// 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
namespace Eigen {
namespace internal {
template<typename A, typename B>
struct make_coherent_impl {
static void run(A&, B&) {}
};
// resize a to match b is a.size()==0, and conversely.
template<typename A, typename B>
void make_coherent(const A& a, const B&b)
{
make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
}
template<typename _DerType, bool Enable> struct auto_diff_special_op;
} // end namespace internal
template<typename _DerType> 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 differentation capability
*
* \param _DerType 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 _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
* existing vector into an AutoDiffScalar.
* Finally, _DerType 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 _DerType>
class AutoDiffScalar
: public internal::auto_diff_special_op
<_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,
typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value>
{
public:
typedef internal::auto_diff_special_op
<_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,
typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value> Base;
typedef typename internal::remove_all<_DerType>::type 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
, typename internal::enable_if<internal::is_same<Scalar, typename internal::traits<typename internal::remove_all<OtherDerType>::type>::Scalar>::value,void*>::type = 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 const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
{
return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
}
friend inline const 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 const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >
operator+(const AutoDiffScalar<OtherDerType>& other) const
{
internal::make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >(
m_value + other.value(),
m_derivatives + other.derivatives());
}
template<typename OtherDerType>
inline AutoDiffScalar&
operator+=(const AutoDiffScalar<OtherDerType>& other)
{
(*this) = (*this) + other;
return *this;
}
inline const AutoDiffScalar<DerType&> operator-(const Scalar& b) const
{
return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);
}
friend inline const 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 const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >
operator-(const AutoDiffScalar<OtherDerType>& other) const
{
internal::make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >(
m_value - other.value(),
m_derivatives - other.derivatives());
}
template<typename OtherDerType>
inline AutoDiffScalar&
operator-=(const AutoDiffScalar<OtherDerType>& other)
{
*this = *this - other;
return *this;
}
inline const 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 const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
operator*(const Scalar& other) const
{
return MakeAutoDiffScalar(m_value * other, m_derivatives * other);
}
friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
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 const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
operator/(const Scalar& other) const
{
return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));
}
friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
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 const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) >,Scalar,product) >
operator/(const AutoDiffScalar<OtherDerType>& other) const
{
internal::make_coherent(m_derivatives, other.derivatives());
return MakeAutoDiffScalar(
m_value / other.value(),
((m_derivatives * other.value()) - (other.derivatives() * m_value))
* (Scalar(1)/(other.value()*other.value())));
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),
const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) > >
operator*(const AutoDiffScalar<OtherDerType>& other) const
{
internal::make_coherent(m_derivatives, other.derivatives());
return MakeAutoDiffScalar(
m_value * other.value(),
(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 _DerType>
struct auto_diff_special_op<_DerType, true>
// : auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real,
// is_same<Scalar,typename NumTraits<Scalar>::Real>::value>
{
typedef typename remove_all<_DerType>::type DerType;
typedef typename traits<DerType>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real Real;
// typedef auto_diff_scalar_op<_DerType, 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<_DerType>& derived() const { return *static_cast<const AutoDiffScalar<_DerType>*>(this); }
AutoDiffScalar<_DerType>& derived() { return *static_cast<AutoDiffScalar<_DerType>*>(this); }
inline const AutoDiffScalar<DerType&> operator+(const Real& other) const
{
return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives());
}
friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<_DerType>& b)
{
return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
}
inline AutoDiffScalar<_DerType>& operator+=(const Real& other)
{
derived().value() += other;
return derived();
}
inline const 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 const AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >
operator*(const Real& other, const AutoDiffScalar<_DerType>& a)
{
return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >(
a.value() * other,
a.derivatives() * other);
}
inline AutoDiffScalar<_DerType>& operator*=(const Scalar& other)
{
*this = *this * other;
return derived();
}
};
template<typename _DerType>
struct auto_diff_special_op<_DerType, false>
{
void operator*() const;
void operator-() const;
void operator+() const;
};
template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B>
struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
static void run(A& a, B& b) {
if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
{
a.resize(b.size());
a.setZero();
}
}
};
template<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
struct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
static void run(A& a, B& b) {
if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
{
b.resize(a.size());
b.setZero();
}
}
};
template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,
typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
static void run(A& a, B& b) {
if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
{
a.resize(b.size());
a.setZero();
}
else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
{
b.resize(a.size());
b.setZero();
}
}
};
} // 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 const Eigen::AutoDiffScalar< \
EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename Eigen::internal::remove_all<DerType>::type, typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar, product) > \
FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
using namespace Eigen; \
EIGEN_UNUSED typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
CODE; \
}
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 AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const AutoDiffScalar<DerType>& x, const T& y) {
typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;
return (x <= y ? ADS(x) : ADS(y));
}
template<typename DerType, typename T>
inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const AutoDiffScalar<DerType>& x, const T& y) {
typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;
return (x >= y ? ADS(x) : ADS(y));
}
template<typename DerType, typename T>
inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const T& x, const AutoDiffScalar<DerType>& y) {
typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;
return (x < y ? ADS(x) : ADS(y));
}
template<typename DerType, typename T>
inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (max)(const T& x, const AutoDiffScalar<DerType>& y) {
typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> ADS;
return (x > y ? ADS(x) : ADS(y));
}
template<typename DerType>
inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (min)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) {
return (x.value() < y.value() ? x : y);
}
template<typename DerType>
inline AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> (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 const Eigen::AutoDiffScalar<
EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<DerType>::type,typename internal::traits<typename internal::remove_all<DerType>::type>::Scalar,product) >
pow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<typename internal::remove_all<DerType>::type>::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 const AutoDiffScalar<Matrix<typename internal::traits<typename internal::remove_all<DerTypeA>::type>::Scalar,Dynamic,1> >
atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)
{
using std::atan2;
typedef typename internal::traits<typename internal::remove_all<DerTypeA>::type>::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<DerType>::type::Scalar>::Real >
{
typedef typename internal::remove_all<DerType>::type 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
};
};
}
#endif // EIGEN_AUTODIFF_SCALAR_H