"""R620：同一合成净值重算样本夏普，缺数据和零波动不填零。"""
from math import sqrt, isclose, isfinite
from statistics import mean, stdev, pstdev


def recalc(equity, annual_sessions=252, annual_rf=0, population=False):
    if type(annual_sessions) is not int or annual_sessions<=0 or not isfinite(annual_rf) or annual_rf<=-1:
        raise ValueError('invalid annualization convention')
    if len(equity) < 3:
        return {'status': 'insufficient', 'sharpe': None}
    if any(x is None or not isfinite(x) or x <= 0 for x in equity):
        return {'status': 'invalid_or_missing', 'sharpe': None}
    returns = [b/a-1 for a,b in zip(equity,equity[1:])]
    rf = (1+annual_rf)**(1/annual_sessions)-1
    excess = [r-rf for r in returns]
    volatility = (pstdev if population else stdev)(excess)
    if volatility == 0:
        return {'status': 'zero_volatility', 'sharpe': None}
    result = sqrt(annual_sessions)*mean(excess)/volatility
    return {'status': 'ok', 'returns': returns, 'sharpe': result}


equity = [100,101,100,102,101]
sample = recalc(equity)
population = recalc(equity, population=True)
calendar = recalc(equity, annual_sessions=365)
r = sample['returns']; avg=sum(r)/len(r)
manual_sd=sqrt(sum((x-avg)**2 for x in r)/(len(r)-1))
assert isclose(sample['sharpe'],sqrt(252)*avg/manual_sd,rel_tol=1e-12)
assert isclose(population['sharpe']/sample['sharpe'],sqrt(4/3),rel_tol=1e-12)
assert isclose(calendar['sharpe']/sample['sharpe'],sqrt(365/252),rel_tol=1e-12)
assert recalc([100,100,100])['status']=='zero_volatility'
assert recalc([100,101])['status']=='insufficient'
assert recalc([100,None,101])['status']=='invalid_or_missing'
assert isclose(101/100-1,.01,abs_tol=1e-12)
print('returns='+str(r))
print('sample_252='+format(sample['sharpe'],'.8f')+' population_252='+format(population['sharpe'],'.8f')+' sample_365='+format(calendar['sharpe'],'.8f'))
print('unified_formula_residual=within_1e-12 zero_vol=unavailable missing=unavailable insufficient=unavailable')