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