TNT::Linear_Algebra::Cholesky< Real > Class Template Reference

#include <tnt_linalg.h>

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

Detailed Description

template<class Real>
class TNT::Linear_Algebra::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:

 Matrix<double> A(n,n);
 Matrix<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()

template<class Real >

TNT::Linear_Algebra::Cholesky< Real >::Cholesky

(

const Matrix< 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

getL()

template<class Real >

Matrix< Real > TNT::Linear_Algebra::Cholesky< Real >::getL

(

)

const

Returns

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

is_spd()

template<class Real >

int TNT::Linear_Algebra::Cholesky< Real >::is_spd

(

)

const

Returns

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

solve() [1/2]

template<class Real >

Matrix< Real > TNT::Linear_Algebra::Cholesky< Real >::solve

(

const Matrix< 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 (Real(0.0)) array is returned.

solve() [2/2]

template<class Real >

Vector< Real > TNT::Linear_Algebra::Cholesky< Real >::solve

(

const Vector< Real > &

b

)

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

Parameters

b	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 (Real(0.0)) array is returned.

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

• tnt_linalg.h