数值分析（php实现)一：Lagrange插值

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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();
?>