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JAMA::Cholesky Class Template Reference

#include <jama_cholesky.h>

List of all members.

Public Methods
	Cholesky ()
	Cholesky (const Array2D< Real > &A)
Array2D<Real>	getL () const
Array1D<Real>	solve (const Array1D< Real > &B)
Array2D<Real>	solve (const Array2D< Real > &B)
int	is_spd () const
	Cholesky ()
	Cholesky (const TNT::Array2D< Real > &A)
TNT::Array2D<Real>	getL () const
int	is_spd () const

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Detailed Description

template<class Real> class JAMA::Cholesky

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).

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Constructor & Destructor Documentation

template<class Real> JAMA::Cholesky< Real >::Cholesky<Real> ( )

template<class Real> JAMA::Cholesky< Real >::Cholesky<Real> ( const Array2D< Real > & 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.

template<class Real> JAMA::Cholesky< Real >::Cholesky<Real> ( )

template<class Real> JAMA::Cholesky< Real >::Cholesky<Real> ( const TNT::Array2D< Real > & 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.

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Member Function Documentation

template<class Real> TNT::Array2D< Real > JAMA::Cholesky< Real >::getL ( ) const

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

template<class Real> TNT::Array2D< Real > JAMA::Cholesky< Real >::getL ( ) const

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

template<class Real> int JAMA::Cholesky< Real >::is_spd ( ) const

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

template<class Real> int JAMA::Cholesky< Real >::is_spd ( ) const

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

template<class Real> Array2D< Real > JAMA::Cholesky< Real >::solve ( const Array2D< Real > & B )

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 Real> Array1D< Real > JAMA::Cholesky< Real >::solve ( const Array1D< Real > & b )

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.

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

• jama_cholesky.h
• jama_cholesky_old.h

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