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| author | Anton Luka Šijanec <anton@sijanec.eu> | 2022-01-11 12:35:47 +0100 |
|---|---|---|
| committer | Anton Luka Šijanec <anton@sijanec.eu> | 2022-01-11 12:35:47 +0100 |
| commit | 19985dbb8c0aa66dc4bf7905abc1148de909097d (patch) | |
| tree | 2cd5a5d20d7e80fc2a51adf60d838d8a2c40999e /admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php | |
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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, 182 insertions, 0 deletions
diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php new file mode 100644 index 0000000..8a66903 --- /dev/null +++ b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/MagicSquareExample.php @@ -0,0 +1,182 @@ +<?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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