數值分析（php兌現)一：Lagrange插值

數值分析（php實現)一：Lagrange插值
在學數值分析，試著用php實現下,有興趣的朋友可以粘下來試試
Lagrange插值就是給出n個已知的點，用多項式函數擬合，求出擬合的函數，進而估算未知點函數值的一種插值過程
插值函數是f(x) = xigma(求和) lk*yk
本類實現了插值後顯示函數映像的功能

dot = $array;    }    /*     * 計算lk     * */private function get_lk($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;//點的半徑        $step = 0.1;//步長        for($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();?>

1 樓 luozhong915127 2011-11-17

全是代碼，沒有解釋呀

