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 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
 // Copyright (C) 2013 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_SPARSEBLOCKMATRIX_H
 #define EIGEN_SPARSEBLOCKMATRIX_H
 
 namespace Eigen { 
 /** \ingroup SparseCore_Module
   *
   * \class BlockSparseMatrix
   *
   * \brief A versatile sparse matrix representation where each element is a block
   *
   * This class provides routines to manipulate block sparse matrices stored in a
   * BSR-like representation. There are two main types :
   *
   * 1. All blocks have the same number of rows and columns, called block size
   * in the following. In this case, if this block size is known at compile time,
   * it can be given as a template parameter like
   * \code
   * BlockSparseMatrix<Scalar, 3, ColMajor> bmat(b_rows, b_cols);
   * \endcode
   * Here, bmat is a b_rows x b_cols block sparse matrix
   * where each coefficient is a 3x3 dense matrix.
   * If the block size is fixed but will be given at runtime,
   * \code
   * BlockSparseMatrix<Scalar, Dynamic, ColMajor> bmat(b_rows, b_cols);
   * bmat.setBlockSize(block_size);
   * \endcode
   *
   * 2. The second case is for variable-block sparse matrices.
   * Here each block has its own dimensions. The only restriction is that all the blocks
   * in a row (resp. a column) should have the same number of rows (resp. of columns).
   * It is thus required in this case to describe the layout of the matrix by calling
   * setBlockLayout(rowBlocks, colBlocks).
   *
   * In any of the previous case, the matrix can be filled by calling setFromTriplets().
   * A regular sparse matrix can be converted to a block sparse matrix and vice versa.
   * It is obviously required to describe the block layout beforehand by calling either
   * setBlockSize() for fixed-size blocks or setBlockLayout for variable-size blocks.
   *
   * \tparam _Scalar The Scalar type
   * \tparam _BlockAtCompileTime The block layout option. It takes the following values
   * Dynamic : block size known at runtime
   * a numeric number : fixed-size block known at compile time
   */
 template<typename _Scalar, int _BlockAtCompileTime=Dynamic, int _Options=ColMajor, typename _StorageIndex=int> class BlockSparseMatrix;
 
 template<typename BlockSparseMatrixT> class BlockSparseMatrixView;
 
 namespace internal {
 template<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _Index>
 struct traits<BlockSparseMatrix<_Scalar,_BlockAtCompileTime,_Options, _Index> >
 {
   typedef _Scalar Scalar;
   typedef _Index Index;
   typedef Sparse StorageKind; // FIXME Where is it used ??
   typedef MatrixXpr XprKind;
   enum {
     RowsAtCompileTime = Dynamic,
     ColsAtCompileTime = Dynamic,
     MaxRowsAtCompileTime = Dynamic,
     MaxColsAtCompileTime = Dynamic,
     BlockSize = _BlockAtCompileTime,
     Flags = _Options | NestByRefBit | LvalueBit,
     CoeffReadCost = NumTraits<Scalar>::ReadCost,
     SupportedAccessPatterns = InnerRandomAccessPattern
   };
 };
 template<typename BlockSparseMatrixT>
 struct traits<BlockSparseMatrixView<BlockSparseMatrixT> >
 {
   typedef Ref<Matrix<typename BlockSparseMatrixT::Scalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > Scalar;
   typedef Ref<Matrix<typename BlockSparseMatrixT::RealScalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > RealScalar;
 
 };
 
 // Function object to sort a triplet list
 template<typename Iterator, bool IsColMajor>
 struct TripletComp
 {
   typedef typename Iterator::value_type Triplet;
   bool operator()(const Triplet& a, const Triplet& b)
   { if(IsColMajor)
       return ((a.col() == b.col() && a.row() < b.row()) || (a.col() < b.col()));
     else
       return ((a.row() == b.row() && a.col() < b.col()) || (a.row() < b.row()));
   }
 };
 } // end namespace internal
 
 
 /* Proxy to view the block sparse matrix as a regular sparse matrix */
 template<typename BlockSparseMatrixT>
 class BlockSparseMatrixView : public SparseMatrixBase<BlockSparseMatrixT>
 {
   public:
     typedef Ref<typename BlockSparseMatrixT::BlockScalar> Scalar;
     typedef Ref<typename BlockSparseMatrixT::BlockRealScalar> RealScalar;
     typedef typename BlockSparseMatrixT::Index Index;
     typedef  BlockSparseMatrixT Nested;
     enum {
       Flags = BlockSparseMatrixT::Options,
       Options = BlockSparseMatrixT::Options,
       RowsAtCompileTime = BlockSparseMatrixT::RowsAtCompileTime,
       ColsAtCompileTime = BlockSparseMatrixT::ColsAtCompileTime,
       MaxColsAtCompileTime = BlockSparseMatrixT::MaxColsAtCompileTime,
       MaxRowsAtCompileTime = BlockSparseMatrixT::MaxRowsAtCompileTime
     };
   public:
     BlockSparseMatrixView(const BlockSparseMatrixT& spblockmat)
      : m_spblockmat(spblockmat)
     {}
 
     Index outerSize() const
     {
       return (Flags&RowMajorBit) == 1 ? this->rows() : this->cols();
     }
     Index cols() const
     {
       return m_spblockmat.blockCols();
     }
     Index rows() const
     {
       return m_spblockmat.blockRows();
     }
     Scalar coeff(Index row, Index col)
     {
       return m_spblockmat.coeff(row, col);
     }
     Scalar coeffRef(Index row, Index col)
     {
       return m_spblockmat.coeffRef(row, col);
     }
     // Wrapper to iterate over all blocks
     class InnerIterator : public BlockSparseMatrixT::BlockInnerIterator
     {
       public:
       InnerIterator(const BlockSparseMatrixView& mat, Index outer)
           : BlockSparseMatrixT::BlockInnerIterator(mat.m_spblockmat, outer)
       {}
 
     };
 
   protected:
     const BlockSparseMatrixT& m_spblockmat;
 };
 
 // Proxy to view a regular vector as a block vector
 template<typename BlockSparseMatrixT, typename VectorType>
 class BlockVectorView
 {
   public:
     enum {
       BlockSize = BlockSparseMatrixT::BlockSize,
       ColsAtCompileTime = VectorType::ColsAtCompileTime,
       RowsAtCompileTime = VectorType::RowsAtCompileTime,
       Flags = VectorType::Flags
     };
     typedef Ref<const Matrix<typename BlockSparseMatrixT::Scalar, (RowsAtCompileTime==1)? 1 : BlockSize, (ColsAtCompileTime==1)? 1 : BlockSize> >Scalar;
     typedef typename BlockSparseMatrixT::Index Index;
   public:
     BlockVectorView(const BlockSparseMatrixT& spblockmat, const VectorType& vec)
     : m_spblockmat(spblockmat),m_vec(vec)
     { }
     inline Index cols() const
     {
       return m_vec.cols();
     }
     inline Index size() const
     {
       return m_spblockmat.blockRows();
     }
     inline Scalar coeff(Index bi) const
     {
       Index startRow = m_spblockmat.blockRowsIndex(bi);
       Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
       return m_vec.middleRows(startRow, rowSize);
     }
     inline Scalar coeff(Index bi, Index j) const
     {
       Index startRow = m_spblockmat.blockRowsIndex(bi);
       Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
       return m_vec.block(startRow, j, rowSize, 1);
     }
   protected:
     const BlockSparseMatrixT& m_spblockmat;
     const VectorType& m_vec;
 };
 
 template<typename VectorType, typename Index> class BlockVectorReturn;
 
 
 // Proxy to view a regular vector as a block vector
 template<typename BlockSparseMatrixT, typename VectorType>
 class BlockVectorReturn
 {
   public:
     enum {
       ColsAtCompileTime = VectorType::ColsAtCompileTime,
       RowsAtCompileTime = VectorType::RowsAtCompileTime,
       Flags = VectorType::Flags
     };
     typedef Ref<Matrix<typename VectorType::Scalar, RowsAtCompileTime, ColsAtCompileTime> > Scalar;
     typedef typename BlockSparseMatrixT::Index Index;
   public:
     BlockVectorReturn(const BlockSparseMatrixT& spblockmat, VectorType& vec)
     : m_spblockmat(spblockmat),m_vec(vec)
     { }
     inline Index size() const
     {
       return m_spblockmat.blockRows();
     }
     inline Scalar coeffRef(Index bi)
     {
       Index startRow = m_spblockmat.blockRowsIndex(bi);
       Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
       return m_vec.middleRows(startRow, rowSize);
     }
     inline Scalar coeffRef(Index bi, Index j)
     {
       Index startRow = m_spblockmat.blockRowsIndex(bi);
       Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
       return m_vec.block(startRow, j, rowSize, 1);
     }
 
   protected:
     const BlockSparseMatrixT& m_spblockmat;
     VectorType& m_vec;
 };
 
 // Block version of the sparse dense product
 template<typename Lhs, typename Rhs>
 class BlockSparseTimeDenseProduct;
 
 namespace internal {
 
 template<typename BlockSparseMatrixT, typename VecType>
 struct traits<BlockSparseTimeDenseProduct<BlockSparseMatrixT, VecType> >
 {
   typedef Dense StorageKind;
   typedef MatrixXpr XprKind;
   typedef typename BlockSparseMatrixT::Scalar Scalar;
   typedef typename BlockSparseMatrixT::Index Index;
   enum {
     RowsAtCompileTime = Dynamic,
     ColsAtCompileTime = Dynamic,
     MaxRowsAtCompileTime = Dynamic,
     MaxColsAtCompileTime = Dynamic,
     Flags = 0,
     CoeffReadCost = internal::traits<BlockSparseMatrixT>::CoeffReadCost
   };
 };
 } // end namespace internal
 
 template<typename Lhs, typename Rhs>
 class BlockSparseTimeDenseProduct
   : public ProductBase<BlockSparseTimeDenseProduct<Lhs,Rhs>, Lhs, Rhs>
 {
   public:
     EIGEN_PRODUCT_PUBLIC_INTERFACE(BlockSparseTimeDenseProduct)
 
     BlockSparseTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
     {}
 
     template<typename Dest> void scaleAndAddTo(Dest& dest, const typename Rhs::Scalar& alpha) const
     {
       BlockVectorReturn<Lhs,Dest> tmpDest(m_lhs, dest);
       internal::sparse_time_dense_product( BlockSparseMatrixView<Lhs>(m_lhs),  BlockVectorView<Lhs, Rhs>(m_lhs, m_rhs), tmpDest, alpha);
     }
 
   private:
     BlockSparseTimeDenseProduct& operator=(const BlockSparseTimeDenseProduct&);
 };
 
 template<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>
 class BlockSparseMatrix : public SparseMatrixBase<BlockSparseMatrix<_Scalar,_BlockAtCompileTime, _Options,_StorageIndex> >
 {
   public:
     typedef _Scalar Scalar;
     typedef typename NumTraits<Scalar>::Real RealScalar;
     typedef _StorageIndex StorageIndex;
     typedef typename internal::ref_selector<BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex> >::type Nested;
 
     enum {
       Options = _Options,
       Flags = Options,
       BlockSize=_BlockAtCompileTime,
       RowsAtCompileTime = Dynamic,
       ColsAtCompileTime = Dynamic,
       MaxRowsAtCompileTime = Dynamic,
       MaxColsAtCompileTime = Dynamic,
       IsVectorAtCompileTime = 0,
       IsColMajor = Flags&RowMajorBit ? 0 : 1
     };
     typedef Matrix<Scalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockScalar;
     typedef Matrix<RealScalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockRealScalar;
     typedef typename internal::conditional<_BlockAtCompileTime==Dynamic, Scalar, BlockScalar>::type BlockScalarReturnType;
     typedef BlockSparseMatrix<Scalar, BlockSize, IsColMajor ? ColMajor : RowMajor, StorageIndex> PlainObject;
   public:
     // Default constructor
     BlockSparseMatrix()
     : m_innerBSize(0),m_outerBSize(0),m_innerOffset(0),m_outerOffset(0),
       m_nonzerosblocks(0),m_values(0),m_blockPtr(0),m_indices(0),
       m_outerIndex(0),m_blockSize(BlockSize)
     { }
 
 
     /**
      * \brief Construct and resize
      *
      */
     BlockSparseMatrix(Index brow, Index bcol)
       : m_innerBSize(IsColMajor ? brow : bcol),
         m_outerBSize(IsColMajor ? bcol : brow),
         m_innerOffset(0),m_outerOffset(0),m_nonzerosblocks(0),
         m_values(0),m_blockPtr(0),m_indices(0),
         m_outerIndex(0),m_blockSize(BlockSize)
     { }
 
     /**
      * \brief Copy-constructor
      */
     BlockSparseMatrix(const BlockSparseMatrix& other)
       : m_innerBSize(other.m_innerBSize),m_outerBSize(other.m_outerBSize),
         m_nonzerosblocks(other.m_nonzerosblocks),m_nonzeros(other.m_nonzeros),
         m_blockPtr(0),m_blockSize(other.m_blockSize)
     {
       // should we allow copying between variable-size blocks and fixed-size blocks ??
       eigen_assert(m_blockSize == BlockSize && " CAN NOT COPY BETWEEN FIXED-SIZE AND VARIABLE-SIZE BLOCKS");
 
       std::copy(other.m_innerOffset, other.m_innerOffset+m_innerBSize+1, m_innerOffset);
       std::copy(other.m_outerOffset, other.m_outerOffset+m_outerBSize+1, m_outerOffset);
       std::copy(other.m_values, other.m_values+m_nonzeros, m_values);
 
       if(m_blockSize != Dynamic)
         std::copy(other.m_blockPtr, other.m_blockPtr+m_nonzerosblocks, m_blockPtr);
 
       std::copy(other.m_indices, other.m_indices+m_nonzerosblocks, m_indices);
       std::copy(other.m_outerIndex, other.m_outerIndex+m_outerBSize, m_outerIndex);
     }
 
     friend void swap(BlockSparseMatrix& first, BlockSparseMatrix& second)
     {
       std::swap(first.m_innerBSize, second.m_innerBSize);
       std::swap(first.m_outerBSize, second.m_outerBSize);
       std::swap(first.m_innerOffset, second.m_innerOffset);
       std::swap(first.m_outerOffset, second.m_outerOffset);
       std::swap(first.m_nonzerosblocks, second.m_nonzerosblocks);
       std::swap(first.m_nonzeros, second.m_nonzeros);
       std::swap(first.m_values, second.m_values);
       std::swap(first.m_blockPtr, second.m_blockPtr);
       std::swap(first.m_indices, second.m_indices);
       std::swap(first.m_outerIndex, second.m_outerIndex);
       std::swap(first.m_BlockSize, second.m_blockSize);
     }
 
     BlockSparseMatrix& operator=(BlockSparseMatrix other)
     {
       //Copy-and-swap paradigm ... avoid leaked data if thrown
       swap(*this, other);
       return *this;
     }
 
     // Destructor
     ~BlockSparseMatrix()
     {
       delete[] m_outerIndex;
       delete[] m_innerOffset;
       delete[] m_outerOffset;
       delete[] m_indices;
       delete[] m_blockPtr;
       delete[] m_values;
     }
 
 
     /**
       * \brief Constructor from a sparse matrix
       *
       */
     template<typename MatrixType>
     inline BlockSparseMatrix(const MatrixType& spmat) : m_blockSize(BlockSize)
     {
       EIGEN_STATIC_ASSERT((m_blockSize != Dynamic), THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE);
 
       *this = spmat;
     }
 
     /**
       * \brief Assignment from a sparse matrix with the same storage order
       *
       * Convert from a sparse matrix to block sparse matrix.
       * \warning Before calling this function, tt is necessary to call
       * either setBlockLayout() (matrices with variable-size blocks)
       * or setBlockSize() (for fixed-size blocks).
       */
     template<typename MatrixType>
     inline BlockSparseMatrix& operator=(const MatrixType& spmat)
     {
       eigen_assert((m_innerBSize != 0 && m_outerBSize != 0)
                    && "Trying to assign to a zero-size matrix, call resize() first");
       eigen_assert(((MatrixType::Options&RowMajorBit) != IsColMajor) && "Wrong storage order");
       typedef SparseMatrix<bool,MatrixType::Options,typename MatrixType::Index> MatrixPatternType;
       MatrixPatternType  blockPattern(blockRows(), blockCols());
       m_nonzeros = 0;
 
       // First, compute the number of nonzero blocks and their locations
       for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
       {
         // Browse each outer block and compute the structure
         std::vector<bool> nzblocksFlag(m_innerBSize,false);  // Record the existing blocks
         blockPattern.startVec(bj);
         for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)
         {
           typename MatrixType::InnerIterator it_spmat(spmat, j);
           for(; it_spmat; ++it_spmat)
           {
             StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block
             if(!nzblocksFlag[bi])
             {
               // Save the index of this nonzero block
               nzblocksFlag[bi] = true;
               blockPattern.insertBackByOuterInnerUnordered(bj, bi) = true;
               // Compute the total number of nonzeros (including explicit zeros in blocks)
               m_nonzeros += blockOuterSize(bj) * blockInnerSize(bi);
             }
           }
         } // end current outer block
       }
       blockPattern.finalize();
 
       // Allocate the internal arrays
       setBlockStructure(blockPattern);
 
       for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);
       for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
       {
         // Now copy the values
         for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)
         {
           // Browse the outer block column by column (for column-major matrices)
           typename MatrixType::InnerIterator it_spmat(spmat, j);
           for(; it_spmat; ++it_spmat)
           {
             StorageIndex idx = 0; // Position of this block in the column block
             StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block
             // Go to the inner block where this element belongs to
             while(bi > m_indices[m_outerIndex[bj]+idx]) ++idx; // Not expensive for ordered blocks
             StorageIndex idxVal;// Get the right position in the array of values for this element
             if(m_blockSize == Dynamic)
             {
               // Offset from all blocks before ...
               idxVal =  m_blockPtr[m_outerIndex[bj]+idx];
               // ... and offset inside the block
               idxVal += (j - blockOuterIndex(bj)) * blockOuterSize(bj) + it_spmat.index() - m_innerOffset[bi];
             }
             else
             {
               // All blocks before
               idxVal = (m_outerIndex[bj] + idx) * m_blockSize * m_blockSize;
               // inside the block
               idxVal += (j - blockOuterIndex(bj)) * m_blockSize + (it_spmat.index()%m_blockSize);
             }
             // Insert the value
             m_values[idxVal] = it_spmat.value();
           } // end of this column
         } // end of this block
       } // end of this outer block
 
       return *this;
     }
 
     /**
       * \brief Set the nonzero block pattern of the matrix
       *
       * Given a sparse matrix describing the nonzero block pattern,
       * this function prepares the internal pointers for values.
       * After calling this function, any *nonzero* block (bi, bj) can be set
       * with a simple call to coeffRef(bi,bj).
       *
       *
       * \warning Before calling this function, tt is necessary to call
       * either setBlockLayout() (matrices with variable-size blocks)
       * or setBlockSize() (for fixed-size blocks).
       *
       * \param blockPattern Sparse matrix of boolean elements describing the block structure
       *
       * \sa setBlockLayout() \sa setBlockSize()
       */
     template<typename MatrixType>
     void setBlockStructure(const MatrixType& blockPattern)
     {
       resize(blockPattern.rows(), blockPattern.cols());
       reserve(blockPattern.nonZeros());
 
       // Browse the block pattern and set up the various pointers
       m_outerIndex[0] = 0;
       if(m_blockSize == Dynamic) m_blockPtr[0] = 0;
       for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);
       for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
       {
         //Browse each outer block
 
         //First, copy and save the indices of nonzero blocks
         //FIXME : find a way to avoid this ...
         std::vector<int> nzBlockIdx;
         typename MatrixType::InnerIterator it(blockPattern, bj);
         for(; it; ++it)
         {
           nzBlockIdx.push_back(it.index());
         }
         std::sort(nzBlockIdx.begin(), nzBlockIdx.end());
 
         // Now, fill block indices and (eventually) pointers to blocks
         for(StorageIndex idx = 0; idx < nzBlockIdx.size(); ++idx)
         {
           StorageIndex offset = m_outerIndex[bj]+idx; // offset in m_indices
           m_indices[offset] = nzBlockIdx[idx];
           if(m_blockSize == Dynamic)
             m_blockPtr[offset] = m_blockPtr[offset-1] + blockInnerSize(nzBlockIdx[idx]) * blockOuterSize(bj);
           // There is no blockPtr for fixed-size blocks... not needed !???
         }
         // Save the pointer to the next outer block
         m_outerIndex[bj+1] = m_outerIndex[bj] + nzBlockIdx.size();
       }
     }
 
     /**
       * \brief Set the number of rows and columns blocks
       */
     inline void resize(Index brow, Index bcol)
     {
       m_innerBSize = IsColMajor ? brow : bcol;
       m_outerBSize = IsColMajor ? bcol : brow;
     }
 
     /**
       * \brief set the block size at runtime for fixed-size block layout
       *
       * Call this only for fixed-size blocks
       */
     inline void setBlockSize(Index blockSize)
     {
       m_blockSize = blockSize;
     }
 
     /**
       * \brief Set the row and column block layouts,
       *
       * This function set the size of each row and column block.
       * So this function should be used only for blocks with variable size.
       * \param rowBlocks : Number of rows per row block
       * \param colBlocks : Number of columns per column block
       * \sa resize(), setBlockSize()
       */
     inline void setBlockLayout(const VectorXi& rowBlocks, const VectorXi& colBlocks)
     {
       const VectorXi& innerBlocks = IsColMajor ? rowBlocks : colBlocks;
       const VectorXi& outerBlocks = IsColMajor ? colBlocks : rowBlocks;
       eigen_assert(m_innerBSize == innerBlocks.size() && "CHECK THE NUMBER OF ROW OR COLUMN BLOCKS");
       eigen_assert(m_outerBSize == outerBlocks.size() && "CHECK THE NUMBER OF ROW OR COLUMN BLOCKS");
       m_outerBSize = outerBlocks.size();
       //  starting index of blocks... cumulative sums
       m_innerOffset = new StorageIndex[m_innerBSize+1];
       m_outerOffset = new StorageIndex[m_outerBSize+1];
       m_innerOffset[0] = 0;
       m_outerOffset[0] = 0;
       std::partial_sum(&innerBlocks[0], &innerBlocks[m_innerBSize-1]+1, &m_innerOffset[1]);
       std::partial_sum(&outerBlocks[0], &outerBlocks[m_outerBSize-1]+1, &m_outerOffset[1]);
 
       // Compute the total number of nonzeros
       m_nonzeros = 0;
       for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
         for(StorageIndex bi = 0; bi < m_innerBSize; ++bi)
           m_nonzeros += outerBlocks[bj] * innerBlocks[bi];
 
     }
 
     /**
       * \brief Allocate the internal array of pointers to blocks and their inner indices
       *
       * \note For fixed-size blocks, call setBlockSize() to set the block.
       * And For variable-size blocks, call setBlockLayout() before using this function
       *
       * \param nonzerosblocks Number of nonzero blocks. The total number of nonzeros is
       * is computed in setBlockLayout() for variable-size blocks
       * \sa setBlockSize()
       */
     inline void reserve(const Index nonzerosblocks)
     {
       eigen_assert((m_innerBSize != 0 && m_outerBSize != 0) &&
           "TRYING TO RESERVE ZERO-SIZE MATRICES, CALL resize() first");
 
       //FIXME Should free if already allocated
       m_outerIndex = new StorageIndex[m_outerBSize+1];
 
       m_nonzerosblocks = nonzerosblocks;
       if(m_blockSize != Dynamic)
       {
         m_nonzeros = nonzerosblocks * (m_blockSize * m_blockSize);
         m_blockPtr = 0;
       }
       else
       {
         // m_nonzeros  is already computed in setBlockLayout()
         m_blockPtr = new StorageIndex[m_nonzerosblocks+1];
       }
       m_indices = new StorageIndex[m_nonzerosblocks+1];
       m_values = new Scalar[m_nonzeros];
     }
 
 
     /**
       * \brief Fill values in a matrix  from a triplet list.
       *
       * Each triplet item has a block stored in an Eigen dense matrix.
       * The InputIterator class should provide the functions row(), col() and value()
       *
       * \note For fixed-size blocks, call setBlockSize() before this function.
       *
       * FIXME Do not accept duplicates
       */
     template<typename InputIterator>
     void setFromTriplets(const InputIterator& begin, const InputIterator& end)
     {
       eigen_assert((m_innerBSize!=0 && m_outerBSize !=0) && "ZERO BLOCKS, PLEASE CALL resize() before");
 
       /* First, sort the triplet list
         * FIXME This can be unnecessarily expensive since only the inner indices have to be sorted
         * The best approach is like in SparseMatrix::setFromTriplets()
         */
       internal::TripletComp<InputIterator, IsColMajor> tripletcomp;
       std::sort(begin, end, tripletcomp);
 
       /* Count the number of rows and column blocks,
        * and the number of nonzero blocks per outer dimension
        */
       VectorXi rowBlocks(m_innerBSize); // Size of each block row
       VectorXi colBlocks(m_outerBSize); // Size of each block column
       rowBlocks.setZero(); colBlocks.setZero();
       VectorXi nzblock_outer(m_outerBSize); // Number of nz blocks per outer vector
       VectorXi nz_outer(m_outerBSize); // Number of nz per outer vector...for variable-size blocks
       nzblock_outer.setZero();
       nz_outer.setZero();
       for(InputIterator it(begin); it !=end; ++it)
       {
         eigen_assert(it->row() >= 0 && it->row() < this->blockRows() && it->col() >= 0 && it->col() < this->blockCols());
         eigen_assert((it->value().rows() == it->value().cols() && (it->value().rows() == m_blockSize))
                      || (m_blockSize == Dynamic));
 
         if(m_blockSize == Dynamic)
         {
           eigen_assert((rowBlocks[it->row()] == 0 || rowBlocks[it->row()] == it->value().rows()) &&
               "NON CORRESPONDING SIZES FOR ROW BLOCKS");
           eigen_assert((colBlocks[it->col()] == 0 || colBlocks[it->col()] == it->value().cols()) &&
               "NON CORRESPONDING SIZES FOR COLUMN BLOCKS");
           rowBlocks[it->row()] =it->value().rows();
           colBlocks[it->col()] = it->value().cols();
         }
         nz_outer(IsColMajor ? it->col() : it->row()) += it->value().rows() * it->value().cols();
         nzblock_outer(IsColMajor ? it->col() : it->row())++;
       }
       // Allocate member arrays
       if(m_blockSize == Dynamic) setBlockLayout(rowBlocks, colBlocks);
       StorageIndex nzblocks = nzblock_outer.sum();
       reserve(nzblocks);
 
        // Temporary markers
       VectorXi block_id(m_outerBSize); // To be used as a block marker during insertion
 
       // Setup outer index pointers and markers
       m_outerIndex[0] = 0;
       if (m_blockSize == Dynamic)  m_blockPtr[0] =  0;
       for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
       {
         m_outerIndex[bj+1] = m_outerIndex[bj] + nzblock_outer(bj);
         block_id(bj) = m_outerIndex[bj];
         if(m_blockSize==Dynamic)
         {
           m_blockPtr[m_outerIndex[bj+1]] = m_blockPtr[m_outerIndex[bj]] + nz_outer(bj);
         }
       }
 
       // Fill the matrix
       for(InputIterator it(begin); it!=end; ++it)
       {
         StorageIndex outer = IsColMajor ? it->col() : it->row();
         StorageIndex inner = IsColMajor ? it->row() : it->col();
         m_indices[block_id(outer)] = inner;
         StorageIndex block_size = it->value().rows()*it->value().cols();
         StorageIndex nz_marker = blockPtr(block_id[outer]);
         memcpy(&(m_values[nz_marker]), it->value().data(), block_size * sizeof(Scalar));
         if(m_blockSize == Dynamic)
         {
           m_blockPtr[block_id(outer)+1] = m_blockPtr[block_id(outer)] + block_size;
         }
         block_id(outer)++;
       }
 
       // An alternative when the outer indices are sorted...no need to use an array of markers
 //      for(Index bcol = 0; bcol < m_outerBSize; ++bcol)
 //      {
 //      Index id = 0, id_nz = 0, id_nzblock = 0;
 //      for(InputIterator it(begin); it!=end; ++it)
 //      {
 //        while (id<bcol) // one pass should do the job unless there are empty columns
 //        {
 //          id++;
 //          m_outerIndex[id+1]=m_outerIndex[id];
 //        }
 //        m_outerIndex[id+1] += 1;
 //        m_indices[id_nzblock]=brow;
 //        Index block_size = it->value().rows()*it->value().cols();
 //        m_blockPtr[id_nzblock+1] = m_blockPtr[id_nzblock] + block_size;
 //        id_nzblock++;
 //        memcpy(&(m_values[id_nz]),it->value().data(), block_size*sizeof(Scalar));
 //        id_nz += block_size;
 //      }
 //      while(id < m_outerBSize-1) // Empty columns at the end
 //      {
 //        id++;
 //        m_outerIndex[id+1]=m_outerIndex[id];
 //      }
 //      }
     }
 
 
     /**
       * \returns the number of rows
       */
     inline Index rows() const
     {
 //      return blockRows();
       return (IsColMajor ? innerSize() : outerSize());
     }
 
     /**
       * \returns the number of cols
       */
     inline Index cols() const
     {
 //      return blockCols();
       return (IsColMajor ? outerSize() : innerSize());
     }
 
     inline Index innerSize() const
     {
       if(m_blockSize == Dynamic) return m_innerOffset[m_innerBSize];
       else return  (m_innerBSize * m_blockSize) ;
     }
 
     inline Index outerSize() const
     {
       if(m_blockSize == Dynamic) return m_outerOffset[m_outerBSize];
       else return  (m_outerBSize * m_blockSize) ;
     }
     /** \returns the number of rows grouped by blocks */
     inline Index blockRows() const
     {
       return (IsColMajor ? m_innerBSize : m_outerBSize);
     }
     /** \returns the number of columns grouped by blocks */
     inline Index blockCols() const
     {
       return (IsColMajor ? m_outerBSize : m_innerBSize);
     }
 
     inline Index outerBlocks() const { return m_outerBSize; }
     inline Index innerBlocks() const { return m_innerBSize; }
 
     /** \returns the block index where outer belongs to */
     inline Index outerToBlock(Index outer) const
     {
       eigen_assert(outer < outerSize() && "OUTER INDEX OUT OF BOUNDS");
 
       if(m_blockSize != Dynamic)
         return (outer / m_blockSize); // Integer division
 
       StorageIndex b_outer = 0;
       while(m_outerOffset[b_outer] <= outer) ++b_outer;
       return b_outer - 1;
     }
     /** \returns  the block index where inner belongs to */
     inline Index innerToBlock(Index inner) const
     {
       eigen_assert(inner < innerSize() && "OUTER INDEX OUT OF BOUNDS");
 
       if(m_blockSize != Dynamic)
         return (inner / m_blockSize); // Integer division
 
       StorageIndex b_inner = 0;
       while(m_innerOffset[b_inner] <= inner) ++b_inner;
       return b_inner - 1;
     }
 
     /**
       *\returns a reference to the (i,j) block as an Eigen Dense Matrix
       */
     Ref<BlockScalar> coeffRef(Index brow, Index bcol)
     {
       eigen_assert(brow < blockRows() && "BLOCK ROW INDEX OUT OF BOUNDS");
       eigen_assert(bcol < blockCols() && "BLOCK nzblocksFlagCOLUMN OUT OF BOUNDS");
 
       StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);
       StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);
       StorageIndex inner = IsColMajor ? brow : bcol;
       StorageIndex outer = IsColMajor ? bcol : brow;
       StorageIndex offset = m_outerIndex[outer];
       while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner)
         offset++;
       if(m_indices[offset] == inner)
       {
         return Map<BlockScalar>(&(m_values[blockPtr(offset)]), rsize, csize);
       }
       else
       {
         //FIXME the block does not exist, Insert it !!!!!!!!!
         eigen_assert("DYNAMIC INSERTION IS NOT YET SUPPORTED");
       }
     }
 
     /**
       * \returns the value of the (i,j) block as an Eigen Dense Matrix
       */
     Map<const BlockScalar> coeff(Index brow, Index bcol) const
     {
       eigen_assert(brow < blockRows() && "BLOCK ROW INDEX OUT OF BOUNDS");
       eigen_assert(bcol < blockCols() && "BLOCK COLUMN OUT OF BOUNDS");
 
       StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);
       StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);
       StorageIndex inner = IsColMajor ? brow : bcol;
       StorageIndex outer = IsColMajor ? bcol : brow;
       StorageIndex offset = m_outerIndex[outer];
       while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner) offset++;
       if(m_indices[offset] == inner)
       {
         return Map<const BlockScalar> (&(m_values[blockPtr(offset)]), rsize, csize);
       }
       else
 //        return BlockScalar::Zero(rsize, csize);
         eigen_assert("NOT YET SUPPORTED");
     }
 
     // Block Matrix times vector product
     template<typename VecType>
     BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType> operator*(const VecType& lhs) const
     {
       return BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType>(*this, lhs);
     }
 
     /** \returns the number of nonzero blocks */
     inline Index nonZerosBlocks() const { return m_nonzerosblocks; }
     /** \returns the total number of nonzero elements, including eventual explicit zeros in blocks */
     inline Index nonZeros() const { return m_nonzeros; }
 
     inline BlockScalarReturnType *valuePtr() {return static_cast<BlockScalarReturnType *>(m_values);}
 //    inline Scalar *valuePtr(){ return m_values; }
     inline StorageIndex *innerIndexPtr() {return m_indices; }
     inline const StorageIndex *innerIndexPtr() const {return m_indices; }
     inline StorageIndex *outerIndexPtr() {return m_outerIndex; }
     inline const StorageIndex* outerIndexPtr() const {return m_outerIndex; }
 
     /** \brief for compatibility purposes with the SparseMatrix class */
     inline bool isCompressed() const {return true;}
     /**
       * \returns the starting index of the bi row block
       */
     inline Index blockRowsIndex(Index bi) const
     {
       return IsColMajor ? blockInnerIndex(bi) : blockOuterIndex(bi);
     }
 
     /**
       * \returns the starting index of the bj col block
       */
     inline Index blockColsIndex(Index bj) const
     {
       return IsColMajor ? blockOuterIndex(bj) : blockInnerIndex(bj);
     }
 
     inline Index blockOuterIndex(Index bj) const
     {
       return (m_blockSize == Dynamic) ? m_outerOffset[bj] : (bj * m_blockSize);
     }
     inline Index blockInnerIndex(Index bi) const
     {
       return (m_blockSize == Dynamic) ? m_innerOffset[bi] : (bi * m_blockSize);
     }
 
     // Not needed ???
     inline Index blockInnerSize(Index bi) const
     {
       return (m_blockSize == Dynamic) ? (m_innerOffset[bi+1] - m_innerOffset[bi]) : m_blockSize;
     }
     inline Index blockOuterSize(Index bj) const
     {
       return (m_blockSize == Dynamic) ? (m_outerOffset[bj+1]- m_outerOffset[bj]) : m_blockSize;
     }
 
     /**
       * \brief Browse the matrix by outer index
       */
     class InnerIterator; // Browse column by column
 
     /**
       * \brief Browse the matrix by block outer index
       */
     class BlockInnerIterator; // Browse block by block
 
     friend std::ostream & operator << (std::ostream & s, const BlockSparseMatrix& m)
     {
       for (StorageIndex j = 0; j < m.outerBlocks(); ++j)
       {
         BlockInnerIterator itb(m, j);
         for(; itb; ++itb)
         {
           s << "("<<itb.row() << ", " << itb.col() << ")\n";
           s << itb.value() <<"\n";
         }
       }
       s << std::endl;
       return s;
     }
 
     /**
       * \returns the starting position of the block \p id in the array of values
       */
     Index blockPtr(Index id) const
     {
       if(m_blockSize == Dynamic) return m_blockPtr[id];
       else return id * m_blockSize * m_blockSize;
       //return blockDynIdx(id, typename internal::conditional<(BlockSize==Dynamic), internal::true_type, internal::false_type>::type());
     }
 
 
   protected:
 //    inline Index blockDynIdx(Index id, internal::true_type) const
 //    {
 //      return m_blockPtr[id];
 //    }
 //    inline Index blockDynIdx(Index id, internal::false_type) const
 //    {
 //      return id * BlockSize * BlockSize;
 //    }
 
     // To be implemented
     // Insert a block at a particular location... need to make a room for that
     Map<BlockScalar> insert(Index brow, Index bcol);
 
     Index m_innerBSize; // Number of block rows
     Index m_outerBSize; // Number of block columns
     StorageIndex *m_innerOffset; // Starting index of each inner block (size m_innerBSize+1)
     StorageIndex *m_outerOffset; // Starting index of each outer block (size m_outerBSize+1)
     Index m_nonzerosblocks; // Total nonzeros blocks (lower than  m_innerBSize x m_outerBSize)
     Index m_nonzeros; // Total nonzeros elements
     Scalar *m_values; //Values stored block column after block column (size m_nonzeros)
     StorageIndex *m_blockPtr; // Pointer to the beginning of each block in m_values, size m_nonzeroblocks ... null for fixed-size blocks
     StorageIndex *m_indices; //Inner block indices, size m_nonzerosblocks ... OK
     StorageIndex *m_outerIndex; // Starting pointer of each block column in m_indices (size m_outerBSize)... OK
     Index m_blockSize; // Size of a block for fixed-size blocks, otherwise -1
 };
 
 template<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>
 class BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex>::BlockInnerIterator
 {
   public:
 
     enum{
       Flags = _Options
     };
 
     BlockInnerIterator(const BlockSparseMatrix& mat, const Index outer)
     : m_mat(mat),m_outer(outer),
       m_id(mat.m_outerIndex[outer]),
       m_end(mat.m_outerIndex[outer+1])
     {
     }
 
     inline BlockInnerIterator& operator++() {m_id++; return *this; }
 
     inline const Map<const BlockScalar> value() const
     {
       return Map<const BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),
           rows(),cols());
     }
     inline Map<BlockScalar> valueRef()
     {
       return Map<BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),
           rows(),cols());
     }
     // Block inner index
     inline Index index() const {return m_mat.m_indices[m_id]; }
     inline Index outer() const { return m_outer; }
     // block row index
     inline Index row() const  {return index(); }
     // block column index
     inline Index col() const {return outer(); }
     // FIXME Number of rows in the current block
     inline Index rows() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_innerOffset[index()+1] - m_mat.m_innerOffset[index()]) : m_mat.m_blockSize; }
     // Number of columns in the current block ...
     inline Index cols() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_outerOffset[m_outer+1]-m_mat.m_outerOffset[m_outer]) : m_mat.m_blockSize;}
     inline operator bool() const { return (m_id < m_end); }
 
   protected:
     const BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, StorageIndex>& m_mat;
     const Index m_outer;
     Index m_id;
     Index m_end;
 };
 
 template<typename _Scalar, int _BlockAtCompileTime, int _Options, typename _StorageIndex>
 class BlockSparseMatrix<_Scalar, _BlockAtCompileTime, _Options, _StorageIndex>::InnerIterator
 {
   public:
     InnerIterator(const BlockSparseMatrix& mat, Index outer)
     : m_mat(mat),m_outerB(mat.outerToBlock(outer)),m_outer(outer),
       itb(mat, mat.outerToBlock(outer)),
       m_offset(outer - mat.blockOuterIndex(m_outerB))
      {
         if (itb)
         {
           m_id = m_mat.blockInnerIndex(itb.index());
           m_start = m_id;
           m_end = m_mat.blockInnerIndex(itb.index()+1);
         }
      }
     inline InnerIterator& operator++()
     {
       m_id++;
       if (m_id >= m_end)
       {
         ++itb;
         if (itb)
         {
           m_id = m_mat.blockInnerIndex(itb.index());
           m_start = m_id;
           m_end = m_mat.blockInnerIndex(itb.index()+1);
         }
       }
       return *this;
     }
     inline const Scalar& value() const
     {
       return itb.value().coeff(m_id - m_start, m_offset);
     }
     inline Scalar& valueRef()
     {
       return itb.valueRef().coeff(m_id - m_start, m_offset);
     }
     inline Index index() const { return m_id; }
     inline Index outer() const {return m_outer; }
     inline Index col() const {return outer(); }
     inline Index row() const { return index();}
     inline operator bool() const
     {
       return itb;
     }
   protected:
     const BlockSparseMatrix& m_mat;
     const Index m_outer;
     const Index m_outerB;
     BlockInnerIterator itb; // Iterator through the blocks
     const Index m_offset; // Position of this column in the block
     Index m_start; // starting inner index of this block
     Index m_id; // current inner index in the block
     Index m_end; // starting inner index of the next block
 
 };
 } // end namespace Eigen
 
 #endif // EIGEN_SPARSEBLOCKMATRIX_H

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