// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 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_SPARSEMATRIX_H
#define EIGEN_SPARSEMATRIX_H
namespace Eigen {
/** \ingroup SparseCore_Module
*
* \class SparseMatrix
*
* \brief A versatible sparse matrix representation
*
* This class implements a more versatile variants of the common \em compressed row/column storage format.
* Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index.
* All the non zeros are stored in a single large buffer. Unlike the \em compressed format, there might be extra
* space inbetween the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero
* can be done with limited memory reallocation and copies.
*
* A call to the function makeCompressed() turns the matrix into the standard \em compressed format
* compatible with many library.
*
* More details on this storage sceheme are given in the \ref TutorialSparse "manual pages".
*
* \tparam _Scalar the scalar type, i.e. the type of the coefficients
* \tparam _Options Union of bit flags controlling the storage scheme. Currently the only possibility
* is RowMajor. The default is 0 which means column-major.
* \tparam _Index the type of the indices. It has to be a \b signed type (e.g., short, int, std::ptrdiff_t). Default is \c int.
*
* This class can be extended with the help of the plugin mechanism described on the page
* \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_SPARSEMATRIX_PLUGIN.
*/
namespace internal {
template<typename _Scalar, int _Options, typename _Index>
struct traits<SparseMatrix<_Scalar, _Options, _Index> >
{
typedef _Scalar Scalar;
typedef _Index Index;
typedef Sparse StorageKind;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = Dynamic,
ColsAtCompileTime = Dynamic,
MaxRowsAtCompileTime = Dynamic,
MaxColsAtCompileTime = Dynamic,
Flags = _Options | NestByRefBit | LvalueBit,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
SupportedAccessPatterns = InnerRandomAccessPattern
};
};
template<typename _Scalar, int _Options, typename _Index, int DiagIndex>
struct traits<Diagonal<const SparseMatrix<_Scalar, _Options, _Index>, DiagIndex> >
{
typedef SparseMatrix<_Scalar, _Options, _Index> MatrixType;
typedef typename nested<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef _Index Index;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = Dynamic,
ColsAtCompileTime = 1,
MaxRowsAtCompileTime = Dynamic,
MaxColsAtCompileTime = 1,
Flags = 0,
CoeffReadCost = _MatrixTypeNested::CoeffReadCost*10
};
};
} // end namespace internal
template<typename _Scalar, int _Options, typename _Index>
class SparseMatrix
: public SparseMatrixBase<SparseMatrix<_Scalar, _Options, _Index> >
{
public:
EIGEN_SPARSE_PUBLIC_INTERFACE(SparseMatrix)
EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, +=)
EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseMatrix, -=)
typedef MappedSparseMatrix<Scalar,Flags> Map;
using Base::IsRowMajor;
typedef internal::CompressedStorage<Scalar,Index> Storage;
enum {
Options = _Options
};
protected:
typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;
Index m_outerSize;
Index m_innerSize;
Index* m_outerIndex;
Index* m_innerNonZeros; // optional, if null then the data is compressed
Storage m_data;
Eigen::Map<Matrix<Index,Dynamic,1> > innerNonZeros() { return Eigen::Map<Matrix<Index,Dynamic,1> >(m_innerNonZeros, m_innerNonZeros?m_outerSize:0); }
const Eigen::Map<const Matrix<Index,Dynamic,1> > innerNonZeros() const { return Eigen::Map<const Matrix<Index,Dynamic,1> >(m_innerNonZeros, m_innerNonZeros?m_outerSize:0); }
public:
/** \returns whether \c *this is in compressed form. */
inline bool isCompressed() const { return m_innerNonZeros==0; }
/** \returns the number of rows of the matrix */
inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
/** \returns the number of columns of the matrix */
inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
/** \returns the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major) */
inline Index innerSize() const { return m_innerSize; }
/** \returns the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major) */
inline Index outerSize() const { return m_outerSize; }
/** \returns a const pointer to the array of values.
* This function is aimed at interoperability with other libraries.
* \sa innerIndexPtr(), outerIndexPtr() */
inline const Scalar* valuePtr() const { return &m_data.value(0); }
/** \returns a non-const pointer to the array of values.
* This function is aimed at interoperability with other libraries.
* \sa innerIndexPtr(), outerIndexPtr() */
inline Scalar* valuePtr() { return &m_data.value(0); }
/** \returns a const pointer to the array of inner indices.
* This function is aimed at interoperability with other libraries.
* \sa valuePtr(), outerIndexPtr() */
inline const Index* innerIndexPtr() const { return &m_data.index(0); }
/** \returns a non-const pointer to the array of inner indices.
* This function is aimed at interoperability with other libraries.
* \sa valuePtr(), outerIndexPtr() */
inline Index* innerIndexPtr() { return &m_data.index(0); }
/** \returns a const pointer to the array of the starting positions of the inner vectors.
* This function is aimed at interoperability with other libraries.
* \sa valuePtr(), innerIndexPtr() */
inline const Index* outerIndexPtr() const { return m_outerIndex; }
/** \returns a non-const pointer to the array of the starting positions of the inner vectors.
* This function is aimed at interoperability with other libraries.
* \sa valuePtr(), innerIndexPtr() */
inline Index* outerIndexPtr() { return m_outerIndex; }
/** \returns a const pointer to the array of the number of non zeros of the inner vectors.
* This function is aimed at interoperability with other libraries.
* \warning it returns the null pointer 0 in compressed mode */
inline const Index* innerNonZeroPtr() const { return m_innerNonZeros; }
/** \returns a non-const pointer to the array of the number of non zeros of the inner vectors.
* This function is aimed at interoperability with other libraries.
* \warning it returns the null pointer 0 in compressed mode */
inline Index* innerNonZeroPtr() { return m_innerNonZeros; }
/** \internal */
inline Storage& data() { return m_data; }
/** \internal */
inline const Storage& data() const { return m_data; }
/** \returns the value of the matrix at position \a i, \a j
* This function returns Scalar(0) if the element is an explicit \em zero */
inline Scalar coeff(Index row, Index col) const
{
const Index outer = IsRowMajor ? row : col;
const Index inner = IsRowMajor ? col : row;
Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
return m_data.atInRange(m_outerIndex[outer], end, inner);
}
/** \returns a non-const reference to the value of the matrix at position \a i, \a j
*
* If the element does not exist then it is inserted via the insert(Index,Index) function
* which itself turns the matrix into a non compressed form if that was not the case.
*
* This is a O(log(nnz_j)) operation (binary search) plus the cost of insert(Index,Index)
* function if the element does not already exist.
*/
inline Scalar& coeffRef(Index row, Index col)
{
const Index outer = IsRowMajor ? row : col;
const Index inner = IsRowMajor ? col : row;
Index start = m_outerIndex[outer];
Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
if(end<=start)
return insert(row,col);
const Index p = m_data.searchLowerIndex(start,end-1,inner);
if((p<end) && (m_data.index(p)==inner))
return m_data.value(p);
else
return insert(row,col);
}
/** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
* The non zero coefficient must \b not already exist.
*
* If the matrix \c *this is in compressed mode, then \c *this is turned into uncompressed
* mode while reserving room for 2 non zeros per inner vector. It is strongly recommended to first
* call reserve(const SizesType &) to reserve a more appropriate number of elements per
* inner vector that better match your scenario.
*
* This function performs a sorted insertion in O(1) if the elements of each inner vector are
* inserted in increasing inner index order, and in O(nnz_j) for a random insertion.
*
*/
EIGEN_DONT_INLINE Scalar& insert(Index row, Index col)
{
if(isCompressed())
{
reserve(VectorXi::Constant(outerSize(), 2));
}
return insertUncompressed(row,col);
}
public:
class InnerIterator;
class ReverseInnerIterator;
/** Removes all non zeros but keep allocated memory */
inline void setZero()
{
m_data.clear();
memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(Index));
if(m_innerNonZeros)
memset(m_innerNonZeros, 0, (m_outerSize)*sizeof(Index));
}
/** \returns the number of non zero coefficients */
inline Index nonZeros() const
{
if(m_innerNonZeros)
return innerNonZeros().sum();
return static_cast<Index>(m_data.size());
}
/** Preallocates \a reserveSize non zeros.
*
* Precondition: the matrix must be in compressed mode. */
inline void reserve(Index reserveSize)
{
eigen_assert(isCompressed() && "This function does not make sense in non compressed mode.");
m_data.reserve(reserveSize);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** Preallocates \a reserveSize[\c j] non zeros for each column (resp. row) \c j.
*
* This function turns the matrix in non-compressed mode */
template<class SizesType>
inline void reserve(const SizesType& reserveSizes);
#else
template<class SizesType>
inline void reserve(const SizesType& reserveSizes, const typename SizesType::value_type& enableif = typename SizesType::value_type())
{
EIGEN_UNUSED_VARIABLE(enableif);
reserveInnerVectors(reserveSizes);
}
template<class SizesType>
inline void reserve(const SizesType& reserveSizes, const typename SizesType::Scalar& enableif =
#if (!defined(_MSC_VER)) || (_MSC_VER>=1500) // MSVC 2005 fails to compile with this typename
typename
#endif
SizesType::Scalar())
{
EIGEN_UNUSED_VARIABLE(enableif);
reserveInnerVectors(reserveSizes);
}
#endif // EIGEN_PARSED_BY_DOXYGEN
protected:
template<class SizesType>
inline void reserveInnerVectors(const SizesType& reserveSizes)
{
if(isCompressed())
{
std::size_t totalReserveSize = 0;
// turn the matrix into non-compressed mode
m_innerNonZeros = new Index[m_outerSize];
// temporarily use m_innerSizes to hold the new starting points.
Index* newOuterIndex = m_innerNonZeros;
Index count = 0;
for(Index j=0; j<m_outerSize; ++j)
{
newOuterIndex[j] = count;
count += reserveSizes[j] + (m_outerIndex[j+1]-m_outerIndex[j]);
totalReserveSize += reserveSizes[j];
}
m_data.reserve(totalReserveSize);
std::ptrdiff_t previousOuterIndex = m_outerIndex[m_outerSize];
for(std::ptrdiff_t j=m_outerSize-1; j>=0; --j)
{
ptrdiff_t innerNNZ = previousOuterIndex - m_outerIndex[j];
for(std::ptrdiff_t i=innerNNZ-1; i>=0; --i)
{
m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
}
previousOuterIndex = m_outerIndex[j];
m_outerIndex[j] = newOuterIndex[j];
m_innerNonZeros[j] = innerNNZ;
}
m_outerIndex[m_outerSize] = m_outerIndex[m_outerSize-1] + m_innerNonZeros[m_outerSize-1] + reserveSizes[m_outerSize-1];
m_data.resize(m_outerIndex[m_outerSize]);
}
else
{
Index* newOuterIndex = new Index[m_outerSize+1];
Index count = 0;
for(Index j=0; j<m_outerSize; ++j)
{
newOuterIndex[j] = count;
Index alreadyReserved = (m_outerIndex[j+1]-m_outerIndex[j]) - m_innerNonZeros[j];
Index toReserve = std::max<std::ptrdiff_t>(reserveSizes[j], alreadyReserved);
count += toReserve + m_innerNonZeros[j];
}
newOuterIndex[m_outerSize] = count;
m_data.resize(count);
for(ptrdiff_t j=m_outerSize-1; j>=0; --j)
{
std::ptrdiff_t offset = newOuterIndex[j] - m_outerIndex[j];
if(offset>0)
{
std::ptrdiff_t innerNNZ = m_innerNonZeros[j];
for(std::ptrdiff_t i=innerNNZ-1; i>=0; --i)
{
m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
}
}
}
std::swap(m_outerIndex, newOuterIndex);
delete[] newOuterIndex;
}
}
public:
//--- low level purely coherent filling ---
/** \internal
* \returns a reference to the non zero coefficient at position \a row, \a col assuming that:
* - the nonzero does not already exist
* - the new coefficient is the last one according to the storage order
*
* Before filling a given inner vector you must call the statVec(Index) function.
*
* After an insertion session, you should call the finalize() function.
*
* \sa insert, insertBackByOuterInner, startVec */
inline Scalar& insertBack(Index row, Index col)
{
return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row);
}
/** \internal
* \sa insertBack, startVec */
inline Scalar& insertBackByOuterInner(Index outer, Index inner)
{
eigen_assert(size_t(m_outerIndex[outer+1]) == m_data.size() && "Invalid ordered insertion (invalid outer index)");
eigen_assert( (m_outerIndex[outer+1]-m_outerIndex[outer]==0 || m_data.index(m_data.size()-1)<inner) && "Invalid ordered insertion (invalid inner index)");
Index p = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
m_data.append(0, inner);
return m_data.value(p);
}
/** \internal
* \warning use it only if you know what you are doing */
inline Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)
{
Index p = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
m_data.append(0, inner);
return m_data.value(p);
}
/** \internal
* \sa insertBack, insertBackByOuterInner */
inline void startVec(Index outer)
{
eigen_assert(m_outerIndex[outer]==int(m_data.size()) && "You must call startVec for each inner vector sequentially");
eigen_assert(m_outerIndex[outer+1]==0 && "You must call startVec for each inner vector sequentially");
m_outerIndex[outer+1] = m_outerIndex[outer];
}
/** \internal
* Must be called after inserting a set of non zero entries using the low level compressed API.
*/
inline void finalize()
{
if(isCompressed())
{
Index size = static_cast<Index>(m_data.size());
Index i = m_outerSize;
// find the last filled column
while (i>=0 && m_outerIndex[i]==0)
--i;
++i;
while (i<=m_outerSize)
{
m_outerIndex[i] = size;
++i;
}
}
}
//---
template<typename InputIterators>
void setFromTriplets(const InputIterators& begin, const InputIterators& end);
void sumupDuplicates();
//---
/** \internal
* same as insert(Index,Index) except that the indices are given relative to the storage order */
EIGEN_DONT_INLINE Scalar& insertByOuterInner(Index j, Index i)
{
return insert(IsRowMajor ? j : i, IsRowMajor ? i : j);
}
/** Turns the matrix into the \em compressed format.
*/
void makeCompressed()
{
if(isCompressed())
return;
Index oldStart = m_outerIndex[1];
m_outerIndex[1] = m_innerNonZeros[0];
for(Index j=1; j<m_outerSize; ++j)
{
Index nextOldStart = m_outerIndex[j+1];
std::ptrdiff_t offset = oldStart - m_outerIndex[j];
if(offset>0)
{
for(Index k=0; k<m_innerNonZeros[j]; ++k)
{
m_data.index(m_outerIndex[j]+k) = m_data.index(oldStart+k);
m_data.value(m_outerIndex[j]+k) = m_data.value(oldStart+k);
}
}
m_outerIndex[j+1] = m_outerIndex[j] + m_innerNonZeros[j];
oldStart = nextOldStart;
}
delete[] m_innerNonZeros;
m_innerNonZeros = 0;
m_data.resize(m_outerIndex[m_outerSize]);
m_data.squeeze();
}
/** Suppresses all nonzeros which are \b much \b smaller \b than \a reference under the tolerence \a epsilon */
void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision())
{
prune(default_prunning_func(reference,epsilon));
}
/** Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate \a keep.
* The functor type \a KeepFunc must implement the following function:
* \code
* bool operator() (const Index& row, const Index& col, const Scalar& value) const;
* \endcode
* \sa prune(Scalar,RealScalar)
*/
template<typename KeepFunc>
void prune(const KeepFunc& keep = KeepFunc())
{
// TODO optimize the uncompressed mode to avoid moving and allocating the data twice
// TODO also implement a unit test
makeCompressed();
Index k = 0;
for(Index j=0; j<m_outerSize; ++j)
{
Index previousStart = m_outerIndex[j];
m_outerIndex[j] = k;
Index end = m_outerIndex[j+1];
for(Index i=previousStart; i<end; ++i)
{
if(keep(IsRowMajor?j:m_data.index(i), IsRowMajor?m_data.index(i):j, m_data.value(i)))
{
m_data.value(k) = m_data.value(i);
m_data.index(k) = m_data.index(i);
++k;
}
}
}
m_outerIndex[m_outerSize] = k;
m_data.resize(k,0);
}
/** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero.
* \sa resizeNonZeros(Index), reserve(), setZero()
*/
void resize(Index rows, Index cols)
{
const Index outerSize = IsRowMajor ? rows : cols;
m_innerSize = IsRowMajor ? cols : rows;
m_data.clear();
if (m_outerSize != outerSize || m_outerSize==0)
{
delete[] m_outerIndex;
m_outerIndex = new Index [outerSize+1];
m_outerSize = outerSize;
}
if(m_innerNonZeros)
{
delete[] m_innerNonZeros;
m_innerNonZeros = 0;
}
memset(m_outerIndex, 0, (m_outerSize+1)*sizeof(Index));
}
/** \internal
* Resize the nonzero vector to \a size */
void resizeNonZeros(Index size)
{
// TODO remove this function
m_data.resize(size);
}
/** \returns a const expression of the diagonal coefficients */
const Diagonal<const SparseMatrix> diagonal() const { return *this; }
/** Default constructor yielding an empty \c 0 \c x \c 0 matrix */
inline SparseMatrix()
: m_outerSize(-1), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
{
check_template_parameters();
resize(0, 0);
}
/** Constructs a \a rows \c x \a cols empty matrix */
inline SparseMatrix(Index rows, Index cols)
: m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
{
check_template_parameters();
resize(rows, cols);
}
/** Constructs a sparse matrix from the sparse expression \a other */
template<typename OtherDerived>
inline SparseMatrix(const SparseMatrixBase<OtherDerived>& other)
: m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
{
check_template_parameters();
*this = other.derived();
}
/** Copy constructor (it performs a deep copy) */
inline SparseMatrix(const SparseMatrix& other)
: Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
{
check_template_parameters();
*this = other.derived();
}
/** Swaps the content of two sparse matrices of the same type.
* This is a fast operation that simply swaps the underlying pointers and parameters. */
inline void swap(SparseMatrix& other)
{
//EIGEN_DBG_SPARSE(std::cout << "SparseMatrix:: swap\n");
std::swap(m_outerIndex, other.m_outerIndex);
std::swap(m_innerSize, other.m_innerSize);
std::swap(m_outerSize, other.m_outerSize);
std::swap(m_innerNonZeros, other.m_innerNonZeros);
m_data.swap(other.m_data);
}
inline SparseMatrix& operator=(const SparseMatrix& other)
{
if (other.isRValue())
{
swap(other.const_cast_derived());
}
else
{
initAssignment(other);
if(other.isCompressed())
{
memcpy(m_outerIndex, other.m_outerIndex, (m_outerSize+1)*sizeof(Index));
m_data = other.m_data;
}
else
{
Base::operator=(other);
}
}
return *this;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Lhs, typename Rhs>
inline SparseMatrix& operator=(const SparseSparseProduct<Lhs,Rhs>& product)
{ return Base::operator=(product); }
template<typename OtherDerived>
inline SparseMatrix& operator=(const ReturnByValue<OtherDerived>& other)
{ return Base::operator=(other.derived()); }
template<typename OtherDerived>
inline SparseMatrix& operator=(const EigenBase<OtherDerived>& other)
{ return Base::operator=(other.derived()); }
#endif
template<typename OtherDerived>
EIGEN_DONT_INLINE SparseMatrix& operator=(const SparseMatrixBase<OtherDerived>& other)
{
initAssignment(other.derived());
const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
if (needToTranspose)
{
// two passes algorithm:
// 1 - compute the number of coeffs per dest inner vector
// 2 - do the actual copy/eval
// Since each coeff of the rhs has to be evaluated twice, let's evaluate it if needed
typedef typename internal::nested<OtherDerived,2>::type OtherCopy;
typedef typename internal::remove_all<OtherCopy>::type _OtherCopy;
OtherCopy otherCopy(other.derived());
Eigen::Map<Matrix<Index, Dynamic, 1> > (m_outerIndex,outerSize()).setZero();
// pass 1
// FIXME the above copy could be merged with that pass
for (Index j=0; j<otherCopy.outerSize(); ++j)
for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
++m_outerIndex[it.index()];
// prefix sum
Index count = 0;
VectorXi positions(outerSize());
for (Index j=0; j<outerSize(); ++j)
{
Index tmp = m_outerIndex[j];
m_outerIndex[j] = count;
positions[j] = count;
count += tmp;
}
m_outerIndex[outerSize()] = count;
// alloc
m_data.resize(count);
// pass 2
for (Index j=0; j<otherCopy.outerSize(); ++j)
{
for (typename _OtherCopy::InnerIterator it(otherCopy, j); it; ++it)
{
Index pos = positions[it.index()]++;
m_data.index(pos) = j;
m_data.value(pos) = it.value();
}
}
return *this;
}
else
{
// there is no special optimization
return Base::operator=(other.derived());
}
}
friend std::ostream & operator << (std::ostream & s, const SparseMatrix& m)
{
EIGEN_DBG_SPARSE(
s << "Nonzero entries:\n";
if(m.isCompressed())
for (Index i=0; i<m.nonZeros(); ++i)
s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
else
for (Index i=0; i<m.outerSize(); ++i)
{
int p = m.m_outerIndex[i];
int pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];
Index k=p;
for (; k<pe; ++k)
s << "(" << m.m_data.value(k) << "," << m.m_data.index(k) << ") ";
for (; k<m.m_outerIndex[i+1]; ++k)
s << "(_,_) ";
}
s << std::endl;
s << std::endl;
s << "Outer pointers:\n";
for (Index i=0; i<m.outerSize(); ++i)
s << m.m_outerIndex[i] << " ";
s << " $" << std::endl;
if(!m.isCompressed())
{
s << "Inner non zeros:\n";
for (Index i=0; i<m.outerSize(); ++i)
s << m.m_innerNonZeros[i] << " ";
s << " $" << std::endl;
}
s << std::endl;
);
s << static_cast<const SparseMatrixBase<SparseMatrix>&>(m);
return s;
}
/** Destructor */
inline ~SparseMatrix()
{
delete[] m_outerIndex;
delete[] m_innerNonZeros;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** Overloaded for performance */
Scalar sum() const;
#endif
# ifdef EIGEN_SPARSEMATRIX_PLUGIN
# include EIGEN_SPARSEMATRIX_PLUGIN
# endif
protected:
template<typename Other>
void initAssignment(const Other& other)
{
resize(other.rows(), other.cols());
if(m_innerNonZeros)
{
delete[] m_innerNonZeros;
m_innerNonZeros = 0;
}
}
/** \internal
* \sa insert(Index,Index) */
EIGEN_DONT_INLINE Scalar& insertCompressed(Index row, Index col)
{
eigen_assert(isCompressed());
const Index outer = IsRowMajor ? row : col;
const Index inner = IsRowMajor ? col : row;
Index previousOuter = outer;
if (m_outerIndex[outer+1]==0)
{
// we start a new inner vector
while (previousOuter>=0 && m_outerIndex[previousOuter]==0)
{
m_outerIndex[previousOuter] = static_cast<Index>(m_data.size());
--previousOuter;
}
m_outerIndex[outer+1] = m_outerIndex[outer];
}
// here we have to handle the tricky case where the outerIndex array
// starts with: [ 0 0 0 0 0 1 ...] and we are inserted in, e.g.,
// the 2nd inner vector...
bool isLastVec = (!(previousOuter==-1 && m_data.size()!=0))
&& (size_t(m_outerIndex[outer+1]) == m_data.size());
size_t startId = m_outerIndex[outer];
// FIXME let's make sure sizeof(long int) == sizeof(size_t)
size_t p = m_outerIndex[outer+1];
++m_outerIndex[outer+1];
float reallocRatio = 1;
if (m_data.allocatedSize()<=m_data.size())
{
// if there is no preallocated memory, let's reserve a minimum of 32 elements
if (m_data.size()==0)
{
m_data.reserve(32);
}
else
{
// we need to reallocate the data, to reduce multiple reallocations
// we use a smart resize algorithm based on the current filling ratio
// in addition, we use float to avoid integers overflows
float nnzEstimate = float(m_outerIndex[outer])*float(m_outerSize)/float(outer+1);
reallocRatio = (nnzEstimate-float(m_data.size()))/float(m_data.size());
// furthermore we bound the realloc ratio to:
// 1) reduce multiple minor realloc when the matrix is almost filled
// 2) avoid to allocate too much memory when the matrix is almost empty
reallocRatio = (std::min)((std::max)(reallocRatio,1.5f),8.f);
}
}
m_data.resize(m_data.size()+1,reallocRatio);
if (!isLastVec)
{
if (previousOuter==-1)
{
// oops wrong guess.
// let's correct the outer offsets
for (Index k=0; k<=(outer+1); ++k)
m_outerIndex[k] = 0;
Index k=outer+1;
while(m_outerIndex[k]==0)
m_outerIndex[k++] = 1;
while (k<=m_outerSize && m_outerIndex[k]!=0)
m_outerIndex[k++]++;
p = 0;
--k;
k = m_outerIndex[k]-1;
while (k>0)
{
m_data.index(k) = m_data.index(k-1);
m_data.value(k) = m_data.value(k-1);
k--;
}
}
else
{
// we are not inserting into the last inner vec
// update outer indices:
Index j = outer+2;
while (j<=m_outerSize && m_outerIndex[j]!=0)
m_outerIndex[j++]++;
--j;
// shift data of last vecs:
Index k = m_outerIndex[j]-1;
while (k>=Index(p))
{
m_data.index(k) = m_data.index(k-1);
m_data.value(k) = m_data.value(k-1);
k--;
}
}
}
while ( (p > startId) && (m_data.index(p-1) > inner) )
{
m_data.index(p) = m_data.index(p-1);
m_data.value(p) = m_data.value(p-1);
--p;
}
m_data.index(p) = inner;
return (m_data.value(p) = 0);
}
/** \internal
* A vector object that is equal to 0 everywhere but v at the position i */
class SingletonVector
{
Index m_index;
Index m_value;
public:
typedef Index value_type;
SingletonVector(Index i, Index v)
: m_index(i), m_value(v)
{}
Index operator[](Index i) const { return i==m_index ? m_value : 0; }
};
/** \internal
* \sa insert(Index,Index) */
EIGEN_DONT_INLINE Scalar& insertUncompressed(Index row, Index col)
{
eigen_assert(!isCompressed());
const Index outer = IsRowMajor ? row : col;
const Index inner = IsRowMajor ? col : row;
std::ptrdiff_t room = m_outerIndex[outer+1] - m_outerIndex[outer];
std::ptrdiff_t innerNNZ = m_innerNonZeros[outer];
if(innerNNZ>=room)
{
// this inner vector is full, we need to reallocate the whole buffer :(
reserve(SingletonVector(outer,std::max<std::ptrdiff_t>(2,innerNNZ)));
}
Index startId = m_outerIndex[outer];
Index p = startId + m_innerNonZeros[outer];
while ( (p > startId) && (m_data.index(p-1) > inner) )
{
m_data.index(p) = m_data.index(p-1);
m_data.value(p) = m_data.value(p-1);
--p;
}
m_innerNonZeros[outer]++;
m_data.index(p) = inner;
return (m_data.value(p) = 0);
}
public:
/** \internal
* \sa insert(Index,Index) */
inline Scalar& insertBackUncompressed(Index row, Index col)
{
const Index outer = IsRowMajor ? row : col;
const Index inner = IsRowMajor ? col : row;
eigen_assert(!isCompressed());
eigen_assert(m_innerNonZeros[outer]<=(m_outerIndex[outer+1] - m_outerIndex[outer]));
Index p = m_outerIndex[outer] + m_innerNonZeros[outer];
m_innerNonZeros[outer]++;
m_data.index(p) = inner;
return (m_data.value(p) = 0);
}
private:
static void check_template_parameters()
{
EIGEN_STATIC_ASSERT(NumTraits<Index>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE);
}
struct default_prunning_func {
default_prunning_func(Scalar ref, RealScalar eps) : reference(ref), epsilon(eps) {}
inline bool operator() (const Index&, const Index&, const Scalar& value) const
{
return !internal::isMuchSmallerThan(value, reference, epsilon);
}
Scalar reference;
RealScalar epsilon;
};
};
template<typename Scalar, int _Options, typename _Index>
class SparseMatrix<Scalar,_Options,_Index>::InnerIterator
{
public:
InnerIterator(const SparseMatrix& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer), m_id(mat.m_outerIndex[outer])
{
if(mat.isCompressed())
m_end = mat.m_outerIndex[outer+1];
else
m_end = m_id + mat.m_innerNonZeros[outer];
}
inline InnerIterator& operator++() { m_id++; return *this; }
inline const Scalar& value() const { return m_values[m_id]; }
inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id]); }
inline Index index() const { return m_indices[m_id]; }
inline Index outer() const { return m_outer; }
inline Index row() const { return IsRowMajor ? m_outer : index(); }
inline Index col() const { return IsRowMajor ? index() : m_outer; }
inline operator bool() const { return (m_id < m_end); }
protected:
const Scalar* m_values;
const Index* m_indices;
const Index m_outer;
Index m_id;
Index m_end;
};
template<typename Scalar, int _Options, typename _Index>
class SparseMatrix<Scalar,_Options,_Index>::ReverseInnerIterator
{
public:
ReverseInnerIterator(const SparseMatrix& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer), m_start(mat.m_outerIndex[outer])
{
if(mat.isCompressed())
m_id = mat.m_outerIndex[outer+1];
else
m_id = m_start + mat.m_innerNonZeros[outer];
}
inline ReverseInnerIterator& operator--() { --m_id; return *this; }
inline const Scalar& value() const { return m_values[m_id-1]; }
inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id-1]); }
inline Index index() const { return m_indices[m_id-1]; }
inline Index outer() const { return m_outer; }
inline Index row() const { return IsRowMajor ? m_outer : index(); }
inline Index col() const { return IsRowMajor ? index() : m_outer; }
inline operator bool() const { return (m_id > m_start); }
protected:
const Scalar* m_values;
const Index* m_indices;
const Index m_outer;
Index m_id;
const Index m_start;
};
namespace internal {
template<typename InputIterator, typename SparseMatrixType>
void set_from_triplets(const InputIterator& begin, const InputIterator& end, SparseMatrixType& mat, int Options = 0)
{
EIGEN_UNUSED_VARIABLE(Options);
enum { IsRowMajor = SparseMatrixType::IsRowMajor };
typedef typename SparseMatrixType::Scalar Scalar;
typedef typename SparseMatrixType::Index Index;
SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor> trMat(mat.rows(),mat.cols());
// pass 1: count the nnz per inner-vector
VectorXi wi(trMat.outerSize());
wi.setZero();
for(InputIterator it(begin); it!=end; ++it)
wi(IsRowMajor ? it->col() : it->row())++;
// pass 2: insert all the elements into trMat
trMat.reserve(wi);
for(InputIterator it(begin); it!=end; ++it)
trMat.insertBackUncompressed(it->row(),it->col()) = it->value();
// pass 3:
trMat.sumupDuplicates();
// pass 4: transposed copy -> implicit sorting
mat = trMat;
}
}
/** Fill the matrix \c *this with the list of \em triplets defined by the iterator range \a begin - \b.
*
* A \em triplet is a tuple (i,j,value) defining a non-zero element.
* The input list of triplets does not have to be sorted, and can contains duplicated elements.
* In any case, the result is a \b sorted and \b compressed sparse matrix where the duplicates have been summed up.
* This is a \em O(n) operation, with \em n the number of triplet elements.
* The initial contents of \c *this is destroyed.
* The matrix \c *this must be properly resized beforehand using the SparseMatrix(Index,Index) constructor,
* or the resize(Index,Index) method. The sizes are not extracted from the triplet list.
*
* The \a InputIterators value_type must provide the following interface:
* \code
* Scalar value() const; // the value
* Scalar row() const; // the row index i
* Scalar col() const; // the column index j
* \endcode
* See for instance the Eigen::Triplet template class.
*
* Here is a typical usage example:
* \code
typedef Triplet<double> T;
std::vector<T> tripletList;
triplets.reserve(estimation_of_entries);
for(...)
{
// ...
tripletList.push_back(T(i,j,v_ij));
}
SparseMatrixType m(rows,cols);
m.setFromTriplets(tripletList.begin(), tripletList.end());
// m is ready to go!
* \endcode
*
* \warning The list of triplets is read multiple times (at least twice). Therefore, it is not recommended to define
* an abstract iterator over a complex data-structure that would be expensive to evaluate. The triplets should rather
* be explicitely stored into a std::vector for instance.
*/
template<typename Scalar, int _Options, typename _Index>
template<typename InputIterators>
void SparseMatrix<Scalar,_Options,_Index>::setFromTriplets(const InputIterators& begin, const InputIterators& end)
{
internal::set_from_triplets(begin, end, *this);
}
/** \internal */
template<typename Scalar, int _Options, typename _Index>
void SparseMatrix<Scalar,_Options,_Index>::sumupDuplicates()
{
eigen_assert(!isCompressed());
// TODO, in practice we should be able to use m_innerNonZeros for that task
VectorXi wi(innerSize());
wi.fill(-1);
Index count = 0;
// for each inner-vector, wi[inner_index] will hold the position of first element into the index/value buffers
for(int j=0; j<outerSize(); ++j)
{
Index start = count;
Index oldEnd = m_outerIndex[j]+m_innerNonZeros[j];
for(Index k=m_outerIndex[j]; k<oldEnd; ++k)
{
Index i = m_data.index(k);
if(wi(i)>=start)
{
// we already meet this entry => accumulate it
m_data.value(wi(i)) += m_data.value(k);
}
else
{
m_data.value(count) = m_data.value(k);
m_data.index(count) = m_data.index(k);
wi(i) = count;
++count;
}
}
m_outerIndex[j] = start;
}
m_outerIndex[m_outerSize] = count;
// turn the matrix into compressed form
delete[] m_innerNonZeros;
m_innerNonZeros = 0;
m_data.resize(m_outerIndex[m_outerSize]);
}
} // end namespace Eigen
#endif // EIGEN_SPARSEMATRIX_H