数值分析（php兑现)一：Lagrange插值

<?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();?>