1 files changed, 0 insertions, 441 deletions
diff --git a/third_party/eigen3/Eigen/src/Householder/HouseholderSequence.h b/third_party/eigen3/Eigen/src/Householder/HouseholderSequence.h
deleted file mode 100644
index d800ca1fa4..0000000000
--- a/third_party/eigen3/Eigen/src/Householder/HouseholderSequence.h
+++ /dev/null
@@ -1,441 +0,0 @@
-// 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::Index Index;
-  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
-  };
-};
-
-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;
-  typedef typename VectorsType::Index Index;
-  static 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;
-  typedef typename VectorsType::Index Index;
-  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 scalar_product_traits<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 typename VectorsType::Index Index;
-
-    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;
-
-    /** \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()
-      */
-    HouseholderSequence(const VectorsType& v, const CoeffsType& h)
-      : m_vectors(v), m_coeffs(h), m_trans(false), m_length(v.diagonalSize()),
-        m_shift(0)
-    {
-    }
-
-    /** \brief Copy constructor. */
-    HouseholderSequence(const HouseholderSequence& other)
-      : m_vectors(other.m_vectors),
-        m_coeffs(other.m_coeffs),
-        m_trans(other.m_trans),
-        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.
-      */
-    Index rows() const { 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(); }
-
-    /** \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()
-      */
-    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. */
-    HouseholderSequence transpose() const
-    {
-      return HouseholderSequence(*this).setTrans(!m_trans);
-    }
-
-    /** \brief Complex conjugate of the Householder sequence. */
-    ConjugateReturnType conjugate() const
-    {
-      return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
-             .setTrans(m_trans)
-             .setLength(m_length)
-             .setShift(m_shift);
-    }
-
-    /** \brief Adjoint (conjugate transpose) of the Householder sequence. */
-    ConjugateReturnType adjoint() const
-    {
-      return conjugate().setTrans(!m_trans);
-    }
-
-    /** \brief Inverse of the Householder sequence (equals the adjoint). */
-    ConjugateReturnType inverse() const { return adjoint(); }
-
-    /** \internal */
-    template<typename DestType> inline 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>
-    void evalTo(Dest& dst, Workspace& workspace) const
-    {
-      workspace.resize(rows());
-      Index vecs = m_length;
-      if(    internal::is_same<typename internal::remove_all<VectorsType>::type,Dest>::value
-          && internal::extract_data(dst) == internal::extract_data(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_trans)
-            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
-      {
-        dst.setIdentity(rows(), rows());
-        for(Index k = vecs-1; k >= 0; --k)
-        {
-          Index cornerSize = rows() - k - m_shift;
-          if(m_trans)
-            dst.bottomRightCorner(cornerSize, cornerSize)
-               .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
-          else
-            dst.bottomRightCorner(cornerSize, cornerSize)
-               .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &workspace.coeffRef(0));
-        }
-      }
-    }
-
-    /** \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_trans ? 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
-    {
-      Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace(dst.cols());
-      applyThisOnTheLeft(dst, workspace);
-    }
-
-    /** \internal */
-    template<typename Dest, typename Workspace>
-    inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace) const
-    {
-      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)
-           .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);
-      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()
-      */
-    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()
-      */
-    HouseholderSequence& setShift(Index shift)
-    {
-      m_shift = shift;
-      return *this;
-    }
-
-    Index length() const { return m_length; }  /**< \brief Returns the length of the Householder sequence. */
-    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:
-
-    /** \brief Sets the transpose flag.
-      * \param [in]  trans  New value of the transpose 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$.
-      *
-      * \sa trans()
-      */
-    HouseholderSequence& setTrans(bool trans)
-    {
-      m_trans = trans;
-      return *this;
-    }
-
-    bool trans() const { return m_trans; }     /**< \brief Returns the transpose flag. */
-
-    typename VectorsType::Nested m_vectors;
-    typename CoeffsType::Nested m_coeffs;
-    bool m_trans;
-    Index m_length;
-    Index m_shift;
-};
-
-/** \brief Computes the product of a matrix with a Householder sequence.
-  * \param[in]  other  %Matrix being multiplied.
-  * \param[in]  h      %HouseholderSequence being multiplied.
-  * \returns    Expression object representing the product.
-  *
-  * This function computes \f$ 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