| // 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_SCALAR_H |
| #define EIGEN_AUTODIFF_SCALAR_H |
| |
| // IWYU pragma: private |
| #include "./InternalHeaderCheck.h" |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| template <typename DerivativeType, bool Enable> |
| struct auto_diff_special_op; |
| |
| template <typename DerivativeType, typename OtherDerivativeType, typename EnableIf = void> |
| struct maybe_coherent_pad_helper { |
| static constexpr int SizeAtCompileTime = |
| max_size_prefer_dynamic(DerivativeType::SizeAtCompileTime, OtherDerivativeType::SizeAtCompileTime); |
| using type = CoherentPadOp<DerivativeType, SizeAtCompileTime>; |
| static type pad(const DerivativeType& x, const OtherDerivativeType& y) { |
| // CoherentPadOp uses variable_if_dynamic<SizeAtCompileTime>. In this case, `SizeAtCompileTime` might |
| // by Dynamic, so we need to take the runtime maximum of x, y. |
| return CoherentPadOp<DerivativeType, SizeAtCompileTime>(x, numext::maxi(x.size(), y.size())); |
| } |
| }; |
| |
| // Both are fixed-sized and equal, don't need to pad. |
| // Both are fixed-size and this is larger than other, don't need to pad. |
| template <typename DerivativeType, typename OtherDerivativeType> |
| struct maybe_coherent_pad_helper< |
| DerivativeType, OtherDerivativeType, |
| std::enable_if_t<DerivativeType::SizeAtCompileTime >= OtherDerivativeType::SizeAtCompileTime && |
| DerivativeType::SizeAtCompileTime != Dynamic && |
| OtherDerivativeType::SizeAtCompileTime != Dynamic>> { |
| using type = const DerivativeType&; |
| static const DerivativeType& pad(const DerivativeType& x, const OtherDerivativeType& /*y*/) { return x; } |
| }; |
| |
| template <typename DerivativeType, typename OtherDerivativeType> |
| typename maybe_coherent_pad_helper<DerivativeType, OtherDerivativeType>::type MaybeCoherentPad( |
| const DerivativeType& x, const OtherDerivativeType& y) { |
| return maybe_coherent_pad_helper<DerivativeType, OtherDerivativeType>::pad(x, y); |
| } |
| |
| template <typename Op, typename LhsDerivativeType, typename RhsDerivativeType> |
| auto MakeCoherentCwiseBinaryOp(const LhsDerivativeType& x, const RhsDerivativeType& y, Op op = Op()) { |
| const auto& lhs = MaybeCoherentPad(x, y); |
| const auto& rhs = MaybeCoherentPad(y, x); |
| return CwiseBinaryOp<Op, remove_all_t<decltype(lhs)>, remove_all_t<decltype(rhs)>>(lhs, rhs, op); |
| } |
| |
| } // namespace internal |
| |
| template <typename DerivativeType> |
| class AutoDiffScalar; |
| |
| template <typename NewDerType> |
| inline AutoDiffScalar<NewDerType> MakeAutoDiffScalar(const typename NewDerType::Scalar& value, const NewDerType& der) { |
| return AutoDiffScalar<NewDerType>(value, der); |
| } |
| |
| /** \class AutoDiffScalar |
| * \brief A scalar type replacement with automatic differentiation capability |
| * |
| * \param DerivativeType the vector type used to store/represent the derivatives. The base scalar type |
| * as well as the number of derivatives to compute are determined from this type. |
| * Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf |
| * if the number of derivatives is not known at compile time, and/or, the number |
| * of derivatives is large. |
| * Note that DerivativeType can also be a reference (e.g., \c VectorXf&) to wrap a |
| * existing vector into an AutoDiffScalar. |
| * Finally, DerivativeType can also be any Eigen compatible expression. |
| * |
| * This class represents a scalar value while tracking its respective derivatives using Eigen's expression |
| * template mechanism. |
| * |
| * 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 DerivativeType> |
| class AutoDiffScalar |
| : public internal::auto_diff_special_op< |
| DerivativeType, !internal::is_same<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar, |
| typename NumTraits<typename internal::traits< |
| internal::remove_all_t<DerivativeType>>::Scalar>::Real>::value> { |
| public: |
| typedef internal::auto_diff_special_op< |
| DerivativeType, |
| !internal::is_same< |
| typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar, |
| typename NumTraits<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar>::Real>::value> |
| Base; |
| typedef internal::remove_all_t<DerivativeType> DerType; |
| typedef typename internal::traits<DerType>::Scalar Scalar; |
| typedef typename NumTraits<Scalar>::Real Real; |
| |
| using Base::operator+; |
| using Base::operator*; |
| |
| /** Default constructor without any initialization. */ |
| AutoDiffScalar() {} |
| |
| /** Constructs an active scalar from its \a value, |
| and initializes the \a nbDer derivatives such that it corresponds to the \a derNumber -th variable */ |
| AutoDiffScalar(const Scalar& value, int nbDer, int derNumber) : m_value(value), m_derivatives(DerType::Zero(nbDer)) { |
| m_derivatives.coeffRef(derNumber) = Scalar(1); |
| } |
| |
| /** Conversion from a scalar constant to an active scalar. |
| * The derivatives are set to zero. */ |
| /*explicit*/ AutoDiffScalar(const Real& value) : m_value(value) { |
| if (m_derivatives.size() > 0) m_derivatives.setZero(); |
| } |
| |
| /** Constructs an active scalar from its \a value and derivatives \a der */ |
| AutoDiffScalar(const Scalar& value, const DerType& der) : m_value(value), m_derivatives(der) {} |
| |
| template <typename OtherDerType> |
| AutoDiffScalar( |
| const AutoDiffScalar<OtherDerType>& other |
| #ifndef EIGEN_PARSED_BY_DOXYGEN |
| , |
| std::enable_if_t< |
| internal::is_same<Scalar, typename internal::traits<internal::remove_all_t<OtherDerType>>::Scalar>::value && |
| internal::is_convertible<OtherDerType, DerType>::value, |
| void*> = 0 |
| #endif |
| ) |
| : m_value(other.value()), m_derivatives(other.derivatives()) { |
| } |
| |
| friend std::ostream& operator<<(std::ostream& s, const AutoDiffScalar& a) { return s << a.value(); } |
| |
| AutoDiffScalar(const AutoDiffScalar& other) : m_value(other.value()), m_derivatives(other.derivatives()) {} |
| |
| template <typename OtherDerType> |
| inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other) { |
| m_value = other.value(); |
| m_derivatives = other.derivatives(); |
| return *this; |
| } |
| |
| inline AutoDiffScalar& operator=(const AutoDiffScalar& other) { |
| m_value = other.value(); |
| m_derivatives = other.derivatives(); |
| return *this; |
| } |
| |
| inline AutoDiffScalar& operator=(const Scalar& other) { |
| m_value = other; |
| if (m_derivatives.size() > 0) m_derivatives.setZero(); |
| return *this; |
| } |
| |
| // inline operator const Scalar& () const { return m_value; } |
| // inline operator Scalar& () { return m_value; } |
| |
| inline const Scalar& value() const { return m_value; } |
| inline Scalar& value() { return m_value; } |
| |
| inline const DerType& derivatives() const { return m_derivatives; } |
| inline DerType& derivatives() { return m_derivatives; } |
| |
| inline bool operator<(const Scalar& other) const { return m_value < other; } |
| inline bool operator<=(const Scalar& other) const { return m_value <= other; } |
| inline bool operator>(const Scalar& other) const { return m_value > other; } |
| inline bool operator>=(const Scalar& other) const { return m_value >= other; } |
| inline bool operator==(const Scalar& other) const { return m_value == other; } |
| inline bool operator!=(const Scalar& other) const { return m_value != other; } |
| |
| friend inline bool operator<(const Scalar& a, const AutoDiffScalar& b) { return a < b.value(); } |
| friend inline bool operator<=(const Scalar& a, const AutoDiffScalar& b) { return a <= b.value(); } |
| friend inline bool operator>(const Scalar& a, const AutoDiffScalar& b) { return a > b.value(); } |
| friend inline bool operator>=(const Scalar& a, const AutoDiffScalar& b) { return a >= b.value(); } |
| friend inline bool operator==(const Scalar& a, const AutoDiffScalar& b) { return a == b.value(); } |
| friend inline bool operator!=(const Scalar& a, const AutoDiffScalar& b) { return a != b.value(); } |
| |
| template <typename OtherDerType> |
| inline bool operator<(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value < b.value(); |
| } |
| template <typename OtherDerType> |
| inline bool operator<=(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value <= b.value(); |
| } |
| template <typename OtherDerType> |
| inline bool operator>(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value > b.value(); |
| } |
| template <typename OtherDerType> |
| inline bool operator>=(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value >= b.value(); |
| } |
| template <typename OtherDerType> |
| inline bool operator==(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value == b.value(); |
| } |
| template <typename OtherDerType> |
| inline bool operator!=(const AutoDiffScalar<OtherDerType>& b) const { |
| return m_value != b.value(); |
| } |
| |
| inline AutoDiffScalar<DerType&> operator+(const Scalar& other) const { |
| return AutoDiffScalar<DerType&>(m_value + other, m_derivatives); |
| } |
| |
| friend inline AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b) { |
| return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); |
| } |
| |
| // inline const AutoDiffScalar<DerType&> operator+(const Real& other) const |
| // { |
| // return AutoDiffScalar<DerType&>(m_value + other, m_derivatives); |
| // } |
| |
| // friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar& b) |
| // { |
| // return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); |
| // } |
| |
| inline AutoDiffScalar& operator+=(const Scalar& other) { |
| value() += other; |
| return *this; |
| } |
| |
| template <typename OtherDerType> |
| inline auto operator+(const AutoDiffScalar<OtherDerType>& other) const { |
| return MakeAutoDiffScalar( |
| m_value + other.value(), |
| internal::MakeCoherentCwiseBinaryOp<internal::scalar_sum_op<Scalar>>(m_derivatives, other.derivatives())); |
| } |
| |
| template <typename OtherDerType> |
| inline AutoDiffScalar& operator+=(const AutoDiffScalar<OtherDerType>& other) { |
| (*this) = (*this) + other; |
| return *this; |
| } |
| |
| inline AutoDiffScalar<DerType&> operator-(const Scalar& b) const { |
| return AutoDiffScalar<DerType&>(m_value - b, m_derivatives); |
| } |
| |
| friend inline AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType>> operator-( |
| const Scalar& a, const AutoDiffScalar& b) { |
| return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType>>(a - b.value(), |
| -b.derivatives()); |
| } |
| |
| inline AutoDiffScalar& operator-=(const Scalar& other) { |
| value() -= other; |
| return *this; |
| } |
| |
| template <typename OtherDerType> |
| inline auto operator-(const AutoDiffScalar<OtherDerType>& other) const { |
| return MakeAutoDiffScalar(m_value - other.value(), |
| internal::MakeCoherentCwiseBinaryOp<internal::scalar_difference_op<Scalar>>( |
| m_derivatives, other.derivatives())); |
| } |
| |
| template <typename OtherDerType> |
| inline AutoDiffScalar& operator-=(const AutoDiffScalar<OtherDerType>& other) { |
| *this = *this - other; |
| return *this; |
| } |
| |
| inline AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType>> operator-() const { |
| return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType>>(-m_value, -m_derivatives); |
| } |
| |
| inline auto operator*(const Scalar& other) const { |
| return MakeAutoDiffScalar(m_value * other, m_derivatives * other); |
| } |
| |
| friend inline auto operator*(const Scalar& other, const AutoDiffScalar& a) { |
| return MakeAutoDiffScalar(a.value() * other, a.derivatives() * other); |
| } |
| |
| // inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > |
| // operator*(const Real& other) const |
| // { |
| // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( |
| // m_value * other, |
| // (m_derivatives * other)); |
| // } |
| // |
| // friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > |
| // operator*(const Real& other, const AutoDiffScalar& a) |
| // { |
| // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( |
| // a.value() * other, |
| // a.derivatives() * other); |
| // } |
| |
| inline auto operator/(const Scalar& other) const { |
| return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1) / other))); |
| } |
| |
| friend inline auto operator/(const Scalar& other, const AutoDiffScalar& a) { |
| return MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value() * a.value()))); |
| } |
| |
| // inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > |
| // operator/(const Real& other) const |
| // { |
| // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( |
| // m_value / other, |
| // (m_derivatives * (Real(1)/other))); |
| // } |
| // |
| // friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type > |
| // operator/(const Real& other, const AutoDiffScalar& a) |
| // { |
| // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >( |
| // other / a.value(), |
| // a.derivatives() * (-Real(1)/other)); |
| // } |
| |
| template <typename OtherDerType> |
| inline auto operator/(const AutoDiffScalar<OtherDerType>& other) const { |
| return MakeAutoDiffScalar(m_value / other.value(), |
| internal::MakeCoherentCwiseBinaryOp<internal::scalar_difference_op<Scalar>>( |
| m_derivatives * other.value(), (other.derivatives() * m_value)) * |
| (Scalar(1) / (other.value() * other.value()))); |
| } |
| |
| template <typename OtherDerType> |
| inline auto operator*(const AutoDiffScalar<OtherDerType>& other) const { |
| return MakeAutoDiffScalar(m_value * other.value(), |
| internal::MakeCoherentCwiseBinaryOp<internal::scalar_sum_op<Scalar>>( |
| m_derivatives * other.value(), other.derivatives() * m_value)); |
| } |
| |
| inline AutoDiffScalar& operator*=(const Scalar& other) { |
| *this = *this * other; |
| return *this; |
| } |
| |
| template <typename OtherDerType> |
| inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other) { |
| *this = *this * other; |
| return *this; |
| } |
| |
| inline AutoDiffScalar& operator/=(const Scalar& other) { |
| *this = *this / other; |
| return *this; |
| } |
| |
| template <typename OtherDerType> |
| inline AutoDiffScalar& operator/=(const AutoDiffScalar<OtherDerType>& other) { |
| *this = *this / other; |
| return *this; |
| } |
| |
| protected: |
| Scalar m_value; |
| DerType m_derivatives; |
| }; |
| |
| namespace internal { |
| |
| template <typename DerivativeType> |
| struct auto_diff_special_op<DerivativeType, true> |
| // : auto_diff_scalar_op<DerivativeType, typename NumTraits<Scalar>::Real, |
| // is_same<Scalar,typename NumTraits<Scalar>::Real>::value> |
| { |
| typedef remove_all_t<DerivativeType> DerType; |
| typedef typename traits<DerType>::Scalar Scalar; |
| typedef typename NumTraits<Scalar>::Real Real; |
| |
| // typedef auto_diff_scalar_op<DerivativeType, typename NumTraits<Scalar>::Real, |
| // is_same<Scalar,typename NumTraits<Scalar>::Real>::value> Base; |
| |
| // using Base::operator+; |
| // using Base::operator+=; |
| // using Base::operator-; |
| // using Base::operator-=; |
| // using Base::operator*; |
| // using Base::operator*=; |
| |
| const AutoDiffScalar<DerivativeType>& derived() const { |
| return *static_cast<const AutoDiffScalar<DerivativeType>*>(this); |
| } |
| AutoDiffScalar<DerivativeType>& derived() { return *static_cast<AutoDiffScalar<DerivativeType>*>(this); } |
| |
| inline AutoDiffScalar<DerType&> operator+(const Real& other) const { |
| return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives()); |
| } |
| |
| friend inline AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<DerivativeType>& b) { |
| return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives()); |
| } |
| |
| inline AutoDiffScalar<DerivativeType>& operator+=(const Real& other) { |
| derived().value() += other; |
| return derived(); |
| } |
| |
| inline AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar, Real>>, DerType>::Type> operator*( |
| const Real& other) const { |
| return AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar, Real>>, DerType>::Type>( |
| derived().value() * other, derived().derivatives() * other); |
| } |
| |
| friend inline AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real, Scalar>>, DerType>::Type> |
| operator*(const Real& other, const AutoDiffScalar<DerivativeType>& a) { |
| return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real, Scalar>>, DerType>::Type>( |
| a.value() * other, a.derivatives() * other); |
| } |
| |
| inline AutoDiffScalar<DerivativeType>& operator*=(const Scalar& other) { |
| *this = *this * other; |
| return derived(); |
| } |
| }; |
| |
| template <typename DerivativeType> |
| struct auto_diff_special_op<DerivativeType, false> { |
| void operator*() const; |
| void operator-() const; |
| void operator+() const; |
| }; |
| |
| } // end namespace internal |
| |
| template <typename DerType, typename BinOp> |
| struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>, typename DerType::Scalar, BinOp> { |
| typedef AutoDiffScalar<DerType> ReturnType; |
| }; |
| |
| template <typename DerType, typename BinOp> |
| struct ScalarBinaryOpTraits<typename DerType::Scalar, AutoDiffScalar<DerType>, BinOp> { |
| typedef AutoDiffScalar<DerType> ReturnType; |
| }; |
| |
| // The following is an attempt to let Eigen's known about expression template, but that's more tricky! |
| |
| // template<typename DerType, typename BinOp> |
| // struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,AutoDiffScalar<DerType>, BinOp> |
| // { |
| // enum { Defined = 1 }; |
| // typedef AutoDiffScalar<typename DerType::PlainObject> ReturnType; |
| // }; |
| // |
| // template<typename DerType1,typename DerType2, typename BinOp> |
| // struct ScalarBinaryOpTraits<AutoDiffScalar<DerType1>,AutoDiffScalar<DerType2>, BinOp> |
| // { |
| // enum { Defined = 1 };//internal::is_same<typename DerType1::Scalar,typename DerType2::Scalar>::value }; |
| // typedef AutoDiffScalar<typename DerType1::PlainObject> ReturnType; |
| // }; |
| |
| #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC, CODE) \ |
| template <typename DerType> \ |
| inline auto FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \ |
| using namespace Eigen; \ |
| typedef typename Eigen::internal::traits<Eigen::internal::remove_all_t<DerType>>::Scalar Scalar; \ |
| EIGEN_UNUSED_VARIABLE(sizeof(Scalar)); \ |
| CODE; \ |
| } |
| |
| template <typename DerType> |
| struct CleanedUpDerType { |
| typedef AutoDiffScalar<typename Eigen::internal::remove_all_t<DerType>::PlainObject> type; |
| }; |
| |
| template <typename DerType> |
| inline const AutoDiffScalar<DerType>& conj(const AutoDiffScalar<DerType>& x) { |
| return x; |
| } |
| template <typename DerType> |
| inline const AutoDiffScalar<DerType>& real(const AutoDiffScalar<DerType>& x) { |
| return x; |
| } |
| template <typename DerType> |
| inline typename DerType::Scalar imag(const AutoDiffScalar<DerType>&) { |
| return 0.; |
| } |
| template <typename DerType, typename T> |
| inline typename CleanedUpDerType<DerType>::type(min)(const AutoDiffScalar<DerType>& x, const T& y) { |
| typedef typename CleanedUpDerType<DerType>::type ADS; |
| return (x <= y ? ADS(x) : ADS(y)); |
| } |
| template <typename DerType, typename T> |
| inline typename CleanedUpDerType<DerType>::type(max)(const AutoDiffScalar<DerType>& x, const T& y) { |
| typedef typename CleanedUpDerType<DerType>::type ADS; |
| return (x >= y ? ADS(x) : ADS(y)); |
| } |
| template <typename DerType, typename T> |
| inline typename CleanedUpDerType<DerType>::type(min)(const T& x, const AutoDiffScalar<DerType>& y) { |
| typedef typename CleanedUpDerType<DerType>::type ADS; |
| return (x < y ? ADS(x) : ADS(y)); |
| } |
| template <typename DerType, typename T> |
| inline typename CleanedUpDerType<DerType>::type(max)(const T& x, const AutoDiffScalar<DerType>& y) { |
| typedef typename CleanedUpDerType<DerType>::type ADS; |
| return (x > y ? ADS(x) : ADS(y)); |
| } |
| template <typename DerType> |
| inline |
| typename CleanedUpDerType<DerType>::type(min)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) { |
| return (x.value() < y.value() ? x : y); |
| } |
| template <typename DerType> |
| inline |
| typename CleanedUpDerType<DerType>::type(max)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) { |
| return (x.value() >= y.value() ? x : y); |
| } |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs, using std::abs; |
| return Eigen::MakeAutoDiffScalar(abs(x.value()), |
| x.derivatives() * (x.value() < 0 ? -1 : 1));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2, using numext::abs2; |
| return Eigen::MakeAutoDiffScalar(abs2(x.value()), |
| x.derivatives() * (Scalar(2) * x.value()));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt, using std::sqrt; Scalar sqrtx = sqrt(x.value()); |
| return Eigen::MakeAutoDiffScalar(sqrtx, x.derivatives() * (Scalar(0.5) / sqrtx));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos, using std::cos; using std::sin; |
| return Eigen::MakeAutoDiffScalar(cos(x.value()), |
| x.derivatives() * (-sin(x.value())));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin, using std::sin; using std::cos; |
| return Eigen::MakeAutoDiffScalar(sin(x.value()), x.derivatives() * cos(x.value()));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp, using std::exp; Scalar expx = exp(x.value()); |
| return Eigen::MakeAutoDiffScalar(expx, x.derivatives() * expx);) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log, using std::log; |
| return Eigen::MakeAutoDiffScalar(log(x.value()), |
| x.derivatives() * (Scalar(1) / x.value()));) |
| |
| template <typename DerType> |
| inline auto pow(const Eigen::AutoDiffScalar<DerType>& x, |
| const typename internal::traits<internal::remove_all_t<DerType>>::Scalar& y) { |
| using namespace Eigen; |
| using std::pow; |
| return Eigen::MakeAutoDiffScalar(pow(x.value(), y), x.derivatives() * (y * pow(x.value(), y - 1))); |
| } |
| |
| template <typename DerTypeA, typename DerTypeB> |
| inline AutoDiffScalar<Matrix<typename internal::traits<internal::remove_all_t<DerTypeA>>::Scalar, Dynamic, 1>> atan2( |
| const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b) { |
| using std::atan2; |
| typedef typename internal::traits<internal::remove_all_t<DerTypeA>>::Scalar Scalar; |
| typedef AutoDiffScalar<Matrix<Scalar, Dynamic, 1>> PlainADS; |
| PlainADS ret; |
| ret.value() = atan2(a.value(), b.value()); |
| |
| Scalar squared_hypot = a.value() * a.value() + b.value() * b.value(); |
| |
| // if (squared_hypot==0) the derivation is undefined and the following results in a NaN: |
| ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot; |
| |
| return ret; |
| } |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan, using std::tan; using std::cos; return Eigen::MakeAutoDiffScalar( |
| tan(x.value()), x.derivatives() * (Scalar(1) / numext::abs2(cos(x.value()))));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin, using std::sqrt; using std::asin; return Eigen::MakeAutoDiffScalar( |
| asin(x.value()), |
| x.derivatives() * (Scalar(1) / sqrt(1 - numext::abs2(x.value()))));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos, using std::sqrt; using std::acos; return Eigen::MakeAutoDiffScalar( |
| acos(x.value()), |
| x.derivatives() * (Scalar(-1) / sqrt(1 - numext::abs2(x.value()))));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY( |
| tanh, using std::cosh; using std::tanh; |
| return Eigen::MakeAutoDiffScalar(tanh(x.value()), x.derivatives() * (Scalar(1) / numext::abs2(cosh(x.value()))));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sinh, using std::sinh; using std::cosh; |
| return Eigen::MakeAutoDiffScalar(sinh(x.value()), |
| x.derivatives() * cosh(x.value()));) |
| |
| EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cosh, using std::sinh; using std::cosh; |
| return Eigen::MakeAutoDiffScalar(cosh(x.value()), |
| x.derivatives() * sinh(x.value()));) |
| |
| #undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY |
| |
| template <typename DerType> |
| struct NumTraits<AutoDiffScalar<DerType>> |
| : NumTraits<typename NumTraits<typename internal::remove_all_t<DerType>::Scalar>::Real> { |
| typedef internal::remove_all_t<DerType> DerTypeCleaned; |
| typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerTypeCleaned::Scalar>::Real, |
| DerTypeCleaned::RowsAtCompileTime, DerTypeCleaned::ColsAtCompileTime, 0, |
| DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime>> |
| Real; |
| typedef AutoDiffScalar<DerType> NonInteger; |
| typedef AutoDiffScalar<DerType> Nested; |
| typedef typename NumTraits<typename DerTypeCleaned::Scalar>::Literal Literal; |
| enum { RequireInitialization = 1 }; |
| }; |
| |
| namespace internal { |
| template <typename DerivativeType> |
| struct is_identically_zero_impl<AutoDiffScalar<DerivativeType>> { |
| static inline bool run(const AutoDiffScalar<DerivativeType>& s) { |
| const DerivativeType& derivatives = s.derivatives(); |
| for (int i = 0; i < derivatives.size(); ++i) { |
| if (!numext::is_exactly_zero(derivatives[i])) { |
| return false; |
| } |
| } |
| return numext::is_exactly_zero(s.value()); |
| } |
| }; |
| } // namespace internal |
| } // namespace Eigen |
| |
| namespace std { |
| |
| template <typename T> |
| class numeric_limits<Eigen::AutoDiffScalar<T>> : public numeric_limits<typename T::Scalar> {}; |
| |
| template <typename T> |
| class numeric_limits<Eigen::AutoDiffScalar<T&>> : public numeric_limits<typename T::Scalar> {}; |
| |
| } // namespace std |
| |
| #endif // EIGEN_AUTODIFF_SCALAR_H |
