数值分析（php兑现)一：Lagrange插值

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

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();?>

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1 楼 luozhong915127 2011-11-17  

全是代码，没有解释呀