867 lines
31 KiB
C++
867 lines
31 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_CWISE_NULLARY_OP_H
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#define EIGEN_CWISE_NULLARY_OP_H
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namespace Eigen {
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namespace internal {
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template<typename NullaryOp, typename PlainObjectType>
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struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
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{
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enum {
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Flags = traits<PlainObjectType>::Flags & RowMajorBit
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};
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};
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} // namespace internal
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/** \class CwiseNullaryOp
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* \ingroup Core_Module
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*
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* \brief Generic expression of a matrix where all coefficients are defined by a functor
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*
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* \tparam NullaryOp template functor implementing the operator
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* \tparam PlainObjectType the underlying plain matrix/array type
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*
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* This class represents an expression of a generic nullary operator.
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* It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
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* and most of the time this is the only way it is used.
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*
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* However, if you want to write a function returning such an expression, you
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* will need to use this class.
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*
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* The functor NullaryOp must expose one of the following method:
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<table class="manual">
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<tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>
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<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>
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<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>
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</table>
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* It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.
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*
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* See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
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* C++11 random number generators.
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*
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* A nullary expression can also be used to implement custom sophisticated matrix manipulations
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* that cannot be covered by the existing set of natively supported matrix manipulations.
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* See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations
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* on the behavior of CwiseNullaryOp.
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*
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* \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
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*/
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template<typename NullaryOp, typename PlainObjectType>
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class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator
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{
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public:
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typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
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EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
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EIGEN_DEVICE_FUNC
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CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
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: m_rows(rows), m_cols(cols), m_functor(func)
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{
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eigen_assert(rows >= 0
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&& (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
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&& cols >= 0
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&& (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
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}
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EIGEN_DEVICE_FUNC
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EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); }
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EIGEN_DEVICE_FUNC
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EIGEN_STRONG_INLINE Index cols() const { return m_cols.value(); }
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/** \returns the functor representing the nullary operation */
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EIGEN_DEVICE_FUNC
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const NullaryOp& functor() const { return m_functor; }
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protected:
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const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
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const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
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const NullaryOp m_functor;
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};
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/** \returns an expression of a matrix defined by a custom functor \a func
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*
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* The parameters \a rows and \a cols are the number of rows and of columns of
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* the returned matrix. Must be compatible with this MatrixBase type.
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*
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* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
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* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
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* instead.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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template<typename CustomNullaryOp>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
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DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
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{
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return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
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}
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/** \returns an expression of a matrix defined by a custom functor \a func
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*
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* The parameter \a size is the size of the returned vector.
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* Must be compatible with this MatrixBase type.
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*
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* \only_for_vectors
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*
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* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
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* it is redundant to pass \a size as argument, so Zero() should be used
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* instead.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* Here is an example with C++11 random generators: \include random_cpp11.cpp
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* Output: \verbinclude random_cpp11.out
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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template<typename CustomNullaryOp>
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EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
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DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
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else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
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}
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/** \returns an expression of a matrix defined by a custom functor \a func
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*
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* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
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* need to use the variants taking size arguments.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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template<typename CustomNullaryOp>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
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DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
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{
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return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
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}
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/** \returns an expression of a constant matrix of value \a value
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*
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* The parameters \a rows and \a cols are the number of rows and of columns of
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* the returned matrix. Must be compatible with this DenseBase type.
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*
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* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
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* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
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* instead.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
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DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
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{
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return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
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}
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/** \returns an expression of a constant matrix of value \a value
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*
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* The parameter \a size is the size of the returned vector.
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* Must be compatible with this DenseBase type.
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*
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* \only_for_vectors
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*
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* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
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* it is redundant to pass \a size as argument, so Zero() should be used
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* instead.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
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DenseBase<Derived>::Constant(Index size, const Scalar& value)
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{
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return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
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}
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/** \returns an expression of a constant matrix of value \a value
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*
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* This variant is only for fixed-size DenseBase types. For dynamic-size types, you
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* need to use the variants taking size arguments.
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*
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* The template parameter \a CustomNullaryOp is the type of the functor.
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*
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* \sa class CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
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DenseBase<Derived>::Constant(const Scalar& value)
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{
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EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
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return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
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}
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/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
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*
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* \sa LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
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DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
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}
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/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
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*
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* \sa LinSpaced(Scalar,Scalar)
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
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DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
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return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
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}
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/**
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* \brief Sets a linearly spaced vector.
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*
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* The function generates 'size' equally spaced values in the closed interval [low,high].
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* When size is set to 1, a vector of length 1 containing 'high' is returned.
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*
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* \only_for_vectors
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*
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* Example: \include DenseBase_LinSpaced.cpp
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* Output: \verbinclude DenseBase_LinSpaced.out
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*
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* For integer scalar types, an even spacing is possible if and only if the length of the range,
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* i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the
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* number of values \c high-low+1 (meaning each value can be repeated the same number of time).
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* If one of these two considions is not satisfied, then \c high is lowered to the largest value
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* satisfying one of this constraint.
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* Here are some examples:
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*
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* Example: \include DenseBase_LinSpacedInt.cpp
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* Output: \verbinclude DenseBase_LinSpacedInt.out
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*
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* \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
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DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
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}
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/**
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* \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
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* Special version for fixed size types which does not require the size parameter.
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
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DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
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return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
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}
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/** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
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template<typename Derived>
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EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant
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(const Scalar& val, const RealScalar& prec) const
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{
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typename internal::nested_eval<Derived,1>::type self(derived());
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for(Index j = 0; j < cols(); ++j)
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for(Index i = 0; i < rows(); ++i)
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if(!internal::isApprox(self.coeff(i, j), val, prec))
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return false;
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return true;
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}
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/** This is just an alias for isApproxToConstant().
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*
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* \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
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template<typename Derived>
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EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant
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(const Scalar& val, const RealScalar& prec) const
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{
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return isApproxToConstant(val, prec);
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}
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/** Alias for setConstant(): sets all coefficients in this expression to \a val.
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*
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* \sa setConstant(), Constant(), class CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
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{
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setConstant(val);
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}
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/** Sets all coefficients in this expression to value \a val.
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*
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* \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
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{
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return derived() = Constant(rows(), cols(), val);
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}
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/** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
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*
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* \only_for_vectors
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*
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* Example: \include Matrix_setConstant_int.cpp
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* Output: \verbinclude Matrix_setConstant_int.out
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*
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* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
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PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
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{
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resize(size);
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return setConstant(val);
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}
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/** Resizes to the given size, and sets all coefficients in this expression to the given value \a val.
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*
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* \param rows the new number of rows
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* \param cols the new number of columns
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* \param val the value to which all coefficients are set
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*
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* Example: \include Matrix_setConstant_int_int.cpp
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* Output: \verbinclude Matrix_setConstant_int_int.out
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*
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* \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
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PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)
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{
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resize(rows, cols);
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return setConstant(val);
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}
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/**
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* \brief Sets a linearly spaced vector.
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*
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* The function generates 'size' equally spaced values in the closed interval [low,high].
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* When size is set to 1, a vector of length 1 containing 'high' is returned.
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*
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* \only_for_vectors
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*
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* Example: \include DenseBase_setLinSpaced.cpp
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* Output: \verbinclude DenseBase_setLinSpaced.out
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*
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* For integer scalar types, do not miss the explanations on the definition
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* of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
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*
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* \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize));
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}
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/**
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* \brief Sets a linearly spaced vector.
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*
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* The function fills \c *this with equally spaced values in the closed interval [low,high].
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* When size is set to 1, a vector of length 1 containing 'high' is returned.
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*
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* \only_for_vectors
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*
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* For integer scalar types, do not miss the explanations on the definition
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* of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
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*
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* \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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return setLinSpaced(size(), low, high);
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}
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// zero:
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/** \returns an expression of a zero matrix.
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*
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* The parameters \a rows and \a cols are the number of rows and of columns of
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* the returned matrix. Must be compatible with this MatrixBase type.
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*
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* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
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* it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
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* instead.
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*
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* Example: \include MatrixBase_zero_int_int.cpp
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* Output: \verbinclude MatrixBase_zero_int_int.out
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*
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* \sa Zero(), Zero(Index)
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
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DenseBase<Derived>::Zero(Index rows, Index cols)
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{
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return Constant(rows, cols, Scalar(0));
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}
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|
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/** \returns an expression of a zero vector.
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*
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* The parameter \a size is the size of the returned vector.
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* Must be compatible with this MatrixBase type.
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*
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* \only_for_vectors
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*
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* This variant is meant to be used for dynamic-size vector types. For fixed-size types,
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* it is redundant to pass \a size as argument, so Zero() should be used
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* instead.
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*
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* Example: \include MatrixBase_zero_int.cpp
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|
* 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
|