package JAMA 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.
author Paul Meagher
author Bartosz Matosiuk
author Michael Bommarito
version 1.1
license PHP v3.0

 Methods

LU Decomposition constructor.

__construct($A) : \Structure

Parameters

$A

Rectangular matrix

Returns

\Structureto access L, U and piv.

Count determinants

det() : array

Returns

arrayd matrix deterninat

Alias for getPivot

getDoublePivot() 
see \getPivot

Get lower triangular factor.

getL() : array

Returns

arrayLower triangular factor

Return pivot permutation vector.

getPivot() : array

Returns

arrayPivot vector

Get upper triangular factor.

getU() : array

Returns

arrayUpper triangular factor

Is the matrix nonsingular?

isNonsingular() : true

Returns

trueif U, and hence A, is nonsingular.

Solve A*X = B

solve($B) : \X
PHPExcel_Calculation_Exception IllegalArgumentException Matrix row dimensions must agree.
PHPExcel_Calculation_Exception RuntimeException Matrix is singular.

Parameters

$B

A Matrix with as many rows as A and any number of columns.

Returns

\Xso that L*U*X = B(piv,:)

 Properties

 

$LU : array
 

$m : int
 

$n : int
 

$piv : array
 

$pivsign : int

 Constants

 

MatrixSingularException

MatrixSingularException 
 

MatrixSquareException

MatrixSquareException