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construction of generic expressions working for both dense and sparse matrix. A nicer solution would be to use CwiseBinaryOp for any kind of matrix. To this end we either need to change the overall design so that the base class(es) depends on the kind of matrix, or we could add a template parameter to each expression type (e.g., int Kind = ei_traits<MatrixType>::Kind) allowing to specialize each expression for each kind of matrix. * Extend AutoDiffScalar to work with sparse vector expression for the derivatives.
409 lines
16 KiB
C++
409 lines
16 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_AUTODIFF_SCALAR_H
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#define EIGEN_AUTODIFF_SCALAR_H
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namespace Eigen {
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template<typename A, typename B>
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struct ei_make_coherent_impl {
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static void run(A& a, B& b) {}
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};
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// resize a to match b is a.size()==0, and conversely.
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template<typename A, typename B>
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void ei_make_coherent(const A& a, const B&b)
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{
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ei_make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
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}
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/** \class AutoDiffScalar
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* \brief A scalar type replacement with automatic differentation capability
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*
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* \param _DerType the vector type used to store/represent the derivatives. The base scalar type
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* as well as the number of derivatives to compute are determined from this type.
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* Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
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* if the number of derivatives is not known at compile time, and/or, the number
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* of derivatives is large.
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* Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
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* existing vector into an AutoDiffScalar.
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* Finally, _DerType can also be any Eigen compatible expression.
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*
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* This class represents a scalar value while tracking its respective derivatives using Eigen's expression
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* template mechanism.
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*
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* It supports the following list of global math function:
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* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
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* - ei_abs, ei_sqrt, ei_pow, ei_exp, ei_log, ei_sin, ei_cos,
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* - ei_conj, ei_real, ei_imag, ei_abs2.
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*
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* AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
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* in that case, the expression template mechanism only occurs at the top Matrix level,
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* while derivatives are computed right away.
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*
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*/
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template<typename _DerType>
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class AutoDiffScalar
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{
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public:
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typedef typename ei_cleantype<_DerType>::type DerType;
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typedef typename ei_traits<DerType>::Scalar Scalar;
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inline AutoDiffScalar() {}
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inline AutoDiffScalar(const Scalar& value)
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: m_value(value)
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{
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if(m_derivatives.size()>0)
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m_derivatives.setZero();
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}
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inline AutoDiffScalar(const Scalar& value, const DerType& der)
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: m_value(value), m_derivatives(der)
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{}
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template<typename OtherDerType>
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inline AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other)
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: m_value(other.value()), m_derivatives(other.derivatives())
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{}
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inline AutoDiffScalar(const AutoDiffScalar& other)
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: m_value(other.value()), m_derivatives(other.derivatives())
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{}
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template<typename OtherDerType>
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inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
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{
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m_value = other.value();
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m_derivatives = other.derivatives();
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return *this;
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}
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inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
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{
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m_value = other.value();
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m_derivatives = other.derivatives();
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return *this;
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}
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// inline operator const Scalar& () const { return m_value; }
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// inline operator Scalar& () { return m_value; }
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inline const Scalar& value() const { return m_value; }
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inline Scalar& value() { return m_value; }
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inline const DerType& derivatives() const { return m_derivatives; }
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inline DerType& derivatives() { return m_derivatives; }
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inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
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{
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return AutoDiffScalar<DerType>(m_value + other, m_derivatives);
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}
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friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
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{
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return AutoDiffScalar<DerType>(a + b.value(), b.derivatives());
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}
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inline AutoDiffScalar& operator+=(const Scalar& other)
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{
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value() += other;
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return *this;
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}
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template<typename OtherDerType>
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inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >
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operator+(const AutoDiffScalar<OtherDerType>& other) const
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{
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ei_make_coherent(m_derivatives, other.derivatives());
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return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
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m_value + other.value(),
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m_derivatives + other.derivatives());
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}
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template<typename OtherDerType>
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inline AutoDiffScalar&
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operator+=(const AutoDiffScalar<OtherDerType>& other)
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{
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(*this) = (*this) + other;
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return *this;
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}
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template<typename OtherDerType>
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inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >
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operator-(const AutoDiffScalar<OtherDerType>& other) const
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{
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ei_make_coherent(m_derivatives, other.derivatives());
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return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
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m_value - other.value(),
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m_derivatives - other.derivatives());
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}
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template<typename OtherDerType>
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inline AutoDiffScalar&
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operator-=(const AutoDiffScalar<OtherDerType>& other)
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{
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*this = *this - other;
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return *this;
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}
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template<typename OtherDerType>
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inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >
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operator-() const
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{
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >(
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-m_value,
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-m_derivatives);
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}
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inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
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operator*(const Scalar& other) const
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{
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
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m_value * other,
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(m_derivatives * other));
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}
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friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
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operator*(const Scalar& other, const AutoDiffScalar& a)
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{
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
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a.value() * other,
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a.derivatives() * other);
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}
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inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
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operator/(const Scalar& other) const
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{
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
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m_value / other,
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(m_derivatives * (Scalar(1)/other)));
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}
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friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
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operator/(const Scalar& other, const AutoDiffScalar& a)
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{
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
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other / a.value(),
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a.derivatives() * (-Scalar(1)/other));
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}
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template<typename OtherDerType>
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inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >
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operator/(const AutoDiffScalar<OtherDerType>& other) const
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{
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ei_make_coherent(m_derivatives, other.derivatives());
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >(
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m_value / other.value(),
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((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
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* (Scalar(1)/(other.value()*other.value())));
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}
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template<typename OtherDerType>
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inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >
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operator*(const AutoDiffScalar<OtherDerType>& other) const
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{
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ei_make_coherent(m_derivatives, other.derivatives());
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return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
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typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >(
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m_value * other.value(),
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(m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
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}
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inline AutoDiffScalar& operator*=(const Scalar& other)
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{
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*this = *this * other;
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return *this;
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}
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template<typename OtherDerType>
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inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
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{
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*this = *this * other;
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return *this;
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}
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protected:
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Scalar m_value;
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DerType m_derivatives;
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};
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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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struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
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typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
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static void run(A& a, B& b) {
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if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
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{
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a.resize(b.size());
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a.setZero();
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}
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}
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};
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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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struct ei_make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
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typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
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static void run(A& a, B& b) {
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if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
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{
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b.resize(a.size());
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b.setZero();
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}
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}
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};
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template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,
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typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
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struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
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Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
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typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
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typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
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static void run(A& a, B& b) {
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if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
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{
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a.resize(b.size());
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a.setZero();
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}
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else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
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{
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b.resize(a.size());
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b.setZero();
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}
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}
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};
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}
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#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
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template<typename DerType> \
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inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type > \
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FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
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using namespace Eigen; \
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typedef typename ei_traits<DerType>::Scalar Scalar; \
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typedef AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type > ReturnType; \
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CODE; \
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}
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namespace std
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{
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
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return ReturnType(std::abs(x.value()), x.derivatives() * (sign(x.value())));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
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Scalar sqrtx = std::sqrt(x.value());
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return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
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return ReturnType(std::cos(x.value()), x.derivatives() * (-std::sin(x.value())));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
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return ReturnType(std::sin(x.value()),x.derivatives() * std::cos(x.value()));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
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Scalar expx = std::exp(x.value());
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return ReturnType(expx,x.derivatives() * expx);)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
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return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
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template<typename DerType>
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inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type >
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pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::ei_traits<DerType>::Scalar y)
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{
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using namespace Eigen;
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typedef typename ei_traits<DerType>::Scalar Scalar;
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return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
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std::pow(x.value(),y),
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x.derivatives() * (y * std::pow(x.value(),y-1)));
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}
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}
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namespace Eigen {
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template<typename DerType>
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inline const AutoDiffScalar<DerType>& ei_conj(const AutoDiffScalar<DerType>& x) { return x; }
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template<typename DerType>
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inline const AutoDiffScalar<DerType>& ei_real(const AutoDiffScalar<DerType>& x) { return x; }
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template<typename DerType>
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inline typename DerType::Scalar ei_imag(const AutoDiffScalar<DerType>&) { return 0.; }
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs,
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return ReturnType(ei_abs(x.value()), x.derivatives() * (sign(x.value())));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_abs2,
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return ReturnType(ei_abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sqrt,
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Scalar sqrtx = ei_sqrt(x.value());
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return ReturnType(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_cos,
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return ReturnType(ei_cos(x.value()), x.derivatives() * (-ei_sin(x.value())));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_sin,
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return ReturnType(ei_sin(x.value()),x.derivatives() * ei_cos(x.value()));)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_exp,
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Scalar expx = ei_exp(x.value());
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return ReturnType(expx,x.derivatives() * expx);)
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EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
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return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)
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template<typename DerType>
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inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType>::Type >
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ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
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{ return std::pow(x,y);}
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#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
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template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
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{
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typedef typename DerType::Scalar Real;
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typedef AutoDiffScalar<DerType> FloatingPoint;
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enum {
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IsComplex = 0,
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HasFloatingPoint = 1,
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ReadCost = 1,
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AddCost = 1,
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MulCost = 1
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};
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};
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}
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#endif // EIGEN_AUTODIFF_SCALAR_H
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