unsupported/Eigen/src/SparseExtra/RandomSetter.h - mirror - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
 // License as published by the Free Software Foundation; either
 // version 3 of the License, or (at your option) any later version.
 //
 // Alternatively, you can redistribute it and/or
 // modify it under the terms of the GNU General Public License as
 // published by the Free Software Foundation; either version 2 of
 // the License, or (at your option) any later version.
 //
 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
 // GNU General Public License for more details.
 //
 // You should have received a copy of the GNU Lesser General Public
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.

 #ifndef EIGEN_RANDOMSETTER_H
 #define EIGEN_RANDOMSETTER_H

 /** Represents a std::map
   *
   * \see RandomSetter
   */
 template<typename Scalar> struct StdMapTraits
 {
   typedef int KeyType;
   typedef std::map<KeyType,Scalar> Type;
   enum {
     IsSorted = 1
   };

   static void setInvalidKey(Type&, const KeyType&) {}
 };

 #ifdef EIGEN_UNORDERED_MAP_SUPPORT
 /** Represents a std::unordered_map
   *
   * To use it you need to both define EIGEN_UNORDERED_MAP_SUPPORT and include the unordered_map header file
   * yourself making sure that unordered_map is defined in the std namespace.
   *
   * For instance, with current version of gcc you can either enable C++0x standard (-std=c++0x) or do:
   * \code
   * #include <tr1/unordered_map>
   * #define EIGEN_UNORDERED_MAP_SUPPORT
   * namespace std {
   *   using std::tr1::unordered_map;
   * }
   * \endcode
   *
   * \see RandomSetter
   */
 template<typename Scalar> struct StdUnorderedMapTraits
 {
   typedef int KeyType;
   typedef std::unordered_map<KeyType,Scalar> Type;
   enum {
     IsSorted = 0
   };

   static void setInvalidKey(Type&, const KeyType&) {}
 };
 #endif // EIGEN_UNORDERED_MAP_SUPPORT

 #ifdef _DENSE_HASH_MAP_H_
 /** Represents a google::dense_hash_map
   *
   * \see RandomSetter
   */
 template<typename Scalar> struct GoogleDenseHashMapTraits
 {
   typedef int KeyType;
   typedef google::dense_hash_map<KeyType,Scalar> Type;
   enum {
     IsSorted = 0
   };

   static void setInvalidKey(Type& map, const KeyType& k)
   { map.set_empty_key(k); }
 };
 #endif

 #ifdef _SPARSE_HASH_MAP_H_
 /** Represents a google::sparse_hash_map
   *
   * \see RandomSetter
   */
 template<typename Scalar> struct GoogleSparseHashMapTraits
 {
   typedef int KeyType;
   typedef google::sparse_hash_map<KeyType,Scalar> Type;
   enum {
     IsSorted = 0
   };

   static void setInvalidKey(Type&, const KeyType&) {}
 };
 #endif

 /** \class RandomSetter
   *
   * \brief The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access
   *
   * \param SparseMatrixType the type of the sparse matrix we are updating
   * \param MapTraits a traits class representing the map implementation used for the temporary sparse storage.
   *                  Its default value depends on the system.
   * \param OuterPacketBits defines the number of rows (or columns) manage by a single map object
   *                        as a power of two exponent.
   *
   * This class temporarily represents a sparse matrix object using a generic map implementation allowing for
   * efficient random access. The conversion from the compressed representation to a hash_map object is performed
   * in the RandomSetter constructor, while the sparse matrix is updated back at destruction time. This strategy
   * suggest the use of nested blocks as in this example:
   *
   * \code
   * SparseMatrix<double> m(rows,cols);
   * {
   *   RandomSetter<SparseMatrix<double> > w(m);
   *   // don't use m but w instead with read/write random access to the coefficients:
   *   for(;;)
   *     w(rand(),rand()) = rand;
   * }
   * // when w is deleted, the data are copied back to m
   * // and m is ready to use.
   * \endcode
   *
   * Since hash_map objects are not fully sorted, representing a full matrix as a single hash_map would
   * involve a big and costly sort to update the compressed matrix back. To overcome this issue, a RandomSetter
   * use multiple hash_map, each representing 2^OuterPacketBits columns or rows according to the storage order.
   * To reach optimal performance, this value should be adjusted according to the average number of nonzeros
   * per rows/columns.
   *
   * The possible values for the template parameter MapTraits are:
   *  - \b StdMapTraits: corresponds to std::map. (does not perform very well)
   *  - \b GnuHashMapTraits: corresponds to __gnu_cxx::hash_map (available only with GCC)
   *  - \b GoogleDenseHashMapTraits: corresponds to google::dense_hash_map (best efficiency, reasonable memory consumption)
   *  - \b GoogleSparseHashMapTraits: corresponds to google::sparse_hash_map (best memory consumption, relatively good performance)
   *
   * The default map implementation depends on the availability, and the preferred order is:
   * GoogleSparseHashMapTraits, GnuHashMapTraits, and finally StdMapTraits.
   *
   * For performance and memory consumption reasons it is highly recommended to use one of
   * the Google's hash_map implementation. To enable the support for them, you have two options:
   *  - \#include <google/dense_hash_map> yourself \b before Eigen/Sparse header
   *  - define EIGEN_GOOGLEHASH_SUPPORT
   * In the later case the inclusion of <google/dense_hash_map> is made for you.
   *
   * \see http://code.google.com/p/google-sparsehash/
   */
 template<typename SparseMatrixType,
          template <typename T> class MapTraits =
 #if defined _DENSE_HASH_MAP_H_
           GoogleDenseHashMapTraits
 #elif defined _HASH_MAP
           GnuHashMapTraits
 #else
           StdMapTraits
 #endif
          ,int OuterPacketBits = 6>
 class RandomSetter
 {
     typedef typename SparseMatrixType::Scalar Scalar;
     typedef typename SparseMatrixType::Index Index;

     struct ScalarWrapper
     {
       ScalarWrapper() : value(0) {}
       Scalar value;
     };
     typedef typename MapTraits<ScalarWrapper>::KeyType KeyType;
     typedef typename MapTraits<ScalarWrapper>::Type HashMapType;
     static const int OuterPacketMask = (1 << OuterPacketBits) - 1;
     enum {
       SwapStorage = 1 - MapTraits<ScalarWrapper>::IsSorted,
       TargetRowMajor = (SparseMatrixType::Flags & RowMajorBit) ? 1 : 0,
       SetterRowMajor = SwapStorage ? 1-TargetRowMajor : TargetRowMajor,
       IsUpper = SparseMatrixType::Flags & Upper,
       IsLower = SparseMatrixType::Flags & Lower
     };

   public:

     /** Constructs a random setter object from the sparse matrix \a target
       *
       * Note that the initial value of \a target are imported. If you want to re-set
       * a sparse matrix from scratch, then you must set it to zero first using the
       * setZero() function.
       */
     inline RandomSetter(SparseMatrixType& target)
       : mp_target(&target)
     {
       const Index outerSize = SwapStorage ? target.innerSize() : target.outerSize();
       const Index innerSize = SwapStorage ? target.outerSize() : target.innerSize();
       m_outerPackets = outerSize >> OuterPacketBits;
       if (outerSize&OuterPacketMask)
         m_outerPackets += 1;
       m_hashmaps = new HashMapType[m_outerPackets];
       // compute number of bits needed to store inner indices
       Index aux = innerSize - 1;
       m_keyBitsOffset = 0;
       while (aux)
       {
         ++m_keyBitsOffset;
         aux = aux >> 1;
       }
       KeyType ik = (1<<(OuterPacketBits+m_keyBitsOffset));
       for (Index k=0; k<m_outerPackets; ++k)
         MapTraits<ScalarWrapper>::setInvalidKey(m_hashmaps[k],ik);

       // insert current coeffs
       for (Index j=0; j<mp_target->outerSize(); ++j)
         for (typename SparseMatrixType::InnerIterator it(*mp_target,j); it; ++it)
           (*this)(TargetRowMajor?j:it.index(), TargetRowMajor?it.index():j) = it.value();
     }

     /** Destructor updating back the sparse matrix target */
     ~RandomSetter()
     {
       KeyType keyBitsMask = (1<<m_keyBitsOffset)-1;
       if (!SwapStorage) // also means the map is sorted
       {
         mp_target->setZero();
         mp_target->reserve(nonZeros());
         Index prevOuter = -1;
         for (Index k=0; k<m_outerPackets; ++k)
         {
           const Index outerOffset = (1<<OuterPacketBits) * k;
           typename HashMapType::iterator end = m_hashmaps[k].end();
           for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
           {
             const Index outer = (it->first >> m_keyBitsOffset) + outerOffset;
             const Index inner = it->first & keyBitsMask;
             if (prevOuter!=outer)
             {
               for (Index j=prevOuter+1;j<=outer;++j)
                 mp_target->startVec(j);
               prevOuter = outer;
             }
             mp_target->insertBackByOuterInner(outer, inner) = it->second.value;
           }
         }
         mp_target->finalize();
       }
       else
       {
         VectorXi positions(mp_target->outerSize());
         positions.setZero();
         // pass 1
         for (Index k=0; k<m_outerPackets; ++k)
         {
           typename HashMapType::iterator end = m_hashmaps[k].end();
           for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
           {
             const Index outer = it->first & keyBitsMask;
             ++positions[outer];
           }
         }
         // prefix sum
         Index count = 0;
         for (Index j=0; j<mp_target->outerSize(); ++j)
         {
           Index tmp = positions[j];
           mp_target->_outerIndexPtr()[j] = count;
           positions[j] = count;
           count += tmp;
         }
         mp_target->_outerIndexPtr()[mp_target->outerSize()] = count;
         mp_target->resizeNonZeros(count);
         // pass 2
         for (Index k=0; k<m_outerPackets; ++k)
         {
           const Index outerOffset = (1<<OuterPacketBits) * k;
           typename HashMapType::iterator end = m_hashmaps[k].end();
           for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
           {
             const Index inner = (it->first >> m_keyBitsOffset) + outerOffset;
             const Index outer = it->first & keyBitsMask;
             // sorted insertion
             // Note that we have to deal with at most 2^OuterPacketBits unsorted coefficients,
             // moreover those 2^OuterPacketBits coeffs are likely to be sparse, an so only a
             // small fraction of them have to be sorted, whence the following simple procedure:
             Index posStart = mp_target->_outerIndexPtr()[outer];
             Index i = (positions[outer]++) - 1;
             while ( (i >= posStart) && (mp_target->_innerIndexPtr()[i] > inner) )
             {
               mp_target->_valuePtr()[i+1] = mp_target->_valuePtr()[i];
               mp_target->_innerIndexPtr()[i+1] = mp_target->_innerIndexPtr()[i];
               --i;
             }
             mp_target->_innerIndexPtr()[i+1] = inner;
             mp_target->_valuePtr()[i+1] = it->second.value;
           }
         }
       }
       delete[] m_hashmaps;
     }

     /** \returns a reference to the coefficient at given coordinates \a row, \a col */
     Scalar& operator() (Index row, Index col)
     {
       ei_assert(((!IsUpper) || (row<=col)) && "Invalid access to an upper triangular matrix");
       ei_assert(((!IsLower) || (col<=row)) && "Invalid access to an upper triangular matrix");
       const Index outer = SetterRowMajor ? row : col;
       const Index inner = SetterRowMajor ? col : row;
       const Index outerMajor = outer >> OuterPacketBits; // index of the packet/map
       const Index outerMinor = outer & OuterPacketMask;  // index of the inner vector in the packet
       const KeyType key = (KeyType(outerMinor)<<m_keyBitsOffset) | inner;
       return m_hashmaps[outerMajor][key].value;
     }

     /** \returns the number of non zero coefficients
       *
       * \note According to the underlying map/hash_map implementation,
       * this function might be quite expensive.
       */
     Index nonZeros() const
     {
       Index nz = 0;
       for (Index k=0; k<m_outerPackets; ++k)
         nz += static_cast<Index>(m_hashmaps[k].size());
       return nz;
     }


   protected:

     HashMapType* m_hashmaps;
     SparseMatrixType* mp_target;
     Index m_outerPackets;
     unsigned char m_keyBitsOffset;
 };

 #endif // EIGEN_RANDOMSETTER_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
	//
	// Eigen is free software; you can redistribute it and/or
	// modify it under the terms of the GNU Lesser General Public
	// License as published by the Free Software Foundation; either
	// version 3 of the License, or (at your option) any later version.
	//
	// Alternatively, you can redistribute it and/or
	// modify it under the terms of the GNU General Public License as
	// published by the Free Software Foundation; either version 2 of
	// the License, or (at your option) any later version.
	//
	// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
	// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
	// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
	// GNU General Public License for more details.
	//
	// You should have received a copy of the GNU Lesser General Public
	// License and a copy of the GNU General Public License along with
	// Eigen. If not, see <http://www.gnu.org/licenses/>.

	#ifndef EIGEN_RANDOMSETTER_H
	#define EIGEN_RANDOMSETTER_H

	/** Represents a std::map
	*
	* \see RandomSetter
	*/
	template<typename Scalar> struct StdMapTraits
	{
	typedef int KeyType;
	typedef std::map<KeyType,Scalar> Type;
	enum {
	IsSorted = 1
	};

	static void setInvalidKey(Type&, const KeyType&) {}
	};

	#ifdef EIGEN_UNORDERED_MAP_SUPPORT
	/** Represents a std::unordered_map
	*
	* To use it you need to both define EIGEN_UNORDERED_MAP_SUPPORT and include the unordered_map header file
	* yourself making sure that unordered_map is defined in the std namespace.
	*
	* For instance, with current version of gcc you can either enable C++0x standard (-std=c++0x) or do:
	* \code
	* #include <tr1/unordered_map>
	* #define EIGEN_UNORDERED_MAP_SUPPORT
	* namespace std {
	* using std::tr1::unordered_map;
	* }
	* \endcode
	*
	* \see RandomSetter
	*/
	template<typename Scalar> struct StdUnorderedMapTraits
	{
	typedef int KeyType;
	typedef std::unordered_map<KeyType,Scalar> Type;
	enum {
	IsSorted = 0
	};

	static void setInvalidKey(Type&, const KeyType&) {}
	};
	#endif // EIGEN_UNORDERED_MAP_SUPPORT

	#ifdef _DENSE_HASH_MAP_H_
	/** Represents a google::dense_hash_map
	*
	* \see RandomSetter
	*/
	template<typename Scalar> struct GoogleDenseHashMapTraits
	{
	typedef int KeyType;
	typedef google::dense_hash_map<KeyType,Scalar> Type;
	enum {
	IsSorted = 0
	};

	static void setInvalidKey(Type& map, const KeyType& k)
	{ map.set_empty_key(k); }
	};
	#endif

	#ifdef _SPARSE_HASH_MAP_H_
	/** Represents a google::sparse_hash_map
	*
	* \see RandomSetter
	*/
	template<typename Scalar> struct GoogleSparseHashMapTraits
	{
	typedef int KeyType;
	typedef google::sparse_hash_map<KeyType,Scalar> Type;
	enum {
	IsSorted = 0
	};

	static void setInvalidKey(Type&, const KeyType&) {}
	};
	#endif

	/** \class RandomSetter
	*
	* \brief The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access
	*
	* \param SparseMatrixType the type of the sparse matrix we are updating
	* \param MapTraits a traits class representing the map implementation used for the temporary sparse storage.
	* Its default value depends on the system.
	* \param OuterPacketBits defines the number of rows (or columns) manage by a single map object
	* as a power of two exponent.
	*
	* This class temporarily represents a sparse matrix object using a generic map implementation allowing for
	* efficient random access. The conversion from the compressed representation to a hash_map object is performed
	* in the RandomSetter constructor, while the sparse matrix is updated back at destruction time. This strategy
	* suggest the use of nested blocks as in this example:
	*
	* \code
	* SparseMatrix<double> m(rows,cols);
	* {
	* RandomSetter<SparseMatrix<double> > w(m);
	* // don't use m but w instead with read/write random access to the coefficients:
	* for(;;)
	* w(rand(),rand()) = rand;
	* }
	* // when w is deleted, the data are copied back to m
	* // and m is ready to use.
	* \endcode
	*
	* Since hash_map objects are not fully sorted, representing a full matrix as a single hash_map would
	* involve a big and costly sort to update the compressed matrix back. To overcome this issue, a RandomSetter
	* use multiple hash_map, each representing 2^OuterPacketBits columns or rows according to the storage order.
	* To reach optimal performance, this value should be adjusted according to the average number of nonzeros
	* per rows/columns.
	*
	* The possible values for the template parameter MapTraits are:
	* - \b StdMapTraits: corresponds to std::map. (does not perform very well)
	* - \b GnuHashMapTraits: corresponds to __gnu_cxx::hash_map (available only with GCC)
	* - \b GoogleDenseHashMapTraits: corresponds to google::dense_hash_map (best efficiency, reasonable memory consumption)
	* - \b GoogleSparseHashMapTraits: corresponds to google::sparse_hash_map (best memory consumption, relatively good performance)
	*
	* The default map implementation depends on the availability, and the preferred order is:
	* GoogleSparseHashMapTraits, GnuHashMapTraits, and finally StdMapTraits.
	*
	* For performance and memory consumption reasons it is highly recommended to use one of
	* the Google's hash_map implementation. To enable the support for them, you have two options:
	* - \#include <google/dense_hash_map> yourself \b before Eigen/Sparse header
	* - define EIGEN_GOOGLEHASH_SUPPORT
	* In the later case the inclusion of <google/dense_hash_map> is made for you.
	*
	* \see http://code.google.com/p/google-sparsehash/
	*/
	template<typename SparseMatrixType,
	template <typename T> class MapTraits =
	#if defined _DENSE_HASH_MAP_H_
	GoogleDenseHashMapTraits
	#elif defined _HASH_MAP
	GnuHashMapTraits
	#else
	StdMapTraits
	#endif
	,int OuterPacketBits = 6>
	class RandomSetter
	{
	typedef typename SparseMatrixType::Scalar Scalar;
	typedef typename SparseMatrixType::Index Index;

	struct ScalarWrapper
	{
	ScalarWrapper() : value(0) {}
	Scalar value;
	};
	typedef typename MapTraits<ScalarWrapper>::KeyType KeyType;
	typedef typename MapTraits<ScalarWrapper>::Type HashMapType;
	static const int OuterPacketMask = (1 << OuterPacketBits) - 1;
	enum {
	SwapStorage = 1 - MapTraits<ScalarWrapper>::IsSorted,
	TargetRowMajor = (SparseMatrixType::Flags & RowMajorBit) ? 1 : 0,
	SetterRowMajor = SwapStorage ? 1-TargetRowMajor : TargetRowMajor,
	IsUpper = SparseMatrixType::Flags & Upper,
	IsLower = SparseMatrixType::Flags & Lower
	};

	public:

	/** Constructs a random setter object from the sparse matrix \a target
	*
	* Note that the initial value of \a target are imported. If you want to re-set
	* a sparse matrix from scratch, then you must set it to zero first using the
	* setZero() function.
	*/
	inline RandomSetter(SparseMatrixType& target)
	: mp_target(&target)
	{
	const Index outerSize = SwapStorage ? target.innerSize() : target.outerSize();
	const Index innerSize = SwapStorage ? target.outerSize() : target.innerSize();
	m_outerPackets = outerSize >> OuterPacketBits;
	if (outerSize&OuterPacketMask)
	m_outerPackets += 1;
	m_hashmaps = new HashMapType[m_outerPackets];
	// compute number of bits needed to store inner indices
	Index aux = innerSize - 1;
	m_keyBitsOffset = 0;
	while (aux)
	{
	++m_keyBitsOffset;
	aux = aux >> 1;
	}
	KeyType ik = (1<<(OuterPacketBits+m_keyBitsOffset));
	for (Index k=0; k<m_outerPackets; ++k)
	MapTraits<ScalarWrapper>::setInvalidKey(m_hashmaps[k],ik);

	// insert current coeffs
	for (Index j=0; j<mp_target->outerSize(); ++j)
	for (typename SparseMatrixType::InnerIterator it(*mp_target,j); it; ++it)
	(*this)(TargetRowMajor?j:it.index(), TargetRowMajor?it.index():j) = it.value();
	}

	/** Destructor updating back the sparse matrix target */
	~RandomSetter()
	{
	KeyType keyBitsMask = (1<<m_keyBitsOffset)-1;
	if (!SwapStorage) // also means the map is sorted
	{
	mp_target->setZero();
	mp_target->reserve(nonZeros());
	Index prevOuter = -1;
	for (Index k=0; k<m_outerPackets; ++k)
	{
	const Index outerOffset = (1<<OuterPacketBits) * k;
	typename HashMapType::iterator end = m_hashmaps[k].end();
	for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
	{
	const Index outer = (it->first >> m_keyBitsOffset) + outerOffset;
	const Index inner = it->first & keyBitsMask;
	if (prevOuter!=outer)
	{
	for (Index j=prevOuter+1;j<=outer;++j)
	mp_target->startVec(j);
	prevOuter = outer;
	}
	mp_target->insertBackByOuterInner(outer, inner) = it->second.value;
	}
	}
	mp_target->finalize();
	}
	else
	{
	VectorXi positions(mp_target->outerSize());
	positions.setZero();
	// pass 1
	for (Index k=0; k<m_outerPackets; ++k)
	{
	typename HashMapType::iterator end = m_hashmaps[k].end();
	for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
	{
	const Index outer = it->first & keyBitsMask;
	++positions[outer];
	}
	}
	// prefix sum
	Index count = 0;
	for (Index j=0; j<mp_target->outerSize(); ++j)
	{
	Index tmp = positions[j];
	mp_target->_outerIndexPtr()[j] = count;
	positions[j] = count;
	count += tmp;
	}
	mp_target->_outerIndexPtr()[mp_target->outerSize()] = count;
	mp_target->resizeNonZeros(count);
	// pass 2
	for (Index k=0; k<m_outerPackets; ++k)
	{
	const Index outerOffset = (1<<OuterPacketBits) * k;
	typename HashMapType::iterator end = m_hashmaps[k].end();
	for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
	{
	const Index inner = (it->first >> m_keyBitsOffset) + outerOffset;
	const Index outer = it->first & keyBitsMask;
	// sorted insertion
	// Note that we have to deal with at most 2^OuterPacketBits unsorted coefficients,
	// moreover those 2^OuterPacketBits coeffs are likely to be sparse, an so only a
	// small fraction of them have to be sorted, whence the following simple procedure:
	Index posStart = mp_target->_outerIndexPtr()[outer];
	Index i = (positions[outer]++) - 1;
	while ( (i >= posStart) && (mp_target->_innerIndexPtr()[i] > inner) )
	{
	mp_target->_valuePtr()[i+1] = mp_target->_valuePtr()[i];
	mp_target->_innerIndexPtr()[i+1] = mp_target->_innerIndexPtr()[i];
	--i;
	}
	mp_target->_innerIndexPtr()[i+1] = inner;
	mp_target->_valuePtr()[i+1] = it->second.value;
	}
	}
	}
	delete[] m_hashmaps;
	}

	/** \returns a reference to the coefficient at given coordinates \a row, \a col */
	Scalar& operator() (Index row, Index col)
	{
	ei_assert(((!IsUpper) \|\| (row<=col)) && "Invalid access to an upper triangular matrix");
	ei_assert(((!IsLower) \|\| (col<=row)) && "Invalid access to an upper triangular matrix");
	const Index outer = SetterRowMajor ? row : col;
	const Index inner = SetterRowMajor ? col : row;
	const Index outerMajor = outer >> OuterPacketBits; // index of the packet/map
	const Index outerMinor = outer & OuterPacketMask; // index of the inner vector in the packet
	const KeyType key = (KeyType(outerMinor)<<m_keyBitsOffset) \| inner;
	return m_hashmaps[outerMajor][key].value;
	}

	/** \returns the number of non zero coefficients
	*
	* \note According to the underlying map/hash_map implementation,
	* this function might be quite expensive.
	*/
	Index nonZeros() const
	{
	Index nz = 0;
	for (Index k=0; k<m_outerPackets; ++k)
	nz += static_cast<Index>(m_hashmaps[k].size());
	return nz;
	}


	protected:

	HashMapType* m_hashmaps;
	SparseMatrixType* mp_target;
	Index m_outerPackets;
	unsigned char m_keyBitsOffset;
	};

	#endif // EIGEN_RANDOMSETTER_H