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diff --git a/src/3rdparty/eigen/Eigen/src/Householder/HouseholderSequence.h b/src/3rdparty/eigen/Eigen/src/Householder/HouseholderSequence.h new file mode 100644 index 000000000..022f6c3db --- /dev/null +++ b/src/3rdparty/eigen/Eigen/src/Householder/HouseholderSequence.h @@ -0,0 +1,545 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// 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_HOUSEHOLDER_SEQUENCE_H +#define EIGEN_HOUSEHOLDER_SEQUENCE_H + +namespace Eigen { + +/** \ingroup Householder_Module + * \householder_module + * \class HouseholderSequence + * \brief Sequence of Householder reflections acting on subspaces with decreasing size + * \tparam VectorsType type of matrix containing the Householder vectors + * \tparam CoeffsType type of vector containing the Householder coefficients + * \tparam Side either OnTheLeft (the default) or OnTheRight + * + * This class represents a product sequence of Householder reflections where the first Householder reflection + * acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by + * the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace + * spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but + * one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections + * are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods + * HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(), + * and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence. + * + * More precisely, the class %HouseholderSequence represents an \f$ n \times n \f$ matrix \f$ H \f$ of the + * 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] + * The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector. + * + * Typical usages are listed below, where H is a HouseholderSequence: + * \code + * A.applyOnTheRight(H); // A = A * H + * A.applyOnTheLeft(H); // A = H * A + * A.applyOnTheRight(H.adjoint()); // A = A * H^* + * A.applyOnTheLeft(H.adjoint()); // A = H^* * A + * MatrixXd Q = H; // conversion to a dense matrix + * \endcode + * In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate operators. + * + * See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example. + * + * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() + */ + +namespace internal { + +template<typename VectorsType, typename CoeffsType, int Side> +struct traits<HouseholderSequence<VectorsType,CoeffsType,Side> > +{ + typedef typename VectorsType::Scalar Scalar; + typedef typename VectorsType::StorageIndex StorageIndex; + typedef typename VectorsType::StorageKind StorageKind; + enum { + RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime + : traits<VectorsType>::ColsAtCompileTime, + ColsAtCompileTime = RowsAtCompileTime, + MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime + : traits<VectorsType>::MaxColsAtCompileTime, + MaxColsAtCompileTime = MaxRowsAtCompileTime, + Flags = 0 + }; +}; + +struct HouseholderSequenceShape {}; + +template<typename VectorsType, typename CoeffsType, int Side> +struct evaluator_traits<HouseholderSequence<VectorsType,CoeffsType,Side> > + : public evaluator_traits_base<HouseholderSequence<VectorsType,CoeffsType,Side> > +{ + typedef HouseholderSequenceShape Shape; +}; + +template<typename VectorsType, typename CoeffsType, int Side> +struct hseq_side_dependent_impl +{ + typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType; + typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType; + 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); + } +}; + +template<typename VectorsType, typename CoeffsType> +struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight> +{ + typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType; + typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType; + static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k) + { + Index start = k+1+h.m_shift; + return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose(); + } +}; + +template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type +{ + typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType + ResultScalar; + typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, + 0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type; +}; + +} // end namespace internal + +template<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence + : 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, + ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime, + MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime, + MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime + }; + typedef typename internal::traits<HouseholderSequence>::Scalar Scalar; + + typedef HouseholderSequence< + typename internal::conditional<NumTraits<Scalar>::IsComplex, + typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type, + VectorsType>::type, + typename internal::conditional<NumTraits<Scalar>::IsComplex, + typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type, + CoeffsType>::type, + 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 + * + * Constructs the Householder sequence with coefficients given by \p h and vectors given by \p v. The + * i-th Householder coefficient \f$ h_i \f$ is given by \p h(i) and the essential part of the i-th + * Householder vector \f$ v_i \f$ is given by \p v(k,i) with \p k > \p i (the subdiagonal part of the + * i-th column). If \p v has fewer columns than rows, then the Householder sequence contains as many + * Householder reflections as there are columns. + * + * \note The %HouseholderSequence object stores \p v and \p h by reference. + * + * Example: \include HouseholderSequence_HouseholderSequence.cpp + * Output: \verbinclude HouseholderSequence_HouseholderSequence.out + * + * \sa setLength(), setShift() + */ + EIGEN_DEVICE_FUNC + HouseholderSequence(const VectorsType& v, const CoeffsType& h) + : 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_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 + * \details This equals the dimension of the space that the transformation acts on. + */ + 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. + */ + 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 + * \returns Vector containing non-trivial entries of k-th Householder vector + * + * 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] + * 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); + return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k); + } + + /** \brief %Transpose of the Householder sequence. */ + TransposeReturnType transpose() const + { + 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()) + .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. */ + AdjointReturnType adjoint() const + { + 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). */ + AdjointReturnType inverse() const { return adjoint(); } + + /** \internal */ + template<typename DestType> + inline EIGEN_DEVICE_FUNC + void evalTo(DestType& dst) const + { + Matrix<Scalar, DestType::RowsAtCompileTime, 1, + AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows()); + evalTo(dst, workspace); + } + + /** \internal */ + template<typename Dest, typename Workspace> + EIGEN_DEVICE_FUNC + void evalTo(Dest& dst, Workspace& workspace) const + { + workspace.resize(rows()); + Index vecs = m_length; + if(internal::is_same_dense(dst,m_vectors)) + { + // in-place + dst.diagonal().setOnes(); + dst.template triangularView<StrictlyUpper>().setZero(); + for(Index k = vecs-1; k >= 0; --k) + { + Index cornerSize = rows() - k - m_shift; + if(m_reverse) + dst.bottomRightCorner(cornerSize, cornerSize) + .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data()); + else + dst.bottomRightCorner(cornerSize, cornerSize) + .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data()); + + // clear the off diagonal vector + dst.col(k).tail(rows()-k-1).setZero(); + } + // clear the remaining columns if needed + 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_reverse) + dst.bottomRightCorner(cornerSize, cornerSize) + .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data()); + else + dst.bottomRightCorner(cornerSize, cornerSize) + .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data()); + } + } + } + + /** \internal */ + template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const + { + Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows()); + applyThisOnTheRight(dst, workspace); + } + + /** \internal */ + template<typename Dest, typename Workspace> + inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const + { + workspace.resize(dst.rows()); + for(Index k = 0; k < m_length; ++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, bool inputIsIdentity = false) const + { + Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace; + applyThisOnTheLeft(dst, workspace, inputIsIdentity); + } + + /** \internal */ + template<typename Dest, typename Workspace> + inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace, bool inputIsIdentity = false) const + { + 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) + { + // 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_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); + + 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 + { + workspace.resize(dst.cols()); + for(Index k = 0; k < m_length; ++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()); + } + } + } + + /** \brief Computes the product of a Householder sequence with a matrix. + * \param[in] other %Matrix being multiplied. + * \returns Expression object representing the product. + * + * This function computes \f$ HM \f$ where \f$ H \f$ is the Householder sequence represented by \p *this + * and \f$ M \f$ is the matrix \p other. + */ + template<typename OtherDerived> + typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const + { + 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, internal::is_identity<OtherDerived>::value && res.rows()==res.cols()); + return res; + } + + template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl; + + /** \brief Sets the length of the Householder sequence. + * \param [in] length New value for the length. + * + * By default, the length \f$ n \f$ of the Householder sequence \f$ H = H_0 H_1 \ldots H_{n-1} \f$ is set + * to the number of columns of the matrix \p v passed to the constructor, or the number of rows if that + * is smaller. After this function is called, the length equals \p length. + * + * \sa length() + */ + EIGEN_DEVICE_FUNC + HouseholderSequence& setLength(Index length) + { + m_length = length; + return *this; + } + + /** \brief Sets the shift of the Householder sequence. + * \param [in] shift New value for the shift. + * + * By default, a %HouseholderSequence object represents \f$ H = H_0 H_1 \ldots H_{n-1} \f$ and the i-th + * column of the matrix \p v passed to the constructor corresponds to the i-th Householder + * reflection. After this function is called, the object represents \f$ H = H_{\mathrm{shift}} + * H_{\mathrm{shift}+1} \ldots H_{n-1} \f$ and the i-th column of \p v corresponds to the (shift+i)-th + * Householder reflection. + * + * \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() */ + template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence; + + protected: + + /** \internal + * \brief Sets the reverse flag. + * \param [in] reverse New value of the reverse flag. + * + * 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$. + * + * \sa reverseFlag(), transpose(), adjoint() + */ + HouseholderSequence& setReverseFlag(bool reverse) + { + m_reverse = reverse; + return *this; + } + + bool reverseFlag() const { return m_reverse; } /**< \internal \brief Returns the reverse flag. */ + + typename VectorsType::Nested m_vectors; + typename CoeffsType::Nested m_coeffs; + bool m_reverse; + Index m_length; + Index m_shift; + enum { BlockSize = 48 }; +}; + +/** \brief Computes the product of a matrix with a Householder sequence. + * \param[in] other %Matrix being multiplied. + * \param[in] h %HouseholderSequence being multiplied. + * \returns Expression object representing the product. + * + * This function computes \f$ MH \f$ where \f$ M \f$ is the matrix \p other and \f$ H \f$ is the + * Householder sequence represented by \p h. + */ +template<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side> +typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h) +{ + typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type + res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>()); + h.applyThisOnTheRight(res); + return res; +} + +/** \ingroup Householder_Module \householder_module + * \brief Convenience function for constructing a Householder sequence. + * \returns A HouseholderSequence constructed from the specified arguments. + */ +template<typename VectorsType, typename CoeffsType> +HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h) +{ + return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h); +} + +/** \ingroup Householder_Module \householder_module + * \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. + */ +template<typename VectorsType, typename CoeffsType> +HouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h) +{ + return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h); +} + +} // end namespace Eigen + +#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H |