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
<?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;$i dot['x'][$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;$k get_lk($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;$i dot['x'][$i],$this->dot['y'][$i],$r,$r,1); } for($i = $this->dot['x'][0]-10;$i 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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