AutoDiffVector.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_AUTODIFF_VECTOR_H
#define EIGEN_AUTODIFF_VECTOR_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

/* \class AutoDiffScalar
 * \brief A scalar type replacement with automatic differentation capability
 *
 * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
 *
 * This class represents a scalar value while tracking its respective derivatives.
 *
 * It supports the following list of global math function:
 *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
 *  - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
 *  - internal::conj, internal::real, internal::imag, numext::abs2.
 *
 * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
 * in that case, the expression template mechanism only occurs at the top Matrix level,
 * while derivatives are computed right away.
 *
 */
template <typename ValueType, typename JacobianType>
class AutoDiffVector {
 public:
  // typedef typename internal::traits<ValueType>::Scalar Scalar;
  typedef typename internal::traits<ValueType>::Scalar BaseScalar;
  typedef AutoDiffScalar<Matrix<BaseScalar, JacobianType::RowsAtCompileTime, 1> > ActiveScalar;
  typedef ActiveScalar Scalar;
  typedef AutoDiffScalar<typename JacobianType::ColXpr> CoeffType;
  typedef typename JacobianType::Index Index;

  inline AutoDiffVector() {}

  inline AutoDiffVector(const ValueType& values) : m_values(values) { m_jacobian.setZero(); }

  CoeffType operator[](Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
  const CoeffType operator[](Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }

  CoeffType operator()(Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
  const CoeffType operator()(Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }

  CoeffType coeffRef(Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
  const CoeffType coeffRef(Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }

  Index size() const { return m_values.size(); }

  // FIXME here we could return an expression of the sum
  Scalar sum() const { /*std::cerr << "sum \n\n";*/ /*std::cerr << m_jacobian.rowwise().sum() << "\n\n";*/
    return Scalar(m_values.sum(), m_jacobian.rowwise().sum());
  }

  inline AutoDiffVector(const ValueType& values, const JacobianType& jac) : m_values(values), m_jacobian(jac) {}

  template <typename OtherValueType, typename OtherJacobianType>
  inline AutoDiffVector(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
      : m_values(other.values()), m_jacobian(other.jacobian()) {}

  inline AutoDiffVector(const AutoDiffVector& other) : m_values(other.values()), m_jacobian(other.jacobian()) {}

  template <typename OtherValueType, typename OtherJacobianType>
  inline AutoDiffVector& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) {
    m_values = other.values();
    m_jacobian = other.jacobian();
    return *this;
  }

  inline AutoDiffVector& operator=(const AutoDiffVector& other) {
    m_values = other.values();
    m_jacobian = other.jacobian();
    return *this;
  }

  inline const ValueType& values() const { return m_values; }
  inline ValueType& values() { return m_values; }

  inline const JacobianType& jacobian() const { return m_jacobian; }
  inline JacobianType& jacobian() { return m_jacobian; }

  template <typename OtherValueType, typename OtherJacobianType>
  inline const AutoDiffVector<
      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>, ValueType, OtherValueType>::Type,
      typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>, JacobianType, OtherJacobianType>::Type>
  operator+(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) const {
    return AutoDiffVector<
        typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>, ValueType, OtherValueType>::Type,
        typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>, JacobianType, OtherJacobianType>::Type>(
        m_values + other.values(), m_jacobian + other.jacobian());
  }

  template <typename OtherValueType, typename OtherJacobianType>
  inline AutoDiffVector& operator+=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) {
    m_values += other.values();
    m_jacobian += other.jacobian();
    return *this;
  }

  template <typename OtherValueType, typename OtherJacobianType>
  inline const AutoDiffVector<
      typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>, ValueType, OtherValueType>::Type,
      typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>, JacobianType, OtherJacobianType>::Type>
  operator-(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) const {
    return AutoDiffVector<
        typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>, ValueType, OtherValueType>::Type,
        typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>, JacobianType, OtherJacobianType>::Type>(
        m_values - other.values(), m_jacobian - other.jacobian());
  }

  template <typename OtherValueType, typename OtherJacobianType>
  inline AutoDiffVector& operator-=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) {
    m_values -= other.values();
    m_jacobian -= other.jacobian();
    return *this;
  }

  inline const AutoDiffVector<typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,
                              typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type>
  operator-() const {
    return AutoDiffVector<typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,
                          typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type>(
        -m_values, -m_jacobian);
  }

  inline const AutoDiffVector<typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
                              typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>
  operator*(const BaseScalar& other) const {
    return AutoDiffVector<typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
                          typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>(
        m_values * other, m_jacobian * other);
  }

  friend inline const AutoDiffVector<
      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
      typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>
  operator*(const Scalar& other, const AutoDiffVector& v) {
    return AutoDiffVector<typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
                          typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>(
        v.values() * other, v.jacobian() * other);
  }

  //     template<typename OtherValueType,typename OtherJacobianType>
  //     inline const AutoDiffVector<
  //       CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>
  //       CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
  //         CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,
  //         CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >
  //     operator*(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
  //     {
  //       return AutoDiffVector<
  //         CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>
  //         CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
  //           CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,
  //           CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >(
  //             m_values.cwise() * other.values(),
  //             (m_jacobian * other.values()) + (m_values * other.jacobian()));
  //     }

  inline AutoDiffVector& operator*=(const Scalar& other) {
    m_values *= other;
    m_jacobian *= other;
    return *this;
  }

  template <typename OtherValueType, typename OtherJacobianType>
  inline AutoDiffVector& operator*=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other) {
    *this = *this * other;
    return *this;
  }

 protected:
  ValueType m_values;
  JacobianType m_jacobian;
};

}  // namespace Eigen

#endif  // EIGEN_AUTODIFF_VECTOR_H