/**
* Build the polynom based on the given points.
*
* @return void
*/
protected function buildPolynom()
{
$points = array();
foreach ($this->source as $key => $value) {
if (!is_numeric($key)) {
throw new ezcGraphDatasetAverageInvalidKeysException();
}
if ($this->min === false || $this->min > $key) {
$this->min = (double) $key;
}
if ($this->max === false || $this->max < $key) {
$this->max = (double) $key;
}
$points[] = new ezcGraphCoordinate((double) $key, (double) $value);
}
// Build transposed and normal Matrix out of coordiantes
$a = new ezcGraphMatrix(count($points), $this->polynomOrder + 1);
$b = new ezcGraphMatrix(count($points), 1);
for ($i = 0; $i <= $this->properties['polynomOrder']; ++$i) {
foreach ($points as $nr => $point) {
$a->set($nr, $i, pow($point->x, $i));
$b->set($nr, 0, $point->y);
}
}
$at = clone $a;
$at->transpose();
$left = $at->multiply($a);
$right = $at->multiply($b);
$this->polynom = $left->solveNonlinearEquatation($right);
}
public function testSolveNonlinearEquatation()
{
if (version_compare(phpversion(), '5.2.1', '<')) {
$this->markTestSkipped("This test is only for PHP after 5.2.1. See PHP bug #40482.");
}
$a = new ezcGraphMatrix(3, 3, array(array(5, 4, 7), array(2, 12, 8), array(3, 6, 10)));
$b = new ezcGraphMatrix(3, 1, array(array(1, 2, 3)));
$polynom = $a->solveNonlinearEquatation($b);
$this->assertEquals('-1.15e-1 x^2 + 1.92e-2 x + 3.46e-1', $polynom->__toString());
}
/**
* Build LR decomposition from matrix
*
* Use Cholesky-Crout algorithm to get LR decomposition of the current
* matrix.
*
* Will return an array with two matrices:
* array(
* 'l' => (ezcGraphMatrix) $left,
* 'r' => (ezcGraphMatrix) $right,
* )
*
* @return array( ezcGraphMatrix )
*/
public function LRdecomposition()
{
/**
* Use Cholesky-Crout algorithm to get LR decomposition
*
* Input: Matrix A ($this)
*
* For i = 1 To n
* For j = i To n
* R(i,j)=A(i,j)
* For k = 1 TO i-1
* R(i,j)-=L(i,k)*R(k,j)
* end
* end
* For j=i+1 To n
* L(j,i)= A(j,i)
* For k = 1 TO i-1
* L(j,i)-=L(j,k)*R(k,i)
* end
* L(j,i)/=R(i,i)
* end
* end
*
* Output: matrices L,R
*/
$l = new ezcGraphMatrix($this->columns, $this->rows);
$r = new ezcGraphMatrix($this->columns, $this->rows);
for ($i = 0; $i < $this->columns; ++$i) {
for ($j = $i; $j < $this->rows; ++$j) {
$r->set($i, $j, $this->matrix[$i][$j]);
for ($k = 0; $k <= $i - 1; ++$k) {
$r->set($i, $j, $r->get($i, $j) - $l->get($i, $k) * $r->get($k, $j));
}
}
for ($j = $i + 1; $j < $this->rows; ++$j) {
$l->set($j, $i, $this->matrix[$j][$i]);
for ($k = 0; $k <= $i - 1; ++$k) {
$l->set($j, $i, $l->get($j, $i) - $l->get($j, $k) * $r->get($k, $i));
}
$l->set($j, $i, $l->get($j, $i) / $r->get($i, $i));
}
}
return array('l' => $l, 'r' => $r);
}
/**
* Transform a coordinate with the current transformation matrix.
*
* @param ezcGraphCoordinate $coordinate
* @return ezcGraphCoordinate
*/
public function transformCoordinate(ezcGraphCoordinate $coordinate)
{
$vector = new ezcGraphMatrix(3, 1, array(array($coordinate->x), array($coordinate->y), array(1)));
$vector = parent::multiply($vector);
return new ezcGraphCoordinate($vector->get(0, 0), $vector->get(1, 0));
}
