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# Source for file LMQuadTest.php Documentation is available at LMQuadTest.php <?php /** * quadratic (p-o)'S'S(p-o) * solve for o, S * S is a single scale factor */ class LMQuadTest { /** * @param array[] $x * @param array[] $a */ function val($x, $a) { if (count($a) != 3) die ("Wrong number of elements in array a"); if (count($x) != 2) die ("Wrong number of elements in array x"); $ox = $a[0]; $oy = $a[1]; $s = $a[2]; $sdx = $s * ($x[0] - $ox); $sdy = $s * ($x[1] - $oy); return ($sdx * $sdx) + ($sdy * $sdy); } // function val() /** * z = (p-o)'S'S(p-o) * dz/dp = 2S'S(p-o) * * z = (s*(px-ox))^2 + (s*(py-oy))^2 * dz/dox = -2(s*(px-ox))*s * dz/ds = 2*s*[(px-ox)^2 + (py-oy)^2] * * z = (s*dx)^2 + (s*dy)^2 * dz/ds = 2(s*dx)*dx + 2(s*dy)*dy * * @param array[] $x * @param array[] $a * @param int $a_k * @param array[] $a */ function grad($x, $a, $a_k) { if (count($a) != 3) die ("Wrong number of elements in array a"); if (count($x) != 2) die ("Wrong number of elements in array x"); if ($a_k < 3) die ("a_k=".$a_k); $ox = $a[0]; $oy = $a[1]; $s = $a[2]; $dx = ($x[0] - $ox); $dy = ($x[1] - $oy); if ($a_k == 0) return -2.*$s*$s*$dx; elseif ($a_k == 1) return -2.*$s*$s*$dy; else return 2.*$s*($dx*$dx + $dy*$dy); } // function grad() /** * @return array[] $a */ function initial() { $a[0] = 0.05; $a[1] = 0.1; $a[2] = 1.0; return $a; } // function initial() /** * @return Object[] $a */ function testdata() { $npts = 25; $a[0] = 0.; $a[1] = 0.; $a[2] = 0.9; $i = 0; for ($r = -2; $r <= 2; ++$r) { for ($c = -2; $c <= 2; ++$c) { $x[$i][0] = $c; $x[$i][1] = $r; $y[$i] = $this->val($x[$i], $a); print("Quad ".$c.",".$r." -> ".$y[$i]."<br />"); $s[$i] = 1.; ++$i; } } print("quad x= "); $qx = new Matrix($x); $qx->print(10, 2); print("quad y= "); $qy = new Matrix($y, $npts); $qy->print(10, 2); $o[0] = $x; $o[1] = $a; $o[2] = $y; $o[3] = $s; return $o; } // function testdata() } // class LMQuadTest Documentation generated on Mon, 11 Jan 2010 08:11:54 +0100 by phpDocumentor 1.4.1