RWBandFact< TypeT > Class Template Reference

Encapsulates the factorization of banded matrices used to solve a system of equations. More...

#include <rw/lapack/bandfct.h>

Public Member Functions
	RWBandFact ()
	RWBandFact (const RWBandMat< TypeT > &A, bool estimateCondition=true)
int	cols () const
rw_numeric_traits< TypeT >::norm_type	condition () const
TypeT	determinant () const
void	factor (const RWBandMat< TypeT > &A, bool estimateCondition=true)
bool	fail () const
bool	good () const
bool	isSingular () const
int	rows () const
RWMathVec< TypeT >	solve (const RWMathVec< TypeT > &b) const
RWGenMat< TypeT >	solve (const RWGenMat< TypeT > &b) const

Related Functions
(Note that these are not member functions.)
template<class TypeT >
rw_numeric_traits< TypeT >::norm_type	condition (const RWBandFact< TypeT > &A)
template<class TypeT >
TypeT	determinant (const RWBandFact< TypeT > &A)
template<class TypeT >
RWMathVec< TypeT >	solve (const RWBandFact< TypeT > &A, const RWMathVec< TypeT > &b)
template<class TypeT >
RWGenMat< TypeT >	solve (const RWBandFact< TypeT > &A, const RWGenMat< TypeT > &b)

Detailed Description

template<class TypeT>
class RWBandFact< TypeT >

A factorization is a representation of a matrix that can be used to efficiently solve systems of equations, and to compute the inverse, determinant, and condition number of a matrix. The class RWBandFact encapsulates factorizations of banded matrices. Provided the matrix being factored is nonsingular, the resulting factorization can always be used to solve a system of equations.

Synopsis

#include <rw/lapack/bandfct.h>

RWBandFact<double> LU5(E);      // E is a RWBandMat<double>

Example

#include <iostream>
#include <rw/lapack/bandmat.h>
#include <rw/math/mathvec.h>
#include <rw/lapack/bandfct.h>

int main()
{
   // Read in a matrix and a right-hand side and
   // print the solution
   RWGenMat<double> A;
   RWMathVec<double> b;
   std::cin >> A >> b;
   RWBandFact<double> BF(A);
   if (BF.good()) {
     std::cout << "solution is " << solve(BF,b) << std::endl;
   } else {
     std::cout << "Could not factor A, perhaps it is singular"
               << std::endl;
   }
     return 0;
}

Constructor & Destructor Documentation

template<class TypeT>

RWBandFact< TypeT >::RWBandFact

(

)

Default constructor. Builds a factorization of a 0 x 0 matrix. You use the member function factor to fill in the factorization.

template<class TypeT>

RWBandFact< TypeT >::RWBandFact	(	const RWBandMat< TypeT > &	A,
		bool	estimateCondition = true
	)

Constructs a factorization of the matrix A. This factorization can be used to solve systems of equations, and to calculate inverses and determinants. If the parameter estimateCondition is true, you can use the function condition() to obtain an estimate of the condition number of the matrix. Setting estimateCondition to false can save some computation if the condition number is not needed.

Member Function Documentation

template<class TypeT>

int RWBandFact< TypeT >::cols ( ) const

inline

Returns the number of columns in the matrix represented by this factorization.

template<class TypeT>

rw_numeric_traits<TypeT>::norm_type RWBandFact< TypeT >::condition

(

)

const

Calculates the reciprocal condition number of the matrix represented by this factorization. If this number is near 0, the matrix is ill-conditioned and solutions to systems of equations computed using this factorization may not be accurate. If the number is near 1, the matrix is well-conditioned. For the condition number to be computed, the norm of the matrix must be computed at the time the factorization is constructed. If you set the optional boolean parameter in RWBandFact() or factor() to false, calling condition() generates an exception.

template<class TypeT>

TypeT RWBandFact< TypeT >::determinant

(

)

const

Calculates the determinant of the matrix represented by this factorization.

template<class TypeT>

void RWBandFact< TypeT >::factor	(	const RWBandMat< TypeT > &	A,
		bool	estimateCondition = true
	)

Factors a matrix. Calling factor() replaces the current factorization with the factorization of the matrix A. This is commonly used to initialize a factorization constructed with the default (no arguments) constructor.

template<class TypeT>

bool RWBandFact< TypeT >::fail

(

)

const

Checks whether the factorization is successfully constructed. If fail() returns true, attempting to use the factorization to solve a system of equations results in an exception being thrown.

template<class TypeT>

bool RWBandFact< TypeT >::good ( ) const

inline

Checks whether the factorization is successfully constructed. If good() returns false, attempting to use the factorization to solve a system of equations results in an exception being thrown.

template<class TypeT>

bool RWBandFact< TypeT >::isSingular

(

)

const

Tests if the matrix is singular to within machine precision. If the factorization is a positive definite type and the matrix that was factored is not actually positive definite, then isSingular() may return true regardless of whether or not the matrix is actually singular.

template<class TypeT>

int RWBandFact< TypeT >::rows ( ) const

inline

Returns the number of rows in the matrix represented by this factorization.

template<class TypeT>

RWMathVec<TypeT> RWBandFact< TypeT >::solve

(

const RWMathVec< TypeT > &

b

)

const

Solves a system of equations. Returns the vector x, which satisfies \(Ax = b\), where A is the matrix represented by this factorization. It is wise to call one of the member functions good() or fail() to make sure that the factorization was successfully constructed.

template<class TypeT>

RWGenMat<TypeT> RWBandFact< TypeT >::solve

(

const RWGenMat< TypeT > &

b

)

const

Solves a system of equations. Returns the matrix x, which satisfies \(Ax = b\), where A is the matrix represented by this factorization. It is wise to call one of the member functions good() or fail() to make sure that the factorization was successfully constructed.

Friends And Related Function Documentation

template<class TypeT >

rw_numeric_traits< TypeT >::norm_type condition ( const RWBandFact< TypeT > &  A )

related

Calculates the reciprocal condition number of the matrix represented by the factorization A. If this number is near 0, the matrix is ill-conditioned and solutions to systems of equations computed using this factorization may not be accurate. If the number is near 1, the matrix is well-conditioned. For the condition number to be computed, the norm of the matrix must be computed at the time the factorization is constructed. If you set the optional boolean parameter in RWBandFact() or factor() member function to false, calling condition() generates an exception.

template<class TypeT >

TypeT determinant ( const RWBandFact< TypeT > &  A )

related

Calculates the determinant of the matrix represented by the factorization A.

template<class TypeT >

RWMathVec< TypeT > solve ( const RWBandFact< TypeT > &  A, const RWMathVec< TypeT > &  b  )

related

Solves a system of equations. Returns the vector x, which satisfies \(Ax = b\), where A is the matrix represented by the factorization. It is wise to call one of the member functions good() or fail() to make sure that the factorization was successfully constructed.

template<class TypeT >

RWGenMat< TypeT > solve ( const RWBandFact< TypeT > &  A, const RWGenMat< TypeT > &  b  )

related

Solves a system of equations. Returns the matrix x, which satisfies \(Ax = b\), where A is the matrix represented by the factorization. It is wise to call one of the member functions good() or fail() to make sure that the factorization was successfully constructed.