Main Page   Namespace List   Compound List   File List   Compound Members

# JAMA::LU Class Template Reference

`#include <jama_lu.h>`

List of all members.

## Public Methods

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)

## Detailed Description

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

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.

## Constructor & Destructor Documentation

 template JAMA::LU::LU ( const Array2D< Real > & A )` [inline]`

LU Decomposition

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

## Member Function Documentation

 template Real JAMA::LU::det ( )` [inline]`
 Compute determinant using LU factors. Returns: determinant of A, or 0 if A is not square.

 template Array2D< Real > JAMA::LU::getL ( )` [inline]`
 Return lower triangular factor Returns: L

 template Array1D< int > JAMA::LU::getPivot ( )` [inline]`
 Return pivot permutation vector Returns: piv

 template Array2D< Real > JAMA::LU::getU ( )` [inline]`
 Return upper triangular factor Returns: U portion of LU factorization.

 template int JAMA::LU::isNonsingular ( )` [inline]`
 Is the matrix nonsingular? Returns: 1 (true) if upper triangular factor U (and hence A) is nonsingular, 0 otherwise.

 template Array1D< Real > JAMA::LU::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.

 template Array2D< Real > JAMA::LU::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.

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