Ejemplo n.º 1
0
 /**
  * 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;
 }
Ejemplo n.º 2
0
 /**
  * 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;
 }