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authorGravatar Gael Guennebaud <g.gael@free.fr>2009-05-20 00:05:28 +0200
committerGravatar Gael Guennebaud <g.gael@free.fr>2009-05-20 00:05:28 +0200
commit6ecd02d7ec85f07e02559cb311d4dd07e844a72d (patch)
tree3703e87d24166af9d2e74a8522c92c3393b6557b /Eigen/src
parent56aad5aafb84b87c9cdf8a237a3d7fdf632b2021 (diff)
parenta697cb409440c3d01eda44f84abe2f1d924270ce (diff)
merge
Diffstat (limited to 'Eigen/src')
-rw-r--r--Eigen/src/LU/PartialLU.h4
-rw-r--r--Eigen/src/Sparse/DynamicSparseMatrix.h30
-rw-r--r--Eigen/src/Sparse/SparseBlock.h27
-rw-r--r--Eigen/src/Sparse/SparseCwiseBinaryOp.h4
-rw-r--r--Eigen/src/Sparse/SparseMatrix.h32
-rw-r--r--Eigen/src/Sparse/SparseMatrixBase.h35
-rw-r--r--Eigen/src/Sparse/SparseRedux.h16
-rw-r--r--Eigen/src/Sparse/SparseTranspose.h10
-rw-r--r--Eigen/src/Sparse/SparseVector.h27
9 files changed, 125 insertions, 60 deletions
diff --git a/Eigen/src/LU/PartialLU.h b/Eigen/src/LU/PartialLU.h
index 7fdbeac38..3a6e9f286 100644
--- a/Eigen/src/LU/PartialLU.h
+++ b/Eigen/src/LU/PartialLU.h
@@ -225,8 +225,8 @@ void PartialLU<MatrixType>::solve(
/* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
* So we proceed as follows:
* Step 1: compute c = Pb.
- * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.
- * Step 3: replace c by the solution x to Ux = c. Check if a solution really exists.
+ * Step 2: replace c by the solution x to Lx = c.
+ * Step 3: replace c by the solution x to Ux = c.
*/
const int size = m_lu.rows();
diff --git a/Eigen/src/Sparse/DynamicSparseMatrix.h b/Eigen/src/Sparse/DynamicSparseMatrix.h
index 2927cd583..ec730dd3f 100644
--- a/Eigen/src/Sparse/DynamicSparseMatrix.h
+++ b/Eigen/src/Sparse/DynamicSparseMatrix.h
@@ -35,7 +35,7 @@
* random read/write accesses in log(rho*outer_size) where \c rho is the probability that a coefficient is
* nonzero and outer_size is the number of columns if the matrix is column-major and the number of rows
* otherwise.
- *
+ *
* Internally, the data are stored as a std::vector of compressed vector. The performances of random writes might
* decrease as the number of nonzeros per inner-vector increase. In practice, we observed very good performance
* till about 100 nonzeros/vector, and the performance remains relatively good till 500 nonzeros/vectors.
@@ -67,23 +67,23 @@ class DynamicSparseMatrix
// EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, +=)
// EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(DynamicSparseMatrix, -=)
typedef MappedSparseMatrix<Scalar,Flags> Map;
+ using Base::IsRowMajor;
protected:
- enum { IsRowMajor = Base::IsRowMajor };
typedef DynamicSparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;
int m_innerSize;
std::vector<CompressedStorage<Scalar> > m_data;
public:
-
+
inline int rows() const { return IsRowMajor ? outerSize() : m_innerSize; }
inline int cols() const { return IsRowMajor ? m_innerSize : outerSize(); }
inline int innerSize() const { return m_innerSize; }
inline int outerSize() const { return m_data.size(); }
inline int innerNonZeros(int j) const { return m_data[j].size(); }
-
+
std::vector<CompressedStorage<Scalar> >& _data() { return m_data; }
const std::vector<CompressedStorage<Scalar> >& _data() const { return m_data; }
@@ -132,7 +132,7 @@ class DynamicSparseMatrix
setZero();
reserve(reserveSize);
}
-
+
void reserve(int reserveSize = 1000)
{
if (outerSize()>0)
@@ -144,13 +144,13 @@ class DynamicSparseMatrix
}
}
}
-
+
inline void startVec(int /*outer*/) {}
-
+
inline Scalar& insertBack(int outer, int inner)
{
ei_assert(outer<int(m_data.size()) && inner<m_innerSize && "out of range");
- ei_assert(((m_data[outer].size()==0) || (m_data[outer].index(m_data[outer].size()-1)<inner))
+ ei_assert(((m_data[outer].size()==0) || (m_data[outer].index(m_data[outer].size()-1)<inner))
&& "wrong sorted insertion");
m_data[outer].append(0, inner);
return m_data[outer].value(m_data[outer].size()-1);
@@ -162,7 +162,7 @@ class DynamicSparseMatrix
* 2 - this the coefficient with greater inner coordinate for the given outer coordinate.
* In other words, assuming \c *this is column-major, then there must not exists any nonzero coefficient of coordinates
* \c i \c x \a col such that \c i >= \a row. Otherwise the matrix is invalid.
- *
+ *
* \see fillrand(), coeffRef()
*/
EIGEN_DEPRECATED Scalar& fill(int row, int col)
@@ -181,12 +181,12 @@ class DynamicSparseMatrix
{
return insert(row,col);
}
-
+
inline Scalar& insert(int row, int col)
{
const int outer = IsRowMajor ? row : col;
const int inner = IsRowMajor ? col : row;
-
+
int startId = 0;
int id = m_data[outer].size() - 1;
m_data[outer].resize(id+2,1);
@@ -205,9 +205,9 @@ class DynamicSparseMatrix
/** \deprecated use finalize()
* Does nothing. Provided for compatibility with SparseMatrix. */
EIGEN_DEPRECATED void endFill() {}
-
+
inline void finalize() {}
-
+
void prune(Scalar reference, RealScalar epsilon = precision<RealScalar>())
{
for (int j=0; j<outerSize(); ++j)
@@ -226,7 +226,7 @@ class DynamicSparseMatrix
m_data.resize(outerSize);
}
}
-
+
void resizeAndKeepData(int rows, int cols)
{
const int outerSize = IsRowMajor ? rows : cols;
@@ -309,7 +309,7 @@ class DynamicSparseMatrix<Scalar,_Flags>::InnerIterator : public SparseVector<Sc
InnerIterator(const DynamicSparseMatrix& mat, int outer)
: Base(mat.m_data[outer]), m_outer(outer)
{}
-
+
inline int row() const { return IsRowMajor ? m_outer : Base::index(); }
inline int col() const { return IsRowMajor ? Base::index() : m_outer; }
diff --git a/Eigen/src/Sparse/SparseBlock.h b/Eigen/src/Sparse/SparseBlock.h
index 72589d0c0..655ba6d93 100644
--- a/Eigen/src/Sparse/SparseBlock.h
+++ b/Eigen/src/Sparse/SparseBlock.h
@@ -43,16 +43,21 @@ template<typename MatrixType, int Size>
class SparseInnerVectorSet : ei_no_assignment_operator,
public SparseMatrixBase<SparseInnerVectorSet<MatrixType, Size> >
{
- enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
public:
+ enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
+
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseInnerVectorSet)
class InnerIterator: public MatrixType::InnerIterator
{
public:
inline InnerIterator(const SparseInnerVectorSet& xpr, int outer)
- : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer)
+ : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
{}
+ inline int row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline int col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ int m_outer;
};
inline SparseInnerVectorSet(const MatrixType& matrix, int outerStart, int outerSize)
@@ -100,16 +105,21 @@ class SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options>, Size>
: public SparseMatrixBase<SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options>, Size> >
{
typedef DynamicSparseMatrix<_Scalar, _Options> MatrixType;
- enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
public:
+ enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
+
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseInnerVectorSet)
class InnerIterator: public MatrixType::InnerIterator
{
public:
inline InnerIterator(const SparseInnerVectorSet& xpr, int outer)
- : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer)
+ : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
{}
+ inline int row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline int col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ int m_outer;
};
inline SparseInnerVectorSet(const MatrixType& matrix, int outerStart, int outerSize)
@@ -193,16 +203,21 @@ class SparseInnerVectorSet<SparseMatrix<_Scalar, _Options>, Size>
: public SparseMatrixBase<SparseInnerVectorSet<SparseMatrix<_Scalar, _Options>, Size> >
{
typedef SparseMatrix<_Scalar, _Options> MatrixType;
- enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
public:
+ enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
+
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseInnerVectorSet)
class InnerIterator: public MatrixType::InnerIterator
{
public:
inline InnerIterator(const SparseInnerVectorSet& xpr, int outer)
- : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer)
+ : MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer), m_outer(outer)
{}
+ inline int row() const { return IsRowMajor ? m_outer : this->index(); }
+ inline int col() const { return IsRowMajor ? this->index() : m_outer; }
+ protected:
+ int m_outer;
};
inline SparseInnerVectorSet(const MatrixType& matrix, int outerStart, int outerSize)
diff --git a/Eigen/src/Sparse/SparseCwiseBinaryOp.h b/Eigen/src/Sparse/SparseCwiseBinaryOp.h
index d19970efc..96fd1d36a 100644
--- a/Eigen/src/Sparse/SparseCwiseBinaryOp.h
+++ b/Eigen/src/Sparse/SparseCwiseBinaryOp.h
@@ -186,8 +186,8 @@ class ei_sparse_cwise_binary_op_inner_iterator_selector<BinaryOp, Lhs, Rhs, Deri
EIGEN_STRONG_INLINE Scalar value() const { return m_value; }
EIGEN_STRONG_INLINE int index() const { return m_id; }
- EIGEN_STRONG_INLINE int row() const { return m_lhsIter.row(); }
- EIGEN_STRONG_INLINE int col() const { return m_lhsIter.col(); }
+ EIGEN_STRONG_INLINE int row() const { return Lhs::IsRowMajor ? m_lhsIter.row() : index(); }
+ EIGEN_STRONG_INLINE int col() const { return Lhs::IsRowMajor ? index() : m_lhsIter.col(); }
EIGEN_STRONG_INLINE operator bool() const { return m_id>=0; }
diff --git a/Eigen/src/Sparse/SparseMatrix.h b/Eigen/src/Sparse/SparseMatrix.h
index 8bcf3c8b9..65cee69cf 100644
--- a/Eigen/src/Sparse/SparseMatrix.h
+++ b/Eigen/src/Sparse/SparseMatrix.h
@@ -25,17 +25,24 @@
#ifndef EIGEN_SPARSEMATRIX_H
#define EIGEN_SPARSEMATRIX_H
-/** \class SparseMatrix
+/** \ingroup Sparse_Module
*
- * \brief Sparse matrix
+ * \class SparseMatrix
+ *
+ * \brief The main sparse matrix class
+ *
+ * This class implements a sparse matrix using the very common compressed row/column storage
+ * scheme.
*
* \param _Scalar the scalar type, i.e. the type of the coefficients
+ * \param _Options Union of bit flags controlling the storage scheme. Currently the only possibility
+ * is RowMajor. The default is 0 which means column-major.
*
* See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
*
*/
-template<typename _Scalar, int _Flags>
-struct ei_traits<SparseMatrix<_Scalar, _Flags> >
+template<typename _Scalar, int _Options>
+struct ei_traits<SparseMatrix<_Scalar, _Options> >
{
typedef _Scalar Scalar;
enum {
@@ -43,17 +50,15 @@ struct ei_traits<SparseMatrix<_Scalar, _Flags> >
ColsAtCompileTime = Dynamic,
MaxRowsAtCompileTime = Dynamic,
MaxColsAtCompileTime = Dynamic,
- Flags = SparseBit | _Flags,
+ Flags = SparseBit | _Options,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
SupportedAccessPatterns = InnerRandomAccessPattern
};
};
-
-
-template<typename _Scalar, int _Flags>
+template<typename _Scalar, int _Options>
class SparseMatrix
- : public SparseMatrixBase<SparseMatrix<_Scalar, _Flags> >
+ : public SparseMatrixBase<SparseMatrix<_Scalar, _Options> >
{
public:
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseMatrix)
@@ -64,10 +69,10 @@ class SparseMatrix
// EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(SparseMatrix, /=)
typedef MappedSparseMatrix<Scalar,Flags> Map;
+ using Base::IsRowMajor;
protected:
- enum { IsRowMajor = Base::IsRowMajor };
typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0)> TransposedSparseMatrix;
int m_outerSize;
@@ -508,10 +513,13 @@ class SparseMatrix
{
delete[] m_outerIndex;
}
+
+ /** Overloaded for performance */
+ Scalar sum() const;
};
-template<typename Scalar, int _Flags>
-class SparseMatrix<Scalar,_Flags>::InnerIterator
+template<typename Scalar, int _Options>
+class SparseMatrix<Scalar,_Options>::InnerIterator
{
public:
InnerIterator(const SparseMatrix& mat, int outer)
diff --git a/Eigen/src/Sparse/SparseMatrixBase.h b/Eigen/src/Sparse/SparseMatrixBase.h
index 948424f90..34779d9e6 100644
--- a/Eigen/src/Sparse/SparseMatrixBase.h
+++ b/Eigen/src/Sparse/SparseMatrixBase.h
@@ -25,6 +25,17 @@
#ifndef EIGEN_SPARSEMATRIXBASE_H
#define EIGEN_SPARSEMATRIXBASE_H
+/** \ingroup Sparse_Module
+ *
+ * \class SparseMatrixBase
+ *
+ * \brief Base class of any sparse matrices or sparse expressions
+ *
+ * \param Derived
+ *
+ *
+ *
+ */
template<typename Derived> class SparseMatrixBase
{
public:
@@ -69,7 +80,7 @@ template<typename Derived> class SparseMatrixBase
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
*/
-
+
CoeffReadCost = ei_traits<Derived>::CoeffReadCost,
/**< This is a rough measure of how expensive it is to read one coefficient from
* this expression.
@@ -156,9 +167,9 @@ template<typename Derived> class SparseMatrixBase
ei_assert(( ((ei_traits<Derived>::SupportedAccessPatterns&OuterRandomAccessPattern)==OuterRandomAccessPattern) ||
(!((Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit)))) &&
"the transpose operation is supposed to be handled in SparseMatrix::operator=");
-
+
enum { Flip = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit) };
-
+
const int outerSize = other.outerSize();
//typedef typename ei_meta_if<transpose, LinkedVectorMatrix<Scalar,Flags&RowMajorBit>, Derived>::ret TempType;
// thanks to shallow copies, we always eval to a tempary
@@ -293,13 +304,13 @@ template<typename Derived> class SparseMatrixBase
template<typename OtherDerived>
const typename SparseProductReturnType<Derived,OtherDerived>::Type
operator*(const SparseMatrixBase<OtherDerived> &other) const;
-
+
// dense * sparse (return a dense object)
- template<typename OtherDerived> friend
+ template<typename OtherDerived> friend
const typename SparseProductReturnType<OtherDerived,Derived>::Type
operator*(const MatrixBase<OtherDerived>& lhs, const Derived& rhs)
{ return typename SparseProductReturnType<OtherDerived,Derived>::Type(lhs.derived(),rhs); }
-
+
template<typename OtherDerived>
const typename SparseProductReturnType<Derived,OtherDerived>::Type
operator*(const MatrixBase<OtherDerived> &other) const;
@@ -340,7 +351,7 @@ template<typename Derived> class SparseMatrixBase
const SparseInnerVectorSet<Derived,1> col(int j) const;
SparseInnerVectorSet<Derived,1> innerVector(int outer);
const SparseInnerVectorSet<Derived,1> innerVector(int outer) const;
-
+
// set of sub-vectors
SparseInnerVectorSet<Derived,Dynamic> subrows(int start, int size);
const SparseInnerVectorSet<Derived,Dynamic> subrows(int start, int size) const;
@@ -432,10 +443,16 @@ template<typename Derived> class SparseMatrixBase
for (int j=0; j<outerSize(); ++j)
{
for (typename Derived::InnerIterator i(derived(),j); i; ++i)
+ {
if(IsRowMajor)
- res.coeffRef(j,i.index()) = i.value();
+ std::cerr << i.row() << "," << i.col() << " == " << j << "," << i.index() << "\n";
else
- res.coeffRef(i.index(),j) = i.value();
+ std::cerr << i.row() << "," << i.col() << " == " << i.index() << "," << j << "\n";
+// if(IsRowMajor)
+ res.coeffRef(i.row(),i.col()) = i.value();
+// else
+// res.coeffRef(i.index(),j) = i.value();
+ }
}
return res;
}
diff --git a/Eigen/src/Sparse/SparseRedux.h b/Eigen/src/Sparse/SparseRedux.h
index f0d370548..e223c37ec 100644
--- a/Eigen/src/Sparse/SparseRedux.h
+++ b/Eigen/src/Sparse/SparseRedux.h
@@ -37,4 +37,20 @@ SparseMatrixBase<Derived>::sum() const
return res;
}
+template<typename _Scalar, int _Options>
+typename ei_traits<SparseMatrix<_Scalar,_Options> >::Scalar
+SparseMatrix<_Scalar,_Options>::sum() const
+{
+ ei_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ return Matrix<Scalar,1,Dynamic>::Map(m_data.value(0), m_data.size()).sum();
+}
+
+template<typename _Scalar, int _Options>
+typename ei_traits<SparseVector<_Scalar,_Options> >::Scalar
+SparseVector<_Scalar,_Options>::sum() const
+{
+ ei_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ return Matrix<Scalar,1,Dynamic>::Map(m_data.value(0), m_data.size()).sum();
+}
+
#endif // EIGEN_SPARSEREDUX_H
diff --git a/Eigen/src/Sparse/SparseTranspose.h b/Eigen/src/Sparse/SparseTranspose.h
index 89a14d707..879c377a9 100644
--- a/Eigen/src/Sparse/SparseTranspose.h
+++ b/Eigen/src/Sparse/SparseTranspose.h
@@ -66,20 +66,26 @@ template<typename MatrixType> class SparseTranspose
template<typename MatrixType> class SparseTranspose<MatrixType>::InnerIterator : public MatrixType::InnerIterator
{
+ typedef typename MatrixType::InnerIterator Base;
public:
EIGEN_STRONG_INLINE InnerIterator(const SparseTranspose& trans, int outer)
- : MatrixType::InnerIterator(trans.m_matrix, outer)
+ : Base(trans.m_matrix, outer)
{}
+ inline int row() const { return Base::col(); }
+ inline int col() const { return Base::row(); }
};
template<typename MatrixType> class SparseTranspose<MatrixType>::ReverseInnerIterator : public MatrixType::ReverseInnerIterator
{
+ typedef typename MatrixType::ReverseInnerIterator Base;
public:
EIGEN_STRONG_INLINE ReverseInnerIterator(const SparseTranspose& xpr, int outer)
- : MatrixType::ReverseInnerIterator(xpr.m_matrix, outer)
+ : Base(xpr.m_matrix, outer)
{}
+ inline int row() const { return Base::col(); }
+ inline int col() const { return Base::row(); }
};
#endif // EIGEN_SPARSETRANSPOSE_H
diff --git a/Eigen/src/Sparse/SparseVector.h b/Eigen/src/Sparse/SparseVector.h
index ac815e698..05356942b 100644
--- a/Eigen/src/Sparse/SparseVector.h
+++ b/Eigen/src/Sparse/SparseVector.h
@@ -34,26 +34,26 @@
* See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
*
*/
-template<typename _Scalar, int _Flags>
-struct ei_traits<SparseVector<_Scalar, _Flags> >
+template<typename _Scalar, int _Options>
+struct ei_traits<SparseVector<_Scalar, _Options> >
{
typedef _Scalar Scalar;
enum {
- IsColVector = _Flags & RowMajorBit ? 0 : 1,
+ IsColVector = _Options & RowMajorBit ? 0 : 1,
RowsAtCompileTime = IsColVector ? Dynamic : 1,
ColsAtCompileTime = IsColVector ? 1 : Dynamic,
MaxRowsAtCompileTime = RowsAtCompileTime,
MaxColsAtCompileTime = ColsAtCompileTime,
- Flags = SparseBit | _Flags,
+ Flags = SparseBit | _Options,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
SupportedAccessPatterns = InnerRandomAccessPattern
};
};
-template<typename _Scalar, int _Flags>
+template<typename _Scalar, int _Options>
class SparseVector
- : public SparseMatrixBase<SparseVector<_Scalar, _Flags> >
+ : public SparseMatrixBase<SparseVector<_Scalar, _Options> >
{
public:
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseVector)
@@ -124,7 +124,7 @@ class SparseVector
{
ei_assert(outer==0);
}
-
+
inline Scalar& insertBack(int outer, int inner)
{
ei_assert(outer==0);
@@ -183,7 +183,7 @@ class SparseVector
m_data.append(0, i);
return m_data.value(m_data.size()-1);
}
-
+
/** \deprecated use insert(int,int) */
EIGEN_DEPRECATED Scalar& fillrand(int r, int c)
{
@@ -196,11 +196,11 @@ class SparseVector
{
return insert(i);
}
-
+
/** \deprecated use finalize() */
EIGEN_DEPRECATED void endFill() {}
inline void finalize() {}
-
+
void prune(Scalar reference, RealScalar epsilon = precision<RealScalar>())
{
m_data.prune(reference,epsilon);
@@ -357,10 +357,13 @@ class SparseVector
/** Destructor */
inline ~SparseVector() {}
+
+ /** Overloaded for performance */
+ Scalar sum() const;
};
-template<typename Scalar, int _Flags>
-class SparseVector<Scalar,_Flags>::InnerIterator
+template<typename Scalar, int _Options>
+class SparseVector<Scalar,_Options>::InnerIterator
{
public:
InnerIterator(const SparseVector& vec, int outer=0)