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Eigen::SparseMatrixBase< Derived > Class Template Reference

Detailed Description

template<typename Derived>
class Eigen::SparseMatrixBase< Derived >

Base class of any sparse matrices or sparse expressions.

Template Parameters
Derivedis the derived type, e.g. a sparse matrix type, or an expression, etc.

This class can be extended with the help of the plugin mechanism described on the page Extending MatrixBase (and other classes) by defining the preprocessor symbol EIGEN_SPARSEMATRIXBASE_PLUGIN.

+ Inheritance diagram for Eigen::SparseMatrixBase< Derived >:

Public Types

enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime ,
  IsVectorAtCompileTime,
  Flags
}
 
typedef internal::traits
< Derived >::StorageIndex 
StorageIndex
 
typedef Scalar value_type
 
- Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
 The interface type of indices. More...
 

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
 
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type block (Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols)
 
template<typename NRowsType , typename NColsType >
const ConstFixedBlockXpr
<...,...>::Type 
block (Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols) const
 This is the const version of block(Index,Index,NRowsType,NColsType)
 
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol)
 
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol) const
 This is the const version of block<>(Index, Index). */.
 
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 This is the const version of block<>(Index, Index, Index, Index).
 
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type bottomLeftCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType , typename NColsType >
ConstFixedBlockXpr<...,...>::Type bottomLeftCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of bottomLeftCorner(NRowsType, NColsType).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner () const
 This is the const version of bottomLeftCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner (Index cRows, Index cCols) const
 This is the const version of bottomLeftCorner<int, int>(Index, Index).
 
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type bottomRightCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType , typename NColsType >
const ConstFixedBlockXpr
<...,...>::Type 
bottomRightCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of bottomRightCorner(NRowsType, NColsType).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner () const
 This is the const version of bottomRightCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner (Index cRows, Index cCols) const
 This is the const version of bottomRightCorner<int, int>(Index, Index).
 
template<typename NRowsType >
NRowsBlockXpr<...>::Type bottomRows (NRowsType n)
 
template<typename NRowsType >
const ConstNRowsBlockXpr<...>::Type bottomRows (NRowsType n) const
 This is the const version of bottomRows(NRowsType).
 
template<int N>
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
 This is the const version of bottomRows<int>().
 
template<typename NewType >
CastXpr< NewType >::Type cast () const
 
ColXpr col (Index i)
 
ConstColXpr col (Index i) const
 This is the const version of col().
 
Index cols () const
 
ConjugateReturnType conjugate () const
 
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, Scalar >, const
Derived, const OtherDerived > 
cwiseMax (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar, Scalar >, const
Derived, const
ConstantReturnType > 
cwiseMax (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, Scalar >, const
Derived, const OtherDerived > 
cwiseMin (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, 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
< Derived::Scalar,
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 CwiseSignReturnType cwiseSign () const
 
const CwiseSqrtReturnType cwiseSqrt () const
 
const internal::eval< Derived >
::type 
eval () const
 
template<typename NType >
FixedSegmentReturnType<...>::Type head (NType n)
 
template<typename NType >
const
ConstFixedSegmentReturnType
<...>::Type 
head (NType n) const
 This is the const version of head(NType).
 
template<int N>
FixedSegmentReturnType< N >::Type head (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
 This is the const version of head<int>().
 
const ImagReturnType imag () const
 
NonConstImagReturnType imag ()
 
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
 
bool isVector () const
 
template<typename NColsType >
NColsBlockXpr<...>::Type leftCols (NColsType n)
 
template<typename NColsType >
const ConstNColsBlockXpr<...>::Type leftCols (NColsType n) const
 This is the const version of leftCols(NColsType).
 
template<int N>
NColsBlockXpr< N >::Type leftCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
 This is the const version of leftCols<int>().
 
template<typename NColsType >
NColsBlockXpr<...>::Type middleCols (Index startCol, NColsType numCols)
 
template<typename NColsType >
const ConstNColsBlockXpr<...>::Type middleCols (Index startCol, NColsType numCols) const
 This is the const version of middleCols(Index,NColsType).
 
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
 This is the const version of middleCols<int>().
 
template<typename NRowsType >
NRowsBlockXpr<...>::Type middleRows (Index startRow, NRowsType n)
 
template<typename NRowsType >
const ConstNRowsBlockXpr<...>::Type middleRows (Index startRow, NRowsType n) const
 This is the const version of middleRows(Index,NRowsType).
 
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
 This is the const version of middleRows<int>().
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_and_op,
const Derived, const
OtherDerived > 
operator&& (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< Scalar, T >, Derived,
Constant< T > > 
operator* (const T &scalar) const
 
template<typename OtherDerived >
const Product< Derived,
OtherDerived, AliasFreeProduct > 
operator* (const SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< sum
< Scalar >, const Derived,
const OtherDerived > 
operator+ (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< difference< Scalar >, const
Derived, const OtherDerived > 
operator- (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
const NegativeReturnType operator- () const
 
template<typename T >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar, T >, Derived,
Constant< T > > 
operator/ (const T &scalar) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_or_op,
const Derived, const
OtherDerived > 
operator|| (const Eigen::SparseMatrixBase< OtherDerived > &other) const
 
Index outerSize () const
 
const SparseView< Derived > pruned (const Scalar &reference=Scalar(0), const RealScalar &epsilon=NumTraits< Scalar >::dummy_precision()) const
 
RealReturnType real () const
 
NonConstRealReturnType real ()
 
template<typename NColsType >
NColsBlockXpr<...>::Type rightCols (NColsType n)
 
template<typename NColsType >
const ConstNColsBlockXpr<...>::Type rightCols (NColsType n) const
 This is the const version of rightCols(NColsType).
 
template<int N>
NColsBlockXpr< N >::Type rightCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
 This is the const version of rightCols<int>().
 
RowXpr row (Index i)
 
ConstRowXpr row (Index i) const
 This is the const version of row(). */.
 
Index rows () const
 
template<typename NType >
FixedSegmentReturnType<...>::Type segment (Index start, NType n)
 
template<typename NType >
const
ConstFixedSegmentReturnType
<...>::Type 
segment (Index start, NType n) const
 This is the const version of segment(Index,NType).
 
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
 This is the const version of segment<int>(Index).
 
Index size () const
 
template<typename NType >
FixedSegmentReturnType<...>::Type tail (NType n)
 
template<typename NType >
const
ConstFixedSegmentReturnType
<...>::Type 
tail (NType n) const
 This is the const version of tail(Index).
 
template<int N>
FixedSegmentReturnType< N >::Type tail (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
 This is the const version of tail<int>.
 
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type topLeftCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType , typename NColsType >
const ConstFixedBlockXpr
<...,...>::Type 
topLeftCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of topLeftCorner(Index, Index).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner () const
 This is the const version of topLeftCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner (Index cRows, Index cCols) const
 This is the const version of topLeftCorner<int, int>(Index, Index).
 
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type topRightCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType , typename NColsType >
const ConstFixedBlockXpr
<...,...>::Type 
topRightCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of topRightCorner(NRowsType, NColsType).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner () const
 This is the const version of topRightCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner (Index cRows, Index cCols) const
 This is the const version of topRightCorner<int, int>(Index, Index).
 
template<typename NRowsType >
NRowsBlockXpr<...>::Type topRows (NRowsType n)
 
template<typename NRowsType >
const ConstNRowsBlockXpr<...>::Type topRows (NRowsType n) const
 This is the const version of topRows(NRowsType).
 
template<int N>
NRowsBlockXpr< N >::Type topRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
 This is the const version of topRows<int>().
 
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
 
- Public Member Functions inherited from Eigen::EigenBase< Derived >
Index cols () const
 
Derived & derived ()
 
const Derived & derived () const
 
Index rows () const
 
Index size () const
 

Friends

template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< T, Scalar >, Constant< T >
, Derived > 
operator* (const T &scalar, const StorageBaseType &expr)
 

Member Typedef Documentation

template<typename Derived>
typedef internal::traits<Derived>::StorageIndex Eigen::SparseMatrixBase< Derived >::StorageIndex

The integer type used to store indices within a SparseMatrix. For a SparseMatrix<Scalar,Options,IndexType> it an alias of the third template parameter IndexType.

template<typename Derived>
typedef Scalar Eigen::SparseMatrixBase< Derived >::value_type

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
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.

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
inline
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>
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
NRowsType  blockRows,
NColsType  blockCols 
)
inline
Returns
an expression of a block in *this with either dynamic or fixed sizes.
Parameters
startRowthe first row in the block
startColthe first column in the block
blockRowsnumber of rows in the block, specified at either run-time or compile-time
blockColsnumber of columns in the block, specified at either run-time or compile-time
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.
NColsTypethe type of the value handling the number of columns in the block, typically Index.

Example using runtime (aka dynamic) sizes:

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

New in Eigen 3.4.:

The number of rows blockRows and columns blockCols can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. In the later case, n plays the role of a runtime fallback value in case N equals Eigen::Dynamic. Here is an example with a fixed number of rows NRows and dynamic number of columns cols:

* mat.block(i,j,fix<NRows>,cols)
*

This function thus fully covers the features offered by the following overloads block<NRows,NCols>(Index, Index), and block<NRows,NCols>(Index, Index, Index, Index) that are thus obsolete. Indeed, this generic version avoids redundancy, it preserves the argument order, and prevents the need to rely on the template keyword in templated code.

but with less redundancy and more consistency as it does not modify the argument order and seamlessly enable hybrid fixed/dynamic sizes.

Note
Even in the case that 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.
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block, fix, fix<N>(int)
template<typename Derived>
template<int NRows, int NCols>
FixedBlockXpr<NRows,NCols>::Type Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol 
)
inline
Returns
a fixed-size expression of a block of *this.

The template parameters NRows and NCols 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
The usage of of this overload is discouraged from Eigen 3.4, better used the generic block(Index,Index,NRowsType,NColsType), here is the one-to-one equivalence:
* mat.template block<NRows,NCols>(i,j) <--> mat.block(i,j,fix<NRows>,fix<NCols>)
*
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);
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int NRows, int NCols>
FixedBlockXpr<NRows,NCols>::Type Eigen::SparseMatrixBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inline
Returns
an expression of a block of *this.
Template Parameters
NRowsnumber of rows in block as specified at compile-time
NColsnumber 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 NRows unless NRows 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;
Note
The usage of of this overload is discouraged from Eigen 3.4, better used the generic block(Index,Index,NRowsType,NColsType), here is the one-to-one complete equivalence:
* mat.template block<NRows,NCols>(i,j,rows,cols) <--> mat.block(i,j,fix<NRows>(rows),fix<NCols>(cols))
*
If we known that, e.g., NRows==Dynamic and NCols!=Dynamic, then the equivalence becomes:
* mat.template block<Dynamic,NCols>(i,j,rows,NCols) <--> mat.block(i,j,rows,fix<NCols>)
*
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( NRowsType  cRows,
NColsType  cCols 
)
inline
Returns
an expression of a bottom-left corner of *this with either dynamic or fixed sizes.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of rows blockRows and columns blockCols can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( )
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block
template<typename Derived>
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( NRowsType  cRows,
NColsType  cCols 
)
inline
Returns
an expression of a bottom-right corner of *this with either dynamic or fixed sizes.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of rows blockRows and columns blockCols can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( )
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
)
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block
template<typename Derived>
template<typename NRowsType >
NRowsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::bottomRows ( NRowsType  n)
inline
Returns
a block consisting of the bottom rows of *this.
Parameters
nthe number of rows in the block
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.

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

The number of rows n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::bottomRows ( Index  n = N)
inline
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
Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<typename NewType >
CastXpr<NewType>::Type Eigen::SparseMatrixBase< Derived >::cast ( ) const
inline
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.

This method does not change the sparsity of *this: the conversion function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
class CwiseUnaryOp
template<typename Derived>
ColXpr Eigen::SparseMatrixBase< Derived >::col ( Index  i)
inline
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
Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
row(), class Block
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::cols ( void  ) const
inline
Returns
the number of columns.
See Also
rows()
template<typename Derived>
ConjugateReturnType Eigen::SparseMatrixBase< Derived >::conjugate ( ) const
inline
Returns
an expression of the complex conjugate of *this.

This method does not change the sparsity of *this: the complex conjugate is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
Math functions, MatrixBase::adjoint()
template<typename Derived>
const CwiseAbsReturnType Eigen::SparseMatrixBase< Derived >::cwiseAbs ( ) const
inline
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

This method does not change the sparsity of *this: the absolute value is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
cwiseAbs2()
template<typename Derived>
const CwiseAbs2ReturnType Eigen::SparseMatrixBase< Derived >::cwiseAbs2 ( ) const
inline
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

This method does not change the sparsity of *this: the squared absolute value is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
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
inline
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
inline
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
inline
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

This method does not change the sparsity of *this: the inverse is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
cwiseProduct()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseMax ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inline
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,Scalar>, const Derived, const ConstantReturnType> Eigen::SparseMatrixBase< Derived >::cwiseMax ( const Scalar &  other) const
inline
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,Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::cwiseMin ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inline
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,Scalar>, const Derived, const ConstantReturnType> Eigen::SparseMatrixBase< Derived >::cwiseMin ( const Scalar &  other) const
inline
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
inline
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 < Derived ::Scalar, OtherDerived ::Scalar>, const Derived , const OtherDerived > Eigen::SparseMatrixBase< Derived >::cwiseProduct ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inline
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
inline
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 CwiseSignReturnType Eigen::SparseMatrixBase< Derived >::cwiseSign ( ) const
inline
Returns
an expression of the coefficient-wise signum of *this.

Example:

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

Output:

 1 -1  1
-1  1  0

This method does not change the sparsity of *this: the sign function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
template<typename Derived>
const CwiseSqrtReturnType Eigen::SparseMatrixBase< Derived >::cwiseSqrt ( ) const
inline
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

This method does not change the sparsity of *this: the square-root is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
cwisePow(), cwiseSquare()
template<typename Derived>
const internal::eval<Derived>::type Eigen::SparseMatrixBase< Derived >::eval ( ) const
inline
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>
template<typename NType >
FixedSegmentReturnType<...>::Type Eigen::SparseMatrixBase< Derived >::head ( NType  n)
inline
Returns
an expression of the first coefficients of *this with either dynamic or fixed sizes.

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
Template Parameters
NTypethe type of the value handling the number of coefficients in the segment, typically Index.

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

The number of coefficients n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Note
Even in the case that 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>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::head ( Index  n = N)
inline
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
head(NType), class Block
template<typename Derived>
const ImagReturnType Eigen::SparseMatrixBase< Derived >::imag ( ) const
inline
Returns
an read-only expression of the imaginary part of *this.

This method does not change the sparsity of *this: the imaginary part function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
real()
template<typename Derived>
NonConstImagReturnType Eigen::SparseMatrixBase< Derived >::imag ( )
inline
Returns
a non const expression of the imaginary part of *this.

This method does not change the sparsity of *this: the imaginary part function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
real()
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::innerSize ( ) const
inline
Returns
the size of the inner dimension according to the storage order, i.e., the number of rows for a columns major matrix, and the number of cols otherwise
template<typename Derived >
SparseMatrixBase< Derived >::InnerVectorReturnType Eigen::SparseMatrixBase< Derived >::innerVector ( Index  outer)
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
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 
)
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
Returns
the outer -th column (resp. row) of the matrix *this if *this is col-major (resp. row-major). Read-only.
template<typename Derived>
bool Eigen::SparseMatrixBase< Derived >::isVector ( ) const
inline
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>
template<typename NColsType >
NColsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::leftCols ( NColsType  n)
inline
Returns
a block consisting of the left columns of *this.
Parameters
nthe number of columns in the block
Template Parameters
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of columns n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::leftCols ( Index  n = N)
inline
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
Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<typename NColsType >
NColsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
NColsType  numCols 
)
inline
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
Template Parameters
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of columns n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleCols ( Index  startCol,
Index  n = N 
)
inline
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
Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<typename NRowsType >
NRowsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
NRowsType  n 
)
inline
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
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.

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

The number of rows n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::middleRows ( Index  startRow,
Index  n = N 
)
inline
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
Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator&& ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise boolean and operator of *this and other
Warning
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) && (v<0)) << endl;

Output:

0
0
0
See Also
operator||(), select()
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > Eigen::SparseMatrixBase< Derived >::operator* ( const T &  scalar) const
Returns
an expression of *this scaled by the scalar factor scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived, AliasFreeProduct > Eigen::SparseMatrixBase< Derived >::operator* ( const SparseMatrixBase< OtherDerived > &  other) const
inline
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.
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< sum <Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator+ ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
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< difference <Scalar>, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator- ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
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
inline
Returns
an expression of the opposite of *this

This method does not change the sparsity of *this: the opposite is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > Eigen::SparseMatrixBase< Derived >::operator/ ( const T &  scalar) const
Returns
an expression of *this divided by the scalar value scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived> Eigen::SparseMatrixBase< Derived >::operator|| ( const Eigen::SparseMatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise boolean or operator of *this and other
Warning
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) || (v<0)) << endl;

Output:

1
0
1
See Also
operator&&(), select()
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::outerSize ( ) const
inline
Returns
the size of the storage major dimension, i.e., the number of columns for a columns major matrix, and the number of rows otherwise
template<typename Derived >
const SparseView< Derived > Eigen::SparseMatrixBase< Derived >::pruned ( const Scalar &  reference = Scalar(0),
const RealScalar &  epsilon = NumTraits<Scalar>::dummy_precision() 
) const
inline
Returns
an expression of *this with values smaller than reference * epsilon 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
inline
Returns
a read-only expression of the real part of *this.

This method does not change the sparsity of *this: the real part function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
imag()
template<typename Derived>
NonConstRealReturnType Eigen::SparseMatrixBase< Derived >::real ( )
inline
Returns
a non const expression of the real part of *this.

This method does not change the sparsity of *this: the real part function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
imag()
template<typename Derived>
template<typename NColsType >
NColsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::rightCols ( NColsType  n)
inline
Returns
a block consisting of the right columns of *this.
Parameters
nthe number of columns in the block
Template Parameters
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of columns n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::rightCols ( Index  n = N)
inline
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
Warning
This method returns a read-write expression for column-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
RowXpr Eigen::SparseMatrixBase< Derived >::row ( Index  i)
inline
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
Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
col(), class Block
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::rows ( void  ) const
inline
Returns
the number of rows.
See Also
cols()
template<typename Derived>
template<typename NType >
FixedSegmentReturnType<...>::Type Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
NType  n 
)
inline
Returns
an expression of a segment (i.e. a vector block) in *this with either dynamic or fixed sizes.

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
Template Parameters
NTypethe type of the value handling the number of coefficients in the segment, typically Index.

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

The number of coefficients n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Note
Even in the case that 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
block(Index,Index,NRowsType,NColsType), fix<N>, fix<N>(int), class Block
template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::segment ( Index  start,
Index  n = N 
)
inline
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
segment(Index,NType), class Block
template<typename Derived>
Index Eigen::SparseMatrixBase< Derived >::size ( ) const
inline
Returns
the number of coefficients, which is rows()*cols().
See Also
rows(), cols().
template<typename Derived>
template<typename NType >
FixedSegmentReturnType<...>::Type Eigen::SparseMatrixBase< Derived >::tail ( NType  n)
inline
Returns
an expression of a last coefficients of *this with either dynamic or fixed sizes.

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
Template Parameters
NTypethe type of the value handling the number of coefficients in the segment, typically Index.

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

The number of coefficients n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Note
Even in the case that 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>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::SparseMatrixBase< Derived >::tail ( Index  n = N)
inline
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
tail(NType), class Block
template<typename Derived>
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type Eigen::SparseMatrixBase< Derived >::topLeftCorner ( NRowsType  cRows,
NColsType  cCols 
)
inline
Returns
an expression of a top-left corner of *this with either dynamic or fixed sizes.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.
NColsTypethe type of the value handling the number of columns in the block, typically Index.

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

The number of rows blockRows and columns blockCols can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::topLeftCorner ( )
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
)
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block
template<typename Derived>
template<typename NRowsType , typename NColsType >
FixedBlockXpr<...,...>::Type Eigen::SparseMatrixBase< Derived >::topRightCorner ( NRowsType  cRows,
NColsType  cCols 
)
inline
Returns
a expression of a top-right corner of *this with either dynamic or fixed sizes.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.
NColsTypethe type of the value handling the number of columns in the block, typically Index.

Example with dynamic sizes:

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

The number of rows blockRows and columns blockCols can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::topRightCorner ( )
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block, block<int,int>(Index,Index)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::SparseMatrixBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
)
inline
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
Warning
This method returns a read-only expression for any sparse matrices.
See Also
Sparse block operations
class Block
template<typename Derived>
template<typename NRowsType >
NRowsBlockXpr<...>::Type Eigen::SparseMatrixBase< Derived >::topRows ( NRowsType  n)
inline
Returns
a block consisting of the top rows of *this.
Parameters
nthe number of rows in the block
Template Parameters
NRowsTypethe type of the value handling the number of rows in the block, typically Index.

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

The number of rows n can also be specified at compile-time by passing Eigen::fix<N>, or Eigen::fix<N>(n) as arguments. See block() for the details.

Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::SparseMatrixBase< Derived >::topRows ( Index  n = N)
inline
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
Warning
This method returns a read-write expression for row-major sparse matrices only. Otherwise, the returned expression is read-only.
See Also
Sparse block operations
block(Index,Index,NRowsType,NColsType), class Block
template<typename Derived>
SparseSymmetricPermutationProduct<Derived,Upper|Lower> Eigen::SparseMatrixBase< Derived >::twistedBy ( const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &  perm) const
inline
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
inline

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

This method does not change the sparsity of *this: the unary function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
unaryViewExpr, binaryExpr, class CwiseUnaryOp
template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, const Derived> Eigen::SparseMatrixBase< Derived >::unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inline
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

This method does not change the sparsity of *this: the unary function is applied to explicitly stored coefficients only.

See Also
SparseCompressedBase::coeffs()
unaryExpr, binaryExpr class CwiseUnaryOp

Friends And Related Function Documentation

template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator* ( const T &  scalar,
const StorageBaseType expr 
)
friend
Returns
an expression of expr scaled by the scalar factor scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.

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