autodiff/cppad/math/quaternion.hpp

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//
// Copyright (c) 2019-2020 INRIA CNRS
//

#ifndef __pinocchio_autodiff_cppad_math_quaternion_hpp__
#define __pinocchio_autodiff_cppad_math_quaternion_hpp__

#include "pinocchio/math/quaternion.hpp"

namespace pinocchio
{
  namespace quaternion
  {
    namespace internal
    {
      
      template<typename _Scalar>
      struct quaternionbase_assign_impl<CppAD::AD<_Scalar>, false >
      {
        typedef _Scalar Scalar;
        typedef CppAD::AD<Scalar> ADScalar;
        template<typename Matrix3, typename QuaternionDerived>
        static inline void run(Eigen::QuaternionBase<QuaternionDerived> & q,
                               const Matrix3 & mat)
        {
          typedef typename Eigen::internal::traits<QuaternionDerived>::Coefficients QuatCoefficients;
          
          typedef typename PINOCCHIO_EIGEN_PLAIN_TYPE(QuatCoefficients) QuatCoefficientsPlainType;
          typedef Eigen::Quaternion<ADScalar,QuatCoefficientsPlainType::Options> QuaternionPlain;
          QuaternionPlain quat_t_positive;
          
          ADScalar t = mat.trace();
          quaternionbase_assign_impl_if_t_positive::run(t,quat_t_positive,mat);
          
          QuaternionPlain quat_t_negative_0, quat_t_negative_1, quat_t_negative_2;
          
          quaternionbase_assign_impl_if_t_negative<0>::run(t,quat_t_negative_0,mat);
          quaternionbase_assign_impl_if_t_negative<1>::run(t,quat_t_negative_1,mat);
          quaternionbase_assign_impl_if_t_negative<2>::run(t,quat_t_negative_2,mat);
          
          // Build the expression graph          
          for(Eigen::DenseIndex k = 0; k < 4; ++k)
          {
            ADScalar t_is_negative_cond1 = CppAD::CondExpGt<Scalar>(mat.coeff(1,1), mat.coeff(0,0),
                                                         quat_t_negative_1.coeffs().coeff(k),
                                                         quat_t_negative_0.coeffs().coeff(k));

            ADScalar t_is_negative_cond2 = CppAD::CondExpGt<Scalar>(mat.coeff(2,2), mat.coeff(0,0),
                                                                    quat_t_negative_2.coeffs().coeff(k),
                                                                    CppAD::CondExpGt<Scalar>(mat.coeff(1,1), mat.coeff(0,0),
                                                                                             CppAD::CondExpGt<Scalar>(mat.coeff(2,2),  mat.coeff(1,1),
                                                                                                                      quat_t_negative_2.coeffs().coeff(k),
                                                                                                                      t_is_negative_cond1),
                                                                                             t_is_negative_cond1));            
            q.coeffs().coeffRef(k) = CppAD::CondExpGt<Scalar>(t,ADScalar(0),
                                                              quat_t_positive.coeffs().coeff(k),
                                                              t_is_negative_cond2);
          }
        }
      };
      
    } // namespace internal
    
  } // namespace quaternion
  
} // namespace pinocchio

#endif // ifndef __pinocchio_autodiff_casadi_math_quaternion_hpp__