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();
?>