import numpy as np
 
def GM11(x,n):
    '''
    灰色预测
    x：序列，numpy对象
    n:需要往后预测的个数
    '''
    x1 = x.cumsum()#一次累加  
    z1 = (x1[:len(x1) - 1] + x1[1:])/2.0#紧邻均值  
    z1 = z1.reshape((len(z1),1))  
    B = np.append(-z1,np.ones_like(z1),axis=1)  
    Y = x[1:].reshape((len(x) - 1,1))
    #a为发展系数 b为灰色作用量
    [[a],[b]] = np.dot(np.dot(np.linalg.inv(np.dot(B.T, B)), B.T), Y)#计算参数  
    result = (x[0]-b/a)*np.exp(-a*(n-1))-(x[0]-b/a)*np.exp(-a*(n-2))  
    S1_2 = x.var()#原序列方差
    e = list()#残差序列
    for index in range(1,x.shape[0]+1):
        predict = (x[0]-b/a)*np.exp(-a*(index-1))-(x[0]-b/a)*np.exp(-a*(index-2))
        e.append(x[index-1]-predict)
    S2_2 = np.array(e).var()#残差方差
    C = S2_2/S1_2#后验差比
    if C<=0.35:
        assess = '后验差比<=0.35，模型精度等级为好'
    elif C<=0.5:
        assess = '后验差比<=0.5，模型精度等级为合格'
    elif C<=0.65:
        assess = '后验差比<=0.65，模型精度等级为勉强'
    else:
        assess = '后验差比>0.65，模型精度等级为不合格'
    #预测数据
    predict = list()
    for index in range(x.shape[0]+1,x.shape[0]+n+1):
        predict.append((x[0]-b/a)*np.exp(-a*(index-1))-(x[0]-b/a)*np.exp(-a*(index-2)))
    predict = np.array(predict)
    return {
            'a':{'value':a,'desc':'发展系数'},
            'b':{'value':b,'desc':'灰色作用量'},
            'predict':{'value':result,'desc':'第%d个预测值'%n},
            'C':{'value':C,'desc':assess},
            'predict':{'value':predict,'desc':'往后预测%d个的序列'%(n)},
            }
 
if __name__ == "__main__":
    data = np.array([1.2,2.2,3.1,4.5,5.6,6.7,7.1,8.2,9.6,10.6,11,12.4,13.5,14.7,15.2])
    x = data[0:5]#输入数据
    y = data[5:7]#需要预测的数据
    result = GM11(x,len(y))
    predict = result['predict']['value']
    predict = np.round(predict,1)
    print('真实值:',y)
    print('预测值:',predict)
    print(result)