mirror of
https://github.com/wassname/catalyst.git
synced 2026-06-30 04:17:29 +08:00
Thomas Wiecki
b976c1252b
I wrote this a little while ago as I noticed that a lot of time is spent computing risk statistics. This is done over the complete history over and over again while this could be done just by using the previously computed value (iteratively). We didn't go forward back then because for minute trade data the difference was not significant enough. However, now with zipline standalone I think most people will use daily (because that's what's available) and it makes a huge difference (speed-up of a couple of 100%). Unfortunately, we can't just replace the existing one with an iterative as for the final cumulative stats the batch is still better. So that's not as nice, but the performance increase is big enough for me to issue this PR (zipline is actually painfully slow with daily data). There is a unittest that compares that both produce exactly the same outputs. Speed measurements (for 500 trading days, daily source): with iterative: real 26.617 user 12.909 sys 6.112 pcpu 71.46 prior: real 44.176 user 31.030 sys 11.381 pcpu 96.00
808 lines
30 KiB
Python
808 lines
30 KiB
Python
#
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# Copyright 2012 Quantopian, Inc.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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import unittest
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import datetime
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import calendar
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import pytz
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import zipline.finance.risk as risk
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from zipline.utils import factory
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from zipline.finance.trading import TradingEnvironment
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class Risk(unittest.TestCase):
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def setUp(self):
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start_date = datetime.datetime(
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year=2006,
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month=1,
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day=1,
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hour=0,
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minute=0,
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tzinfo=pytz.utc)
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end_date = datetime.datetime(
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year=2006, month=12, day=31, tzinfo=pytz.utc)
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self.benchmark_returns, self.treasury_curves = \
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factory.load_market_data()
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self.trading_env = TradingEnvironment(
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self.benchmark_returns,
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self.treasury_curves,
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period_start=start_date,
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period_end=end_date
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)
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self.onesec = datetime.timedelta(seconds=1)
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self.oneday = datetime.timedelta(days=1)
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self.tradingday = datetime.timedelta(hours=6, minutes=30)
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self.dt = datetime.datetime.utcnow()
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self.algo_returns_06 = factory.create_returns_from_list(
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RETURNS,
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self.trading_env
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)
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self.metrics_06 = risk.RiskReport(
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self.algo_returns_06,
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self.trading_env
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)
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start_08 = datetime.datetime(
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year=2008,
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month=1,
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day=1,
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hour=0,
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minute=0,
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tzinfo=pytz.utc)
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end_08 = datetime.datetime(
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year=2008,
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month=12,
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day=31,
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tzinfo=pytz.utc
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)
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self.trading_env08 = TradingEnvironment(
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self.benchmark_returns,
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self.treasury_curves,
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period_start=start_08,
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period_end=end_08
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)
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def tearDown(self):
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return
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def test_factory(self):
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returns = [0.1] * 100
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r_objects = factory.create_returns_from_list(returns, self.trading_env)
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self.assertTrue(r_objects[-1].date <=
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datetime.datetime(
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year=2006, month=12, day=31, tzinfo=pytz.utc))
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def test_drawdown(self):
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returns = factory.create_returns_from_list(
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[1.0, -0.5, 0.8, .17, 1.0, -0.1, -0.45], self.trading_env)
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#200, 100, 180, 210.6, 421.2, 379.8, 208.494
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metrics = risk.RiskMetricsBatch(returns[0].date,
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returns[-1].date,
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returns,
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self.trading_env)
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self.assertEqual(metrics.max_drawdown, 0.505)
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def test_benchmark_returns_06(self):
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returns = factory.create_returns_from_range(self.trading_env)
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metrics = risk.RiskReport(returns, self.trading_env)
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self.assertEqual([round(x.benchmark_period_returns, 4)
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for x in metrics.month_periods],
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[0.0255,
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0.0005,
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0.0111,
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0.0122,
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-0.0309,
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0.0001,
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0.0051,
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0.0213,
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0.0246,
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0.0315,
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0.0165,
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0.0126])
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self.assertEqual([round(x.benchmark_period_returns, 4)
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for x in metrics.three_month_periods],
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[0.0373,
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0.0239,
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-0.0083,
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-0.0191,
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-0.0259,
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0.0266,
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0.0517,
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0.0793,
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0.0743,
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0.0617])
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self.assertEqual([round(x.benchmark_period_returns, 4)
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for x in metrics.six_month_periods],
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[0.0176,
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-0.0027,
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0.0181,
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0.0316,
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0.0514,
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0.1028,
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0.1166])
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self.assertEqual([round(x.benchmark_period_returns, 4)
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for x in metrics.year_periods],
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[0.1362])
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def test_trading_days_06(self):
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returns = factory.create_returns_from_range(self.trading_env)
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metrics = risk.RiskReport(returns, self.trading_env)
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self.assertEqual([x.trading_days for x in metrics.year_periods],
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[251])
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self.assertEqual([x.trading_days for x in metrics.month_periods],
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[20, 19, 23, 19, 22, 22, 20, 23, 20, 22, 21, 20])
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def test_benchmark_volatility_06(self):
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returns = factory.create_returns_from_range(self.trading_env)
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metrics = risk.RiskReport(returns, self.trading_env)
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self.assertEqual([round(x.benchmark_volatility, 3)
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for x in metrics.month_periods],
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[0.031,
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0.026,
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0.024,
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0.025,
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0.037,
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0.047,
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0.039,
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0.022,
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0.023,
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0.021,
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0.025,
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0.019])
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self.assertEqual([round(x.benchmark_volatility, 3)
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for x in metrics.three_month_periods],
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[0.047,
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0.042,
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0.050,
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0.064,
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0.070,
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0.064,
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0.049,
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0.037,
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0.039,
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0.037])
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self.assertEqual([round(x.benchmark_volatility, 3)
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for x in metrics.six_month_periods],
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[0.079,
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0.082,
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0.081,
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0.081,
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0.08,
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0.074,
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0.061])
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self.assertEqual([round(x.benchmark_volatility, 3)
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for x in metrics.year_periods],
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[0.100])
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def test_algorithm_returns_06(self):
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self.assertEqual([round(x.algorithm_period_returns, 3)
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for x in self.metrics_06.month_periods],
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[0.101,
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-0.062,
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-0.041,
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0.092,
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0.135,
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-0.25,
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0.076,
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-0.003,
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-0.024,
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0.072,
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0.063,
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-0.071])
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self.assertEqual([round(x.algorithm_period_returns, 3)
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for x in self.metrics_06.three_month_periods],
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[-0.009,
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-0.017,
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0.188,
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-0.071,
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-0.085,
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-0.196,
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0.047,
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0.043,
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0.112,
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0.058])
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self.assertEqual([round(x.algorithm_period_returns, 3)
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for x in self.metrics_06.six_month_periods],
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[-0.08,
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-0.101,
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-0.044,
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-0.027,
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-0.045,
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-0.106,
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0.108])
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self.assertEqual([round(x.algorithm_period_returns, 3)
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for x in self.metrics_06.year_periods],
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[0.02])
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def test_algorithm_volatility_06(self):
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self.assertEqual([round(x.algorithm_volatility, 3)
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for x in self.metrics_06.month_periods],
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[0.137,
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0.12,
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0.13,
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0.142,
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0.128,
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0.14,
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0.141,
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0.118,
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0.143,
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0.144,
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0.117,
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0.135])
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self.assertEqual([round(x.algorithm_volatility, 3)
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for x in self.metrics_06.three_month_periods],
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[0.222,
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0.224,
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0.229,
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0.243,
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0.243,
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0.235,
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0.23,
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0.231,
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0.231,
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0.227])
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self.assertEqual([round(x.algorithm_volatility, 3)
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for x in self.metrics_06.six_month_periods],
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[0.328,
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0.329,
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0.329,
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0.333,
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0.334,
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0.329,
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0.321])
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self.assertEqual([round(x.algorithm_volatility, 3)
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for x in self.metrics_06.year_periods],
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[0.458])
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def test_algorithm_sharpe_06(self):
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self.assertEqual([round(x.sharpe, 3)
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for x in self.metrics_06.month_periods],
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[0.711,
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-0.541,
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-0.348,
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0.625,
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1.017,
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-1.809,
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0.508,
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-0.062,
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-0.193,
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0.467,
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0.502,
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-0.557])
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self.assertEqual([round(x.sharpe, 3)
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for x in self.metrics_06.three_month_periods],
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[-0.094,
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-0.129,
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0.769,
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-0.342,
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-0.402,
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-0.888,
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0.153,
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0.131,
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0.432,
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0.2])
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self.assertEqual([round(x.sharpe, 3)
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for x in self.metrics_06.six_month_periods],
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[-0.322,
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-0.383,
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-0.213,
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-0.156,
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-0.213,
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-0.398,
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0.257])
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self.assertEqual([round(x.sharpe, 3)
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for x in self.metrics_06.year_periods],
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[-0.066])
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def dtest_algorithm_beta_06(self):
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self.assertEqual([round(x.beta, 3)
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for x in self.metrics_06.month_periods],
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[0.553,
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0.583,
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-2.168,
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-0.548,
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1.463,
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-0.322,
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-1.38,
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1.473,
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-1.315,
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-0.7,
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0.352,
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-2.002])
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self.assertEqual([round(x.beta, 3)
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for x in self.metrics_06.three_month_periods],
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[-0.075,
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-0.637,
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0.124,
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0.186,
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-0.204,
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-0.497,
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-0.867,
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-0.173,
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-0.499,
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-0.563])
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self.assertEqual([round(x.beta, 3)
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for x in self.metrics_06.six_month_periods],
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[-0.075,
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-0.637,
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0.124,
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0.186,
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-0.204,
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-0.497,
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-0.867,
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-0.173,
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-0.499,
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-0.563])
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self.assertEqual([round(x.beta, 3)
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for x in self.metrics_06.year_periods], [-0.219])
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def dtest_algorithm_alpha_06(self):
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self.assertEqual([round(x.alpha, 3)
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for x in self.metrics_06.month_periods],
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[0.085,
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-0.063,
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-0.03,
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0.093,
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0.182,
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-0.255,
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0.073,
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-0.032,
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0,
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0.086,
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0.054,
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-0.058])
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self.assertEqual([round(x.alpha, 3)
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for x in self.metrics_06.three_month_periods],
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[-0.051,
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-0.021,
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0.179,
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-0.077,
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-0.106,
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-0.202,
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0.069,
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0.042,
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0.13,
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0.073])
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self.assertEqual([round(x.alpha, 3)
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for x in self.metrics_06.six_month_periods],
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[-0.105,
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-0.135,
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-0.072,
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-0.051,
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-0.066,
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-0.094,
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0.152])
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self.assertEqual([round(x.alpha, 3)
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for x in self.metrics_06.year_periods],
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[-0.011])
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# FIXME: Covariance is not matching excel precisely enough to run the test.
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# Month 4 seems to be the problem. Variance is disabled
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# just to avoid distraction - it is much closer than covariance
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# and can probably pass with 6 significant digits instead of 7.
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#re-enable variance, alpha, and beta tests once this is resolved
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def dtest_algorithm_covariance_06(self):
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metric = self.metrics_06.month_periods[3]
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print repr(metric)
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print "----"
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self.assertEqual([round(x.algorithm_covariance, 7)
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for x in self.metrics_06.month_periods],
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[0.0000289,
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0.0000222,
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-0.0000554,
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-0.0000192,
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0.0000954,
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-0.0000333,
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-0.0001111,
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0.0000322,
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-0.0000349,
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-0.0000143,
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0.0000108,
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-0.0000386])
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self.assertEqual([round(x.algorithm_covariance, 7)
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for x in self.metrics_06.three_month_periods],
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[-0.0000026,
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-0.0000189,
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0.0000049,
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0.0000121,
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-0.0000158,
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-0.000031,
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-0.0000336,
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-0.0000036,
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-0.0000119,
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-0.0000122])
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self.assertEqual([round(x.algorithm_covariance, 7)
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for x in self.metrics_06.six_month_periods],
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[0.000005,
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-0.0000172,
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-0.0000142,
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-0.0000102,
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-0.0000089,
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-0.0000207,
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-0.0000229])
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self.assertEqual([round(x.algorithm_covariance, 7)
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for x in self.metrics_06.year_periods],
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[-8.75273E-06])
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def dtest_benchmark_variance_06(self):
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self.assertEqual([round(x.benchmark_variance, 7)
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for x in self.metrics_06.month_periods],
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[0.0000496,
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0.000036,
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0.0000244,
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0.0000332,
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0.0000623,
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0.0000989,
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0.0000765,
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0.0000209,
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0.0000252,
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0.0000194,
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0.0000292,
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0.0000183])
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self.assertEqual([round(x.benchmark_variance, 7)
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for x in self.metrics_06.three_month_periods],
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[0.0000351,
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0.0000298,
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0.0000395,
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0.0000648,
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0.0000773,
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0.0000625,
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0.0000387,
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0.0000211,
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0.0000238,
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0.0000217])
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self.assertEqual([round(x.benchmark_variance, 7)
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for x in self.metrics_06.six_month_periods],
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[0.0000499,
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0.0000538,
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0.0000508,
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0.0000517,
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0.0000492,
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0.0000432,
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0.00003])
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self.assertEqual([round(x.benchmark_variance, 7)
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for x in self.metrics_06.year_periods],
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[0.0000399])
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def test_benchmark_returns_08(self):
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returns = factory.create_returns_from_range(self.trading_env08)
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metrics = risk.RiskReport(returns, self.trading_env08)
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monthly = [round(x.benchmark_period_returns, 3)
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for x in metrics.month_periods]
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self.assertEqual(monthly,
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[-0.061,
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-0.035,
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-0.006,
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0.048,
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0.011,
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-0.086,
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-0.01,
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0.012,
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-0.091,
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-0.169,
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-0.075,
|
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0.008])
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self.assertEqual([round(x.benchmark_period_returns, 3)
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for x in metrics.three_month_periods],
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[-0.099,
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0.005,
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0.052,
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-0.032,
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-0.085,
|
|
-0.084,
|
|
-0.089,
|
|
-0.236,
|
|
-0.301,
|
|
-0.226])
|
|
|
|
self.assertEqual([round(x.benchmark_period_returns, 3)
|
|
for x in metrics.six_month_periods],
|
|
[-0.128,
|
|
-0.081,
|
|
-0.036,
|
|
-0.118,
|
|
-0.301,
|
|
-0.360,
|
|
-0.294])
|
|
|
|
self.assertEqual([round(x.benchmark_period_returns, 3)
|
|
for x in metrics.year_periods],
|
|
[-0.385])
|
|
|
|
def test_trading_days_08(self):
|
|
returns = factory.create_returns_from_range(self.trading_env08)
|
|
metrics = risk.RiskReport(returns, self.trading_env08)
|
|
self.assertEqual([x.trading_days for x in metrics.year_periods],
|
|
[253])
|
|
|
|
self.assertEqual([x.trading_days for x in metrics.month_periods],
|
|
[21, 20, 20, 22, 21, 21, 22, 21, 21, 23, 19, 22])
|
|
|
|
def test_benchmark_volatility_08(self):
|
|
returns = factory.create_returns_from_range(self.trading_env08)
|
|
metrics = risk.RiskReport(returns, self.trading_env08)
|
|
self.assertEqual([round(x.benchmark_volatility, 3)
|
|
for x in metrics.month_periods],
|
|
[0.07,
|
|
0.058,
|
|
0.082,
|
|
0.054,
|
|
0.041,
|
|
0.057,
|
|
0.068,
|
|
0.06,
|
|
0.157,
|
|
0.244,
|
|
0.195,
|
|
0.145])
|
|
|
|
self.assertEqual([round(x.benchmark_volatility, 3)
|
|
for x in metrics.three_month_periods],
|
|
[0.120,
|
|
0.113,
|
|
0.105,
|
|
0.09,
|
|
0.098,
|
|
0.107,
|
|
0.179,
|
|
0.293,
|
|
0.344,
|
|
0.340])
|
|
|
|
self.assertEqual([round(x.benchmark_volatility, 3)
|
|
for x in metrics.six_month_periods],
|
|
[0.15, 0.149, 0.15, 0.2, 0.308, 0.36, 0.383])
|
|
# TODO: ugly, but I can't get the rounded float to match.
|
|
# maybe we need a different test that checks the
|
|
# difference between the numbers
|
|
self.assertEqual([round(x.benchmark_volatility, 3)
|
|
for x in metrics.year_periods],
|
|
[0.41099999999999998])
|
|
|
|
def test_treasury_returns_06(self):
|
|
returns = factory.create_returns_from_range(self.trading_env)
|
|
metrics = risk.RiskReport(returns, self.trading_env)
|
|
self.assertEqual([round(x.treasury_period_return, 4)
|
|
for x in metrics.month_periods],
|
|
[0.0037,
|
|
0.0034,
|
|
0.0039,
|
|
0.0038,
|
|
0.0040,
|
|
0.0037,
|
|
0.0043,
|
|
0.0043,
|
|
0.0038,
|
|
0.0044,
|
|
0.0043,
|
|
0.0041])
|
|
|
|
self.assertEqual([round(x.treasury_period_return, 4)
|
|
for x in metrics.three_month_periods],
|
|
[0.0114,
|
|
0.0118,
|
|
0.0122,
|
|
0.0125,
|
|
0.0129,
|
|
0.0127,
|
|
0.0123,
|
|
0.0128,
|
|
0.0125,
|
|
0.0128])
|
|
self.assertEqual([round(x.treasury_period_return, 4)
|
|
for x in metrics.six_month_periods],
|
|
[0.0260,
|
|
0.0257,
|
|
0.0258,
|
|
0.0252,
|
|
0.0259,
|
|
0.0256,
|
|
0.0258])
|
|
|
|
self.assertEqual([round(x.treasury_period_return, 4)
|
|
for x in metrics.year_periods],
|
|
[0.0500])
|
|
|
|
def test_benchmarkrange(self):
|
|
self.check_year_range(datetime.datetime(year=2008, month=1, day=1),
|
|
2)
|
|
|
|
def test_partial_month(self):
|
|
|
|
start = datetime.datetime(
|
|
year=1991,
|
|
month=1,
|
|
day=1,
|
|
hour=0,
|
|
minute=0,
|
|
tzinfo=pytz.utc)
|
|
|
|
#1992 and 1996 were leap years
|
|
total_days = 365 * 5 + 2
|
|
end = start + datetime.timedelta(days=total_days)
|
|
trading_env90s = TradingEnvironment(
|
|
self.benchmark_returns,
|
|
self.treasury_curves,
|
|
period_start=start,
|
|
period_end=end
|
|
)
|
|
|
|
returns = factory.create_returns(total_days, trading_env90s)
|
|
returns = returns[:-10] # truncate the returns series to end mid-month
|
|
metrics = risk.RiskReport(returns, trading_env90s)
|
|
total_months = 60
|
|
self.check_metrics(metrics, total_months, start)
|
|
|
|
def check_year_range(self, start_date, years):
|
|
if(start_date.month <= 2):
|
|
ld = calendar.leapdays(start_date.year, start_date.year + years)
|
|
else:
|
|
# because we may catch the leap of the last year,
|
|
# and i think this func is [start,end)
|
|
ld = calendar.leapdays(start_date.year,
|
|
start_date.year + years + 1)
|
|
returns = factory.create_returns(365 * years + ld, self.trading_env08)
|
|
metrics = risk.RiskReport(returns, self.trading_env)
|
|
total_months = years * 12
|
|
self.check_metrics(metrics, total_months, start_date)
|
|
|
|
def check_metrics(self, metrics, total_months, start_date):
|
|
"""
|
|
confirm that the right number of riskmetrics were calculated for each
|
|
window length.
|
|
"""
|
|
self.assert_range_length(
|
|
metrics.month_periods,
|
|
total_months,
|
|
1,
|
|
start_date
|
|
)
|
|
|
|
self.assert_range_length(
|
|
metrics.three_month_periods,
|
|
total_months,
|
|
3,
|
|
start_date
|
|
)
|
|
|
|
self.assert_range_length(
|
|
metrics.six_month_periods,
|
|
total_months,
|
|
6,
|
|
start_date
|
|
)
|
|
|
|
self.assert_range_length(
|
|
metrics.year_periods,
|
|
total_months,
|
|
12,
|
|
start_date
|
|
)
|
|
|
|
def assert_last_day(self, period_end):
|
|
#30 days has september, april, june and november
|
|
if period_end.month in [9, 4, 6, 11]:
|
|
self.assertEqual(period_end.day, 30)
|
|
#all the rest have 31, except for february
|
|
elif(period_end.month != 2):
|
|
self.assertEqual(period_end.day, 31)
|
|
else:
|
|
if calendar.isleap(period_end.year):
|
|
self.assertEqual(period_end.day, 29)
|
|
else:
|
|
self.assertEqual(period_end.day, 28)
|
|
|
|
def assert_month(self, start_month, actual_end_month):
|
|
if start_month == 1:
|
|
expected_end_month = 12
|
|
else:
|
|
expected_end_month = start_month - 1
|
|
|
|
self.assertEqual(expected_end_month, actual_end_month)
|
|
|
|
def assert_range_length(self, col, total_months,
|
|
period_length, start_date):
|
|
if(period_length > total_months):
|
|
self.assertEqual(len(col), 0)
|
|
else:
|
|
self.assertEqual(
|
|
len(col),
|
|
total_months - (period_length - 1),
|
|
"mismatch for total months - \
|
|
expected:{total_months}/actual:{actual}, \
|
|
period:{period_length}, start:{start_date}, \
|
|
calculated end:{end}".format(
|
|
total_months=total_months,
|
|
period_length=period_length,
|
|
start_date=start_date,
|
|
end=col[-1].end_date,
|
|
actual=len(col)
|
|
))
|
|
self.assert_month(start_date.month, col[-1].end_date.month)
|
|
self.assert_last_day(col[-1].end_date)
|
|
|
|
RETURNS = [
|
|
0.0093, -0.0193, 0.0351, 0.0396, 0.0338, -0.0211, 0.0389,
|
|
0.0326, -0.0137, -0.0411, -0.0032, 0.0149, 0.0133, 0.0348,
|
|
0.042, -0.0455, 0.0262, -0.0461, 0.0021, -0.0273, -0.0429,
|
|
0.0427, -0.0104, 0.0346, -0.0311, 0.0003, 0.0211, 0.0248,
|
|
-0.0215, 0.004, 0.0267, 0.0029, -0.0369, 0.0057, 0.0298,
|
|
-0.0179, -0.0361, -0.0401, -0.0123, -0.005, 0.0203, -0.041,
|
|
0.0011, 0.0118, 0.0103, -0.0184, -0.0437, 0.0411, -0.0242,
|
|
-0.0054, -0.0039, -0.0273, -0.0075, 0.0064, -0.0376, 0.0424,
|
|
0.0399, 0.019, 0.0236, -0.0284, -0.0341, 0.0266, 0.05,
|
|
0.0069, -0.0442, -0.016, 0.0173, 0.0348, -0.0404, -0.0068,
|
|
-0.0376, 0.0356, 0.0043, -0.0481, -0.0134, 0.0257, 0.0442,
|
|
0.0234, 0.0394, 0.0376, -0.0147, -0.0098, 0.0474, -0.0102,
|
|
0.0138, 0.0286, 0.0347, 0.0279, -0.0067, 0.0462, -0.0432,
|
|
0.0247, 0.0174, -0.0305, -0.0317, -0.0068, 0.0264, -0.0257,
|
|
-0.0328, 0.0092, 0.0288, -0.002, 0.0288, 0.028, -0.0093,
|
|
0.0178, -0.0365, -0.0086, -0.0133, -0.0309, 0.0473, -0.0149,
|
|
0.0378, -0.0316, -0.0292, -0.0453, -0.0451, 0.0093, 0.0397,
|
|
-0.0361, -0.0168, -0.0494, -0.0143, -0.0405, -0.0349, 0.0069,
|
|
0.0378, -0.0233, -0.0492, 0.018, -0.0386, 0.0339, 0.0119,
|
|
0.0454, 0.0118, -0.011, -0.0254, 0.0266, -0.0366, -0.0211,
|
|
0.0399, 0.0307, 0.035, -0.0402, 0.0304, -0.0031, 0.0256,
|
|
0.0134, -0.0019, -0.0235, -0.0058, -0.0117, 0.0051, -0.0451,
|
|
-0.0466, -0.0124, 0.0283, -0.0499, 0.0318, -0.0028, 0.0203,
|
|
0.005, 0.0085, 0.0048, 0.0277, 0.0159, -0.0149, 0.035,
|
|
0.0404, -0.01, 0.0377, 0.0302, 0.0046, -0.0328, -0.0469,
|
|
0.0071, -0.0382, -0.0214, 0.0429, 0.0145, -0.0279, -0.0172,
|
|
0.0423, 0.041, -0.0183, 0.0137, -0.0412, -0.0348, 0.0302,
|
|
0.0248, 0.0051, -0.0298, -0.0103, -0.0333, -0.0399, 0.0485,
|
|
-0.0166, 0.0384, 0.0259, -0.0163, 0.0357, 0.0308, -0.0386,
|
|
0.0481, -0.0446, -0.0282, -0.0037, 0.0202, 0.0216, 0.0113,
|
|
0.0194, 0.0392, 0.0016, 0.0268, -0.0155, -0.027, 0.02,
|
|
0.0216, -0.0009, 0.022, 0., 0.041, 0.0133, -0.0382,
|
|
0.0495, -0.0221, -0.0329, -0.0033, -0.0089, -0.0129, -0.0252,
|
|
0.048, -0.0307, -0.0357, 0.0033, -0.0412, -0.0407, 0.0455,
|
|
0.0159, -0.0051, -0.0274, -0.0213, 0.0361, 0.0051, -0.0378,
|
|
0.0084, 0.0066, -0.0103, -0.0037, 0.0478, -0.0278
|
|
]
|