Numerical analysis (php implementation) 1: Lagrange interpolation_PHP tutorial

I am learning numerical analysis and try to implement it with php. Friends who are interested can stick it down and try it

Lagrange interpolation is an interpolation process that gives n known points, fits them with a polynomial function, finds the fitted function, and then estimates the function value of the unknown point

The interpolation function is f(x) = xigma (summation) lk*yk

This class implements the function of displaying function images after interpolation

/*

* Lagrange interpolation

* @wangbin

* */

class Lagrange{

        private $dot = array();

Public function __construct($array){

$this->dot = $array;

}

/*

* Calculate lk

* */

        private function get_lk($x,$k){

          $num = count($this->dot['x']);

                  $omiga_xk = 1;

$omiga_x = 1;

for($i = 0;$i < $num;$i++){

If($i != $k){

                               $omiga_xk *= ($this->dot['x'][$k]-$this->dot['x'][$i]);

$omiga_x *= ($x - $this->dot['x'][$i]);

                    }

              }

                $lk = $omiga_x/$omiga_xk;

                  return $lk;

}

        public function get_y($x){

          $num = count($this->dot['x']);

                  $L = 0;

for($k = 0;$k < $num;$k++){

$lk = $this->get_lk($x,$k);

               $L += ($this->dot['y'][$k]*$lk);

              }

                  return $L;

}

Public function draw(){

          $img = imagecreate(500,500);

Imagecolorallocate($img,255,255,2);

          $num = count($this->dot['x']);

         $max = 0;

for($i = 0;$i < $num;$i++) $max = $max < $this->dot['x'][$i] ? $this->dot['x' ][$i]:$max;

         $r = 7;//Radius of point

         $step = 0.1;//Step size

for($i = 0;$i < $num;$i++){

imagefilledellipse($img,$this->dot['x'][$i],$this->dot['y'][$i],$r,$r,1);

}

for($i = $this->dot['x'][0]-10;$i < $max + 10;$i += $step){

               $current_x = $i;

                $current_y = $this->get_y($current_x);

                $next_x = $i + $step;

                 $next_y = $this->get_y($next_x);

              imageline($img,$current_x,$current_y,$next_x,$next_y,1);

}

header("Content-type: image/png");

         imagepng($img);

         imagedestroy($img);

}

}

$x = new Lagrange(array('x'=>array(10,30,100,120,220),'y'=>array(20,40,240,220,340)));

$x->draw();

?>

Excerpted from pcenshao

http://www.bkjia.com/PHPjc/478527.htmlwww.bkjia.comtruehttp: //www.bkjia.com/PHPjc/478527.htmlTechArticleI am learning numerical analysis and try to use php to implement it. Interested friends can stick it down and try Lagrange interpolation which is given n known points, fit with a polynomial function, find the fitted function, proceed...