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Diffstat (limited to 'admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php')
| -rw-r--r-- | admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php | 182 |
1 files changed, 0 insertions, 182 deletions
diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php deleted file mode 100644 index 8a66903..0000000 --- a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php +++ /dev/null @@ -1,182 +0,0 @@ -<?php
-/**
-* @package JAMA
-*/
-
-require_once "../Matrix.php";
-
-/**
-* Example of use of Matrix Class, featuring magic squares.
-*/
-class MagicSquareExample {
-
- /**
- * Generate magic square test matrix.
- * @param int n dimension of matrix
- */
- function magic($n) {
-
- // Odd order
-
- if (($n % 2) == 1) {
- $a = ($n+1)/2;
- $b = ($n+1);
- for ($j = 0; $j < $n; ++$j)
- for ($i = 0; $i < $n; ++$i)
- $M[$i][$j] = $n*(($i+$j+$a) % $n) + (($i+2*$j+$b) % $n) + 1;
-
- // Doubly Even Order
-
- } else if (($n % 4) == 0) {
- for ($j = 0; $j < $n; ++$j) {
- for ($i = 0; $i < $n; ++$i) {
- if ((($i+1)/2)%2 == (($j+1)/2)%2)
- $M[$i][$j] = $n*$n-$n*$i-$j;
- else
- $M[$i][$j] = $n*$i+$j+1;
- }
- }
-
- // Singly Even Order
-
- } else {
-
- $p = $n/2;
- $k = ($n-2)/4;
- $A = $this->magic($p);
- $M = array();
- for ($j = 0; $j < $p; ++$j) {
- for ($i = 0; $i < $p; ++$i) {
- $aij = $A->get($i,$j);
- $M[$i][$j] = $aij;
- $M[$i][$j+$p] = $aij + 2*$p*$p;
- $M[$i+$p][$j] = $aij + 3*$p*$p;
- $M[$i+$p][$j+$p] = $aij + $p*$p;
- }
- }
-
- for ($i = 0; $i < $p; ++$i) {
- for ($j = 0; $j < $k; ++$j) {
- $t = $M[$i][$j];
- $M[$i][$j] = $M[$i+$p][$j];
- $M[$i+$p][$j] = $t;
- }
- for ($j = $n-$k+1; $j < $n; ++$j) {
- $t = $M[$i][$j];
- $M[$i][$j] = $M[$i+$p][$j];
- $M[$i+$p][$j] = $t;
- }
- }
-
- $t = $M[$k][0]; $M[$k][0] = $M[$k+$p][0]; $M[$k+$p][0] = $t;
- $t = $M[$k][$k]; $M[$k][$k] = $M[$k+$p][$k]; $M[$k+$p][$k] = $t;
-
- }
-
- return new Matrix($M);
-
- }
-
- /**
- * Simple function to replicate PHP 5 behaviour
- */
- function microtime_float() {
- list($usec, $sec) = explode(" ", microtime());
- return ((float)$usec + (float)$sec);
- }
-
- /**
- * Tests LU, QR, SVD and symmetric Eig decompositions.
- *
- * n = order of magic square.
- * trace = diagonal sum, should be the magic sum, (n^3 + n)/2.
- * max_eig = maximum eigenvalue of (A + A')/2, should equal trace.
- * rank = linear algebraic rank, should equal n if n is odd,
- * be less than n if n is even.
- * cond = L_2 condition number, ratio of singular values.
- * lu_res = test of LU factorization, norm1(L*U-A(p,:))/(n*eps).
- * qr_res = test of QR factorization, norm1(Q*R-A)/(n*eps).
- */
- function main() {
- ?>
- <p>Test of Matrix Class, using magic squares.</p>
- <p>See MagicSquareExample.main() for an explanation.</p>
- <table border='1' cellspacing='0' cellpadding='4'>
- <tr>
- <th>n</th>
- <th>trace</th>
- <th>max_eig</th>
- <th>rank</th>
- <th>cond</th>
- <th>lu_res</th>
- <th>qr_res</th>
- </tr>
- <?php
- $start_time = $this->microtime_float();
- $eps = pow(2.0,-52.0);
- for ($n = 3; $n <= 6; ++$n) {
- echo "<tr>";
-
- echo "<td align='right'>$n</td>";
-
- $M = $this->magic($n);
- $t = (int) $M->trace();
-
- echo "<td align='right'>$t</td>";
-
- $O = $M->plus($M->transpose());
- $E = new EigenvalueDecomposition($O->times(0.5));
- $d = $E->getRealEigenvalues();
-
- echo "<td align='right'>".$d[$n-1]."</td>";
-
- $r = $M->rank();
-
- echo "<td align='right'>".$r."</td>";
-
- $c = $M->cond();
-
- if ($c < 1/$eps)
- echo "<td align='right'>".sprintf("%.3f",$c)."</td>";
- else
- echo "<td align='right'>Inf</td>";
-
- $LU = new LUDecomposition($M);
- $L = $LU->getL();
- $U = $LU->getU();
- $p = $LU->getPivot();
- // Java version: R = L.times(U).minus(M.getMatrix(p,0,n-1));
- $S = $L->times($U);
- $R = $S->minus($M->getMatrix($p,0,$n-1));
- $res = $R->norm1()/($n*$eps);
-
- echo "<td align='right'>".sprintf("%.3f",$res)."</td>";
-
- $QR = new QRDecomposition($M);
- $Q = $QR->getQ();
- $R = $QR->getR();
- $S = $Q->times($R);
- $R = $S->minus($M);
- $res = $R->norm1()/($n*$eps);
-
- echo "<td align='right'>".sprintf("%.3f",$res)."</td>";
-
- echo "</tr>";
-
- }
- echo "<table>";
- echo "<br />";
-
- $stop_time = $this->microtime_float();
- $etime = $stop_time - $start_time;
-
- echo "<p>Elapsed time is ". sprintf("%.4f",$etime) ." seconds.</p>";
-
- }
-
-}
-
-$magic = new MagicSquareExample();
-$magic->main();
-
-?>
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