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  •  JAMA Pythagorean Theorem: a = 3 b = 4 r = sqrt(square(a) + square(b)) r = 5 r = sqrt(a^2 + b^2) without under/overflow
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    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