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

// BSD 3-Clause License

//

// Copyright (C) 2019-2023, LAAS-CNRS, University of Edinburgh,

//                          University of Oxford, Heriot-Watt University

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

// All rights reserved.

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

#ifndef CROCODDYL_CORE_DIFF_ACTION_BASE_HPP_

#define CROCODDYL_CORE_DIFF_ACTION_BASE_HPP_

#include <boost/make_shared.hpp>

#include <boost/shared_ptr.hpp>

#include <stdexcept>

#include "crocoddyl/core/fwd.hpp"

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

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

namespace crocoddyl {

/**

 * @brief Abstract class for differential action model

 *

 * A differential action model combines dynamics, cost and constraints models.

 * We can use it in each node of our optimal control problem thanks to dedicated

 * integration rules (e.g., `IntegratedActionModelEulerTpl` or

 * `IntegratedActionModelRK4Tpl`). These integrated action models produce action

 * models (`ActionModelAbstractTpl`). Thus, every time that we want to describe

 * a problem, we need to provide ways of computing the dynamics, cost,

 * constraints functions and their derivatives. All these are described inside

 * the differential action model.

 *

 * Concretely speaking, the differential action model is the time-continuous

 * version of an action model, i.e., \f[ \begin{aligned}

 * &\dot{\mathbf{v}} = \mathbf{f}(\mathbf{q}, \mathbf{v}, \mathbf{u}),

 * &\textrm{(dynamics)}\\

 * &\ell(\mathbf{q}, \mathbf{v},\mathbf{u}) = \int_0^{\delta t}

 * a(\mathbf{r}(\mathbf{q}, \mathbf{v},\mathbf{u}))\,dt,

 * &\textrm{(cost)}\\

 * &\mathbf{g}(\mathbf{q}, \mathbf{v},\mathbf{u})<\mathbf{0},

 * &\textrm{(inequality constraint)}\\

 * &\mathbf{h}(\mathbf{q}, \mathbf{v},\mathbf{u})=\mathbf{0}, &\textrm{(equality

 * constraint)} \end{aligned} \f] where

 *  - the configuration \f$\mathbf{q}\in\mathcal{Q}\f$ lies in the configuration

 * manifold described with a `nq`-tuple,

 *  - the velocity \f$\mathbf{v}\in T_{\mathbf{q}}\mathcal{Q}\f$ is the tangent

 * vector to the configuration manifold with `nv` dimension,

 *  - the control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ is an Euclidean

 * vector,

 *  - \f$\mathbf{r}(\cdot)\f$ and \f$a(\cdot)\f$ are the residual and activation

 * functions (see `ResidualModelAbstractTpl` and `ActivationModelAbstractTpl`,

 * respectively),

 *  - \f$\mathbf{g}(\cdot)\in\mathbb{R}^{ng}\f$ and

 * \f$\mathbf{h}(\cdot)\in\mathbb{R}^{nh}\f$ are the inequality and equality

 * vector functions, respectively.

 *

 * Both configuration and velocity describe the system space

 * \f$\mathbf{x}=(\mathbf{q}, \mathbf{v})\in\mathcal{X}\f$ which lies in the

 * state manifold. Note that the acceleration \f$\dot{\mathbf{v}}\in

 * T_{\mathbf{q}}\mathcal{Q}\f$ lies also in the tangent space of the

 * configuration manifold. The computation of these equations are carried out

 * inside `calc()` function. In short, this function computes the system

 * acceleration, cost and constraints values (also called constraints

 * violations). This procedure is equivalent to running a forward pass of the

 * action model.

 *

 * However, during numerical optimization, we also need to run backward passes

 * of the differential action model. These calculations are performed by

 * `calcDiff()`. In short, this function builds a linear-quadratic approximation

 * of the differential action model, i.e., \f[ \begin{aligned}

 * &\delta\dot{\mathbf{v}} =

 * \mathbf{f_{q}}\delta\mathbf{q}+\mathbf{f_{v}}\delta\mathbf{v}+\mathbf{f_{u}}\delta\mathbf{u},

 * &\textrm{(dynamics)}\\

 * &\ell(\delta\mathbf{q},\delta\mathbf{v},\delta\mathbf{u}) = \begin{bmatrix}1

 * \\ \delta\mathbf{q} \\ \delta\mathbf{v}

 * \\ \delta\mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & \mathbf{\ell_q}^T &

 * \mathbf{\ell_v}^T & \mathbf{\ell_u}^T \\ \mathbf{\ell_q} & \mathbf{\ell_{qq}}

 * &

 * \mathbf{\ell_{qv}} & \mathbf{\ell_{uq}}^T \\

 * \mathbf{\ell_v} & \mathbf{\ell_{vq}} & \mathbf{\ell_{vv}} &

 * \mathbf{\ell_{uv}}^T \\

 * \mathbf{\ell_u} & \mathbf{\ell_{uq}} & \mathbf{\ell_{uv}} &

 * \mathbf{\ell_{uu}}\end{bmatrix} \begin{bmatrix}1 \\ \delta\mathbf{q}

 * \\ \delta\mathbf{v} \\

 * \delta\mathbf{u}\end{bmatrix}, &\textrm{(cost)}\\

 * &\mathbf{g_q}\delta\mathbf{q}+\mathbf{g_v}\delta\mathbf{v}+\mathbf{g_u}\delta\mathbf{u}\leq\mathbf{0},

 * &\textrm{(inequality constraints)}\\

 * &\mathbf{h_q}\delta\mathbf{q}+\mathbf{h_v}\delta\mathbf{v}+\mathbf{h_u}\delta\mathbf{u}=\mathbf{0},

 * &\textrm{(equality constraints)} \end{aligned} \f] where

 *  - \f$\mathbf{f_x}=(\mathbf{f_q};\,\, \mathbf{f_v})\in\mathbb{R}^{nv\times

 * ndx}\f$ and \f$\mathbf{f_u}\in\mathbb{R}^{nv\times nu}\f$ are the Jacobians

 * of the dynamics,

 *  - \f$\mathbf{\ell_x}=(\mathbf{\ell_q};\,\,

 * \mathbf{\ell_v})\in\mathbb{R}^{ndx}\f$ and

 * \f$\mathbf{\ell_u}\in\mathbb{R}^{nu}\f$ are the Jacobians of the cost

 * function,

 *  - \f$\mathbf{\ell_{xx}}=(\mathbf{\ell_{qq}}\,\, \mathbf{\ell_{qv}};\,\,

 * \mathbf{\ell_{vq}}\, \mathbf{\ell_{vv}})\in\mathbb{R}^{ndx\times ndx}\f$,

 * \f$\mathbf{\ell_{xu}}=(\mathbf{\ell_q};\,\,

 * \mathbf{\ell_v})\in\mathbb{R}^{ndx\times nu}\f$ and

 * \f$\mathbf{\ell_{uu}}\in\mathbb{R}^{nu\times nu}\f$ are the Hessians of the

 * cost function,

 *  - \f$\mathbf{g_x}=(\mathbf{g_q};\,\, \mathbf{g_v})\in\mathbb{R}^{ng\times

 * ndx}\f$ and \f$\mathbf{g_u}\in\mathbb{R}^{ng\times nu}\f$ are the Jacobians

 * of the inequality constraints, and

 *  - \f$\mathbf{h_x}=(\mathbf{h_q};\,\, \mathbf{h_v})\in\mathbb{R}^{nh\times

 * ndx}\f$ and \f$\mathbf{h_u}\in\mathbb{R}^{nh\times nu}\f$ are the Jacobians

 * of the equality constraints.

 *

 * 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 `ActionModelAbstractTpl`, `calc()`, `calcDiff()`, `createData()`

 */

template <typename _Scalar>

class DifferentialActionModelAbstractTpl {

 public:

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef DifferentialActionDataAbstractTpl<Scalar>

      DifferentialActionDataAbstract;

  typedef StateAbstractTpl<Scalar> StateAbstract;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  /**

   * @brief Initialize the differential action model

   *

   * @param[in] state  State description

   * @param[in] nu     Dimension of control vector

   * @param[in] nr     Dimension of cost-residual vector

   * @param[in] ng     Number of inequality constraints

   * @param[in] nh     Number of equality constraints

   */

  DifferentialActionModelAbstractTpl(boost::shared_ptr<StateAbstract> state,

                                     const std::size_t nu,

                                     const std::size_t nr = 0,

                                     const std::size_t ng = 0,

                                     const std::size_t nh = 0);

  virtual ~DifferentialActionModelAbstractTpl();

  /**

   * @brief Compute the system acceleration and cost value

   *

   * @param[in] data  Differential action 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<DifferentialActionDataAbstract>& 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 and the system acceleration is not updated as the

   * control input is undefined. This function is used in the terminal nodes of

   * an optimal control problem.

   *

   * @param[in] data  Differential action data

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

   */

  virtual void calc(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

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

  /**

   * @brief Compute the derivatives of the dynamics and cost functions

   *

   * It computes the partial derivatives of the dynamical system and the cost

   * function. It assumes that `calc()` has been run first. This function builds

   * a quadratic approximation of the time-continuous action model (i.e.

   * dynamical system and cost function).

   *

   * @param[in] data  Differential action 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<DifferentialActionDataAbstract>& data,

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

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

  /**

   * @brief Compute the derivatives of the cost functions with respect to the

   * state only

   *

   * It updates the derivatives of the cost function with respect to the state

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

   * problem.

   *

   * @param[in] data  Differential action data

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

   */

  virtual void calcDiff(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

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

  /**

   * @brief Create the differential action data

   *

   * @return the differential action data

   */

  virtual boost::shared_ptr<DifferentialActionDataAbstract> createData();

  /**

   * @brief Checks that a specific data belongs to this model

   */

  virtual bool checkData(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data);

  /**

   * @brief Computes the quasic static commands

   *

   * The quasic static commands are the ones produced for a the reference

   * posture as an equilibrium point, i.e. for

   * \f$\mathbf{f}(\mathbf{q},\mathbf{v}=\mathbf{0},\mathbf{u})=\mathbf{0}\f$

   *

   * @param[in] data    Differential action data

   * @param[out] u      Quasic static commands

   * @param[in] x       State point (velocity has to be zero)

   * @param[in] maxiter Maximum allowed number of iterations

   * @param[in] tol     Tolerance

   */

  virtual void quasiStatic(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

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

      const std::size_t maxiter = 100, const Scalar tol = Scalar(1e-9));

  /**

   * @copybrief quasicStatic()

   *

   * @copydetails quasicStatic()

   *

   * @param[in] data    Differential action data

   * @param[in] x       State point (velocity has to be zero)

   * @param[in] maxiter Maximum allowed number of iterations

   * @param[in] tol     Tolerance

   * @return Quasic static commands

   */

  VectorXs quasiStatic_x(

      const boost::shared_ptr<DifferentialActionDataAbstract>& data,

      const VectorXs& x, const std::size_t maxiter = 100,

      const Scalar tol = Scalar(1e-9));

  /**

   * @brief Return the dimension of the control input

   */

  std::size_t get_nu() const;

  /**

   * @brief Return the dimension of the cost-residual vector

   */

  std::size_t get_nr() const;

  /**

   * @brief Return the number of inequality constraints

   */

  virtual std::size_t get_ng() const;

  /**

   * @brief Return the number of equality constraints

   */

  virtual std::size_t get_nh() const;

  /**

   * @brief Return the state

   */

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

  /**

   * @brief Return the lower bound of the inequality constraints

   */

  virtual const VectorXs& get_g_lb() const;

  /**

   * @brief Return the upper bound of the inequality constraints

   */

  virtual const VectorXs& get_g_ub() const;

  /**

   * @brief Return the control lower bound

   */

  const VectorXs& get_u_lb() const;

  /**

   * @brief Return the control upper bound

   */

  const VectorXs& get_u_ub() const;

  /**

   * @brief Indicates if there are defined control limits

   */

  bool get_has_control_limits() const;

  /**

   * @brief Modify the lower bound of the inequality constraints

   */

  void set_g_lb(const VectorXs& g_lb);

  /**

   * @brief Modify the upper bound of the inequality constraints

   */

  void set_g_ub(const VectorXs& g_ub);

  /**

   * @brief Modify the control lower bounds

   */

  void set_u_lb(const VectorXs& u_lb);

  /**

   * @brief Modify the control upper bounds

   */

  void set_u_ub(const VectorXs& u_ub);

  /**

   * @brief Print information on the differential action model

   */

  template <class Scalar>

  friend std::ostream& operator<<(

      std::ostream& os,

      const DifferentialActionModelAbstractTpl<Scalar>& model);

  /**

   * @brief Print relevant information of the differential action model

   *

   * @param[out] os  Output stream object

   */

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

 private:

  std::size_t ng_internal_;  //!< Internal object for storing the number of

                             //!< inequality constraints

  std::size_t nh_internal_;  //!< Internal object for storing the number of

                             //!< equality constraints

 protected:

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

  std::size_t nr_;  //!< Dimension of the cost residual

  std::size_t ng_;  //!< Number of inequality constraints

  std::size_t nh_;  //!< Number of equality constraints

  boost::shared_ptr<StateAbstract> state_;  //!< Model of the state

  VectorXs unone_;                          //!< Neutral state

  VectorXs g_lb_;            //!< Lower bound of the inequality constraints

  VectorXs g_ub_;            //!< Lower bound of the inequality constraints

  VectorXs u_lb_;            //!< Lower control limits

  VectorXs u_ub_;            //!< Upper control limits

  bool has_control_limits_;  //!< Indicates whether any of the control limits is

                             //!< finite

  /**

   * @brief Update the status of the control limits (i.e. if there are defined

   * limits)

   */

  void update_has_control_limits();

  template <class Scalar>

  friend class IntegratedActionModelAbstractTpl;

  template <class Scalar>

  friend class ConstraintModelManagerTpl;

};

template <typename _Scalar>

struct DifferentialActionDataAbstractTpl {

  typedef _Scalar Scalar;

  typedef MathBaseTpl<Scalar> MathBase;

  typedef typename MathBase::VectorXs VectorXs;

  typedef typename MathBase::MatrixXs MatrixXs;

  template <template <typename Scalar> class Model>

      : cost(Scalar(0.)),

        r(model->get_nr()),

        Lu(model->get_nu()),

        Luu(model->get_nu(), model->get_nu()),

        g(model->get_ng()),

        Gu(model->get_ng(), model->get_nu()),

        h(model->get_nh()),

  Scalar cost;    //!< cost value

  VectorXs xout;  //!< evolution state

  MatrixXs Fx;  //!< Jacobian of the dynamics w.r.t. the state \f$\mathbf{x}\f$

  MatrixXs

      Fu;      //!< Jacobian of the dynamics w.r.t. the control \f$\mathbf{u}\f$

  VectorXs r;  //!< Cost residual

  VectorXs Lx;   //!< Jacobian of the cost w.r.t. the state \f$\mathbf{x}\f$

  VectorXs Lu;   //!< Jacobian of the cost w.r.t. the control \f$\mathbf{u}\f$

  MatrixXs Lxx;  //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$

  MatrixXs Lxu;  //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ and

                 //!< control u

  MatrixXs Luu;  //!< Hessian of the cost w.r.t. the control \f$\mathbf{u}\f$

  VectorXs g;    //!< Inequality constraint values

  MatrixXs Gx;   //!< Jacobian of the inequality constraint w.r.t. the state

                 //!< \f$\mathbf{x}\f$

  MatrixXs Gu;   //!< Jacobian of the inequality constraint w.r.t. the control

                 //!< \f$\mathbf{u}\f$

  VectorXs h;    //!< Equality constraint values

  MatrixXs Hx;   //!< Jacobian of the equality constraint w.r.t. the state

                 //!< \f$\mathbf{x}\f$

  MatrixXs Hu;   //!< Jacobian of the equality constraint w.r.t the control

                 //!< \f$\mathbf{u}\f$

};

}  // namespace crocoddyl

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

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

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

#include "crocoddyl/core/diff-action-base.hxx"

#endif  // CROCODDYL_CORE_DIFF_ACTION_BASE_HPP_