///////////////////////////////////////////////////////////////////////////////

// BSD 3-Clause License

//

// Copyright (C) 2019-2021, LAAS-CNRS, University of Edinburgh

// Copyright note valid unless otherwise stated in individual files.

// All rights reserved.

///////////////////////////////////////////////////////////////////////////////

#ifndef CROCODDYL_CORE_COST_BASE_HPP_

#define CROCODDYL_CORE_COST_BASE_HPP_

#include <boost/make_shared.hpp>

#include <boost/shared_ptr.hpp>

#include "crocoddyl/core/activation-base.hpp"

#include "crocoddyl/core/activations/quadratic.hpp"

#include "crocoddyl/core/data-collector-base.hpp"

#include "crocoddyl/core/fwd.hpp"

#include "crocoddyl/core/residual-base.hpp"

#include "crocoddyl/core/state-base.hpp"

#include "crocoddyl/core/utils/deprecate.hpp"

namespace crocoddyl {

/**

 * @brief Abstract class for cost models

 *

 * A cost model is defined by the scalar activation function \f$a(\cdot)\f$ and

 * by the residual function \f$\mathbf{r}(\cdot)\f$ as follows: \f[

 * \ell(\mathbf{x},\mathbf{u}) = a(\mathbf{r}(\mathbf{x}, \mathbf{u})), \f]

 * where the residual function depends on the state point

 * \f$\mathbf{x}\in\mathcal{X}\f$, which lies in the state manifold described

 * with a `nx`-tuple, its velocity \f$\dot{\mathbf{x}}\in

 * T_{\mathbf{x}}\mathcal{X}\f$ that belongs to the tangent space with `ndx`

 * dimension, and the control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$. The

 * residual vector is defined by \f$\mathbf{r}\in\mathbb{R}^{nr}\f$ where `nr`

 * describes its dimension in the Euclidean space. On the other hand, the

 * activation function builds a cost value based on the definition of the

 * residual vector. The residual vector has to be specialized in a derived

 * classes.

 *

 * The main computations are carring out in `calc()` and `calcDiff()` routines.

 * `calc()` computes the cost (and its residual) and `calcDiff()` computes the

 * derivatives of the cost function (and its residual). Concretely speaking,

 * `calcDiff()` builds a linear-quadratic approximation of the cost function

 * with the form: \f$\mathbf{l_x}\in\mathbb{R}^{ndx}\f$,

 * \f$\mathbf{l_u}\in\mathbb{R}^{nu}\f$,

 * \f$\mathbf{l_{xx}}\in\mathbb{R}^{ndx\times ndx}\f$,

 * \f$\mathbf{l_{xu}}\in\mathbb{R}^{ndx\times nu}\f$,

 * \f$\mathbf{l_{uu}}\in\mathbb{R}^{nu\times nu}\f$ are the Jacobians and

 * Hessians, respectively. Additionally, it is important to note that

 * `calcDiff()` computes the derivatives using the latest stored values by

 * `calc()`. Thus, we need to first run `calc()`.

 *

 * \sa `ActivationModelAbstractTpl`, `ResidualModelAbstractTpl` `calc()`,

 * `calcDiff()`, `createData()`

 */

template <typename _Scalar>

class CostModelAbstractTpl {

 public:

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef CostDataAbstractTpl<Scalar> CostDataAbstract;

  typedef StateAbstractTpl<Scalar> StateAbstract;

  typedef ActivationModelAbstractTpl<Scalar> ActivationModelAbstract;

  typedef ResidualModelAbstractTpl<Scalar> ResidualModelAbstract;

  typedef ActivationModelQuadTpl<Scalar> ActivationModelQuad;

  typedef DataCollectorAbstractTpl<Scalar> DataCollectorAbstract;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  /**

   * @brief Initialize the cost model

   *

   * @param[in] state       State of the dynamical system

   * @param[in] activation  Activation model

   * @param[in] residual    Residual model

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       boost::shared_ptr<ActivationModelAbstract> activation,

                       boost::shared_ptr<ResidualModelAbstract> residual);

  /**

   * @brief Initialize the cost model

   *

   * @param[in] state       State of the dynamical system

   * @param[in] activation  Activation model

   * @param[in] nu          Dimension of control vector

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       boost::shared_ptr<ActivationModelAbstract> activation,

                       const std::size_t nu);

  /**

   * @copybrief CostModelAbstractTpl()

   *

   * The default `nu` value is obtained from `StateAbstractTpl::get_nv()`.

   *

   * @param[in] state       State of the dynamical system

   * @param[in] activation  Activation model

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       boost::shared_ptr<ActivationModelAbstract> activation);

  /**

   * @copybrief CostModelAbstractTpl()

   *

   * We use `ActivationModelQuadTpl` as a default activation model (i.e.,

   * \f$a=\frac{1}{2}\|\mathbf{r}\|^2\f$)

   *

   * @param[in] state     State of the dynamical system

   * @param[in] residual  Residual model

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       boost::shared_ptr<ResidualModelAbstract> residual);

  /**

   * @copybrief CostModelAbstractTpl()

   *

   * We use `ActivationModelQuadTpl` as a default activation model (i.e.,

   * \f$a=\frac{1}{2}\|\mathbf{r}\|^2\f$)

   *

   * @param[in] state  State of the system

   * @param[in] nr     Dimension of residual vector

   * @param[in] nu     Dimension of control vector

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       const std::size_t nr, const std::size_t nu);

  /**

   * @copybrief CostModelAbstractTpl()

   *

   * We use `ActivationModelQuadTpl` as a default activation model (i.e.,

   * \f$a=\frac{1}{2}\|\mathbf{r}\|^2\f$). Furthermore, the default `nu` value

   * is obtained from `StateAbstractTpl::get_nv()`.

   *

   * @param[in] state  State of the dynamical system

   * @param[in] nr     Dimension of residual vector

   * @param[in] nu     Dimension of control vector

   */

  CostModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                       const std::size_t nr);

  virtual ~CostModelAbstractTpl();

  /**

   * @brief Compute the cost value and its residual vector

   *

   * @param[in] data  Cost data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   * @param[in] u     Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$

   */

  virtual void calc(const boost::shared_ptr<CostDataAbstract>& data,

                    const Eigen::Ref<const VectorXs>& x,

                    const Eigen::Ref<const VectorXs>& u) = 0;

  /**

   * @brief Compute the total cost value for nodes that depends only on the

   * state

   *

   * It updates the total cost based on the state only. This function is used in

   * the terminal nodes of an optimal control problem.

   *

   * @param[in] data  Cost data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   */

  virtual void calc(const boost::shared_ptr<CostDataAbstract>& data,

                    const Eigen::Ref<const VectorXs>& x);

  /**

   * @brief Compute the Jacobian and Hessian of cost and its residual vector

   *

   * It computes the Jacobian and Hessian of the cost function. It assumes that

   * `calc()` has been run first.

   *

   * @param[in] data  Cost data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   * @param[in] u     Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$

   */

  virtual void calcDiff(const boost::shared_ptr<CostDataAbstract>& data,

                        const Eigen::Ref<const VectorXs>& x,

                        const Eigen::Ref<const VectorXs>& u) = 0;

  /**

   * @brief Compute the Jacobian and Hessian of the cost functions with respect

   * to the state only

   *

   * It updates the Jacobian and Hessian of the cost function based on the state

   * only. This function is used in the terminal nodes of an optimal control

   * problem.

   *

   * @param[in] data  Cost data

   * @param[in] x     State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$

   */

  virtual void calcDiff(const boost::shared_ptr<CostDataAbstract>& data,

                        const Eigen::Ref<const VectorXs>& x);

  /**

   * @brief Create the cost data

   *

   * The default data contains objects to store the values of the cost, residual

   * vector and their derivatives (first and second order derivatives). However,

   * it is possible to specialize this function if we need to create additional

   * data, for instance, to avoid dynamic memory allocation.

   *

   * @param data  Data collector

   * @return the cost data

   */

  virtual boost::shared_ptr<CostDataAbstract> createData(

      DataCollectorAbstract* const data);

  /**

   * @brief Return the state

   */

  const boost::shared_ptr<StateAbstract>& get_state() const;

  /**

   * @brief Return the activation model

   */

  const boost::shared_ptr<ActivationModelAbstract>& get_activation() const;

  /**

   * @brief Return the residual model

   */

  const boost::shared_ptr<ResidualModelAbstract>& get_residual() const;

  /**

   * @brief Return the dimension of the control input

   */

  std::size_t get_nu() const;

  /**

   * @brief Print information on the cost model

   */

  template <class Scalar>

  friend std::ostream& operator<<(std::ostream& os,

                                  const CostModelAbstractTpl<Scalar>& model);

  /**

   * @brief Modify the cost reference

   */

  template <class ReferenceType>

  void set_reference(ReferenceType ref);

  /**

   * @brief Return the cost reference

   */

  template <class ReferenceType>

  ReferenceType get_reference();

  /**

   * @brief Print relevant information of the cost model

   *

   * @param[out] os  Output stream object

   */

  virtual void print(std::ostream& os) const;

 protected:

  /**

   * @copybrief set_reference()

   */

  virtual void set_referenceImpl(const std::type_info&, const void*);

  /**

   * @copybrief get_reference()

   */

  virtual void get_referenceImpl(const std::type_info&, void*);

  boost::shared_ptr<StateAbstract> state_;  //!< State description

  boost::shared_ptr<ActivationModelAbstract> activation_;  //!< Activation model

  boost::shared_ptr<ResidualModelAbstract> residual_;      //!< Residual model

  std::size_t nu_;  //!< Control dimension

  VectorXs unone_;  //!< No control vector

};

template <typename _Scalar>

struct CostDataAbstractTpl {

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef ActivationDataAbstractTpl<Scalar> ActivationDataAbstract;

  typedef ResidualDataAbstractTpl<Scalar> ResidualDataAbstract;

  typedef DataCollectorAbstractTpl<Scalar> DataCollectorAbstract;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  template <template <typename Scalar> class Model>

                      DataCollectorAbstract* const data)

      : shared(data),

        cost(Scalar(0.)),

        Lu(model->get_nu()),

      "Use residual.r", const VectorXs& get_r() const { return residual->r; };)

      "Use residual.Rx",

      const MatrixXs& get_Rx() const { return residual->Rx; };)

      "Use residual.Ru",

      const MatrixXs& get_Ru() const { return residual->Ru; };)

      "Use residual.r", void set_r(const VectorXs& r) { residual->r = r; };)

      "Use residual.Rx",

      void set_Rx(const MatrixXs& Rx) { residual->Rx = Rx; };)

      "Use residual.Ru",

      void set_Ru(const MatrixXs& Ru) { residual->Ru = Ru; };)

  DataCollectorAbstract* shared;

  boost::shared_ptr<ActivationDataAbstract> activation;

  boost::shared_ptr<ResidualDataAbstract> residual;

  Scalar cost;

  VectorXs Lx;

  VectorXs Lu;

  MatrixXs Lxx;

  MatrixXs Lxu;

  MatrixXs Luu;

};

}  // namespace crocoddyl

/* --- Details -------------------------------------------------------------- */

/* --- Details -------------------------------------------------------------- */

/* --- Details -------------------------------------------------------------- */

#include "crocoddyl/core/cost-base.hxx"

#endif  // CROCODDYL_CORE_COST_BASE_HPP_