def check(cls, code, start_date, end_date):
table = 'kline_min5'
table2 = 'tmp_kline_min5'
path = 'f:/zjf/data/check6/'
data = KlineData.read_data(code=code,
start_date=start_date,
end_date=end_date,
kline=table,
timemerge=True)
if len(data) <= 0:
return
data = data.sort_values(by=['date'], ascending=True)
data = data[data.time <= 955]
data2 = KlineData.read_data(code=code,
start_date=start_date,
end_date=end_date,
kline=table2,
timemerge=True)
if len(data2) <= 0:
return
data2 = data2.sort_values(by=['date'], ascending=True)
data2 = data2[data2.time <= 955]
print('start draw.......')
# fig, ax = plt.subplots()
# fig.subplots_adjust(bottom=0.2)
ax = plt.subplot(211)
# plt.title('本地')
ax.set_xticks([])
candlestick2_ohlc(ax,
data.open,
data.high,
data.low,
data.close,
width=1,
colorup='red',
colordown='green')
plt.title(table + '--' + code)
ax = plt.subplot(212)
# plt.title('远程')
plt.title(table2 + '--' + code)
candlestick2_ohlc(ax,
data2.open,
data2.high,
data2.low,
data2.close,
width=1,
colorup='red',
colordown='green')
File.check_file(path=path)
ax.set_xticks([])
plt.savefig(path + code + '.png', transparent=True)
plt.close()
def unreplenishment(cls, data, method='local'):
"""
将XDXR_day复权后的价格更新至现价
:param method:获取现价的方法：net表示从网络接口获取最新价作为现价
local表示从本地数据库获取。
目前反复权操作指针对中国A股XDXR_day 表,将其close-->现价
:param data:
:return:
"""
try:
if method == 'net':
from Calf.data import RealData as rd
real_data = rd.get_stocks_data(list(data.stock_code))
data.drop('close', axis=1, inplace=True)
data = pd.merge(data,
real_data.loc[:, ['stock_code', 'price']],
on='stock_code')
data.rename(columns={'price': 'open_price'}, inplace=True)
if method == 'local':
# 注意使用的是open_date
from Calf.data import KlineData as kd
data['open_price'] = data.apply(lambda r: kd.read_one(
r['stock_code'], r['open_date'], 'kline_day')['close'],
axis=1)
return data
except Exception as e:
ExceptionInfo(e)
return pd.DataFrame()
def get_data(self):
data = KlineData.read_data(code='000001',
kline='kline_day',
start_date=dt.datetime(2015, 1, 1),
end_date=dt.datetime(2018, 9, 3))
# print(data.loc[:,['date']])
return data
def get_data(self, stockno, start_date, end_date, kline):
data = KlineData.read_data(code=stockno,
start_date=start_date,
end_date=end_date,
kline=kline,
timemerge=True)
data = data[::-1]
return data
def deal_data(code):
data = KlineData.read_data(code=code, start_date=dt.datetime(2016, 1, 1), end_date=dt.datetime(2018, 9, 18),
kline='index_min5',timemerge=True)
if len(data):
data = n_KDJ(data, 9, 3)
# t1 = time.clock()
# print(t1-t)
# t = time.clock()
data = n_MA(data)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_MACD(data, 12, 26, 9)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_RSI(data, 6, 12, 24)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_DMI(data, 14, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BRAR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CR(data, 26, 10, 20, 40)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_VR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_WR(data, 10, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CCI(data, 14)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BOLL(data, 20)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_PSY(data, 12)
data.dropna(inplace=True)
data=data[data.time==955]
BaseModel('features_index_min5').insert_batch(data.to_dict(orient='records'))
def get(code, table='kline_tick'):
print(code)
start_date = dt.datetime(2018, 6, 12)
end_date = dt.datetime(2018, 6, 12)
data = KlineData.read_data(code=code,
start_date=start_date,
end_date=end_date,
kline=table,
timemerge=True)
if len(data) <= 0:
return {}
data = data.sort_values(by=['_id'])
data['pre_price'] = data.price.shift(-1)
data['change'] = data.pre_price - data.price
data['amount'] = data.price * data.volume
data0 = data[data.price == data.price.max()]
max_price_amount = data0.amount.sum()
data1 = data[data.price == data.price.min()]
min_price_amount = data1.amount.sum()
up = (data[data.change > 0])
down = data[data.change < 0]
ping = data[data.change == 0]
up_volume = up['amount'].sum()
down_volume = down['amount'].sum()
ping_volume = ping['amount'].sum()
up_max_amount = up['amount'].max()
down_max_amount = down['amount'].max()
return dict(code=code,
date=start_date,
up_amount=up_volume,
down_amount=down_volume,
ping_amount=ping_volume,
up_max_amount=up_max_amount,
down_max_amount=down_max_amount,
max_price_amount=max_price_amount,
min_price_amount=min_price_amount)
def get_result(sc, kline, start, end, table_name):
data = KlineData.read_data(code=sc,
start_date=start,
end_date=end,
kline=kline,
timemerge=True)
data = cal_ma(data)
data = data.dropna()
while len(data) >= 64:
last_one = data.iloc[-1]
if last_one.time != 1500:
break
elif abs(last_one.profit_self) >= 0.097:
continue
else:
date = last_one.date
data = data[data.date <= dt.datetime(date.year, date.month,
date.day, 9, 55)]
if len(data) >= 64:
profit = data.iloc[-1].profit
date = data.iloc[-1].date
idata = data.tail(64)
data = data[
data.date < dt.datetime(date.year, date.month, date.day)]
idata = idata.loc[:, [
'close', 'open', 'high', 'low', 'ma5', 'ma10', 'ma20',
'ma60', 'ma120', 'ma200'
]]
idata = np.array(idata)
amin, amax = idata.min(), idata.max() # 求最大最小值
idata = (idata - amin) / (amax - amin)
BaseModel(table_name).insert_batch({
'stock_code': sc,
'profit': profit,
'date': date,
'value': idata.tolist()
})
def get_result(sc, kline, start, end, table_name):
data = KlineData.read_data(code=sc,
start_date=start,
end_date=end,
kline=kline,
timemerge=True)
data = cal_macd(data)
data = data.dropna()
while len(data) >= 64:
last_one = data.iloc[-1]
if last_one.time != 1500:
break
elif abs(last_one.profit_self) >= 0.097:
continue
else:
date = last_one.date
data = data[data.date <= dt.datetime(date.year, date.month,
date.day, 9, 55)]
if len(data) >= 64:
profit = data.iloc[-1].profit
date = data.iloc[-1].date
idata = data.tail(64)
idata = idata.loc[:, ['macd', 'dif', 'dea']]
data = data[
data.date < dt.datetime(date.year, date.month, date.day)]
idata = np.array(idata)
amin, amax = idata.min(), idata.max() # 求最大最小值
max = -amax if abs(amax) > abs(amin) else amin
idata = idata * (64 / 2 - 1) / max
idata = idata + 64 / 2
BaseModel(table_name).insert_batch({
'stock_code': sc,
'profit': profit,
'date': date,
'value': idata.tolist()
})
import numpy as np
def normal(employment):
mean = employment.mean() # 计算平均数
deviation = employment.std() # 计算标准差
# 标准化数据的公式: (数据值 - 平均数) / 标准差
standardized_employment = (employment - mean) / deviation
return standardized_employment
if __name__ == '__main__':
data = KlineData.read_data(code='880302',
start_date=dt.datetime(2018, 9, 10),
end_date=dt.datetime(2018, 9, 18),
kline='index_min5',
timemerge=True)
name = data.columns.values.tolist()
if len(data):
data = data.drop(['_id', 'classtype', 'market'], axis=1)
data = n_KDJ(data, 9, 3)
# t1 = time.clock()
# print(t1-t)
# t = time.clock()
data = n_MA(data)
# t1 = time.clock()
# print(t1 - t1)
# t = time.clock()
def deal_data(code):
data = KlineData.read_data(code=code,
start_date=dt.datetime(2015, 1, 1),
end_date=dt.datetime(2018, 9, 17),
kline='kline_day',
timemerge=True)
name = data.columns.values.tolist()
if len(data):
data = data.drop(['_id', 'classtype', 'market'], axis=1)
data = n_KDJ(data, 9, 3)
# t1 = time.clock()
# print(t1-t)
# t = time.clock()
data = n_MA(data)
# t1 = time.clock()
# print(t1 - t1)
# t = time.clock()
data = n_MACD(data, 12, 26, 9)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_RSI(data, 6, 12, 24)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_DMI(data, 14, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BRAR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CR(data, 26, 10, 20, 40)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_VR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_WR(data, 10, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CCI(data, 14)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BOLL(data, 20)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_PSY(data, 12)
columns = data.columns.values.tolist()
data = data.replace(to_replace=np.Infinity, value=np.NaN)
fund_data = pd.DataFrame(
list(BaseModel('jq_fund_data').query({'code': code})))
jq_name = [
'capitalization', 'circulating_cap', 'circulating_market_cap',
'market_cap', 'pb_ratio', 'pcf_ratio', 'pe_ratio', 'pe_ratio_lyr',
'ps_ratio', 'turnover_ratio'
]
for i in jq_name:
data[i] = 0
# data['circulating_market_cap'] = 0
for i in columns:
if i not in name and 'change_r_next' not in i:
v = data[i].iloc[0]
if type(v).__name__ != 'bool_':
# print(i, v, type(v))
if data[i].min() == 0:
# pass
# print(i, data[i].loc[0])
data.loc[data[i] != 0,
i] = (data.loc[data[i] != 0, i] -
data.loc[data[i] != 0, i].min()) / (
data.loc[data[i] != 0, i].max() -
data.loc[data[i] != 0, i].min())
# print(i,data[i].loc[0])
else:
# print(i, v, type(v))
data[i] = (data[i] - data[i].min()) / (data[i].max() -
data[i].min())
# data['up'] = data['up'] / (data['up'] + data['down'])
# data['down'] = data['down'] / (data['up'] + data['down'])
data.loc[
(data.date >= dt.datetime(2015, 12, 31)) & (data.date < dt.datetime(2016, 3, 31)), jq_name] = \
fund_data[fund_data.day == '2015-12-31'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2016, 3, 31)) & (data.date <= dt.datetime(2016, 6, 30)), jq_name] = \
fund_data[fund_data.day == '2016-03-31'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date < dt.datetime(2016, 9, 30)) & (data.date >= dt.datetime(2016, 6, 30)), jq_name] = \
fund_data[fund_data.day == '2016-06-30'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2016, 9, 30)) & (data.date < dt.datetime(2016, 12, 30)), jq_name] = \
fund_data[fund_data.day == '2016-09-30'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date < dt.datetime(2017, 3, 31)) & (data.date >= dt.datetime(2016, 12, 30)), jq_name] = \
fund_data[fund_data.day == '2016-12-30'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2017, 3, 31)) & (data.date < dt.datetime(2017, 6, 30)), jq_name] = \
fund_data[fund_data.day == '2017-03-31'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2017, 6, 30)) & (data.date < dt.datetime(2017, 9, 29)), jq_name] = \
fund_data[fund_data.day == '2017-06-30'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2017, 9, 29)) & (data.date < dt.datetime(2017, 12, 29)), jq_name] = \
fund_data[fund_data.day == '2017-09-29'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2017, 12, 29)) & (data.date < dt.datetime(2018, 3, 30)), jq_name] = \
fund_data[fund_data.day == '2017-12-29'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2018, 3, 30)) & (data.date < dt.datetime(2018, 6, 29)), jq_name] = \
fund_data[fund_data.day == '2018-03-30'].loc[:,jq_name].iloc[0].tolist()
data.loc[
(data.date >= dt.datetime(2018, 6, 29)), jq_name] = \
fund_data[fund_data.day == '2018-06-29'].loc[:,jq_name].iloc[0].tolist()
name = ['open', 'close', 'high', 'low', 'amount', 'volume']
data['turnover_ratio'] = data.volume / (data.circulating_cap * 10000)
for i in name:
data[i] = (data[i] - data[i].min()) / (data[i].max() -
data[i].min())
data = data[::-1]
data = data.reset_index(drop=True)
# data['count'] = data.index.tolist()
curror = BaseModel('LaunchDate').query(sql={'stock_code': code})
data['count'] = 0
if curror.count():
launchdate = list(curror)[0]['date']
data['count'] = data.date.map(lambda x: (x - launchdate).days)
data = data[data.date >= dt.datetime(2016, 1, 1)]
BaseModel('features_kline_day').insert_batch(
data.to_dict(orient='records'))
from Calf.data import KlineData
import datetime as dt
from sklearn.cross_validation import train_test_split
import matplotlib.pyplot as plt
from Calf.models.base_model import BaseModel
import pandas as pd
import numpy as np
data = KlineData.read_data(code='000001',
start_date=dt.datetime(2016, 1, 1),
end_date=dt.datetime(2018, 9, 2),
kline='index_min5',
timemerge=True)
data = data.loc[:, ['date', 'close', 'open', 'high', 'low', 'volume']]
data['close2'] = data.close.shift(-48)
data['profit'] = data.close / data.close2 - 1
data = data.drop(['close2'], axis=1)
data = data.dropna()
y = data.loc[:, ['profit']]
X = data.loc[:, ['close', 'open', 'low', 'high', 'volume']]
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
print(X_train.shape)
print(y_test.shape)
from sklearn.linear_model import LinearRegression
linreg = LinearRegression()
linreg.fit(X_train, y_train)
a = (linreg.intercept_)
print(a)
print((linreg.coef_))
# 模型拟合测试集
y_pred = linreg.predict(X_test)
from sklearn import metrics
from Calf.data import KlineData import datetime as dt import matplotlib.pyplot as plt from Visual.DMI.caculate import Caculate data=KlineData().read_data(code='001979',start_date=dt.datetime(2018,5,1),end_date=dt.datetime(2018,9,1),kline='kline_day') data=data.sort_values(by=['date'],ascending=True) data=Caculate.n_DMI(data) data=data[::-1] print(data.date.tolist()) fig=plt.figure(figsize=(9,6)) plt.plot(data.date,data['PDI']) plt.plot(data.date,data['MDI']) plt.plot(data.date,data['ADX']) plt.show()
from Calf.data import KlineData
import datetime as dt
def deal(data):
columns = data.columns.values.tolist()
for i in columns:
if i not in ['_id', 'classtype']:
v = data[i].iloc[0]
if type(v).__name__ not in ['bool_', 'str']:
data[i] = (data[i] - data[i].min()) / (data[i].max() -
data[i].min())
return data
data = KlineData.read_data(code='000001',
start_date=dt.datetime(2018, 9, 1),
end_date=dt.datetime(2018, 10, 10),
kline='kline_day')
data = deal(data)
print(data.head(10))
def deal_data(code):
data = KlineData.read_data(code=code, start_date=dt.datetime(2015, 1, 1), end_date=dt.datetime(2018, 9, 17),
kline='index_day', timemerge=True)
name = data.columns.values.tolist()
if len(data):
data = data.drop(['_id', 'classtype', 'market'], axis=1)
data = n_KDJ(data, 9, 3)
# t1 = time.clock()
# print(t1-t)
# t = time.clock()
data = n_MA(data)
# t1 = time.clock()
# print(t1 - t1)
# t = time.clock()
data = n_MACD(data, 12, 26, 9)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_RSI(data, 6, 12, 24)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_DMI(data, 14, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BRAR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CR(data, 26, 10, 20, 40)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_VR(data, 26)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_WR(data, 10, 6)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_CCI(data, 14)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_BOLL(data, 20)
# t1 = time.clock()
# print(t1 - t)
# t = time.clock()
data = n_PSY(data, 12)
columns = data.columns.values.tolist()
data = data.replace(to_replace=np.Infinity, value=np.NaN)
for i in columns:
if i not in name and 'change_r_next' not in i:
v = data[i].iloc[0]
if type(v).__name__ != 'bool_':
# print(i, v, type(v))
if data[i].min() == 0:
# pass
# print(i, data[i].loc[0])
data.loc[data[i] != 0, i] = (data.loc[data[i] != 0, i] - data.loc[data[i] != 0, i].min()) / (
data.loc[data[i] != 0, i].max() - data.loc[data[i] != 0, i].min())
# print(i,data[i].loc[0])
else:
# print(i, v, type(v))
data[i] = (data[i] - data[i].min()) / (data[i].max() - data[i].min())
data['up'] = data['up'] / (data['up'] + data['down'])
data['down'] = data['down'] / (data['up'] + data['down'])
name = ['open', 'close', 'high', 'low', 'amount', 'volume']
for i in name:
data[i] = (data[i] - data[i].min()) / (data[i].max() - data[i].min())
data = data[::-1]
data = data.reset_index(drop=True)
data['count'] = data.index.tolist()
data = data[data.date >= dt.datetime(2016, 1, 1)]
BaseModel('features_index_day').insert_batch(data.to_dict(orient='records'))
def KScheduler(cls, action, tz=None, deep_sleep=list()):
"""
适用于A股的信号采集实时任务，适用于跨时区任务
:param tz:
:param deep_sleep:
:param action: 模型的运行管理对象
:return:
"""
if not isinstance(action, type(ModelAction)):
raise TypeError('Object action must be a subclass of ModelAction')
if tz is not None:
if tz not in pytz.all_timezones:
raise ValueError('this tz: %s not in pytz time zones' % tz)
else:
tz = pytz.timezone(tz)
profit_probe_period = dt.timedelta(minutes=1)
profit_probe_next = dt.datetime.now(
) if tz is None else dt.datetime.now(tz=tz).replace(tzinfo=None)
_f = False # 记录当天是否收盘
klines = action.klines # 需要跟踪的bar周期
_id = cls.open_kline_update_log() # 记录bar更新
from Calf.data import KlineData as kd
while 1:
try:
crt = dt.datetime.now() if tz is None else dt.datetime.now(
tz=tz).replace(tzinfo=None)
if not action.is_trade_day(
dt.datetime(crt.year, crt.month, crt.day)):
print('{0} today is not in business'.format(crt))
time.sleep(60 * 60 * 2) # sleep two hours
continue
if action.trade_day_end(crt) and _f:
print(fontcolor.F_GREEN + '-' * 80)
print('# %s Today Overview #' % action.name)
print('Signal:')
action.signals_summary()
print('Order:')
action.orders_summary()
print(fontcolor.F_GREEN + '-' * 80 + fontcolor.END)
sound_notice('close.wav').start()
_f = False
# open_am <= crt <= close_am or open_pm <= crt < close_pm
if action.trade_date(crt):
# 交易日盘中
s_d = crt - dt.timedelta(minutes=3)
e_d = crt + dt.timedelta(minutes=3)
log = kd.read_log(start_date=s_d, end_date=e_d, status=200)
if len(log):
log['_id'] = log['_id'].astype('str')
for i, r in log.iterrows():
if r.kline in klines and r['_id'] != _id[r.kline]:
print('this kline %s find update' % r.kline)
action.real(r.kline)
print(r.kline + ' id update:' + _id[r.kline] +
'-->' + r['_id'])
_id[r.kline] = r['_id']
cls.set_kline_update_log(_id)
if profit_probe_next <= crt:
print('profit probing date:{0}'.format(crt))
action.probing()
profit_probe_next += profit_probe_period
_f = True
time.sleep(5)
else:
print('{0} this datetime is not in business'.format(crt))
profit_probe_next = crt
_f = False
sleep = 60 * 5 if crt.hour in deep_sleep else 60 * 30
time.sleep(sleep)
except Exception as e:
ExceptionInfo(e)
def rerun(cls, action, deep_sleep, offset=None):
"""
复盘演示
:param action:
:param deep_sleep:
:param offset:
:return:
"""
from Calf.data import KlineData as kd
profit_probe_period = dt.timedelta(minutes=1)
profit_probe_next = CalfDateTime.now(offset=offset)
_f = False # 记录当天是否收盘
klines = action.klines # 需要跟踪的bar周期
_id = cls.open_kline_update_log() # 记录bar更新
while 1:
try:
crt = CalfDateTime.now(offset=offset)
if not trading.is_trade_day(
dt.datetime(crt.year, crt.month, crt.day)):
print('{0} today is not in business'.format(crt))
time.sleep(60 * 60 * 2) # sleep two hours
continue
if action.trade_day_end(crt) and _f:
print(fontcolor.F_GREEN + '-' * 80)
print('# %s Today Overview #' % action.name)
print('Signal:')
action.signals_summary()
print('Order:')
action.orders_summary()
print(fontcolor.F_GREEN + '-' * 80 + fontcolor.END)
sound_notice('close.wav').start()
_f = False
# open_am <= crt <= close_am or open_pm <= crt < close_pm
if action.trade_date(crt):
# 交易日盘中
s_d = crt - dt.timedelta(minutes=3)
e_d = crt + dt.timedelta(minutes=3)
log = kd.read_log(start_date=s_d, end_date=e_d, status=200)
if len(log):
log['_id'] = log['_id'].astype('str')
for i, r in log.iterrows():
if r.kline in klines and r['_id'] != _id[r.kline]:
print('this kline %s find update' % r.kline)
action.real(r.kline, start_time=crt)
print(r.kline + ' id update:' + _id[r.kline] +
'-->' + r['_id'])
_id[r.kline] = r['_id']
cls.set_kline_update_log(_id)
if profit_probe_next <= crt:
print('profit probing date:{0}'.format(crt))
# action.probing()
profit_probe_next += profit_probe_period
_f = True
time.sleep(5)
else:
print('{0} this datetime is not in business'.format(crt))
profit_probe_next = crt
_f = False
# sleep = 60 * 30
# if crt.hour == 9 or crt.hour == 12:
# sleep = 60 * 5
sleep = 60 * 5 if crt.hour in deep_sleep else 60 * 30
time.sleep(sleep)
except Exception as e:
ExceptionInfo(e)