person correlation,spearman correlation and kendall's t的算法(python,算法来自ＦＲＭ－market risk )

# this module aims to calculate the correlation:
# person correlation,spearman correlation and kendall's t
# note:there is also maturity algorithm in pandas,numpy
# scipy,and statsmodels and so on,this module just write
# my mind when I read market risk measurement and management
###########################################################
import pandas as pd
import numpy as  np
from collections import Iterable
from itertools import combinations
# person correlation
def person_cor(x,y):
    '''this function  is uesed to calculate person correlation,
    it requires pandas:import pandas as pd
    Arguments:
        data {[list,array,series]} -- [python's list,
                pandas's series,numpy's array]
    '''
    if isinstance(x,Iterable):
        x=pd.Series(x)
    else:
        print('x is not a iterable')
        return 
    if isinstance(y,Iterable):
        y=pd.Series(y)
    else:
        print('y is not a iterable')
        return 
    xy=x*y
    xx=x*x
    yy=y*y
    e_x=x.mean()
    e_y=y.mean()
    e_xy=xy.mean()
    e_x_e_y=x.mean()*y.mean()
    e_xx=xx.mean()
    e_yy=yy.mean()
    return (e_xy-e_x_e_y)/((e_xx-e_x**2)*(e_yy-e_y**2))**0.5
def spearman_cor(x,y):
    '''this function  is uesed to calculate person correlation,
    it requires pandas:import pandas as pd
    Arguments:
        data {[list,array,series]} -- [python's list,
                pandas's series,numpy's array]
    '''
    if isinstance(x,Iterable):
        x=pd.Series(x)
    else:
        print('x is not a iterable')
        return 
    if isinstance(y,Iterable):
        y=pd.Series(y)
    else:
        print('y is not a iterable')
        return 
    df=pd.DataFrame() 
    df['x']=x
    df['y']=y
    #sort value according x
    df=df.sort_values('x')  
    # x rank from low to high
    df['x_rank']=range(1,len(x)+1)
    # sort values according y
    df=df.sort_values('y')
    # y rank from low to high
    df['y_rank']=range(1,len(y)+1)
    # diff square
    df['diff']=df['x_rank']-df['y_rank']
    df['diff_square']=df['diff']**2
    # num length
    n=len(df)
    diff_2_sum=df['diff_square'].sum()
    return 1-(6*diff_2_sum/(n*(n*n-1)))
def kendall_t(x,y):
    '''this function  is uesed to calculate person correlation,
    it requires pandas:import pandas as pd
    Arguments:
        data {[list,array,series]} -- [python's list,
                pandas's series,numpy's array]
    '''
    x=[1,2,3]
    y=[2,3,4]
    if isinstance(x,Iterable):
        x=pd.Series(x)
    else:
        print('x is not a iterable')
        return 
    if isinstance(y,Iterable):
        y=pd.Series(y)
    else:
        print('y is not a iterable')
        return 
    df=pd.DataFrame() 
    df['x']=x
    df['y']=y
    #sort value according x
    df=df.sort_values('x')  
    # x rank from low to high
    df['x_rank']=range(1,len(x)+1)
    # sort values according y
    df=df.sort_values('y')
    # y rank from low to high
    df['y_rank']=rang(1,len(y)+1)
    tuple_list=list(zip(df['x_rank'],df['y_rank']))
    #tuple_list=list(zip(df['x_rank'],df['y_rank']))
    com_list=list(combinations(tuple_list,2))
    com_list=[[com[0][0],com[0][1],com[1][0],com[1][1]] for com in com_list]
    com_df=pd.DataFrame(com_list)
    com_df.columns=['x0','y0','x1','y1']
    com_df['num']=(com_df['x0']-com_df['y0'])*(com_df['x1']-com_df['y1'])
    con_num=len(com_df[com_df['num']>0])
    dis_num=len(com_df[com_df['num']<0])
    equal_num=len(com_df[com_df['num']==0])
    n=len(com_df)
    return 2*(con_num-dis_num)/(n*(n-1))