diff options
Diffstat (limited to 'Eigen/src/Householder/HouseholderSequence.h')
| -rw-r--r-- | Eigen/src/Householder/HouseholderSequence.h | 171 |
1 files changed, 123 insertions, 48 deletions
diff --git a/Eigen/src/Householder/HouseholderSequence.h b/Eigen/src/Householder/HouseholderSequence.h index 3ce0a693d..022f6c3db 100644 --- a/Eigen/src/Householder/HouseholderSequence.h +++ b/Eigen/src/Householder/HouseholderSequence.h @@ -11,7 +11,7 @@ #ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H #define EIGEN_HOUSEHOLDER_SEQUENCE_H -namespace Eigen { +namespace Eigen { /** \ingroup Householder_Module * \householder_module @@ -34,8 +34,8 @@ namespace Eigen { * form \f$ H = \prod_{i=0}^{n-1} H_i \f$ where the i-th Householder reflection is \f$ H_i = I - h_i v_i * v_i^* \f$. The i-th Householder coefficient \f$ h_i \f$ is a scalar and the i-th Householder vector \f$ * v_i \f$ is a vector of the form - * \f[ - * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. + * \f[ + * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. * \f] * The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector. * @@ -87,7 +87,7 @@ struct hseq_side_dependent_impl { typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType; typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType; - static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) + static EIGEN_DEVICE_FUNC inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) { Index start = k+1+h.m_shift; return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1); @@ -120,7 +120,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS : public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> > { typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType; - + public: enum { RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime, @@ -140,6 +140,28 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS Side > ConjugateReturnType; + typedef HouseholderSequence< + VectorsType, + typename internal::conditional<NumTraits<Scalar>::IsComplex, + typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type, + CoeffsType>::type, + Side + > AdjointReturnType; + + typedef HouseholderSequence< + typename internal::conditional<NumTraits<Scalar>::IsComplex, + typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type, + VectorsType>::type, + CoeffsType, + Side + > TransposeReturnType; + + typedef HouseholderSequence< + typename internal::add_const<VectorsType>::type, + typename internal::add_const<CoeffsType>::type, + Side + > ConstHouseholderSequence; + /** \brief Constructor. * \param[in] v %Matrix containing the essential parts of the Householder vectors * \param[in] h Vector containing the Householder coefficients @@ -157,33 +179,37 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS * * \sa setLength(), setShift() */ + EIGEN_DEVICE_FUNC HouseholderSequence(const VectorsType& v, const CoeffsType& h) - : m_vectors(v), m_coeffs(h), m_trans(false), m_length(v.diagonalSize()), + : m_vectors(v), m_coeffs(h), m_reverse(false), m_length(v.diagonalSize()), m_shift(0) { } /** \brief Copy constructor. */ + EIGEN_DEVICE_FUNC HouseholderSequence(const HouseholderSequence& other) : m_vectors(other.m_vectors), m_coeffs(other.m_coeffs), - m_trans(other.m_trans), + m_reverse(other.m_reverse), m_length(other.m_length), m_shift(other.m_shift) { } /** \brief Number of rows of transformation viewed as a matrix. - * \returns Number of rows + * \returns Number of rows * \details This equals the dimension of the space that the transformation acts on. */ - Index rows() const { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); } /** \brief Number of columns of transformation viewed as a matrix. * \returns Number of columns * \details This equals the dimension of the space that the transformation acts on. */ - Index cols() const { return rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { return rows(); } /** \brief Essential part of a Householder vector. * \param[in] k Index of Householder reflection @@ -191,14 +217,15 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS * * This function returns the essential part of the Householder vector \f$ v_i \f$. This is a vector of * length \f$ n-i \f$ containing the last \f$ n-i \f$ entries of the vector - * \f[ - * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. + * \f[ + * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ]. * \f] * The index \f$ i \f$ equals \p k + shift(), corresponding to the k-th column of the matrix \p v * passed to the constructor. * * \sa setShift(), shift() */ + EIGEN_DEVICE_FUNC const EssentialVectorType essentialVector(Index k) const { eigen_assert(k >= 0 && k < m_length); @@ -206,31 +233,51 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS } /** \brief %Transpose of the Householder sequence. */ - HouseholderSequence transpose() const + TransposeReturnType transpose() const { - return HouseholderSequence(*this).setTrans(!m_trans); + return TransposeReturnType(m_vectors.conjugate(), m_coeffs) + .setReverseFlag(!m_reverse) + .setLength(m_length) + .setShift(m_shift); } /** \brief Complex conjugate of the Householder sequence. */ ConjugateReturnType conjugate() const { return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate()) - .setTrans(m_trans) + .setReverseFlag(m_reverse) .setLength(m_length) .setShift(m_shift); } + /** \returns an expression of the complex conjugate of \c *this if Cond==true, + * returns \c *this otherwise. + */ + template<bool Cond> + EIGEN_DEVICE_FUNC + inline typename internal::conditional<Cond,ConjugateReturnType,ConstHouseholderSequence>::type + conjugateIf() const + { + typedef typename internal::conditional<Cond,ConjugateReturnType,ConstHouseholderSequence>::type ReturnType; + return ReturnType(m_vectors.template conjugateIf<Cond>(), m_coeffs.template conjugateIf<Cond>()); + } + /** \brief Adjoint (conjugate transpose) of the Householder sequence. */ - ConjugateReturnType adjoint() const + AdjointReturnType adjoint() const { - return conjugate().setTrans(!m_trans); + return AdjointReturnType(m_vectors, m_coeffs.conjugate()) + .setReverseFlag(!m_reverse) + .setLength(m_length) + .setShift(m_shift); } /** \brief Inverse of the Householder sequence (equals the adjoint). */ - ConjugateReturnType inverse() const { return adjoint(); } + AdjointReturnType inverse() const { return adjoint(); } /** \internal */ - template<typename DestType> inline void evalTo(DestType& dst) const + template<typename DestType> + inline EIGEN_DEVICE_FUNC + void evalTo(DestType& dst) const { Matrix<Scalar, DestType::RowsAtCompileTime, 1, AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows()); @@ -239,6 +286,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS /** \internal */ template<typename Dest, typename Workspace> + EIGEN_DEVICE_FUNC void evalTo(Dest& dst, Workspace& workspace) const { workspace.resize(rows()); @@ -251,7 +299,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS for(Index k = vecs-1; k >= 0; --k) { Index cornerSize = rows() - k - m_shift; - if(m_trans) + if(m_reverse) dst.bottomRightCorner(cornerSize, cornerSize) .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data()); else @@ -265,18 +313,26 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS for(Index k = 0; k<cols()-vecs ; ++k) dst.col(k).tail(rows()-k-1).setZero(); } + else if(m_length>BlockSize) + { + dst.setIdentity(rows(), rows()); + if(m_reverse) + applyThisOnTheLeft(dst,workspace,true); + else + applyThisOnTheLeft(dst,workspace,true); + } else { dst.setIdentity(rows(), rows()); for(Index k = vecs-1; k >= 0; --k) { Index cornerSize = rows() - k - m_shift; - if(m_trans) + if(m_reverse) dst.bottomRightCorner(cornerSize, cornerSize) - .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0)); + .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data()); else dst.bottomRightCorner(cornerSize, cornerSize) - .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0)); + .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data()); } } } @@ -295,42 +351,52 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS workspace.resize(dst.rows()); for(Index k = 0; k < m_length; ++k) { - Index actual_k = m_trans ? m_length-k-1 : k; + Index actual_k = m_reverse ? m_length-k-1 : k; dst.rightCols(rows()-m_shift-actual_k) .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data()); } } /** \internal */ - template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const + template<typename Dest> inline void applyThisOnTheLeft(Dest& dst, bool inputIsIdentity = false) const { Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace; - applyThisOnTheLeft(dst, workspace); + applyThisOnTheLeft(dst, workspace, inputIsIdentity); } /** \internal */ template<typename Dest, typename Workspace> - inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace) const + inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace, bool inputIsIdentity = false) const { - const Index BlockSize = 48; + if(inputIsIdentity && m_reverse) + inputIsIdentity = false; // if the entries are large enough, then apply the reflectors by block if(m_length>=BlockSize && dst.cols()>1) { - for(Index i = 0; i < m_length; i+=BlockSize) + // Make sure we have at least 2 useful blocks, otherwise it is point-less: + Index blockSize = m_length<Index(2*BlockSize) ? (m_length+1)/2 : Index(BlockSize); + for(Index i = 0; i < m_length; i+=blockSize) { - Index end = m_trans ? (std::min)(m_length,i+BlockSize) : m_length-i; - Index k = m_trans ? i : (std::max)(Index(0),end-BlockSize); + Index end = m_reverse ? (std::min)(m_length,i+blockSize) : m_length-i; + Index k = m_reverse ? i : (std::max)(Index(0),end-blockSize); Index bs = end-k; Index start = k + m_shift; - + typedef Block<typename internal::remove_all<VectorsType>::type,Dynamic,Dynamic> SubVectorsType; SubVectorsType sub_vecs1(m_vectors.const_cast_derived(), Side==OnTheRight ? k : start, Side==OnTheRight ? start : k, Side==OnTheRight ? bs : m_vectors.rows()-start, Side==OnTheRight ? m_vectors.cols()-start : bs); typename internal::conditional<Side==OnTheRight, Transpose<SubVectorsType>, SubVectorsType&>::type sub_vecs(sub_vecs1); - Block<Dest,Dynamic,Dynamic> sub_dst(dst,dst.rows()-rows()+m_shift+k,0, rows()-m_shift-k,dst.cols()); - apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_trans); + + Index dstStart = dst.rows()-rows()+m_shift+k; + Index dstRows = rows()-m_shift-k; + Block<Dest,Dynamic,Dynamic> sub_dst(dst, + dstStart, + inputIsIdentity ? dstStart : 0, + dstRows, + inputIsIdentity ? dstRows : dst.cols()); + apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse); } } else @@ -338,8 +404,9 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS workspace.resize(dst.cols()); for(Index k = 0; k < m_length; ++k) { - Index actual_k = m_trans ? k : m_length-k-1; - dst.bottomRows(rows()-m_shift-actual_k) + Index actual_k = m_reverse ? k : m_length-k-1; + Index dstStart = rows()-m_shift-actual_k; + dst.bottomRightCorner(dstStart, inputIsIdentity ? dstStart : dst.cols()) .applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data()); } } @@ -357,7 +424,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS { typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>()); - applyThisOnTheLeft(res); + applyThisOnTheLeft(res, internal::is_identity<OtherDerived>::value && res.rows()==res.cols()); return res; } @@ -372,6 +439,7 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS * * \sa length() */ + EIGEN_DEVICE_FUNC HouseholderSequence& setLength(Index length) { m_length = length; @@ -389,13 +457,17 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS * * \sa shift() */ + EIGEN_DEVICE_FUNC HouseholderSequence& setShift(Index shift) { m_shift = shift; return *this; } + EIGEN_DEVICE_FUNC Index length() const { return m_length; } /**< \brief Returns the length of the Householder sequence. */ + + EIGEN_DEVICE_FUNC Index shift() const { return m_shift; } /**< \brief Returns the shift of the Householder sequence. */ /* Necessary for .adjoint() and .conjugate() */ @@ -403,27 +475,30 @@ template<typename VectorsType, typename CoeffsType, int Side> class HouseholderS protected: - /** \brief Sets the transpose flag. - * \param [in] trans New value of the transpose flag. + /** \internal + * \brief Sets the reverse flag. + * \param [in] reverse New value of the reverse flag. * - * By default, the transpose flag is not set. If the transpose flag is set, then this object represents - * \f$ H^T = H_{n-1}^T \ldots H_1^T H_0^T \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$. + * By default, the reverse flag is not set. If the reverse flag is set, then this object represents + * \f$ H^r = H_{n-1} \ldots H_1 H_0 \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$. + * \note For real valued HouseholderSequence this is equivalent to transposing \f$ H \f$. * - * \sa trans() + * \sa reverseFlag(), transpose(), adjoint() */ - HouseholderSequence& setTrans(bool trans) + HouseholderSequence& setReverseFlag(bool reverse) { - m_trans = trans; + m_reverse = reverse; return *this; } - bool trans() const { return m_trans; } /**< \brief Returns the transpose flag. */ + bool reverseFlag() const { return m_reverse; } /**< \internal \brief Returns the reverse flag. */ typename VectorsType::Nested m_vectors; typename CoeffsType::Nested m_coeffs; - bool m_trans; + bool m_reverse; Index m_length; Index m_shift; + enum { BlockSize = 48 }; }; /** \brief Computes the product of a matrix with a Householder sequence. @@ -444,7 +519,7 @@ typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,Ot } /** \ingroup Householder_Module \householder_module - * \brief Convenience function for constructing a Householder sequence. + * \brief Convenience function for constructing a Householder sequence. * \returns A HouseholderSequence constructed from the specified arguments. */ template<typename VectorsType, typename CoeffsType> @@ -454,7 +529,7 @@ HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsTyp } /** \ingroup Householder_Module \householder_module - * \brief Convenience function for constructing a Householder sequence. + * \brief Convenience function for constructing a Householder sequence. * \returns A HouseholderSequence constructed from the specified arguments. * \details This function differs from householderSequence() in that the template argument \p OnTheSide of * the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft. |