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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 singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'. The singular values, sigma[$k] = S[$k][$k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1]. The singular value decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
    author Paul Meagher
    license PHP v3.0
    version 1.1

     Methods

    Construct the singular value decomposition

    __construct($Arg) : \Structure

    Derived from LINPACK code.

    Parameters

    $Arg

    Returns

    \Structureto access U, S and V.

    Two norm condition number

    cond() : \max(S)/min(S)
    access public

    Returns

    \max(S)/min(S)

    Return the diagonal matrix of singular values

    getS() : \S
    access public

    Returns

    \S

    Return the one-dimensional array of singular values

    getSingularValues() : \diagonal
    access public

    Returns

    \diagonalof S.

    Return the left singular vectors

    getU() : \U
    access public

    Returns

    \U

    Return the right singular vectors

    getV() : \V
    access public

    Returns

    \V

    Two norm

    norm2() : \max(S)
    access public

    Returns

    \max(S)

    Effective numerical matrix rank

    rank() : \Number
    access public

    Returns

    \Numberof nonnegligible singular values.

     Properties

     

    $U : array
     

    $V : array
     

    $m : int
     

    $n : int
     

    $s : array