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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // 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_CWISE_NULLARY_OP_H
- #define EIGEN_CWISE_NULLARY_OP_H
- namespace Eigen {
- namespace internal {
- template<typename NullaryOp, typename PlainObjectType>
- struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
- {
- enum {
- Flags = traits<PlainObjectType>::Flags & RowMajorBit
- };
- };
- } // namespace internal
- /** \class CwiseNullaryOp
- * \ingroup Core_Module
- *
- * \brief Generic expression of a matrix where all coefficients are defined by a functor
- *
- * \tparam NullaryOp template functor implementing the operator
- * \tparam PlainObjectType the underlying plain matrix/array type
- *
- * This class represents an expression of a generic nullary operator.
- * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
- * and most of the time this is the only way it is used.
- *
- * However, if you want to write a function returning such an expression, you
- * will need to use this class.
- *
- * The functor NullaryOp must expose one of the following method:
- <table class="manual">
- <tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>
- <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr>
- <tr ><td>\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)</td></tr>
- </table>
- * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.
- *
- * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
- * C++11 random number generators.
- *
- * A nullary expression can also be used to implement custom sophisticated matrix manipulations
- * that cannot be covered by the existing set of natively supported matrix manipulations.
- * See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations
- * on the behavior of CwiseNullaryOp.
- *
- * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
- */
- template<typename NullaryOp, typename PlainObjectType>
- class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator
- {
- public:
- typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
- EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
- EIGEN_DEVICE_FUNC
- CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
- : m_rows(rows), m_cols(cols), m_functor(func)
- {
- eigen_assert(rows >= 0
- && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
- && cols >= 0
- && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
- }
- EIGEN_DEVICE_FUNC
- EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
- EIGEN_DEVICE_FUNC
- EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
- /** \returns the functor representing the nullary operation */
- EIGEN_DEVICE_FUNC
- const NullaryOp& functor() const { return m_functor; }
- protected:
- const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
- const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
- const NullaryOp m_functor;
- };
- /** \returns an expression of a matrix defined by a custom functor \a func
- *
- * The parameters \a rows and \a cols are the number of rows and of columns of
- * the returned matrix. Must be compatible with this MatrixBase type.
- *
- * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
- * instead.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- template<typename CustomNullaryOp>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
- DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
- {
- return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
- }
- /** \returns an expression of a matrix defined by a custom functor \a func
- *
- * The parameter \a size is the size of the returned vector.
- * Must be compatible with this MatrixBase type.
- *
- * \only_for_vectors
- *
- * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Zero() should be used
- * instead.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * Here is an example with C++11 random generators: \include random_cpp11.cpp
- * Output: \verbinclude random_cpp11.out
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- template<typename CustomNullaryOp>
- EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
- DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
- else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
- }
- /** \returns an expression of a matrix defined by a custom functor \a func
- *
- * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
- * need to use the variants taking size arguments.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- template<typename CustomNullaryOp>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
- DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
- {
- return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
- }
- /** \returns an expression of a constant matrix of value \a value
- *
- * The parameters \a rows and \a cols are the number of rows and of columns of
- * the returned matrix. Must be compatible with this DenseBase type.
- *
- * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
- * instead.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
- {
- return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
- }
- /** \returns an expression of a constant matrix of value \a value
- *
- * The parameter \a size is the size of the returned vector.
- * Must be compatible with this DenseBase type.
- *
- * \only_for_vectors
- *
- * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Zero() should be used
- * instead.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Constant(Index size, const Scalar& value)
- {
- return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
- }
- /** \returns an expression of a constant matrix of value \a value
- *
- * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
- * need to use the variants taking size arguments.
- *
- * The template parameter \a CustomNullaryOp is the type of the functor.
- *
- * \sa class CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Constant(const Scalar& value)
- {
- EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
- return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
- }
- /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
- *
- * \sa LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
- DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
- }
- /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
- *
- * \sa LinSpaced(Scalar,Scalar)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
- DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
- return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
- }
- /**
- * \brief Sets a linearly spaced vector.
- *
- * The function generates 'size' equally spaced values in the closed interval [low,high].
- * When size is set to 1, a vector of length 1 containing 'high' is returned.
- *
- * \only_for_vectors
- *
- * Example: \include DenseBase_LinSpaced.cpp
- * Output: \verbinclude DenseBase_LinSpaced.out
- *
- * For integer scalar types, an even spacing is possible if and only if the length of the range,
- * i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the
- * number of values \c high-low+1 (meaning each value can be repeated the same number of time).
- * If one of these two considions is not satisfied, then \c high is lowered to the largest value
- * satisfying one of this constraint.
- * Here are some examples:
- *
- * Example: \include DenseBase_LinSpacedInt.cpp
- * Output: \verbinclude DenseBase_LinSpacedInt.out
- *
- * \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
- DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
- }
- /**
- * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
- * Special version for fixed size types which does not require the size parameter.
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
- DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
- return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
- }
- /** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
- template<typename Derived>
- EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant
- (const Scalar& val, const RealScalar& prec) const
- {
- typename internal::nested_eval<Derived,1>::type self(derived());
- for(Index j = 0; j < cols(); ++j)
- for(Index i = 0; i < rows(); ++i)
- if(!internal::isApprox(self.coeff(i, j), val, prec))
- return false;
- return true;
- }
- /** This is just an alias for isApproxToConstant().
- *
- * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
- template<typename Derived>
- EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant
- (const Scalar& val, const RealScalar& prec) const
- {
- return isApproxToConstant(val, prec);
- }
- /** Alias for setConstant(): sets all coefficients in this expression to \a val.
- *
- * \sa setConstant(), Constant(), class CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
- {
- setConstant(val);
- }
- /** Sets all coefficients in this expression to value \a val.
- *
- * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
- {
- return derived() = Constant(rows(), cols(), val);
- }
- /** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
- *
- * \only_for_vectors
- *
- * Example: \include Matrix_setConstant_int.cpp
- * Output: \verbinclude Matrix_setConstant_int.out
- *
- * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
- {
- resize(size);
- return setConstant(val);
- }
- /** Resizes to the given size, and sets all coefficients in this expression to the given value \a val.
- *
- * \param rows the new number of rows
- * \param cols the new number of columns
- * \param val the value to which all coefficients are set
- *
- * Example: \include Matrix_setConstant_int_int.cpp
- * Output: \verbinclude Matrix_setConstant_int_int.out
- *
- * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)
- {
- resize(rows, cols);
- return setConstant(val);
- }
- /**
- * \brief Sets a linearly spaced vector.
- *
- * The function generates 'size' equally spaced values in the closed interval [low,high].
- * When size is set to 1, a vector of length 1 containing 'high' is returned.
- *
- * \only_for_vectors
- *
- * Example: \include DenseBase_setLinSpaced.cpp
- * Output: \verbinclude DenseBase_setLinSpaced.out
- *
- * For integer scalar types, do not miss the explanations on the definition
- * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
- *
- * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize));
- }
- /**
- * \brief Sets a linearly spaced vector.
- *
- * The function fills \c *this with equally spaced values in the closed interval [low,high].
- * When size is set to 1, a vector of length 1 containing 'high' is returned.
- *
- * \only_for_vectors
- *
- * For integer scalar types, do not miss the explanations on the definition
- * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
- *
- * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return setLinSpaced(size(), low, high);
- }
- // zero:
- /** \returns an expression of a zero matrix.
- *
- * The parameters \a rows and \a cols are the number of rows and of columns of
- * the returned matrix. Must be compatible with this MatrixBase type.
- *
- * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
- * instead.
- *
- * Example: \include MatrixBase_zero_int_int.cpp
- * Output: \verbinclude MatrixBase_zero_int_int.out
- *
- * \sa Zero(), Zero(Index)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Zero(Index rows, Index cols)
- {
- return Constant(rows, cols, Scalar(0));
- }
- /** \returns an expression of a zero vector.
- *
- * The parameter \a size is the size of the returned vector.
- * Must be compatible with this MatrixBase type.
- *
- * \only_for_vectors
- *
- * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Zero() should be used
- * instead.
- *
- * Example: \include MatrixBase_zero_int.cpp
- * Output: \verbinclude MatrixBase_zero_int.out
- *
- * \sa Zero(), Zero(Index,Index)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Zero(Index size)
- {
- return Constant(size, Scalar(0));
- }
- /** \returns an expression of a fixed-size zero matrix or vector.
- *
- * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
- * need to use the variants taking size arguments.
- *
- * Example: \include MatrixBase_zero.cpp
- * Output: \verbinclude MatrixBase_zero.out
- *
- * \sa Zero(Index), Zero(Index,Index)
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Zero()
- {
- return Constant(Scalar(0));
- }
- /** \returns true if *this is approximately equal to the zero matrix,
- * within the precision given by \a prec.
- *
- * Example: \include MatrixBase_isZero.cpp
- * Output: \verbinclude MatrixBase_isZero.out
- *
- * \sa class CwiseNullaryOp, Zero()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const
- {
- typename internal::nested_eval<Derived,1>::type self(derived());
- for(Index j = 0; j < cols(); ++j)
- for(Index i = 0; i < rows(); ++i)
- if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec))
- return false;
- return true;
- }
- /** Sets all coefficients in this expression to zero.
- *
- * Example: \include MatrixBase_setZero.cpp
- * Output: \verbinclude MatrixBase_setZero.out
- *
- * \sa class CwiseNullaryOp, Zero()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
- {
- return setConstant(Scalar(0));
- }
- /** Resizes to the given \a size, and sets all coefficients in this expression to zero.
- *
- * \only_for_vectors
- *
- * Example: \include Matrix_setZero_int.cpp
- * Output: \verbinclude Matrix_setZero_int.out
- *
- * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setZero(Index newSize)
- {
- resize(newSize);
- return setConstant(Scalar(0));
- }
- /** Resizes to the given size, and sets all coefficients in this expression to zero.
- *
- * \param rows the new number of rows
- * \param cols the new number of columns
- *
- * Example: \include Matrix_setZero_int_int.cpp
- * Output: \verbinclude Matrix_setZero_int_int.out
- *
- * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setZero(Index rows, Index cols)
- {
- resize(rows, cols);
- return setConstant(Scalar(0));
- }
- // ones:
- /** \returns an expression of a matrix where all coefficients equal one.
- *
- * The parameters \a rows and \a cols are the number of rows and of columns of
- * the returned matrix. Must be compatible with this MatrixBase type.
- *
- * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
- * instead.
- *
- * Example: \include MatrixBase_ones_int_int.cpp
- * Output: \verbinclude MatrixBase_ones_int_int.out
- *
- * \sa Ones(), Ones(Index), isOnes(), class Ones
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Ones(Index rows, Index cols)
- {
- return Constant(rows, cols, Scalar(1));
- }
- /** \returns an expression of a vector where all coefficients equal one.
- *
- * The parameter \a newSize is the size of the returned vector.
- * Must be compatible with this MatrixBase type.
- *
- * \only_for_vectors
- *
- * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Ones() should be used
- * instead.
- *
- * Example: \include MatrixBase_ones_int.cpp
- * Output: \verbinclude MatrixBase_ones_int.out
- *
- * \sa Ones(), Ones(Index,Index), isOnes(), class Ones
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Ones(Index newSize)
- {
- return Constant(newSize, Scalar(1));
- }
- /** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
- *
- * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
- * need to use the variants taking size arguments.
- *
- * Example: \include MatrixBase_ones.cpp
- * Output: \verbinclude MatrixBase_ones.out
- *
- * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
- DenseBase<Derived>::Ones()
- {
- return Constant(Scalar(1));
- }
- /** \returns true if *this is approximately equal to the matrix where all coefficients
- * are equal to 1, within the precision given by \a prec.
- *
- * Example: \include MatrixBase_isOnes.cpp
- * Output: \verbinclude MatrixBase_isOnes.out
- *
- * \sa class CwiseNullaryOp, Ones()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes
- (const RealScalar& prec) const
- {
- return isApproxToConstant(Scalar(1), prec);
- }
- /** Sets all coefficients in this expression to one.
- *
- * Example: \include MatrixBase_setOnes.cpp
- * Output: \verbinclude MatrixBase_setOnes.out
- *
- * \sa class CwiseNullaryOp, Ones()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
- {
- return setConstant(Scalar(1));
- }
- /** Resizes to the given \a newSize, and sets all coefficients in this expression to one.
- *
- * \only_for_vectors
- *
- * Example: \include Matrix_setOnes_int.cpp
- * Output: \verbinclude Matrix_setOnes_int.out
- *
- * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setOnes(Index newSize)
- {
- resize(newSize);
- return setConstant(Scalar(1));
- }
- /** Resizes to the given size, and sets all coefficients in this expression to one.
- *
- * \param rows the new number of rows
- * \param cols the new number of columns
- *
- * Example: \include Matrix_setOnes_int_int.cpp
- * Output: \verbinclude Matrix_setOnes_int_int.out
- *
- * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
- PlainObjectBase<Derived>::setOnes(Index rows, Index cols)
- {
- resize(rows, cols);
- return setConstant(Scalar(1));
- }
- // Identity:
- /** \returns an expression of the identity matrix (not necessarily square).
- *
- * The parameters \a rows and \a cols are the number of rows and of columns of
- * the returned matrix. Must be compatible with this MatrixBase type.
- *
- * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
- * instead.
- *
- * Example: \include MatrixBase_identity_int_int.cpp
- * Output: \verbinclude MatrixBase_identity_int_int.out
- *
- * \sa Identity(), setIdentity(), isIdentity()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
- MatrixBase<Derived>::Identity(Index rows, Index cols)
- {
- return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
- }
- /** \returns an expression of the identity matrix (not necessarily square).
- *
- * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
- * need to use the variant taking size arguments.
- *
- * Example: \include MatrixBase_identity.cpp
- * Output: \verbinclude MatrixBase_identity.out
- *
- * \sa Identity(Index,Index), setIdentity(), isIdentity()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
- MatrixBase<Derived>::Identity()
- {
- EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
- return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
- }
- /** \returns true if *this is approximately equal to the identity matrix
- * (not necessarily square),
- * within the precision given by \a prec.
- *
- * Example: \include MatrixBase_isIdentity.cpp
- * Output: \verbinclude MatrixBase_isIdentity.out
- *
- * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
- */
- template<typename Derived>
- bool MatrixBase<Derived>::isIdentity
- (const RealScalar& prec) const
- {
- typename internal::nested_eval<Derived,1>::type self(derived());
- for(Index j = 0; j < cols(); ++j)
- {
- for(Index i = 0; i < rows(); ++i)
- {
- if(i == j)
- {
- if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec))
- return false;
- }
- else
- {
- if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec))
- return false;
- }
- }
- }
- return true;
- }
- namespace internal {
- template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
- struct setIdentity_impl
- {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Derived& run(Derived& m)
- {
- return m = Derived::Identity(m.rows(), m.cols());
- }
- };
- template<typename Derived>
- struct setIdentity_impl<Derived, true>
- {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Derived& run(Derived& m)
- {
- m.setZero();
- const Index size = numext::mini(m.rows(), m.cols());
- for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
- return m;
- }
- };
- } // end namespace internal
- /** Writes the identity expression (not necessarily square) into *this.
- *
- * Example: \include MatrixBase_setIdentity.cpp
- * Output: \verbinclude MatrixBase_setIdentity.out
- *
- * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
- {
- return internal::setIdentity_impl<Derived>::run(derived());
- }
- /** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
- *
- * \param rows the new number of rows
- * \param cols the new number of columns
- *
- * Example: \include Matrix_setIdentity_int_int.cpp
- * Output: \verbinclude Matrix_setIdentity_int_int.out
- *
- * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)
- {
- derived().resize(rows, cols);
- return setIdentity();
- }
- /** \returns an expression of the i-th unit (basis) vector.
- *
- * \only_for_vectors
- *
- * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i);
- }
- /** \returns an expression of the i-th unit (basis) vector.
- *
- * \only_for_vectors
- *
- * This variant is for fixed-size vector only.
- *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
- {
- EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
- return BasisReturnType(SquareMatrixType::Identity(),i);
- }
- /** \returns an expression of the X axis unit vector (1{,0}^*)
- *
- * \only_for_vectors
- *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
- { return Derived::Unit(0); }
- /** \returns an expression of the Y axis unit vector (0,1{,0}^*)
- *
- * \only_for_vectors
- *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
- { return Derived::Unit(1); }
- /** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
- *
- * \only_for_vectors
- *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
- { return Derived::Unit(2); }
- /** \returns an expression of the W axis unit vector (0,0,0,1)
- *
- * \only_for_vectors
- *
- * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
- { return Derived::Unit(3); }
- } // end namespace Eigen
- #endif // EIGEN_CWISE_NULLARY_OP_H
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