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

`#include <jama_lu.h>`

## Public Member Functions

LU (const Array2D< Real > &A)

int isNonsingular ()

Array2D< Real > getL ()

Array2D< Real > getU ()

Array1D< int > getPivot ()

Real det ()

Array2D< Real > solve (const Array2D< Real > &B)

Array1D< Real > solve (const Array1D< Real > &b)

## Private Member Functions

Array2D< Real > permute_copy (const Array2D< Real > &A, const Array1D< int > &piv, int j0, int j1)

Array1D< Real > permute_copy (const Array1D< Real > &A, const Array1D< int > &piv)

## Private Attributes

Array2D< Real > LU_

int m

int n

int pivsign

Array1D< int > piv

## Detailed Description

### template<class Real> class JAMA::LU< Real >

LU Decomposition.

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

## ◆ LU()

 LU ( const Array2D< Real > & A )
inline

LU Decomposition

Parameters
 A Rectangular matrix
Returns
LU Decomposition object to access L, U and piv.

## ◆ det()

 Real det ( )
inline

Compute determinant using LU factors.

Returns
determinant of A, or 0 if A is not square.

## ◆ getL()

 Array2D getL ( )
inline

Return lower triangular factor

Returns
L

## ◆ getPivot()

 Array1D getPivot ( )
inline

Return pivot permutation vector

Returns
piv

## ◆ getU()

 Array2D getU ( )
inline

Return upper triangular factor

Returns
U portion of LU factorization.

## ◆ isNonsingular()

 int isNonsingular ( )
inline

Is the matrix nonsingular?

Returns
1 (true) if upper triangular factor U (and hence A) is nonsingular, 0 otherwise.

## ◆ permute_copy() [1/2]

 Array2D permute_copy ( const Array2D< Real > & A, const Array1D< int > & piv, int j0, int j1 )
inlineprivate

References Array1D< T >::dim().

## ◆ permute_copy() [2/2]

 Array1D permute_copy ( const Array1D< Real > & A, const Array1D< int > & piv )
inlineprivate

References Array1D< T >::dim().

## ◆ solve() [1/2]

 Array2D solve ( const Array2D< Real > & B )
inline

Solve A*X = B

Parameters
 B A Matrix with as many rows as A and any number of columns.
Returns
X so that L*U*X = B(piv,:), if B is nonconformant, returns 0x0 (null) array.

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

## ◆ solve() [2/2]

 Array1D solve ( const Array1D< Real > & b )
inline

Solve A*x = b, where x and b are vectors of length equal to the number of rows in A.

Parameters
 b a vector (Array1D> of length equal to the first dimension of A.
Returns
x a vector (Array1D> so that L*U*x = b(piv), if B is nonconformant, returns 0x0 (null) array.

References Array1D< T >::dim1().

## ◆ LU_

 Array2D LU_
private

 int m
private

 int n
private

## ◆ piv

 Array1D piv
private

## ◆ pivsign

 int pivsign
private

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