Пример #1
0
LOCA::TurningPoint::MooreSpence::ExtendedMultiVector::ExtendedMultiVector(
		  const Teuchos::RCP<LOCA::GlobalData>& global_data,
		  const NOX::Abstract::MultiVector& xVec,
		  const NOX::Abstract::MultiVector& nullVec,
		  const NOX::Abstract::MultiVector::DenseMatrix& bifParams) :
  LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 2, 1)
{
  LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::setMultiVectorPtr(1, 
						 nullVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::getScalars()->assign(bifParams);
}
LOCA::Hopf::MooreSpence::ExtendedMultiVector::ExtendedMultiVector(
		  const Teuchos::RCP<LOCA::GlobalData>& global_data,
		  const NOX::Abstract::MultiVector& xVec,
		  const NOX::Abstract::MultiVector& realEigenVec,
		  const NOX::Abstract::MultiVector& imagEigenVec,
		  const NOX::Abstract::MultiVector::DenseMatrix& freqs,
		  const NOX::Abstract::MultiVector::DenseMatrix& bifParams) :
  LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 3, 2)
{
  LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::setMultiVectorPtr(1, realEigenVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::setMultiVectorPtr(2, imagEigenVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::getScalarRows(1,0)->assign(freqs);
  LOCA::Extended::MultiVector::getScalarRows(1,1)->assign(bifParams);
}
Пример #3
0
LOCA::Pitchfork::MooreSpence::ExtendedMultiVector::ExtendedMultiVector(
		  const Teuchos::RCP<LOCA::GlobalData>& global_data,
		  const NOX::Abstract::MultiVector& xVec,
		  const NOX::Abstract::MultiVector& nullVec,
		  const NOX::Abstract::MultiVector::DenseMatrix& slacks,
		  const NOX::Abstract::MultiVector::DenseMatrix& bifParams) :
  LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 2, 2)
{
  LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::setMultiVectorPtr(1, 
						 nullVec.clone(NOX::DeepCopy));

  LOCA::Extended::MultiVector::getScalarRows(1,0)->assign(slacks);
  LOCA::Extended::MultiVector::getScalarRows(1,1)->assign(bifParams);
}
void
LOCA::AnasaziOperator::Cayley2Matrix::apply(const NOX::Abstract::MultiVector& input,
                     NOX::Abstract::MultiVector& output) const
{
  std::string callingFunction =
    "LOCA::AnasaziOperator::Cayley2Matrix::apply()";

  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  // Allocate temporary vector
  if (tmp_r == Teuchos::null || tmp_r->numVectors() != input.numVectors())
    tmp_r = input.clone(NOX::ShapeCopy);

  // Compute J-mu*M -- moved to preProcessSeedVector

  // Compute (J-mu*M)*input
  status = grp->applySecondShiftedMatrixMultiVector(input, *tmp_r);
  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);

  // Compute J-sigma*M -- moved to preProcessSeedVector

  // Solve (J-sigma*M)*output = (J-mu*M)*input
  status = grp->applyShiftedMatrixInverseMultiVector(*solverParams, *tmp_r,
                             output);

  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);
}
LOCA::MultiContinuation::ExtendedMultiVector::ExtendedMultiVector(
		    const Teuchos::RCP<LOCA::GlobalData>& global_data,
		    const NOX::Abstract::MultiVector& xVec, 
		    int nScalarRows) :
  LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 1, nScalarRows)
{
  LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
}
void
LOCA::Epetra::AnasaziOperator::Floquet::apply(const NOX::Abstract::MultiVector& input, 
				     NOX::Abstract::MultiVector& output) const
{

  // Apply first part of monodromy operator on input vector
  Teuchos::RCP<NOX::Abstract::MultiVector> tmpVec =  input.clone();
  for (int i=0; i < input.numVectors(); i++) {
    NOX::Abstract::Vector& nAV = tmpVec->operator[](i);
    NOX::Epetra::Vector& nEV = dynamic_cast<NOX::Epetra::Vector&>(nAV);
    Epetra_Vector& eV = nEV.getEpetraVector();

    xyztInterface->beginFloquetOperatorApplication(eV);
  }
    
  // Now apply the main part of the monodromy matrix
  NOX::Abstract::Group::ReturnType status =
    grp->applyJacobianInverseMultiVector(*solverParams, *(tmpVec.get()), output);
  globalData->locaErrorCheck->checkReturnType(status,
                       "LOCA::Epetra::AnasaziOperator::Floquet::apply()");


  for (int i=0; i < input.numVectors(); i++) {
    NOX::Abstract::Vector& nAV = output.operator[](i);
    NOX::Epetra::Vector& nEV = dynamic_cast<NOX::Epetra::Vector&>(nAV);
    Epetra_Vector& eV = nEV.getEpetraVector();

    xyztInterface->finishFloquetOperatorApplication(eV);
  }

// Was this needed?

// TESTING:  Doubling the call to this routine resulted in the
//  squaring of the Floquet multipliers, as they should.
//  Replacing the apply function so the operator is diagonal
//  with entries 1/(i+2) led to the Floquet multipliers.

/*
  std::cout << " Fixing apply so Floquets at 1/2 1/3 1/4 ... " << std::endl;

  Teuchos::RCP<NOX::Abstract::MultiVector> tmpVec =  input.clone();
  for (int i=0; i < input.numVectors(); i++) {
    NOX::Abstract::Vector& nAV = output.operator[](i);
    NOX::Epetra::Vector& nEV = dynamic_cast<NOX::Epetra::Vector&>(nAV);
    Epetra_Vector& oV = nEV.getEpetraVector();

    NOX::Abstract::Vector& nAV2 = tmpVec->operator[](i);
    NOX::Epetra::Vector& nEV2 = dynamic_cast<NOX::Epetra::Vector&>(nAV2);
    Epetra_Vector& iV = nEV2.getEpetraVector();

    for (int j=0; j < iV.MyLength(); j++) {
     oV[j] = iV[j] / (j + 2.0);
    }
  }
*/
}
LOCA::MultiContinuation::ExtendedMultiVector::ExtendedMultiVector(
		     const Teuchos::RCP<LOCA::GlobalData>& global_data,
		     const NOX::Abstract::MultiVector& xVec,
		     const NOX::Abstract::MultiVector::DenseMatrix& params) :
  LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 1, 
			      params.numRows())
{
  LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
  LOCA::Extended::MultiVector::getScalars()->assign(params);
}
Пример #8
0
NOX::Abstract::Group::ReturnType 
LOCA::DerivUtils::computeDwtJnDx(LOCA::MultiContinuation::AbstractGroup& grp,
				 const NOX::Abstract::MultiVector& w,
				 const NOX::Abstract::Vector& nullVector,
				 NOX::Abstract::MultiVector& result) const
{
  string callingFunction = 
    "LOCA::DerivUtils::computeDwtJnDx()";
  NOX::Abstract::Group::ReturnType status, finalStatus;

  // Vector to store w^T*J
  Teuchos::RCP<NOX::Abstract::MultiVector> wtJ = 
    w.clone(NOX::ShapeCopy);
  
  // Compute base w^T*J
  finalStatus = grp.computeJacobian();
  globalData->locaErrorCheck->checkReturnType(finalStatus, callingFunction);

  status = grp.applyJacobianTransposeMultiVector(w, *wtJ);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  
  // Copy original solution vector
  Teuchos::RCP<NOX::Abstract::Vector> Xvec = 
    grp.getX().clone(NOX::DeepCopy);

  // Perturb solution vector in direction of nullVector, return perturbation
  double eps = perturbXVec(grp, *Xvec, nullVector);

  // Fill perturbed w^T*J vector
  finalStatus = grp.computeJacobian();
  globalData->locaErrorCheck->checkReturnType(finalStatus, callingFunction);
    
  status = grp.applyJacobianTransposeMultiVector(w, result);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);

  // Difference perturbed and base vector 
  result.update(-1.0, *wtJ, 1.0);
  result.scale(1.0/eps);
  
  // Restore original solution vector
  grp.setX(*Xvec);

  return finalStatus;
}
void
LOCA::AnasaziOperator::Cayley2Matrix::preProcessSeedVector(NOX::Abstract::MultiVector& ivec)
{
  // Changes random seed vector ivec:   ivec = (J - sigma*M)^{-1}*M*ivec
  std::string callingFunction =
    "LOCA::AnasaziOperator::Cayley2Matrix::preProcessSeedVector()";

  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  // Allocate temporary vector
  if (tmp_r == Teuchos::null || tmp_r->numVectors() != ivec.numVectors())
    tmp_r = ivec.clone(NOX::ShapeCopy);

  // Compute M
  status = grp->computeShiftedMatrix(0.0, 1.0);
  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);

  // Compute M*ivec
  status = grp->applyShiftedMatrixMultiVector(ivec, *tmp_r);
  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);

  // Compute J-sigma*M
  status = grp->computeShiftedMatrix(1.0, -sigma);
  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);

  // Solve (J-sigma*M)*output = (M)*ivec
  status = grp->applyShiftedMatrixInverseMultiVector(*solverParams, *tmp_r,
                             ivec);

  finalStatus =
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
                               finalStatus,
                               callingFunction);

  // Compute J-mu*M
  status = grp->computeSecondShiftedMatrix(1.0, -mu);
}
void
LOCA::AnasaziOperator::ShiftInvert::apply(
				     const NOX::Abstract::MultiVector& input, 
				     NOX::Abstract::MultiVector& output) const
{
  std::string callingFunction = 
    "LOCA::AnasaziOperator::ShiftInvert::apply()";

  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  // Allocate temporary vector
  if (tmp_r == Teuchos::null || tmp_r->numVectors() != input.numVectors())
    tmp_r = input.clone(NOX::ShapeCopy);

  // Compute M
  status = grp->computeShiftedMatrix(0.0, 1.0);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);

  // Compute M*input
  status = grp->applyShiftedMatrixMultiVector(input, *tmp_r);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);

  // Compute J-omega*M
  status = grp->computeShiftedMatrix(1.0, -shift);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);

  // Solve (J-omega*M)*output = M*input
  status = grp->applyShiftedMatrixInverseMultiVector(*solverParams, *tmp_r, 
						     output);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);
}
// Solves turning point equations via classic Salinger bordering
// The first m columns of input_x and input_null store the RHS while
// the last column stores df/dp, d(Jn)/dp respectively.  Note however
// input_param has only m columns (not m+1).  result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType 
LOCA::TurningPoint::MooreSpence::PhippsBordering::solveTransposeContiguous(
		  Teuchos::ParameterList& params,
		  const NOX::Abstract::MultiVector& input_x,
		  const NOX::Abstract::MultiVector& input_null,
	          const NOX::Abstract::MultiVector::DenseMatrix& input_param,
		  NOX::Abstract::MultiVector& result_x,
		  NOX::Abstract::MultiVector& result_null,
	          NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
  std::string callingFunction = 
    "LOCA::TurningPoint::MooreSpence::PhippsBordering::solveTransposeContiguous()";
  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  int m = input_x.numVectors()-2;
  std::vector<int> index_input(m);
  std::vector<int> index_input_dp(m+1);
  std::vector<int> index_null(1);
  std::vector<int> index_dp(1);
  for (int i=0; i<m; i++) {
    index_input[i] = i;
    index_input_dp[i] = i;
  }
  index_input_dp[m] = m;
  index_dp[0] = m;
  index_null[0] = m+1;

  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+1);
  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+2);

  // Create view of first m+1 columns of input_null, result_null
  Teuchos::RCP<NOX::Abstract::MultiVector> input_null_view = 
      input_null.subView(index_input_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> result_null_view = 
      result_null.subView(index_input_dp);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // Solve  |J^T v||A B| = |G -phi|
  //        |u^T 0||a b|   |0   0 |
  status =
    transposeBorderedSolver->applyInverseTranspose(params, 
						   input_null_view.get(), 
						   NULL, 
						   *result_null_view, 
						   tmp_mat_1);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> A = 
    result_null.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> B = 
    result_null.subView(index_dp);
  double b = tmp_mat_1(0,m);

  // compute (Jv)_x^T[A B u]
  result_null[m+1] = *uVector;
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp = 
    result_null.clone(NOX::ShapeCopy);
  status = group->computeDwtJnDxMulti(result_null, *nullVector, *tmp);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							   finalStatus,
							   callingFunction);

  // compute [F 0 0] - (Jv)_x^T[A B u]
  tmp->update(1.0, input_x, -1.0);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // Solve  |J^T v||C D E| = |F - (Jv)_x^T A  -(Jv)_x^T B  -(Jv)_x^T u|
  //        |u^T 0||c d e|   |         0             0            0   |
  status = 
    transposeBorderedSolver->applyInverseTranspose(params, 
						   tmp.get(), 
						   NULL, 
						   result_x,
						   tmp_mat_2);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> C = 
    result_x.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> D = 
    result_x.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> E = 
    result_x.subView(index_null);
  double d = tmp_mat_2(0, m);
  double e = tmp_mat_2(0, m+1);

  // compute (Jv)_p^T*[A B u]
  NOX::Abstract::MultiVector::DenseMatrix t1(1,m+2);
  result_null.multiply(1.0, *dJndp, t1);

  // compute f_p^T*[C D E]
  NOX::Abstract::MultiVector::DenseMatrix t2(1,m+2);
  result_x.multiply(1.0, *dfdp, t2);

  // compute f_p^T*u
  double fptu = uVector->innerProduct((*dfdp)[0]);

  // Fill coefficient arrays
  double M[9];
  M[0] = st;   M[1] =  -e;   M[2] = t1(0,m+1) + t2(0,m+1);
  M[3] = 0.0;  M[4] =   st;  M[5] = fptu;
  M[6] = -b;   M[7] =  -d;   M[8] = t1(0,m) + t2(0,m);

  // Compute RHS
  double *R = new double[3*m];
  for (int i=0; i<m; i++) {
    R[3*i]   = tmp_mat_1(0,i);
    R[3*i+1] = tmp_mat_2(0,i);
    R[3*i+2] = result_param(0,i) - t1(0,i) - t2(0,i);
  }

  // Solve M*P = R
  int three = 3;
  int piv[3];
  int info;
  Teuchos::LAPACK<int,double> L;
  L.GESV(three, m, M, three, piv, R, three, &info);
  if (info != 0) {
    globalData->locaErrorCheck->throwError(
				    callingFunction,
				    "Solve of 3x3 coefficient matrix failed!");
    return NOX::Abstract::Group::Failed;
  }

  NOX::Abstract::MultiVector::DenseMatrix alpha(1,m);
  NOX::Abstract::MultiVector::DenseMatrix beta(1,m);
  for (int i=0; i<m; i++) {
    alpha(0,i)        = R[3*i];
    beta(0,i)         = R[3*i+1];
    result_param(0,i) = R[3*i+2];
  }

  // compute A = A + B*z + alpha*u (remember A is a sub-view of result_null)
  A->update(Teuchos::NO_TRANS, 1.0, *B, result_param, 1.0);
  A->update(Teuchos::NO_TRANS, 1.0, *uMultiVector, alpha, 1.0);

  // compute C = C + D*z + alpha*E + beta*u 
  // (remember C is a sub-view of result_x)
  C->update(Teuchos::NO_TRANS, 1.0, *D, result_param, 1.0);
  C->update(Teuchos::NO_TRANS, 1.0, *E, alpha, 1.0);
  C->update(Teuchos::NO_TRANS, 1.0, *uMultiVector, beta, 1.0);

  delete [] R;

  return finalStatus;
}
// Solves turning point equations via Phipps modified bordering
// The first m columns of input_x and input_null store the RHS while
// the last column stores df/dp, d(Jn)/dp respectively.  Note however
// input_param has only m columns (not m+1).  result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType 
LOCA::TurningPoint::MooreSpence::PhippsBordering::solveContiguous(
		  Teuchos::ParameterList& params,
		  const NOX::Abstract::MultiVector& input_x,
		  const NOX::Abstract::MultiVector& input_null,
	          const NOX::Abstract::MultiVector::DenseMatrix& input_param,
		  NOX::Abstract::MultiVector& result_x,
		  NOX::Abstract::MultiVector& result_null,
	          NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
  std::string callingFunction = 
    "LOCA::TurningPoint::MooreSpence::PhippsBordering::solveContiguous()";
  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  int m = input_x.numVectors()-2;
  std::vector<int> index_input(m);
  std::vector<int> index_input_dp(m+1);
  std::vector<int> index_null(1);
  std::vector<int> index_dp(1);
  for (int i=0; i<m; i++) {
    index_input[i] = i;
    index_input_dp[i] = i;
  }
  index_input_dp[m] = m;
  index_dp[0] = m;
  index_null[0] = m+1;

  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+1);
  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+2);

  // Create view of first m+1 columns of input_x, result_x
  Teuchos::RCP<NOX::Abstract::MultiVector> input_x_view = 
      input_x.subView(index_input_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> result_x_view = 
      result_x.subView(index_input_dp);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }
  
  // Solve  |J   u||A B| = |F df/dp|
  //        |v^T 0||a b|   |0   0  |
  status = borderedSolver->applyInverse(params, input_x_view.get(), NULL, 
					*result_x_view, tmp_mat_1);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> A = 
    result_x.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> B = 
    result_x.subView(index_dp);
  double b = tmp_mat_1(0,m);

  // compute (Jv)_x[A B v]
  result_x[m+1] = *nullVector;
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp = 
    result_x.clone(NOX::ShapeCopy);
  status = group->computeDJnDxaMulti(*nullVector, *JnVector, result_x,
				     *tmp);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);

  // compute (Jv)_x[A B v] - [G d(Jn)/dp 0]
  tmp->update(-1.0, input_null, 1.0);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // Solve  |J   u||C D E| = |(Jv)_x A - G  (Jv)_x B - d(Jv)/dp  (Jv)_x v|
  //        |v^T 0||c d e|   |         0             0               0   |
  status = borderedSolver->applyInverse(params, tmp.get(), NULL, result_null,
					tmp_mat_2);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> C = 
    result_null.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> D = 
    result_null.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> E = 
    result_null.subView(index_null);
  double d = tmp_mat_2(0, m);
  double e = tmp_mat_2(0, m+1);

  // Fill coefficient arrays
  double M[9];
  M[0] = s;   M[1] =  e;  M[2] = -tpGroup->lTransNorm((*E)[0]);
  M[3] = 0.0; M[4] =  s;  M[5] =  tpGroup->lTransNorm(*nullVector);
  M[6] = b;   M[7] = -d;  M[8] =  tpGroup->lTransNorm((*D)[0]);

  // compute h + phi^T C
  tpGroup->lTransNorm(*C, result_param);
  result_param += input_param;

  double *R = new double[3*m];
  for (int i=0; i<m; i++) {
    R[3*i]   =  tmp_mat_1(0,i);
    R[3*i+1] = -tmp_mat_2(0,i);
    R[3*i+2] =  result_param(0,i);
  }

  // Solve M*P = R
  int three = 3;
  int piv[3];
  int info;
  Teuchos::LAPACK<int,double> L;
  L.GESV(three, m, M, three, piv, R, three, &info);
  if (info != 0) {
    globalData->locaErrorCheck->throwError(
				    callingFunction,
				    "Solve of 3x3 coefficient matrix failed!");
    return NOX::Abstract::Group::Failed;
  }

  NOX::Abstract::MultiVector::DenseMatrix alpha(1,m);
  NOX::Abstract::MultiVector::DenseMatrix beta(1,m);
  for (int i=0; i<m; i++) {
    alpha(0,i)        = R[3*i];
    beta(0,i)         = R[3*i+1];
    result_param(0,i) = R[3*i+2];
  }

  // compute A = A - B*z + v*alpha (remember A is a sub-view of result_x)
  A->update(Teuchos::NO_TRANS, -1.0, *B, result_param, 1.0);
  A->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, alpha, 1.0);

  // compute C = -C + d*z - E*alpha + v*beta 
  // (remember C is a sub-view of result_null)
  C->update(Teuchos::NO_TRANS, 1.0, *D, result_param, -1.0);
  C->update(Teuchos::NO_TRANS, -1.0, *E, alpha, 1.0);
  C->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, beta, 1.0);

  delete [] R;

  return finalStatus;
}
// Solves Hopf equations via classic Salinger bordering
// The first m columns of input_x, input_y, input_z store the RHS, the
// next column stores df/dp, (Jy-wBz)_p and (Jz+wBy)_p respectively, the
// last column of input_y and input_z store Bz and -By respectively.  Note 
// input_x has m+1 columns, input_y and input_z have m+2, and input_w and
// input_p have m columns.  result_x, result_y, result_z, result_w and 
// result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType 
LOCA::Hopf::MooreSpence::SalingerBordering::solveContiguous(
		      Teuchos::ParameterList& params,
		      const NOX::Abstract::MultiVector& input_x,
		      const NOX::Abstract::MultiVector& input_y,
		      const NOX::Abstract::MultiVector& input_z,
		      const NOX::Abstract::MultiVector::DenseMatrix& input_w,
		      const NOX::Abstract::MultiVector::DenseMatrix& input_p,
		      NOX::Abstract::MultiVector& result_x,
		      NOX::Abstract::MultiVector& result_y,
		      NOX::Abstract::MultiVector& result_z,
		      NOX::Abstract::MultiVector::DenseMatrix& result_w,
	              NOX::Abstract::MultiVector::DenseMatrix& result_p) const
{
  std::string callingFunction = 
    "LOCA::Hopf::MooreSpence::SalingerBordering::solveContiguous()";
  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  int m = input_x.numVectors()-1;
  std::vector<int> index_input(m);
  std::vector<int> index_dp(1);
  std::vector<int> index_B(1);
  std::vector<int> index_ip(m+1);
  for (int i=0; i<m; i++) {
    index_input[i] = i;
    index_ip[i] = i;
  }
  index_ip[m] = m;
  index_dp[0] = m;
  index_B[0] = m+1;

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }
  
  // compute [A b] = J^-1 [F df/dp]
  status = group->applyJacobianInverseMultiVector(params, input_x, result_x);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> A = 
    result_x.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> b = 
    result_x.subView(index_dp);

  // verify underlying complex matrix is valid
   if (!group->isComplex()) {
    status = group->computeComplex(w);
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // compute (J+iwB)(y+iz)_x [A b]
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp_real = 
    result_y.clone(NOX::ShapeCopy);
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp_real_sub =
    tmp_real->subView(index_ip);
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp_imag = 
    result_y.clone(NOX::ShapeCopy);
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp_imag_sub =
    tmp_imag->subView(index_ip);
  tmp_real->init(0.0);
  tmp_imag->init(0.0);
  status = group->computeDCeDxa(*yVector, *zVector, w, result_x,
				*CeRealVector, *CeImagVector, *tmp_real_sub,
				*tmp_imag_sub);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);

  // compute [G+iH d(J+iwB)(y+iz)/dp iB(y+iz)] - [(J+iwB)_x[A b] 0+i0]
  tmp_real->update(1.0, input_y, -1.0);
  tmp_imag->update(1.0, input_z, -1.0);

  // verify underlying complex matrix is valid
  if (!group->isComplex()) {
    status = group->computeComplex(w);
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // compute [C+iD e+if g+ih] = (J+iwB)^-1 (tmp_real + i tmp_imag)
  status = group->applyComplexInverseMultiVector(params, *tmp_real, *tmp_imag,
						 result_y, result_z);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> C = 
    result_y.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> D = 
    result_z.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> e = 
    result_y.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> f = 
    result_z.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> g = 
    result_y.subView(index_B);
  Teuchos::RCP<NOX::Abstract::MultiVector> h = 
    result_z.subView(index_B);

  // compute lambda = ((phi^T h)(phi^T C-u) - (phi^T g)(phi^T D-v)) /
  //                  ((phi^T h)(phi^T e)-(phi^T g)(phi^T f))
  NOX::Abstract::MultiVector::DenseMatrix ltC(1,m);
  NOX::Abstract::MultiVector::DenseMatrix ltD(1,m);
  double lte = hopfGroup->lTransNorm((*e)[0]);
  double ltf = hopfGroup->lTransNorm((*f)[0]);
  double ltg = hopfGroup->lTransNorm((*g)[0]);
  double lth = hopfGroup->lTransNorm((*h)[0]);
  double denom = lth*lte - ltg*ltf;
  hopfGroup->lTransNorm(*C, ltC); 
  ltC -= input_w; 
  ltC.scale(lth);
  hopfGroup->lTransNorm(*D, ltD); 
  ltD -= input_p; 
  result_p.assign(ltD);
  result_p.scale(-ltg);
  result_p += ltC;
  result_p.scale(1.0/denom);

  // compute omega = (phi^T D-v - (phi^T f)lambda)/(phi^T h)
  result_w.assign(result_p);
  result_w.scale(-ltf);
  result_w += ltD;
  result_w.scale(1.0/lth);

  // compute A = A - b*lambda (remember A is a sub-view of result_x)
  A->update(Teuchos::NO_TRANS, -1.0, *b, result_p, 1.0);

  // compute C = C - e*lambda - g*omega (remember C is a sub-view of result_y)
  C->update(Teuchos::NO_TRANS, -1.0, *e, result_p, 1.0);
  C->update(Teuchos::NO_TRANS, -1.0, *g, result_w, 1.0);

  // compute D = D - f*lambda - h*omega (remember D is a sub-view of result_z)
  D->update(Teuchos::NO_TRANS, -1.0, *f, result_p, 1.0);
  D->update(Teuchos::NO_TRANS, -1.0, *h, result_w, 1.0);

  return finalStatus;
}
void
LOCA::BorderedSolver::HouseholderQR::computeQR(
                const NOX::Abstract::MultiVector::DenseMatrix& C,
                const NOX::Abstract::MultiVector& B,
                bool use_c_transpose,
                NOX::Abstract::MultiVector::DenseMatrix& Y1,
                NOX::Abstract::MultiVector& Y2,
                NOX::Abstract::MultiVector::DenseMatrix& T,
                NOX::Abstract::MultiVector::DenseMatrix& R)
{
  double beta;
  int m = B.numVectors();

  // Initialize
  Y1.putScalar(0.0);
  T.putScalar(0.0);
  Y2 = B;
  if (use_c_transpose) {
    for (int i=0; i<m; i++)
      for (int j=0; j<m; j++)
    R(i,j) = C(j,i);        // Copy transpose of C into R
  }
  else
    R.assign(C);

  // A temporary vector
  Teuchos::RCP<NOX::Abstract::MultiVector> v2 = Y2.clone(1);

  Teuchos::RCP<NOX::Abstract::MultiVector::DenseMatrix> v1;
  Teuchos::RCP<NOX::Abstract::MultiVector> h2;
  Teuchos::RCP<NOX::Abstract::MultiVector::DenseMatrix> h1;
  Teuchos::RCP<NOX::Abstract::MultiVector> y2;
  Teuchos::RCP<NOX::Abstract::MultiVector::DenseMatrix> y1;
  Teuchos::RCP<NOX::Abstract::MultiVector::DenseMatrix> z;
  std::vector<int> h_idx;
  std::vector<int> y_idx;
  y_idx.reserve(m);

  for (int i=0; i<m; i++) {

    // Create view of column i of Y1 starting at row i
    v1 =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(Teuchos::View,
                                   Y1,
                                   m-i,
                                   1, i, i));

    // Create view of columns i through m-1 of Y2
    h_idx.resize(m-i);
    for (unsigned int j=0; j<h_idx.size(); j++)
      h_idx[j] = i+j;
    h2 = Y2.subView(h_idx);

    // Create view of columns i thru m-1 of R, starting at row i
    h1 =
      Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(Teuchos::View,
                                   R,
                                   m-i,
                                   m-i,
                                   i, i));

    if (i > 0) {

      // Create view of columns 0 through i-1 of Y2
      y_idx.push_back(i-1);
      y2 = Y2.subView(y_idx);

      // Create view of columns 0 through i-1 of Y1, starting at row i
      y1 =
    Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(Teuchos::View,
                                 Y1,
                                 m-i,
                                 i, i, 0));

      // Create view of column i, row 0 through i-1 of T
      z =
    Teuchos::rcp(new NOX::Abstract::MultiVector::DenseMatrix(Teuchos::View,
                                 T,
                                 i,
                                 1,
                                 0, i));
    }

    // Compute Householder Vector
    computeHouseholderVector(i, R, Y2, *v1, *v2, beta);

    // Apply Householder reflection
    applyHouseholderVector(*v1, *v2, beta, *h1, *h2);

    // Copy v2 into Y2
    Y2[i] = (*v2)[0];

    T(i,i) = -beta;

    if (i > 0) {

      // Compute z = y2^T * v2
      v2->multiply(1.0, *y2, *z);

      // Compute z = -beta * (z + y1^T * v1)
      z->multiply(Teuchos::TRANS, Teuchos::NO_TRANS, -beta, *y1, *v1, -beta);

      // Compute z = T * z
      dblas.TRMV(Teuchos::UPPER_TRI, Teuchos::NO_TRANS, Teuchos::NON_UNIT_DIAG,
         i, T.values(), m, z->values(), 1);

    }
  }

}
Пример #15
0
// Solves pitchfork equations via Phipps modified bordering
// The first m columns of input_x and input_null store the RHS,
// column m+1 stores df/dp, d(Jn)/dp, column m+2 stores psi and 0,
// and the last column provides space for solving (Jv_x) v.  Note however
// input_param has only m columns.  result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType 
LOCA::Pitchfork::MooreSpence::PhippsBordering::solveContiguous(
		  Teuchos::ParameterList& params,
		  const NOX::Abstract::MultiVector& input_x,
		  const NOX::Abstract::MultiVector& input_null,
		  const NOX::Abstract::MultiVector::DenseMatrix& input_slack,
	          const NOX::Abstract::MultiVector::DenseMatrix& input_param,
		  NOX::Abstract::MultiVector& result_x,
		  NOX::Abstract::MultiVector& result_null,
		  NOX::Abstract::MultiVector::DenseMatrix& result_slack,
	          NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
  string callingFunction = 
    "LOCA::Pitchfork::MooreSpence::PhippsBordering::solveContiguous()";
  NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
  NOX::Abstract::Group::ReturnType status;

  int m = input_x.numVectors()-3;
  vector<int> index_input(m);
  vector<int> index_input_dp(m+2);
  vector<int> index_null(1);
  vector<int> index_dp(1);
  vector<int> index_s(1);
  for (int i=0; i<m; i++) {
    index_input[i] = i;
    index_input_dp[i] = i;
  }
  index_input_dp[m] = m;
  index_input_dp[m+1] = m+1;
  index_dp[0] = m;
  index_s[0] = m+1;
  index_null[0] = m+2;

  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+2);
  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+3);

  // Create view of first m+2 columns of input_x, result_x
  Teuchos::RCP<NOX::Abstract::MultiVector> input_x_view = 
      input_x.subView(index_input_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> result_x_view = 
      result_x.subView(index_input_dp);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }
  
  // Solve  |J   u||A B C| = |F df/dp psi|
  //        |v^T 0||a b c|   |0   0    0 |
  status = borderedSolver->applyInverse(params, input_x_view.get(), NULL, 
					*result_x_view, tmp_mat_1);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> A = 
    result_x.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> B = 
    result_x.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> C = 
    result_x.subView(index_s);
  double b = tmp_mat_1(0,m);
  double c = tmp_mat_1(0,m+1);

  // compute (Jv)_x[A B C v]
  result_x[m+2] = *nullVector;
  Teuchos::RCP<NOX::Abstract::MultiVector> tmp = 
    result_x.clone(NOX::ShapeCopy);
  status = group->computeDJnDxaMulti(*nullVector, *JnVector, result_x,
				     *tmp);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);

  // compute [G d(Jn)/dp 0 0] - (Jv)_x[A B C v]
  tmp->update(1.0, input_null, -1.0);

  // verify underlying Jacobian is valid
  if (!group->isJacobian()) {
    status = group->computeJacobian();
    finalStatus = 
      globalData->locaErrorCheck->combineAndCheckReturnTypes(status, 
							     finalStatus,
							     callingFunction);
  }

  // Solve  |J   u||D E K L| = |G-(Jv)_xA  d(Jv)/dp-(Jv)_xB  -(Jv)_xC -(Jv)_xv|
  //        |v^T 0||d e k l|   |    0             0              0        0   |
  status = borderedSolver->applyInverse(params, tmp.get(), NULL, result_null,
					tmp_mat_2);
  finalStatus = 
    globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
							   callingFunction);
  Teuchos::RCP<NOX::Abstract::MultiVector> D = 
    result_null.subView(index_input);
  Teuchos::RCP<NOX::Abstract::MultiVector> E = 
    result_null.subView(index_dp);
  Teuchos::RCP<NOX::Abstract::MultiVector> K = 
    result_null.subView(index_s);
  Teuchos::RCP<NOX::Abstract::MultiVector> L = 
    result_null.subView(index_null);
  double e = tmp_mat_2(0, m);
  double k = tmp_mat_2(0, m+1);
  double l = tmp_mat_2(0, m+2);

  double ltE = pfGroup->lTransNorm((*E)[0]);
  double ltK = pfGroup->lTransNorm((*K)[0]);
  double ltL = pfGroup->lTransNorm((*L)[0]);
  double ltv = pfGroup->lTransNorm(*nullVector);
  double ipv = group->innerProduct(*nullVector, *asymVector);
  double ipB = group->innerProduct((*B)[0], *asymVector);
  double ipC = group->innerProduct((*C)[0], *asymVector);

  // Fill coefficient arrays
  double M[16];
  M[0]  = sigma; M[1]  = -l;     M[2]  =  ipv; M[3]  =  ltL;
  M[4]  = 0.0;   M[5]  =  sigma; M[6]  =  0.0; M[7]  =  ltv;
  M[8]  = b;     M[9]  =  e;     M[10] = -ipB; M[11] = -ltE;
  M[12] = c;     M[13] =  k;     M[14] = -ipC; M[15] = -ltK;

  // compute s - <A,psi>
  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_3(1, m);
  group->innerProduct(*asymMultiVector, *A, tmp_mat_3);
  tmp_mat_3 -= input_slack;
  tmp_mat_3.scale(-1.0);

  // compute h - phi^T D
  NOX::Abstract::MultiVector::DenseMatrix tmp_mat_4(1, m);
  pfGroup->lTransNorm(*D, tmp_mat_4);
  tmp_mat_4 -= input_param;
  tmp_mat_4.scale(-1.0);

  double *R = new double[4*m];
  for (int i=0; i<m; i++) {
    R[4*i]   = tmp_mat_1(0,i);
    R[4*i+1] = tmp_mat_2(0,i);
    R[4*i+2] = tmp_mat_3(0,i);
    R[4*i+3] = tmp_mat_4(0,i);
  }

  // Solve M*P = R
  int piv[4];
  int info;
  Teuchos::LAPACK<int,double> dlapack;
  dlapack.GESV(4, m, M, 4, piv, R, 4, &info);
  if (info != 0) {
    globalData->locaErrorCheck->throwError(
				    callingFunction,
				    "Solve of 4x4 coefficient matrix failed!");
    return NOX::Abstract::Group::Failed;
  }

  NOX::Abstract::MultiVector::DenseMatrix alpha(1,m);
  NOX::Abstract::MultiVector::DenseMatrix beta(1,m);
  for (int i=0; i<m; i++) {
    alpha(0,i)        = R[4*i];
    beta(0,i)         = R[4*i+1];
    result_param(0,i) = R[4*i+2];
    result_slack(0,i) = R[4*i+3];
  }

  // compute A = A - B*z -C*w + v*alpha (remember A is a sub-view of result_x)
  A->update(Teuchos::NO_TRANS, -1.0, *B, result_param, 1.0);
  A->update(Teuchos::NO_TRANS, -1.0, *C, result_slack, 1.0);
  A->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, alpha, 1.0);

  // compute D = D - E*z - K*w + L*alpha + v*beta 
  // (remember D is a sub-view of result_null)
  D->update(Teuchos::NO_TRANS, -1.0, *E, result_param, 1.0);
  D->update(Teuchos::NO_TRANS, -1.0, *K, result_slack, 1.0);
  D->update(Teuchos::NO_TRANS, 1.0, *L, alpha, 1.0);
  D->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, beta, 1.0);

  delete [] R;

  return finalStatus;
}