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

/*

* 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