Essentia  2.1-beta5-dev
Cholesky< Real > Class Template Reference

#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).

## ◆ 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.

## ◆ getL()

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

References Cholesky< Real >::L_.

## ◆ is_spd()

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

References Cholesky< Real >::isspd.

## ◆ 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.

## ◆ 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.

## ◆ isspd

 int isspd
private

## ◆ L_

 Array2D L_
private

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