// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen 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 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen 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 or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#ifndef EIGEN_AUTODIFF_SCALAR_H
#define EIGEN_AUTODIFF_SCALAR_H

namespace Eigen {

/** \class AutoDiffScalar
  * \brief A scalar type replacement with automatic differentation capability
  *
  * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
  *
  * This class represents a scalar value while tracking its respective derivatives.
  *
  * It supports the following list of global math function:
  *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos, 
  *  - ei_abs, ei_sqrt, ei_pow, ei_exp, ei_log, ei_sin, ei_cos,
  *  - ei_conj, ei_real, ei_imag, ei_abs2.
  *
  * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
  * in that case, the expression template mechanism only occurs at the top Matrix level,
  * while derivatives are computed right away.
  *
  */
template<typename DerType>
class AutoDiffScalar
{
  public:
    typedef typename ei_traits<DerType>::Scalar Scalar;
    
    inline AutoDiffScalar() {}
    
    inline AutoDiffScalar(const Scalar& value)
      : m_value(value)
    {
      if(m_derivatives.size()>0)
        m_derivatives.setZero();
    }
    
    inline AutoDiffScalar(const Scalar& value, const DerType& der)
      : m_value(value), m_derivatives(der)
    {}
    
    template<typename OtherDerType>
    inline AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other)
      : m_value(other.value()), m_derivatives(other.derivatives())
    {}
    
    inline AutoDiffScalar(const AutoDiffScalar& other)
      : m_value(other.value()), m_derivatives(other.derivatives())
    {}
    
    template<typename OtherDerType>
    inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
    {
      m_value = other.value();
      m_derivatives = other.derivatives();
      return *this;
    }
    
    inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
    {
      m_value = other.value();
      m_derivatives = other.derivatives();
      return *this;
    }
    
//     inline operator const Scalar& () const { return m_value; }
//     inline operator Scalar& () { return m_value; }

    inline const Scalar& value() const { return m_value; }
    inline Scalar& value() { return m_value; }
    
    inline const DerType& derivatives() const { return m_derivatives; }
    inline DerType& derivatives() { return m_derivatives; }
    
    template<typename OtherDerType>
    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >
    operator+(const AutoDiffScalar<OtherDerType>& other) const
    {
      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >(
        m_value + other.value(),
        m_derivatives + other.derivatives());
    }
    
    template<typename OtherDerType>
    inline AutoDiffScalar&
    operator+=(const AutoDiffScalar<OtherDerType>& other)
    {
      (*this) = (*this) + other;
      return *this;
    }
    
    template<typename OtherDerType>
    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >
    operator-(const AutoDiffScalar<OtherDerType>& other) const
    {
      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >(
        m_value - other.value(),
        m_derivatives - other.derivatives());
    }
    
    template<typename OtherDerType>
    inline AutoDiffScalar&
    operator-=(const AutoDiffScalar<OtherDerType>& other)
    {
      *this = *this - other;
      return *this;
    }
    
    template<typename OtherDerType>
    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >
    operator-() const
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >(
        -m_value,
        -m_derivatives);
    }
    
    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
    operator*(const Scalar& other) const
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
        m_value * other,
        (m_derivatives * other));
    }
    
    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
    operator*(const Scalar& other, const AutoDiffScalar& a)
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
        a.value() * other,
        a.derivatives() * other);
    }
    
    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
    operator/(const Scalar& other) const
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
        m_value / other,
        (m_derivatives * (Scalar(1)/other)));
    }
    
    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
    operator/(const Scalar& other, const AutoDiffScalar& a)
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
        other / a.value(),
        a.derivatives() * (-Scalar(1)/other));
    }
    
    template<typename OtherDerType>
    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >
    operator/(const AutoDiffScalar<OtherDerType>& other) const
    {
      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >(
        m_value / other.value(),
          ((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
        * (Scalar(1)/(other.value()*other.value())));
    }
    
    template<typename OtherDerType>
    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >
    operator*(const AutoDiffScalar<OtherDerType>& other) const
    {
      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >(
        m_value * other.value(),
        (m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
    }
    
    inline AutoDiffScalar& operator*=(const Scalar& other)
    {
      *this = *this * other;
      return *this;
    }
    
    template<typename OtherDerType>
    inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
    {
      *this = *this * other;
      return *this;
    }
    
  protected:
    Scalar m_value;
    DerType m_derivatives;
    
};

}

#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
  template<typename DerType> \
  inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> > \
  FUNC(const AutoDiffScalar<DerType>& x) { \
    typedef typename ei_traits<DerType>::Scalar Scalar; \
    typedef AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> > ReturnType; \
    CODE; \
  }

namespace std
{
  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
    return ReturnType(std::abs(x.value()), x.derivatives() * (sign(x.value())));)
  
  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
    Scalar sqrtx = std::sqrt(x.value());
    return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
  
  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
    return ReturnType(std::cos(x.value()), x.derivatives() * (-std::sin(x.value())));)
  
  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
    return ReturnType(std::sin(x.value()),x.derivatives() * std::cos(x.value()));)
  
  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
    Scalar expx = std::exp(x.value());
    return ReturnType(expx,x.derivatives() * expx);)

  EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
    return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
  
  template<typename DerType>
  inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
  pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
  {
    typedef typename ei_traits<DerType>::Scalar Scalar;
    return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
      std::pow(x.value(),y),
      x.derivatives() * (y * std::pow(x.value(),y-1)));
  }
  
}

namespace Eigen {

template<typename DerType>
inline const AutoDiffScalar<DerType>& ei_conj(const AutoDiffScalar<DerType>& x)  { return x; }
template<typename DerType>
inline const AutoDiffScalar<DerType>& ei_real(const AutoDiffScalar<DerType>& x)  { return x; }
template<typename DerType>
inline typename DerType::Scalar ei_imag(const AutoDiffScalar<DerType>&)    { return 0.; }

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs,
  return ReturnType(ei_abs(x.value()), x.derivatives() * (sign(x.value())));)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs2,
  return ReturnType(ei_abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sqrt,
  Scalar sqrtx = ei_sqrt(x.value());
  return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_cos,
  return ReturnType(ei_cos(x.value()), x.derivatives() * (-ei_sin(x.value())));)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sin,
  return ReturnType(ei_sin(x.value()),x.derivatives() * ei_cos(x.value()));)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_exp,
  Scalar expx = ei_exp(x.value());
  return ReturnType(expx,x.derivatives() * expx);)

EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
  return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)

template<typename DerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
{ return std::pow(x,y);}

#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY

template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
{
  typedef typename DerType::Scalar Real;
  typedef AutoDiffScalar<DerType> FloatingPoint;
  enum {
    IsComplex = 0,
    HasFloatingPoint = 1,
    ReadCost = 1,
    AddCost = 1,
    MulCost = 1
  };
};

}

#endif // EIGEN_AUTODIFF_SCALAR_H