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 < $num;$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);