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#ifndef LOCA_HOPF_MOORESPENCE_EXTENDEDGROUP_H
#define LOCA_HOPF_MOORESPENCE_EXTENDEDGROUP_H

#include "Teuchos_RCP.hpp"

#include "LOCA_MultiContinuation_AbstractGroup.H"         // base class
#include "LOCA_Extended_MultiAbstractGroup.H"             // base class
#include "LOCA_Hopf_MooreSpence_ExtendedVector.H" // class data element
#include "LOCA_Hopf_MooreSpence_ExtendedMultiVector.H" // class data element

namespace LOCA {
  class ParameterVector;
  class GlobalData;
  namespace Parameter {
    class SublistParser;
  }

  namespace Hopf {
    namespace MooreSpence {
      class AbstractGroup;
      class SolverStrategy;
    }
  }
}
namespace LOCA {

  namespace Hopf {

    namespace MooreSpence {

      /*!
       * \brief A group representing the Moore-Spence Hopf equations.
       */
      /*!
       * The LOCA::Hopf::MooreSpence::ExtendedGroup is a concrete
       * implementation of the NOX::Abstract::Group,
       * LOCA::MultiContinuation::AbstractGroup and
       * LOCA::Extended::MultiAbstractGroup that defines the following
       * extended set of equations that are regular at a generic Hopf point:
       * \f[
       *     G(z) = \left[
       *     \begin{array}{c}
       *         F(x,p) \\
       *         Jy-\omega Bz \\
       *         Jz+\omega By \\
       *         l^Ty-1 \\
       *         l^Tz
       *      \end{array}
       *      \right] = 0
       * \f]
       * where \f$ z = [x, y, z, \omega, p]\in\Re^{3n+2}\f$, \f$ x\f$ is the
       * solution vector, \f$ y+i\omega z\f$ is the complex eigenvector of
       * \f$ J\f$ with corresponding eigenvalues \f$\pm i\omega\f$, \f$ l\f$
       * is the length normalization vector and \f$ J\f$ is the Jacobian of F
       * w.r.t \f$ x\f$.
       *
       * The group stores an underlying group of type
       * LOCA::Hopf::MooreSpence AbstractGroup to represent the equations
       * \f$ F(x,p) = 0\f$ and to manipulate the underlying Jacobian \f$ J\f$.
       * Note that the entire extended Jacobian \f$ D_z G\f$ is not stored in
       * memory, rather a block-elimination algorithm (bordering algorithm) is
       * used to compute linear solves of the extended Jacobian (see
       * LOCA::Hopf::MooreSpence::SolverFactory() for more details).
       *
       * This class implements all of the NOX::Abstract::Group,
       * LOCA::MultiContinuation::AbstractGroup, and
       * LOCA::Extended::MultiAbstractGroup
       * methods for this extended set of equations and therefore is a complete
       * group which can be passed to most %NOX solvers to locate a single
       * Hopf point or to the LOCA::Stepper to compute a family of Hopf
       * points in a second parameter.
       *
       * However, Jacobian-tranpose operations and gradient calculations
       * cannot be implemented efficiently and therefore gradient-base
       * nonlinear solvers such as steepest descent and Trust region methods
       * cannot be used to solve the extended Hopf point equations.
       *
       * The class is intialized via the \c hopfParams parameter list argument
       * to the constructor.  The parameters this class recognizes are:
       * <ul>
       * <li> "Bifurcation Parameter" -- [string] (Must be supplied) Name of
       *      the bifurcation parameter \f$ p\f$
       * <li> "Length Normalization Vector" --
       *      [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied)
       *     Vector storing length normalization vector \f$ l\f$
       * <li> "Initial Real Eigenvector"  --
       *      [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied)
       *     Vector storing initial guess for the real component of the
       *     eigenvector \f$ y\f$
       * <li> "Initial Imaginary Eigenvector"  --
       *      [Teuchos::RCP<NOX::Abstract::Vector>] (Must be supplied)
       *     Vector storing initial guess for the imaginary component of the
       *     eigenvector \f$ z\f$
       * <li> "Initial Frequency" -- [double] (Must be supplied)
       *      Initial guess for the Hopf frequency \f$\omega\f$.
       * <li> "Perturb Initial Solution" -- [bool] (default: false) Flag
       *      indicating whether to perturb the initial solution
       * <li> "Relative Perturbation Size" -- [double] (default: 1.0e-3)
       *      Relative perturbation size if perturbing the initial solution
       * </ul>
       */
      class ExtendedGroup
    : public virtual LOCA::Extended::MultiAbstractGroup,
      public virtual LOCA::MultiContinuation::AbstractGroup {

      public:

    /*!
     * \brief Constructor with initial data passed through parameter lists.
     */
    ExtendedGroup(
     const Teuchos::RCP<LOCA::GlobalData>& global_data,
         const Teuchos::RCP<LOCA::Parameter::SublistParser>& topParams,
     const Teuchos::RCP<Teuchos::ParameterList>& hopfParams,
     const Teuchos::RCP<LOCA::Hopf::MooreSpence::AbstractGroup>& g);

    //! Copy constructor.
    ExtendedGroup(const ExtendedGroup& source,
              NOX::CopyType type = NOX::DeepCopy);

    //! Destructor.
    virtual ~ExtendedGroup();

    /*!
     * @name Implementation of NOX::Abstract::Group virtual methods
     */
    //@{

    //! Assignment operator
    virtual NOX::Abstract::Group&
    operator=(const NOX::Abstract::Group& source);

    //! Cloning function
    virtual Teuchos::RCP<NOX::Abstract::Group>
    clone(NOX::CopyType type = NOX::DeepCopy) const;

    //! Set the solution vector, x, to y.
    virtual void setX(const NOX::Abstract::Vector& y);

    //! Compute this.x = grp.x + step * d.
    virtual void computeX(const NOX::Abstract::Group& g,
                  const NOX::Abstract::Vector& d,
                  double step);

    //! Compute the Hopf point equation residual \f$ G\f$.
    virtual NOX::Abstract::Group::ReturnType computeF();

    //! Compute the blocks of the Jacobian derivative of \f$ G\f$
    virtual NOX::Abstract::Group::ReturnType computeJacobian();

    //! Gradient computation is not defined for this group
    virtual NOX::Abstract::Group::ReturnType computeGradient();

    //! Compute %Newton direction using applyJacobianInverse().
    virtual NOX::Abstract::Group::ReturnType
    computeNewton(Teuchos::ParameterList& params);

    //! Computes the extended Jacobian vector product
    virtual NOX::Abstract::Group::ReturnType
    applyJacobian(const NOX::Abstract::Vector& input,
              NOX::Abstract::Vector& result) const;

    //! Jacobian transpose product is not defined by this group
    virtual NOX::Abstract::Group::ReturnType
    applyJacobianTranspose(const NOX::Abstract::Vector& input,
                   NOX::Abstract::Vector& result) const;

    /*!
     * \brief Applies the inverse of the extended Jacobian matrix using
     * the bordering algorithm.
     */
    /*!
     * This method is a special case of applyJacobianInverseMultiVector()
     * for a single right-hand-side.
     */
    virtual NOX::Abstract::Group::ReturnType
    applyJacobianInverse(Teuchos::ParameterList& params,
                 const NOX::Abstract::Vector& input,
                 NOX::Abstract::Vector& result) const;

    //! Applies Jacobian for extended system
    virtual NOX::Abstract::Group::ReturnType
    applyJacobianMultiVector(const NOX::Abstract::MultiVector& input,
                 NOX::Abstract::MultiVector& result) const;

    //! Jacobian transpose not defined for this system
    virtual NOX::Abstract::Group::ReturnType
    applyJacobianTransposeMultiVector(
                     const NOX::Abstract::MultiVector& input,
                     NOX::Abstract::MultiVector& result) const;

    //! Applies Jacobian inverse for extended system
    /*!
     * Uses a LOCA::Hopf::MooreSpence::SolverStrategy instantiated
     * by the LOCA::Hopf::MooreSpence::SolverFactory to
     * implement the solve.
     */
    virtual NOX::Abstract::Group::ReturnType
    applyJacobianInverseMultiVector(
                    Teuchos::ParameterList& params,
                    const NOX::Abstract::MultiVector& input,
                    NOX::Abstract::MultiVector& result) const;

    //! Return \c true if the extended residual \f$ G\f$ is valid.
    virtual bool isF() const;

    //! Return \c true if the extended Jacobian is valid.
    virtual bool isJacobian() const;

    //! Always returns false.
    virtual bool isGradient() const;

    //! Return \c true if the extended Newton direction is valid.
    virtual bool isNewton() const;

    //! Return extended solution vector \f$ z\f$.
    virtual const NOX::Abstract::Vector& getX() const;

    //! Return extended equation residual \f$ G(z)\f$
    virtual const NOX::Abstract::Vector& getF() const;

    //! Return 2-norm of \f$ G(z)\f$.
    virtual double getNormF() const;

    //! Vector returned is not valid.
    virtual const NOX::Abstract::Vector& getGradient() const;

    //! Return extended Newton direction.
    virtual const NOX::Abstract::Vector& getNewton() const;

    //! Return RCP to extended solution vector \f$ z\f$.
    virtual Teuchos::RCP< const NOX::Abstract::Vector > getXPtr() const;

    //! Return RCP to extended equation residual \f$ G(z)\f$
    virtual Teuchos::RCP< const NOX::Abstract::Vector > getFPtr() const;

    //! Vector returned is not valid.
    virtual Teuchos::RCP< const NOX::Abstract::Vector > getGradientPtr() const;

    //! Return RCP to extended Newton direction.
    virtual Teuchos::RCP< const NOX::Abstract::Vector > getNewtonPtr() const;

    //! Return the norm of the %Newton solve residual.
    virtual double getNormNewtonSolveResidual() const;

    //@}

    /*!
     * @name Implementation of LOCA::Extended::MultiAbstractGroup
     * virtual methods
     */
    //@{

    //! Return underlying group
    virtual
    Teuchos::RCP<const LOCA::MultiContinuation::AbstractGroup>
    getUnderlyingGroup() const;

    //! Return underlying group
    virtual
    Teuchos::RCP<LOCA::MultiContinuation::AbstractGroup>
    getUnderlyingGroup();

    //@}

    /*!
     * @name Implementation of LOCA::MultiContinuation::AbstractGroup
     * virtual methods
     */
    //@{

    //! Assignment operator
    virtual void copy(const NOX::Abstract::Group& source);

    //! Set parameters indexed by (integer) paramIDs
    virtual void setParamsMulti(
              const std::vector<int>& paramIDs,
              const NOX::Abstract::MultiVector::DenseMatrix& vals);

    //! Set the parameter vector in the group to p.
    virtual void setParams(const ParameterVector& p);

    //! Set parameter indexed by paramID
    virtual void setParam(int paramID, double val);

    //! Set parameter indexed by paramID
    virtual void setParam(std::string paramID, double val);

    //! Return a const reference to the paramter vector owned by the group.
    virtual const ParameterVector& getParams() const;

    //! Return copy of parameter indexed by paramID
    virtual double getParam(int paramID) const;

    //! Return copy of parameter indexed by paramID
    virtual double getParam(std::string paramID) const;

    /*!
     * Compute \f$\partial F/\partial p\f$ for each parameter \f$ p\f$
     * indexed by paramIDs.  The first column of \em dfdp holds F,
     * which is valid if \em isValidF is true.  Otherwise F must be
     * computed.
     */
    virtual NOX::Abstract::Group::ReturnType
    computeDfDpMulti(const std::vector<int>& paramIDs,
             NOX::Abstract::MultiVector& dfdp,
             bool isValidF);

    //! Perform any preprocessing before a continuation step starts.
    /*!
     * The \c stepStatus argument indicates whether the previous step was
     * successful.
     */
    virtual void
    preProcessContinuationStep(
             LOCA::Abstract::Iterator::StepStatus stepStatus);

    //! Perform any postprocessing after a continuation step finishes.
    /*!
     * The \c stepStatus argument indicates whether the step was
     * successful.
     */
    virtual void
    postProcessContinuationStep(
             LOCA::Abstract::Iterator::StepStatus stepStatus);

    //! Projects solution to a few scalars for multiparameter continuation
    virtual void projectToDraw(const NOX::Abstract::Vector& x,
                   double *px) const;

    //! Returns the dimension of the project to draw array
    virtual int projectToDrawDimension() const;

    /*!
     * \brief Function to print out extended solution and continuation
     * parameter after successful continuation step.
     */
    /*!
     * This method prints the solution, null-vector, and parameter
     * components of the extended solution vector using the printSolution
     * method of the underlying group.
     */
    virtual void printSolution(const double conParam) const;

    /*!
     * \brief Function to print out extended solution and continuation
     * parameter after successful continuation step.
     */
    /*!
     * This method prints the solution, null-vector, and parameter
     * components of the extended solution vector using the printSolution
     * method of the underlying group.
     */
     virtual void printSolution(const NOX::Abstract::Vector& x_,
                    const double conParam) const;

    //! Get bifurcation parameter
    double getBifParam() const;

    //! Get bifurcation frequency
    double getFrequency() const;

    //! Defines null vector normalization \f$ l^Tz\f$ equation
    double lTransNorm(const NOX::Abstract::Vector& z) const;

    //! null vector normalization for multivectors
    /*!
     * Note:  result should have 1 row and z.numVectors() columns.
     */
    void lTransNorm(const NOX::Abstract::MultiVector& z,
            NOX::Abstract::MultiVector::DenseMatrix& result) const;

      protected:

    //! Set bifurcation parameter
    void setBifParam(double param);

    //! Sets up multivector views
    void setupViews();

    //! Initializes group
    void init(bool perturbSoln = false, double perturbSize = 0.0);

      private:

    //! Prohibit generation and use of operator=()
    ExtendedGroup& operator=(const ExtendedGroup&);

      protected:

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

    //! Parsed top-level parameters
    Teuchos::RCP<LOCA::Parameter::SublistParser> parsedParams;

    //! Bifurcation parameter list
    Teuchos::RCP<Teuchos::ParameterList> hopfParams;

    //! Pointer to base group that defines \f$ F\f$
    Teuchos::RCP<LOCA::Hopf::MooreSpence::AbstractGroup> grpPtr;

    //! Stores the extended solution vector
    LOCA::Hopf::MooreSpence::ExtendedMultiVector xMultiVec;

    //! Stores the extended residual vector and df/dp
    LOCA::Hopf::MooreSpence::ExtendedMultiVector fMultiVec;

    //! Stores the extended Newton vector
    LOCA::Hopf::MooreSpence::ExtendedMultiVector newtonMultiVec;

    //! Stores the length normalization vector
    Teuchos::RCP<NOX::Abstract::MultiVector> lengthMultiVec;

    //! Stores view of first column of xMultiVec
    Teuchos::RCP<LOCA::Hopf::MooreSpence::ExtendedVector> xVec;

    //! Stores view of first column of fMultiVec
    Teuchos::RCP<LOCA::Hopf::MooreSpence::ExtendedVector> fVec;

    //! Stores view of first column of fMultiVec as a multivec
    Teuchos::RCP<LOCA::Hopf::MooreSpence::ExtendedMultiVector> ffMultiVec;

    //! Stores view of df/dp columns of fMultiVec
    Teuchos::RCP<LOCA::Hopf::MooreSpence::ExtendedMultiVector> dfdpMultiVec;

    //! Stores view of first column of newtonMultiVec
    Teuchos::RCP<LOCA::Hopf::MooreSpence::ExtendedVector> newtonVec;

    //! Stores view of first column of lengthMultiVec
    Teuchos::RCP<NOX::Abstract::Vector> lengthVec;

    //! Stores mass matrix times real component of eigenvector
    Teuchos::RCP<NOX::Abstract::MultiVector> massTimesY;

    /*!
     * \brief Stores negative of mass matrix times imaginary component of
     eigenvector
    */
    Teuchos::RCP<NOX::Abstract::MultiVector> minusMassTimesZ;

    //! Stores bordering strategy
    Teuchos::RCP<LOCA::Hopf::MooreSpence::SolverStrategy> solverStrategy;

    //! Stores indices for getting f part of fMultiVec
    std::vector<int> index_f;

    //! Stores indices for getting df/dp part of fMultiVec
    std::vector<int> index_dfdp;

    //! Stores the bifurcation parameter index
    std::vector<int> bifParamID;

    //! Is residual vector valid
    bool isValidF;

    //! Is Jacobian matrix valid
    bool isValidJacobian;

    //! Is Newton vector valid
    bool isValidNewton;

      }; // class ExtendedGroup

    } // namespace MooreSpence

  } // namespace Hopf

} // namespace LOCA

#endif
