import numpy as np
import pandas as pd
#數(shù)據(jù)讀取
#利用pandas讀取csv，讀取的數(shù)據(jù)為DataFrame對(duì)象
data = pd.read_csv('sn.csv')
# 將DataFrame對(duì)象轉(zhuǎn)化為數(shù)組,數(shù)組的最后一列為預(yù)報(bào)對(duì)象
data= data.values.copy()
# print(data)
 
# 計(jì)算回歸系數(shù)，參數(shù)
def get_regre_coef(X,Y):
  S_xy=0
  S_xx=0
  S_yy=0
  # 計(jì)算預(yù)報(bào)因子和預(yù)報(bào)對(duì)象的均值
  X_mean = np.mean(X)
  Y_mean = np.mean(Y)
  for i in range(len(X)):
    S_xy += (X[i] - X_mean) * (Y[i] - Y_mean)
    S_xx += pow(X[i] - X_mean, 2)
    S_yy += pow(Y[i] - Y_mean, 2)
  return S_xy/pow(S_xx*S_yy,0.5)
#構(gòu)建原始增廣矩陣
def get_original_matrix():
  # 創(chuàng)建一個(gè)數(shù)組存儲(chǔ)相關(guān)系數(shù),data.shape幾行(維)幾列，結(jié)果用一個(gè)tuple表示
  # print(data.shape[1])
  col=data.shape[1]
  # print(col)
  r=np.ones((col,col))#np.ones參數(shù)為一個(gè)元組(tuple)
  # print(np.ones((col,col)))
  # for row in data.T:#運(yùn)用數(shù)組的迭代，只能迭代行，迭代轉(zhuǎn)置后的數(shù)組，結(jié)果再進(jìn)行轉(zhuǎn)置就相當(dāng)于迭代了每一列
    # print(row.T)
  for i in range(col):
    for j in range(col):
      r[i,j]=get_regre_coef(data[:,i],data[:,j])
  return r

def get_vari_contri(r):
  col = data.shape[1]
   #創(chuàng)建一個(gè)矩陣來(lái)存儲(chǔ)方差貢獻(xiàn)值
  v=np.ones((1,col-1))
  # print(v)
  for i in range(col-1):
    # v[0,i]=pow(r[i,col-1],2)/r[i,i]
    v[0, i] = pow(r[i, col - 1], 2) / r[i, i]
  return v
#選擇因子是否進(jìn)入方程，
#參數(shù)說(shuō)明：r為增廣矩陣，v為方差貢獻(xiàn)值，k為方差貢獻(xiàn)值最大的因子下標(biāo),p為當(dāng)前進(jìn)入方程的因子數(shù)
def select_factor(r,v,k,p):
  row=data.shape[0]#樣本容量
  col=data.shape[1]-1#預(yù)報(bào)因子數(shù)
  #計(jì)算方差比
  f=(row-p-2)*v[0,k-1]/(r[col,col]-v[0,k-1])
  # print(calc_vari_contri(r))
  return f

#計(jì)算第零步增廣矩陣
r=get_original_matrix()
# print(r)
#計(jì)算方差貢獻(xiàn)值
v=get_vari_contri(r)
print(v)
#計(jì)算方差比

# #計(jì)算方差比
# print(data.shape[0])
f=select_factor(r,v,4,0)
print(f)
#######輸出##########
22.79852020138227

#逐步回歸分析與計(jì)算
#通過(guò)矩陣轉(zhuǎn)換公式來(lái)計(jì)算各部分增廣矩陣的元素值
def convert_matrix(r,k):
  col=data.shape[1]
  k=k-1#從第零行開(kāi)始計(jì)數(shù)
  #第k行的元素單不屬于k列的元素
  r1 = np.ones((col, col)) # np.ones參數(shù)為一個(gè)元組(tuple)
  for i in range(col):
    for j in range(col):
      if (i==k and j!=k):
        r1[i,j]=r[k,j]/r[k,k]
      elif (i!=k and j!=k):
        r1[i,j]=r[i,j]-r[i,k]*r[k,j]/r[k,k]
      elif (i!= k and j== k):
        r1[i,j] = -r[i,k]/r[k,k]
      else:
        r1[i,j] = 1/r[k,k]
  return r1

#矩陣轉(zhuǎn)換，計(jì)算第一步矩陣
r=convert_matrix(r,4)
# print(r)
#計(jì)算第一步方差貢獻(xiàn)值
v=get_vari_contri(r)
#print(v)
f=select_factor(r,v,1,1)
print(f)
#########輸出#####
108.22390933074443

f=select_factor(r,v,2,2)
print(f)
##########輸出#########
5.025864648951804

#選擇是否剔除因子，
#參數(shù)說(shuō)明：r為增廣矩陣，v為方差貢獻(xiàn)值，k為方差貢獻(xiàn)值最大的因子下標(biāo),t為當(dāng)前進(jìn)入方程的因子數(shù)
def delete_factor(r,v,k,t):
  row = data.shape[0] # 樣本容量
  col = data.shape[1] - 1 # 預(yù)報(bào)因子數(shù)
  # 計(jì)算方差比
  f = (row - t - 1) * v[0, k - 1] / r[col, col]
  # print(calc_vari_contri(r))
  return f
#因子3的引進(jìn)檢驗(yàn)值0.018233473487350636
f=select_factor(r,v,3,3)
print(f)
#因子4的剔除檢驗(yàn)值1.863262422188088
f=delete_factor(r,v,4,3)
print(f)

#因子4的引進(jìn)檢驗(yàn)值1.8632624221880876，小于3.28不能引進(jìn)
f=select_factor(r,v,4,2)
print(f)
#因子1的剔除檢驗(yàn)值146.52265486251397,大于3.28不能剔除
f=delete_factor(r,v,1,2)
print(f)

#因子1和因子2進(jìn)入方程
#對(duì)進(jìn)入方程的預(yù)報(bào)因子進(jìn)行多元回歸
# regs=LinearRegression()
X=data[:,0:2]
Y=data[:,4]
X=np.mat(np.c_[np.ones(X.shape[0]),X])#為系數(shù)矩陣增加常數(shù)項(xiàng)系數(shù)
Y=np.mat(Y)#數(shù)組轉(zhuǎn)化為矩陣
#print(X)
B=np.linalg.inv(X.T*X)*(X.T)*(Y.T)
print(B.T)#輸出系數(shù),第一項(xiàng)為常數(shù)項(xiàng)，其他為回歸系數(shù)
###輸出##
#[[52.57734888 1.46830574 0.66225049]]