数值分析（php实现)一：Lagrange插值

 

在学数值分析，试着用php实现下,有兴趣的朋友可以粘下来试试

lagrange插值就是给出n个已知的点，用多项式函数拟合，求出拟合的函数，进而估算未知点函数值的一种插值过程

插值函数是f(x) = xigma(求和) lk*yk

本类实现了插值后显示函数图像的功能

 

<?php

/*

 * lagrange插值

 * @wangbin

 * */

class lagrange{

       private $dot = array();

       public function __construct($array){

        $this->dot = $array;

    }

 

    /*

     * 计算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;//点的半径

        $step = 0.1;//步长

        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();

?>

 

摘自 pcenshao