灰色预测程序

• 结果图

• 源码

function pre_data = Gray_Prediction(data, m)
%{
函数功能：灰色预测；
输入：
  data：参考数据，一行；
  m：预测点数；
输出：
  pre_data：预测数据；
示例：
clear; clc;
% data = [89677, 99215, 109655, 120333, 135823, 159878, 182321, 209407, 246619, 300670];
% data = [174, 179, 183, 189, 207, 234, 220.5, 256, 270, 285];
m = 2;
t1 = 1 : length(data);
t2 = 1 : m + length(data);
pre_data = Grey_Prediction(data, m);
plot(t1, data, 'o', t2, pre_data, 'linewidth', 2)
%} 
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
if nargin < 2
   error('输入参数不足！');
end
% 原始数据累加
csum_data = cumsum(data);  
n = length(data);
csum_at = zeros(1, n - 1);
for i = 1 : n - 1
    csum_at(i) = (csum_data(i) + csum_data(i + 1))/2;  % 生成累加矩阵
end
% 计算待定参数的值
D = data(2 : end)';
E = [- csum_at; ones(1, n - 1)];
c = (E*E')\E*D;
a = c(1);
b = c(2);
% 预测后续数据
pre = zeros(1, n + m);
pre(1) = data(1);
for i = 2 : n + m
    pre(i) = (data(1) - b/a)/exp(a*(i - 1)) + b/a ;
end
% 计算预测数据
pre_data = zeros(1, n + m);
pre_data(1) = data(1);
for i = 2 : n + m
    pre_data(i) = pre(i) - pre(i - 1); 
end