Eigen::internal::TridiagonalMatrix< Scalar, Size, Options > Class Template Reference

Represents a tridiagonal matrix with a compact banded storage. More...

#include <src/eigen/Eigen/src/Core/BandMatrix.h>

Inheritance diagram for Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >:

Collaboration diagram for Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >:

Public Types
typedef internal::traits< BandMatrix >::Scalar	Scalar
typedef internal::traits< BandMatrix >::CoefficientsType	CoefficientsType
enum	{   Flags = internal::traits<Derived>::Flags , CoeffReadCost = internal::traits<Derived>::CoeffReadCost , RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime , ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime ,   MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime , MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime , Supers = internal::traits<Derived>::Supers , Subs = internal::traits<Derived>::Subs ,   Options = internal::traits<Derived>::Options }
typedef Matrix< Scalar, RowsAtCompileTime, ColsAtCompileTime >	DenseMatrixType
typedef Eigen::Index	Index
	The interface type of indices.
typedef internal::traits< Derived >::StorageKind	StorageKind

Public Member Functions
	TridiagonalMatrix (Index size=Size)
Base::template DiagonalIntReturnType< 1 >::Type	super ()
const Base::template DiagonalIntReturnType< 1 >::Type	super () const
Base::template DiagonalIntReturnType<-1 >::Type	sub ()
const Base::template DiagonalIntReturnType<-1 >::Type	sub () const
Index	rows () const
Index	cols () const
Index	supers () const
Index	subs () const
const CoefficientsType &	coeffs () const
CoefficientsType &	coeffs ()
Block< CoefficientsType, Dynamic, 1 >	col (Index i)
Block< CoefficientsType, 1, SizeAtCompileTime >	diagonal ()
const Block< const CoefficientsType, 1, SizeAtCompileTime >	diagonal () const
template<int N>
DiagonalIntReturnType< N >::Type	diagonal ()
template<int N>
const DiagonalIntReturnType< N >::Type	diagonal () const
Block< CoefficientsType, 1, Dynamic >	diagonal (Index i)
const Block< const CoefficientsType, 1, Dynamic >	diagonal (Index i) const
template<typename Dest >
void	evalTo (Dest &dst) const
DenseMatrixType	toDenseMatrix () const
EIGEN_DEVICE_FUNC Derived &	derived ()
EIGEN_DEVICE_FUNC const Derived &	derived () const
EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const
EIGEN_DEVICE_FUNC const Derived &	const_derived () const
EIGEN_DEVICE_FUNC Index	size () const
template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Protected Types
enum	{ DataRowsAtCompileTime , SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime) }

Protected Member Functions
Index	diagonalLength (Index i) const

Protected Attributes
CoefficientsType	m_coeffs
internal::variable_if_dynamic< Index, Rows >	m_rows
internal::variable_if_dynamic< Index, Supers >	m_supers
internal::variable_if_dynamic< Index, Subs >	m_subs

Private Types
typedef BandMatrix< Scalar, Size, Size, Options &SelfAdjoint?0:1, 1, Options|RowMajor >	Base
typedef Base::StorageIndex	StorageIndex

Detailed Description

template<typename Scalar, int Size, int Options>
class Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >

Represents a tridiagonal matrix with a compact banded storage.

Template Parameters

Scalar	Numeric type, i.e. float, double, int
Size	Number of rows and cols, or Dynamic
Options	Can be 0 or SelfAdjoint

See also

class BandMatrix

Member Typedef Documentation

Base

template<typename Scalar , int Size, int Options>

typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::Base

private

CoefficientsType

typedef internal::traits<BandMatrix>::CoefficientsType Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::CoefficientsType

inherited

DenseMatrixType

template<typename Derived >

typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> Eigen::internal::BandMatrixBase< Derived >::DenseMatrixType

inherited

Index

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.

See also

StorageIndex, TopicPreprocessorDirectives.

Scalar

typedef internal::traits<BandMatrix>::Scalar Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::Scalar

inherited

StorageIndex

template<typename Scalar , int Size, int Options>

typedef Base::StorageIndex Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::StorageIndex

private

StorageKind

template<typename Derived >

typedef internal::traits<Derived>::StorageKind Eigen::EigenBase< Derived >::StorageKind

inherited

Member Enumeration Documentation

anonymous enum

template<typename Derived >

anonymous enum

inherited

Enumerator
Flags
CoeffReadCost
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
Supers
Subs
Options

         {
      Flags = internal::traits<Derived>::Flags,
      CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
      Supers = internal::traits<Derived>::Supers,
      Subs   = internal::traits<Derived>::Subs,
      Options = internal::traits<Derived>::Options
    };

anonymous enum

template<typename Derived >

anonymous enum

protectedinherited

Enumerator
DataRowsAtCompileTime
SizeAtCompileTime

         {
      DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
                            ? 1 + Supers + Subs
                            : Dynamic,
      SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime)
    };

Constructor & Destructor Documentation

TridiagonalMatrix()

template<typename Scalar , int Size, int Options>

Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::TridiagonalMatrix ( Index  size = Size )

inlineexplicit

: Base(size,size,Options&SelfAdjoint?0:1,1) {}

References Eigen::SelfAdjoint.

Member Function Documentation

addTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::addTo ( Dest &  dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst += res;
  }

applyThisOnTheLeft()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheLeft ( Dest &  dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = this->derived() * dst;
  }

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

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applyThisOnTheRight()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheRight ( Dest &  dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = dst * this->derived();
  }

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

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coeffs() [1/2]

CoefficientsType & Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::coeffs ( )

inlineinherited

{ return m_coeffs; }

coeffs() [2/2]

const CoefficientsType & Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::coeffs ( ) const

inlineinherited

{ return m_coeffs; }

col()

template<typename Derived >

Block< CoefficientsType, Dynamic, 1 > Eigen::internal::BandMatrixBase< Derived >::col ( Index  i )

inlineinherited

Returns

a vector expression of the i -th column, only the meaningful part is returned.

Warning

the internal storage must be column major.

    {
      EIGEN_STATIC_ASSERT((Options&RowMajor)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
      Index start = 0;
      Index len = coeffs().rows();
      if (i<=supers())
      {
        start = supers()-i;
        len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
      }
      else if (i>=rows()-subs())
        len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
      return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
    }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), EIGEN_STATIC_ASSERT, Eigen::internal::BandMatrixBase< Derived >::Options, Eigen::RowMajor, Eigen::internal::BandMatrixBase< Derived >::rows(), Eigen::internal::BandMatrixBase< Derived >::subs(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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cols()

Index Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::cols ( ) const

inlineinherited

Returns

the number of rows

{ return m_coeffs.cols(); }

const_cast_derived()

template<typename Derived >

EIGEN_DEVICE_FUNC Derived & Eigen::EigenBase< Derived >::const_cast_derived ( ) const

inlineinherited

  { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }

Referenced by Eigen::TriangularViewImpl< _MatrixType, _Mode, Dense >::swap().

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const_derived()

template<typename Derived >

EIGEN_DEVICE_FUNC const Derived & Eigen::EigenBase< Derived >::const_derived ( ) const

inlineinherited

  { return *static_cast<const Derived*>(this); }

derived() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC Derived & Eigen::EigenBase< Derived >::derived ( )

inlineinherited

Returns

a reference to the derived object

{ return *static_cast<Derived*>(this); }

Referenced by Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::subs(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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derived() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC const Derived & Eigen::EigenBase< Derived >::derived ( ) const

inlineinherited

Returns

a const reference to the derived object

{ return *static_cast<const Derived*>(this); }

diagonal() [1/6]

template<typename Derived >

Block< CoefficientsType, 1, SizeAtCompileTime > Eigen::internal::BandMatrixBase< Derived >::diagonal ( )

inlineinherited

Returns

a vector expression of the main diagonal

    { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::cols(), Eigen::internal::BandMatrixBase< Derived >::rows(), and Eigen::internal::BandMatrixBase< Derived >::supers().

Referenced by Eigen::internal::BandMatrixBase< Derived >::evalTo().

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diagonal() [2/6]

template<typename Derived >

template<int N>

DiagonalIntReturnType< N >::Type Eigen::internal::BandMatrixBase< Derived >::diagonal ( )

inlineinherited

Returns

a vector expression of the N -th sub or super diagonal

    {
      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
    }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::diagonalLength(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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diagonal() [3/6]

template<typename Derived >

const Block< const CoefficientsType, 1, SizeAtCompileTime > Eigen::internal::BandMatrixBase< Derived >::diagonal ( ) const

inlineinherited

Returns

a vector expression of the main diagonal (const version)

    { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::cols(), Eigen::internal::BandMatrixBase< Derived >::rows(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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diagonal() [4/6]

template<typename Derived >

template<int N>

const DiagonalIntReturnType< N >::Type Eigen::internal::BandMatrixBase< Derived >::diagonal ( ) const

inlineinherited

Returns

a vector expression of the N -th sub or super diagonal

    {
      return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
    }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::diagonalLength(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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diagonal() [5/6]

template<typename Derived >

Block< CoefficientsType, 1, Dynamic > Eigen::internal::BandMatrixBase< Derived >::diagonal ( Index  i )

inlineinherited

Returns

a vector expression of the i -th sub or super diagonal

    {
      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
      return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
    }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::diagonalLength(), eigen_assert, Eigen::internal::BandMatrixBase< Derived >::subs(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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diagonal() [6/6]

template<typename Derived >

const Block< const CoefficientsType, 1, Dynamic > Eigen::internal::BandMatrixBase< Derived >::diagonal ( Index  i ) const

inlineinherited

Returns

a vector expression of the i -th sub or super diagonal

    {
      eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
      return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
    }

References Eigen::internal::BandMatrixBase< Derived >::coeffs(), Eigen::internal::BandMatrixBase< Derived >::diagonalLength(), eigen_assert, Eigen::internal::BandMatrixBase< Derived >::subs(), and Eigen::internal::BandMatrixBase< Derived >::supers().

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diagonalLength()

template<typename Derived >

Index Eigen::internal::BandMatrixBase< Derived >::diagonalLength ( Index  i ) const

inlineprotectedinherited

    { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }

References Eigen::internal::BandMatrixBase< Derived >::cols(), and Eigen::internal::BandMatrixBase< Derived >::rows().

Referenced by Eigen::internal::BandMatrixBase< Derived >::diagonal(), Eigen::internal::BandMatrixBase< Derived >::diagonal(), Eigen::internal::BandMatrixBase< Derived >::diagonal(), and Eigen::internal::BandMatrixBase< Derived >::diagonal().

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evalTo()

template<typename Derived >

template<typename Dest >

void Eigen::internal::BandMatrixBase< Derived >::evalTo ( Dest &  dst ) const

inlineinherited

    {
      dst.resize(rows(),cols());
      dst.setZero();
      dst.diagonal() = diagonal();
      for (Index i=1; i<=supers();++i)
        dst.diagonal(i) = diagonal(i);
      for (Index i=1; i<=subs();++i)
        dst.diagonal(-i) = diagonal(-i);
    }

References Eigen::internal::BandMatrixBase< Derived >::cols(), Eigen::internal::BandMatrixBase< Derived >::diagonal(), Eigen::internal::BandMatrixBase< Derived >::rows(), Eigen::internal::BandMatrixBase< Derived >::subs(), and Eigen::internal::BandMatrixBase< Derived >::supers().

Referenced by Eigen::internal::BandMatrixBase< Derived >::toDenseMatrix().

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rows()

Index Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::rows ( ) const

inlineinherited

Returns

the number of columns

{ return m_rows.value(); }

size()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::EigenBase< Derived >::size ( ) const

inlineinherited

Returns

the number of coefficients, which is rows()*cols().

See also

rows(), cols(), SizeAtCompileTime.

{ return rows() * cols(); }

References Eigen::EigenBase< Derived >::cols(), and Eigen::EigenBase< Derived >::rows().

Referenced by Eigen::PlainObjectBase< Derived >::_resize_to_match(), Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::resize(), Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::setIdentity(), and Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::setZero().

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sub() [1/2]

template<typename Scalar , int Size, int Options>

Base::template DiagonalIntReturnType<-1 >::Type Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::sub ( )

inline

    { return Base::template diagonal<-1>(); }

sub() [2/2]

template<typename Scalar , int Size, int Options>

const Base::template DiagonalIntReturnType<-1 >::Type Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::sub ( ) const

inline

    { return Base::template diagonal<-1>(); }

subs()

Index Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::subs ( ) const

inlineinherited

Returns

the number of sub diagonals

{ return m_subs.value(); }

subTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::subTo ( Dest &  dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst -= res;
  }

References Eigen::EigenBase< Derived >::cols(), Eigen::EigenBase< Derived >::evalTo(), and Eigen::EigenBase< Derived >::rows().

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super() [1/2]

template<typename Scalar , int Size, int Options>

Base::template DiagonalIntReturnType< 1 >::Type Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::super ( )

inline

    { return Base::template diagonal<1>(); }

super() [2/2]

template<typename Scalar , int Size, int Options>

const Base::template DiagonalIntReturnType< 1 >::Type Eigen::internal::TridiagonalMatrix< Scalar, Size, Options >::super ( ) const

inline

    { return Base::template diagonal<1>(); }

supers()

Index Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::supers ( ) const

inlineinherited

Returns

the number of super diagonals

{ return m_supers.value(); }

toDenseMatrix()

template<typename Derived >

DenseMatrixType Eigen::internal::BandMatrixBase< Derived >::toDenseMatrix ( ) const

inlineinherited

    {
      DenseMatrixType res(rows(),cols());
      evalTo(res);
      return res;
    }

References Eigen::internal::BandMatrixBase< Derived >::cols(), Eigen::internal::BandMatrixBase< Derived >::evalTo(), and Eigen::internal::BandMatrixBase< Derived >::rows().

Referenced by Eigen::BDCSVD< _MatrixType >::compute().

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Member Data Documentation

m_coeffs

CoefficientsType Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::m_coeffs

protectedinherited

m_rows

internal::variable_if_dynamic<Index, Rows> Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::m_rows

protectedinherited

m_subs

internal::variable_if_dynamic<Index, Subs> Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::m_subs

protectedinherited

m_supers

internal::variable_if_dynamic<Index, Supers> Eigen::internal::BandMatrix< Scalar , Rows, Cols, Supers, Subs, Options >::m_supers

protectedinherited

---

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

• src/eigen/Eigen/src/Core/BandMatrix.h