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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

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).

Constructor & Destructor Documentation

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

 template JAMA::Cholesky< Real >::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.

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

 template JAMA::Cholesky< Real >::Cholesky ( 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.

Member Function Documentation

 template TNT::Array2D< Real > JAMA::Cholesky< Real >::getL ( ) const
 Returns: the lower triangular factor, L, such that L*L'=A.

 template TNT::Array2D< Real > JAMA::Cholesky< Real >::getL ( ) const
 Returns: the lower triangular factor, L, such that L*L'=A.

 template int JAMA::Cholesky< Real >::is_spd ( ) const
 Returns: 1, if original matrix to be factored was symmetric positive-definite (SPD).

 template int JAMA::Cholesky< Real >::is_spd ( ) const
 Returns: 1, if original matrix to be factored was symmetric positive-definite (SPD).

 template 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 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.

The documentation for this class was generated from the following files:
Generated at Mon Jan 20 07:47:18 2003 for JAMA/C++ by 1.2.5 written by Dimitri van Heesch, © 1997-2001