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<?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
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