LMQuadTest Class Reference

quadratic (p-o)'S'S(p-o) solve for o, S S is a single scale factor More...

Collaboration diagram for LMQuadTest:

Public Member Functions
	val ($x, $a)
	grad ($x, $a, $a_k)
	z = (p-o)'S'S(p-o) dz/dp = 2S'S(p-o)
	initial ()
	testdata ()

Detailed Description

quadratic (p-o)'S'S(p-o) solve for o, S S is a single scale factor

Definition at line 7 of file LMQuadTest.php.

Member Function Documentation

LMQuadTest::grad	(		$x,
			$a,
			$a_k
	)

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

Parameters

	array[]	$x
	array[]	$a
int	$a_k
	array[]	$a

Definition at line 44 of file LMQuadTest.php.

References $x.

                                    {
                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()

LMQuadTest::initial

(

)

Returns

array[] $a

Definition at line 68 of file LMQuadTest.php.

                           {
                $a[0] = 0.05;
                $a[1] = 0.1;
                $a[2] = 1.0;

                return $a;
        }       //      function initial()

LMQuadTest::testdata

(

)

Returns

Object[] $a

Definition at line 80 of file LMQuadTest.php.

References $x, $y, and val().

                            {
                $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()

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LMQuadTest::val	(		$x,
			$a
	)

Parameters

array[]	$x
array[]	$a

Definition at line 13 of file LMQuadTest.php.

References $x.

Referenced by testdata().

                             {
                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()

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The documentation for this class was generated from the following file:

• Services/Excel/PHPExcel/1.7.6/Classes/PHPExcel/Shared/JAMA/examples/LMQuadTest.php