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198 lines
8.8 KiB
Plaintext
198 lines
8.8 KiB
Plaintext
namespace Eigen {
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/** \page TopicCustomizingEigen Customizing/Extending Eigen
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Eigen can be extended in several ways, for instance, by defining global methods, \ref ExtendingMatrixBase "by adding custom methods to MatrixBase", adding support to \ref CustomScalarType "custom types" etc.
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\b Table \b of \b contents
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- \ref ExtendingMatrixBase
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- \ref InheritingFromMatrix
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- \ref CustomScalarType
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- \ref PreprocessorDirectives
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\section ExtendingMatrixBase Extending MatrixBase
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In this section we will see how to add custom methods to MatrixBase. Since all expressions and matrix types inherit MatrixBase, adding a method to MatrixBase make it immediately available to all expressions ! A typical use case is, for instance, to make Eigen compatible with another API.
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You certainly know that in C++ it is not possible to add methods to an existing class. So how that's possible ? Here the trick is to include in the declaration of MatrixBase a file defined by the preprocessor token \c EIGEN_MATRIXBASE_PLUGIN:
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\code
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class MatrixBase {
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// ...
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#ifdef EIGEN_MATRIXBASE_PLUGIN
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#include EIGEN_MATRIXBASE_PLUGIN
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#endif
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};
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\endcode
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Therefore to extend MatrixBase with you own methods you just have to create a file with your method declaration and define EIGEN_MATRIXBASE_PLUGIN before you include any Eigen's header file.
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Here is an example of such an extension file: \n
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\b MatrixBaseAddons.h
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\code
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inline Scalar at(uint i, uint j) const { return this->operator()(i,j); }
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inline Scalar& at(uint i, uint j) { return this->operator()(i,j); }
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inline Scalar at(uint i) const { return this->operator[](i); }
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inline Scalar& at(uint i) { return this->operator[](i); }
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inline RealScalar squaredLength() const { return squaredNorm(); }
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inline RealScalar length() const { return norm(); }
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inline RealScalar invLength(void) const { return fast_inv_sqrt(squaredNorm()); }
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template<typename OtherDerived>
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inline Scalar squaredDistanceTo(const MatrixBase<OtherDerived>& other) const
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{ return (derived() - other.derived()).squaredNorm(); }
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template<typename OtherDerived>
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inline RealScalar distanceTo(const MatrixBase<OtherDerived>& other) const
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{ return internal::sqrt(derived().squaredDistanceTo(other)); }
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inline void scaleTo(RealScalar l) { RealScalar vl = norm(); if (vl>1e-9) derived() *= (l/vl); }
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inline Transpose<Derived> transposed() {return this->transpose();}
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inline const Transpose<Derived> transposed() const {return this->transpose();}
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inline uint minComponentId(void) const { int i; this->minCoeff(&i); return i; }
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inline uint maxComponentId(void) const { int i; this->maxCoeff(&i); return i; }
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template<typename OtherDerived>
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void makeFloor(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMin(other.derived()); }
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template<typename OtherDerived>
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void makeCeil(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMax(other.derived()); }
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const CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>
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operator+(const Scalar& scalar) const
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{ return CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>(derived(), internal::scalar_add_op<Scalar>(scalar)); }
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friend const CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>
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operator+(const Scalar& scalar, const MatrixBase<Derived>& mat)
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{ return CwiseUnaryOp<internal::scalar_add_op<Scalar>, Derived>(mat.derived(), internal::scalar_add_op<Scalar>(scalar)); }
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\endcode
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Then one can the following declaration in the config.h or whatever prerequisites header file of his project:
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\code
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#define EIGEN_MATRIXBASE_PLUGIN "MatrixBaseAddons.h"
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\endcode
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\section InheritingFromMatrix Inheriting from Matrix
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Before inheriting from Matrix, be really, i mean REALLY sure that using
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EIGEN_MATRIX_PLUGIN is not what you really want (see previous section).
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If you just need to add few members to Matrix, this is the way to go.
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An example of when you actually need to inherit Matrix, is when you have
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several layers of heritage such as MyVerySpecificVector1,MyVerySpecificVector1 -> MyVector1 -> Matrix and.
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MyVerySpecificVector3,MyVerySpecificVector4 -> MyVector2 -> Matrix.
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In order for your object to work within the Eigen framework, you need to
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define a few members in your inherited class.
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Here is a minimalistic example:\n
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\code
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class MyVectorType : public Eigen::VectorXd
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{
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public:
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MyVectorType(void):Eigen::VectorXd() {}
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// You need to define this for your object to work
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typedef Eigen::VectorXd Base;
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template<typename OtherDerived>
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MyVectorType & operator= (const Eigen::MatrixBase <OtherDerived>& other)
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{
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this->Base::operator=(other);
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return *this;
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}
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};
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\endcode
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This is the kind of error you can get if you don't provide those methods
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\code
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error: no match for ‘operator=’ in ‘delta =
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(((Eigen::MatrixBase<Eigen::Matrix<std::complex<float>, 10000, 1, 2, 10000,
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1> >*)(& delta)) + 8u)->Eigen::MatrixBase<Derived>::cwise [with Derived =
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Eigen::Matrix<std::complex<float>, 10000, 1, 2, 10000,
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1>]().Eigen::Cwise<ExpressionType>::operator* [with OtherDerived =
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Eigen::Matrix<std::complex<float>, 10000, 1, 2, 10000, 1>, ExpressionType =
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Eigen::Matrix<std::complex<float>, 10000, 1, 2, 10000, 1>](((const
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Eigen::MatrixBase<Eigen::Matrix<std::complex<float>, 10000, 1, 2, 10000, 1>
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>&)(((const Eigen::MatrixBase<Eigen::Matrix<std::complex<float>, 10000, 1,
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>2, 10000, 1> >*)((const spectral1d*)where)) + 8u)))’
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\endcode
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\anchor user_defined_scalars \section CustomScalarType Using custom scalar types
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By default, Eigen currently supports the following scalar types: \c int, \c float, \c double, \c std::complex<float>, \c std::complex<double>, \c long \c double, \c long \c long \c int (64 bits integers), and \c bool. The \c long \c double is especially useful on x86-64 systems or when the SSE2 instruction set is enabled because it enforces the use of x87 registers with extended accuracy.
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In order to add support for a custom type \c T you need:
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1 - make sure the common operator (+,-,*,/,etc.) are supported by the type \c T
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2 - add a specialization of struct Eigen::NumTraits<T> (see \ref NumTraits)
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3 - define a couple of math functions for your type such as: internal::sqrt, internal::abs, etc...
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(see the file Eigen/src/Core/MathFunctions.h)
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Here is a concrete example adding support for the Adolc's \c adouble type. <a href="https://projects.coin-or.org/ADOL-C">Adolc</a> is an automatic differentiation library. The type \c adouble is basically a real value tracking the values of any number of partial derivatives.
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\code
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#ifndef ADLOCSUPPORT_H
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#define ADLOCSUPPORT_H
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#define ADOLC_TAPELESS
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#include <adolc/adouble.h>
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#include <Eigen/Core>
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namespace Eigen {
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template<> struct NumTraits<adtl::adouble>
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{
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typedef adtl::adouble Real;
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typedef adtl::adouble NonInteger;
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typedef adtl::adouble Nested;
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enum {
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IsComplex = 0,
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IsInteger = 0,
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IsSigned,
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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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// the Adolc's type adouble is defined in the adtl namespace
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// therefore, the following internal::* functions *must* be defined
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// in the same namespace
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namespace adtl {
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inline const adouble& internal::conj(const adouble& x) { return x; }
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inline const adouble& internal::real(const adouble& x) { return x; }
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inline adouble internal::imag(const adouble&) { return 0.; }
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inline adouble internal::abs(const adouble& x) { return fabs(x); }
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inline adouble internal::abs2(const adouble& x) { return x*x; }
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inline adouble internal::sqrt(const adouble& x) { return sqrt(x); }
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inline adouble internal::exp(const adouble& x) { return exp(x); }
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inline adouble internal::log(const adouble& x) { return log(x); }
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inline adouble internal::sin(const adouble& x) { return sin(x); }
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inline adouble internal::cos(const adouble& x) { return cos(x); }
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inline adouble internal::pow(const adouble& x, adouble y) { return pow(x, y); }
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}
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#endif // ADLOCSUPPORT_H
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\endcode
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\section PreprocessorDirectives Preprocessor directives
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You can control some aspects of Eigen by defining the following preprocessor tokens them before including any of Eigen's headers.
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- \b #EIGEN_NO_DEBUG disables Eigen assertions. Like NDEBUG but only affects Eigen's assertions.
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- \b EIGEN_DONT_VECTORIZE disables explicit vectorization when defined.
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- \b EIGEN_UNROLLING_LIMIT defines the maximal instruction counts to enable meta unrolling of loops. Set it to zero to disable unrolling. The default is 100.
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- \b EIGEN_DEFAULT_TO_ROW_MAJOR the default storage order for matrices becomes row-major instead of column-major.
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- \b EIGEN_TUNE_FOR_CPU_CACHE_SIZE represents the maximal size in Bytes of L2 blocks. Since several blocks have to stay concurently in L2 cache, this value should correspond to at most 1/4 of the size of L2 cache.
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- \b EIGEN_NO_STATIC_ASSERT replaces compile time static assertions by runtime assertions
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- \b EIGEN_MATRIXBASE_PLUGIN see \ref ExtendingMatrixBase
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*/
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}
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