#include <jama_cholesky.h>

Public Member Functions
	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

Private Attributes
Array2D< Real >	L_

int	isspd

Detailed Description

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

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

◆ Cholesky() [1/2]

Cholesky

◆ Cholesky() [2/2]

Cholesky ( 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.

References Array2D< T >::dim1(), and Array2D< T >::dim2().

Member Function Documentation

◆ getL()

Array2D< Real > getL

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

◆ is_spd()

int is_spd

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

◆ solve() [1/2]

Array1D< 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.

References Array1D< T >::copy(), and Array1D< T >::dim1().

◆ solve() [2/2]

Array2D< 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.

References Array2D< T >::copy(), Array1D< T >::dim1(), Array2D< T >::dim1(), and Array2D< T >::dim2().

Member Data Documentation

◆ isspd

int isspd

private

◆ L_

Array2D<Real> L_