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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
namespace Eigen {
/** \class MatrixBase
* \ingroup Core_Module
*
* \brief Base class for all dense matrices, vectors, and expressions
*
* This class is the base that is inherited by all matrix, vector, and related expression
* types. Most of the Eigen API is contained in this class, and its base classes. Other important
* classes for the Eigen API are Matrix, and VectorwiseOp.
*
* Note that some methods are defined in other modules such as the \ref LU_Module LU module
* for all functions related to matrix inversions.
*
* \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
*
* When writing a function taking Eigen objects as argument, if you want your function
* to take as argument any matrix, vector, or expression, just let it take a
* MatrixBase argument. As an example, here is a function printFirstRow which, given
* a matrix, vector, or expression \a x, prints the first row of \a x.
*
* \code
template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
* \endcode
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
*
* \sa \ref TopicClassHierarchy
*/
template<typename Derived> class MatrixBase
: public DenseBase<Derived>
{
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef MatrixBase StorageBaseType;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
typedef typename internal::traits<Derived>::Scalar Scalar;
typedef typename internal::packet_traits<Scalar>::type PacketScalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef DenseBase<Derived> Base;
using Base::RowsAtCompileTime;
using Base::ColsAtCompileTime;
using Base::SizeAtCompileTime;
using Base::MaxRowsAtCompileTime;
using Base::MaxColsAtCompileTime;
using Base::MaxSizeAtCompileTime;
using Base::IsVectorAtCompileTime;
using Base::Flags;
using Base::CoeffReadCost;
using Base::derived;
using Base::const_cast_derived;
using Base::rows;
using Base::cols;
using Base::size;
using Base::coeff;
using Base::coeffRef;
using Base::lazyAssign;
using Base::eval;
using Base::operator+=;
using Base::operator-=;
using Base::operator*=;
using Base::operator/=;
typedef typename Base::CoeffReturnType CoeffReturnType;
typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
typedef typename Base::RowXpr RowXpr;
typedef typename Base::ColXpr ColXpr;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** type of the equivalent square matrix */
typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
/** \returns the size of the main diagonal, which is min(rows(),cols()).
* \sa rows(), cols(), SizeAtCompileTime. */
inline Index diagonalSize() const { return (std::min)(rows(),cols()); }
/** \brief The plain matrix type corresponding to this expression.
*
* This is not necessarily exactly the return type of eval(). In the case of plain matrices,
* the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
* that the return type of eval() is either PlainObject or const PlainObject&.
*/
typedef Matrix<typename internal::traits<Derived>::Scalar,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime,
AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
internal::traits<Derived>::MaxRowsAtCompileTime,
internal::traits<Derived>::MaxColsAtCompileTime
> PlainObject;
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal Represents a matrix with all coefficients equal to one another*/
typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
/** \internal the return type of MatrixBase::adjoint() */
typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
ConstTransposeReturnType
>::type AdjointReturnType;
/** \internal Return type of eigenvalues() */
typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
/** \internal the return type of identity */
typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,Derived> IdentityReturnType;
/** \internal the return type of unit vectors */
typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
internal::traits<Derived>::RowsAtCompileTime,
internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
#endif // not EIGEN_PARSED_BY_DOXYGEN
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
# include "../plugins/CommonCwiseUnaryOps.h"
# include "../plugins/CommonCwiseBinaryOps.h"
# include "../plugins/MatrixCwiseUnaryOps.h"
# include "../plugins/MatrixCwiseBinaryOps.h"
# ifdef EIGEN_MATRIXBASE_PLUGIN
# include EIGEN_MATRIXBASE_PLUGIN
# endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
Derived& operator=(const MatrixBase& other);
// We cannot inherit here via Base::operator= since it is causing
// trouble with MSVC.
template <typename OtherDerived>
Derived& operator=(const DenseBase<OtherDerived>& other);
template <typename OtherDerived>
Derived& operator=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator=(const ReturnByValue<OtherDerived>& other);
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
#endif // not EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
Derived& operator+=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
const typename ProductReturnType<Derived,OtherDerived>::Type
operator*(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const typename LazyProductReturnType<Derived,OtherDerived>::Type
lazyProduct(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
Derived& operator*=(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheLeft(const EigenBase<OtherDerived>& other);
template<typename OtherDerived>
void applyOnTheRight(const EigenBase<OtherDerived>& other);
template<typename DiagonalDerived>
const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
template<typename OtherDerived>
typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
dot(const MatrixBase<OtherDerived>& other) const;
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
#endif
RealScalar squaredNorm() const;
RealScalar norm() const;
RealScalar stableNorm() const;
RealScalar blueNorm() const;
RealScalar hypotNorm() const;
const PlainObject normalized() const;
void normalize();
const AdjointReturnType adjoint() const;
void adjointInPlace();
typedef Diagonal<Derived> DiagonalReturnType;
DiagonalReturnType diagonal();
typedef const Diagonal<const Derived> ConstDiagonalReturnType;
const ConstDiagonalReturnType diagonal() const;
template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
// Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
// On the other hand they confuse MSVC8...
#if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
typename MatrixBase::template DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
typename MatrixBase::template ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
#else
typename DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
typename ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
#endif
#ifdef EIGEN2_SUPPORT
template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
// huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
// of an integer constant. Solution: overload the part() method template wrt template parameters list.
template<template<typename T, int n> class U>
const DiagonalWrapper<ConstDiagonalReturnType> part() const
{ return diagonal().asDiagonal(); }
#endif // EIGEN2_SUPPORT
template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
template<unsigned int Mode> typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
template<unsigned int UpLo> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
static const IdentityReturnType Identity();
static const IdentityReturnType Identity(Index rows, Index cols);
static const BasisReturnType Unit(Index size, Index i);
static const BasisReturnType Unit(Index i);
static const BasisReturnType UnitX();
static const BasisReturnType UnitY();
static const BasisReturnType UnitZ();
static const BasisReturnType UnitW();
const DiagonalWrapper<const Derived> asDiagonal() const;
const PermutationWrapper<const Derived> asPermutation() const;
Derived& setIdentity();
Derived& setIdentity(Index rows, Index cols);
bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
template<typename OtherDerived>
bool isOrthogonal(const MatrixBase<OtherDerived>& other,
const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
/** \returns true if each coefficients of \c *this and \a other are all exactly equal.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator!= */
template<typename OtherDerived>
inline bool operator==(const MatrixBase<OtherDerived>& other) const
{ return cwiseEqual(other).all(); }
/** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
* \warning When using floating point scalar values you probably should rather use a
* fuzzy comparison such as isApprox()
* \sa isApprox(), operator== */
template<typename OtherDerived>
inline bool operator!=(const MatrixBase<OtherDerived>& other) const
{ return cwiseNotEqual(other).any(); }
NoAlias<Derived,Eigen::MatrixBase > noalias();
inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
inline ForceAlignedAccess<Derived> forceAlignedAccess();
template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
Scalar trace() const;
/////////// Array module ///////////
template<int p> RealScalar lpNorm() const;
MatrixBase<Derived>& matrix() { return *this; }
const MatrixBase<Derived>& matrix() const { return *this; }
/** \returns an \link ArrayBase Array \endlink expression of this matrix
* \sa ArrayBase::matrix() */
ArrayWrapper<Derived> array() { return derived(); }
const ArrayWrapper<const Derived> array() const { return derived(); }
/////////// LU module ///////////
const FullPivLU<PlainObject> fullPivLu() const;
const PartialPivLU<PlainObject> partialPivLu() const;
#if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
const LU<PlainObject> lu() const;
#endif
#ifdef EIGEN2_SUPPORT
const LU<PlainObject> eigen2_lu() const;
#endif
#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
const PartialPivLU<PlainObject> lu() const;
#endif
#ifdef EIGEN2_SUPPORT
template<typename ResultType>
void computeInverse(MatrixBase<ResultType> *result) const {
*result = this->inverse();
}
#endif
const internal::inverse_impl<Derived> inverse() const;
template<typename ResultType>
void computeInverseAndDetWithCheck(
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
template<typename ResultType>
void computeInverseWithCheck(
ResultType& inverse,
bool& invertible,
const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
) const;
Scalar determinant() const;
/////////// Cholesky module ///////////
const LLT<PlainObject> llt() const;
const LDLT<PlainObject> ldlt() const;
/////////// QR module ///////////
const HouseholderQR<PlainObject> householderQr() const;
const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
#ifdef EIGEN2_SUPPORT
const QR<PlainObject> qr() const;
#endif
EigenvaluesReturnType eigenvalues() const;
RealScalar operatorNorm() const;
/////////// SVD module ///////////
JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
#ifdef EIGEN2_SUPPORT
SVD<PlainObject> svd() const;
#endif
/////////// Geometry module ///////////
#ifndef EIGEN_PARSED_BY_DOXYGEN
/// \internal helper struct to form the return type of the cross product
template<typename OtherDerived> struct cross_product_return_type {
typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
};
#endif // EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>
typename cross_product_return_type<OtherDerived>::type
cross(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>
PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
PlainObject unitOrthogonal(void) const;
Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?)
enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
HomogeneousReturnType homogeneous() const;
#endif
enum {
SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
};
typedef Block<const Derived,
internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
const ConstStartMinusOne > HNormalizedReturnType;
const HNormalizedReturnType hnormalized() const;
////////// Householder module ///////////
void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
template<typename EssentialPart>
void makeHouseholder(EssentialPart& essential,
Scalar& tau, RealScalar& beta) const;
template<typename EssentialPart>
void applyHouseholderOnTheLeft(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
template<typename EssentialPart>
void applyHouseholderOnTheRight(const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace);
///////// Jacobi module /////////
template<typename OtherScalar>
void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
template<typename OtherScalar>
void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
///////// MatrixFunctions module /////////
typedef typename internal::stem_function<Scalar>::type StemFunction;
const MatrixExponentialReturnValue<Derived> exp() const;
const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
const MatrixFunctionReturnValue<Derived> cosh() const;
const MatrixFunctionReturnValue<Derived> sinh() const;
const MatrixFunctionReturnValue<Derived> cos() const;
const MatrixFunctionReturnValue<Derived> sin() const;
const MatrixSquareRootReturnValue<Derived> sqrt() const;
const MatrixLogarithmReturnValue<Derived> log() const;
#ifdef EIGEN2_SUPPORT
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
EvalBeforeAssigningBit>& other);
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
EvalBeforeAssigningBit>& other);
/** \deprecated because .lazy() is deprecated
* Overloaded for cache friendly product evaluation */
template<typename OtherDerived>
Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
{ return lazyAssign(other._expression()); }
template<unsigned int Added>
const Flagged<Derived, Added, 0> marked() const;
const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
inline const Cwise<Derived> cwise() const;
inline Cwise<Derived> cwise();
VectorBlock<Derived> start(Index size);
const VectorBlock<const Derived> start(Index size) const;
VectorBlock<Derived> end(Index size);
const VectorBlock<const Derived> end(Index size) const;
template<int Size> VectorBlock<Derived,Size> start();
template<int Size> const VectorBlock<const Derived,Size> start() const;
template<int Size> VectorBlock<Derived,Size> end();
template<int Size> const VectorBlock<const Derived,Size> end() const;
Minor<Derived> minor(Index row, Index col);
const Minor<Derived> minor(Index row, Index col) const;
#endif
protected:
MatrixBase() : Base() {}
private:
explicit MatrixBase(int);
MatrixBase(int,int);
template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
protected:
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
// mixing arrays and matrices is not legal
template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
{EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
};
} // end namespace Eigen
#endif // EIGEN_MATRIXBASE_H