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当前路径:Classes/PHPExcel/Shared/JAMA/SingularValueDecomposition.php
<?php
/**
 *    @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
 */
class SingularValueDecomposition
{
    /**
     *    Internal storage of U.
     *    @var array
     */
    private $U = array();

    /**
     *    Internal storage of V.
     *    @var array
     */
    private $V = array();

    /**
     *    Internal storage of singular values.
     *    @var array
     */
    private $s = array();

    /**
     *    Row dimension.
     *    @var int
     */
    private $m;

    /**
     *    Column dimension.
     *    @var int
     */
    private $n;

    /**
     *    Construct the singular value decomposition
     *
     *    Derived from LINPACK code.
     *
     *    @param $A Rectangular matrix
     *    @return Structure to access U, S and V.
     */
    public function __construct($Arg)
    {
        // Initialize.
        $A = $Arg->getArrayCopy();
        $this->m = $Arg->getRowDimension();
        $this->n = $Arg->getColumnDimension();
        $nu      = min($this->m, $this->n);
        $e       = array();
        $work    = array();
        $wantu   = true;
        $wantv   = true;
        $nct = min($this->m - 1, $this->n);
        $nrt = max(0, min($this->n - 2, $this->m));

        // Reduce A to bidiagonal form, storing the diagonal elements
        // in s and the super-diagonal elements in e.
        for ($k = 0; $k < max($nct, $nrt); ++$k) {
            if ($k < $nct) {
                // Compute the transformation for the k-th column and
                // place the k-th diagonal in s[$k].
                // Compute 2-norm of k-th column without under/overflow.
                $this->s[$k] = 0;
                for ($i = $k; $i < $this->m; ++$i) {
                    $this->s[$k] = hypo($this->s[$k], $A[$i][$k]);
                }
                if ($this->s[$k] != 0.0) {
                    if ($A[$k][$k] < 0.0) {
                        $this->s[$k] = -$this->s[$k];
                    }
                    for ($i = $k; $i < $this->m; ++$i) {
                        $A[$i][$k] /= $this->s[$k];
                    }
                    $A[$k][$k] += 1.0;
                }
                $this->s[$k] = -$this->s[$k];
            }

            for ($j = $k + 1; $j < $this->n; ++$j) {
                if (($k < $nct) & ($this->s[$k] != 0.0)) {
                    // Apply the transformation.
                    $t = 0;
                    for ($i = $k; $i < $this->m; ++$i) {
                        $t += $A[$i][$k] * $A[$i][$j];
                    }
                    $t = -$t / $A[$k][$k];
                    for ($i = $k; $i < $this->m; ++$i) {
                        $A[$i][$j] += $t * $A[$i][$k];
                    }
                    // Place the k-th row of A into e for the
                    // subsequent calculation of the row transformation.
                    $e[$j] = $A[$k][$j];
                }
            }

            if ($wantu and ($k < $nct)) {
                // Place the transformation in U for subsequent back
                // multiplication.
                for ($i = $k; $i < $this->m; ++$i) {
                    $this->U[$i][$k] = $A[$i]...
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