Eigen  3.2.91
Eigen::SparseMatrix< _Scalar, _Options, _Index > Class Template Reference

Detailed Description

template<typename _Scalar, int _Options, typename _Index>
class Eigen::SparseMatrix< _Scalar, _Options, _Index >

A versatible sparse matrix representation.

This class implements a more versatile variants of the common 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 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 compressed format compatible with many library.

More details on this storage sceheme are given in the manual pages.

Template Parameters
_Scalarthe scalar type, i.e. the type of the coefficients
_OptionsUnion of bit flags controlling the storage scheme. Currently the only possibility is ColMajor or RowMajor. The default is 0 which means column-major.
_Indexthe type of the indices. It has to be a signed type (e.g., short, int, std::ptrdiff_t). Default is int.

This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_SPARSEMATRIX_PLUGIN.

Inherits Eigen::SparseCompressedBase< Derived >.

Public Types

enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime ,
  IsVectorAtCompileTime,
  Flags
}
 
typedef Eigen::Index Index
 The interface type of indices. More...
 
typedef Scalar value_type
 

Public Member Functions

template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp< CustomBinaryOp, const Derived, const OtherDerived > binaryExpr (const Eigen::SparseMatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
 
Block< Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
const Block< const Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows, BlockCols > block (Index startRow, Index startCol)
 
template<int BlockRows, int BlockCols>
const Block< const Derived, BlockRows, BlockCols > block (Index startRow, Index startCol) const
 
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows, BlockCols > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
template<int BlockRows, int BlockCols>
const Block< const Derived, BlockRows, BlockCols > block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 
Block< Derived > bottomLeftCorner (Index cRows, Index cCols)
 
const Block< const Derived > bottomLeftCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner ()
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomLeftCorner () const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomLeftCorner (Index cRows, Index cCols) const
 
Block< Derived > bottomRightCorner (Index cRows, Index cCols)
 
const Block< const Derived > bottomRightCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner ()
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomRightCorner () const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomRightCorner (Index cRows, Index cCols) const
 
RowsBlockXpr bottomRows (Index n)
 
ConstRowsBlockXpr bottomRows (Index n) const
 
template<int N>
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
 
template<typename NewType >
CastXpr< NewType >::Type cast () const
 
Scalar coeff (Index row, Index col) const
 
Scalar & coeffRef (Index row, Index col)
 
ColXpr col (Index i)
 
ConstColXpr col (Index i) const
 
Index cols () const
 
ConjugateReturnType conjugate () const
 
void conservativeResize (Index rows, Index cols)
 
const CwiseAbsReturnType cwiseAbs () const
 
const CwiseAbs2ReturnType cwiseAbs2 () const
 
template<typename OtherDerived >
const CwiseBinaryOp< std::equal_to< Scalar >, const Derived, const OtherDerived > cwiseEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
 
const CwiseInverseReturnType cwiseInverse () const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_max_op< Scalar >, const Derived, const OtherDerived > cwiseMax (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp< internal::scalar_max_op< Scalar >, const Derived, const ConstantReturnType > cwiseMax (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_min_op< Scalar >, const Derived, const OtherDerived > cwiseMin (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp< internal::scalar_min_op< Scalar >, const Derived, const ConstantReturnType > cwiseMin (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< std::not_equal_to< Scalar >, const Derived, const OtherDerived > cwiseNotEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_product_op< typename Derived::Scalar, typename OtherDerived::Scalar >, const Derived, const OtherDerived > cwiseProduct (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const Derived, const OtherDerived > cwiseQuotient (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseSqrtReturnType cwiseSqrt () const
 
Derived & derived ()
 
const Derived & derived () const
 
const ConstDiagonalReturnType diagonal () const
 
DiagonalReturnType diagonal ()
 
const internal::eval< Derived >::type eval () const
 
SegmentReturnType head (Index n)
 
ConstSegmentReturnType head (Index n) const
 
template<int N>
FixedSegmentReturnType< N >::Type head (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >::Type head (Index n=N) const
 
const ImagReturnType imag () const
 
NonConstImagReturnType imag ()
 
const StorageIndex * innerIndexPtr () const
 
StorageIndex * innerIndexPtr ()
 
const StorageIndex * innerNonZeroPtr () const
 
StorageIndex * innerNonZeroPtr ()
 
Index innerSize () const
 
InnerVectorReturnType innerVector (Index outer)
 
const ConstInnerVectorReturnType innerVector (Index outer) const
 
InnerVectorsReturnType innerVectors (Index outerStart, Index outerSize)
 
const ConstInnerVectorsReturnType innerVectors (Index outerStart, Index outerSize) const
 
Scalar & insert (Index row, Index col)
 
bool isCompressed () const
 
bool isVector () const
 
ColsBlockXpr leftCols (Index n)
 
ConstColsBlockXpr leftCols (Index n) const
 
template<int N>
NColsBlockXpr< N >::Type leftCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
 
void makeCompressed ()
 
ColsBlockXpr middleCols (Index startCol, Index numCols)
 
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
 
template<int N>
NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
 
RowsBlockXpr middleRows (Index startRow, Index n)
 
ConstRowsBlockXpr middleRows (Index startRow, Index n) const
 
template<int N>
NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
 
Index nonZeros () const
 
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
 
const ScalarComplexMultipleReturnType operator* (const std::complex< Scalar > &scalar) const
 
template<typename OtherDerived >
const Product< Derived, OtherDerived > operator* (const SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const Derived, const OtherDerived > operator+ (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_difference_op< Scalar >, const Derived, const OtherDerived > operator- (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const NegativeReturnType operator- () const
 
const ScalarQuotient1ReturnType operator/ (const Scalar &scalar) const
 
const StorageIndex * outerIndexPtr () const
 
StorageIndex * outerIndexPtr ()
 
Index outerSize () const
 
void prune (const Scalar &reference, const RealScalar &epsilon=NumTraits< RealScalar >::dummy_precision())
 
template<typename KeepFunc >
void prune (const KeepFunc &keep=KeepFunc())
 
const SparseView< Derived > pruned (const Scalar &reference=Scalar(0), const RealScalar &epsilon=NumTraits< Scalar >::dummy_precision()) const
 
RealReturnType real () const
 
NonConstRealReturnType real ()
 
void reserve (Index reserveSize)
 
template<class SizesType >
void reserve (const SizesType &reserveSizes)
 
void resize (Index rows, Index cols)
 
ColsBlockXpr rightCols (Index n)
 
ConstColsBlockXpr rightCols (Index n) const
 
template<int N>
NColsBlockXpr< N >::Type rightCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
 
RowXpr row (Index i)
 
ConstRowXpr row (Index i) const
 
Index rows () const
 
SegmentReturnType segment (Index start, Index n)
 
ConstSegmentReturnType segment (Index start, Index n) const
 
template<int N>
FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >::Type segment (Index start, Index n=N) const
 
template<typename InputIterators >
void setFromTriplets (const InputIterators &begin, const InputIterators &end)
 
void setIdentity ()
 
void setZero ()
 
Index size () const
 
 SparseMatrix ()
 
 SparseMatrix (Index rows, Index cols)
 
template<typename OtherDerived >
 SparseMatrix (const SparseMatrixBase< OtherDerived > &other)
 
template<typename OtherDerived , unsigned int UpLo>
 SparseMatrix (const SparseSelfAdjointView< OtherDerived, UpLo > &other)
 
 SparseMatrix (const SparseMatrix &other)
 
template<typename OtherDerived >
 SparseMatrix (const ReturnByValue< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 
template<typename OtherDerived >
 SparseMatrix (const DiagonalBase< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 
Scalar sum () const
 
void swap (SparseMatrix &other)
 
SegmentReturnType tail (Index n)
 
ConstSegmentReturnType tail (Index n) const
 
template<int N>
FixedSegmentReturnType< N >::Type tail (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >::Type tail (Index n=N) const
 
Block< Derived > topLeftCorner (Index cRows, Index cCols)
 
const Block< const Derived > topLeftCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner ()
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topLeftCorner () const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topLeftCorner (Index cRows, Index cCols) const
 
Block< Derived > topRightCorner (Index cRows, Index cCols)
 
const Block< const Derived > topRightCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner ()
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topRightCorner () const
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topRightCorner (Index cRows, Index cCols) const
 
RowsBlockXpr topRows (Index n)
 
ConstRowsBlockXpr topRows (Index n) const
 
template<int N>
NRowsBlockXpr< N >::Type topRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
 
SparseSymmetricPermutationProduct< Derived, Upper|Lower > twistedBy (const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &perm) const
 
template<typename CustomUnaryOp >
const CwiseUnaryOp< CustomUnaryOp, const Derived > unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise. More...
 
template<typename CustomViewOp >
const CwiseUnaryView< CustomViewOp, const Derived > unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
 
void uncompress ()
 
const Scalar * valuePtr () const
 
Scalar * valuePtr ()
 
 ~SparseMatrix ()
 

Member Typedef Documentation

template<typename Derived>
typedef Eigen::Index Eigen::EigenBase< Derived >::Index
inherited

The interface type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

Deprecated:
Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
See also
StorageIndex, Preprocessor directives.
template<typename Derived>
typedef Scalar Eigen::SparseMatrixBase< Derived >::value_type
inherited

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

It is an alias for the Scalar type

Member Enumeration Documentation

template<typename Derived>
anonymous enum
inherited
Enumerator
RowsAtCompileTime 

The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also
MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime
ColsAtCompileTime 

The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also
MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime
SizeAtCompileTime 

This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.

See also
RowsAtCompileTime, ColsAtCompileTime
IsVectorAtCompileTime 

This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row).

Flags 

This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags.

Constructor & Destructor Documentation

template<typename _Scalar, int _Options, typename _Index>
Eigen::SparseMatrix< _Scalar, _Options, _Index >::SparseMatrix ( )
inline

Default constructor yielding an empty 0 x 0 matrix

template<typename _Scalar, int _Options, typename _Index>
Eigen::SparseMatrix< _Scalar, _Options, _Index >::SparseMatrix ( Index  rows,
Index  cols 
)
inline

Constructs a rows x cols empty matrix

template<typename _Scalar, int _Options, typename _Index>
template<typename OtherDerived >
Eigen::SparseMatrix< _Scalar, _Options, _Index >::SparseMatrix ( const SparseMatrixBase< OtherDerived > &  other)
inline

Constructs a sparse matrix from the sparse expression other

template<typename _Scalar, int _Options, typename _Index>
template<typename OtherDerived , unsigned int UpLo>
Eigen::SparseMatrix< _Scalar, _Options, _Index >::SparseMatrix ( const SparseSelfAdjointView< OtherDerived, UpLo > &  other)
inline

Constructs a sparse matrix from the sparse selfadjoint view other

template<typename _Scalar, int _Options, typename _Index>
Eigen::SparseMatrix< _Scalar, _Options, _Index >::SparseMatrix ( const SparseMatrix< _Scalar, _Options, _Index > &  other)
inline

Copy constructor (it performs a deep copy)

template<typename _Scalar, int _Options, typename _Index>
Eigen::SparseMatrix< _Scalar, _Options, _Index >::~SparseMatrix ( )
inline

Destructor

Member Function Documentation

template<typename Derived>
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::binaryExpr ( const Eigen::SparseMatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const
inlineinherited
Returns
an expression of a custom coefficient-wise operator func of *this and other

The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)

Here is an example illustrating the use of custom functors:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template binary functor
template<typename Scalar> struct MakeComplexOp {
EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)
typedef complex<Scalar> result_type;
complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }
};
int main(int, char**)
{
cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;
return 0;
}

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)
See also
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
template<typename Derived>
Block<Derived> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inlineinherited
Returns
a dynamic-size expression of a block in *this.
Parameters
startRowthe first row in the block
startColthe first column in the block
blockRowsthe number of rows in the block
blockColsthe number of columns in the block

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
m.block(1, 1, 2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also
class Block, block(Index,Index)
template<typename Derived>
const Block<const Derived> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

This is the const version of block(Index,Index,Index,Index).

template<typename Derived>
template<int BlockRows, int BlockCols>
Block<Derived, BlockRows, BlockCols> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol 
)
inlineinherited
Returns
a fixed-size expression of a block in *this.

The template parameters BlockRows and BlockCols are the number of rows and columns in the block.

Parameters
startRowthe first row in the block
startColthe first column in the block

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
m.block<2,2>(1,1).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note
since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:
m.template block<3,3>(1,1);
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int BlockRows, int BlockCols>
const Block<const Derived, BlockRows, BlockCols> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol 
) const
inlineinherited

This is the const version of block<>(Index, Index).

template<typename Derived>
template<int BlockRows, int BlockCols>
Block<Derived, BlockRows, BlockCols> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inlineinherited
Returns
an expression of a block in *this.
Template Parameters
BlockRowsnumber of rows in block as specified at compile-time
BlockColsnumber of columns in block as specified at compile-time
Parameters
startRowthe first row in the block
startColthe first column in the block
blockRowsnumber of rows in block as specified at run-time
blockColsnumber of columns in block as specified at run-time

This function is mainly useful for blocks where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, blockRows should equal BlockRows unless BlockRows is Dynamic, and the same for the number of columns.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;
m.block<2, Dynamic>(1, 1, 2, 3).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;
m.block<2, Dynamic>(1, 1, 2, 3).setZero();
cout << "Now the matrix m is:" << endl << m << endl;
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int BlockRows, int BlockCols>
const Block<const Derived, BlockRows, BlockCols> Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

This is the const version of block<>(Index, Index, Index, Index).

template<typename Derived>
Block<Derived> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a bottom-left corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
cout << m.bottomLeftCorner(2, 2) << endl;
m.bottomLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
const Block<const Derived> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomLeftCorner(Index, Index).

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( )
inlineinherited
Returns
an expression of a fixed-size bottom-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
cout << m.bottomLeftCorner<2,2>() << endl;
m.bottomLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( ) const
inlineinherited

This is the const version of bottomLeftCorner<int, int>().

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a bottom-left corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,Dynamic>(2,2):" << endl;
cout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl;
m.bottomLeftCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,Dynamic>(2,2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also
class Block
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomLeftCorner<int, int>(Index, Index).

template<typename Derived>
Block<Derived> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a bottom-right corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner(2, 2):" << endl;
cout << m.bottomRightCorner(2, 2) << endl;
m.bottomRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
const Block<const Derived> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomRightCorner(Index, Index).

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( )
inlineinherited
Returns
an expression of a fixed-size bottom-right corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,2>():" << endl;
cout << m.bottomRightCorner<2,2>() << endl;
m.bottomRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( ) const
inlineinherited

This is the const version of bottomRightCorner<int, int>().

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a bottom-right corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,Dynamic>(2,2):" << endl;
cout << m.bottomRightCorner<2,Dynamic>(2,2) << endl;
m.bottomRightCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,Dynamic>(2,2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also
class Block
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomRightCorner<int, int>(Index, Index).

template<typename Derived>
RowsBlockXpr Eigen::SparseMatrixBase< Derived >::bottomRows ( Index  n)
inlineinherited
Returns
a block consisting of the bottom rows of *this.
Parameters
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows(2):" << endl;
cout << a.bottomRows(2) << endl;
a.bottomRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstRowsBlockXpr Eigen::SparseMatrixBase< Derived >::bottomRows ( Index  n) const
inlineinherited

This is the const version of bottomRows(Index).

template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::bottomRows ( Index  n = N)
inlineinherited
Returns
a block consisting of the bottom rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
nthe number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows<2>():" << endl;
cout << a.bottomRows<2>() << endl;
a.bottomRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::bottomRows ( Index  n = N) const
inlineinherited

This is the const version of bottomRows<int>().

template<typename Derived>
template<typename NewType >
CastXpr<NewType>::Type Eigen::SparseMatrixBase< Derived >::cast ( ) const
inlineinherited
Returns
an expression of *this with the Scalar type casted to NewScalar.

The template parameter NewScalar is the type we are casting the scalars to.

See also
class CwiseUnaryOp
template<typename _Scalar, int _Options, typename _Index>
Scalar Eigen::SparseMatrix< _Scalar, _Options, _Index >::coeff ( Index  row,
Index  col 
) const
inline
Returns
the value of the matrix at position i, j This function returns Scalar(0) if the element is an explicit zero
template<typename _Scalar, int _Options, typename _Index>
Scalar& Eigen::SparseMatrix< _Scalar, _Options, _Index >::coeffRef ( Index  row,
Index  col 
)
inline
Returns
a non-const reference to the value of the matrix at position i, 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.

template<typename Derived>
ColXpr Eigen::SparseMatrixBase< Derived >::col ( Index  i)
inlineinherited
Returns
an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

m.col(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 4 0
0 5 0
0 6 1
See also
row(), class Block

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::coeff(), Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::coeffRef(), and Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner().

template<typename Derived>
ConstColXpr Eigen::SparseMatrixBase< Derived >::col ( Index  i) const
inlineinherited

This is the const version of col().

template<typename Derived>
ConjugateReturnType Eigen::SparseMatrixBase< Derived >::conjugate ( ) const
inlineinherited
Returns
an expression of the complex conjugate of *this.
See also
adjoint()
template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::conservativeResize ( Index  rows,
Index  cols 
)
inline

Resizes the matrix to a rows x cols matrix leaving old values untouched.

See also
resizeNonZeros(Index), reserve(), setZero()
template<typename Derived>
const CwiseAbsReturnType Eigen::SparseMatrixBase< Derived >::cwiseAbs ( ) const
inlineinherited
Returns
an expression of the coefficient-wise absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,
-5, 1, 0;
cout << m.cwiseAbs() << endl;

Output:

2 4 6
5 1 0
See also
cwiseAbs2()
template<typename Derived>
const CwiseAbs2ReturnType Eigen::SparseMatrixBase< Derived >::cwiseAbs2 ( ) const
inlineinherited
Returns
an expression of the coefficient-wise squared absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,
-5, 1, 0;
cout << m.cwiseAbs2() << endl;

Output:

 4 16 36
25  1  0
See also
cwiseAbs()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseEqual ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise == operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

MatrixXi m(2,2);
m << 1, 0,
1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are equal: " << count << endl;

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3
See also
cwiseNotEqual(), isApprox(), isMuchSmallerThan()
template<typename Derived>
const CwiseScalarEqualReturnType Eigen::SparseMatrixBase< Derived >::cwiseEqual ( const Scalar &  s) const
inlineinherited
Returns
an expression of the coefficient-wise == operator of *this and a scalar s
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().
See also
cwiseEqual(const MatrixBase<OtherDerived> &) const
template<typename Derived>
const CwiseInverseReturnType Eigen::SparseMatrixBase< Derived >::cwiseInverse ( ) const
inlineinherited
Returns
an expression of the coefficient-wise inverse of *this.

Example:

MatrixXd m(2,3);
m << 2, 0.5, 1,
3, 0.25, 1;
cout << m.cwiseInverse() << endl;

Output:

  0.5     2     1
0.333     4     1
See also
cwiseProduct()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseMax ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise max of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMax(w) << endl;

Output:

4
3
4
See also
class CwiseBinaryOp, min()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType> Eigen::SparseMatrixBase< Derived >::cwiseMax ( const Scalar &  other) const
inlineinherited
Returns
an expression of the coefficient-wise max of *this and scalar other
See also
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseMin ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise min of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMin(w) << endl;

Output:

2
2
3
See also
class CwiseBinaryOp, max()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType> Eigen::SparseMatrixBase< Derived >::cwiseMin ( const Scalar &  other) const
inlineinherited
Returns
an expression of the coefficient-wise min of *this and scalar other
See also
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseNotEqual ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise != operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

MatrixXi m(2,2);
m << 1, 0,
1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are not equal: " << count << endl;

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1
See also
cwiseEqual(), isApprox(), isMuchSmallerThan()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_product_op<typename Derived ::Scalar, typename OtherDerived ::Scalar >, const Derived , const OtherDerived > Eigen::SparseMatrixBase< Derived >::cwiseProduct ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the Schur product (coefficient wise product) of *this and other

Example:

Matrix3i c = a.cwiseProduct(b);
cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25
See also
class CwiseBinaryOp, cwiseAbs2
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseQuotient ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise quotient of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseQuotient(w) << endl;

Output:

 0.5
 1.5
1.33
See also
class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
template<typename Derived>
const CwiseSqrtReturnType Eigen::SparseMatrixBase< Derived >::cwiseSqrt ( ) const
inlineinherited
Returns
an expression of the coefficient-wise square root of *this.

Example:

Vector3d v(1,2,4);
cout << v.cwiseSqrt() << endl;

Output:

   1
1.41
   2
See also
cwisePow(), cwiseSquare()
template<typename Derived>
Derived& Eigen::EigenBase< Derived >::derived ( )
inlineinherited
Returns
a reference to the derived object

Referenced by Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::analyzePattern(), Eigen::MatrixBase< Derived >::applyOnTheLeft(), Eigen::MatrixBase< Derived >::applyOnTheRight(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::applyTranspositionOnTheLeft(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::applyTranspositionOnTheRight(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::bottomRightCorner(), Eigen::EigenBase< BandMatrixWrapper< _CoefficientsType, _Rows, _Cols, _Supers, _Subs, _Options > >::cols(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::cols(), Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::compute(), Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >::copyCoeff(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::eval(), Eigen::IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::factorize(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::indices(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::inverse(), Eigen::RotationBase< Derived, 3 >::operator*(), Eigen::SparseSelfAdjointView< MatrixType, _Mode >::operator*(), Eigen::Translation< _Scalar, _Dim >::operator*(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::operator*(), Eigen::SparseMatrixBase< Derived >::operator*(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator*(), Eigen::MatrixBase< Derived >::operator*=(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::operator=(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::operator=(), Eigen::DenseBase< Derived >::operator=(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::operator=(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::PlainObjectBase(), Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::resizeLike(), Eigen::EigenBase< BandMatrixWrapper< _CoefficientsType, _Rows, _Cols, _Supers, _Subs, _Options > >::rows(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::rows(), Eigen::SparseSolverBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::solve(), Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::SparseMatrix(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::toDenseMatrix(), Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::Transform(), Eigen::PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex > >::transpose(), and Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::twistedBy().

template<typename Derived>
const Derived& Eigen::EigenBase< Derived >::derived ( ) const
inlineinherited
Returns
a const reference to the derived object
template<typename _Scalar, int _Options, typename _Index>
const ConstDiagonalReturnType Eigen::SparseMatrix< _Scalar, _Options, _Index >::diagonal ( ) const
inline
Returns
a const expression of the diagonal coefficients.
template<typename _Scalar, int _Options, typename _Index>
DiagonalReturnType Eigen::SparseMatrix< _Scalar, _Options, _Index >::diagonal ( )
inline
Returns
a read-write expression of the diagonal coefficients.
Warning
If the diagonal entries are written, then all diagonal entries must already exist, otherwise an assertion will be raised.
template<typename Derived>
const internal::eval<Derived>::type Eigen::SparseMatrixBase< Derived >::eval ( ) const
inlineinherited
Returns
the matrix or vector obtained by evaluating this expression.

Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.

template<typename Derived>
SegmentReturnType Eigen::SparseMatrixBase< Derived >::head ( Index  n)
inlineinherited
Returns
a dynamic-size expression of the first coefficients of *this.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Parameters
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head(2) << endl;
v.head(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also
class Block, block(Index,Index)
template<typename Derived>
ConstSegmentReturnType Eigen::SparseMatrixBase< Derived >::head ( Index  n) const
inlineinherited

This is the const version of head(Index).

template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::head ( Index  n = N)
inlineinherited
Returns
a fixed-size expression of the first coefficients of *this.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
nthe number of coefficients in the segment as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
v.head<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
See also
class Block
template<typename Derived>
template<int N>
ConstFixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::head ( Index  n = N) const
inlineinherited

This is the const version of head<int>().

template<typename Derived>
const ImagReturnType Eigen::SparseMatrixBase< Derived >::imag ( ) const
inlineinherited
Returns
an read-only expression of the imaginary part of *this.
See also
real()
template<typename Derived>
NonConstImagReturnType Eigen::SparseMatrixBase< Derived >::imag ( )
inlineinherited
Returns
a non const expression of the imaginary part of *this.
See also
real()
template<typename _Scalar, int _Options, typename _Index>
const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::innerIndexPtr ( ) const
inline
Returns
a const pointer to the array of inner indices. This function is aimed at interoperability with other libraries.
See also
valuePtr(), outerIndexPtr()
template<typename _Scalar, int _Options, typename _Index>
StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::innerIndexPtr ( )
inline
Returns
a non-const pointer to the array of inner indices. This function is aimed at interoperability with other libraries.
See also
valuePtr(), outerIndexPtr()
template<typename _Scalar, int _Options, typename _Index>
const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::innerNonZeroPtr ( ) const
inline
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
template<typename _Scalar, int _Options, typename _Index>
StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::innerNonZeroPtr ( )
inline
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
template<typename _Scalar, int _Options, typename _Index>
Index Eigen::SparseMatrix< _Scalar, _Options, _Index >::innerSize ( ) const
inline
Returns
the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major)
template<typename Derived >
SparseMatrixBase< Derived >::InnerVectorReturnType Eigen::SparseMatrixBase< Derived >::innerVector ( Index  outer)
inherited
Returns
the outer -th column (resp. row) of the matrix *this if *this is col-major (resp. row-major).
template<typename Derived >
const SparseMatrixBase< Derived >::ConstInnerVectorReturnType Eigen::SparseMatrixBase< Derived >::innerVector ( Index  outer) const
inherited
Returns
the outer -th column (resp. row) of the matrix *this if *this is col-major (resp. row-major). Read-only.
template<typename Derived >
SparseMatrixBase< Derived >::InnerVectorsReturnType Eigen::SparseMatrixBase< Derived >::innerVectors ( Index  outerStart,
Index  outerSize 
)
inherited
Returns
the outer -th column (resp. row) of the matrix *this if *this is col-major (resp. row-major).
template<typename Derived >
const SparseMatrixBase< Derived >::ConstInnerVectorsReturnType Eigen::SparseMatrixBase< Derived >::innerVectors ( Index  outerStart,
Index  outerSize 
) const
inherited
Returns
the outer -th column (resp. row) of the matrix *this if *this is col-major (resp. row-major). Read-only.
template<typename _Scalar , int _Options, typename _Index >
SparseMatrix< _Scalar, _Options, _Index >::Scalar & Eigen::SparseMatrix< _Scalar, _Options, _Index >::insert ( Index  row,
Index  col 
)
Returns
a reference to a novel non zero coefficient with coordinates row x col. The non zero coefficient must not already exist.

If the matrix *this is in compressed mode, then *this is turned into uncompressed mode while reserving room for 2 x this->innerSize() non zeros if reserve(Index) has not been called earlier. In this case, the insertion procedure is optimized for a sequential insertion mode where elements are assumed to be inserted by increasing outer-indices.

If that's not the case, then it is strongly recommended to either use a triplet-list to assemble the matrix, or to first call reserve(const SizesType &) to reserve the appropriate number of non-zero elements per inner vector.

Assuming memory has been appropriately reserved, 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.

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::coeffRef().

template<typename Derived>
bool Eigen::SparseCompressedBase< Derived >::isCompressed ( ) const
inlineinherited
Returns
whether *this is in compressed form.
template<typename Derived>
bool Eigen::SparseMatrixBase< Derived >::isVector ( ) const
inlineinherited
Returns
true if either the number of rows or the number of columns is equal to 1. In other words, this function returns
rows()==1 || cols()==1
See also
rows(), cols(), IsVectorAtCompileTime.
template<typename Derived>
ColsBlockXpr Eigen::SparseMatrixBase< Derived >::leftCols ( Index  n)
inlineinherited
Returns
a block consisting of the left columns of *this.
Parameters
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols(2):" << endl;
cout << a.leftCols(2) << endl;
a.leftCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstColsBlockXpr Eigen::SparseMatrixBase< Derived >::leftCols ( Index  n) const
inlineinherited

This is the const version of leftCols(Index).

template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::leftCols ( Index  n = N)
inlineinherited
Returns
a block consisting of the left columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
nthe number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols<2>():" << endl;
cout << a.leftCols<2>() << endl;
a.leftCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::leftCols ( Index  n = N) const
inlineinherited

This is the const version of leftCols<int>().

template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::makeCompressed ( )
inline

Turns the matrix into the compressed format.

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::prune().

template<typename Derived>
ColsBlockXpr Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
Index  numCols 
)
inlineinherited
Returns
a block consisting of a range of columns of *this.
Parameters
startColthe index of the first column in the block
numColsthe number of columns in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstColsBlockXpr Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
Index  numCols 
) const
inlineinherited

This is the const version of middleCols(Index,Index).

template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
Index  n = N 
)
inlineinherited
Returns
a block consisting of a range of columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
startColthe index of the first column in the block
nthe number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
Index  n = N 
) const
inlineinherited

This is the const version of middleCols<int>().

template<typename Derived>
RowsBlockXpr Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
Index  n 
)
inlineinherited
Returns
a block consisting of a range of rows of *this.
Parameters
startRowthe index of the first row in the block
nthe number of rows in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstRowsBlockXpr Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
Index  n 
) const
inlineinherited

This is the const version of middleRows(Index,Index).

template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
Index  n = N 
)
inlineinherited
Returns
a block consisting of a range of rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
startRowthe index of the first row in the block
nthe number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
Index  n = N 
) const
inlineinherited

This is the const version of middleRows<int>().

template<typename Derived>
Index Eigen::SparseCompressedBase< Derived >::nonZeros ( ) const
inlineinherited
Returns
the number of non zero coefficients
template<typename Derived>
const ScalarMultipleReturnType Eigen::SparseMatrixBase< Derived >::operator* ( const Scalar &  scalar) const
inlineinherited
Returns
an expression of *this scaled by the scalar factor scalar
template<typename Derived>
const ScalarComplexMultipleReturnType Eigen::SparseMatrixBase< Derived >::operator* ( const std::complex< Scalar > &  scalar) const
inlineinherited

Overloaded for efficient real matrix times complex scalar value

template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived > Eigen::SparseMatrixBase< Derived >::operator* ( const SparseMatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the product of two sparse matrices. By default a conservative product preserving the symbolic non zeros is performed. The automatic pruning of the small values can be achieved by calling the pruned() function in which case a totally different product algorithm is employed:
C = (A*B).pruned(); // supress numerical zeros (exact)
C = (A*B).pruned(ref);
C = (A*B).pruned(ref,epsilon);
where ref is a meaningful non zero reference value.

References Eigen::EigenBase< Derived >::derived().

template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator+ ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inherited
Returns
an expression of the sum of *this and other
Note
If you want to add a given scalar to all coefficients, see Cwise::operator+().
See also
class CwiseBinaryOp, operator+=()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator- ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inherited
Returns
an expression of the difference of *this and other
Note
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See also
class CwiseBinaryOp, operator-=()
template<typename Derived>
const NegativeReturnType Eigen::SparseMatrixBase< Derived >::operator- ( ) const
inlineinherited
Returns
an expression of the opposite of *this
template<typename Derived>
const ScalarQuotient1ReturnType Eigen::SparseMatrixBase< Derived >::operator/ ( const Scalar &  scalar) const
inlineinherited
Returns
an expression of *this divided by the scalar value scalar
template<typename _Scalar, int _Options, typename _Index>
const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::outerIndexPtr ( ) const
inline
Returns
a const pointer to the array of the starting positions of the inner vectors. This function is aimed at interoperability with other libraries.
See also
valuePtr(), innerIndexPtr()
template<typename _Scalar, int _Options, typename _Index>
StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _Index >::outerIndexPtr ( )
inline
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.
See also
valuePtr(), innerIndexPtr()
template<typename _Scalar, int _Options, typename _Index>
Index Eigen::SparseMatrix< _Scalar, _Options, _Index >::outerSize ( ) const
inline
Returns
the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major)

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::resize().

template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::prune ( const Scalar &  reference,
const RealScalar &  epsilon = NumTraits<RealScalar>::dummy_precision() 
)
inline

Suppresses all nonzeros which are much smaller than reference under the tolerence epsilon

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::prune().

template<typename _Scalar, int _Options, typename _Index>
template<typename KeepFunc >
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::prune ( const KeepFunc &  keep = KeepFunc())
inline

Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate keep. The functor type KeepFunc must implement the following function:

bool operator() (const Index& row, const Index& col, const Scalar& value) const;
See also
prune(Scalar,RealScalar)
template<typename Derived >
const SparseView< Derived > Eigen::SparseMatrixBase< Derived >::pruned ( const Scalar &  reference = Scalar(0),
const RealScalar &  epsilon = NumTraits<Scalar>::dummy_precision() 
) const
inlineinherited
Returns
an expression of *this with values smaller than reference * epsilon are removed.

This method is typically used in conjunction with the product of two sparse matrices to automatically prune the smallest values as follows:

C = (A*B).pruned(); // suppress numerical zeros (exact)
C = (A*B).pruned(ref);
C = (A*B).pruned(ref,epsilon);

where ref is a meaningful non zero reference value.

template<typename Derived>
RealReturnType Eigen::SparseMatrixBase< Derived >::real ( ) const
inlineinherited
Returns
a read-only expression of the real part of *this.
See also
imag()
template<typename Derived>
NonConstRealReturnType Eigen::SparseMatrixBase< Derived >::real ( )
inlineinherited
Returns
a non const expression of the real part of *this.
See also
imag()
template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::reserve ( Index  reserveSize)
inline

Preallocates reserveSize non zeros.

Precondition: the matrix must be in compressed mode.

template<typename _Scalar, int _Options, typename _Index>
template<class SizesType >
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::reserve ( const SizesType &  reserveSizes)
inline

Preallocates reserveSize[j] non zeros for each column (resp. row) j.

This function turns the matrix in non-compressed mode.

The type SizesType must expose the following interface:

typedef value_type;
const value_type& operator[](i) const;

for i in the [0,this->outerSize()[ range. Typical choices include std::vector<int>, Eigen::VectorXi, Eigen::VectorXi::Constant, etc.

template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::resize ( Index  rows,
Index  cols 
)
inline

Resizes the matrix to a rows x cols matrix and initializes it to zero.

This function does not free the currently allocated memory. To release as much as memory as possible, call

mat.data().squeeze();

after resizing it.

See also
resizeNonZeros(Index), reserve(), setZero()

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::conservativeResize(), and Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::SparseMatrix().

template<typename Derived>
ColsBlockXpr Eigen::SparseMatrixBase< Derived >::rightCols ( Index  n)
inlineinherited
Returns
a block consisting of the right columns of *this.
Parameters
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols(2):" << endl;
cout << a.rightCols(2) << endl;
a.rightCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstColsBlockXpr Eigen::SparseMatrixBase< Derived >::rightCols ( Index  n) const
inlineinherited

This is the const version of rightCols(Index).

template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::rightCols ( Index  n = N)
inlineinherited
Returns
a block consisting of the right columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
nthe number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols<2>():" << endl;
cout << a.rightCols<2>() << endl;
a.rightCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols<2>():
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::rightCols ( Index  n = N) const
inlineinherited

This is the const version of rightCols<int>().

template<typename Derived>
RowXpr Eigen::SparseMatrixBase< Derived >::row ( Index  i)
inlineinherited
Returns
an expression of the i-th row of *this. Note that the numbering starts at 0.

Example:

m.row(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 0 0
4 5 6
0 0 1
See also
col(), class Block

Referenced by Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::coeff(), Eigen::SparseMatrix< Scalar, RowMajor, StorageIndex >::coeffRef(), and Eigen::SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner().

template<typename Derived>
ConstRowXpr Eigen::SparseMatrixBase< Derived >::row ( Index  i) const
inlineinherited

This is the const version of row().

template<typename Derived>
SegmentReturnType Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
Index  n 
)
inlineinherited
Returns
a dynamic-size expression of a segment (i.e. a vector block) in *this.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Parameters
startthe first coefficient in the segment
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl;
v.segment(1, 2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment(1, 2):
-2  6
Now the vector v is:
7 0 0 6
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also
class Block, segment(Index)
template<typename Derived>
ConstSegmentReturnType Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
Index  n 
) const
inlineinherited

This is the const version of segment(Index,Index).

template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
Index  n = N 
)
inlineinherited
Returns
a fixed-size expression of a segment (i.e. a vector block) in *this

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
startthe index of the first element in the segment
nthe number of coefficients in the segment as specified at compile-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl;
v.segment<2>(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment<2>(1):
-2  6
Now the vector v is:
 7 -2  0  0
See also
class Block
template<typename Derived>
template<int N>
ConstFixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
Index  n = N 
) const
inlineinherited

This is the const version of segment<int>(Index).

template<typename Scalar , int _Options, typename _Index >
template<typename InputIterators >
void Eigen::SparseMatrix< Scalar, _Options, _Index >::setFromTriplets ( const InputIterators &  begin,
const InputIterators &  end 
)

Fill the matrix *this with the list of triplets defined by the iterator range begin - end.

A 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 sorted and compressed sparse matrix where the duplicates have been summed up. This is a O(n) operation, with n the number of triplet elements. The initial contents of *this is destroyed. The matrix *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 InputIterators value_type must provide the following interface:

Scalar value() const; // the value
Scalar row() const; // the row index i
Scalar col() const; // the column index j

See for instance the Eigen::Triplet template class.

Here is a typical usage example:

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!
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>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::setIdentity ( )
inline

Sets *this to the identity matrix

template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::setZero ( )
inline

Removes all non zeros but keep allocated memory

This function does not free the currently allocated memory. To release as much as memory as possible, call

mat.data().squeeze();

after resizing it.

See also
resize(Index,Index), data()
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::size ( ) const
inlineinherited
Returns
the number of coefficients, which is rows()*cols().
See also
rows(), cols().
template<typename _Scalar , int _Options, typename _Index >
internal::traits< SparseMatrix< _Scalar, _Options, _Index > >::Scalar Eigen::SparseMatrix< _Scalar, _Options, _Index >::sum ( ) const

Overloaded for performance

template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::swap ( SparseMatrix< _Scalar, _Options, _Index > &  other)
inline

Swaps the content of two sparse matrices of the same type. This is a fast operation that simply swaps the underlying pointers and parameters.

template<typename Derived>
SegmentReturnType Eigen::SparseMatrixBase< Derived >::tail ( Index  n)
inlineinherited
Returns
a dynamic-size expression of the last coefficients of *this.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Parameters
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail(2) << endl;
v.tail(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also
class Block, block(Index,Index)
template<typename Derived>
ConstSegmentReturnType Eigen::SparseMatrixBase< Derived >::tail ( Index  n) const
inlineinherited

This is the const version of tail(Index).

template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::tail ( Index  n = N)
inlineinherited
Returns
a fixed-size expression of the last coefficients of *this.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
nthe number of coefficients in the segment as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl;
v.tail<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
See also
class Block
template<typename Derived>
template<int N>
ConstFixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::tail ( Index  n = N) const
inlineinherited

This is the const version of tail<int>.

template<typename Derived>
Block<Derived> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a top-left corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner(2, 2):" << endl;
cout << m.topLeftCorner(2, 2) << endl;
m.topLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
const Block<const Derived> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topLeftCorner(Index, Index).

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( )
inlineinherited
Returns
an expression of a fixed-size top-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,2>():" << endl;
cout << m.topLeftCorner<2,2>() << endl;
m.topLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,2>():
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( ) const
inlineinherited

This is the const version of topLeftCorner<int, int>().

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a top-left corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,Dynamic>(2,2):" << endl;
cout << m.topLeftCorner<2,Dynamic>(2,2) << endl;
m.topLeftCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,Dynamic>(2,2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also
class Block
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topLeftCorner<int, int>(Index, Index).

template<typename Derived>
Block<Derived> Eigen::SparseMatrixBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a top-right corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner(2, 2):" << endl;
cout << m.topRightCorner(2, 2) << endl;
m.topRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
const Block<const Derived> Eigen::SparseMatrixBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topRightCorner(Index, Index).

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topRightCorner ( )
inlineinherited
Returns
an expression of a fixed-size top-right corner of *this.
Template Parameters
CRowsthe number of rows in the corner
CColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,2>():" << endl;
cout << m.topRightCorner<2,2>() << endl;
m.topRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,2>():
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block<int,int>(Index,Index)
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topRightCorner ( ) const
inlineinherited

This is the const version of topRightCorner<int, int>().

template<typename Derived>
template<int CRows, int CCols>
Block<Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a top-right corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,Dynamic>(2,2):" << endl;
cout << m.topRightCorner<2,Dynamic>(2,2) << endl;
m.topRightCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,Dynamic>(2,2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also
class Block
template<typename Derived>
template<int CRows, int CCols>
const Block<const Derived, CRows, CCols> Eigen::SparseMatrixBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topRightCorner<int, int>(Index, Index).

template<typename Derived>
RowsBlockXpr Eigen::SparseMatrixBase< Derived >::topRows ( Index  n)
inlineinherited
Returns
a block consisting of the top rows of *this.
Parameters
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows(2):" << endl;
cout << a.topRows(2) << endl;
a.topRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ConstRowsBlockXpr Eigen::SparseMatrixBase< Derived >::topRows ( Index  n) const
inlineinherited

This is the const version of topRows(Index).

template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::topRows ( Index  n = N)
inlineinherited
Returns
a block consisting of the top rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
nthe number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows<2>():" << endl;
cout << a.topRows<2>() << endl;
a.topRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
ConstNRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::topRows ( Index  n = N) const
inlineinherited

This is the const version of topRows<int>().

template<typename Derived>
SparseSymmetricPermutationProduct<Derived,Upper|Lower> Eigen::SparseMatrixBase< Derived >::twistedBy ( const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &  perm) const
inlineinherited
Returns
an expression of P H P^-1 where H is the matrix represented by *this
template<typename Derived>
template<typename CustomUnaryOp >
const CwiseUnaryOp<CustomUnaryOp, const Derived> Eigen::SparseMatrixBase< Derived >::unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp()) const
inlineinherited

Apply a unary operator coefficient-wise.

Parameters
[in]funcFunctor implementing the unary operator
Template Parameters
CustomUnaryOpType of func
Returns
An expression of a custom coefficient-wise unary operator func of *this

The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define function to be applied coefficient-wise
double ramp(double x)
{
if (x > 0)
return x;
else
return 0;
}
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
  0.68  0.823      0      0
     0      0  0.108 0.0268
 0.566      0      0  0.904
 0.597  0.536  0.258  0.832

Genuine functors allow for more possibilities, for instance it may contain a state.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also
class CwiseUnaryOp, class CwiseBinaryOp
template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, const Derived> Eigen::SparseMatrixBase< Derived >::unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inlineinherited
Returns
an expression of a custom coefficient-wise unary operator func of *this

The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also
class CwiseUnaryOp, class CwiseBinaryOp
template<typename _Scalar, int _Options, typename _Index>
void Eigen::SparseMatrix< _Scalar, _Options, _Index >::uncompress ( )
inline

Turns the matrix into the uncompressed mode

template<typename _Scalar, int _Options, typename _Index>
const Scalar* Eigen::SparseMatrix< _Scalar, _Options, _Index >::valuePtr ( ) const
inline
Returns
a const pointer to the array of values. This function is aimed at interoperability with other libraries.
See also
innerIndexPtr(), outerIndexPtr()
template<typename _Scalar, int _Options, typename _Index>
Scalar* Eigen::SparseMatrix< _Scalar, _Options, _Index >::valuePtr ( )
inline
Returns
a non-const pointer to the array of values. This function is aimed at interoperability with other libraries.
See also
innerIndexPtr(), outerIndexPtr()

The documentation for this class was generated from the following files: