Cholesky< ValueType > Class Template Reference

#include <Cholesky.h>

Public Member Functions
	Cholesky (const Matrix &A)
Matrix	getL () const
Vector	solve (const Vector &b)
Matrix	solve (const Matrix &B)
int	is_spd () const

Detailed Description

template<class ValueType>
class Cholesky< ValueType >

For a symmetric, positive definite matrix A, this function computes the Cholesky factorization, i.e. it computes a lower triangular matrix L such that A = L*L'. If the matrix is not symmetric or positive definite, the function computes only a partial decomposition. This can be tested with the is_spd() flag.

Typical usage looks like:

     Array2D<double> A(n,n);
     Array2D<double> L;

      ...

     Cholesky<double> chol(A);

     if (chol.is_spd())
        L = chol.getL();

     else
        cout << "factorization was not complete.\n";

(Adapted from JAMA, a Java Matrix Library, developed by jointly by the Mathworks and NIST; see http://math.nist.gov/javanumerics/jama).

Constructor & Destructor Documentation

template<class ValueType >

Cholesky< ValueType >::Cholesky

(

const Matrix &

A

)

Constructs a lower triangular matrix L, such that L*L'= A. If A is not symmetric positive-definite (SPD), only a partial factorization is performed. If is_spd() evalutate true (1) then the factorizaiton was successful.

Member Function Documentation

template<class ValueType>

Matrix Cholesky< ValueType >::getL ( ) const

inline

Returns

the lower triangular factor, L, such that L*L'=A.

Referenced by CMDS< ValueType >::CMDS().

template<class ValueType>

int Cholesky< ValueType >::is_spd ( ) const

inline

Returns

1, if original matrix to be factored was symmetric positive-definite (SPD).

template<class ValueType>

Vector Cholesky< ValueType >::solve ( const Vector &  b )

inline

Solve a linear system A*x = b, using the previously computed cholesky factorization of A: L*L'.

Parameters

B	A Matrix with as many rows as A and any number of columns.

Returns

x so that L*L'*x = b. If b is nonconformat, or if A was not symmetric posidtive definite, a null (0x0) array is returned.

template<class ValueType>

Matrix Cholesky< ValueType >::solve ( const Matrix &  B )

inline

Solve a linear system A*X = B, using the previously computed cholesky factorization of A: L*L'.

Parameters

B	A Matrix with as many rows as A and any number of columns.

Returns

X so that L*L'*X = B. If B is nonconformat, or if A was not symmetric posidtive definite, a null (0x0) array is returned.