LOGIC
    {
      //utilsPtr->out() << "  Initial guess is BAD... do not use!\n";
      isInitialGuessGood = false;
      *residualVecPtr = solver.getPreviousSolutionGroup().getF();
    }

    // Compute the term inv(J)*Fp....
    tmpVecPtr->init(0.0);
    dir_status = soln.applyJacobianInverse(linearParams, *residualVecPtr,
                       *tmpVecPtr);

    // If it didn't converge, maybe we can recover.
    if (dir_status != NOX::Abstract::Group::Ok)
    {
      if (doRescue == false)
    throwError("computeTensorDirection", "Unable to apply Jacobian inverse");
      else if ((doRescue == true) &&
           (utilsPtr->isPrintType(NOX::Utils::Warning)))
    utilsPtr->out() << "WARNING: NOX::Solver::TensorBased::computeTensorDirection() - "
         << "Linear solve failed to achieve convergence - "
         << "using the step anyway "
         << "since \"Rescue Bad Newton Solve\" is true." << std::endl;
    }

    // Continue processing
#ifdef USE_INITIAL_GUESS_LOGIC
    if (isInitialGuessGood)
    {
      tmpVecPtr->update(1.0, *tensorVecPtr, 1.0);
      linearParams.set("Tolerance",  tol);
    }
#endif

    // Save iteration count for comparison later
    if (linearParams.sublist("Output").
    isParameter("Number of Linear Iterations"))
      tempVal1 = linearParams.sublist("Output").
    get("Number of Linear Iterations",0);

#if DEBUG_LEVEL > 0
    // Compute residual of linear system with initial guess...
    soln.applyJacobian(*tmpVecPtr, *residualVecPtr);
    numJvMults++;
    residualVec.update(-1.0, solver.getPreviousSolutionGroup().getF(),1.0);
    double residualNorm2 = residualVec.norm();
    double residualNorm2Rel = residualNorm2 /
      solver.getPreviousSolutionGroup().getNormF();
    if (utilsPtr->isPrintType(NOX::Utils::Details))
      utilsPtr->out() << " jifp norm of model residual =   "
       << utilsPtr->sciformat(residualNorm2, 6) << " (abs)     "
       << utilsPtr->sciformat(residualNorm2Rel, 6) << " (rel)" << std::endl;
#endif
  }

  // Compute the Newton direction
  dir_status = soln.computeNewton(linearParams);

  // If it didn't converge, maybe we can recover.
  if (dir_status != NOX::Abstract::Group::Ok)
  {
    if (doRescue == false)
      throwError("computeTensorDirection", "Unable to apply Jacobian inverse");
    else if ((doRescue == true) &&
         (utilsPtr->isPrintType(NOX::Utils::Warning)))
      utilsPtr->out() << "WARNING: NOX::Solver::TensorBased::computeTensorDirection() - "
       << "Linear solve failed to achieve convergence - "
       << "using the step anyway "
       << "since \"Rescue Bad Newton Solve\" is true." << std::endl;
  }

  // Set Newton direction
  *newtonVecPtr = soln.getNewton();

  // Update counter
  int tempVal2 = 0;
  if (linearParams.sublist("Output").
      isParameter("Number of Linear Iterations"))
    tempVal2 = linearParams.sublist("Output").
      get("Number of Linear Iterations",0);
  numJ2vMults += (tempVal1 > tempVal2) ? tempVal1 : tempVal2;

#ifdef CHECK_RESIDUALS
  printDirectionInfo("newtonVec", *newtonVecPtr, soln, false);
#endif // CHECK_RESIDUALS

  // Continue processing the tensor step, if necessary
  if ((nIter > 0)  &&  (requestedBaseStep == TensorStep))
  {
    // Form the term inv(J)*a...  (note that a is not multiplied by 2)
    // The next line does not work in some implementations for some reason
    //tmpVec.update(1.0, newtonVec, -1.0, sVec, 1.0);
    tmpVecPtr->update(1.0, *newtonVecPtr, 1.0);
    tmpVecPtr->update(-1.0, *sVecPtr, 1.0);
    if (sDotS != 0.0)
      tmpVecPtr->scale( 1.0 / (sDotS * sDotS));

    // Calculate value of beta
    sTinvJF = -sVecPtr->innerProduct(*newtonVecPtr);
    sTinvJa = sVecPtr->innerProduct(*tmpVecPtr);
    double qval = 0;
    double lambdaBar = 1;
    beta = calculateBeta(sTinvJa, 1.0, sTinvJF, qval, lambdaBar);

    double sVecNorm = sVecPtr->norm();
    double aVecNorm = aVecPtr->norm();
    if (utilsPtr->isPrintType(NOX::Utils::Details))
    {
      utilsPtr->out() << " sTinvJF = " << utilsPtr->sciformat(sTinvJF, 6)
       << "  sTinvJa = " << utilsPtr->sciformat(sTinvJa, 6) << std::endl;
      utilsPtr->out() << " norm(s) = " << utilsPtr->sciformat(sVecNorm, 6)
       << "  norm(a) = " << utilsPtr->sciformat(aVecNorm, 6) << std::endl;
    }

    if (useModifiedMethod)
    {
      double alpha2 = lambdaBar;
      if (utilsPtr->isPrintType(NOX::Utils::Details))
    utilsPtr->out() << " Beta = " << utilsPtr->sciformat(beta, 6)
         << "  Alpha2 = " << utilsPtr->sciformat(alpha2, 6) << std::endl;
      if (alpha2 != 1.0)
      {
    if (utilsPtr->isPrintType(NOX::Utils::Details))
      utilsPtr->out() << "   *** Scaling tensor term a ***" << std::endl;
    aVecPtr->scale(alpha2);
    tmpVecPtr->scale(alpha2);
    sTinvJa *= alpha2;
    beta /= alpha2;
    lambdaBar = 1.0;
    qval = 0;
      }
    }

    // Form the tensor step
    tensorVecPtr->update(1.0, *newtonVecPtr, -beta*beta, *tmpVecPtr, 0.0);

#ifdef CHECK_RESIDUALS
    printDirectionInfo("tensorVec", *tensorVecPtr, soln, true);
#endif // CHECK_RESIDUALS
#if DEBUG_LEVEL > 0
    double sDotT = tensorVecPtr->innerProduct(sVec);
    if (utilsPtr->isPrintType(NOX::Utils::Details))
      utilsPtr->out() << "  Beta = " << utilsPtr->sciformat(beta, 6)
       << "  std = " << utilsPtr->sciformat(sDotT, 6)
       << "  qval = " << utilsPtr->sciformat(qval, 2)
       << "  lambdaBar = " << lambdaBar << std::endl;
#endif
  }
  else
    *tensorVecPtr = *newtonVecPtr;

  return true;
}