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#-*- coding: utf-8 -*-
def GM11 ( x0 ) : #自定义灰色预测函数
import numpy as np
x1 = x0 . cumsum ( ) #1-AGO序列
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 )
Yn = x0 [ 1 : ] . reshape ( ( len ( x0 ) - 1 , 1 ) )
[ [ a ] , [ b ] ] = np . dot ( np . dot ( np . linalg . inv ( np . dot ( B . T , B ) ) , B . T ) , Yn ) #计算参数
f = lambda k : ( x0 [ 0 ] - b / a ) * np . exp ( - a * ( k - 1 ) ) - ( x0 [ 0 ] - b / a ) * np . exp ( - a * ( k - 2 ) ) #还原值
delta = np . abs ( x0 - np . array ( [ f ( i ) for i in range ( 1 , len ( x0 ) + 1 ) ] ) )
C = delta . std ( ) / x0 . std ( )
P = 1.0 * ( np . abs ( delta - delta . mean ( ) ) < 0.6745 * x0 . std ( ) ) . sum ( ) / len ( x0 )
return f , a , b , x0 [ 0 ] , C , P #返回灰色预测函数、a、b、首项、方差比、小残差概率
