/**
* 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>";
}
/**
* Solve A*X = B.
* @param Matrix $B Right hand side
* @return Matrix ... Solution if A is square, least squares solution otherwise
*/
function solve($B)
{
if ($this->m == $this->n) {
$LU = new LUDecomposition($this);
return $LU->solve($B);
} else {
$QR = new QRDecomposition($this);
return $QR->solve($B);
}
}
/**
* Solve A*X = B.
*
* @param Matrix $B Right hand side
* @return Matrix ... Solution if A is square, least squares solution otherwise
*/
public function solve($B)
{
if ($this->m == $this->n) {
$LU = new PHPExcel_Shared_JAMA_LUDecomposition($this);
return $LU->solve($B);
} else {
$QR = new QRDecomposition($this);
return $QR->solve($B);
}
}
