RWHermFact< TypeT > Class Template Reference

Encapsulates factorizations of Hermitian matrices. More...

#include <rw/lapack/hermfct.h>

Public Member Functions
	RWHermFact ()
	RWHermFact (const RWHermMat< TypeT > &A, bool estimateCondition=true)
int	cols () const
double	condition () const
TypeT	determinant () const
void	factor (const RWHermMat< TypeT > &A, bool estimateCondition=true)
bool	fail () const
bool	good () const
RWHermMat< TypeT >	inverse () const
bool	isSingular () const
int	rows () const
RWGenMat< TypeT >	solve (const RWGenMat< TypeT > &b) const
RWMathVec< TypeT >	solve (const RWMathVec< TypeT > &b) const

Related Symbols
(Note that these are not member symbols.)
template<class TypeT >
double	condition (const RWHermFact< TypeT > &A)
template<class TypeT >
TypeT	determinant (const RWHermFact< TypeT > &A)
template<class TypeT >
RWHermMat< TypeT >	inverse (const RWHermFact< TypeT > &A)
template<class TypeT >
RWGenMat< TypeT >	solve (const RWHermFact< TypeT > &A, const RWGenMat< TypeT > &b)
template<class TypeT >
RWMathVec< TypeT >	solve (const RWHermFact< TypeT > &A, const RWMathVec< TypeT > &b)

Detailed Description

template<class TypeT>
class RWHermFact< 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 RWHermFact encapsulates factorizations of Hermitian 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/hermfct.h>
 
RWHermFact<DComplex> LU3(C);  // C is a RWHermMat<DComplex>

Example

#include <rw/lapack/hermfct.h>
#include <rw/lapack/hermmat.h>
#include <iostream>
 
int main() {
  // Read in a matrix and a right-hand side and
  // print the solution
  RWHermMat<DComplex> A;
  RWMathVec<DComplex> b;
  std::cin >> A >> b;
  RWHermFact<DComplex> HF(A);
  if (HF.good()) {
    std::cout << "solution is " << solve(HF, b) << std::endl;
  } else {
    std::cout << "Could not factor A, perhaps it is singular"
              << std::endl;
  }
  return 0;
}

Constructor & Destructor Documentation

RWHermFact() [1/2]

template<class TypeT >

RWHermFact< TypeT >::RWHermFact

(

)

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

RWHermFact() [2/2]

template<class TypeT >

RWHermFact< TypeT >::RWHermFact	(	const RWHermMat< 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

cols()

template<class TypeT >

int RWHermFact< TypeT >::cols ( ) const

inline

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

condition()

template<class TypeT >

double RWHermFact< 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 the RWHermFact() or factor() to false, calling condition() generates an exception.

determinant()

template<class TypeT >

TypeT RWHermFact< TypeT >::determinant

(

)

const

Calculates the determinant of the matrix represented by this factorization.

factor()

template<class TypeT >

void RWHermFact< TypeT >::factor	(	const RWHermMat< 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.

fail()

template<class TypeT >

bool RWHermFact< 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.

good()

template<class TypeT >

bool RWHermFact< 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.

inverse()

template<class TypeT >

RWHermMat< TypeT > RWHermFact< TypeT >::inverse

(

)

const

Computes the inverse of the matrix represented by this factorization. Although matrix inverses are very useful in theoretical analysis, they are rarely necessary in implementation. A factorization is nearly always as useful as the actual inverse, and can be constructed at far less cost.

isSingular()

template<class TypeT >

bool RWHermFact< 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.

rows()

template<class TypeT >

int RWHermFact< TypeT >::rows ( ) const

inline

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

solve() [1/2]

template<class TypeT >

RWGenMat< TypeT > RWHermFact< 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.

solve() [2/2]

template<class TypeT >

RWMathVec< TypeT > RWHermFact< 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.

Friends And Related Symbol Documentation

condition()

template<class TypeT >

double condition ( const RWHermFact< 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 the RWHermFact() or factor() member function to false, calling condition() generates an exception.

determinant()

template<class TypeT >

TypeT determinant ( const RWHermFact< TypeT > & A )

related

Calculates the determinant of the matrix represented by the factorization A

inverse()

template<class TypeT >

RWHermMat< TypeT > inverse ( const RWHermFact< TypeT > & A )

related

Computes the inverse of the matrix represented by this factorization. Although matrix inverses are very useful in theoretical analysis, they are rarely necessary in implementation. A factorization is nearly always as useful as the actual inverse, and can be constructed at far less cost.

solve() [1/2]

template<class TypeT >

RWGenMat< TypeT > solve ( const RWHermFact< 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.

solve() [2/2]

template<class TypeT >

RWMathVec< TypeT > solve ( const RWHermFact< 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.