lti::backSubstitution< T > Class Template Reference

Backsubstitution. More...

#include <ltiBackSubstitution.h>

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List of all members.

Classes
class	parameters
	the parameters for the class backSubstitution More...
Public Member Functions
	backSubstitution ()
	backSubstitution (const matrix< T > &theMatrix, const typename parameters::eTriangularType &tType=parameters::Lower)
	backSubstitution (const parameters &par)
	backSubstitution (const backSubstitution &other)
virtual	~backSubstitution ()
virtual const char *	getTypeName () const
bool	apply (vector< T > &b) const
bool	apply (const vector< T > &b, vector< T > &x) const
bool	apply (const matrix< T > &theMatrix, vector< T > &b, const typename parameters::eTriangularType &tType) const
bool	apply (const matrix< T > &theMatrix, const vector< T > &b, vector< T > &x, const typename parameters::eTriangularType &tType) const
bool	apply (matrix< T > &b) const
bool	apply (const matrix< T > &b, matrix< T > &x) const
bool	apply (const matrix< T > &theMatrix, matrix< T > &b, const typename parameters::eTriangularType &tType) const
bool	apply (const matrix< T > &theMatrix, const matrix< T > &b, matrix< T > &x, const typename parameters::eTriangularType &tType) const
backSubstitution &	copy (const backSubstitution &other)
backSubstitution &	operator= (const backSubstitution &other)
virtual functor *	clone () const
const parameters &	getParameters () const

Detailed Description

template<class T>
class lti::backSubstitution< T >

Backsubstitution.

Let L be a lower triangular matrix and U an upper triangular matrix. Backsubstitution solves the following linear equation systems for x:

U*x=b or x*L=b

In the first case, x and b are column vectors, in the latter case they are row vectors. The data matrix can be given to the functor via the parameters or directly in the apply methods. There are also apply methods that calculate the backsubstitution for multiple right-sides b. The vectors are treated as before, ie they are in columns for the first case and in rows for the second.

Note that the column vector matrix will be transposed twice and thus takes longer to compute, try to use the vector-apply instead.

See also:: lti::backSubstitution

Constructor & Destructor Documentation

template<class T >

lti::backSubstitution< T >::backSubstitution ( )

default constructor

template<class T >

lti::backSubstitution< T >::backSubstitution	(	const matrix< T > &	theMatrix,
		const typename parameters::eTriangularType &	tType = `parameters::Lower`
	)

constructor, sets the data matrix and its triangular type in the parameters.

Note: Using this constructor, the data matrix is copied twice (Once to internally put it into a parameters object and then when setting the parameters). It can be better to let parameters::theMatrix use the data of some matrix you have:

 matrix<double> myData; //let this contain the data
 backSubstitution<double>::parameters param;
 param.theMatrix.useExternData(myData.rows(),myData.columns(),&myData.at(0,0))
 backSubstitution<double> mySubst(param);

The fastest method is to use one of the apply-methods where the data matrix is an argument.

Parameters:

	theMatrix	the data matrix
	tType	triangularType of theMatrix

template<class T >

lti::backSubstitution< T >::backSubstitution ( const parameters & par )

Construct a functor using the given parameters.

template<class T >

lti::backSubstitution< T >::backSubstitution ( const backSubstitution< T > & other )

copy constructor

Parameters:

other

the object to be copied

template<class T >

virtual lti::backSubstitution< T >::~backSubstitution ( ) [virtual]

destructor

Member Function Documentation

template<class T >

bool lti::backSubstitution< T >::apply	(	const matrix< T > &	theMatrix,
		const matrix< T > &	b,
		matrix< T > &	x,
		const typename parameters::eTriangularType &	tType
	)			const

Performs backsubstitution with unknowns X.

U*X=B if theMatrix is upper triagonal and X*L=B if theMatrix is lower triagonal. In the first case X and B contain the vectors in colums, in the latter case in rows.

Parameters:

	theMatrix	data matrix (L or U)
	b	the right side of the backsubstitution. The result will be left here too.
	x	the result
	tType	defines whether theMatrix is lower or upper triangular

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply	(	const matrix< T > &	theMatrix,
		matrix< T > &	b,
		const typename parameters::eTriangularType &	tType
	)			const

Performs backsubstitution with unknowns X.

U*X=B if theMatrix is upper triagonal and X*L=B if theMatrix is lower triagonal. In the first case X and B contain the vectors in colums, in the latter case in rows. The result x is left in b.

Parameters:

	theMatrix	data matrix (L or U)
	b	the right side of the backsubstitution. The result will be left here too.
	tType	defines whether theMatrix is lower or upper triangular

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply	(	const matrix< T > &	b,
		matrix< T > &	x
	)			const

Performs backsubstitution with unknowns X.

U*X=B if theMatrix is upper triagonal and X*L=B if theMatrix is lower triagonal. In the first case X and B contain the vectors in colums, in the latter case in rows. The data matrix in the parameters is used.

Parameters:

	b	the right side of the backsubstitution.
	x	the result

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply ( matrix< T > & b ) const

Performs backsubstitution with unknowns X.

U*X=B if theMatrix is upper triagonal and X*L=B if theMatrix is lower triagonal. In the first case X and B contain the vectors in colums, in the latter case in rows. The result x is left in b. The matrix in the parameters is used.

Parameters:

b

the right side of the backsubstitution. The result will be left here too.

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply	(	const matrix< T > &	theMatrix,
		const vector< T > &	b,
		vector< T > &	x,
		const typename parameters::eTriangularType &	tType
	)			const

Performs backsubstitution with unknown x.

U*x=b if theMatrix is upper triagonal and x*L=b if theMatrix is lower triagonal.

Parameters:

	theMatrix	data matrix (L or U)
	b	the right side of the backsubstitution. The result will be left here too.
	x	the result.
	tType	defines whether theMatrix is lower or upper triangular

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply	(	const matrix< T > &	theMatrix,
		vector< T > &	b,
		const typename parameters::eTriangularType &	tType
	)			const

Performs backsubstitution with unknown x.

U*x=b if theMatrix is upper triagonal and x*L=b if theMatrix is lower triagonal. The result x is left in b.

Parameters:

	theMatrix	data matrix (L or U)
	b	the right side of the backsubstitution. The result will be left here too.
	tType	defines whether theMatrix is lower or upper triangular

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply	(	const vector< T > &	b,
		vector< T > &	x
	)			const

Performs backsubstitution with unknown x.

U*x=b if theMatrix is upper triagonal and x*L=b if theMatrix is lower triagonal. The matrix in the parameters is used.

Parameters:

	b	the right side of the backsubstitution.
	x	the result.

Returns:: true if apply successful or false otherwise.

template<class T >

bool lti::backSubstitution< T >::apply ( vector< T > & b ) const

Performs backsubstitution with unknown x.

U*x=b if theMatrix is upper triagonal and x*L=b if theMatrix is lower triagonal. The result x is left in b. The matrix in the parameters is used.

Parameters:

b

the right side of the backsubstitution. The result will be left here too.

Returns:: true if apply successful or false otherwise.

template<class T >

virtual functor* lti::backSubstitution< T >::clone ( ) const [virtual]

returns a pointer to a clone of this functor.

Implements lti::functor.

template<class T >

backSubstitution& lti::backSubstitution< T >::copy ( const backSubstitution< T > & other )

copy data of "other" functor.

Parameters:

other

the functor to be copied

Returns:: a reference to this functor object

Reimplemented from lti::functor.

template<class T >

const parameters& lti::backSubstitution< T >::getParameters ( ) const

returns used parameters

Reimplemented from lti::functor.

template<class T >

virtual const char* lti::backSubstitution< T >::getTypeName ( ) const [virtual]

returns the name of this type ("backSubstitution")

Reimplemented from lti::linearAlgebraFunctor.

template<class T >

backSubstitution& lti::backSubstitution< T >::operator= ( const backSubstitution< T > & other )

alias for copy member

Parameters:

other

the functor to be copied

Returns:: a reference to this functor object

Reimplemented from lti::functor.

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

ltiBackSubstitution.h

lti::backSubstitution< T > Class Template Reference

Classes

Public Member Functions

Detailed Description

template<class T> class lti::backSubstitution< T >

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class lti::backSubstitution< T >