RWGenFact< T > Class Template Reference
[LU Factorization]

A templatized LU factorization class that holds the LU factorization of a general square matrix of type T. More...

#include <rw/math/genfact.h>

List of all members.

Public Types
typedef rw_numeric_traits< T > ::norm_type	norm_type
Public Member Functions
	RWGenFact ()
	RWGenFact (const RWGenFact< T > &A)
	RWGenFact (const RWGenMat< T > &A, bool estimateCondition=true)
void	factor (const RWGenMat< T > &A, bool estimateCondition=true)
bool	good () const
bool	fail () const
bool	isSingular () const
norm_type	condition () const
Related Functions
(Note that these are not member functions.)
template<class T >
RWMathVec< T >	solve (const RWGenFact< T > &m, const RWMathVec< T > &b)
template<class T >
RWMathVec< T >	solve (const RWGenMat< T > &A, const RWMathVec< T > &b)
template<class T >
RWGenMat< T >	solve (const RWGenFact< T > &m, const RWGenMat< T > &b)
template<class T >
RWGenMat< T >	solve (const RWGenMat< T > &A, const RWGenMat< T > &b)
template<class T >
T	determinant (const RWGenFact< T > &A)
template<class T >
RWGenMat< T >	inverse (const RWGenFact< T > &A)
template<class T >
RWGenMat< T >	inverse (const RWGenMat< T > &A)
template<class T >
double	condition (const RWGenFact< T > &A)
template<class T >
double	condition (const RWGenMat< T > &A)

---

Detailed Description

template<class T>
class RWGenFact< T >

Class RWGenFact<T> is a templatized LU factorization class. This class holds the LU factorization of a general square matrix of type T. Once such a factorization is built, it can be used to invert a matrix, calculate its determinant, or solve a set of simultaneous linear equations.

Optionally, a condition number can be calculated and then recovered via member function condition(), which returns the reciprocal of the standard definition for the condition number of a matrix.

The result is in the range [0,1]. The closer the result is to 0, the closer the matrix is to being singular. See Dongarra et al. (1979) for additional information.

Synopsis

 #include <rw/math/genfact.h>
 #include <rw/math/genmat.h>
 RWGenMat<T> matrix;
 template <class T>
 RWGenFact<T> LUFactor(matrix);

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Member Typedef Documentation

template<class T>

typedef rw_numeric_traits<T>::norm_type RWGenFact< T >::norm_type

This is a convenience typedef. The condition numbers have type dependent on the traits class.

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Constructor & Destructor Documentation

template<class T>

RWGenFact< T >::RWGenFact

(

)

Sets up an empty LU factorization. Member function factor() can then be used to actually calculate the factorization.

template<class T>

RWGenFact< T >::RWGenFact

(

const RWGenFact< T > &

A

)

Copy constructor. Reference semantics are used; that is, a shallow copy of the argument is made.

template<class T>

RWGenFact< T >::RWGenFact	(	const RWGenMat< T > &	A,
		bool	estimateCondition = true
	)

Constructs an LU factorization from the matrix m. If the argument estimateCondition is true, a condition number is also calculated. Setting estimateCondition to false saves some time (perhaps 20%), but gives you less information about how ill-conditioned the matrix is. If the matrix m is not square, an exception with value RWLAPK_NOTSQUARE occurs. This constructor also serves as a type conversion from RWGenMat<T> to RWGenFact<T>

---

Member Function Documentation

template<class T>

norm_type RWGenFact< T >::condition

(

)

const

An exception with value RWMATH_NOCONDITION occurs if the condition number is not calculated.

template<class T>

void RWGenFact< T >::factor	(	const RWGenMat< T > &	A,
		bool	estimateCondition = true
	)

Recalculates the factorization, this time using the matrix m. If the argument estimateCondition is true, a condition number is also calculated.

template<class T>

bool RWGenFact< T >::fail

(

)

const

Returns true if the factorization fails, perhaps due to singularity, otherwise returns false.

template<class T>

bool RWGenFact< T >::good

(

)

const [inline]

Returns true if the factorization succeeds.

template<class T>

bool RWGenFact< T >::isSingular

(

)

const

Checks to see if the matrix is singular. If isSingular() returns a non-zero value, the matrix is singular. Note that the LU factorization is still defined; however, an attempt to use it to compute the matrix inverse fails.

---

Friends And Related Function Documentation

template<class T >

double condition

(

const RWGenMat< T > &

A

)

[related]

Returns the inverse condition number of matrix A

template<class T >

double condition

(

const RWGenFact< T > &

A

)

[related]

Returns the inverse condition number of the matrix whose LU factorization is A.

template<class T >

T determinant

(

const RWGenFact< T > &

A

)

[related]

Returns the determinant of the matrix from which an LU factorization A is constructed.

template<class T >

RWGenMat< T > inverse

(

const RWGenMat< T > &

A

)

[related]

Returns the inverse of the matrix from which an existing LU factorization was constructed. If the factorization of A is invalid, perhaps because the original matrix was singular, an exception with value LPAK_CANTSOLVE occurs.

template<class T >

RWGenMat< T > inverse

(

const RWGenFact< T > &

A

)

[related]

Returns the inverse of the matrix from which an existing LU factorization was constructed. If the factorization A is invalid, perhaps because the original matrix was singular, an exception with value LPAK_CANTSOLVE occurs.

template<class T >

RWGenMat< T > solve	(	const RWGenMat< T > &	A,
		const RWGenMat< T > &	b
	)			[related]

Calculates the solution to .

template<class T >

RWGenMat< T > solve	(	const RWGenFact< T > &	m,
		const RWGenMat< T > &	b
	)			[related]

Calculates the solution to , where b is an LU factorization constructed from the RWGenMat<T> A.

If the factorization m is invalid, perhaps because the original matrix A was singular, an exception with value LPAK_CANTSOLVE occurs. If the number of elements in x does not match the order of A, an exception with value LPAK_VECLENGTH occurs.

template<class T >

RWMathVec< T > solve	(	const RWGenMat< T > &	A,
		const RWMathVec< T > &	b
	)			[related]

Calculates the solution to .

template<class T >

RWMathVec< T > solve	(	const RWGenFact< T > &	m,
		const RWMathVec< T > &	b
	)			[related]

Calculates the solution to , where m is an LU factorization constructed from the RWGenMat<T> A.

If the factorization m is invalid, perhaps because the original matrix A was singular, an exception with value LPAK_CANTSOLVE occurs. If the number of elements in x does not match the order of A, an exception with value LPAK_VECLENGTH occurs.