Home >php教程 >php手册 >数值分析(php实现)一:Lagrange插值

数值分析(php实现)一:Lagrange插值

WBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWB
WBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOriginal
2016-06-13 10:45:421208browse

 

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

 

/*

 * 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

                     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

                     $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 dot['x'][$i] ? $this->dot['x'][$i]:$max;

        $r = 7;//点的半径

        $step = 0.1;//步长

        for($i = 0;$i

            imagefilledellipse($img,$this->dot['x'][$i],$this->dot['y'][$i],$r,$r,1);

        }

        for($i = $this->dot['x'][0]-10;$i

            $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

Statement:
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn
Previous article:PHP var_dump()Next article:php 试题总结(附参考答案)