import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
import math
import pandas as pd

# 对数据进行分级的一个例子
l = [10, 9, 5, 7, 5]
print '原始数据: ', l
print '秩: ', list(stats.rankdata(l, method='average'))

## 示例
n = 100

def compare_correlation_and_spearman_rank(n, noise):
    X = np.random.poisson(size=n)
    Y = np.exp(X) + noise * np.random.normal(size=n)

    Xrank = stats.rankdata(X, method='average')
    # n-2是指倒数第二个元素 
    Yrank = stats.rankdata(Y, method='average')

    diffs = Xrank - Yrank # 这个地方Xrank和Yrank的顺序不重要，因为要对它们进行平方 
    r_s = 1 - 6*sum(diffs*diffs)/(n*(n**2 - 1))
    c_c = np.corrcoef(X, Y)[0,1]
    
    return r_s, c_c

experiments = 1000
spearman_dist = np.ndarray(experiments)
correlation_dist = np.ndarray(experiments)
for i in range(experiments):
    r_s, c_c = compare_correlation_and_spearman_rank(n, 1.0)
    spearman_dist[i] = r_s
    correlation_dist[i] = c_c
    
print '斯皮尔曼秩相关系数: ' + str(np.mean(spearman_dist))
# 与通常意义上的相关系数进行对比 
print '通常意义下的相关系数: ' + str(np.mean(correlation_dist))

plt.hist(spearman_dist, bins=50, alpha=0.5)
plt.hist(correlation_dist, bins=50, alpha=0.5)
plt.legend(['Spearman Rank', 'Regular Correlation'])
plt.xlabel('Correlation Coefficient')
plt.ylabel('Frequency');

n = 100
noises = np.linspace(0, 3, 30)
experiments = 100
spearman = np.ndarray(len(noises))
correlation = np.ndarray(len(noises))

for i in range(len(noises)):
    # Run many experiments for each noise setting
    rank_coef = 0.0
    corr_coef = 0.0
    noise = noises[i]
    for j in range(experiments):
        r_s, c_c = compare_correlation_and_spearman_rank(n, noise)
        rank_coef += r_s
        corr_coef += c_c
    spearman[i] = rank_coef/experiments
    correlation[i] = corr_coef/experiments
    
plt.scatter(noises, spearman, color='r')
plt.scatter(noises, correlation)
plt.legend(['Spearman', 'regular'])
plt.xlabel('amount of noise')
plt.ylabel('average correlational coefficient')

n = 100

X = np.random.rand(n)
Xrank = stats.rankdata(X, method='average')
# n-2 is the second to last element
Yrank = stats.rankdata([1,1] + list(X[:(n-2)]), method='average')

diffs = Xrank - Yrank # order doesn't matter since we'll be squaring these values
r_s = 1 - 6*sum(diffs*diffs)/(n*(n**2 - 1))
print r_s

# 生成两组随机数 
np.random.seed(161)
X = np.random.rand(10)
Y = np.random.rand(10)

r_s = stats.spearmanr(X, Y)
print '斯皮尔曼秩相关系数: ', r_s[0]
print 'p-value: ', r_s[1]

mutual_fund_data= pd.read_csv('mutual_fund_data.csv')
expense = mutual_fund_data['Annual Expense Ratio'].values
sharpe = mutual_fund_data['Three Year Sharpe Ratio'].values
 
plt.scatter(expense, sharpe)
plt.xlabel('Expense Ratio')
plt.ylabel('Sharpe Ratio')

r_S = stats.spearmanr(expense, sharpe)
print '斯皮尔曼秩相关系数: ', r_S[0]
print 'p-value: ', r_S[1]

symbol_list =get_industry_stocks('I64')

# 获取上个月的收益率
start = '2015-08-01'
end = '2015-09-01'
historical_returns = get_price(symbol_list, fields='price', start_date=start, end_date=end).pct_change()[0:]

# 计算各只股票的平均收益率
scores = np.mean(historical_returns)
print 'average return of last month\n'
print scores
print '\n'

#获取这个月的收益率
start = '2015-09-01'
end = '2015-10-01'
walk_forward_returns = get_price(symbol_list, fields='price', start_date=start, end_date=end).pct_change()[0:]

#计算各只股票的平均收益率
walk_forward_returns = np.mean(walk_forward_returns)
print 'average return of this month\n'
print walk_forward_returns
print '\n'

plt.scatter(scores, walk_forward_returns)
plt.xlabel('average return of last month')
plt.ylabel('average return of this month')

r_s = stats.spearmanr(scores, walk_forward_returns)
print '相关系数: ' + str(r_s[0])
print 'p-value: ' + str(r_s[1])