| // This file is part of Eigen, a lightweight C++ template library | 
 | // for linear algebra. | 
 | // | 
 | // Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com> | 
 | // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr> | 
 | // | 
 | // This Source Code Form is subject to the terms of the Mozilla | 
 | // Public License v. 2.0. If a copy of the MPL was not distributed | 
 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. | 
 |  | 
 | #ifndef EIGEN_DENSEBASE_H | 
 | #define EIGEN_DENSEBASE_H | 
 |  | 
 | // IWYU pragma: private | 
 | #include "./InternalHeaderCheck.h" | 
 |  | 
 | namespace Eigen { | 
 |  | 
 | // The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type. | 
 | EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned, THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE) | 
 |  | 
 | /** \class DenseBase | 
 |  * \ingroup Core_Module | 
 |  * | 
 |  * \brief Base class for all dense matrices, vectors, and arrays | 
 |  * | 
 |  * This class is the base that is inherited by all dense objects (matrix, vector, arrays, | 
 |  * and related expression types). The common Eigen API for dense objects is contained in this class. | 
 |  * | 
 |  * \tparam Derived is the derived type, e.g., a matrix type or an expression. | 
 |  * | 
 |  * This class can be extended with the help of the plugin mechanism described on the page | 
 |  * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN. | 
 |  * | 
 |  * \sa \blank \ref TopicClassHierarchy | 
 |  */ | 
 | template <typename Derived> | 
 | class DenseBase | 
 | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
 |     : public DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> | 
 | #else | 
 |     : public DenseCoeffsBase<Derived, DirectWriteAccessors> | 
 | #endif  // not EIGEN_PARSED_BY_DOXYGEN | 
 | { | 
 |  public: | 
 |   /** Inner iterator type to iterate over the coefficients of a row or column. | 
 |    * \sa class InnerIterator | 
 |    */ | 
 |   typedef Eigen::InnerIterator<Derived> InnerIterator; | 
 |  | 
 |   typedef typename internal::traits<Derived>::StorageKind StorageKind; | 
 |  | 
 |   /** | 
 |    * \brief The type used to store indices | 
 |    * \details This typedef is relevant for types that store multiple indices such as | 
 |    *          PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index | 
 |    * \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase. | 
 |    */ | 
 |   typedef typename internal::traits<Derived>::StorageIndex StorageIndex; | 
 |  | 
 |   /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. */ | 
 |   typedef typename internal::traits<Derived>::Scalar Scalar; | 
 |  | 
 |   /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. | 
 |    * | 
 |    * It is an alias for the Scalar type */ | 
 |   typedef Scalar value_type; | 
 |  | 
 |   typedef typename NumTraits<Scalar>::Real RealScalar; | 
 |   typedef DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> Base; | 
 |  | 
 |   using Base::coeff; | 
 |   using Base::coeffByOuterInner; | 
 |   using Base::colIndexByOuterInner; | 
 |   using Base::cols; | 
 |   using Base::const_cast_derived; | 
 |   using Base::derived; | 
 |   using Base::rowIndexByOuterInner; | 
 |   using Base::rows; | 
 |   using Base::size; | 
 |   using Base::operator(); | 
 |   using Base::operator[]; | 
 |   using Base::colStride; | 
 |   using Base::innerStride; | 
 |   using Base::outerStride; | 
 |   using Base::rowStride; | 
 |   using Base::stride; | 
 |   using Base::w; | 
 |   using Base::x; | 
 |   using Base::y; | 
 |   using Base::z; | 
 |   typedef typename Base::CoeffReturnType CoeffReturnType; | 
 |  | 
 |   enum { | 
 |  | 
 |     RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, | 
 |     /**< The number of rows at compile-time. This is just a copy of the value provided | 
 |      * by the \a Derived type. If a value is not known at compile-time, | 
 |      * it is set to the \a Dynamic constant. | 
 |      * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */ | 
 |  | 
 |     ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, | 
 |     /**< The number of columns at compile-time. This is just a copy of the value provided | 
 |      * by the \a Derived type. If a value is not known at compile-time, | 
 |      * it is set to the \a Dynamic constant. | 
 |      * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */ | 
 |  | 
 |     SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret), | 
 |     /**< This is equal to the number of coefficients, i.e. the number of | 
 |      * rows times the number of columns, or to \a Dynamic if this is not | 
 |      * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */ | 
 |  | 
 |     MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime, | 
 |     /**< This value is equal to the maximum possible number of rows that this expression | 
 |      * might have. If this expression might have an arbitrarily high number of rows, | 
 |      * this value is set to \a Dynamic. | 
 |      * | 
 |      * This value is useful to know when evaluating an expression, in order to determine | 
 |      * whether it is possible to avoid doing a dynamic memory allocation. | 
 |      * | 
 |      * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime | 
 |      */ | 
 |  | 
 |     MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime, | 
 |     /**< This value is equal to the maximum possible number of columns that this expression | 
 |      * might have. If this expression might have an arbitrarily high number of columns, | 
 |      * this value is set to \a Dynamic. | 
 |      * | 
 |      * This value is useful to know when evaluating an expression, in order to determine | 
 |      * whether it is possible to avoid doing a dynamic memory allocation. | 
 |      * | 
 |      * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime | 
 |      */ | 
 |  | 
 |     MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime, | 
 |                                                           internal::traits<Derived>::MaxColsAtCompileTime), | 
 |     /**< This value is equal to the maximum possible number of coefficients that this expression | 
 |      * might have. If this expression might have an arbitrarily high number of coefficients, | 
 |      * this value is set to \a Dynamic. | 
 |      * | 
 |      * This value is useful to know when evaluating an expression, in order to determine | 
 |      * whether it is possible to avoid doing a dynamic memory allocation. | 
 |      * | 
 |      * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime | 
 |      */ | 
 |  | 
 |     IsVectorAtCompileTime = | 
 |         internal::traits<Derived>::RowsAtCompileTime == 1 || internal::traits<Derived>::ColsAtCompileTime == 1, | 
 |     /**< This is set to true if either the number of rows or the number of | 
 |      * columns is known at compile-time to be equal to 1. Indeed, in that case, | 
 |      * we are dealing with a column-vector (if there is only one column) or with | 
 |      * a row-vector (if there is only one row). */ | 
 |  | 
 |     NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 | 
 |                     : bool(IsVectorAtCompileTime)  ? 1 | 
 |                                                    : 2, | 
 |     /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors, | 
 |      * and 2 for matrices. | 
 |      */ | 
 |  | 
 |     Flags = internal::traits<Derived>::Flags, | 
 |     /**< This stores expression \ref flags flags which may or may not be inherited by new expressions | 
 |      * constructed from this one. See the \ref flags "list of flags". | 
 |      */ | 
 |  | 
 |     IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */ | 
 |  | 
 |     InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime) | 
 |                              : int(IsRowMajor)          ? int(ColsAtCompileTime) | 
 |                                                         : int(RowsAtCompileTime), | 
 |  | 
 |     InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret, | 
 |     OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret | 
 |   }; | 
 |  | 
 |   typedef typename internal::find_best_packet<Scalar, SizeAtCompileTime>::type PacketScalar; | 
 |  | 
 |   enum { IsPlainObjectBase = 0 }; | 
 |  | 
 |   /** The plain matrix type corresponding to this expression. | 
 |    * \sa 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> | 
 |       PlainMatrix; | 
 |  | 
 |   /** The plain array type corresponding to this expression. | 
 |    * \sa PlainObject */ | 
 |   typedef Array<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> | 
 |       PlainArray; | 
 |  | 
 |   /** \brief The plain matrix or array 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 std::conditional_t<internal::is_same<typename internal::traits<Derived>::XprKind, MatrixXpr>::value, | 
 |                              PlainMatrix, PlainArray> | 
 |       PlainObject; | 
 |  | 
 |   /** \returns the outer size. | 
 |    * | 
 |    * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension | 
 |    * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a | 
 |    * column-major matrix, and the number of rows for a row-major matrix. */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerSize() const { | 
 |     return IsVectorAtCompileTime ? 1 : int(IsRowMajor) ? this->rows() : this->cols(); | 
 |   } | 
 |  | 
 |   /** \returns the inner size. | 
 |    * | 
 |    * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension | 
 |    * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a | 
 |    * column-major matrix, and the number of columns for a row-major matrix. */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerSize() const { | 
 |     return IsVectorAtCompileTime ? this->size() : int(IsRowMajor) ? this->cols() : this->rows(); | 
 |   } | 
 |  | 
 |   /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are | 
 |    * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and | 
 |    * does nothing else. | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC void resize(Index newSize) { | 
 |     EIGEN_ONLY_USED_FOR_DEBUG(newSize); | 
 |     eigen_assert(newSize == this->size() && "DenseBase::resize() does not actually allow to resize."); | 
 |   } | 
 |   /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are | 
 |    * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and | 
 |    * does nothing else. | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) { | 
 |     EIGEN_ONLY_USED_FOR_DEBUG(rows); | 
 |     EIGEN_ONLY_USED_FOR_DEBUG(cols); | 
 |     eigen_assert(rows == this->rows() && cols == this->cols() && | 
 |                  "DenseBase::resize() does not actually allow to resize."); | 
 |   } | 
 |  | 
 | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
 |   /** \internal Represents a matrix with all coefficients equal to one another*/ | 
 |   typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType; | 
 |   /** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */ | 
 |   EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> SequentialLinSpacedReturnType; | 
 |   /** \internal Represents a vector with linearly spaced coefficients that allows random access. */ | 
 |   typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> RandomAccessLinSpacedReturnType; | 
 |   /** \internal Represents a vector with equally spaced coefficients that allows random access. */ | 
 |   typedef CwiseNullaryOp<internal::equalspaced_op<Scalar>, PlainObject> RandomAccessEqualSpacedReturnType; | 
 |   /** \internal the return type of MatrixBase::eigenvalues() */ | 
 |   typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, | 
 |                  internal::traits<Derived>::ColsAtCompileTime, 1> | 
 |       EigenvaluesReturnType; | 
 |  | 
 | #endif  // not EIGEN_PARSED_BY_DOXYGEN | 
 |  | 
 |   /** Copies \a other into *this. \returns a reference to *this. */ | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other); | 
 |  | 
 |   /** Special case of the template operator=, in order to prevent the compiler | 
 |    * from generating a default operator= (issue hit with g++ 4.1) | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator=(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator+=(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator-=(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator=(const ReturnByValue<OtherDerived>& func); | 
 |  | 
 |   /** \internal | 
 |    * Copies \a other into *this without evaluating other. \returns a reference to *this. */ | 
 |   template <typename OtherDerived> | 
 |   /** \deprecated */ | 
 |   EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived& lazyAssign(const DenseBase<OtherDerived>& other); | 
 |  | 
 |   EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const Scalar& s); | 
 |  | 
 |   template <unsigned int Added, unsigned int Removed> | 
 |   /** \deprecated it now returns \c *this */ | 
 |   EIGEN_DEPRECATED const Derived& flagged() const { | 
 |     return derived(); | 
 |   } | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC CommaInitializer<Derived> operator<<(const DenseBase<OtherDerived>& other); | 
 |  | 
 |   typedef Transpose<Derived> TransposeReturnType; | 
 |   EIGEN_DEVICE_FUNC TransposeReturnType transpose(); | 
 |   typedef Transpose<const Derived> ConstTransposeReturnType; | 
 |   EIGEN_DEVICE_FUNC const ConstTransposeReturnType transpose() const; | 
 |   EIGEN_DEVICE_FUNC void transposeInPlace(); | 
 |  | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index rows, Index cols, const Scalar& value); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index size, const Scalar& value); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(const Scalar& value); | 
 |  | 
 |   EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, Index size, | 
 |                                                                                             const Scalar& low, | 
 |                                                                                             const Scalar& high); | 
 |   EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, | 
 |                                                                                             const Scalar& low, | 
 |                                                                                             const Scalar& high); | 
 |  | 
 |   EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Index size, const Scalar& low, | 
 |                                                                            const Scalar& high); | 
 |   EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(const Scalar& low, const Scalar& high); | 
 |  | 
 |   EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(Index size, const Scalar& low, | 
 |                                                                                const Scalar& step); | 
 |   EIGEN_DEVICE_FUNC static const RandomAccessEqualSpacedReturnType EqualSpaced(const Scalar& low, const Scalar& step); | 
 |  | 
 |   template <typename CustomNullaryOp> | 
 |   EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index rows, Index cols, | 
 |                                                                                           const CustomNullaryOp& func); | 
 |   template <typename CustomNullaryOp> | 
 |   EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(Index size, | 
 |                                                                                           const CustomNullaryOp& func); | 
 |   template <typename CustomNullaryOp> | 
 |   EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(const CustomNullaryOp& func); | 
 |  | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size); | 
 |   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(); | 
 |  | 
 |   EIGEN_DEVICE_FUNC void fill(const Scalar& value); | 
 |   EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value); | 
 |   EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high); | 
 |   EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high); | 
 |   EIGEN_DEVICE_FUNC Derived& setEqualSpaced(Index size, const Scalar& low, const Scalar& step); | 
 |   EIGEN_DEVICE_FUNC Derived& setEqualSpaced(const Scalar& low, const Scalar& step); | 
 |   EIGEN_DEVICE_FUNC Derived& setZero(); | 
 |   EIGEN_DEVICE_FUNC Derived& setOnes(); | 
 |   EIGEN_DEVICE_FUNC Derived& setRandom(); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC bool isApprox(const DenseBase<OtherDerived>& other, | 
 |                                   const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const RealScalar& other, | 
 |                                            const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC bool isMuchSmallerThan(const DenseBase<OtherDerived>& other, | 
 |                                            const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, | 
 |                                             const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, | 
 |                                     const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC inline bool hasNaN() const; | 
 |   EIGEN_DEVICE_FUNC inline bool allFinite() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const Scalar& other); | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const Scalar& other); | 
 |  | 
 |   typedef internal::add_const_on_value_type_t<typename internal::eval<Derived>::type> EvalReturnType; | 
 |   /** \returns the matrix or vector obtained by evaluating this expression. | 
 |    * | 
 |    * Notice that in the case of a plain matrix or vector (not an expression) this function just returns | 
 |    * a const reference, in order to avoid a useless copy. | 
 |    * | 
 |    * \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page | 
 |    * \endlink. | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType eval() const { | 
 |     // Even though MSVC does not honor strong inlining when the return type | 
 |     // is a dynamic matrix, we desperately need strong inlining for fixed | 
 |     // size types on MSVC. | 
 |     return typename internal::eval<Derived>::type(derived()); | 
 |   } | 
 |  | 
 |   /** swaps *this with the expression \a other. | 
 |    * | 
 |    */ | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(const DenseBase<OtherDerived>& other) { | 
 |     EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase, THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY); | 
 |     eigen_assert(rows() == other.rows() && cols() == other.cols()); | 
 |     call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>()); | 
 |   } | 
 |  | 
 |   /** swaps *this with the matrix or array \a other. | 
 |    * | 
 |    */ | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void swap(PlainObjectBase<OtherDerived>& other) { | 
 |     eigen_assert(rows() == other.rows() && cols() == other.cols()); | 
 |     call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>()); | 
 |   } | 
 |  | 
 |   EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const; | 
 |   EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const; | 
 |   EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess(); | 
 |   template <bool Enable> | 
 |   EIGEN_DEVICE_FUNC inline const std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> | 
 |   forceAlignedAccessIf() const; | 
 |   template <bool Enable> | 
 |   EIGEN_DEVICE_FUNC inline std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> forceAlignedAccessIf(); | 
 |  | 
 |   EIGEN_DEVICE_FUNC Scalar sum() const; | 
 |   EIGEN_DEVICE_FUNC Scalar mean() const; | 
 |   EIGEN_DEVICE_FUNC Scalar trace() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC Scalar prod() const; | 
 |  | 
 |   template <int NaNPropagation> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const; | 
 |   template <int NaNPropagation> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const; | 
 |  | 
 |   // By default, the fastest version with undefined NaN propagation semantics is | 
 |   // used. | 
 |   // TODO(rmlarsen): Replace with default template argument when we move to | 
 |   // c++11 or beyond. | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff() const { | 
 |     return minCoeff<PropagateFast>(); | 
 |   } | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff() const { | 
 |     return maxCoeff<PropagateFast>(); | 
 |   } | 
 |  | 
 |   template <int NaNPropagation, typename IndexType> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const; | 
 |   template <int NaNPropagation, typename IndexType> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const; | 
 |   template <int NaNPropagation, typename IndexType> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const; | 
 |   template <int NaNPropagation, typename IndexType> | 
 |   EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const; | 
 |  | 
 |   // TODO(rmlarsen): Replace these methods with a default template argument. | 
 |   template <typename IndexType> | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const { | 
 |     return minCoeff<PropagateFast>(row, col); | 
 |   } | 
 |   template <typename IndexType> | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const { | 
 |     return maxCoeff<PropagateFast>(row, col); | 
 |   } | 
 |   template <typename IndexType> | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const { | 
 |     return minCoeff<PropagateFast>(index); | 
 |   } | 
 |   template <typename IndexType> | 
 |   EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const { | 
 |     return maxCoeff<PropagateFast>(index); | 
 |   } | 
 |  | 
 |   template <typename BinaryOp> | 
 |   EIGEN_DEVICE_FUNC Scalar redux(const BinaryOp& func) const; | 
 |  | 
 |   template <typename Visitor> | 
 |   EIGEN_DEVICE_FUNC void visit(Visitor& func) const; | 
 |  | 
 |   /** \returns a WithFormat proxy object allowing to print a matrix the with given | 
 |    * format \a fmt. | 
 |    * | 
 |    * See class IOFormat for some examples. | 
 |    * | 
 |    * \sa class IOFormat, class WithFormat | 
 |    */ | 
 |   inline const WithFormat<Derived> format(const IOFormat& fmt) const { return WithFormat<Derived>(derived(), fmt); } | 
 |  | 
 |   /** \returns the unique coefficient of a 1x1 expression */ | 
 |   EIGEN_DEVICE_FUNC CoeffReturnType value() const { | 
 |     EIGEN_STATIC_ASSERT_SIZE_1x1(Derived) eigen_assert(this->rows() == 1 && this->cols() == 1); | 
 |     return derived().coeff(0, 0); | 
 |   } | 
 |  | 
 |   EIGEN_DEVICE_FUNC bool all() const; | 
 |   EIGEN_DEVICE_FUNC bool any() const; | 
 |   EIGEN_DEVICE_FUNC Index count() const; | 
 |  | 
 |   typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType; | 
 |   typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType; | 
 |   typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType; | 
 |   typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType; | 
 |  | 
 |   /** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions | 
 |    * | 
 |    * Example: \include MatrixBase_rowwise.cpp | 
 |    * Output: \verbinclude MatrixBase_rowwise.out | 
 |    * | 
 |    * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting | 
 |    */ | 
 |   // Code moved here due to a CUDA compiler bug | 
 |   EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const { return ConstRowwiseReturnType(derived()); } | 
 |   EIGEN_DEVICE_FUNC RowwiseReturnType rowwise(); | 
 |  | 
 |   /** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions | 
 |    * | 
 |    * Example: \include MatrixBase_colwise.cpp | 
 |    * Output: \verbinclude MatrixBase_colwise.out | 
 |    * | 
 |    * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const { return ConstColwiseReturnType(derived()); } | 
 |   EIGEN_DEVICE_FUNC ColwiseReturnType colwise(); | 
 |  | 
 |   typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>, PlainObject> RandomReturnType; | 
 |   static const RandomReturnType Random(Index rows, Index cols); | 
 |   static const RandomReturnType Random(Index size); | 
 |   static const RandomReturnType Random(); | 
 |  | 
 |   template <typename ThenDerived, typename ElseDerived> | 
 |   inline EIGEN_DEVICE_FUNC | 
 |       CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar, | 
 |                                                         typename DenseBase<ElseDerived>::Scalar, Scalar>, | 
 |                      ThenDerived, ElseDerived, Derived> | 
 |       select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const; | 
 |  | 
 |   template <typename ThenDerived> | 
 |   inline EIGEN_DEVICE_FUNC | 
 |       CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar, | 
 |                                                         typename DenseBase<ThenDerived>::Scalar, Scalar>, | 
 |                      ThenDerived, typename DenseBase<ThenDerived>::ConstantReturnType, Derived> | 
 |       select(const DenseBase<ThenDerived>& thenMatrix, const typename DenseBase<ThenDerived>::Scalar& elseScalar) const; | 
 |  | 
 |   template <typename ElseDerived> | 
 |   inline EIGEN_DEVICE_FUNC | 
 |       CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar, | 
 |                                                         typename DenseBase<ElseDerived>::Scalar, Scalar>, | 
 |                      typename DenseBase<ElseDerived>::ConstantReturnType, ElseDerived, Derived> | 
 |       select(const typename DenseBase<ElseDerived>::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const; | 
 |  | 
 |   template <int p> | 
 |   RealScalar lpNorm() const; | 
 |  | 
 |   template <int RowFactor, int ColFactor> | 
 |   EIGEN_DEVICE_FUNC const Replicate<Derived, RowFactor, ColFactor> replicate() const; | 
 |   /** | 
 |    * \return an expression of the replication of \c *this | 
 |    * | 
 |    * Example: \include MatrixBase_replicate_int_int.cpp | 
 |    * Output: \verbinclude MatrixBase_replicate_int_int.out | 
 |    * | 
 |    * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate | 
 |    */ | 
 |   // Code moved here due to a CUDA compiler bug | 
 |   EIGEN_DEVICE_FUNC const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const { | 
 |     return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor); | 
 |   } | 
 |  | 
 |   typedef Reverse<Derived, BothDirections> ReverseReturnType; | 
 |   typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType; | 
 |   EIGEN_DEVICE_FUNC ReverseReturnType reverse(); | 
 |   /** This is the const version of reverse(). */ | 
 |   // Code moved here due to a CUDA compiler bug | 
 |   EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const { return ConstReverseReturnType(derived()); } | 
 |   EIGEN_DEVICE_FUNC void reverseInPlace(); | 
 |  | 
 | #ifdef EIGEN_PARSED_BY_DOXYGEN | 
 |   /** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a> | 
 |    * iterator type as returned by the begin() and end() methods. | 
 |    */ | 
 |   typedef random_access_iterator_type iterator; | 
 |   /** This is the const version of iterator (aka read-only) */ | 
 |   typedef random_access_iterator_type const_iterator; | 
 | #else | 
 |   typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit, | 
 |                              internal::pointer_based_stl_iterator<Derived>, | 
 |                              internal::generic_randaccess_stl_iterator<Derived> > | 
 |       iterator_type; | 
 |  | 
 |   typedef std::conditional_t<(Flags & DirectAccessBit) == DirectAccessBit, | 
 |                              internal::pointer_based_stl_iterator<const Derived>, | 
 |                              internal::generic_randaccess_stl_iterator<const Derived> > | 
 |       const_iterator_type; | 
 |  | 
 |   // Stl-style iterators are supported only for vectors. | 
 |  | 
 |   typedef std::conditional_t<IsVectorAtCompileTime, iterator_type, void> iterator; | 
 |  | 
 |   typedef std::conditional_t<IsVectorAtCompileTime, const_iterator_type, void> const_iterator; | 
 | #endif | 
 |  | 
 |   inline iterator begin(); | 
 |   inline const_iterator begin() const; | 
 |   inline const_iterator cbegin() const; | 
 |   inline iterator end(); | 
 |   inline const_iterator end() const; | 
 |   inline const_iterator cend() const; | 
 |  | 
 | #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase | 
 | #define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL | 
 | #define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND) | 
 | #define EIGEN_DOC_UNARY_ADDONS(X, Y) | 
 | #include "../plugins/CommonCwiseUnaryOps.inc" | 
 | #include "../plugins/BlockMethods.inc" | 
 | #include "../plugins/IndexedViewMethods.inc" | 
 | #include "../plugins/ReshapedMethods.inc" | 
 | #ifdef EIGEN_DENSEBASE_PLUGIN | 
 | #include EIGEN_DENSEBASE_PLUGIN | 
 | #endif | 
 | #undef EIGEN_CURRENT_STORAGE_BASE_CLASS | 
 | #undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL | 
 | #undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF | 
 | #undef EIGEN_DOC_UNARY_ADDONS | 
 |  | 
 |   // disable the use of evalTo for dense objects with a nice compilation error | 
 |   template <typename Dest> | 
 |   EIGEN_DEVICE_FUNC inline void evalTo(Dest&) const { | 
 |     EIGEN_STATIC_ASSERT((internal::is_same<Dest, void>::value), | 
 |                         THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS); | 
 |   } | 
 |  | 
 |  protected: | 
 |   EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase) | 
 |   /** Default constructor. Do nothing. */ | 
 |   EIGEN_DEVICE_FUNC constexpr DenseBase() { | 
 |     /* Just checks for self-consistency of the flags. | 
 |      * Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down | 
 |      */ | 
 | #ifdef EIGEN_INTERNAL_DEBUGGING | 
 |     EIGEN_STATIC_ASSERT( | 
 |         (internal::check_implication(MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1, int(IsRowMajor)) && | 
 |          internal::check_implication(MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1, int(!IsRowMajor))), | 
 |         INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION) | 
 | #endif | 
 |   } | 
 |  | 
 |  private: | 
 |   EIGEN_DEVICE_FUNC explicit DenseBase(int); | 
 |   EIGEN_DEVICE_FUNC DenseBase(int, int); | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&); | 
 | }; | 
 |  | 
 | }  // end namespace Eigen | 
 |  | 
 | #endif  // EIGEN_DENSEBASE_H |