/usr/include/trilinos/LOCA_Epetra

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#ifndef LOCA_EPETRA_AUGMENTEDOP_H
#define LOCA_EPETRA_AUGMENTEDOP_H

#include "Teuchos_RCP.hpp"

#include "Epetra_Operator.h"           // base class
#include "Epetra_LocalMap.h"           // class data element
#include "Epetra_MultiVector.h"        // class data element

#include "NOX_Common.H"                // for std::string data member
#include "NOX_Abstract_MultiVector.H"  // for DenseMatrix

#include "Teuchos_LAPACK.hpp" // class data element

// Forward declarations
namespace LOCA {
  class GlobalData;
}

namespace LOCA {

  namespace Epetra {

    /*!
     * \brief %Epetra operator representing a \f$n+m\f$ bordered matrix.
     */
    /*!
     * The %LOCA::Epetra::AugmentedOp is an Epetra_Operator representing the
     * \f$n+m\f$ bordered matrix
     * \f[
     *     \begin{bmatrix}
     *        J & A \\
     *        B^T & C
     *     \end{bmatrix}
     * \f]
     * where \f$J\f$ is an Epetra_Operator representing an \f$n\times n\f$
     * matrix, and \f$A\f$ and \f$B\f$ are length \f$n\f$ Epetra_MultiVector's
     * with \f$m\f$ columns, and \f$C\f$ is an \f$m\times m\f$ dense matrix.
     * It is assumed the Epetra_Map's for \f$A\f$, \f$B\f$, and
     * \f$J\f$ are the same and the corresponding map for the bordered
     * matrix is constructed from this map by storing the additional components
     * on processor 0.  The buildEpetraAugmentedMultiVec() method can be used
     * to construct an Epetra_MultiVector using this map, a supplied
     * length \f$n\f$ Epetra_MultiVector and an \f$m\times m\f$ matrix, while
     * setEpetraAugmentedMultiVec() splits an extended multivector into its
     * length \f$n\f$ and \f$m\f$ components.  The
     * Apply() method performs the \f$n+m\times n+m\f$ matrix multiplication
     * while ApplyInverse() uses a block-elimination algorithm to compute
     * the inverse using the ApplyInverse() method of the underlying operator
     * \f$J\f$.  In this way, linear systems of the form
     * \f[
     *     \begin{bmatrix}
     *        J & A \\
     *        B^T & C
     *     \end{bmatrix}
     *     \begin{bmatrix}
     *       X \\
     *       Y
     *     \end{bmatrix} =
     *     \begin{bmatrix}
     *       F \\
     *       G
     *     \end{bmatrix}
     * \f]
     * can be solved in a matrix-free mode using the Apply() method.  This
     * operator can also represent a preconditioner of the form
     * \f[
     *     \begin{bmatrix}
     *        M & A \\
     *        B^T & C
     *     \end{bmatrix}
     * \f]
     * using the ApplyInvese() method, where \f$M\f$ is a preconditioner
     * for \f$J\f$.  Note that if \f$J\f$ is nearly singular, the
     * preconditioner should not be too good because otherwise the
     * preconditining operation represented by ApplyInverse() becomes unstable.
     */
    class AugmentedOp : public Epetra_Operator {

    public:

      //! Constructor
      /*!
       * Builds the bordered operator using the supplied operator \em jac
       * and Epetra_Vector's \em a and \em b.  It is assumed \em a, \em b,
       * and \em jac all have the same map.
       */
      AugmentedOp(const Teuchos::RCP<LOCA::GlobalData>& global_data,
          const Teuchos::RCP<Epetra_Operator>& jac,
          const Teuchos::RCP<const Epetra_MultiVector>& a,
          const Teuchos::RCP<const Epetra_MultiVector>& b,
                  const Teuchos::RCP<const NOX::Abstract::MultiVector::DenseMatrix> c);

      //! Destructor
      virtual ~AugmentedOp();

      //! If set true, transpose of this operator will be applied.
      /*!
       * Note that is only valid if the underlying operator \f$J\f$
       * supports a transpose.
       */
      virtual int SetUseTranspose(bool UseTranspose);

      /*!
       * \brief Returns the result of a Epetra_Operator applied to a
       * Epetra_MultiVector Input in Result.
       */
      /*!
       * Computes the extended matrix-vector product
       * \f[
       *     \begin{bmatrix}
       *        J & A \\
       *        B^T & C
       *     \end{bmatrix}
       *     \begin{bmatrix}
       *       X \\
       *       Y
       *     \end{bmatrix} =
       *     \begin{bmatrix}
       *       JX + AY \\
       *       B^T X + CY
       *     \end{bmatrix}
       * \f]
       * or its transpose if UseTranpose() is \em true.
       */
      virtual int Apply(const Epetra_MultiVector& Input,
            Epetra_MultiVector& Result) const;

      /*!
       * \brief Returns the result of a Epetra_Operator inverse applied to
       * an Epetra_MultiVector Input in Result.
       */
      /*!
       * Solves the extended system
       * \f[
       *     \begin{bmatrix}
       *        J & A \\
       *        B^T & C
       *     \end{bmatrix}
       *     \begin{bmatrix}
       *       X \\
       *       Y
       *     \end{bmatrix} =
       *     \begin{bmatrix}
       *       F \\
       *       G
       *     \end{bmatrix}
       * \f]
       * using the following block-elimination algorithm:
       * \f[
       *  \begin{split}
       *    X_1 &= J^{-1} F, \\
       *    X_2 &= J^{-1} A, \\
       *    Y &= (C-B^T X_2)^{-1}(G-B^T X_1), \\
       *    X &= X_1 - X_2 Y
       *  \end{split}
       * \f]
       * If UseTranpose() is \em true, the tranpose of the system is solved.
       */
      virtual int ApplyInverse(const Epetra_MultiVector& X,
                   Epetra_MultiVector& Y) const;

      //! Returns the infinity norm of the bordered matrix.
      /*!
       * This is defined only if %NormInf() of the underlying operator \f$J\f$
       * is defined and is given by
       * \f$\|J\|_\infty+\|A\|_\infty+\|B\|_\infty\f$.
       */
      virtual double NormInf() const;

      //! Returns a character std::string describing the operator
      virtual const char* Label () const;

      //! Returns the current UseTranspose setting.
      virtual bool UseTranspose() const;

      /*!
       * \brief Returns true if the \e this object can provide an
       * approximate Inf-norm, false otherwise.
       */
      virtual bool HasNormInf() const;

      /*!
       * \brief Returns a reference to the Epetra_Comm communicator
       * associated with this operator.
       */
      virtual const Epetra_Comm & Comm() const;

      /*!
       * \brief Returns the Epetra_Map object associated with the
       * domain of this matrix operator.
       */
      virtual const Epetra_Map& OperatorDomainMap () const;

      /*!
       * \brief Returns the Epetra_Map object associated with the
       * range of this matrix operator.
       */
      virtual const Epetra_Map& OperatorRangeMap () const;

      //! Initialiazes operator for a solve
      virtual void init(const Epetra_MultiVector& x);

      /*!
       * \brief Builds an extended  vector from components
       */
      /*!
       * Builds an extended vector using the map representing the bordered
       * matrix.  If \em doCopy is \em true, the contents of \em x are
       * copied into the extended vector, otherwise only space for the
       * extended vector is created.
       */
      virtual Teuchos::RCP<Epetra_MultiVector>
      buildEpetraAugmentedMultiVec(
                 const Epetra_MultiVector& x,
                 const NOX::Abstract::MultiVector::DenseMatrix *y,
                 bool doCopy) const;

      /*!
       * \brief Sets components from extended vector
       */
      /*!
       * Splits the extended vector \em augMultiVec into components \em x and
       * \em y by copying values out of \em extVec.
       */
      virtual void
      setEpetraAugmentedMultiVec(Epetra_MultiVector& x,
                 NOX::Abstract::MultiVector::DenseMatrix& y,
                 const Epetra_MultiVector& augMultiVec) const;

    protected:

      //! Builds extended domain, range maps
      void buildExtendedMap(const Epetra_BlockMap& map,
                Epetra_Map*& extMapPtr, bool buildImporter,
                bool haveParam);

      //! Converts a block map to an equivalent point map
      int blockMap2PointMap(const Epetra_BlockMap& BlockMap,
                Epetra_Map*& PointMap) const;

    private:

      //! Private to prohibit copying
      AugmentedOp(const AugmentedOp&);

      //! Private to prohibit copying
      AugmentedOp& operator=(const AugmentedOp&);

    protected:

      //! LOCA global data object
      Teuchos::RCP<LOCA::GlobalData> globalData;

      //! Label for operator
      std::string label;

      //! Stores operator representing \f$J\f$
      Teuchos::RCP<Epetra_Operator> jacOperator;

       //! Stores underlying domain map
      const Epetra_BlockMap& underlyingMap;

      //! Stores comm
      const Epetra_Comm& underlyingComm;

      //! Local map for generating Epetra matrices
      Epetra_LocalMap localMap;

      //! Stores pointer to a multivector
      Teuchos::RCP<const Epetra_MultiVector> a;

      //! Stores pointer to b multivector
      Teuchos::RCP<const Epetra_MultiVector> b;

      //! Stores c matrix
      Epetra_MultiVector c;

      //! Stores underlying vector local length
      int underlyingLength;

      //! Number of constraints
      int numConstraints;

      //! Stores extended domain map
      Epetra_Map* extendedMapPtr;

      //! Stores extended turning point map for importing param component
      Epetra_Map* extendedImportMapPtr;

      //! Stores importer object for importing param component
      Epetra_Import* extendedImporter;

      //! Stores imported input multivector
      Epetra_MultiVector* importedInput;

      //! Stores parameter component of result multivector
      Epetra_MultiVector* result_y;

      //! Stores temporary multivector used in ApplyInverse()
      Epetra_MultiVector* tmp;

      //! Flag indicating whether we have the parameter component
      bool haveParamComponent;

      //! Flag indicating whether to use transpose of operator
      bool useTranspose;

      //! LAPACK Wrappers
      Teuchos::LAPACK<int,double> dlapack;

    };
  } // namespace Epetra
} // namespace LOCA

#endif
libtrilinos-nox-dev 12.4.2-2 / usr / include / trilinos / LOCA_Epetra_AugmentedOp.H
