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Public Member Functions | Protected Types | Protected Member Functions | Protected Attributes | List of all members
LOCA::BorderedSolver::EpetraHouseholder Class Reference

Bordered system solver strategy based on Householder transformations. More...

#include <LOCA_BorderedSolver_EpetraHouseholder.H>

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Public Member Functions

 EpetraHouseholder (const Teuchos::RCP< LOCA::GlobalData > &global_data, const Teuchos::RCP< LOCA::Parameter::SublistParser > &topParams, const Teuchos::RCP< Teuchos::ParameterList > &solverParams)
 Constructor.
virtual ~EpetraHouseholder ()
 Destructor.
virtual void setMatrixBlocks (const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > &op, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockA, const Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > &blockB, const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > &blockC)
 Set blocks.
virtual NOX::Abstract::Group::ReturnType initForSolve ()
 Intialize solver for a solve.
virtual NOX::Abstract::Group::ReturnType initForTransposeSolve ()
 Intialize solver for a transpose solve.
virtual NOX::Abstract::Group::ReturnType apply (const NOX::Abstract::MultiVector &X, const NOX::Abstract::MultiVector::DenseMatrix &Y, NOX::Abstract::MultiVector &U, NOX::Abstract::MultiVector::DenseMatrix &V) const
 Computed extended matrix-multivector product.
virtual NOX::Abstract::Group::ReturnType applyTranspose (const NOX::Abstract::MultiVector &X, const NOX::Abstract::MultiVector::DenseMatrix &Y, NOX::Abstract::MultiVector &U, NOX::Abstract::MultiVector::DenseMatrix &V) const
 Computed extended matrix transpose-multivector product.
virtual NOX::Abstract::Group::ReturnType applyInverse (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector *F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
 Solves the extended system using the technique described above.
virtual NOX::Abstract::Group::ReturnType applyInverseTranspose (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector *F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
 Solves the transpose of the extended system as defined above.
Public Member Functions inherited from LOCA::BorderedSolver::AbstractStrategy
 AbstractStrategy ()
 Constructor.
virtual ~AbstractStrategy ()
 Destructor.
virtual void setMatrixBlocksMultiVecConstraint (const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > &op, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockA, const Teuchos::RCP< const NOX::Abstract::MultiVector > &blockB, const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > &blockC)
 Set blocks with multivector constraint.

Protected Types

enum  PRECONDITIONER_METHOD { JACOBIAN , SMW }
 Enumerated type indicating preconditioner method.

Protected Member Functions

virtual NOX::Abstract::Group::ReturnType solve (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector *F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
 Solves the extended system using the technique described above.
virtual NOX::Abstract::Group::ReturnType solveTranspose (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector *F, const NOX::Abstract::MultiVector::DenseMatrix *G, NOX::Abstract::MultiVector &X, NOX::Abstract::MultiVector::DenseMatrix &Y) const
 Solves the transpose of the extended system as defined above.
NOX::Abstract::Group::ReturnType computeUV (const NOX::Abstract::MultiVector::DenseMatrix &Y1, const NOX::Abstract::MultiVector &Y2, const NOX::Abstract::MultiVector::DenseMatrix &T, const NOX::Abstract::MultiVector &A, NOX::Abstract::MultiVector &U, NOX::Abstract::MultiVector &V, bool use_jac_transpose)
 Compute $U$ and $V$ multivectors in $P = J+U V^T$.
void updateJacobianForPreconditioner (const NOX::Abstract::MultiVector &U, const NOX::Abstract::MultiVector &V, Epetra_CrsMatrix &jac) const
 Overwrites the Jacobian $J$ with $J + U V^T$ for computing the preconditioner of $P$.
Teuchos::RCP< NOX::Abstract::MultiVector > createBlockMV (const NOX::Abstract::MultiVector &v) const
void setBlockMV (const NOX::Abstract::MultiVector &bv, NOX::Abstract::MultiVector &v) const

Protected Attributes

Teuchos::RCP< LOCA::GlobalData > globalData
 Global data object.
Teuchos::RCP< Teuchos::ParameterList > solverParams
 Solver parameters.
Teuchos::RCP< LOCA::Epetra::Group > grp
 Pointer to group storing J.
Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > op
Teuchos::RCP< const NOX::Abstract::MultiVector > A
 Pointer to A block.
Teuchos::RCP< const NOX::Abstract::MultiVector > B
 Pointer to B block.
Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > C
 Pointer to C block.
Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterfaceMVDX > constraints
 Pointer to constraint interface.
LOCA::BorderedSolver::HouseholderQR qrFact
 QR Factorization object.
Teuchos::RCP< NOX::Abstract::MultiVector > house_x
 Solution component of Householder multivec.
NOX::Abstract::MultiVector::DenseMatrix house_p
 Parameter component of Householder multivec.
NOX::Abstract::MultiVector::DenseMatrix T
 T matrix in compact WY representation.
NOX::Abstract::MultiVector::DenseMatrix R
 R matrix in QR factorization.
Teuchos::RCP< NOX::Abstract::MultiVector > U
 U matrix in low-rank update form P = J + U*V^T.
Teuchos::RCP< NOX::Abstract::MultiVector > V
 V matrix in low-rank update form P = J + U*V^T.
Teuchos::RCP< NOX::Abstract::MultiVector > house_x_trans
 Solution component of Householder multivec for transposed system.
NOX::Abstract::MultiVector::DenseMatrix house_p_trans
 Parameter component of Householder multivec for transposed system.
NOX::Abstract::MultiVector::DenseMatrix T_trans
 T matrix in compact WY representation for transposed system.
NOX::Abstract::MultiVector::DenseMatrix R_trans
 R matrix in QR factorization for transposed system.
Teuchos::RCP< NOX::Abstract::MultiVector > U_trans
 U matrix in low-rank update form P = J + U*V^T for transposed system.
Teuchos::RCP< NOX::Abstract::MultiVector > V_trans
 V matrix in low-rank update form P = J + U*V^T for transposed system.
Teuchos::RCP< const NOX::Abstract::MultiVector > Ablock
 Pointer to A block as an Epetra multivector.
Teuchos::RCP< const NOX::Abstract::MultiVector > Bblock
 Pointer to B block as an Epetra multivector.
Teuchos::RCP< NOX::Abstract::MultiVector > Ascaled
 Pointer to scaled A block.
Teuchos::RCP< NOX::Abstract::MultiVector > Bscaled
 Pointer to scaled B block.
Teuchos::RCP< NOX::Abstract::MultiVector::DenseMatrix > Cscaled
 Pointer to scaled C block.
Teuchos::RCP< NOX::Epetra::LinearSystem > linSys
 Pointer to linear system.
Teuchos::RCP< Epetra_Operator > epetraOp
 Pointer to Epetra operator.
Teuchos::RCP< const Epetra_BlockMap > baseMap
 Pointer to base map for block vectors.
Teuchos::RCP< const Epetra_BlockMap > globalMap
 Pointer to global map for block vectors.
int numConstraints
 Number of constraint equations.
bool isZeroA
 flag indicating whether A block is zero
bool isZeroB
 flag indicating whether B block is zero
bool isZeroC
 flag indicating whether C block is zero
bool isValidForSolve
 Flag indicating whether constraint factorization for solve has been computed.
bool isValidForTransposeSolve
 Flag indicating whether constraint factorization for transpoe solve has been computed.
Teuchos::BLAS< int, double > dblas
 BLAS Wrappers.
bool scale_rows
 Whether we should scale augmented rows to have unit 2-norm.
std::vector< double > scale_vals
 Scale values for each row.
PRECONDITIONER_METHOD precMethod
 Preconditioner method.
bool includeUV
 Flag indicating whether to include U*V^T terms in preconditioner.
bool use_P_For_Prec
 Flag indicating whether to use P = J + U*V^T in preconditioner.
bool isComplex
 Flag indicating whether we are doing a complex solve.
double omega
 Frequency for complex systems.

Detailed Description

Bordered system solver strategy based on Householder transformations.

This class solves the extended system of equations

\‍[ \begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} F \\ G \end{bmatrix} \‍]

using Householder tranformations. The algorithm works as follows: First consider a slightly rearranged version of the extended system of equations:

\‍[ \begin{bmatrix} C & B^T \\ A & J \end{bmatrix} \begin{bmatrix} Y \\ X \end{bmatrix} = \begin{bmatrix} G \\ F \end{bmatrix}. \‍]

Let

\‍[ Q^T \begin{bmatrix} C^T \\ B \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix} \‍]

be the QR decomposition of the constraints matrix where $Q\in\Re^{n+m\times n+m}$ and $R\in\Re^{m\times m}$. Define

\‍[ \begin{bmatrix} Z_Y \\ Z_X \end{bmatrix} = Q^T \begin{bmatrix} Y \\ X \end{bmatrix}, \‍]

then the extended system of equations is equivalent to

\‍[ \begin{bmatrix} R^T & 0 \\ [A & J] Q \end{bmatrix} \begin{bmatrix} Z_Y \\ Z_X \end{bmatrix} = \begin{bmatrix} G \\ F \end{bmatrix} \‍]

and hence

\‍[ \begin{split} Z_Y &= R^{-T} G \\ [A \;\; J] Q \begin{bmatrix} 0 \\ Z_X \end{bmatrix} &= F - [A \;\; J] Q \begin{bmatrix} Z_Y \\ 0 \end{bmatrix}. \end{split} \‍]

This last equation equation can be written

\‍[ P Z_X = \tilde{F} \‍]

where $P\in\Re^{n\times n}$ is given by

\‍[ P Z_X = [A \;\; J] Q \begin{bmatrix} 0 \\ Z_X \end{bmatrix} \‍]

and

\‍[ \tilde{F} = F - [A \;\; J] Q \begin{bmatrix} Z_Y \\ 0 \end{bmatrix}. \‍]

We then recover $X$ and $Y$ by

\‍[ \begin{bmatrix} Y \\ X \end{bmatrix} = Q \begin{bmatrix} Z_Y \\ Z_X \end{bmatrix}. \‍]

It can be further shown that the $P$ operator above can be written

\‍[ P = J + U V^T \‍]

where $U = A*Y_1 + J*Y_2$, $V = Y_2*T^T$ and $Y = [Y_1 ; Y_2]$. The equation $P Z_X = \tilde{F}$ is solved using an iterative solver using the definition of $P Z_X$ above, in this case AztecOO. The system is preconditioned using the preconditioner for $J$. The operator $Q$ is generated using the standard Householder QR algorithm (Algorithm 5.2.1, G. Golub and C. Van Loan, "Matrix Computations," 3rd Edition, Johns Hopkins, Baltimore, 1996) and is stored using the compact WY representation: $Q = I + Y T Y^T$ (see R. Schreiber and C. Van Loan, "A Storage-Efficient WY Representation for Products of Householder Transformations," SIAM J. Sci. Stat. Comput., Vol. 10, No. 1, pp. 53-57, January 1989).

The operator representing $P$ is encapsulated in the class LOCA::Epetra::LowRankUpdateRowMatrix if $J$ is an Epetra_RowMatrix and LOCA::Epetra::LowRankUpdateOp otherwise. If the row matrix version is available $P$ can be scaled and also used to construct a preconditioner. If "Include UV In Preconditioner" is true as discussed below, the $U$ and $V$ terms will be included when computing this preconditioner, which can help stability when $J$ is nearly singular.

The class is intialized via the solverParams parameter list argument to the constructor. The parameters this class recognizes are:

  • "Preconditioner Method" – [string] (default: "Jacobian") - Method for preconditioning the $P$ operator. Choices are:
    • "Jacobian" (default) – Use the preconditioner for $J$
    • "SMW" – Use the Sherman-Morrison-Woodbury formula for the inverse of $P$, replacing the inverse of $J$ with the preconditioner for $J$.
  • "Scale Augmented Rows" – [bool] (default: true) - Scale augmented rows to unit 2-norm before computing QR factorization.
  • "Include UV In Preconditioner" – [bool] (default: false) - Flag indicating whether to use the $U$ and $V$ terms in the preconditioner for $P$ when using the "Jacobian" preconditioner method.
  • "Use P For Preconditioner" – [bool] (default: false) - Flag indicating whether to use the representation of $P$ as a LOCA::Epetra::LowRankUpdateRowMatrix for computing the preconditioner when using the "Jacobian" preconditioner method. This is valid only for preconditioners that accept an Epetra_RowMatrix interface.
  • "Transpose Solver Method" – [string] (default: "Transpose Preconditioner") Method for preconditioning the transpose linear system. See LOCA::Epetra::TransposeLinearSystem::Factory for available choices.

Constructor & Destructor Documentation

◆ EpetraHouseholder()

LOCA::BorderedSolver::EpetraHouseholder::EpetraHouseholder ( const Teuchos::RCP< LOCA::GlobalData > & global_data,
const Teuchos::RCP< LOCA::Parameter::SublistParser > & topParams,
const Teuchos::RCP< Teuchos::ParameterList > & solverParams )

Constructor.

Parameters
global_data[in] Global data object
topParams[in] Parsed top-level parameter list
solverParams[in] Bordered solver parameters as described above

References A, Ablock, Ascaled, B, baseMap, Bblock, Bscaled, C, constraints, Cscaled, dblas, epetraOp, globalData, globalMap, grp, house_p, house_p_trans, house_x, house_x_trans, includeUV, isComplex, isValidForSolve, isValidForTransposeSolve, isZeroA, isZeroB, isZeroC, linSys, numConstraints, omega, precMethod, qrFact, R, R_trans, scale_rows, scale_vals, solverParams, T, T_trans, U, U_trans, use_P_For_Prec, V, and V_trans.

Member Function Documentation

◆ apply()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::apply ( const NOX::Abstract::MultiVector & X,
const NOX::Abstract::MultiVector::DenseMatrix & Y,
NOX::Abstract::MultiVector & U,
NOX::Abstract::MultiVector::DenseMatrix & V ) const
virtual

Computed extended matrix-multivector product.

Computes

\‍[ \begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J & A \\ B^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J*X + A*Y \\ B^T*X + C*Y \end{bmatrix}. \‍]

Implements LOCA::BorderedSolver::AbstractStrategy.

References A, C, constraints, NOX::Abstract::Group::Failed, isZeroA, isZeroB, isZeroC, and NOX::Abstract::MultiVector::update().

◆ applyInverse()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::applyInverse ( Teuchos::ParameterList & params,
const NOX::Abstract::MultiVector * F,
const NOX::Abstract::MultiVector::DenseMatrix * G,
NOX::Abstract::MultiVector & X,
NOX::Abstract::MultiVector::DenseMatrix & Y ) const
virtual

Solves the extended system using the technique described above.

The params argument is the linear solver parameters. If isZeroF or isZeroG is true, than the corresponding F or G pointers may be NULL.

Note that if either the A or B blocks are zero, the system is solved using a simple block elimination scheme instead of the Householder scheme.

Implements LOCA::BorderedSolver::AbstractStrategy.

References A, C, constraints, globalData, NOX::Abstract::MultiVector::init(), isComplex, isZeroA, isZeroB, NOX::Abstract::Group::Ok, scale_rows, scale_vals, solve(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solve(), and LOCA::BorderedSolver::UpperTriangularBlockElimination::solve().

◆ applyInverseTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::applyInverseTranspose ( Teuchos::ParameterList & params,
const NOX::Abstract::MultiVector * F,
const NOX::Abstract::MultiVector::DenseMatrix * G,
NOX::Abstract::MultiVector & X,
NOX::Abstract::MultiVector::DenseMatrix & Y ) const
virtual

Solves the transpose of the extended system as defined above.

The params argument is the linear solver parameters.

Implements LOCA::BorderedSolver::AbstractStrategy.

References A, B, C, globalData, grp, NOX::Abstract::MultiVector::init(), isComplex, isZeroA, isZeroB, NOX::Abstract::Group::Ok, scale_rows, scale_vals, solveTranspose(), LOCA::BorderedSolver::LowerTriangularBlockElimination::solveTranspose(), and LOCA::BorderedSolver::UpperTriangularBlockElimination::solveTranspose().

◆ applyTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::applyTranspose ( const NOX::Abstract::MultiVector & X,
const NOX::Abstract::MultiVector::DenseMatrix & Y,
NOX::Abstract::MultiVector & U,
NOX::Abstract::MultiVector::DenseMatrix & V ) const
virtual

Computed extended matrix transpose-multivector product.

Computes

\‍[ \begin{bmatrix} U \\ V \end{bmatrix} = \begin{bmatrix} J^T & B \\ A^T & C \end{bmatrix} \begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} J^T*X + B*Y \\ A^T*X + C^T*Y \end{bmatrix}. \‍]

Implements LOCA::BorderedSolver::AbstractStrategy.

References A, C, constraints, NOX::Abstract::Group::Failed, isZeroA, isZeroB, isZeroC, and NOX::Abstract::MultiVector::multiply().

◆ computeUV()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::computeUV ( const NOX::Abstract::MultiVector::DenseMatrix & Y1,
const NOX::Abstract::MultiVector & Y2,
const NOX::Abstract::MultiVector::DenseMatrix & T,
const NOX::Abstract::MultiVector & A,
NOX::Abstract::MultiVector & U,
NOX::Abstract::MultiVector & V,
bool use_jac_transpose )
protected

Compute $U$ and $V$ multivectors in $P = J+U V^T$.

References epetraOp, NOX::Abstract::Group::Failed, NOX::Epetra::MultiVector::getEpetraMultiVector(), NOX::Abstract::Group::Ok, and NOX::Abstract::MultiVector::update().

Referenced by initForSolve(), and initForTransposeSolve().

◆ initForSolve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::initForSolve ( )
virtual

Intialize solver for a solve.

This should be called after setMatrixBlocks(), but before applyInverse().

Implements LOCA::BorderedSolver::AbstractStrategy.

References Ablock, Bblock, Bscaled, C, computeUV(), Cscaled, globalData, house_p, house_x, isValidForSolve, isZeroA, isZeroB, numConstraints, NOX::Abstract::Group::Ok, qrFact, R, scale_rows, scale_vals, NOX::ShapeCopy, T, U, and V.

◆ initForTransposeSolve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::initForTransposeSolve ( )
virtual

Intialize solver for a transpose solve.

This should be called after setMatrixBlocks(), but before applyInverseTranspose().

Implements LOCA::BorderedSolver::AbstractStrategy.

References Ablock, Ascaled, Bblock, C, computeUV(), Cscaled, globalData, house_p_trans, house_x_trans, isValidForTransposeSolve, isZeroA, isZeroB, numConstraints, NOX::Abstract::Group::Ok, qrFact, R_trans, scale_rows, scale_vals, NOX::ShapeCopy, T_trans, U_trans, and V_trans.

◆ setMatrixBlocks()

void LOCA::BorderedSolver::EpetraHouseholder::setMatrixBlocks ( const Teuchos::RCP< const LOCA::BorderedSolver::AbstractOperator > & op,
const Teuchos::RCP< const NOX::Abstract::MultiVector > & blockA,
const Teuchos::RCP< const LOCA::MultiContinuation::ConstraintInterface > & blockB,
const Teuchos::RCP< const NOX::Abstract::MultiVector::DenseMatrix > & blockC )
virtual

Set blocks.

The blockA or blockC pointer may be null if either is zero. Whether block B is zero will be determined by querying blockB via ConstraintInterface::isConstraintDerivativesXZero.

Implements LOCA::BorderedSolver::AbstractStrategy.

References A, Ablock, Ascaled, B, baseMap, Bblock, Bscaled, C, constraints, Cscaled, epetraOp, globalData, globalMap, grp, isComplex, isValidForSolve, isValidForTransposeSolve, isZeroA, isZeroB, isZeroC, linSys, numConstraints, and omega.

◆ solve()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::solve ( Teuchos::ParameterList & params,
const NOX::Abstract::MultiVector * F,
const NOX::Abstract::MultiVector::DenseMatrix * G,
NOX::Abstract::MultiVector & X,
NOX::Abstract::MultiVector::DenseMatrix & Y ) const
protectedvirtual

Solves the extended system using the technique described above.

References Ablock, NOX::Abstract::MultiVector::clone(), dblas, epetraOp, NOX::Abstract::Group::Failed, globalData, grp, house_p, house_x, includeUV, NOX::Abstract::MultiVector::init(), isComplex, isValidForSolve, linSys, NOX::Abstract::Group::NotConverged, NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::Group::Ok, omega, precMethod, qrFact, R, NOX::ShapeCopy, T, U, updateJacobianForPreconditioner(), use_P_For_Prec, and V.

Referenced by applyInverse().

◆ solveTranspose()

NOX::Abstract::Group::ReturnType LOCA::BorderedSolver::EpetraHouseholder::solveTranspose ( Teuchos::ParameterList & params,
const NOX::Abstract::MultiVector * F,
const NOX::Abstract::MultiVector::DenseMatrix * G,
NOX::Abstract::MultiVector & X,
NOX::Abstract::MultiVector::DenseMatrix & Y ) const
protectedvirtual

Solves the transpose of the extended system as defined above.

References Bblock, NOX::Abstract::MultiVector::clone(), LOCA::Epetra::TransposeLinearSystem::Factory::create(), dblas, epetraOp, NOX::Abstract::Group::Failed, globalData, grp, house_p_trans, house_x_trans, includeUV, NOX::Abstract::MultiVector::init(), isComplex, isValidForTransposeSolve, linSys, NOX::Abstract::Group::NotConverged, NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::Group::Ok, omega, precMethod, qrFact, R_trans, NOX::ShapeCopy, solverParams, T_trans, U_trans, updateJacobianForPreconditioner(), use_P_For_Prec, and V_trans.

Referenced by applyInverseTranspose().

◆ updateJacobianForPreconditioner()

void LOCA::BorderedSolver::EpetraHouseholder::updateJacobianForPreconditioner ( const NOX::Abstract::MultiVector & U,
const NOX::Abstract::MultiVector & V,
Epetra_CrsMatrix & jac ) const
protected

Overwrites the Jacobian $J$ with $J + U V^T$ for computing the preconditioner of $P$.

References Epetra_CrsMatrix::ColMap(), Epetra_CrsMatrix::ExtractMyRowView(), Epetra_MultiVector::ExtractView(), NOX::Epetra::MultiVector::getEpetraMultiVector(), Epetra_BlockMap::GID(), Epetra_BlockMap::LID(), Epetra_DistObject::Map(), Epetra_BlockMap::MyGID(), numConstraints, Epetra_CrsMatrix::NumMyRows(), and Epetra_CrsMatrix::RowMap().

Referenced by solve(), and solveTranspose().

Member Data Documentation

◆ A

Teuchos::RCP<const NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::A
protected

Pointer to A block.

Referenced by apply(), applyInverse(), applyInverseTranspose(), applyTranspose(), EpetraHouseholder(), and setMatrixBlocks().

◆ Ablock

Teuchos::RCP<const NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::Ablock
protected

Pointer to A block as an Epetra multivector.

Referenced by EpetraHouseholder(), initForSolve(), initForTransposeSolve(), setMatrixBlocks(), and solve().

◆ Ascaled

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::Ascaled
protected

Pointer to scaled A block.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and setMatrixBlocks().

◆ B

Teuchos::RCP<const NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::B
protected

Pointer to B block.

Referenced by applyInverseTranspose(), EpetraHouseholder(), and setMatrixBlocks().

◆ baseMap

Teuchos::RCP<const Epetra_BlockMap> LOCA::BorderedSolver::EpetraHouseholder::baseMap
protected

Pointer to base map for block vectors.

Referenced by EpetraHouseholder(), and setMatrixBlocks().

◆ Bblock

Teuchos::RCP<const NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::Bblock
protected

Pointer to B block as an Epetra multivector.

Referenced by EpetraHouseholder(), initForSolve(), initForTransposeSolve(), setMatrixBlocks(), and solveTranspose().

◆ Bscaled

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::Bscaled
protected

Pointer to scaled B block.

Referenced by EpetraHouseholder(), initForSolve(), and setMatrixBlocks().

◆ C

Teuchos::RCP<const NOX::Abstract::MultiVector::DenseMatrix> LOCA::BorderedSolver::EpetraHouseholder::C
protected

Pointer to C block.

Referenced by apply(), applyInverse(), applyInverseTranspose(), applyTranspose(), EpetraHouseholder(), initForSolve(), initForTransposeSolve(), and setMatrixBlocks().

◆ constraints

Teuchos::RCP<const LOCA::MultiContinuation::ConstraintInterfaceMVDX> LOCA::BorderedSolver::EpetraHouseholder::constraints
protected

Pointer to constraint interface.

Referenced by apply(), applyInverse(), applyTranspose(), EpetraHouseholder(), and setMatrixBlocks().

◆ Cscaled

Teuchos::RCP<NOX::Abstract::MultiVector::DenseMatrix> LOCA::BorderedSolver::EpetraHouseholder::Cscaled
protected

Pointer to scaled C block.

Referenced by EpetraHouseholder(), initForSolve(), initForTransposeSolve(), and setMatrixBlocks().

◆ dblas

Teuchos::BLAS<int,double> LOCA::BorderedSolver::EpetraHouseholder::dblas
protected

BLAS Wrappers.

Referenced by EpetraHouseholder(), solve(), and solveTranspose().

◆ epetraOp

Teuchos::RCP<Epetra_Operator> LOCA::BorderedSolver::EpetraHouseholder::epetraOp
protected

Pointer to Epetra operator.

Referenced by computeUV(), EpetraHouseholder(), setMatrixBlocks(), solve(), and solveTranspose().

◆ globalData

Teuchos::RCP<LOCA::GlobalData> LOCA::BorderedSolver::EpetraHouseholder::globalData
protected

Global data object.

Referenced by applyInverse(), applyInverseTranspose(), EpetraHouseholder(), initForSolve(), initForTransposeSolve(), setMatrixBlocks(), solve(), and solveTranspose().

◆ globalMap

Teuchos::RCP<const Epetra_BlockMap> LOCA::BorderedSolver::EpetraHouseholder::globalMap
protected

Pointer to global map for block vectors.

Referenced by EpetraHouseholder(), and setMatrixBlocks().

◆ grp

Teuchos::RCP<LOCA::Epetra::Group> LOCA::BorderedSolver::EpetraHouseholder::grp
protected

Pointer to group storing J.

Referenced by applyInverseTranspose(), EpetraHouseholder(), setMatrixBlocks(), solve(), and solveTranspose().

◆ house_p

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::house_p
protected

Parameter component of Householder multivec.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ house_p_trans

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::house_p_trans
protected

Parameter component of Householder multivec for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

◆ house_x

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::house_x
protected

Solution component of Householder multivec.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ house_x_trans

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::house_x_trans
protected

Solution component of Householder multivec for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

◆ includeUV

bool LOCA::BorderedSolver::EpetraHouseholder::includeUV
protected

Flag indicating whether to include U*V^T terms in preconditioner.

Referenced by EpetraHouseholder(), solve(), and solveTranspose().

◆ isComplex

bool LOCA::BorderedSolver::EpetraHouseholder::isComplex
protected

Flag indicating whether we are doing a complex solve.

Referenced by applyInverse(), applyInverseTranspose(), EpetraHouseholder(), setMatrixBlocks(), solve(), and solveTranspose().

◆ isValidForSolve

bool LOCA::BorderedSolver::EpetraHouseholder::isValidForSolve
protected

Flag indicating whether constraint factorization for solve has been computed.

Referenced by EpetraHouseholder(), initForSolve(), setMatrixBlocks(), and solve().

◆ isValidForTransposeSolve

bool LOCA::BorderedSolver::EpetraHouseholder::isValidForTransposeSolve
protected

Flag indicating whether constraint factorization for transpoe solve has been computed.

Referenced by EpetraHouseholder(), initForTransposeSolve(), setMatrixBlocks(), and solveTranspose().

◆ isZeroA

bool LOCA::BorderedSolver::EpetraHouseholder::isZeroA
protected

flag indicating whether A block is zero

Referenced by apply(), applyInverse(), applyInverseTranspose(), applyTranspose(), EpetraHouseholder(), initForSolve(), initForTransposeSolve(), and setMatrixBlocks().

◆ isZeroB

bool LOCA::BorderedSolver::EpetraHouseholder::isZeroB
protected

flag indicating whether B block is zero

Referenced by apply(), applyInverse(), applyInverseTranspose(), applyTranspose(), EpetraHouseholder(), initForSolve(), initForTransposeSolve(), and setMatrixBlocks().

◆ isZeroC

bool LOCA::BorderedSolver::EpetraHouseholder::isZeroC
protected

flag indicating whether C block is zero

Referenced by apply(), applyTranspose(), EpetraHouseholder(), and setMatrixBlocks().

◆ linSys

Teuchos::RCP<NOX::Epetra::LinearSystem> LOCA::BorderedSolver::EpetraHouseholder::linSys
protected

Pointer to linear system.

Referenced by EpetraHouseholder(), setMatrixBlocks(), solve(), and solveTranspose().

◆ numConstraints

int LOCA::BorderedSolver::EpetraHouseholder::numConstraints
protected

Number of constraint equations.

Referenced by EpetraHouseholder(), initForSolve(), initForTransposeSolve(), setMatrixBlocks(), and updateJacobianForPreconditioner().

◆ omega

double LOCA::BorderedSolver::EpetraHouseholder::omega
protected

Frequency for complex systems.

Referenced by EpetraHouseholder(), setMatrixBlocks(), solve(), and solveTranspose().

◆ precMethod

PRECONDITIONER_METHOD LOCA::BorderedSolver::EpetraHouseholder::precMethod
protected

Preconditioner method.

Referenced by EpetraHouseholder(), solve(), and solveTranspose().

◆ qrFact

LOCA::BorderedSolver::HouseholderQR LOCA::BorderedSolver::EpetraHouseholder::qrFact
protected

QR Factorization object.

Referenced by EpetraHouseholder(), initForSolve(), initForTransposeSolve(), solve(), and solveTranspose().

◆ R

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::R
protected

R matrix in QR factorization.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ R_trans

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::R_trans
protected

R matrix in QR factorization for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

◆ scale_rows

bool LOCA::BorderedSolver::EpetraHouseholder::scale_rows
protected

Whether we should scale augmented rows to have unit 2-norm.

Referenced by applyInverse(), applyInverseTranspose(), EpetraHouseholder(), initForSolve(), and initForTransposeSolve().

◆ scale_vals

std::vector<double> LOCA::BorderedSolver::EpetraHouseholder::scale_vals
protected

Scale values for each row.

Referenced by applyInverse(), applyInverseTranspose(), EpetraHouseholder(), initForSolve(), and initForTransposeSolve().

◆ solverParams

Teuchos::RCP<Teuchos::ParameterList> LOCA::BorderedSolver::EpetraHouseholder::solverParams
protected

Solver parameters.

Referenced by EpetraHouseholder(), and solveTranspose().

◆ T

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::T
protected

T matrix in compact WY representation.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ T_trans

NOX::Abstract::MultiVector::DenseMatrix LOCA::BorderedSolver::EpetraHouseholder::T_trans
protected

T matrix in compact WY representation for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

◆ U

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::U
protected

U matrix in low-rank update form P = J + U*V^T.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ U_trans

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::U_trans
protected

U matrix in low-rank update form P = J + U*V^T for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

◆ use_P_For_Prec

bool LOCA::BorderedSolver::EpetraHouseholder::use_P_For_Prec
protected

Flag indicating whether to use P = J + U*V^T in preconditioner.

Referenced by EpetraHouseholder(), solve(), and solveTranspose().

◆ V

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::V
protected

V matrix in low-rank update form P = J + U*V^T.

Referenced by EpetraHouseholder(), initForSolve(), and solve().

◆ V_trans

Teuchos::RCP<NOX::Abstract::MultiVector> LOCA::BorderedSolver::EpetraHouseholder::V_trans
protected

V matrix in low-rank update form P = J + U*V^T for transposed system.

Referenced by EpetraHouseholder(), initForTransposeSolve(), and solveTranspose().

The documentation for this class was generated from the following files:
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