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

// BSD 3-Clause License

//

// Copyright (C) 2021-2023, University of Edinburgh, Heriot-Watt University

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

// All rights reserved.

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

#ifndef CROCODDYL_CORE_COSTS_RESIDUAL_COST_HPP_

#define CROCODDYL_CORE_COSTS_RESIDUAL_COST_HPP_

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

#include "crocoddyl/core/fwd.hpp"

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

namespace crocoddyl {

/**

 * @brief Residual-based cost

 *

 * This cost function uses a residual model to compute the cost, i.e., \f[ cost

 * = a(\mathbf{r}(\mathbf{x}, \mathbf{u})), \f] where \f$\mathbf{r}(\cdot)\f$

 * and \f$a(\cdot)\f$ define the residual and activation functions,

 * respectively.

 *

 * Note that we only compute the Jacobians of the residual function. Therefore,

 * this cost model computes its Hessians through a Gauss-Newton approximation,

 * e.g., \f$\mathbf{l_{xu}} = \mathbf{R_x}^T \mathbf{A_{rr}} \mathbf{R_u} \f$,

 * where \f$\mathbf{R_x}\f$ and \f$\mathbf{R_u}\f$ are the Jacobians of the

 * residual function, and \f$\mathbf{A_{rr}}\f$ is the Hessian of the activation

 * model.

 *

 * As described in `CostModelAbstractTpl()`, the cost value and its derivatives

 * are calculated by `calc` and `calcDiff`, respectively.

 *

 * \sa `CostModelAbstractTpl`, `calc()`, `calcDiff()`, `createData()`

 */

template <typename _Scalar>

class CostModelResidualTpl : public CostModelAbstractTpl<_Scalar> {

 public:

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef CostModelAbstractTpl<Scalar> Base;

  typedef CostDataResidualTpl<Scalar> Data;

  typedef CostDataAbstractTpl<Scalar> CostDataAbstract;

  typedef ResidualModelAbstractTpl<Scalar> ResidualModelAbstract;

  typedef ActivationModelAbstractTpl<Scalar> ActivationModelAbstract;

  typedef DataCollectorAbstractTpl<Scalar> DataCollectorAbstract;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  /**

   * @brief Initialize the residual cost model

   *

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

   * @param[in] activation  Activation model

   * @param[in] residual    Residual model

   */

  CostModelResidualTpl(boost::shared_ptr<typename Base::StateAbstract> state,

                       boost::shared_ptr<ActivationModelAbstract> activation,

                       boost::shared_ptr<ResidualModelAbstract> residual);

  /**

   * @brief Initialize the residual cost model

   *

   * 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 multibody system

   * @param[in] residual    Residual model

   */

  CostModelResidualTpl(boost::shared_ptr<typename Base::StateAbstract> state,

                       boost::shared_ptr<ResidualModelAbstract> residual);

  virtual ~CostModelResidualTpl();

  /**

   * @brief Compute the residual cost

   *

   * @param[in] data  Residual 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);

  /**

   * @brief Compute the residual cost based on state only

   *

   * 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  Residual 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 derivatives of the residual cost

   *

   * @param[in] data  Residual 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);

  /**

   * @brief Compute the derivatives of the residual cost 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  Residual 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 residual cost data

   */

  virtual boost::shared_ptr<CostDataAbstract> createData(

      DataCollectorAbstract* const data);

  /**

   * @brief Print relevant information of the cost-residual model

   *

   * @param[out] os  Output stream object

   */

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

 protected:

  using Base::activation_;

  using Base::nu_;

  using Base::residual_;

  using Base::state_;

  using Base::unone_;

};

template <typename _Scalar>

struct CostDataResidualTpl : public CostDataAbstractTpl<_Scalar> {

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef CostDataAbstractTpl<Scalar> Base;

  typedef DataCollectorAbstractTpl<Scalar> DataCollectorAbstract;

  template <template <typename Scalar> class Model>

                      DataCollectorAbstract* const data)

  using Base::activation;

  using Base::cost;

  using Base::Lu;

  using Base::Luu;

  using Base::Lx;

  using Base::Lxu;

  using Base::Lxx;

  using Base::residual;

  using Base::shared;

};

}  // namespace crocoddyl

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

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

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

#include "crocoddyl/core/costs/residual.hxx"

#endif  // CROCODDYL_CORE_COSTS_RESIDUAL_COST_HPP_