同花顺Supermind量化交易 多因子专题(一)--因子暴露值的不同取法 附源代码

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多因子模型分回归和排序两类,其中回归重在解释,而排序旨在选股收益。回归中的因子暴露也有两类求取方式,一类是直接提取因子值,另一类是在时序回归下得到的因子暴露值。

一、提取数据

In [9]:

import pandas as pd
import numpy as np
import datetime
import matplotlib.pyplot as plt
plt.style.use('seaborn')

start_date='2018-01-10'
end_date='2019-01-10'

start_date=datetime.datetime.strptime(start_date,'%Y-%m-%d')
end_date=datetime.datetime.strptime(end_date,'%Y-%m-%d')+datetime.timedelta(days=1)
    
stock_list1=get_index_stocks('000300.SH',start_date)
stock_list2=get_index_stocks('000300.SH',end_date)
stock_list=list(set(stock_list1).intersection(set(stock_list2))) 
#df = get_fundamentals(query(asharevalue.symbol, asharevalue.pb_mrq).filter(asharevalue.symbol.in_(stocklist)),date=start_date)
#df = df.set_index('asharevalue_symbol')
    
price = get_price(stock_list, start_date,end_date, '1d', ['quote_rate'], True, None, is_panel=1)['quote_rate']
print(price)

    
                                                        
            000001.SZ  000002.SZ  000063.SZ  000069.SZ  000100.SZ  000157.SZ  \
2018-01-10     2.9817    -0.4743    -1.1829    -1.3684    -0.9926    -0.2160   
2018-01-11    -0.5197    -1.4578     1.3920     0.4269    -0.7519    -0.8658   
2018-01-12     1.1194     1.1380    -1.6474     1.2752     1.0101    -0.6550   
2018-01-15     4.7970     4.3319     1.6471     1.4690     0.7500    -1.3187   
2018-01-16     0.0000     8.3850     6.0148     0.0000     0.4963     2.0045   
2018-01-17     0.2113    -1.0697    -4.1969     5.6877    -3.2099    -0.4367   
2018-01-18     3.4434    -0.0251    -1.1087    -1.1742    -0.7653     1.0965   
2018-01-19     0.5435    -0.8551    -0.2188     1.0891     0.0000     0.0000   
2018-01-22    -2.4324     0.2790    -0.1644     0.0000    -0.2571     1.0846   
2018-01-23     1.4543     3.6681    -0.1372     1.5671    -1.0309    -0.2146   
2018-01-24    -0.0683     0.3660     1.8417     0.3857    -0.7813    -0.4301   
2018-01-25    -3.0055    -2.2611    -2.6721     2.7858    -0.5249     0.8639   
2018-01-26    -1.0563    -0.3980    -2.9395     0.8411    -1.8470    -0.8565   
2018-01-29    -2.2064    -3.6713    -9.4000    -3.2437    -3.2258    -1.7279   
2018-01-30    -0.6550    -5.7298    -1.9237    -1.8199     0.5556    -1.0989   
2018-01-31     2.9304     3.3003     0.0643     0.9756    -1.3812    -0.2222   
2018-02-01    -0.1423    -0.1597    -9.9936    -2.7053    -4.7619    -3.1180   
2018-02-02     0.1426    -0.3200     2.8918     1.0924     1.7647     0.4598   
2018-02-05     3.5587    -1.0433     1.5961     0.8841     0.5780     0.9153   
2018-02-06    -3.7801    -3.1630    -2.8347    -3.7001    -3.7356    -3.1746   
2018-02-07    -7.7143    -7.9285     0.9139    -9.3023     0.0000     0.4684   
2018-02-08    -2.9412    -0.6974     3.2741    -1.7837     3.5821     0.9324   
2018-02-09    -6.7783    -4.5191    -4.0472    -5.7889    -3.7464    -4.1570   
2018-02-12     0.2566     2.0147     3.4095     1.4458     2.0958     1.4458   
2018-02-13     1.8771     2.6019     1.0877     1.4252     0.0000     0.7126   
2018-02-14     0.5025     1.3443     2.5555     1.4052     0.8798     0.0000   
2018-02-22     3.8333     1.5978     2.3607     0.8083     0.8721     0.9434   
2018-02-23     1.2039     3.0267     0.3203     0.4582    -1.1527     0.0000   
2018-02-26     0.1586    -1.5553     3.9272    -0.7982     6.9971     1.1682   
2018-02-27    -2.7712    -3.7449    -0.5530    -2.6437     1.3624    -0.9238   
...               ...        ...        ...        ...        ...        ...   
2018-11-29    -0.7782    -2.2798    -5.2043    -4.3619    -2.7778    -1.3850   
2018-11-30     1.5686     0.5931     1.9497     1.5203     0.8163    -0.2809   
2018-12-03     2.2201     1.1399     7.9014     2.3295     2.8340     3.6620   
2018-12-04     0.0000    -2.3319    -0.7929    -1.1382     0.0000     1.9022   
2018-12-05    -1.3220     0.6765    -0.8463     0.1645    -0.3937    -0.5333   
2018-12-06    -1.9139    -0.7905    -5.6899    -1.9704    -1.5810    -2.1448   
2018-12-07     0.2927     0.9562     0.5028     0.6700     2.8112     1.9178   
2018-12-10    -1.0700    -1.3418     0.2501    -2.3295    -5.8594    -2.4194   
2018-12-11     0.5900     3.8800     1.4970     2.2147     0.4149    -0.2755   
2018-12-12     0.0978     1.4632    -1.6716     1.1667     0.4132     0.5525   
2018-12-13     1.4648     2.8463     1.0000     2.6359     0.4115     1.9231   
2018-12-14    -2.1174    -2.3616    -2.7228    -1.7657     0.4098    -1.0782   
2018-12-17     1.1799     0.2268    -2.0356     0.3268     0.0000     0.8174   
2018-12-18    -1.6521    -3.8462    -0.7792    -1.9544    -0.8163    -1.6216   
2018-12-19    -1.7787    -0.4706    -0.4188     0.9967    -0.4115     0.2747   
2018-12-20    -2.3139    -0.3152     1.7876    -0.4934    -0.4132    -1.0959   
2018-12-21    -2.6777    -4.1502    -0.6198    -2.1488    -0.4149     1.1080   
2018-12-24    -0.3175    -1.5258     5.3015     0.3378     0.0000     0.5479   
2018-12-25    -0.8493     0.3769     0.4936    -0.8418     0.4167    -1.6349   
2018-12-26    -0.4283    -0.7092    -2.4558     3.3956    -0.4149    -0.8310   
2018-12-27    -0.2151    -1.5126     0.2014     1.1494     0.8333     0.0000   
2018-12-28     1.0776     1.6212    -1.5578     3.0844     1.2397    -0.5587   
2019-01-02    -2.0256     0.3359    -0.1531    -5.9843     2.4490    -2.5281   
2019-01-03     0.9793     0.7113    -3.9877     0.1675     0.7968     1.4409   
2019-01-04     5.0647     3.5729     2.2364     2.5084     1.5810     1.1364   
2019-01-07    -0.1026     0.4813     4.2708     0.9788     3.5019     1.4045   
2019-01-08    -0.8214    -0.1996    -0.5994    -1.1309     6.7669     0.5540   
2019-01-09     2.8986     1.3200     0.1005     1.9608    -0.7042     0.2755   
2019-01-10     1.6097    -0.8685     0.7530     0.4808    -4.6099    -0.5495   
2019-01-11     0.9901     0.7567     2.1923    -0.3190     1.8587     0.2762   

            000166.SZ  000333.SZ  000338.SZ  000402.SZ    ...      601989.SH  \
2018-01-10    -0.5597     1.8157     0.5637    -0.6832    ...        -1.2987   
2018-01-11     0.0000    -1.5522    -2.0179    -0.2580    ...         0.3289   
2018-01-12     0.0000     1.9792    -0.8009     1.1207    ...         0.3279   
2018-01-15    -1.3133     0.5921    -0.9227     1.1083    ...        -2.7778   
2018-01-16     1.1407    -0.1145     4.7730     5.8179    ...         0.6723   
2018-01-17     2.8195    -3.8304     0.8889    -2.3904    ...         0.5008   
2018-01-18     0.0000     0.3404    -0.3304    -0.9796    ...         0.8306   
2018-01-19     2.1938    -1.3232    -0.6630    -1.5664    ...         2.1417   
2018-01-22     0.0000     5.6043     1.2236     0.4188    ...         0.1613   
2018-01-23    -0.3578     1.1232     0.8791     2.0017    ...         0.4831   
2018-01-24     2.3339    -2.7527    -1.7429    -0.3271    ...         2.0833   
2018-01-25    -2.4561     1.4733    -0.4435    -2.1329    ...         0.3140   
2018-01-26     0.7194     1.1419    -0.2227     2.4308    ...        -0.6260   
2018-01-29     0.0000    -3.4355     1.0045    -1.1457    ...        -2.0472   
2018-01-30    -2.1429    -1.8540    -1.5470    -3.3940    ...         0.3215   
2018-01-31    -2.3723     1.8039    -1.4590     1.1140    ...        -0.3205   
2018-02-01    -0.5607    -0.8024    -1.4806    -2.3729    ...        -3.6977   
2018-02-02     0.9398     0.9437     4.0462    -1.8229    ...         2.1703   
2018-02-05     0.0000    -4.3072     0.0000     1.6799    ...        -0.8170   
2018-02-06    -0.7449    -3.1752    -3.7778    -3.9130    ...        -3.2949   
2018-02-07    -2.2514    -4.8829    -4.1570    -3.1674    ...         0.6814   
2018-02-08     0.3839     1.8564     0.9639     0.5607    ...         0.6768   
2018-02-09    -4.2065    -3.3290    -7.5179    -6.1338    ...        -9.2437   
2018-02-12    -0.7984     4.6941     2.7097     0.0990    ...         0.7407   
2018-02-13    -0.2012     1.6354     1.5075     0.1978    ...         0.1838   
2018-02-14     0.4032     2.9109     1.3614    -0.2962    ...        -0.3670   
2018-02-22     0.2008     2.1434     4.5177     1.7822    ...         1.6575   
2018-02-23     0.2004    -1.0148    -0.4673     1.8482    ...         0.1812   
2018-02-26     1.6000     0.2606     1.8779     0.8596    ...         1.2658   
2018-02-27    -0.7874    -5.3726    -2.9954    -2.5568    ...         0.5357   
...               ...        ...        ...        ...    ...            ...   
2018-11-29    -1.7738    -3.0485    -0.7968    -2.2857    ...        -0.7126   
2018-11-30     0.2257    -0.2835     0.6693    -0.8772    ...         1.4354   
2018-12-03     2.7027     5.5311     2.2606     3.3923    ...         1.4151   
2018-12-04     0.8772    -0.7103     0.7802    -0.7133    ...        -0.2326   
2018-12-05    -1.7391    -1.3320    -0.7742    -1.0057    ...        -0.4662   
2018-12-06    -1.9912    -2.6000    -1.1704    -1.7417    ...        -0.7026   
2018-12-07     0.4515    -1.2320     0.2632     0.4431    ...         0.4717   
2018-12-10    -1.3483    -3.6902    -1.4436    -2.2059    ...        -0.4695   
2018-12-11     0.0000    -0.0540     0.5326     0.9023    ...         0.2358   
2018-12-12     0.0000     1.8898     0.5298     1.0432    ...         0.2353   
2018-12-13     0.6834     6.3063     1.7128     2.2124    ...         0.7042   
2018-12-14    -3.8462    -0.9222    -0.2591    -1.7316    ...        -1.8648   
2018-12-17    -0.7059    -0.7296     2.0779     1.9090    ...         0.4751   
2018-12-18    -0.4739    -1.6472    -0.6361    -3.3141    ...         0.0000   
2018-12-19    -0.9524    -1.4429     0.3841    -1.7884    ...        -0.9456   
2018-12-20     1.6827     0.2092    -0.7653     0.3035    ...        -0.9547   
2018-12-21    -2.1277    -1.0697     0.3856    -0.1513    ...        -1.6867   
2018-12-24     0.2415    -0.4747    -0.6402     1.3636    ...         3.4314   
2018-12-25    -1.9277    -0.9539    -1.2887    -1.9432    ...        -0.4739   
2018-12-26    -1.4742    -0.6688    -0.7833    -0.3049    ...        -0.4762   
2018-12-27    -0.4988    -0.8888     0.3947    -1.5291    ...         1.9139   
2018-12-28     2.0050     0.1630     0.9174     0.0000    ...        -0.2347   
2019-01-02    -0.7371    -1.1394    -1.8182    -1.5528    ...         0.2353   
2019-01-03     2.2277    -0.6586    -0.9259    -1.7350    ...         2.1127   
2019-01-04     7.0218     2.1823     1.6021     3.8523    ...         3.6782   
2019-01-07    -0.9050     0.0000     0.6570     2.9366    ...         2.6608   
2019-01-08     0.4566    -0.3514     0.0000     0.3003    ...        -2.1598   
2019-01-09     0.0000     5.8058     1.3055     2.3952    ...        -1.3245   
2019-01-10    -1.5909     0.7436     0.7732    -0.8772    ...        -0.4474   
2019-01-11     0.6928     1.3998     1.0230     0.0000    ...         0.6742   

            601991.SH  601992.SH  601997.SH  601998.SH  603160.SH  603799.SH  \
2018-01-10    -0.7059    -1.1551     0.7117     1.8519     0.4359    -0.6992   
2018-01-11     0.9479    -1.5025    -0.7067     1.8182    -0.4038     2.0799   
2018-01-12     0.2347     1.1864     0.1423     1.9345    -2.0878    -2.7698   
2018-01-15    -3.7471    -2.3451     1.7768     1.7518    -3.9437    -5.8939   
2018-01-16     0.0000     4.1166     2.3045     0.4304     0.1293     2.5168   
2018-01-17     0.0000    -2.6359     0.4096    -1.2857     0.4628    -5.3513   
2018-01-18    -0.4866    -0.1692     0.8158     4.1968    -1.5533     0.0956   
2018-01-19     0.9780     0.5085     3.1018     0.0000     0.3156     2.6869   
2018-01-22     1.2107    -0.8432    -1.9621    -1.1111     0.9003     1.3374   
2018-01-23     0.2392     0.0000     2.0013     3.6517     0.6128     6.2084   
2018-01-24     0.4773     0.6803     0.5886     0.2710     1.3997     0.9941   
2018-01-25     0.2375     0.8446     1.9506    -1.8919    -2.3077     0.3745   
2018-01-26     0.0000    -0.3350     0.0638     1.5152    -0.9276     3.3362   
2018-01-29     0.2370    -1.0084     8.0943    -1.2212    -3.5928     5.1882   
2018-01-30    -0.7092    -2.2071     0.2948    -1.7857    -0.7340    -8.7860   
2018-01-31    -2.3810    -2.9514     1.9400     0.9790    -3.4130     7.5038   
2018-02-01    -3.1707    -5.3667    -4.1522     2.2161    -5.6537    -2.1800   
2018-02-02     0.7557    -0.3781     0.9627     0.5420    -0.0624     2.8726   
2018-02-05     0.0000     0.1898     4.2908     9.7035    -0.8245    -5.5749   
2018-02-06    -3.7500    -7.9545    -4.2857    -1.5971    -8.1496    -6.6723   
2018-02-07    -1.0390     0.0000    -2.8060    -3.2459     1.4399    -0.8796   
2018-02-08     1.5748     1.8519    -0.7985    -6.4516     2.9877     4.4482   
2018-02-09    -3.3592    -6.4646    -6.1300    -4.8276    -0.3807    -5.2282   
2018-02-12     0.2674     1.0799    -0.6596    -2.7536     3.3206     9.4587   
2018-02-13    -0.8000     1.7094     0.7304     1.4903    -0.8417     0.7350   
2018-02-14    -0.5376     0.4202    -0.9888    -1.0279    -1.8650     4.2214   
2018-02-22     1.3514     9.6234     2.0639     5.4896     4.7969    10.0010   
2018-02-23     0.5333     1.5267     0.6523     0.4219    -0.6628     3.5731   
2018-02-26     1.0610     3.1955     1.2314     0.0000     4.1672     0.5355   
2018-02-27     0.7874    -2.5501    -1.9206    -1.5406     2.0425    -1.8947   
...               ...        ...        ...        ...        ...        ...   
2018-11-29     0.3236    -3.0812    -1.4311    -0.5300     0.7013    -2.8872   
2018-11-30     1.2903    -0.2890     0.7260     0.7105     0.3900     5.3267   
2018-12-03     1.5924     3.1884     1.7117     1.0582     5.2026     2.9697   
2018-12-04     0.3135     2.5281     0.1771     0.0000     2.8617    -0.1428   
2018-12-05    -0.6250     2.4658    -1.0610    -0.6981     1.3205     3.3743   
2018-12-06    -0.3145    -1.0695    -0.8043    -1.2302    -5.5802     0.2490   
2018-12-07    -0.9464     4.5946     0.1802     0.1779     1.8092    -2.0419   
2018-12-10     0.3185    -0.5168    -1.1691    -1.4210     0.4344    -4.6197   
2018-12-11    -0.9524    -2.5974     0.8189     0.1802     1.0092     0.1477   
2018-12-12    -0.3205     0.5333     0.1805     0.1799     2.5950     0.5898   
2018-12-13     0.9646     1.0610     0.8108     0.3591     4.9450     1.1434   
2018-12-14    -0.6369    -1.5748    -1.6979    -0.7156    -0.5182    -3.1884   
2018-12-17     0.0000     3.4667    -0.4545     0.3604    -6.4930     2.2156   
2018-12-18    -0.3205    -3.8660    -0.7306    -0.8977    -0.4793     0.7616   
2018-12-19     0.6431    -1.0724    -0.4600    -0.3623     1.6532    -1.7442   
2018-12-20    -0.3195     0.5420    -0.4621    -1.0909     1.2037    -0.3254   
2018-12-21    -0.6410    -2.9650    -0.6500    -0.5515    -1.4425    -4.1852   
2018-12-24     0.0000    -0.2778     0.2804     1.2939     2.9144     0.1859   
2018-12-25    -0.6452    -1.9499    -0.3728    -1.6423    -3.1687    -4.0816   
2018-12-26    -0.9740     1.7045    -0.2806     0.0000    -0.0129    -2.0954   
2018-12-27     1.3115    -1.3966    -0.7505    -0.3711     2.4353    -1.9756   
2018-12-28     1.9417    -0.8499     0.9452     1.4898    -1.0063     1.1421   
2019-01-02    -0.6349    -4.0000    -1.0300    -2.2018    -7.3062    -2.6237   
2019-01-03     0.0000    -2.3810     0.3784     0.1876    -0.7265     0.2387   
2019-01-04     1.5974     2.1341     2.6390     1.8727     0.1105     2.8241   
2019-01-07     1.2579     1.7910    -0.0918    -0.3676     2.0000     1.1251   
2019-01-08     0.3106    -0.2933    -0.7353     0.1845     0.8790    -1.4071   
2019-01-09    -0.9288     0.5882     0.3704     0.9208    -0.0804    -2.6884   
2019-01-10    -0.3125     0.5848    -0.6458    -1.0949    -0.1878    -0.0341   
2019-01-11     0.3135     2.9070     0.3714     0.1845     0.0000     0.7506   

            603833.SH  603858.SH  603993.SH  
2018-01-10     0.0937    -1.7554    -0.4144  
2018-01-11    -2.4809     0.0971     7.7670  
2018-01-12     3.4080    -1.0283    -1.6731  
2018-01-15     4.1931    -2.6857    -1.7016  
2018-01-16     3.5714    -0.3425     7.7230  
2018-01-17    -0.3298     1.4756    -0.2472  
2018-01-18     1.8341    -0.4382     0.1239  
2018-01-19    -3.2490     3.8615     0.2475  
2018-01-22     1.0147    -1.9649     2.7160  
2018-01-23     3.1293     0.0000    -0.2404  
2018-01-24    -2.5718     0.0393    -1.6867  
2018-01-25    -0.2877    -0.8250     0.1225  
2018-01-26     2.0775     0.0000    -4.7736  
2018-01-29    -4.3106    -1.0299     0.5141  
2018-01-30    -1.7798     0.2802    -4.7315  
2018-01-31     7.4737    -1.5167     1.4765  
2018-02-01    -3.6169    -3.6677    -1.4550  
2018-02-02     1.5315    -0.0841     5.3691  
2018-02-05    -0.4647     2.5474     0.2548  
2018-02-06    -5.8177    -3.9622    -8.7675  
2018-02-07     1.4032     1.1543    -2.5070  
2018-02-08     0.9777     0.8876    -1.5714  
2018-02-09    -5.3921    -4.0846   -10.0145  
2018-02-12     7.8800     1.5287     4.5161  
2018-02-13     2.8240     4.3665     1.5432  
2018-02-14     3.8180     5.1113     2.4316  
2018-02-22     3.2401    -0.4118     9.9407  
2018-02-23    -0.7482    -1.9295     8.2321  
2018-02-26    -2.2815     1.8671     7.3566  
2018-02-27    -3.0653    -1.2810    -4.4135  
...               ...        ...        ...  
2018-11-29    -1.8509    -1.0674     0.0000  
2018-11-30     1.2530    -0.7068     2.3196  
2018-12-03     4.8750     4.6459     3.0227  
2018-12-04     1.3826     2.1482    -0.4890  
2018-12-05    -1.2462     0.5608     1.4742  
2018-12-06    -1.3214    -1.6731    -1.6949  
2018-12-07     1.3512    -2.9422    -0.2463  
2018-12-10    -4.9756    -2.5566    -1.9753  
2018-12-11     2.4677     0.2249     1.2594  
2018-12-12     3.3374    -1.0845     1.7413  
2018-12-13     5.4655     0.6805     1.4670  
2018-12-14    -2.7818    -2.3282    -1.6867  
2018-12-17    -0.4846     0.8074     1.7157  
2018-12-18     1.6464    -1.2967     0.0000  
2018-12-19    -4.9618    -1.9320    -1.4458  
2018-12-20    -0.5041     0.5910    -0.9780  
2018-12-21    -0.9771    -0.9792    -2.9630  
2018-12-24     2.3267     0.7120     0.5089  
2018-12-25    -1.4524    -0.1571    -1.5190  
2018-12-26    -1.5221     0.3147    -1.2853  
2018-12-27    -0.8832    -0.9412    -2.0833  
2018-12-28    -1.3366     0.0792     0.0000  
2019-01-02    -3.0231    -1.2263    -1.3298  
2019-01-03    -1.8497    -0.4806     0.8086  
2019-01-04     2.3458     2.5352     2.4064  
2019-01-07     4.1463     0.9027     1.5666  
2019-01-08    -1.0509    -0.3112    -1.0283  
2019-01-09     3.0489    -0.1561     0.2597  
2019-01-10     2.1584    -0.7034    -1.5544  
2019-01-11    -0.9970    -0.1181     0.7895  

[245 rows x 249 columns]

二、获取每日因子收益率

In [10]:

flag1=True
while start_date<=end_date: 
    next_date=start_date+datetime.timedelta(days=1)
    #print(next_date)
    
    #取全市场股票各股票市值因子
    df = get_fundamentals(query(asharevalue.symbol, asharevalue.total_mv).filter(\
                        asharevalue.symbol.in_(stock_list)).order_by(asharevalue.total_mv.asc()),date=start_date)
    df.set_index('asharevalue_symbol',inplace=True)
    df.index.name='symbol'
    
    stocklist_cap_top=list(df[:int(len(df)*0.3)].index)
    stocklist_cap_bottom=list(df[int(len(df)*0.7):].index)
   
    try:
        value_top = get_price(stocklist_cap_top,None, start_date, '1d', \
                              ['quote_rate'],True, None,1,is_panel=1)['quote_rate']
        return_sum_top=value_top.apply(lambda x:x.mean(),axis=1)    
        
        value_bottom = get_price(stocklist_cap_bottom,None, start_date, '1d', \
                                 ['quote_rate'], True, None,1,is_panel=1)['quote_rate']
        return_sum_bottom=value_bottom.apply(lambda x:x.mean(),axis=1) 
        return_factor=return_sum_top-return_sum_bottom
        
    except:
        
        start_date=start_date+datetime.timedelta(days=1)
        continue
  
    if flag1:
        flag1=False
        return_date_total_factor = return_factor
   
    else:
        return_date_total_factor = return_date_total_factor.append(return_factor)
        
    
    start_date=start_date+datetime.timedelta(days=1)
return_date_total_factor_array=np.array(return_date_total_factor)
return_date_total_factor_array

Out[10]:

array([-1.00484001,  0.62972498, -1.16946325, -2.49245642, -0.19890814,
        0.19051704, -0.76825396,  0.09867922,  0.17386311, -0.9645638 ,
        1.02585072,  0.28857345, -0.57885896,  0.08338763,  1.04119189,
       -2.6161901 , -3.20911127, -0.01550025, -0.9822674 , -2.5516373 ,
        2.34369859,  2.23938179, -0.60763779,  1.16781562, -0.46350538,
       -0.29765282, -0.75236175, -0.60026862,  1.06718711,  1.64165773,
        1.0355747 ,  0.73811368, -0.03581922,  0.09775101,  0.15879017,
       -0.1926726 , -0.39136396,  0.78650045,  0.5657264 , -0.0039845 ,
       -0.46152611, -0.68760461,  0.28538649, -0.29943236, -0.3908633 ,
        0.22121498,  0.40373624, -2.21538381,  2.17630921,  1.42087478,
        0.85210426, -0.24112186,  1.39104872,  0.88127721, -0.16933303,
       -1.06727102,  0.06093629, -1.53836031, -0.30853247,  0.59239521,
        0.54981569,  1.01811794, -0.39564507,  0.25226129, -0.50983944,
       -0.75257345, -1.70750065, -0.12632062,  0.31378809, -0.39872486,
        0.12895861, -0.87423384,  0.09945976,  0.04572701, -0.14132773,
       -0.47543099,  0.04508169, -0.18409437, -0.21907426, -1.39644225,
        0.81781268,  0.5994169 ,  0.52905352, -0.50499045,  0.70131307,
        0.56279755, -0.0680511 ,  0.26792025, -1.07704047, -0.71420251,
       -0.14035748, -0.75437642, -1.10975053,  0.17084654, -1.93982304,
        0.36130822, -0.05631377, -0.1642714 , -0.20772825, -0.31357517,
       -0.5356692 , -0.76035068,  0.03729041, -1.21346575, -3.75293304,
        0.53920261, -1.37870742,  1.11894365,  0.50196729,  1.47340948,
        1.09686923,  0.23147686,  0.30301764,  0.70349991,  1.71335533,
       -0.54083956, -2.06272669, -0.42057778, -0.71270822,  0.0263863 ,
       -0.97716939,  0.55302329, -0.49080548,  0.24471918,  0.43509178,
       -0.48209178, -1.01703288, -0.72295616,  0.41680611,  0.45489863,
        0.17870274,  0.62583562, -0.28976123, -1.43106513,  0.32674102,
       -0.02115698, -1.38033708,  0.53485   , -1.28092099, -0.55118767,
       -0.12998356, -0.09812603,  0.62986467,  0.51267399,  0.07209252,
        0.09255906, -0.22048326, -0.39247123, -0.68187751, -0.80243095,
        0.05370342,  0.12508438, -0.04678034, -0.38711272,  0.45731416,
        0.22637121, -0.43477701, -0.70546694,  0.33348745,  0.25484215,
        0.63418367,  0.27823373, -0.46608923, -0.60191644,  0.44036301,
        0.68029178, -0.49456164, -0.88941507, -0.40525479, -0.66579041,
       -0.14868082, -0.19473151, -1.57722877,  0.25177945, -0.52984161,
       -1.22386547,  0.06582673,  0.72291781, -0.10017397, -0.3170411 ,
       -3.36568482, -3.17932635, -0.50523265, -1.52582494,  0.23569237,
        0.82142987,  0.3981874 ,  1.23471781,  1.44571857, -0.04764583,
        0.27582858,  0.71470875,  1.46542022,  0.55368341, -0.62729643,
       -0.02930959, -0.40611946,  1.46189115, -0.0136303 , -0.1512669 ,
       -0.71159345,  1.09134558,  1.68240011,  1.11828375,  0.37860807,
        0.73635514,  0.61367785, -0.63900167, -0.70071633, -0.29444572,
        0.30406708, -1.90565349, -0.11020113,  0.51997851,  0.5234112 ,
       -1.56473965, -0.05815718,  0.06624013, -0.05567618, -0.47458765,
       -0.12200687,  0.22191792, -0.3535855 ,  0.18534404, -0.34314342,
       -0.31504443, -0.83706225, -0.12148159,  0.13596171, -0.34318933,
        1.17190416,  0.37687119, -0.13076326, -1.17908784, -0.3778973 ,
       -0.69000946, -0.50458378,  0.67633243, -0.08483378,  0.87665405,
        0.95962838, -0.16407027, -0.82504459,  0.0534529 , -0.10627517])

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