/**
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Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
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@file
@brief Definition of static IMU biases used for calibration
*/

#pragma once

#include <Eigen/Dense>

namespace basalt {

/// @brief Static calibration for accelerometer.
///
/// Calibrates axis scaling and misalignment and has 9 parameters \f$ [b_x,
/// b_y, b_z, s_1, s_2, s_3, s_4, s_5, s_6]^T \f$.
/// \f[
/// a_c = \begin{bmatrix} s_1 + 1 & 0 & 0 \\ s_2 & s_4 + 1 & 0 \\ s_3 & s_5 &
/// s_6 + 1 \\  \end{bmatrix} a_r -  \begin{bmatrix} b_x \\ b_y \\ b_z
/// \end{bmatrix}
/// \f] where  \f$ a_c \f$ is a calibrated measurement and \f$ a_r \f$ is a
/// raw measurement. When all elements are zero applying calibration results in
/// Identity mapping.
template <typename Scalar>
class CalibAccelBias {
 public:
  using Vec3 = Eigen::Matrix<Scalar, 3, 1>;
  using Mat33 = Eigen::Matrix<Scalar, 3, 3>;

  /// @brief Default constructor with zero initialization.
  inline CalibAccelBias() { accel_bias_full_.setZero(); }

  /// @brief  Set calibration to random values (used in unit-tests).
  inline void setRandom() {
    accel_bias_full_.setRandom();
    accel_bias_full_.template head<3>() /= 10;
    accel_bias_full_.template tail<6>() /= 100;
  }

  /// @brief Return const vector of parameters.
  /// See detailed description in \ref CalibAccelBias.
  inline const Eigen::Matrix<Scalar, 9, 1>& getParam() const {
    return accel_bias_full_;
  }

  /// @brief Return vector of parameters. See detailed description in \ref
  /// CalibAccelBias.
  inline Eigen::Matrix<Scalar, 9, 1>& getParam() { return accel_bias_full_; }

  /// @brief Increment the calibration vector
  ///
  /// @param inc increment vector
  inline void operator+=(const Eigen::Matrix<Scalar, 9, 1>& inc) {
    accel_bias_full_ += inc;
  }

  /// @brief Return bias vector and scale matrix. See detailed description in
  /// \ref CalibAccelBias.
  inline void getBiasAndScale(Vec3& accel_bias, Mat33& accel_scale) const {
    accel_bias = accel_bias_full_.template head<3>();

    accel_scale.setZero();
    accel_scale.col(0) = accel_bias_full_.template segment<3>(3);
    accel_scale(1, 1) = accel_bias_full_(6);
    accel_scale(2, 1) = accel_bias_full_(7);
    accel_scale(2, 2) = accel_bias_full_(8);
  }

  /// @brief Calibrate the measurement. See detailed description in
  /// \ref CalibAccelBias.
  ///
  /// @param raw_measurement
  /// @return calibrated measurement
  inline Vec3 getCalibrated(const Vec3& raw_measurement) const {
    Vec3 accel_bias;
    Mat33 accel_scale;

    getBiasAndScale(accel_bias, accel_scale);

    return (raw_measurement + accel_scale * raw_measurement - accel_bias);
  }

  /// @brief Invert calibration (used in unit-tests).
  ///
  /// @param calibrated_measurement
  /// @return raw measurement
  inline Vec3 invertCalibration(const Vec3& calibrated_measurement) const {
    Vec3 accel_bias;
    Mat33 accel_scale;

    getBiasAndScale(accel_bias, accel_scale);

    Mat33 accel_scale_inv =
        (Eigen::Matrix3d::Identity() + accel_scale).inverse();

    return accel_scale_inv * (calibrated_measurement + accel_bias);
  }

 private:
  Eigen::Matrix<Scalar, 9, 1> accel_bias_full_;
};

/// @brief Static calibration for gyroscope.
///
/// Calibrates rotation, axis scaling and misalignment and has 12 parameters \f$
/// [b_x, b_y, b_z, s_1, s_2, s_3, s_4, s_5, s_6, s_7, s_8, s_9]^T \f$. \f[
/// \omega_c = \begin{bmatrix} s_1 + 1 & s_4 & s_7 \\ s_2 & s_5 + 1 & s_8 \\ s_3
/// & s_6 & s_9 +1 \\  \end{bmatrix} \omega_r -  \begin{bmatrix} b_x \\ b_y
/// \\ b_z \end{bmatrix} \f] where  \f$ \omega_c \f$ is a calibrated measurement
/// and \f$ \omega_r \f$ is a raw measurement. When all elements are zero
/// applying calibration results in Identity mapping.
template <typename Scalar>
class CalibGyroBias {
 public:
  using Vec3 = Eigen::Matrix<Scalar, 3, 1>;
  using Mat33 = Eigen::Matrix<Scalar, 3, 3>;

  /// @brief Default constructor with zero initialization.
  inline CalibGyroBias() { gyro_bias_full_.setZero(); }

  /// @brief  Set calibration to random values (used in unit-tests).
  inline void setRandom() {
    gyro_bias_full_.setRandom();
    gyro_bias_full_.template head<3>() /= 10;
    gyro_bias_full_.template tail<9>() /= 100;
  }

  /// @brief Return const vector of parameters.
  /// See detailed description in \ref CalibGyroBias.
  inline const Eigen::Matrix<Scalar, 12, 1>& getParam() const {
    return gyro_bias_full_;
  }

  /// @brief Return vector of parameters.
  /// See detailed description in \ref CalibGyroBias.
  inline Eigen::Matrix<Scalar, 12, 1>& getParam() { return gyro_bias_full_; }

  /// @brief Increment the calibration vector
  ///
  /// @param inc increment vector
  inline void operator+=(const Eigen::Matrix<Scalar, 12, 1>& inc) {
    gyro_bias_full_ += inc;
  }

  /// @brief Return bias vector and scale matrix. See detailed description in
  /// \ref CalibGyroBias.
  inline void getBiasAndScale(Vec3& gyro_bias, Mat33& gyro_scale) const {
    gyro_bias = gyro_bias_full_.template head<3>();
    gyro_scale.col(0) = gyro_bias_full_.template segment<3>(3);
    gyro_scale.col(1) = gyro_bias_full_.template segment<3>(6);
    gyro_scale.col(2) = gyro_bias_full_.template segment<3>(9);
  }

  /// @brief Calibrate the measurement. See detailed description in
  /// \ref CalibGyroBias.
  ///
  /// @param raw_measurement
  /// @return calibrated measurement
  inline Vec3 getCalibrated(const Vec3& raw_measurement) const {
    Vec3 gyro_bias;
    Mat33 gyro_scale;

    getBiasAndScale(gyro_bias, gyro_scale);

    return (raw_measurement + gyro_scale * raw_measurement - gyro_bias);
  }

  /// @brief Invert calibration (used in unit-tests).
  ///
  /// @param calibrated_measurement
  /// @return raw measurement
  inline Vec3 invertCalibration(const Vec3& calibrated_measurement) const {
    Vec3 gyro_bias;
    Mat33 gyro_scale;

    getBiasAndScale(gyro_bias, gyro_scale);

    Mat33 gyro_scale_inv = (Eigen::Matrix3d::Identity() + gyro_scale).inverse();

    return gyro_scale_inv * (calibrated_measurement + gyro_bias);
  }

 private:
  Eigen::Matrix<Scalar, 12, 1> gyro_bias_full_;
};

}  // namespace basalt