"""只多头的滞后20期OLS残差反转，五期累计、恢复/十期退出及现金账。"""
from fractions import Fraction as F
from decimal import Decimal as D
from math import isfinite
import json


def indicators(market,stock):
    if len(market)!=len(stock): raise ValueError('returns_alignment')
    residuals,output=[],[]
    for i in range(len(stock)):
        alpha=beta=residual=None;reason='warmup'
        if i>=20:
            xs,ys=market[i-20:i],stock[i-20:i]
            if any(v is None or not isfinite(float(v)) for v in xs+ys+[market[i],stock[i]]):
                reason='invalid_input'
            else:
                xm,ym=sum(xs)/20,sum(ys)/20
                variance=sum((v-xm)**2 for v in xs)
                if variance==0:
                    reason='unidentified_market_variance'
                else:
                    beta=sum((x-xm)*(y-ym) for x,y in zip(xs,ys))/variance
                    alpha=ym-beta*xm
                    residual=stock[i]-alpha-beta*market[i];reason='ready'
        residuals.append(residual)
        tail=residuals[max(0,i-4):i+1]
        cumulative=sum(tail) if len(tail)==5 and all(r is not None for r in tail) else None
        output.append({'i':i,'alpha':str(alpha) if alpha is not None else None,
                       'beta':str(beta) if beta is not None else None,
                       'residual':str(residual) if residual is not None else None,
                       'sum5':str(cumulative) if cumulative is not None else None,'reason':reason})
    return output


def run(market,stock,opens):
    rows=indicators(market,stock)
    if len(opens)!=len(rows): raise ValueError('open_alignment')
    cash,quantity,fees,entry=D(1000),0,0,None
    pending_buy,pending_exit=False,None
    ledger=[]
    for i,row in enumerate(rows):
        price=D(str(opens[i]))
        if not price.is_finite() or price<=0: raise ValueError('invalid_open')
        orders=[]
        reason=pending_exit or ('max_holding' if quantity and i>=entry+10 else None)
        if quantity and reason:
            cash+=quantity*price-1;fees+=1
            orders.append(['sell',quantity,str(price),1,reason]);quantity=0;entry=None;pending_exit=None
        if pending_buy and not quantity:
            if 40*price+1>cash: raise ValueError('cash')
            cash-=40*price+1;quantity=40;entry=i;fees+=1
            orders.append(['buy',40,str(price),1,'negative_residual_long'])
        pending_buy=False
        value=F(row['sum5']) if row['sum5'] is not None else None
        if not quantity and value is not None and value<F(-3,50): pending_buy=True
        if quantity and value is not None and value>=0: pending_exit='residual_recovered'
        ledger.append({**row,'orders':orders,'quantity':quantity,'cash':str(cash),
                       'fees':fees,'equity':str(cash+quantity*price),
                       'entry_requested':pending_buy,'exit_requested':pending_exit})
    return ledger


market=[F(1 if i%2 else -1,100) for i in range(40)]
stock=[F(3,2)*m+(F(-1,50) if 20<=i<=24 else F(3,100) if 25<=i<=29 else 0)
       for i,m in enumerate(market)]
opens=[10]*40;opens[27]=10.5;opens[35]=9.5
rows=run(market,stock,opens)
assert rows[20]['alpha']=='0' and rows[20]['beta']=='3/2' and rows[20]['residual']=='-1/50'
assert rows[24]['sum5']=='-23/250' and rows[24]['entry_requested']
assert rows[25]['orders']==[['buy',40,'10',1,'negative_residual_long']]
assert rows[26]['sum5']=='9/500' and rows[26]['exit_requested']=='residual_recovered'
assert rows[27]['orders']==[['sell',40,'10.5',1,'residual_recovered']]
assert D(rows[-1]['cash'])==D(rows[-1]['equity'])==1018 and rows[-1]['quantity']==0 and rows[-1]['fees']==2
common_market=[F(-1,100) if 20<=i<=24 else m for i,m in enumerate(market)]
common_stock=[F(3,2)*m for m in common_market]
common=run(common_market,common_stock,opens)
assert all(not row['orders'] for row in common) and common[-1]['cash']=='1000'
cold_stock=[F(3,2)*m+(F(-1,50) if i>=20 else 0) for i,m in enumerate(market)]
cold=run(market,cold_stock,opens)
assert cold[35]['orders']==[['sell',40,'9.5',1,'max_holding']]
assert D(cold[-1]['cash'])==978 and cold[-1]['fees']==2 and cold[-1]['quantity']==0
constant=indicators([F(0)]*40,[F(0)]*40)
assert constant[20]['reason']=='unidentified_market_variance' and constant[24]['sum5'] is None
for invalid in [None,float('nan'),float('inf'),float('-inf')]:
    sparse=list(stock);sparse[24]=invalid
    check=indicators(market,sparse)
    assert check[24]['reason']=='invalid_input' and check[24]['residual'] is None and check[24]['sum5'] is None
assert run(market[:26],stock[:26],opens[:26])==rows[:26]
future=list(stock);future[30]=F(100)
assert indicators(market,future)[:26]==indicators(market,stock)[:26]
print(json.dumps({'first_fit':rows[20],'trigger':rows[24],'entry':rows[25],
                  'recovery_exit':rows[27],'ending_cash':rows[-1]['cash'],
                  'maximum_exit':cold[35],'market_only_final':common[-1],
                  'constant_market_status':constant[20]['reason'],
                  'scope':'synthetic lagged OLS; market input never traded or shorted'}))