text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_SPARSE_SELFADJOINTVIEW_H
  #define EIGEN_SPARSE_SELFADJOINTVIEW_H
  
  namespace Eigen { 
    
  /** \ingroup SparseCore_Module
    * \class SparseSelfAdjointView
    *
    * \brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.
    *
    * \param MatrixType the type of the dense matrix storing the coefficients
    * \param Mode can be either \c #Lower or \c #Upper
    *
    * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
    * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
    * and most of the time this is the only way that it is used.
    *
    * \sa SparseMatrixBase::selfadjointView()
    */
  namespace internal {
    
  template<typename MatrixType, unsigned int Mode>
  struct traits<SparseSelfAdjointView<MatrixType,Mode> > : traits<MatrixType> {
  };
  
  template<int SrcMode,int DstMode,typename MatrixType,int DestOrder>
  void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);
  
  template<int Mode,typename MatrixType,int DestOrder>
  void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);
  
  }
  
  template<typename MatrixType, unsigned int _Mode> class SparseSelfAdjointView
    : public EigenBase<SparseSelfAdjointView<MatrixType,_Mode> >
  {
    public:
      
      enum {
        Mode = _Mode,
        TransposeMode = ((Mode & Upper) ? Lower : 0) | ((Mode & Lower) ? Upper : 0),
        RowsAtCompileTime = internal::traits<SparseSelfAdjointView>::RowsAtCompileTime,
        ColsAtCompileTime = internal::traits<SparseSelfAdjointView>::ColsAtCompileTime
      };
  
      typedef EigenBase<SparseSelfAdjointView> Base;
      typedef typename MatrixType::Scalar Scalar;
      typedef typename MatrixType::StorageIndex StorageIndex;
      typedef Matrix<StorageIndex,Dynamic,1> VectorI;
      typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
      typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
      
      explicit inline SparseSelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
      {
        eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
      }
  
      inline Index rows() const { return m_matrix.rows(); }
      inline Index cols() const { return m_matrix.cols(); }
  
      /** \internal \returns a reference to the nested matrix */
      const _MatrixTypeNested& matrix() const { return m_matrix; }
      typename internal::remove_reference<MatrixTypeNested>::type& matrix() { return m_matrix; }
  
      /** \returns an expression of the matrix product between a sparse self-adjoint matrix \c *this and a sparse matrix \a rhs.
        *
        * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
        * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
        */
      template<typename OtherDerived>
      Product<SparseSelfAdjointView, OtherDerived>
      operator*(const SparseMatrixBase<OtherDerived>& rhs) const
      {
        return Product<SparseSelfAdjointView, OtherDerived>(*this, rhs.derived());
      }
  
      /** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
        *
        * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
        * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
        */
      template<typename OtherDerived> friend
      Product<OtherDerived, SparseSelfAdjointView>
      operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
      {
        return Product<OtherDerived, SparseSelfAdjointView>(lhs.derived(), rhs);
      }
      
      /** Efficient sparse self-adjoint matrix times dense vector/matrix product */
      template<typename OtherDerived>
      Product<SparseSelfAdjointView,OtherDerived>
      operator*(const MatrixBase<OtherDerived>& rhs) const
      {
        return Product<SparseSelfAdjointView,OtherDerived>(*this, rhs.derived());
      }
  
      /** Efficient dense vector/matrix times sparse self-adjoint matrix product */
      template<typename OtherDerived> friend
      Product<OtherDerived,SparseSelfAdjointView>
      operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
      {
        return Product<OtherDerived,SparseSelfAdjointView>(lhs.derived(), rhs);
      }
  
      /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
        * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
        *
        * \returns a reference to \c *this
        *
        * To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
        * call this function with u.adjoint().
        */
      template<typename DerivedU>
      SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
      
      /** \returns an expression of P H P^-1 */
      // TODO implement twists in a more evaluator friendly fashion
      SparseSymmetricPermutationProduct<_MatrixTypeNested,Mode> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const
      {
        return SparseSymmetricPermutationProduct<_MatrixTypeNested,Mode>(m_matrix, perm);
      }
  
      template<typename SrcMatrixType,int SrcMode>
      SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcMode>& permutedMatrix)
      {
        internal::call_assignment_no_alias_no_transpose(*this, permutedMatrix);
        return *this;
      }
  
      SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)
      {
        PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;
        return *this = src.twistedBy(pnull);
      }
  
      template<typename SrcMatrixType,unsigned int SrcMode>
      SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcMode>& src)
      {
        PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;
        return *this = src.twistedBy(pnull);
      }
      
      void resize(Index rows, Index cols)
      {
        EIGEN_ONLY_USED_FOR_DEBUG(rows);
        EIGEN_ONLY_USED_FOR_DEBUG(cols);
        eigen_assert(rows == this->rows() && cols == this->cols()
                  && "SparseSelfadjointView::resize() does not actually allow to resize.");
      }
      
    protected:
  
      MatrixTypeNested m_matrix;
      //mutable VectorI m_countPerRow;
      //mutable VectorI m_countPerCol;
    private:
      template<typename Dest> void evalTo(Dest &) const;
  };
  
  /***************************************************************************
  * Implementation of SparseMatrixBase methods
  ***************************************************************************/
  
  template<typename Derived>
  template<unsigned int UpLo>
  typename SparseMatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView() const
  {
    return SparseSelfAdjointView<const Derived, UpLo>(derived());
  }
  
  template<typename Derived>
  template<unsigned int UpLo>
  typename SparseMatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView()
  {
    return SparseSelfAdjointView<Derived, UpLo>(derived());
  }
  
  /***************************************************************************
  * Implementation of SparseSelfAdjointView methods
  ***************************************************************************/
  
  template<typename MatrixType, unsigned int Mode>
  template<typename DerivedU>
  SparseSelfAdjointView<MatrixType,Mode>&
  SparseSelfAdjointView<MatrixType,Mode>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)
  {
    SparseMatrix<Scalar,(MatrixType::Flags&RowMajorBit)?RowMajor:ColMajor> tmp = u * u.adjoint();
    if(alpha==Scalar(0))
      m_matrix = tmp.template triangularView<Mode>();
    else
      m_matrix += alpha * tmp.template triangularView<Mode>();
  
    return *this;
  }
  
  namespace internal {
    
  // TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>
  //      in the future selfadjoint-ness should be defined by the expression traits
  //      such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)
  template<typename MatrixType, unsigned int Mode>
  struct evaluator_traits<SparseSelfAdjointView<MatrixType,Mode> >
  {
    typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
    typedef SparseSelfAdjointShape Shape;
  };
  
  struct SparseSelfAdjoint2Sparse {};
  
  template<> struct AssignmentKind<SparseShape,SparseSelfAdjointShape> { typedef SparseSelfAdjoint2Sparse Kind; };
  template<> struct AssignmentKind<SparseSelfAdjointShape,SparseShape> { typedef Sparse2Sparse Kind; };
  
  template< typename DstXprType, typename SrcXprType, typename Functor>
  struct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse>
  {
    typedef typename DstXprType::StorageIndex StorageIndex;
    typedef internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> AssignOpType;
  
    template<typename DestScalar,int StorageOrder>
    static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignOpType&/*func*/)
    {
      internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), dst);
    }
  
    // FIXME: the handling of += and -= in sparse matrices should be cleanup so that next two overloads could be reduced to:
    template<typename DestScalar,int StorageOrder,typename AssignFunc>
    static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignFunc& func)
    {
      SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
      run(tmp, src, AssignOpType());
      call_assignment_no_alias_no_transpose(dst, tmp, func);
    }
  
    template<typename DestScalar,int StorageOrder>
    static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,
                    const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)
    {
      SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
      run(tmp, src, AssignOpType());
      dst += tmp;
    }
  
    template<typename DestScalar,int StorageOrder>
    static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,
                    const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)
    {
      SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
      run(tmp, src, AssignOpType());
      dst -= tmp;
    }
    
    template<typename DestScalar>
    static void run(DynamicSparseMatrix<DestScalar,ColMajor,StorageIndex>& dst, const SrcXprType &src, const AssignOpType&/*func*/)
    {
      // TODO directly evaluate into dst;
      SparseMatrix<DestScalar,ColMajor,StorageIndex> tmp(dst.rows(),dst.cols());
      internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), tmp);
      dst = tmp;
    }
  };
  
  } // end namespace internal
  
  /***************************************************************************
  * Implementation of sparse self-adjoint time dense matrix
  ***************************************************************************/
  
  namespace internal {
  
  template<int Mode, typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>
  inline void sparse_selfadjoint_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)
  {
    EIGEN_ONLY_USED_FOR_DEBUG(alpha);
    
    typedef typename internal::nested_eval<SparseLhsType,DenseRhsType::MaxColsAtCompileTime>::type SparseLhsTypeNested;
    typedef typename internal::remove_all<SparseLhsTypeNested>::type SparseLhsTypeNestedCleaned;
    typedef evaluator<SparseLhsTypeNestedCleaned> LhsEval;
    typedef typename LhsEval::InnerIterator LhsIterator;
    typedef typename SparseLhsType::Scalar LhsScalar;
    
    enum {
      LhsIsRowMajor = (LhsEval::Flags&RowMajorBit)==RowMajorBit,
      ProcessFirstHalf =
                ((Mode&(Upper|Lower))==(Upper|Lower))
            || ( (Mode&Upper) && !LhsIsRowMajor)
            || ( (Mode&Lower) && LhsIsRowMajor),
      ProcessSecondHalf = !ProcessFirstHalf
    };
    
    SparseLhsTypeNested lhs_nested(lhs);
    LhsEval lhsEval(lhs_nested);
  
    // work on one column at once
    for (Index k=0; k<rhs.cols(); ++k)
    {
      for (Index j=0; j<lhs.outerSize(); ++j)
      {
        LhsIterator i(lhsEval,j);
        // handle diagonal coeff
        if (ProcessSecondHalf)
        {
          while (i && i.index()<j) ++i;
          if(i && i.index()==j)
          {
            res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);
            ++i;
          }
        }
  
        // premultiplied rhs for scatters
        typename ScalarBinaryOpTraits<AlphaType, typename DenseRhsType::Scalar>::ReturnType rhs_j(alpha*rhs(j,k));
        // accumulator for partial scalar product
        typename DenseResType::Scalar res_j(0);
        for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
        {
          LhsScalar lhs_ij = i.value();
          if(!LhsIsRowMajor) lhs_ij = numext::conj(lhs_ij);
          res_j += lhs_ij * rhs.coeff(i.index(),k);
          res(i.index(),k) += numext::conj(lhs_ij) * rhs_j;
        }
        res.coeffRef(j,k) += alpha * res_j;
  
        // handle diagonal coeff
        if (ProcessFirstHalf && i && (i.index()==j))
          res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);
      }
    }
  }
  
  
  template<typename LhsView, typename Rhs, int ProductType>
  struct generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType>
  : generic_product_impl_base<LhsView, Rhs, generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType> >
  {
    template<typename Dest>
    static void scaleAndAddTo(Dest& dst, const LhsView& lhsView, const Rhs& rhs, const typename Dest::Scalar& alpha)
    {
      typedef typename LhsView::_MatrixTypeNested Lhs;
      typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
      typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
      LhsNested lhsNested(lhsView.matrix());
      RhsNested rhsNested(rhs);
      
      internal::sparse_selfadjoint_time_dense_product<LhsView::Mode>(lhsNested, rhsNested, dst, alpha);
    }
  };
  
  template<typename Lhs, typename RhsView, int ProductType>
  struct generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType>
  : generic_product_impl_base<Lhs, RhsView, generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType> >
  {
    template<typename Dest>
    static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const RhsView& rhsView, const typename Dest::Scalar& alpha)
    {
      typedef typename RhsView::_MatrixTypeNested Rhs;
      typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
      typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
      LhsNested lhsNested(lhs);
      RhsNested rhsNested(rhsView.matrix());
      
      // transpose everything
      Transpose<Dest> dstT(dst);
      internal::sparse_selfadjoint_time_dense_product<RhsView::TransposeMode>(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);
    }
  };
  
  // NOTE: these two overloads are needed to evaluate the sparse selfadjoint view into a full sparse matrix
  // TODO: maybe the copy could be handled by generic_product_impl so that these overloads would not be needed anymore
  
  template<typename LhsView, typename Rhs, int ProductTag>
  struct product_evaluator<Product<LhsView, Rhs, DefaultProduct>, ProductTag, SparseSelfAdjointShape, SparseShape>
    : public evaluator<typename Product<typename Rhs::PlainObject, Rhs, DefaultProduct>::PlainObject>
  {
    typedef Product<LhsView, Rhs, DefaultProduct> XprType;
    typedef typename XprType::PlainObject PlainObject;
    typedef evaluator<PlainObject> Base;
  
    product_evaluator(const XprType& xpr)
      : m_lhs(xpr.lhs()), m_result(xpr.rows(), xpr.cols())
    {
      ::new (static_cast<Base*>(this)) Base(m_result);
      generic_product_impl<typename Rhs::PlainObject, Rhs, SparseShape, SparseShape, ProductTag>::evalTo(m_result, m_lhs, xpr.rhs());
    }
    
  protected:
    typename Rhs::PlainObject m_lhs;
    PlainObject m_result;
  };
  
  template<typename Lhs, typename RhsView, int ProductTag>
  struct product_evaluator<Product<Lhs, RhsView, DefaultProduct>, ProductTag, SparseShape, SparseSelfAdjointShape>
    : public evaluator<typename Product<Lhs, typename Lhs::PlainObject, DefaultProduct>::PlainObject>
  {
    typedef Product<Lhs, RhsView, DefaultProduct> XprType;
    typedef typename XprType::PlainObject PlainObject;
    typedef evaluator<PlainObject> Base;
  
    product_evaluator(const XprType& xpr)
      : m_rhs(xpr.rhs()), m_result(xpr.rows(), xpr.cols())
    {
      ::new (static_cast<Base*>(this)) Base(m_result);
      generic_product_impl<Lhs, typename Lhs::PlainObject, SparseShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), m_rhs);
    }
    
  protected:
    typename Lhs::PlainObject m_rhs;
    PlainObject m_result;
  };
  
  } // namespace internal
  
  /***************************************************************************
  * Implementation of symmetric copies and permutations
  ***************************************************************************/
  namespace internal {
  
  template<int Mode,typename MatrixType,int DestOrder>
  void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)
  {
    typedef typename MatrixType::StorageIndex StorageIndex;
    typedef typename MatrixType::Scalar Scalar;
    typedef SparseMatrix<Scalar,DestOrder,StorageIndex> Dest;
    typedef Matrix<StorageIndex,Dynamic,1> VectorI;
    typedef evaluator<MatrixType> MatEval;
    typedef typename evaluator<MatrixType>::InnerIterator MatIterator;
    
    MatEval matEval(mat);
    Dest& dest(_dest.derived());
    enum {
      StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)
    };
    
    Index size = mat.rows();
    VectorI count;
    count.resize(size);
    count.setZero();
    dest.resize(size,size);
    for(Index j = 0; j<size; ++j)
    {
      Index jp = perm ? perm[j] : j;
      for(MatIterator it(matEval,j); it; ++it)
      {
        Index i = it.index();
        Index r = it.row();
        Index c = it.col();
        Index ip = perm ? perm[i] : i;
        if(Mode==int(Upper|Lower))
          count[StorageOrderMatch ? jp : ip]++;
        else if(r==c)
          count[ip]++;
        else if(( Mode==Lower && r>c) || ( Mode==Upper && r<c))
        {
          count[ip]++;
          count[jp]++;
        }
      }
    }
    Index nnz = count.sum();
    
    // reserve space
    dest.resizeNonZeros(nnz);
    dest.outerIndexPtr()[0] = 0;
    for(Index j=0; j<size; ++j)
      dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
    for(Index j=0; j<size; ++j)
      count[j] = dest.outerIndexPtr()[j];
    
    // copy data
    for(StorageIndex j = 0; j<size; ++j)
    {
      for(MatIterator it(matEval,j); it; ++it)
      {
        StorageIndex i = internal::convert_index<StorageIndex>(it.index());
        Index r = it.row();
        Index c = it.col();
        
        StorageIndex jp = perm ? perm[j] : j;
        StorageIndex ip = perm ? perm[i] : i;
        
        if(Mode==int(Upper|Lower))
        {
          Index k = count[StorageOrderMatch ? jp : ip]++;
          dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;
          dest.valuePtr()[k] = it.value();
        }
        else if(r==c)
        {
          Index k = count[ip]++;
          dest.innerIndexPtr()[k] = ip;
          dest.valuePtr()[k] = it.value();
        }
        else if(( (Mode&Lower)==Lower && r>c) || ( (Mode&Upper)==Upper && r<c))
        {
          if(!StorageOrderMatch)
            std::swap(ip,jp);
          Index k = count[jp]++;
          dest.innerIndexPtr()[k] = ip;
          dest.valuePtr()[k] = it.value();
          k = count[ip]++;
          dest.innerIndexPtr()[k] = jp;
          dest.valuePtr()[k] = numext::conj(it.value());
        }
      }
    }
  }
  
  template<int _SrcMode,int _DstMode,typename MatrixType,int DstOrder>
  void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)
  {
    typedef typename MatrixType::StorageIndex StorageIndex;
    typedef typename MatrixType::Scalar Scalar;
    SparseMatrix<Scalar,DstOrder,StorageIndex>& dest(_dest.derived());
    typedef Matrix<StorageIndex,Dynamic,1> VectorI;
    typedef evaluator<MatrixType> MatEval;
    typedef typename evaluator<MatrixType>::InnerIterator MatIterator;
  
    enum {
      SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,
      StorageOrderMatch = int(SrcOrder) == int(DstOrder),
      DstMode = DstOrder==RowMajor ? (_DstMode==Upper ? Lower : Upper) : _DstMode,
      SrcMode = SrcOrder==RowMajor ? (_SrcMode==Upper ? Lower : Upper) : _SrcMode
    };
  
    MatEval matEval(mat);
    
    Index size = mat.rows();
    VectorI count(size);
    count.setZero();
    dest.resize(size,size);
    for(StorageIndex j = 0; j<size; ++j)
    {
      StorageIndex jp = perm ? perm[j] : j;
      for(MatIterator it(matEval,j); it; ++it)
      {
        StorageIndex i = it.index();
        if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))
          continue;
                    
        StorageIndex ip = perm ? perm[i] : i;
        count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
      }
    }
    dest.outerIndexPtr()[0] = 0;
    for(Index j=0; j<size; ++j)
      dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
    dest.resizeNonZeros(dest.outerIndexPtr()[size]);
    for(Index j=0; j<size; ++j)
      count[j] = dest.outerIndexPtr()[j];
    
    for(StorageIndex j = 0; j<size; ++j)
    {
      
      for(MatIterator it(matEval,j); it; ++it)
      {
        StorageIndex i = it.index();
        if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))
          continue;
                    
        StorageIndex jp = perm ? perm[j] : j;
        StorageIndex ip = perm? perm[i] : i;
        
        Index k = count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
        dest.innerIndexPtr()[k] = int(DstMode)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);
        
        if(!StorageOrderMatch) std::swap(ip,jp);
        if( ((int(DstMode)==int(Lower) && ip<jp) || (int(DstMode)==int(Upper) && ip>jp)))
          dest.valuePtr()[k] = numext::conj(it.value());
        else
          dest.valuePtr()[k] = it.value();
      }
    }
  }
  
  }
  
  // TODO implement twists in a more evaluator friendly fashion
  
  namespace internal {
  
  template<typename MatrixType, int Mode>
  struct traits<SparseSymmetricPermutationProduct<MatrixType,Mode> > : traits<MatrixType> {
  };
  
  }
  
  template<typename MatrixType,int Mode>
  class SparseSymmetricPermutationProduct
    : public EigenBase<SparseSymmetricPermutationProduct<MatrixType,Mode> >
  {
    public:
      typedef typename MatrixType::Scalar Scalar;
      typedef typename MatrixType::StorageIndex StorageIndex;
      enum {
        RowsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::RowsAtCompileTime,
        ColsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::ColsAtCompileTime
      };
    protected:
      typedef PermutationMatrix<Dynamic,Dynamic,StorageIndex> Perm;
    public:
      typedef Matrix<StorageIndex,Dynamic,1> VectorI;
      typedef typename MatrixType::Nested MatrixTypeNested;
      typedef typename internal::remove_all<MatrixTypeNested>::type NestedExpression;
      
      SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)
        : m_matrix(mat), m_perm(perm)
      {}
      
      inline Index rows() const { return m_matrix.rows(); }
      inline Index cols() const { return m_matrix.cols(); }
          
      const NestedExpression& matrix() const { return m_matrix; }
      const Perm& perm() const { return m_perm; }
      
    protected:
      MatrixTypeNested m_matrix;
      const Perm& m_perm;
  
  };
  
  namespace internal {
    
  template<typename DstXprType, typename MatrixType, int Mode, typename Scalar>
  struct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>, internal::assign_op<Scalar,typename MatrixType::Scalar>, Sparse2Sparse>
  {
    typedef SparseSymmetricPermutationProduct<MatrixType,Mode> SrcXprType;
    typedef typename DstXprType::StorageIndex DstIndex;
    template<int Options>
    static void run(SparseMatrix<Scalar,Options,DstIndex> &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
    {
      // internal::permute_symm_to_fullsymm<Mode>(m_matrix,_dest,m_perm.indices().data());
      SparseMatrix<Scalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
      internal::permute_symm_to_fullsymm<Mode>(src.matrix(),tmp,src.perm().indices().data());
      dst = tmp;
    }
    
    template<typename DestType,unsigned int DestMode>
    static void run(SparseSelfAdjointView<DestType,DestMode>& dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
    {
      internal::permute_symm_to_symm<Mode,DestMode>(src.matrix(),dst.matrix(),src.perm().indices().data());
    }
  };
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
  