// $Id$ 
// $Source$ 
// @HEADER
// ***********************************************************************
// 
//                           Sacado Package
//                 Copyright (2006) Sandia Corporation
// 
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
// 
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//  
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//  
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
// USA
// Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
// (etphipp@sandia.gov).
// 
// ***********************************************************************
//
// The forward-mode AD classes in Sacado are a derivative work of the
// expression template classes in the Fad package by Nicolas Di Cesare.  
// The following banner is included in the original Fad source code:
//
// ************ DO NOT REMOVE THIS BANNER ****************
//
//  Nicolas Di Cesare <Nicolas.Dicesare@ann.jussieu.fr>
//  http://www.ann.jussieu.fr/~dicesare
//
//            CEMRACS 98 : C++ courses, 
//         templates : new C++ techniques 
//            for scientific computing 
// 
//********************************************************
//
//  A short implementation ( not all operators and 
//  functions are overloaded ) of 1st order Automatic
//  Differentiation in forward mode (FAD) using
//  EXPRESSION TEMPLATES.
//
//********************************************************
// @HEADER

#ifndef SACADO_ELRFAD_SFAD_HPP
#define SACADO_ELRFAD_SFAD_HPP

#include "Sacado_ELRFad_SFadTraits.hpp"
#include "Sacado_ELRFad_Expression.hpp"
#include "Sacado_StaticArrayTraits.hpp"
#include "Sacado_dummy_arg.hpp"

namespace Sacado {

  namespace ELRFad {

    //! A tag for specializing Expr for SFad expressions
    template <typename T, int Num> 
    struct SFadExprTag {};

    /*!
     * \brief Expression template forward-mode AD class with static memory
     * allocation.
     */
    /*!
     * This classes specializes Expr to SFad expressions.
     */
    template <typename T, int Num> 
    class Expr< SFadExprTag<T,Num> > {

    public:

      //! Typename of values
      typedef T value_type;

      //! Typename of base-expressions
      typedef Expr< SFadExprTag<T,Num> > base_expr_type;

      //! Number of arguments
      static const int num_args = 1;

      //! Is expression linear
      static const bool is_linear = true;

      /*!
       * @name Initialization methods
       */
      //@{

      //! Default constructor
      Expr() : val_( T(0.)), update_val_(true) { ss_array<T>::zero(dx_, Num); }

      //! Constructor with supplied value \c x
      /*!
       * Initializes value to \c x and derivative array is empty
       */
      Expr(const T & x) : val_(x), update_val_(true)  { 
	ss_array<T>::zero(dx_, Num); }

      //! Constructor with size \c sz and value \c x
      /*!
       * Initializes value to \c x and derivative array 0 of length \c sz
       */
      Expr(const int sz, const T & x);

      //! Constructor with size \c sz, index \c i, and value \c x
      /*!
       * Initializes value to \c x and derivative array of length \c sz
       * as row \c i of the identity matrix, i.e., sets derivative component
       * \c i to 1 and all other's to zero.
       */
      Expr(const int sz, const int i, const T & x);

      //! Copy constructor
      Expr(const Expr& x) : val_(x.val_), update_val_(x.update_val_) { 
	//ss_array<T>::copy(x.dx_, dx_, Num);
	for (int i=0; i<Num; i++)
	  dx_[i] = x.dx_[i];
      }

      //! Copy constructor from any Expression object
      template <typename S> Expr(const Expr<S>& x);

      //! Destructor
      ~Expr() {}

      //! Set %Fad object as the \c ith independent variable
      /*!
       * Sets the derivative array of length \c n to the \c ith row of the
       * identity matrix and has the same affect as the 
       * Implementation(const int sz, const int i, const T & x) 
       * constructor.
       */
      void diff(const int ith, const int n);

      //! Resize derivative array to length \c sz
      /*!
       * Since the derivative array length is not dynamic, this method
       * throws an error if compiled with SACADO_DEBUG defined.
       */
      void resize(int sz);

      //! Expand derivative array to size sz
      /*!
       * Since the derivative array length is not dynamic, this method
       * throws an error if compiled with SACADO_DEBUG defined.
       */
      void expand(int sz) { resize(sz); }

      //! Zero out the derivative array
      void zero() { ss_array<T>::zero(dx_, Num); }

      //! Set whether this Fad object should update values
      void setUpdateValue(bool update_val) { update_val_ = update_val; }

      //! Return whether this Fad object has an updated value
      bool updateValue() const { return update_val_; }

      //! Returns whether two Fad objects have the same values
      template <typename S>
      bool isEqualTo(const Expr<S>& x) const {
	typedef IsEqual<value_type> IE;
	if (x.size() != this->size()) return false;
	bool eq = IE::eval(x.val(), this->val());
	for (int i=0; i<this->size(); i++)
	  eq = eq && IE::eval(x.dx(i), this->dx(i));
	return eq;
      }

      //@}

      /*!
       * @name Value accessor methods
       */
      //@{

      //! Returns value
      const T& val() const { return val_;}

      //! Returns value
      T& val() { return val_;}

      //@}

      /*!
       * @name Derivative accessor methods
       */
      //@{

      //! Returns number of derivative components
      int size() const { return Num;}

      /*! 
       * \brief Returns number of derivative components that can be stored 
       * without reallocation
       */
      int availableSize() const { return Num; }

      //! Returns true if derivative array is not empty
      bool hasFastAccess() const { return true; }

      //! Returns true if derivative array is empty
      bool isPassive() const { return false; }
      
      //! Set whether variable is constant
      void setIsConstant(bool is_const) {}

      //! Returns derivative array
      const T* dx() const { return &(dx_[0]);}

      //! Returns derivative component \c i with bounds checking
      const T& dx(int i) const { return dx_[i]; }
    
      //! Returns derivative component \c i without bounds checking
      T& fastAccessDx(int i) { return dx_[i];}

      //! Returns derivative component \c i without bounds checking
      const T& fastAccessDx(int i) const { return dx_[i];}

      //! Return partials w.r.t. arguments
      void computePartials(const T& bar, T partials[]) const { 
	partials[0] = bar; 
      }

      //! Return tangent component \c i of arguments
      void getTangents(int i, T dots[]) const { 
	dots[0] = this->dx_[i];
      }

      //! Return whether argument is active
      template <int Arg>
      bool isActive() const { return true; }

      //! Return tangent component \c i of argument \c Arg
      template <int Arg>
      const T& getTangent(int i) const { return this->dx_[i]; }
    
      //@}

      /*!
       * @name Assignment operators
       */
      //@{

      //! Assignment operator with constant right-hand-side
      Expr< SFadExprTag<T,Num> >& operator=(const T& val);

      //! Assignment with Expr right-hand-side
      Expr< SFadExprTag<T,Num> >& 
      operator=(const Expr< SFadExprTag<T,Num> >& x);

      //! Assignment operator with any expression right-hand-side
      template <typename S> 
      Expr< SFadExprTag<T,Num> >& operator=(const Expr<S>& x); 

      //@}

      /*!
       * @name Unary operators
       */
      //@{

      //! Addition-assignment operator with constant right-hand-side
      Expr< SFadExprTag<T,Num> >& operator += (const T& x);

      //! Subtraction-assignment operator with constant right-hand-side
      Expr< SFadExprTag<T,Num> >& operator -= (const T& x);

      //! Multiplication-assignment operator with constant right-hand-side
      Expr< SFadExprTag<T,Num> >& operator *= (const T& x);

      //! Division-assignment operator with constant right-hand-side
      Expr< SFadExprTag<T,Num> >& operator /= (const T& x);

      //! Addition-assignment operator with Expr right-hand-side
      template <typename S> 
      Expr< SFadExprTag<T,Num> >& operator += (const Expr<S>& x);

      //! Subtraction-assignment operator with Expr right-hand-side
      template <typename S> 
      Expr< SFadExprTag<T,Num> >& operator -= (const Expr<S>& x);
  
      //! Multiplication-assignment operator with Expr right-hand-side
      template <typename S> 
      Expr< SFadExprTag<T,Num> >& operator *= (const Expr<S>& x);

      //! Division-assignment operator with Expr right-hand-side
      template <typename S> 
      Expr< SFadExprTag<T,Num> >& operator /= (const Expr<S>& x);

      //@}

    protected:

      //! Value
      T val_;

      //! Derivatives
      T dx_[Num];

      //! Update value
      bool update_val_;

      // Functor for mpl::for_each to compute the local accumulation
      // of a tangent derivative
      template <typename ExprT>
      struct LocalAccumOp {
	typedef typename ExprT::value_type value_type;
	static const int N = ExprT::num_args;
	const ExprT& x;
	mutable value_type t;
	value_type partials[N];
	int i;
	inline LocalAccumOp(const ExprT& x_) :
	  x(x_) { x.computePartials(value_type(1.), partials); }
	inline void getTangents(int i_) { i = i_; }
	template <typename ArgT>
	inline void operator () (ArgT arg) const {
	  const int Arg = ArgT::value;
	  if (x.template isActive<Arg>())
	    t += partials[Arg] * x.template getTangent<Arg>(i);
	}
      };

    }; // class Expr<SFadExprTag>

    /*!
     * Forward-mode AD class using static memory allocation and
     * expression level reverse mode.
     */
    /*!
     * This is the user-level class for forward mode AD with static
     * memory allocation, and is appropriate for whenever the number
     * of derivative components is known at compile time.  The size
     * of the derivative array is fixed by the template parameter \c Num.  
     */
    template <typename ValueT, int Num>
    class SFad : 
      public Expr< SFadExprTag<ValueT,Num > > {

    public:

      //! Typename of scalar's (which may be different from ValueT)
      typedef typename ScalarType<ValueT>::type ScalarT;

      //! Turn SFad into a meta-function class usable with mpl::apply
      template <typename T> 
      struct apply {
	typedef SFad<T,Num> type;
      };

      /*!
       * @name Initialization methods
       */
      //@{

      //! Default constructor.
      /*!
       * Initializes value to 0 and derivative array is empty
       */
      SFad() : 
	Expr< SFadExprTag< ValueT,Num > >() {}

      //! Constructor with supplied value \c x
      /*!
       * Initializes value to \c x and derivative array is empty
       */
      SFad(const ValueT & x) : 
	Expr< SFadExprTag< ValueT,Num > >(x) {}

      //! Constructor with supplied value \c x of type ScalarT
      /*!
       * Initializes value to \c ValueT(x) and derivative array is empty.
       * Creates a dummy overload when ValueT and ScalarT are the same type.
       */
      SFad(const typename dummy<ValueT,ScalarT>::type& x) : 
	Expr< SFadExprTag< ValueT,Num > >(ValueT(x)) {}

      //! Constructor with size \c sz and value \c x
      /*!
       * Initializes value to \c x and derivative array 0 of length \c sz
       */
      SFad(const int sz, const ValueT & x) : 
	Expr< SFadExprTag< ValueT,Num > >(sz,x) {}

      //! Constructor with size \c sz, index \c i, and value \c x
      /*!
       * Initializes value to \c x and derivative array of length \c sz
       * as row \c i of the identity matrix, i.e., sets derivative component
       * \c i to 1 and all other's to zero.
       */
      SFad(const int sz, const int i, const ValueT & x) : 
	Expr< SFadExprTag< ValueT,Num > >(sz,i,x) {}

      //! Copy constructor
      SFad(const SFad& x) : 
	Expr< SFadExprTag< ValueT,Num > >(static_cast<const Expr< SFadExprTag< ValueT,Num > >&>(x)) {}

      //! Copy constructor from any Expression object
      template <typename S> SFad(const Expr<S>& x) : 
	Expr< SFadExprTag< ValueT,Num > >(x) {}

      //@}

      //! Destructor
      ~SFad() {}

      //! Assignment operator with constant right-hand-side
      SFad& operator=(const ValueT& v) {
	Expr< SFadExprTag< ValueT,Num > >::operator=(v);
	return *this;
      }

      //! Assignment operator with constant right-hand-side
      /*!
       * Creates a dummy overload when ValueT and ScalarT are the same type.
       */
      SFad& operator=(const typename dummy<ValueT,ScalarT>::type& v) {
	Expr< SFadExprTag< ValueT,Num > >::operator=(ValueT(v));
	return *this;
      }

      //! Assignment operator with DFad right-hand-side
      SFad& operator=(const SFad& x) {
	Expr< SFadExprTag< ValueT,Num > >::operator=(static_cast<const Expr< SFadExprTag< ValueT,Num > >&>(x));
	return *this;
      }

      //! Assignment operator with any expression right-hand-side
      template <typename S> SFad& operator=(const Expr<S>& x) 
      {
	Expr< SFadExprTag< ValueT,Num > >::operator=(x);
	return *this;
      }

    }; // class SFad<ValueT,Num>

    //! Specialization of %ExprPromote to Expr<SFadExprTag> types
    template <typename T, int Num>
    struct ExprPromote< Expr< SFadExprTag<T,Num> >, T > {
      typedef Expr< SFadExprTag<T,Num> > type;
    };
    
    //! Specialization of %ExprPromote to GeneralFad types
    template <typename T, int Num>
    struct ExprPromote< T, Expr< SFadExprTag<T,Num> > > {
      typedef Expr< SFadExprTag<T,Num> > type;
    };

    template <typename T, int Num>
    std::ostream& operator << (std::ostream& os, 
                               const Expr< SFadExprTag<T,Num> >& x) {
      os << x.val() << " [";
      
      for (int i=0; i< x.size(); i++) {
        os << " " << x.dx(i);
      }

      os << " ]";
      return os;
    }

  } // namespace ELRFad

} // namespace Sacado

#include "Sacado_ELRFad_SFadImp.hpp"
#include "Sacado_ELRFad_Ops.hpp"

#endif // SACADO_ELRFAD_SFAD_HPP
