[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_AUTODIFF_SCALAR_H
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| 11 | #define EIGEN_AUTODIFF_SCALAR_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | namespace internal {
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| 16 |
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| 17 | template<typename A, typename B>
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| 18 | struct make_coherent_impl {
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| 19 | static void run(A&, B&) {}
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| 20 | };
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| 21 |
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| 22 | // resize a to match b is a.size()==0, and conversely.
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| 23 | template<typename A, typename B>
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| 24 | void make_coherent(const A& a, const B&b)
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| 25 | {
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| 26 | make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
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| 27 | }
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| 28 |
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| 29 | template<typename _DerType, bool Enable> struct auto_diff_special_op;
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| 30 |
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| 31 | } // end namespace internal
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| 32 |
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| 33 | /** \class AutoDiffScalar
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| 34 | * \brief A scalar type replacement with automatic differentation capability
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| 35 | *
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| 36 | * \param _DerType the vector type used to store/represent the derivatives. The base scalar type
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| 37 | * as well as the number of derivatives to compute are determined from this type.
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| 38 | * Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
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| 39 | * if the number of derivatives is not known at compile time, and/or, the number
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| 40 | * of derivatives is large.
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| 41 | * Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
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| 42 | * existing vector into an AutoDiffScalar.
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| 43 | * Finally, _DerType can also be any Eigen compatible expression.
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| 44 | *
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| 45 | * This class represents a scalar value while tracking its respective derivatives using Eigen's expression
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| 46 | * template mechanism.
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| 47 | *
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| 48 | * It supports the following list of global math function:
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| 49 | * - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
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| 50 | * - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
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| 51 | * - internal::conj, internal::real, internal::imag, numext::abs2.
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| 52 | *
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| 53 | * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
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| 54 | * in that case, the expression template mechanism only occurs at the top Matrix level,
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| 55 | * while derivatives are computed right away.
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| 56 | *
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| 57 | */
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| 58 |
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| 59 | template<typename _DerType>
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| 60 | class AutoDiffScalar
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| 61 | : public internal::auto_diff_special_op
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| 62 | <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,
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| 63 | typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value>
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| 64 | {
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| 65 | public:
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| 66 | typedef internal::auto_diff_special_op
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| 67 | <_DerType, !internal::is_same<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar,
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| 68 | typename NumTraits<typename internal::traits<typename internal::remove_all<_DerType>::type>::Scalar>::Real>::value> Base;
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| 69 | typedef typename internal::remove_all<_DerType>::type DerType;
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| 70 | typedef typename internal::traits<DerType>::Scalar Scalar;
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| 71 | typedef typename NumTraits<Scalar>::Real Real;
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| 72 |
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| 73 | using Base::operator+;
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| 74 | using Base::operator*;
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| 75 |
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| 76 | /** Default constructor without any initialization. */
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| 77 | AutoDiffScalar() {}
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| 78 |
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| 79 | /** Constructs an active scalar from its \a value,
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| 80 | and initializes the \a nbDer derivatives such that it corresponds to the \a derNumber -th variable */
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| 81 | AutoDiffScalar(const Scalar& value, int nbDer, int derNumber)
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| 82 | : m_value(value), m_derivatives(DerType::Zero(nbDer))
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| 83 | {
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| 84 | m_derivatives.coeffRef(derNumber) = Scalar(1);
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| 85 | }
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| 86 |
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| 87 | /** Conversion from a scalar constant to an active scalar.
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| 88 | * The derivatives are set to zero. */
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| 89 | /*explicit*/ AutoDiffScalar(const Real& value)
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| 90 | : m_value(value)
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| 91 | {
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| 92 | if(m_derivatives.size()>0)
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| 93 | m_derivatives.setZero();
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| 94 | }
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| 95 |
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| 96 | /** Constructs an active scalar from its \a value and derivatives \a der */
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| 97 | AutoDiffScalar(const Scalar& value, const DerType& der)
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| 98 | : m_value(value), m_derivatives(der)
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| 99 | {}
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| 100 |
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| 101 | template<typename OtherDerType>
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| 102 | AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other)
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| 103 | : m_value(other.value()), m_derivatives(other.derivatives())
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| 104 | {}
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| 105 |
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| 106 | friend std::ostream & operator << (std::ostream & s, const AutoDiffScalar& a)
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| 107 | {
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| 108 | return s << a.value();
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| 109 | }
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| 110 |
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| 111 | AutoDiffScalar(const AutoDiffScalar& other)
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| 112 | : m_value(other.value()), m_derivatives(other.derivatives())
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| 113 | {}
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| 114 |
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| 115 | template<typename OtherDerType>
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| 116 | inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
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| 117 | {
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| 118 | m_value = other.value();
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| 119 | m_derivatives = other.derivatives();
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| 120 | return *this;
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| 121 | }
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| 122 |
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| 123 | inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
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| 124 | {
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| 125 | m_value = other.value();
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| 126 | m_derivatives = other.derivatives();
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| 127 | return *this;
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| 128 | }
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| 129 |
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| 130 | // inline operator const Scalar& () const { return m_value; }
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| 131 | // inline operator Scalar& () { return m_value; }
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| 132 |
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| 133 | inline const Scalar& value() const { return m_value; }
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| 134 | inline Scalar& value() { return m_value; }
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| 135 |
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| 136 | inline const DerType& derivatives() const { return m_derivatives; }
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| 137 | inline DerType& derivatives() { return m_derivatives; }
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| 138 |
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| 139 | inline bool operator< (const Scalar& other) const { return m_value < other; }
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| 140 | inline bool operator<=(const Scalar& other) const { return m_value <= other; }
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| 141 | inline bool operator> (const Scalar& other) const { return m_value > other; }
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| 142 | inline bool operator>=(const Scalar& other) const { return m_value >= other; }
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| 143 | inline bool operator==(const Scalar& other) const { return m_value == other; }
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| 144 | inline bool operator!=(const Scalar& other) const { return m_value != other; }
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| 145 |
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| 146 | friend inline bool operator< (const Scalar& a, const AutoDiffScalar& b) { return a < b.value(); }
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| 147 | friend inline bool operator<=(const Scalar& a, const AutoDiffScalar& b) { return a <= b.value(); }
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| 148 | friend inline bool operator> (const Scalar& a, const AutoDiffScalar& b) { return a > b.value(); }
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| 149 | friend inline bool operator>=(const Scalar& a, const AutoDiffScalar& b) { return a >= b.value(); }
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| 150 | friend inline bool operator==(const Scalar& a, const AutoDiffScalar& b) { return a == b.value(); }
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| 151 | friend inline bool operator!=(const Scalar& a, const AutoDiffScalar& b) { return a != b.value(); }
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| 152 |
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| 153 | template<typename OtherDerType> inline bool operator< (const AutoDiffScalar<OtherDerType>& b) const { return m_value < b.value(); }
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| 154 | template<typename OtherDerType> inline bool operator<=(const AutoDiffScalar<OtherDerType>& b) const { return m_value <= b.value(); }
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| 155 | template<typename OtherDerType> inline bool operator> (const AutoDiffScalar<OtherDerType>& b) const { return m_value > b.value(); }
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| 156 | template<typename OtherDerType> inline bool operator>=(const AutoDiffScalar<OtherDerType>& b) const { return m_value >= b.value(); }
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| 157 | template<typename OtherDerType> inline bool operator==(const AutoDiffScalar<OtherDerType>& b) const { return m_value == b.value(); }
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| 158 | template<typename OtherDerType> inline bool operator!=(const AutoDiffScalar<OtherDerType>& b) const { return m_value != b.value(); }
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| 159 |
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| 160 | inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
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| 161 | {
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| 162 | return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
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| 163 | }
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| 164 |
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| 165 | friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
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| 166 | {
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| 167 | return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
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| 168 | }
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| 169 |
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| 170 | // inline const AutoDiffScalar<DerType&> operator+(const Real& other) const
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| 171 | // {
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| 172 | // return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
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| 173 | // }
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| 174 |
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| 175 | // friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar& b)
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| 176 | // {
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| 177 | // return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
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| 178 | // }
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| 179 |
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| 180 | inline AutoDiffScalar& operator+=(const Scalar& other)
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| 181 | {
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| 182 | value() += other;
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| 183 | return *this;
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| 184 | }
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| 185 |
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| 186 | template<typename OtherDerType>
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| 187 | inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >
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| 188 | operator+(const AutoDiffScalar<OtherDerType>& other) const
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| 189 | {
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| 190 | internal::make_coherent(m_derivatives, other.derivatives());
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| 191 | return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> >(
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| 192 | m_value + other.value(),
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| 193 | m_derivatives + other.derivatives());
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| 194 | }
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| 195 |
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| 196 | template<typename OtherDerType>
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| 197 | inline AutoDiffScalar&
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| 198 | operator+=(const AutoDiffScalar<OtherDerType>& other)
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| 199 | {
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| 200 | (*this) = (*this) + other;
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| 201 | return *this;
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| 202 | }
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| 203 |
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| 204 | inline const AutoDiffScalar<DerType&> operator-(const Scalar& b) const
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| 205 | {
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| 206 | return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);
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| 207 | }
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| 208 |
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| 209 | friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
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| 210 | operator-(const Scalar& a, const AutoDiffScalar& b)
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| 211 | {
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| 212 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
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| 213 | (a - b.value(), -b.derivatives());
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| 214 | }
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| 215 |
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| 216 | inline AutoDiffScalar& operator-=(const Scalar& other)
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| 217 | {
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| 218 | value() -= other;
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| 219 | return *this;
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| 220 | }
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| 221 |
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| 222 | template<typename OtherDerType>
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| 223 | inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >
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| 224 | operator-(const AutoDiffScalar<OtherDerType>& other) const
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| 225 | {
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| 226 | internal::make_coherent(m_derivatives, other.derivatives());
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| 227 | return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> >(
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| 228 | m_value - other.value(),
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| 229 | m_derivatives - other.derivatives());
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| 230 | }
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| 231 |
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| 232 | template<typename OtherDerType>
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| 233 | inline AutoDiffScalar&
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| 234 | operator-=(const AutoDiffScalar<OtherDerType>& other)
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| 235 | {
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| 236 | *this = *this - other;
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| 237 | return *this;
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| 238 | }
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| 239 |
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| 240 | inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
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| 241 | operator-() const
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| 242 | {
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| 243 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >(
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| 244 | -m_value,
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| 245 | -m_derivatives);
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| 246 | }
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| 247 |
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| 248 | inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
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| 249 | operator*(const Scalar& other) const
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| 250 | {
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| 251 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
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| 252 | m_value * other,
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| 253 | (m_derivatives * other));
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| 254 | }
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| 255 |
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| 256 | friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
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| 257 | operator*(const Scalar& other, const AutoDiffScalar& a)
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| 258 | {
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| 259 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
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| 260 | a.value() * other,
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| 261 | a.derivatives() * other);
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| 262 | }
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| 263 |
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| 264 | // inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
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| 265 | // operator*(const Real& other) const
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| 266 | // {
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| 267 | // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
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| 268 | // m_value * other,
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| 269 | // (m_derivatives * other));
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| 270 | // }
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| 271 | //
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| 272 | // friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
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| 273 | // operator*(const Real& other, const AutoDiffScalar& a)
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| 274 | // {
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| 275 | // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
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| 276 | // a.value() * other,
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| 277 | // a.derivatives() * other);
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| 278 | // }
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| 279 |
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| 280 | inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
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| 281 | operator/(const Scalar& other) const
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| 282 | {
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| 283 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
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| 284 | m_value / other,
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| 285 | (m_derivatives * (Scalar(1)/other)));
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| 286 | }
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| 287 |
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| 288 | friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >
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| 289 | operator/(const Scalar& other, const AutoDiffScalar& a)
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| 290 | {
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| 291 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> >(
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| 292 | other / a.value(),
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| 293 | a.derivatives() * (Scalar(-other) / (a.value()*a.value())));
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| 294 | }
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| 295 |
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| 296 | // inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
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| 297 | // operator/(const Real& other) const
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| 298 | // {
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| 299 | // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
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| 300 | // m_value / other,
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| 301 | // (m_derivatives * (Real(1)/other)));
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| 302 | // }
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| 303 | //
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| 304 | // friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
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| 305 | // operator/(const Real& other, const AutoDiffScalar& a)
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| 306 | // {
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| 307 | // return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
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| 308 | // other / a.value(),
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| 309 | // a.derivatives() * (-Real(1)/other));
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| 310 | // }
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| 311 |
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| 312 | template<typename OtherDerType>
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| 313 | inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,
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| 314 | const CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
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| 315 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
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| 316 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > >
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| 317 | operator/(const AutoDiffScalar<OtherDerType>& other) const
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| 318 | {
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| 319 | internal::make_coherent(m_derivatives, other.derivatives());
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| 320 | return AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>,
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| 321 | const CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
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| 322 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
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| 323 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > > >(
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| 324 | m_value / other.value(),
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| 325 | ((m_derivatives * other.value()) - (m_value * other.derivatives()))
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| 326 | * (Scalar(1)/(other.value()*other.value())));
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| 327 | }
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| 328 |
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| 329 | template<typename OtherDerType>
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| 330 | inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
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| 331 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
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| 332 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type> > >
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| 333 | operator*(const AutoDiffScalar<OtherDerType>& other) const
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| 334 | {
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| 335 | internal::make_coherent(m_derivatives, other.derivatives());
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| 336 | return AutoDiffScalar<const CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
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| 337 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType>,
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| 338 | const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const typename internal::remove_all<OtherDerType>::type > > >(
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| 339 | m_value * other.value(),
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| 340 | (m_derivatives * other.value()) + (m_value * other.derivatives()));
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| 341 | }
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| 342 |
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| 343 | inline AutoDiffScalar& operator*=(const Scalar& other)
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| 344 | {
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| 345 | *this = *this * other;
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| 346 | return *this;
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| 347 | }
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| 348 |
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| 349 | template<typename OtherDerType>
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| 350 | inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
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| 351 | {
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| 352 | *this = *this * other;
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| 353 | return *this;
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| 354 | }
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| 355 |
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| 356 | inline AutoDiffScalar& operator/=(const Scalar& other)
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| 357 | {
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| 358 | *this = *this / other;
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| 359 | return *this;
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| 360 | }
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| 361 |
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| 362 | template<typename OtherDerType>
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| 363 | inline AutoDiffScalar& operator/=(const AutoDiffScalar<OtherDerType>& other)
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| 364 | {
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| 365 | *this = *this / other;
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| 366 | return *this;
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| 367 | }
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| 368 |
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| 369 | protected:
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| 370 | Scalar m_value;
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| 371 | DerType m_derivatives;
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| 372 |
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| 373 | };
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| 374 |
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| 375 | namespace internal {
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| 376 |
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| 377 | template<typename _DerType>
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| 378 | struct auto_diff_special_op<_DerType, true>
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| 379 | // : auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real,
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| 380 | // is_same<Scalar,typename NumTraits<Scalar>::Real>::value>
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| 381 | {
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| 382 | typedef typename remove_all<_DerType>::type DerType;
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| 383 | typedef typename traits<DerType>::Scalar Scalar;
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| 384 | typedef typename NumTraits<Scalar>::Real Real;
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| 385 |
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| 386 | // typedef auto_diff_scalar_op<_DerType, typename NumTraits<Scalar>::Real,
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| 387 | // is_same<Scalar,typename NumTraits<Scalar>::Real>::value> Base;
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| 388 |
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| 389 | // using Base::operator+;
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| 390 | // using Base::operator+=;
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| 391 | // using Base::operator-;
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| 392 | // using Base::operator-=;
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| 393 | // using Base::operator*;
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| 394 | // using Base::operator*=;
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| 395 |
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| 396 | const AutoDiffScalar<_DerType>& derived() const { return *static_cast<const AutoDiffScalar<_DerType>*>(this); }
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| 397 | AutoDiffScalar<_DerType>& derived() { return *static_cast<AutoDiffScalar<_DerType>*>(this); }
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| 398 |
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| 399 |
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| 400 | inline const AutoDiffScalar<DerType&> operator+(const Real& other) const
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| 401 | {
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| 402 | return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives());
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| 403 | }
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| 404 |
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| 405 | friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<_DerType>& b)
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| 406 | {
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| 407 | return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
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| 408 | }
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| 409 |
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| 410 | inline AutoDiffScalar<_DerType>& operator+=(const Real& other)
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| 411 | {
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| 412 | derived().value() += other;
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| 413 | return derived();
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| 414 | }
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| 415 |
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| 416 |
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| 417 | inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >
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| 418 | operator*(const Real& other) const
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| 419 | {
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| 420 | return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >(
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| 421 | derived().value() * other,
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| 422 | derived().derivatives() * other);
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| 423 | }
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| 424 |
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| 425 | friend inline const AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >
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| 426 | operator*(const Real& other, const AutoDiffScalar<_DerType>& a)
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| 427 | {
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| 428 | return AutoDiffScalar<typename CwiseUnaryOp<scalar_multiple2_op<Scalar,Real>, DerType>::Type >(
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| 429 | a.value() * other,
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| 430 | a.derivatives() * other);
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| 431 | }
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| 432 |
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| 433 | inline AutoDiffScalar<_DerType>& operator*=(const Scalar& other)
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| 434 | {
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| 435 | *this = *this * other;
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| 436 | return derived();
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| 437 | }
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| 438 | };
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| 439 |
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| 440 | template<typename _DerType>
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| 441 | struct auto_diff_special_op<_DerType, false>
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| 442 | {
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| 443 | void operator*() const;
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| 444 | void operator-() const;
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| 445 | void operator+() const;
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| 446 | };
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| 447 |
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| 448 | template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B>
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| 449 | struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
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| 450 | typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
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| 451 | static void run(A& a, B& b) {
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| 452 | if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
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| 453 | {
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| 454 | a.resize(b.size());
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| 455 | a.setZero();
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| 456 | }
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| 457 | }
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| 458 | };
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| 459 |
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| 460 | template<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
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| 461 | struct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
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| 462 | typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
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| 463 | static void run(A& a, B& b) {
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| 464 | if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
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| 465 | {
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| 466 | b.resize(a.size());
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| 467 | b.setZero();
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| 468 | }
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| 469 | }
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| 470 | };
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| 471 |
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| 472 | template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,
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| 473 | typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
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| 474 | struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
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| 475 | Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
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| 476 | typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
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| 477 | typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
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| 478 | static void run(A& a, B& b) {
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| 479 | if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
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| 480 | {
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| 481 | a.resize(b.size());
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| 482 | a.setZero();
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| 483 | }
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| 484 | else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
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| 485 | {
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| 486 | b.resize(a.size());
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| 487 | b.setZero();
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| 488 | }
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| 489 | }
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| 490 | };
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| 491 |
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| 492 | template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
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| 493 | struct scalar_product_traits<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,A_Scalar>
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| 494 | {
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| 495 | enum { Defined = 1 };
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| 496 | typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
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| 497 | };
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| 498 |
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| 499 | template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols>
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| 500 | struct scalar_product_traits<A_Scalar, Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> >
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| 501 | {
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| 502 | enum { Defined = 1 };
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| 503 | typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> ReturnType;
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| 504 | };
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| 505 |
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| 506 | template<typename DerType>
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| 507 | struct scalar_product_traits<AutoDiffScalar<DerType>,typename DerType::Scalar>
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| 508 | {
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| 509 | enum { Defined = 1 };
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| 510 | typedef AutoDiffScalar<DerType> ReturnType;
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| 511 | };
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| 512 |
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| 513 | template<typename DerType>
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| 514 | struct scalar_product_traits<typename DerType::Scalar,AutoDiffScalar<DerType> >
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| 515 | {
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| 516 | enum { Defined = 1 };
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| 517 | typedef AutoDiffScalar<DerType> ReturnType;
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| 518 | };
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| 519 |
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| 520 | } // end namespace internal
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| 521 |
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| 522 | #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
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| 523 | template<typename DerType> \
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| 524 | inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > \
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| 525 | FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
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| 526 | using namespace Eigen; \
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| 527 | typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
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| 528 | typedef AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const typename Eigen::internal::remove_all<DerType>::type> > ReturnType; \
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| 529 | CODE; \
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| 530 | }
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| 531 |
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| 532 | template<typename DerType>
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| 533 | inline const AutoDiffScalar<DerType>& conj(const AutoDiffScalar<DerType>& x) { return x; }
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| 534 | template<typename DerType>
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| 535 | inline const AutoDiffScalar<DerType>& real(const AutoDiffScalar<DerType>& x) { return x; }
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| 536 | template<typename DerType>
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| 537 | inline typename DerType::Scalar imag(const AutoDiffScalar<DerType>&) { return 0.; }
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| 538 | template<typename DerType, typename T>
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| 539 | inline AutoDiffScalar<DerType> (min)(const AutoDiffScalar<DerType>& x, const T& y) { return (x <= y ? x : y); }
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| 540 | template<typename DerType, typename T>
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| 541 | inline AutoDiffScalar<DerType> (max)(const AutoDiffScalar<DerType>& x, const T& y) { return (x >= y ? x : y); }
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| 542 | template<typename DerType, typename T>
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| 543 | inline AutoDiffScalar<DerType> (min)(const T& x, const AutoDiffScalar<DerType>& y) { return (x < y ? x : y); }
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| 544 | template<typename DerType, typename T>
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| 545 | inline AutoDiffScalar<DerType> (max)(const T& x, const AutoDiffScalar<DerType>& y) { return (x > y ? x : y); }
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| 546 |
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| 547 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
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| 548 | using std::abs;
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| 549 | return ReturnType(abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)
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| 550 |
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| 551 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2,
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| 552 | using numext::abs2;
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| 553 | return ReturnType(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
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| 554 |
|
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| 555 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
|
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| 556 | using std::sqrt;
|
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| 557 | Scalar sqrtx = sqrt(x.value());
|
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| 558 | return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
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| 559 |
|
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| 560 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
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| 561 | using std::cos;
|
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| 562 | using std::sin;
|
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| 563 | return ReturnType(cos(x.value()), x.derivatives() * (-sin(x.value())));)
|
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| 564 |
|
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| 565 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
|
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| 566 | using std::sin;
|
---|
| 567 | using std::cos;
|
---|
| 568 | return ReturnType(sin(x.value()),x.derivatives() * cos(x.value()));)
|
---|
| 569 |
|
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| 570 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
|
---|
| 571 | using std::exp;
|
---|
| 572 | Scalar expx = exp(x.value());
|
---|
| 573 | return ReturnType(expx,x.derivatives() * expx);)
|
---|
| 574 |
|
---|
| 575 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log,
|
---|
| 576 | using std::log;
|
---|
| 577 | return ReturnType(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)
|
---|
| 578 |
|
---|
| 579 | template<typename DerType>
|
---|
| 580 | inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::internal::scalar_multiple_op<typename Eigen::internal::traits<DerType>::Scalar>, const DerType> >
|
---|
| 581 | pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::internal::traits<DerType>::Scalar y)
|
---|
| 582 | {
|
---|
| 583 | using namespace Eigen;
|
---|
| 584 | typedef typename Eigen::internal::traits<DerType>::Scalar Scalar;
|
---|
| 585 | return AutoDiffScalar<CwiseUnaryOp<Eigen::internal::scalar_multiple_op<Scalar>, const DerType> >(
|
---|
| 586 | std::pow(x.value(),y),
|
---|
| 587 | x.derivatives() * (y * std::pow(x.value(),y-1)));
|
---|
| 588 | }
|
---|
| 589 |
|
---|
| 590 |
|
---|
| 591 | template<typename DerTypeA,typename DerTypeB>
|
---|
| 592 | inline const AutoDiffScalar<Matrix<typename internal::traits<DerTypeA>::Scalar,Dynamic,1> >
|
---|
| 593 | atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)
|
---|
| 594 | {
|
---|
| 595 | using std::atan2;
|
---|
| 596 | using std::max;
|
---|
| 597 | typedef typename internal::traits<DerTypeA>::Scalar Scalar;
|
---|
| 598 | typedef AutoDiffScalar<Matrix<Scalar,Dynamic,1> > PlainADS;
|
---|
| 599 | PlainADS ret;
|
---|
| 600 | ret.value() = atan2(a.value(), b.value());
|
---|
| 601 |
|
---|
| 602 | Scalar tmp2 = a.value() * a.value();
|
---|
| 603 | Scalar tmp3 = b.value() * b.value();
|
---|
| 604 | Scalar tmp4 = tmp3/(tmp2+tmp3);
|
---|
| 605 |
|
---|
| 606 | if (tmp4!=0)
|
---|
| 607 | ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) * (tmp2+tmp3);
|
---|
| 608 |
|
---|
| 609 | return ret;
|
---|
| 610 | }
|
---|
| 611 |
|
---|
| 612 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan,
|
---|
| 613 | using std::tan;
|
---|
| 614 | using std::cos;
|
---|
| 615 | return ReturnType(tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cos(x.value()))));)
|
---|
| 616 |
|
---|
| 617 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin,
|
---|
| 618 | using std::sqrt;
|
---|
| 619 | using std::asin;
|
---|
| 620 | return ReturnType(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-numext::abs2(x.value()))));)
|
---|
| 621 |
|
---|
| 622 | EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos,
|
---|
| 623 | using std::sqrt;
|
---|
| 624 | using std::acos;
|
---|
| 625 | return ReturnType(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-numext::abs2(x.value()))));)
|
---|
| 626 |
|
---|
| 627 | #undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
|
---|
| 628 |
|
---|
| 629 | template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
|
---|
| 630 | : NumTraits< typename NumTraits<typename DerType::Scalar>::Real >
|
---|
| 631 | {
|
---|
| 632 | typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerType::Scalar>::Real,DerType::RowsAtCompileTime,DerType::ColsAtCompileTime> > Real;
|
---|
| 633 | typedef AutoDiffScalar<DerType> NonInteger;
|
---|
| 634 | typedef AutoDiffScalar<DerType> Nested;
|
---|
| 635 | enum{
|
---|
| 636 | RequireInitialization = 1
|
---|
| 637 | };
|
---|
| 638 | };
|
---|
| 639 |
|
---|
| 640 | }
|
---|
| 641 |
|
---|
| 642 | #endif // EIGEN_AUTODIFF_SCALAR_H
|
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