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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 QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R. The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.
    author Paul Meagher
    license PHP v3.0
    version 1.1

     Methods

    QR Decomposition computed by Householder reflections.

    __construct(\matrix $A) : \Structure

    Parameters

    $A

    \matrix

    Rectangular matrix

    Returns

    \Structureto access R and the Householder vectors and compute Q.

    Return the Householder vectors

    getH() : \Matrix

    Returns

    \MatrixLower trapezoidal matrix whose columns define the reflections

    Generate and return the (economy-sized) orthogonal factor

    getQ() : \Matrix

    Returns

    \Matrixorthogonal factor

    Return the upper triangular factor

    getR() : \Matrix

    Returns

    \Matrixupper triangular factor

    Is the matrix full rank?

    isFullRank() : boolean

    Returns

    booleantrue if R, and hence A, has full rank, else false.

    Least squares solution of A*X = B

    solve(\Matrix $B) : \Matrix

    Parameters

    $B

    \Matrix

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

    Returns

    \MatrixMatrix that minimizes the two norm of Q*R*X-B.

     Properties

     

    $QR : array
     

    $Rdiag : array
     

    $m : integer
     

    $n : integer

     Constants

     

    MatrixRankException

    MatrixRankException