/**
* Solve nonlinear equatation
*
* Tries to solve equatation given by two matrices, with assumption, that:
* A * x = B
* where $this is A, and the paramenter B. x is cosnidered as a vector
* x = ( x^n, x^(n-1), ..., x^2, x, 1 )
*
* Will return a polynomial solution for x.
*
* See: http://en.wikipedia.org/wiki/Gauss-Newton_algorithm
*
* @param ezcGraphMatrix $matrix B
* @return ezcGraphPolygon Solution of equatation
*/
public function solveNonlinearEquatation(ezcGraphMatrix $matrix)
{
// Build complete equatation
$equatation = new ezcGraphMatrix($this->rows, $columns = $this->columns + 1);
for ($i = 0; $i < $this->rows; ++$i) {
for ($j = 0; $j < $this->columns; ++$j) {
$equatation->set($i, $j, $this->matrix[$i][$j]);
}
$equatation->set($i, $this->columns, $matrix->get($i, 0));
}
// Compute upper triangular matrix on left side of equatation
for ($i = 0; $i < $this->rows - 1; ++$i) {
for ($j = $i + 1; $j < $this->rows; ++$j) {
if ($equatation->get($j, $i) !== 0) {
if ($equatation->get($j, $i) == 0) {
continue;
} else {
$factor = -($equatation->get($i, $i) / $equatation->get($j, $i));
}
for ($k = $i; $k < $columns; ++$k) {
$equatation->set($j, $k, $equatation->get($i, $k) + $factor * $equatation->get($j, $k));
}
}
}
}
// Normalize values on left side matrix diagonale
for ($i = 0; $i < $this->rows; ++$i) {
if (($value = $equatation->get($i, $i)) != 1 && $value != 0) {
$factor = 1 / $value;
for ($k = $i; $k < $columns; ++$k) {
$equatation->set($i, $k, $equatation->get($i, $k) * $factor);
}
}
}
// Build up solving polynom
$polynom = new ezcGraphPolynom();
for ($i = $this->rows - 1; $i >= 0; --$i) {
for ($j = $i + 1; $j < $this->columns; ++$j) {
$equatation->set($i, $this->columns, $equatation->get($i, $this->columns) + -$equatation->get($i, $j) * $polynom->get($j));
$equatation->set($i, $j, 0);
}
$polynom->set($i, $equatation->get($i, $this->columns));
}
return $polynom;
}
/**
* Adds polynom to current polynom
*
* @param ezcGraphPolynom $polynom Polynom to add
* @return ezcGraphPolynom Modified polynom
*/
public function add(ezcGraphPolynom $polynom)
{
$order = max($this->getOrder(), $polynom->getOrder());
for ($i = 0; $i <= $order; ++$i) {
$this->set($i, $this->get($i) + $polynom->get($i));
}
return $this;
}