/*
 * Copyright (C) 2020 Open Source Robotics Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
*/
#ifndef GZ_MATH_GAUSSMARKOVPROCESS_HH_
#define GZ_MATH_GAUSSMARKOVPROCESS_HH_

#include <chrono>
#include <gz/math/Export.hh>
#include <gz/math/config.hh>
#include <gz/utils/ImplPtr.hh>

namespace gz::math
{
  // Use a steady clock
  using clock = std::chrono::steady_clock;

  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  /** \class GaussMarkovProcess GaussMarkovProcess.hh\
   * gz/math/GaussMarkovProcess.hh
   **/
  /// \brief Implementation of a stationary gauss-markov process, also
  /// known as a Ornstein Ulenbeck process.
  ///
  /// See the Update(const clock::duration &) for details on the forumla
  /// used to update the process.
  ///
  /// ## Example usage
  ///
  /// \snippet examples/gauss_markov_process_example.cc complete
  class GZ_MATH_VISIBLE GaussMarkovProcess
  {
    // Default constructor. This sets all the parameters to zero.
    public: GaussMarkovProcess();

    /// \brief Create a process with the provided process parameters.
    /// This will also call Set(), and in turn Reset().
    /// \param[in] _start The start value of the process.
    /// \param[in] _theta The theta (\f$\theta\f$) parameter. A value of
    /// zero will be used if this parameter is negative.
    /// \param[in] _mu The mu (\f$\mu\f$) parameter.
    /// \param[in] _sigma The sigma (\f$\sigma\f$) parameter. A value of
    /// zero will be used if this parameter is negative.
    /// \sa Update(const clock::duration &)
    public: GaussMarkovProcess(double _start, double _theta, double _mu,
                double _sigma);

    /// \brief Set the process parameters. This will also call Reset().
    /// \param[in] _start The start value of the process.
    /// \param[in] _theta The theta (\f$\theta\f$) parameter.
    /// \param[in] _mu The mu (\f$\mu\f$) parameter.
    /// \param[in] _sigma The sigma (\f$\sigma\f$) parameter.
    /// \sa Update(const clock::duration &)
    public: void Set(double _start, double _theta, double _mu, double _sigma);

    /// \brief Get the start value.
    /// \return The start value.
    /// \sa Set(double, double, double, double)
    public: double Start() const;

    /// \brief Get the current process value.
    /// \return The value of the process.
    public: double Value() const;

    /// \brief Get the theta (\f$\theta\f$) value.
    /// \return The theta value.
    /// \sa Set(double, double, double, double)
    public: double Theta() const;

    /// \brief Get the mu (\f$\mu\f$) value.
    /// \return The mu value.
    /// \sa Set(double, double, double, double)
    public: double Mu() const;

    /// \brief Get the sigma (\f$\sigma\f$) value.
    /// \return The sigma value.
    /// \sa Set(double, double, double, double)
    public: double Sigma() const;

    /// \brief Reset the process. This will set the current process value
    /// to the start value.
    public: void Reset();

    /// \brief Update the process and get the new value.
    ///
    /// The following equation is computed:
    ///
    /// \f$x_{t+1} += \theta * (\mu - x_t) * dt + \sigma * dW_t\f$
    ///
    /// where
    ///
    ///   * \f$\theta, \mu, \sigma\f$ are parameters specified by the
    ///     user. In order, the parameters are theta, mu, and sigma. Theta
    ///     and sigma must be greater than or equal to zero. You can think
    ///     of mu as representing the mean or equilibrium value, sigma as the
    ///     degree of volatility, and theta as the rate by which changes
    ///     dissipate and revert towards the mean.
    ///   * \f$dt\f$ is the time step in seconds.
    ///   * \f$dW_t\f$ is a random number drawm from a normal distribution
    ///     with mean of zero and variance of 1.
    ///   * \f$x_t\f$ is the current value of the Gauss-Markov process
    ///   * \f$x_{t+1}\f$ is the new value of the Gauss-Markvov process
    ///
    /// See also: https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process
    ///
    /// This implementation include a drift parameter, mu. In financial
    /// mathematics, this is known as a Vasicek model.
    ///
    /// \param[in] _dt Length of the timestep after which a new sample
    /// should be taken.
    /// \return The new value of this process.
    public: double Update(const clock::duration &_dt);

    public: double Update(double _dt);

    /// \brief Private data pointer.
    GZ_UTILS_IMPL_PTR(dataPtr)
  };
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_GAUSSMARKOVPROCESS_HH_
