Opm::TridiagonalMatrix< Scalar > Class Template Reference

Provides a tridiagonal matrix that also supports non-zero entries in the upper right and lower left. More...

#include <TridiagonalMatrix.hpp>

Public Types
typedef Scalar	FieldType
typedef TridiagRow_	RowType
typedef size_t	SizeType
typedef TridiagRow_	iterator
typedef TridiagRow_	const_iterator

Public Member Functions
	TridiagonalMatrix (size_t numRows=0)
	TridiagonalMatrix (size_t numRows, Scalar value)
	TridiagonalMatrix (const TridiagonalMatrix &source)
	Copy constructor. More...
size_t	size () const
	Return the number of rows/columns of the matrix. More...
size_t	rows () const
	Return the number of rows of the matrix. More...
size_t	cols () const
	Return the number of columns of the matrix. More...
void	resize (size_t n)
	Change the number of rows of the matrix. More...
Scalar &	at (size_t rowIdx, size_t colIdx)
	Access an entry. More...
Scalar	at (size_t rowIdx, size_t colIdx) const
	Access an entry. More...
TridiagonalMatrix &	operator= (const TridiagonalMatrix &source)
	Assignment operator from another tridiagonal matrix. More...
TridiagonalMatrix &	operator= (Scalar value)
	Assignment operator from a Scalar. More...
iterator	begin ()
const_iterator	begin () const
const_iterator	end () const
TridiagRow_	operator[] (size_t rowIdx)
	Row access operator. More...
const TridiagRow_	operator[] (size_t rowIdx) const
	Row access operator. More...
TridiagonalMatrix &	operator*= (Scalar alpha)
	Multiplication with a Scalar. More...
TridiagonalMatrix &	operator/= (Scalar alpha)
	Division by a Scalar. More...
TridiagonalMatrix &	operator-= (const TridiagonalMatrix &other)
	Subtraction operator. More...
TridiagonalMatrix &	operator+= (const TridiagonalMatrix &other)
	Addition operator. More...
TridiagonalMatrix &	axpy (Scalar alpha, const TridiagonalMatrix &other)
	Multiply and add the matrix entries of another tridiagonal matrix. More...
template<class Vector >
void	mv (const Vector &source, Vector &dest) const
	Matrix-vector product. More...
template<class Vector >
void	umv (const Vector &source, Vector &dest) const
	Additive matrix-vector product. More...
template<class Vector >
void	mmv (const Vector &source, Vector &dest) const
	Subtractive matrix-vector product. More...
template<class Vector >
void	usmv (Scalar alpha, const Vector &source, Vector &dest) const
	Scaled additive matrix-vector product. More...
template<class Vector >
void	mtv (const Vector &source, Vector &dest) const
	Transposed matrix-vector product. More...
template<class Vector >
void	umtv (const Vector &source, Vector &dest) const
	Transposed additive matrix-vector product. More...
template<class Vector >
void	mmtv (const Vector &source, Vector &dest) const
	Transposed subtractive matrix-vector product. More...
template<class Vector >
void	usmtv (Scalar alpha, const Vector &source, Vector &dest) const
	Transposed scaled additive matrix-vector product. More...
Scalar	frobeniusNorm () const
	Calculate the frobenius norm. More...
Scalar	frobeniusNormSquared () const
	Calculate the squared frobenius norm. More...
Scalar	infinityNorm () const
	Calculate the infinity norm. More...
template<class XVector , class BVector >
void	solve (XVector &x, const BVector &b) const
	Calculate the solution for a linear system of equations. More...
void	print (std::ostream &os=std::cout) const
	Print the matrix to a given output stream. More...

Detailed Description

template<class Scalar>
class Opm::TridiagonalMatrix< Scalar >

Provides a tridiagonal matrix that also supports non-zero entries in the upper right and lower left.

The entries in the lower left and upper right are supported to make implementing periodic systems easy.

The API of this class is designed to be close to the one used by the DUNE matrix classes.

Member Typedef Documentation

template<class Scalar >

typedef TridiagRow_ Opm::TridiagonalMatrix< Scalar >::const_iterator

template<class Scalar >

typedef Scalar Opm::TridiagonalMatrix< Scalar >::FieldType

template<class Scalar >

typedef TridiagRow_ Opm::TridiagonalMatrix< Scalar >::iterator

template<class Scalar >

typedef TridiagRow_ Opm::TridiagonalMatrix< Scalar >::RowType

template<class Scalar >

typedef size_t Opm::TridiagonalMatrix< Scalar >::SizeType

Constructor & Destructor Documentation

template<class Scalar >

Opm::TridiagonalMatrix< Scalar >::TridiagonalMatrix ( size_t  numRows = 0 )

inlineexplicit

References Opm::TridiagonalMatrix< Scalar >::resize().

template<class Scalar >

Opm::TridiagonalMatrix< Scalar >::TridiagonalMatrix ( size_t  numRows, Scalar  value  )

inline

References Opm::TridiagonalMatrix< Scalar >::operator=(), and Opm::TridiagonalMatrix< Scalar >::resize().

template<class Scalar >

Opm::TridiagonalMatrix< Scalar >::TridiagonalMatrix ( const TridiagonalMatrix< Scalar > &  source )

inline

Copy constructor.

Member Function Documentation

template<class Scalar >

Scalar& Opm::TridiagonalMatrix< Scalar >::at ( size_t  rowIdx, size_t  colIdx  )

inline

Access an entry.

References Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::TridiagonalMatrix< Scalar >::print().

template<class Scalar >

Scalar Opm::TridiagonalMatrix< Scalar >::at ( size_t  rowIdx, size_t  colIdx  ) const

inline

Access an entry.

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::axpy ( Scalar  alpha, const TridiagonalMatrix< Scalar > &  other  )

inline

Multiply and add the matrix entries of another tridiagonal matrix.

This means that

A.axpy(alpha, B)

is equivalent to

A += alpha*C

References Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::TridiagonalMatrix< Scalar >::operator+=(), and Opm::TridiagonalMatrix< Scalar >::operator-=().

template<class Scalar >

iterator Opm::TridiagonalMatrix< Scalar >::begin ( )

inline

Iterator for the first row

template<class Scalar >

const_iterator Opm::TridiagonalMatrix< Scalar >::begin ( ) const

inline

Const iterator for the first row

template<class Scalar >

size_t Opm::TridiagonalMatrix< Scalar >::cols ( ) const

inline

Return the number of columns of the matrix.

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

const_iterator Opm::TridiagonalMatrix< Scalar >::end ( ) const

inline

Const iterator for the next-to-last row

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

Scalar Opm::TridiagonalMatrix< Scalar >::frobeniusNorm ( ) const

inline

Calculate the frobenius norm.

i.e., the square root of the sum of all squared entries. This corresponds to the euclidean norm for vectors.

References Opm::TridiagonalMatrix< Scalar >::frobeniusNormSquared(), and Opm::LocalAd::sqrt().

template<class Scalar >

Scalar Opm::TridiagonalMatrix< Scalar >::frobeniusNormSquared ( ) const

inline

Calculate the squared frobenius norm.

i.e., the sum of all squared entries.

References Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::TridiagonalMatrix< Scalar >::frobeniusNorm().

template<class Scalar >

Scalar Opm::TridiagonalMatrix< Scalar >::infinityNorm ( ) const

inline

Calculate the infinity norm.

i.e., the maximum of the sum of the absolute values of all rows.

References Opm::LocalAd::abs(), Opm::LocalAd::max(), and Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::mmtv ( const Vector &  source, Vector &  dest  ) const

inline

Transposed subtractive matrix-vector product.

This means that

A.mmtv(x, y)

is equivalent to

y -= A^T*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::mmv ( const Vector &  source, Vector &  dest  ) const

inline

Subtractive matrix-vector product.

This means that

A.mmv(x, y)

is equivalent to

y -= A*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::mtv ( const Vector &  source, Vector &  dest  ) const

inline

Transposed matrix-vector product.

This means that

A.mtv(x, y)

is equivalent to

y = A^T*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::mv ( const Vector &  source, Vector &  dest  ) const

inline

Matrix-vector product.

This means that

A.mv(x, y)

is equivalent to

y = A*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator*= ( Scalar  alpha )

inline

Multiplication with a Scalar.

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator+= ( const TridiagonalMatrix< Scalar > &  other )

inline

Addition operator.

References Opm::TridiagonalMatrix< Scalar >::axpy().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator-= ( const TridiagonalMatrix< Scalar > &  other )

inline

Subtraction operator.

References Opm::TridiagonalMatrix< Scalar >::axpy().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator/= ( Scalar  alpha )

inline

Division by a Scalar.

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator= ( const TridiagonalMatrix< Scalar > &  source )

inline

Assignment operator from another tridiagonal matrix.

Referenced by Opm::TridiagonalMatrix< Scalar >::TridiagonalMatrix().

template<class Scalar >

TridiagonalMatrix& Opm::TridiagonalMatrix< Scalar >::operator= ( Scalar  value )

inline

Assignment operator from a Scalar.

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

TridiagRow_ Opm::TridiagonalMatrix< Scalar >::operator[] ( size_t  rowIdx )

inline

Row access operator.

template<class Scalar >

const TridiagRow_ Opm::TridiagonalMatrix< Scalar >::operator[] ( size_t  rowIdx ) const

inline

Row access operator.

template<class Scalar >

void Opm::TridiagonalMatrix< Scalar >::print ( std::ostream &  os = std::cout ) const

inline

Print the matrix to a given output stream.

References Opm::TridiagonalMatrix< Scalar >::at(), and Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

void Opm::TridiagonalMatrix< Scalar >::resize ( size_t  n )

inline

Change the number of rows of the matrix.

References Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::TridiagonalMatrix< Scalar >::TridiagonalMatrix().

template<class Scalar >

size_t Opm::TridiagonalMatrix< Scalar >::rows ( ) const

inline

Return the number of rows of the matrix.

References Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::Spline< Scalar >::makePeriodicSystem_().

template<class Scalar >

size_t Opm::TridiagonalMatrix< Scalar >::size ( ) const

inline

Return the number of rows/columns of the matrix.

Referenced by Opm::TridiagonalMatrix< Scalar >::at(), Opm::TridiagonalMatrix< Scalar >::axpy(), Opm::TridiagonalMatrix< Scalar >::cols(), Opm::TridiagonalMatrix< Scalar >::end(), Opm::TridiagonalMatrix< Scalar >::frobeniusNormSquared(), Opm::TridiagonalMatrix< Scalar >::infinityNorm(), Opm::TridiagonalMatrix< Scalar >::mmtv(), Opm::TridiagonalMatrix< Scalar >::mmv(), Opm::TridiagonalMatrix< Scalar >::mtv(), Opm::TridiagonalMatrix< Scalar >::mv(), Opm::TridiagonalMatrix< Scalar >::operator*=(), Opm::TridiagonalMatrix< Scalar >::operator/=(), Opm::TridiagonalMatrix< Scalar >::operator=(), Opm::TridiagonalMatrix< Scalar >::print(), Opm::TridiagonalMatrix< Scalar >::resize(), Opm::TridiagonalMatrix< Scalar >::rows(), Opm::TridiagonalMatrix< Scalar >::solve(), Opm::TridiagonalMatrix< Scalar >::umtv(), Opm::TridiagonalMatrix< Scalar >::umv(), Opm::TridiagonalMatrix< Scalar >::usmtv(), and Opm::TridiagonalMatrix< Scalar >::usmv().

template<class Scalar >

template<class XVector , class BVector >

void Opm::TridiagonalMatrix< Scalar >::solve ( XVector &  x, const BVector &  b  ) const

inline

Calculate the solution for a linear system of equations.

i.e., calculate x, so that it solves Ax = b, where A is a tridiagonal matrix.

References Opm::LocalAd::abs(), and Opm::TridiagonalMatrix< Scalar >::size().

Referenced by Opm::Spline< Scalar >::makeFullSpline_(), Opm::Spline< Scalar >::makeNaturalSpline_(), Opm::Spline< Scalar >::makePeriodicSpline_(), and Opm::Spline< Scalar >::set().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::umtv ( const Vector &  source, Vector &  dest  ) const

inline

Transposed additive matrix-vector product.

This means that

A.umtv(x, y)

is equivalent to

y += A^T*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::umv ( const Vector &  source, Vector &  dest  ) const

inline

Additive matrix-vector product.

This means that

A.umv(x, y)

is equivalent to

y += A*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::usmtv ( Scalar  alpha, const Vector &  source, Vector &  dest  ) const

inline

Transposed scaled additive matrix-vector product.

This means that

A.umtv(alpha, x, y)

is equivalent to

y += alpha*A^T*x

References Opm::TridiagonalMatrix< Scalar >::size().

template<class Scalar >

template<class Vector >

void Opm::TridiagonalMatrix< Scalar >::usmv ( Scalar  alpha, const Vector &  source, Vector &  dest  ) const

inline

Scaled additive matrix-vector product.

This means that

A.usmv(x, y)

is equivalent to

y += alpha*(A*x)

References Opm::TridiagonalMatrix< Scalar >::size().

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

• TridiagonalMatrix.hpp