Error Estimation in model fitting
Errors - Monte Carlo simulations¶
In this project, I will show how to extract errors on best-fit parameters estimated from the curve fitting techniques introduced in curve_fitting. I will use the same example (the limb data) for illustration.¶
In [1]:
## importing the libraries
import numpy as np
import math as m
import scipy
import matplotlib.pyplot as plt
from scipy import special
from scipy.optimize import curve_fit
In [2]:
def Erfc(x,sigma):
y = special.erfc(x/(sigma*np.sqrt(2)))
return y
## Introducing the model to be used later for the fitting
def SL_fit(x,w1,w2,w3,s1,s2,s3):
f = 0.5*(w1*Erfc(x,s1)+w2*Erfc(x,s2)+w3*Erfc(x,s3)+ (1-w1-w2-w3))
return f
From now on I will use scipy.optimize.curve_fit for the fitting problem¶
In [3]:
## Jacobian matrix
def DF(x,w1,w2,w3,s1,s2,s3):
dfw1 = 0.5*(Erfc(x,s1)-1)
dfw2 = 0.5*(Erfc(x,s2)-1)
dfw3 = 0.5*(Erfc(x,s3)-1)
dfs1 = w1*x*np.exp(-x**2/(2*s1**2))/ (np.sqrt(2*np.pi)*s1**2)
dfs2 = w2*x*np.exp(-x**2/(2*s2**2))/ (np.sqrt(2*np.pi)*s2**2)
dfs3 = w3*x*np.exp(-x**2/(2*s3**2))/ (np.sqrt(2*np.pi)*s3**2)
return np.transpose(np.array([dfw1,dfw2,dfw3,dfs1,dfs2,dfs3]))
In [4]:
## Loading the data:
path = "/home/fatima/Desktop/project_3/"
file = np.loadtxt(path+'limb_profile_av_norm_shifted')
x = file[:,0]
y = file[:,1]
In [5]:
ind = np.where(x>=0)
x = x[ind]
y = y[ind]
weights = np.sqrt(np.abs(y)) ## Poisson weighting
In [6]:
p0=[0.3, 0.3, 0.2, 1, 2, 3] ## initial guess best-fit parameters
popt, pcov = curve_fit(SL_fit,x,y,p0,method='lm',sigma=weights,jac=DF,ftol=1e-8,xtol=1e-8,maxfev=5000)
chi_sq_w = np.sum((1/weights**2)*(SL_fit(x,*popt)-y)**2)
red_chi_sq = chi_sq_w/(len(y)-len(popt))
print popt # to print the best-fit parameters
[ 0.52750103 0.28882569 0.10191755 0.25905336 0.76540583 2.83343005]
In the lines above, popt is the array of best-fit parameters, while pcov is the covariance matrix, the diagonal of which can give an estimate of the errors by typing the following:¶
In [7]:
perr = np.sqrt(np.diag(pcov))
print perr ## to print the error
[ 0.00349415 0.0028457 0.00119396 0.00135734 0.00715294 0.04738134]
One can also use another method to compute the errors on the best-fit parameters. The so called "Monte Carlo" method.¶
In [8]:
### The "true" solution is assumed to be that returned by curve_fit, popt
w10, w20, w30, s10, s20, s30 = popt
w40 = 1-w10-w20-w30
In [9]:
### we will make a copy for our data set so we don't alter the original data set
xr = x.copy()
yr = y.copy()
ery = weights.copy()
In [10]:
N = len(y)
trials = 1000 ## number of synthetic data sets
omegas1, omegas2, omegas3,omegas4,sigmas1,sigmas2, sigmas3 = [],[],[],[],[],[],[] #defining the arrays of best-fit parameters corresponding to the number of trials "trials"
chi_s = [] ## the array of dimension "trials" of chi-square values
Now generating synthetic data sets using numpy.random.randint.¶
In [11]:
from numpy.random import normal, randint
In [12]:
for i in range(trials):
indx = randint(0, N, N)
xr[:] = x[indx]
yr[:] = y[indx]
ery[:] = weights[indx]
ok = (xr != xr[0]).any()
if (not ok):
print "All elements are the same. Invalid sample."
print xr, yr
else:
## now preforming the fit using curve_fit on the synthetic data sets and saving results to popti
popti, pcovi = curve_fit(SL_fit,xr,yr,p0,method='lm',sigma=ery,ftol=1e-8,xtol=1e-8,maxfev=5000)
chi_sq_wi = np.sum((1/ery**2)*(SL_fit(xr,*popti)-yr)**2) ## chi_squared values
red_chi_sqi = chi_sq_wi/(len(yr)-len(popti)) ## reduced chi_squared values
om1, om2,om3,sig1,sig2,sig3 = popti
om4 = 1-om1-om2-om3
## saving best-fit parameters and reduced chi_sq values
omegas1.append(om1)
omegas2.append(om2)
omegas3.append(om3)
omegas4.append(om4)
sigmas1.append(sig1)
sigmas2.append(sig2)
sigmas3.append(sig3)
chi_s.append(red_chi_sqi)
print popti ##to print the output for each trial
[ 0.51780298 0.29471219 0.10472405 0.25423208 0.74833391 2.72665156] [ 0.52129061 0.29353422 0.10319298 0.2550758 0.75857336 2.79692301] [ 0.51306274 0.30034848 0.10439981 0.25379152 0.73951306 2.77894058] [ 0.53365379 0.28457255 0.10031272 0.26452477 0.7753637 2.87604064] [ 0.52833911 0.28897794 0.10118776 0.2593886 0.77123206 2.86117997] [ 0.52448991 0.29194521 0.10179544 0.25803698 0.76412923 2.84068826] [ 0.54145759 0.27780062 0.09965041 0.26467896 0.78719177 2.91283197] [ 0.53095848 0.28561657 0.10171466 0.26005834 0.76725018 2.8396865 ] [ 0.52902465 0.28694202 0.10166209 0.25976067 0.76918532 2.79408516] [ 0.54044506 0.27784204 0.1002904 0.26247875 0.78540453 2.8818541 ] [ 0.52980677 0.2848685 0.10290806 0.25969338 0.76599433 2.77238101] [ 0.52936404 0.28811663 0.10103488 0.25763627 0.77464682 2.86450959] [ 0.52031571 0.29408812 0.10352346 0.25716309 0.75133869 2.79816134] [ 0.53425524 0.28351565 0.10073671 0.26173649 0.78007644 2.86371769] [ 0.52515741 0.28956341 0.10315384 0.25922337 0.75885906 2.79361747] [ 0.51899082 0.2945735 0.10360002 0.255167 0.75219202 2.73482613] [ 0.5218894 0.29408037 0.10216375 0.25756991 0.75511623 2.82536094] [ 0.52853154 0.28842998 0.10141798 0.26000835 0.76844709 2.85127265] [ 0.52815104 0.28843112 0.10192589 0.25950146 0.76886055 2.85364331] [ 0.53360273 0.28576337 0.09928717 0.26173305 0.7830851 2.89852059] [ 0.52204151 0.29233396 0.10328523 0.25873909 0.75201407 2.77735066] [ 0.51866219 0.29387625 0.1049722 0.25642266 0.74445909 2.742996 ] [ 0.52906746 0.2877442 0.10146078 0.26094375 0.76587507 2.8384926 ] [ 0.53584421 0.28274972 0.10026819 0.26255011 0.78053902 2.90331845] [ 0.51887346 0.29665653 0.10248813 0.25653415 0.74956729 2.80152054] [ 0.53108297 0.28665445 0.1009335 0.26043897 0.7729498 2.87108095] [ 0.52685987 0.2888314 0.10249911 0.25913196 0.76147299 2.82142032] [ 0.54017045 0.27871703 0.0998245 0.26518477 0.78541285 2.8887926 ] [ 0.53022644 0.28672234 0.1013302 0.25859413 0.77036623 2.84287173] [ 0.54733647 0.27251123 0.09905496 0.26910571 0.79753272 2.91732056] [ 0.51937106 0.29502811 0.10347749 0.25479263 0.74988821 2.79294131] [ 0.51739323 0.29523463 0.10479817 0.25401795 0.74502829 2.74293187] [ 0.52915109 0.28817407 0.10125565 0.25950374 0.76757865 2.86817532] [ 0.53306179 0.28411622 0.10097527 0.26196024 0.7730975 2.84264287] [ 0.52885325 0.28706008 0.10220443 0.25949511 0.76326387 2.81412979] [ 0.52797155 0.28743078 0.10246057 0.26054388 0.76328628 2.79907809] [ 0.53983871 0.27951028 0.09955391 0.26420222 0.78808278 2.91201211] [ 0.53148125 0.28619176 0.10106313 0.26118841 0.77183837 2.88317282] [ 0.52984477 0.28650414 0.10211959 0.26002912 0.76585282 2.84931195] [ 0.53157433 0.28550868 0.10152619 0.2579675 0.77326808 2.85639131] [ 0.53105041 0.28181661 0.10421625 0.26224994 0.76027829 2.72299557] [ 0.53673428 0.2797915 0.10155536 0.26386323 0.77657085 2.81816039] [ 0.5298782 0.28518858 0.10280104 0.26022372 0.7645057 2.79015965] [ 0.52490549 0.29082052 0.10235153 0.2576387 0.76165986 2.81743732] [ 0.04817047 0.65777412 0.20194525 0.00311151 0.35519261 1.65868417] [ 0.52435533 0.29291365 0.10109621 0.25848203 0.76372694 2.85510656] [ 0.5238041 0.29090919 0.10326393 0.25788355 0.75801648 2.79553583] [ 0.52026936 0.2956229 0.10244452 0.25686709 0.75328162 2.83559207] [ 0.53170099 0.28562563 0.10115767 0.26266288 0.77361804 2.85646775] [ 0.53765856 0.28197284 0.09922508 0.25992331 0.78876513 2.9126246 ] [ 0.52945642 0.28755166 0.10127724 0.26022237 0.77074051 2.84176161] [ 0.53165007 0.28406189 0.10216629 0.25915915 0.76982017 2.80149857] [ 0.52935689 0.28558829 0.10284512 0.26035905 0.76299218 2.79076794] [ 0.53501335 0.28235071 0.10100644 0.26339321 0.77668433 2.85707295] [ 0.51791949 0.29536824 0.10439053 0.25507422 0.74717649 2.76472253] [ 0.53342661 0.28463055 0.10044943 0.26281666 0.77641539 2.8742317 ] [ 0.53697732 0.28309165 0.09878887 0.26038958 0.79096146 2.92168894] [ 0.52396484 0.29256016 0.10189808 0.25795387 0.76216299 2.85272257] [ 0.04820996 0.65811469 0.20143962 0.00260661 0.34733674 1.64119181] [ 0.09869318 0.6311405 0.17871208 0.00300649 0.38939967 1.78158904] [ 0.52756506 0.29006987 0.10125325 0.25909286 0.76793509 2.8882305 ] [ 0.52663053 0.28895002 0.10236282 0.25828862 0.76393726 2.80627512] [ 0.50332216 0.30500018 0.10824363 0.25136455 0.72119488 2.64959239] [ 0.04824597 0.66668275 0.19274531 0.00225873 0.36123416 1.68070973] [ 0.52725424 0.28712168 0.10329474 0.2599475 0.7582369 2.77504338] [ 0.52557529 0.28886487 0.10346344 0.25924467 0.75706314 2.79048071]
/usr/local/lib/python2.7/dist-packages/scipy/optimize/minpack.py:779: OptimizeWarning: Covariance of the parameters could not be estimated category=OptimizeWarning)
[ 0.28731485 0.5292576 0.10167048 0.76798473 0.26162477 2.83761925] [ 0.5247599 0.29226996 0.10126959 0.2578713 0.76648919 2.84495703] [ 0.52591027 0.28932518 0.10281447 0.26021156 0.75974466 2.81205229] [ 0.52037307 0.29353716 0.10386839 0.25815326 0.74868591 2.77357637] [ 0.52476081 0.29207564 0.10170637 0.25701154 0.76487136 2.86056447] [ 0.53456731 0.28252339 0.10129951 0.26120784 0.77489021 2.84490542] [ 0.09315831 0.61875699 0.19572435 0.00336271 0.37164124 1.67974338] [ 0.53191365 0.28413132 0.1019134 0.26093346 0.77191662 2.81049658] [ 0.53334859 0.2847749 0.10058468 0.2608581 0.7765642 2.8836232 ] [ 0.5260746 0.28839298 0.1031883 0.25905232 0.76100372 2.77683836] [ 0.52388349 0.29319221 0.10129585 0.25735639 0.76616122 2.84936941] [ 0.53808165 0.28137813 0.09941461 0.26333898 0.78439046 2.90885228] [ 0.52392466 0.29098829 0.10279606 0.25801993 0.75619837 2.79025982] [ 0.52959063 0.28844162 0.10051073 0.26101499 0.76919164 2.87444553] [ 0.53387061 0.28275679 0.10162025 0.26333165 0.77316462 2.83513094] [ 0.53275046 0.28412264 0.10163749 0.26110506 0.77028075 2.85729407] [ 0.52350126 0.29231492 0.10218213 0.25553595 0.76303664 2.81295625] [ 0.53461894 0.28300599 0.10098527 0.26410606 0.77491479 2.8673768 ] [ 0.52996507 0.28631572 0.10201854 0.25958218 0.76919512 2.83426272] [ 0.53768163 0.28074159 0.10030041 0.26426115 0.78185016 2.88738778] [ 0.52808802 0.28874585 0.10170162 0.2579407 0.76579437 2.85824368] [ 0.52793391 0.28862634 0.10185228 0.25903145 0.76978775 2.84036451] [ 0.51596141 0.29577514 0.10537201 0.25479675 0.74013017 2.71476991] [ 0.52024823 0.29444328 0.10340306 0.25636758 0.75373919 2.80613817] [ 0.52842688 0.28800853 0.1017072 0.25961012 0.76540611 2.82977111] [ 0.52810476 0.28974054 0.10058083 0.25857623 0.77441036 2.85946852] [ 0.52010941 0.29432289 0.10346299 0.25588554 0.75528002 2.78771055] [ 0.52207546 0.2923195 0.10340722 0.25811799 0.75580232 2.77928213] [ 0.52571316 0.29052209 0.1019723 0.25828595 0.761784 2.83417689] [ 0.52127484 0.29385726 0.10256796 0.25630281 0.75834375 2.78969464] [ 0.53063608 0.28664035 0.10103743 0.25967061 0.77031866 2.8485453 ] [ 0.52668923 0.28917258 0.10216876 0.25837876 0.76377929 2.81549101] [ 0.53831612 0.28130419 0.09916822 0.26253678 0.7872912 2.91003431] [ 0.51267625 0.29963155 0.10513996 0.25401855 0.73391206 2.73338008] [ 0.53799073 0.28081994 0.10010491 0.26309897 0.78380204 2.89996546] [ 0.53217017 0.28555031 0.10080887 0.25928077 0.77337876 2.86908183] [ 0.52843261 0.28740251 0.10214367 0.26006555 0.76479631 2.8073539 ] [ 0.52458872 0.28934816 0.10359292 0.25896272 0.75538009 2.76774731] [ 0.52742177 0.29044311 0.10064737 0.25995096 0.7703261 2.8660103 ] [ 0.52715763 0.29119084 0.10039792 0.2565737 0.77101801 2.88789429] [ 0.53669113 0.28029765 0.10112486 0.26214718 0.77540674 2.8368101 ] [ 0.5221116 0.2931623 0.10273945 0.25675468 0.75797176 2.80767979] [ 0.53219672 0.28639422 0.10008798 0.25754499 0.77868186 2.89287432] [ 0.52620887 0.28964929 0.10261971 0.25882503 0.76060212 2.84168073] [ 0.52456655 0.2911372 0.10241308 0.25815847 0.76015179 2.81974419] [ 0.53174718 0.28714574 0.0999884 0.25947232 0.77577987 2.90240833] [ 0.52862451 0.28869241 0.1013857 0.25982705 0.76806424 2.87532395] [ 0.52298098 0.29428238 0.10128944 0.25670279 0.76356445 2.86615625] [ 0.52252536 0.29350432 0.10235644 0.25779508 0.75898026 2.83105879] [ 0.53918651 0.27806765 0.10107459 0.2622425 0.78094466 2.84962486] [ 0.53251231 0.28400849 0.10171876 0.26166664 0.7713953 2.83613609] [ 0.52545535 0.29050358 0.10195923 0.25842814 0.76193598 2.80870963] [ 0.52870608 0.28668473 0.10253607 0.25829897 0.76730997 2.80270869] [ 0.52405615 0.29053071 0.10307536 0.25767571 0.75754558 2.7741122 ] [ 0.53377187 0.2828234 0.1019679 0.26149681 0.7717643 2.8540883 ] [ 0.52907221 0.28598805 0.10285333 0.260045 0.76212763 2.80026312] [ 0.53650945 0.28291743 0.09976867 0.26312847 0.78471718 2.9336462 ] [ 0.53105713 0.28740937 0.10037984 0.26252089 0.77225666 2.90372595] [ 0.52714945 0.28951862 0.10160736 0.25864276 0.76570338 2.84655343] [ 0.52537376 0.2904728 0.10223838 0.25885511 0.75932895 2.81532376] [ 0.53034644 0.28568507 0.10241338 0.25990602 0.76544748 2.84103101] [ 0.5208124 0.29226539 0.10430927 0.2568336 0.75210129 2.74159952] [ 0.51592218 0.29489078 0.10628553 0.25540555 0.73966975 2.69811318] [ 0.53766858 0.28100067 0.10035566 0.26270389 0.78262331 2.91102692] [ 0.53553954 0.28328807 0.10007881 0.26040352 0.78175166 2.91012435] [ 0.53727298 0.28162813 0.09999701 0.26362228 0.78456668 2.90361671] [ 0.52818202 0.28700043 0.10270494 0.25949758 0.76230592 2.79725846] [ 0.51272247 0.30206853 0.10286594 0.25257957 0.74670418 2.7769073 ] [ 0.53002241 0.28669679 0.10186423 0.26030046 0.76872889 2.86202332] [ 0.53653313 0.28340424 0.09915201 0.2602396 0.79003565 2.92934369] [ 0.52395671 0.29336302 0.10127089 0.25747311 0.7650367 2.86741626] [ 0.51710074 0.29765233 0.10306706 0.25476752 0.75219921 2.79161253] [ 0.52937893 0.28702532 0.10184153 0.26056903 0.76691895 2.83322453] [ 0.52134643 0.29157213 0.1047956 0.25590068 0.75247561 2.75339579] [ 0.53701264 0.28083976 0.10068385 0.26385377 0.78121344 2.87183887] [ 0.52696793 0.28766139 0.10309847 0.26118941 0.7582619 2.78452005] [ 0.5352989 0.28401087 0.09952072 0.26091262 0.78505689 2.90418045] [ 0.53033826 0.28689381 0.10103001 0.26103038 0.77254703 2.84637251] [ 0.52508878 0.29095602 0.10196504 0.25790374 0.76289577 2.81676817] [ 0.52112771 0.29259163 0.10364721 0.25826317 0.75257338 2.75236528] [ 0.5384658 0.27972493 0.10060054 0.26617779 0.77863729 2.88673251] [ 0.53542212 0.2835966 0.09998805 0.26181245 0.78377076 2.90709414] [ 0.52448732 0.29208547 0.10166187 0.25816044 0.76582781 2.8361584 ] [ 0.53189987 0.28406127 0.10219495 0.26362587 0.77089331 2.8205457 ] [ 0.5332084 0.28584719 0.0999367 0.26230471 0.77668727 2.91719336] [ 0.5131005 0.29725261 0.10658518 0.25488925 0.73313815 2.6831872 ] [ 0.53253475 0.28293427 0.10270887 0.25903791 0.76905454 2.81722249] [ 0.53260362 0.28476647 0.1011027 0.26241984 0.77303943 2.86025695] [ 0.52973693 0.28614852 0.10270323 0.25926804 0.76365111 2.85706936] [ 0.52881528 0.28864531 0.10103104 0.26150719 0.76889126 2.86427845] [ 0.53546474 0.28187503 0.10121126 0.26289931 0.77547356 2.86366535] [ 0.52286243 0.29261594 0.10266402 0.25870329 0.75683872 2.8191088 ] [ 0.53373906 0.28530709 0.09985832 0.26161023 0.77879854 2.90428302] [ 0.53359094 0.28556838 0.10003875 0.26153665 0.7797316 2.92533087] [ 0.52918367 0.28716992 0.10198146 0.25984469 0.7671166 2.83899858] [ 0.52514867 0.29113762 0.1020899 0.25630067 0.76116783 2.84010377] [ 0.52273027 0.29380164 0.10210716 0.25775067 0.76056953 2.86198041] [ 0.52413373 0.29261832 0.10159965 0.25672418 0.76550112 2.84088573] [ 0.54186925 0.27743508 0.09964562 0.26534427 0.787653 2.91389804] [ 0.51484408 0.29869468 0.10457653 0.25388755 0.74186003 2.79754843] [ 0.53479408 0.28356497 0.10029534 0.26115251 0.77909584 2.88220532] [ 0.51402727 0.30001642 0.10345317 0.25392482 0.74796735 2.76115961] [ 0.51994558 0.29537824 0.10267021 0.25552308 0.75444866 2.80509828] [ 0.54377507 0.27540114 0.09962179 0.26880249 0.79050194 2.9003 ] [ 0.52497904 0.29009114 0.10283184 0.25880742 0.7581116 2.79581781] [ 0.53365347 0.28365941 0.10081274 0.26078156 0.77615281 2.84069742] [ 0.53068534 0.28683864 0.10114516 0.25958866 0.77015884 2.87213381] [ 0.52597074 0.29057329 0.10208454 0.25893079 0.76077672 2.86359021] [ 0.52303047 0.29128736 0.10328983 0.258234 0.75643708 2.77129524] [ 0.07668249 0.64956267 0.1824732 0.00626176 0.37981295 1.77552062] [ 0.52397956 0.29364576 0.10111718 0.25510868 0.76754564 2.88417242] [ 0.52713395 0.28862869 0.10232128 0.25694877 0.76292006 2.81529619] [ 0.52241024 0.29472727 0.1012112 0.25707017 0.76384065 2.84637476] [ 0.52350797 0.29241004 0.10242388 0.25872845 0.75908705 2.83191808] [ 0.51361189 0.29800037 0.1058675 0.25478373 0.73696839 2.73238729] [ 0.5159334 0.29879142 0.10305166 0.25251536 0.75346608 2.78825043] [ 0.53327135 0.28395029 0.10107258 0.26229795 0.77494876 2.84610268] [ 0.52322509 0.29328905 0.10171574 0.25519057 0.76276621 2.83714417] [ 0.53347676 0.28366388 0.10105427 0.25972619 0.77719126 2.835816 ] [ 0.51425591 0.2986053 0.10482548 0.25384469 0.73995652 2.75872811] [ 0.51445546 0.29912783 0.10408588 0.25356376 0.74425508 2.76882373] [ 0.52250919 0.29058146 0.10463738 0.25823901 0.75110024 2.75932997] [ 0.52911984 0.28664528 0.10227801 0.2594402 0.76642612 2.8115285 ] [ 0.53534966 0.2819865 0.10107243 0.26125857 0.77546283 2.85786351] [ 0.52630209 0.29025312 0.10192653 0.25712975 0.76378061 2.85159543] [ 0.52711995 0.28821072 0.10258416 0.25780268 0.76155858 2.80302378] [ 0.52336361 0.29202943 0.10245 0.2575119 0.76241662 2.79057595] [ 0.54146252 0.27809212 0.0993454 0.26588019 0.79170102 2.91019014] [ 0.52038995 0.29531919 0.10221233 0.25669747 0.75747156 2.80588171] [ 0.52541899 0.28973083 0.10301623 0.25844946 0.75809407 2.81187752] [ 0.5319576 0.28547726 0.10119652 0.25996102 0.77422179 2.87288352] [ 0.52876107 0.2878591 0.10140257 0.25952417 0.77100842 2.82419938] [ 0.07127846 0.6461383 0.19080611 0.00426523 0.36587666 1.71109834] [ 0.5152671 0.2993416 0.10315691 0.25510515 0.7460802 2.7909378 ] [ 0.52766433 0.28694785 0.10321582 0.26016951 0.7619919 2.78499356] [ 0.52873652 0.28807465 0.1017274 0.25825151 0.77044067 2.85694999] [ 0.52772129 0.28829933 0.10198788 0.25747681 0.76664463 2.81820052] [ 0.5374271 0.2831179 0.09885107 0.26180639 0.78825924 2.96268529] [ 0.52764556 0.28681522 0.10331025 0.25953514 0.76202706 2.77571494] [ 0.53506797 0.28320095 0.1002793 0.26263525 0.77742655 2.87715834] [ 0.53510354 0.28384882 0.09997592 0.26264366 0.78094287 2.90538489] [ 0.52909751 0.28735371 0.10158576 0.25945873 0.76794944 2.82171756] [ 0.5343892 0.28435677 0.10002604 0.26150995 0.78482334 2.89274464] [ 0.52155826 0.29472407 0.10199496 0.25534874 0.75974841 2.83610105] [ 0.52949053 0.28873567 0.10044898 0.25702152 0.77406211 2.88618097] [ 0.52882801 0.28758276 0.1016049 0.25776401 0.76567389 2.82052094] [ 0.52441747 0.29218926 0.10175913 0.25959043 0.76165458 2.84730479] [ 0.52809749 0.28846061 0.10186219 0.25900985 0.76672471 2.85699002] [ 0.52603057 0.2874494 0.10422204 0.25960312 0.75547961 2.7636034 ] [ 0.53091922 0.28495157 0.10209466 0.26016816 0.76827034 2.80773836] [ 0.53291465 0.2838604 0.10113282 0.26092761 0.77547051 2.81649973] [ 0.53264155 0.28448928 0.10138001 0.26029076 0.7737999 2.86078074] [ 0.51586787 0.29727193 0.10422668 0.25646421 0.74250708 2.74780503] [ 0.52138837 0.29378053 0.10261305 0.25701772 0.75515337 2.79624684] [ 0.52443954 0.2899073 0.1032023 0.2572626 0.75809968 2.76841646] [ 0.53567074 0.28178735 0.10104354 0.26333466 0.77523109 2.86593003] [ 0.51883098 0.29423562 0.10452616 0.25474319 0.74986484 2.74822524] [ 0.53835605 0.27923113 0.1007374 0.26244015 0.78194044 2.84989631] [ 0.53458306 0.28216114 0.10183219 0.26348239 0.77060972 2.86131532] [ 0.54191451 0.27962573 0.09796964 0.26503901 0.79809016 2.97742281] [ 0.52689436 0.28842947 0.10259167 0.2593475 0.7601122 2.8043319 ] [ 0.53198288 0.28801345 0.09912927 0.26065265 0.78156228 2.93549156] [ 0.52876687 0.28867183 0.10108017 0.25990377 0.77053056 2.86629339] [ 0.52959865 0.28743098 0.10132111 0.25920909 0.76930437 2.84718502] [ 0.51976852 0.29461176 0.103511 0.25427167 0.75548567 2.78793151] [ 0.53585063 0.28267425 0.10008503 0.26248759 0.78179027 2.88534293] [ 0.52587189 0.29053851 0.10183271 0.25783799 0.76194425 2.83248788] [ 0.52247242 0.2928288 0.10260602 0.25646272 0.75825142 2.80360368] [ 0.53220149 0.28505063 0.10107009 0.26020821 0.77170763 2.84859869] [ 0.51733572 0.29772106 0.10272108 0.25471827 0.75304282 2.78698783] [ 0.52414682 0.29053215 0.10339993 0.25708837 0.75488233 2.80055979] [ 0.52534888 0.29395053 0.0997467 0.25723743 0.77312332 2.92191848] [ 0.51872891 0.29413887 0.10477192 0.25558981 0.74751663 2.76270243] [ 8.10250116e-02 6.31993964e-01 1.95114502e-01 4.44572020e-04 3.67769618e-01 1.68965158e+00] [ 0.51823999 0.29584931 0.10340398 0.25510604 0.75155898 2.76001944] [ 0.53071127 0.28814773 0.09975402 0.25934051 0.78075399 2.88420661] [ 0.53321647 0.2839372 0.10113513 0.26043144 0.77102499 2.84889975] [ 0.53781294 0.2812344 0.09941679 0.2645576 0.78713487 2.87992189] [ 0.52915534 0.28819462 0.10116237 0.25888966 0.77218696 2.86286259] [ 0.52295873 0.29236279 0.10277129 0.25723659 0.75687363 2.81593951] [ 0.51773996 0.29863618 0.1018593 0.2553943 0.75408801 2.83517365] [ 0.53035291 0.28613248 0.10182697 0.25935076 0.76967253 2.84262106] [ 0.53158715 0.28591802 0.10089458 0.26059971 0.77309997 2.85285615] [ 0.52926742 0.28515868 0.10326937 0.25955776 0.76155923 2.783086 ] [ 0.51017373 0.30221355 0.1049435 0.25230365 0.73826154 2.72561772] [ 0.53271875 0.28378667 0.10162875 0.26216517 0.77348723 2.82405216] [ 0.54031498 0.2804133 0.09842802 0.26296994 0.7936368 2.94061094] [ 0.53360055 0.2839938 0.10070615 0.25962219 0.77696369 2.85094193] [ 0.53326918 0.283715 0.10111645 0.26247513 0.7740761 2.83302721] [ 0.53312561 0.28480012 0.10084947 0.26205994 0.77834369 2.88753452] [ 0.51781679 0.29630806 0.10347844 0.25555517 0.75080895 2.77473025] [ 0.53235764 0.28405872 0.10199334 0.26172093 0.76999987 2.84354676] [ 0.54643581 0.27542222 0.09746356 0.26677288 0.80580235 2.96924033] [ 0.52910932 0.28795778 0.10137622 0.25969844 0.76611763 2.8572956 ] [ 0.52956543 0.2874837 0.10132937 0.26096689 0.76729186 2.85049082] [ 0.53593913 0.28187906 0.10046472 0.26114146 0.78028983 2.85489394] [ 0.52840905 0.28961012 0.10072129 0.26007295 0.77136349 2.88860104] [ 0.53717804 0.28212569 0.09955885 0.26456167 0.78411733 2.9068097 ] [ 0.51987993 0.29601063 0.10214315 0.25667368 0.75473736 2.8186073 ] [ 0.5246134 0.28862039 0.10421518 0.25726607 0.75344539 2.75025985] [ 0.5336436 0.28464877 0.10060808 0.26227386 0.77702791 2.89778315] [ 0.52516458 0.29203337 0.10143749 0.2574839 0.76615516 2.86862686] [ 0.03958691 0.66536249 0.20247845 0.00299769 0.3497698 1.63491169] [ 0.52149215 0.29207105 0.10393872 0.25657392 0.75453904 2.7531066 ] [ 0.53506544 0.28438857 0.09977008 0.26330846 0.78441444 2.93348246] [ 0.52185134 0.29512006 0.10166154 0.25765105 0.76011596 2.86181037] [ 0.5188063 0.29435853 0.10447781 0.25768043 0.74620974 2.7590966 ] [ 0.52843363 0.28811212 0.10159274 0.25866147 0.76926428 2.83005681] [ 0.52575082 0.29073734 0.1017462 0.25905994 0.76508786 2.83289385] [ 0.53281177 0.28550589 0.10035436 0.2622903 0.77691881 2.88326871] [ 0.52057417 0.29406132 0.1033782 0.25487095 0.75516582 2.79514265] [ 0.52761884 0.287866 0.10244208 0.2589818 0.76517116 2.80102934] [ 0.524867 0.29114841 0.10225676 0.25867629 0.76244481 2.82993651] [ 0.52179179 0.29341119 0.10265967 0.2561276 0.75537523 2.7965863 ] [ 0.53613054 0.28246456 0.09990761 0.26205677 0.77817485 2.8790542 ] [ 0.52168159 0.29418339 0.10248045 0.25877896 0.75462162 2.8403333 ] [ 0.52205241 0.29202348 0.10382224 0.25755586 0.75746063 2.78219569] [ 0.53742983 0.27996469 0.10119272 0.26447754 0.7776091 2.86326596] [ 0.52111273 0.29417468 0.10297027 0.25489255 0.7560282 2.82541137] [ 0.54046033 0.28019852 0.09870475 0.2641966 0.79210997 2.95286923] [ 0.53721443 0.28299766 0.09921407 0.26291624 0.78801456 2.95734924] [ 0.54408465 0.27801176 0.09763716 0.26505038 0.79982854 2.99777418] [ 0.52635152 0.29017589 0.10180428 0.25803602 0.76565417 2.83543323] [ 0.52833125 0.29059873 0.09998913 0.25966379 0.7730709 2.90597068] [ 0.52031731 0.29338013 0.10396597 0.25591355 0.75237402 2.76724066] [ 0.51403712 0.29748368 0.10587112 0.25361819 0.73846037 2.72654339] [ 0.52600078 0.29066111 0.10159932 0.25689685 0.76878265 2.8374515 ] [ 0.51443345 0.29885048 0.10438757 0.25470049 0.74013571 2.76658225] [ 0.52992712 0.28755125 0.10119555 0.25922063 0.77018753 2.87234021] [ 0.52640145 0.29245654 0.10020478 0.25989222 0.77002777 2.91347614] [ 0.52989635 0.28920748 0.10003519 0.25956739 0.77378944 2.92689133] [ 0.53483249 0.28155056 0.10168462 0.26227302 0.77631919 2.81764036] [ 0.53189022 0.28638701 0.10023867 0.26007057 0.77811668 2.87546198] [ 0.526223 0.2912155 0.1010406 0.2591323 0.76703304 2.85655491] [ 0.52689979 0.2866411 0.10420977 0.25908772 0.75571972 2.76718735] [ 0.51514585 0.29838322 0.10422278 0.25376347 0.74593534 2.77296603] [ 0.53049225 0.28529931 0.10223301 0.25926889 0.76805594 2.81010405] [ 0.53073031 0.28601687 0.10134122 0.26021618 0.77239869 2.83172837] [ 0.52295473 0.2933375 0.10203588 0.25785673 0.75947287 2.84132018] [ 0.52285107 0.29456282 0.10108697 0.25753572 0.76132584 2.86439025] [ 0.52581211 0.29074722 0.1016776 0.25780555 0.76349122 2.83946023] [ 0.52949582 0.28800339 0.101109 0.25965288 0.76655621 2.87244009] [ 0.52635034 0.28850529 0.10312254 0.2576991 0.76005331 2.80173956] [ 0.53769548 0.28225489 0.09937686 0.26460958 0.78646957 2.94631795] [ 0.5322743 0.2843095 0.10166949 0.2620043 0.76957379 2.83551255] [ 0.52775144 0.28924148 0.10137576 0.26063865 0.76959072 2.85056646] [ 0.52710912 0.28866884 0.10225792 0.25977138 0.76251926 2.81431172] [ 0.29357765 0.5198607 0.10431444 0.74849487 0.25471892 2.7679751 ] [ 0.52812251 0.28631115 0.10337887 0.25882837 0.75915733 2.77952096] [ 0.53380455 0.28363436 0.10126716 0.26353256 0.77217167 2.87965068] [ 0.51787947 0.2959151 0.10364456 0.25511938 0.75030034 2.75580938] [ 0.53542145 0.28052517 0.10220858 0.26070359 0.77393372 2.81172927] [ 0.52157414 0.29259138 0.10379363 0.25732786 0.75233293 2.79156025] [ 0.52524862 0.28952025 0.10277273 0.2589276 0.75897665 2.77010331] [ 0.51879567 0.29688778 0.10253273 0.25609551 0.75119801 2.82765493] [ 0.52838924 0.28842424 0.1015291 0.25965788 0.76638238 2.84425995] [ 0.51848156 0.29426153 0.10448664 0.2570702 0.74655656 2.7317089 ] [ 0.53275545 0.2850493 0.10071207 0.25998526 0.77509839 2.87016247] [ 0.52696821 0.2882145 0.10294566 0.25955236 0.75941763 2.81822776] [ 0.52323598 0.29145984 0.10304685 0.25721948 0.75773539 2.78061024] [ 0.52810615 0.28846572 0.10183329 0.25893396 0.76755759 2.84821266] [ 0.52890008 0.28802828 0.10133791 0.2598659 0.76910411 2.84449868] [ 0.53185369 0.28491811 0.10167053 0.26144874 0.76977949 2.8513376 ] [ 0.53871698 0.28083803 0.09949343 0.26068755 0.78657477 2.92322912] [ 0.52584537 0.29038932 0.10191628 0.25710713 0.76485402 2.82759243] [ 0.53005953 0.28868578 0.10017788 0.26070273 0.77312545 2.90357484] [ 0.53071099 0.28792002 0.10028873 0.25975889 0.77411502 2.90229044] [ 0.5277887 0.28853556 0.10190857 0.25671258 0.76869267 2.83104877] [ 0.53002065 0.28906103 0.09971211 0.25865153 0.78334714 2.90104323] [ 0.52170571 0.29493112 0.10181181 0.25641641 0.76242181 2.84426062] [ 0.52945729 0.28802734 0.10110843 0.2592543 0.77074397 2.87119057] [ 0.29442545 0.51967932 0.10345638 0.75145287 0.25643708 2.76580399] [ 0.52895579 0.28700236 0.10222006 0.25947982 0.76577554 2.82678098] [ 0.53173512 0.28505199 0.10153531 0.26106916 0.76904845 2.84298196] [ 0.53390225 0.28308616 0.10135923 0.26147182 0.77613361 2.84538307] [ 0.52006615 0.29439292 0.10333691 0.25744208 0.75082772 2.78338339] [ 0.5251413 0.28929254 0.10357379 0.25911398 0.75716734 2.79384278] [ 0.53057903 0.28636245 0.10149392 0.26229509 0.76956509 2.85199686] [ 0.53051655 0.28669613 0.10140683 0.26085676 0.76978765 2.8656458 ] [ 0.52921361 0.28778745 0.10129321 0.25980817 0.76969876 2.84231109] [ 0.52285553 0.29067588 0.10376066 0.2588627 0.75413518 2.74220343] [ 0.52741242 0.28893919 0.10180476 0.25984596 0.765959 2.83129275] [ 0.52507849 0.29100116 0.10205171 0.25836438 0.76268851 2.82736808] [ 0.53219443 0.28498059 0.10104217 0.25911239 0.7728482 2.84543105] [ 0.5218337 0.29182782 0.10407392 0.25724267 0.7534697 2.76709047] [ 0.5181651 0.29296141 0.10584249 0.25627049 0.74054524 2.69969815] [ 0.52566114 0.28963561 0.10303947 0.25821675 0.75964184 2.82799992] [ 0.51085229 0.3007426 0.10578105 0.25393051 0.73404862 2.72775203] [ 0.53253354 0.2858788 0.10030151 0.258618 0.7781607 2.88633269] [ 0.52511974 0.29088163 0.10222856 0.25762768 0.76267763 2.82777954] [ 0.53227805 0.2866293 0.09990856 0.25940053 0.77857147 2.9007661 ] [ 0.52370538 0.29240392 0.10229455 0.2585105 0.75895293 2.84240952] [ 0.52021143 0.29338278 0.10403346 0.25823784 0.74877668 2.76322102] [ 0.52383666 0.29195581 0.10256835 0.25777373 0.76073396 2.83637286] [ 0.51984687 0.29858118 0.1005428 0.25697146 0.75801363 2.90669257] [ 0.53627623 0.28140528 0.10070629 0.26151923 0.78027067 2.85997105] [ 0.53348132 0.28520984 0.10031946 0.26149118 0.77737539 2.91024091] [ 0.52272061 0.29324248 0.10186636 0.25774222 0.76074553 2.81214854] [ 0.53028865 0.28495243 0.10245015 0.2596612 0.76316333 2.79255573] [ 0.53176484 0.28536803 0.10118723 0.26202792 0.77465396 2.8387264 ] [ 0.53158351 0.28547059 0.10123968 0.26163423 0.77223607 2.84212543] [ 0.52888815 0.287768 0.10152904 0.25940724 0.76662736 2.8385244 ] [ 0.53532589 0.2846807 0.09878252 0.26140657 0.79177144 2.91106126] [ 0.52437908 0.29222935 0.10176036 0.25912593 0.75815872 2.84704839] [ 0.51586265 0.29818259 0.10357083 0.25489658 0.75009944 2.76779725] [ 0.5375789 0.28149944 0.09990731 0.26130903 0.78416124 2.91714345] [ 0.52311316 0.29175227 0.10313908 0.25802467 0.75896079 2.79624979] [ 0.53219044 0.28572115 0.10078159 0.26219632 0.77486854 2.87662061] [ 0.53715331 0.27908947 0.1016088 0.26523412 0.77558419 2.81131769] [ 0.52810563 0.28805302 0.10226124 0.25944688 0.76294515 2.84594341] [ 0.54065467 0.27744947 0.1007321 0.2664002 0.78345438 2.88988499] [ 0.52056279 0.2951344 0.10247454 0.25675802 0.75908145 2.82362397] [ 0.53314016 0.2837366 0.10155913 0.25919155 0.77436264 2.84650148] [ 0.52065417 0.29559588 0.10209741 0.25549433 0.75692287 2.84134311] [ 0.52939802 0.28808488 0.10096117 0.25960114 0.77429179 2.8573813 ] [ 0.5272612 0.29227445 0.09969933 0.25748541 0.78093701 2.93128351] [ 0.55099431 0.26972358 0.09837504 0.26931525 0.8044535 2.93879798] [ 0.53631104 0.28164967 0.1007919 0.26325885 0.77795773 2.87716493] [ 0.5324389 0.28588451 0.10047108 0.26159824 0.77410827 2.89400005] [ 0.53722666 0.28076141 0.10054204 0.26256849 0.78170239 2.86877179] [ 0.53015054 0.28669828 0.1015299 0.26179345 0.76834008 2.84470156] [ 0.5342609 0.2848535 0.09954212 0.2628383 0.78080377 2.89544224] [ 0.53475765 0.28344138 0.10045914 0.2622376 0.778203 2.88332556] [ 0.52680568 0.29056684 0.10123117 0.25681628 0.76996684 2.86703841] [ 0.51909769 0.29370853 0.10470921 0.25498358 0.74663782 2.74937969] [ 0.53281 0.28450368 0.10109598 0.26065947 0.77415107 2.8551505 ] [ 0.52412573 0.2893581 0.10389003 0.25810648 0.75645051 2.74673441] [ 0.52061265 0.29336751 0.10367153 0.25623271 0.75501269 2.76866926] [ 0.53049103 0.28458073 0.10290498 0.26208413 0.76362733 2.79887927] [ 0.28632455 0.53093684 0.10134216 0.77278585 0.26037314 2.87087027] [ 0.53489835 0.28191701 0.10139365 0.26135685 0.77553803 2.84158719] [ 0.52620244 0.28806157 0.10323664 0.25824745 0.75999106 2.76180796] [ 0.5233833 0.2928832 0.10201312 0.25723652 0.75910185 2.83018719] [ 0.5268438 0.28714752 0.10366218 0.25976644 0.75750856 2.77231753] [ 0.51790291 0.29503545 0.10432713 0.25559032 0.74779344 2.73390499] [ 0.52216402 0.2937515 0.10211778 0.25630508 0.76019072 2.81660015] [ 0.52686885 0.28964048 0.10165738 0.25810512 0.76535094 2.82802842] [ 0.52914877 0.28683779 0.10210442 0.25982616 0.76657161 2.8190521 ] [ 0.52362506 0.29133859 0.1030788 0.25846684 0.75487294 2.80206642] [ 0.52697022 0.28857318 0.10277068 0.25924224 0.76260984 2.82933468] [ 0.54669334 0.27633413 0.09684683 0.26522946 0.80713061 3.0208092 ] [ 0.52780336 0.28724288 0.10241075 0.25878063 0.76547402 2.7770398 ] [ 0.52130704 0.29039657 0.10504155 0.25766566 0.74811071 2.69348074] [ 0.53077893 0.28697641 0.1007302 0.25921095 0.77642499 2.86722655] [ 0.52713669 0.2910367 0.10069002 0.2580023 0.76979126 2.89579634] [ 0.52669413 0.29111012 0.10089902 0.25756434 0.77191885 2.87751723] [ 0.52112604 0.29324148 0.10338064 0.25748517 0.74989026 2.78013891] [ 0.5357445 0.28300731 0.10004327 0.26291675 0.78379732 2.89161021] [ 0.53026308 0.28789118 0.10065696 0.26148609 0.77028785 2.88837361] [ 0.52850393 0.28653317 0.10296631 0.25908068 0.76154759 2.80464645] [ 0.53792073 0.27831019 0.10183708 0.2638628 0.77669143 2.82031559] [ 0.52445468 0.29343143 0.10071229 0.25543977 0.7694313 2.8756148 ] [ 0.52706113 0.2887437 0.10238932 0.2604 0.76515342 2.82007801] [ 0.52783333 0.28801628 0.10216476 0.26041373 0.7659203 2.81017117] [ 0.52654384 0.28862973 0.10298725 0.25913119 0.76374034 2.80727831] [ 0.52316608 0.29132042 0.10329912 0.25763435 0.75554167 2.78148201] [ 0.10551896 0.62745491 0.17599475 0.01378443 0.38903247 1.80535024] [ 0.53443531 0.28416366 0.10011167 0.26374843 0.77972402 2.89190953] [ 0.54269633 0.2779323 0.09870236 0.26483802 0.79291483 2.9564703 ] [ 0.52811479 0.28755864 0.10252277 0.26038015 0.76541406 2.81698262] [ 0.52150464 0.29329757 0.10322982 0.25630324 0.7541301 2.8049907 ] [ 0.52943189 0.28759912 0.10131672 0.26058899 0.76979325 2.84341573] [ 0.52467066 0.28902021 0.10393133 0.25936036 0.75562758 2.75994296] [ 0.29016975 0.52641255 0.10172961 0.76564431 0.25814047 2.83779598] [ 0.52764056 0.28712111 0.10288766 0.25837719 0.76325159 2.78326046] [ 0.52251538 0.29322779 0.10272077 0.25849025 0.75459738 2.84152354] [ 0.51934069 0.29635616 0.10227989 0.25485911 0.75399251 2.80838859] [ 0.5275772 0.28999446 0.10085656 0.25726157 0.7683976 2.85868449] [ 0.52986175 0.28694753 0.10169817 0.25823994 0.77065629 2.85383855] [ 0.53202021 0.28579661 0.10091513 0.26114791 0.77368294 2.87810319] [ 0.52495193 0.28910547 0.10363415 0.25766505 0.75673946 2.77229637] [ 0.52437399 0.29083191 0.1027135 0.25749929 0.7611234 2.80254148] [ 0.5288668 0.28732595 0.10166389 0.25953327 0.76528946 2.81020385] [ 0.53241343 0.2861656 0.10041337 0.26307128 0.77465766 2.9081249 ] [ 0.53069625 0.284562 0.10286396 0.26144929 0.76439167 2.81392104] [ 0.53781783 0.28259941 0.09875183 0.26364922 0.78914844 2.94765091] [ 0.53070412 0.28607834 0.101763 0.26074403 0.76806605 2.86279487] [ 0.53402342 0.28307197 0.10145442 0.26246687 0.77186894 2.86202633] [ 0.52126033 0.29355124 0.10288704 0.2569623 0.75673521 2.78442925] [ 0.53177389 0.28599224 0.10081072 0.26106421 0.77369328 2.8732381 ] [ 0.29054057 0.52577383 0.10200755 0.7624946 0.2570842 2.83902141] [ 0.51871337 0.29344062 0.10499751 0.25565101 0.74485128 2.72124719] [ 0.53232386 0.28430874 0.10146579 0.25891374 0.77056573 2.82515972] [ 0.53042559 0.2865571 0.10123196 0.2595224 0.774309 2.84119324] [ 0.51303982 0.30054838 0.10442975 0.25349823 0.7390918 2.79503713] [ 0.53557075 0.28195108 0.10084816 0.26048467 0.77755568 2.85128363] [ 0.5348236 0.28282444 0.10103581 0.26121868 0.77541022 2.88286901] [ 0.53901897 0.27975741 0.09991441 0.26380142 0.78522169 2.89191833] [ 0.50735969 0.30448335 0.10552916 0.2517438 0.73439578 2.73316818] [ 0.52558481 0.29130244 0.10116698 0.25570525 0.76749564 2.82798292] [ 0.51645548 0.29763429 0.10365836 0.25292674 0.74925682 2.77507381] [ 0.06456655 0.65356935 0.18991465 0.00199903 0.37229998 1.70342854] [ 0.51734911 0.29685125 0.10329125 0.25632633 0.74758247 2.76504872] [ 0.52134874 0.29203876 0.10413449 0.25777643 0.75165954 2.75462823] [ 0.52967394 0.28742591 0.10171897 0.25693707 0.77118619 2.87764286] [ 0.5296514 0.28597223 0.10256885 0.26018921 0.76523204 2.81762034] [ 0.52448979 0.28885218 0.10407638 0.25805246 0.7531888 2.74995749] [ 0.54227349 0.27836422 0.09845911 0.26431167 0.795334 2.94152679] [ 0.52405634 0.29306578 0.10142244 0.25646197 0.76536706 2.86560066] [ 1.00465324e-01 6.25118684e-01 1.82813895e-01 1.51483457e-03 3.86911167e-01 1.75289880e+00] [ 0.52153973 0.29229444 0.10370888 0.25835928 0.75175459 2.75713406] [ 0.52538994 0.29074066 0.10217283 0.25739622 0.76171763 2.83921822] [ 0.52270932 0.29290691 0.10270579 0.25839863 0.75618868 2.82864244] [ 0.52194004 0.29159935 0.10421088 0.2555741 0.75220773 2.76929819] [ 0.52691155 0.28800027 0.10294229 0.25835641 0.76152099 2.80057983] [ 0.52956703 0.28719326 0.10170334 0.25947321 0.77039481 2.85175854] [ 0.53534519 0.28388169 0.0995424 0.26378375 0.78386522 2.89739104] [ 0.53217276 0.2854683 0.10096891 0.25901003 0.7735743 2.86878943] [ 0.53105658 0.28413945 0.10269786 0.26175149 0.7654422 2.79732347] [ 0.52045864 0.29525269 0.1024012 0.25428233 0.75649903 2.8187563 ] [ 0.53139352 0.28410706 0.10240998 0.25982309 0.76759788 2.8030316 ] [ 0.53485685 0.28403649 0.1001187 0.26111388 0.77935095 2.91310508] [ 0.52675176 0.2887142 0.10263187 0.25682328 0.76098283 2.81515752] [ 0.53783149 0.28245146 0.09877664 0.26379599 0.78866795 2.94008962] [ 0.53227058 0.28501675 0.10109564 0.25912696 0.77476034 2.85154963] [ 0.52979522 0.28652196 0.10202795 0.26020955 0.76720189 2.84000495] [ 0.52589417 0.28852347 0.10345649 0.26055559 0.75724186 2.78767556] [ 8.48863937e-02 6.37059640e-01 1.86371968e-01 7.59724499e-05 3.77813283e-01 1.73411554e+00] [ 0.52860769 0.28704087 0.10251994 0.25987696 0.7640095 2.81643165] [ 0.52168069 0.29509262 0.10167022 0.25419066 0.76125764 2.84886307] [ 0.53859305 0.28018906 0.10013363 0.26366945 0.780745 2.90465476] [ 0.52866749 0.28738841 0.10188115 0.25918437 0.76475246 2.81244089] [ 0.53137574 0.28764835 0.09977593 0.25964849 0.77675582 2.9026952 ] [ 0.51919445 0.29628706 0.10268165 0.25584802 0.75312897 2.81844183] [ 0.53438765 0.28248704 0.10145031 0.26133665 0.77415744 2.84625913] [ 0.53812141 0.28272066 0.09870905 0.26366283 0.79078037 2.96949808] [ 0.52004377 0.29741181 0.1010309 0.25515969 0.75991222 2.86466603] [ 0.52399193 0.2913219 0.10261812 0.25586143 0.75835695 2.79929685] [ 0.52354579 0.29176181 0.10290488 0.25771221 0.75827167 2.82225628] [ 0.52954776 0.28892531 0.10051708 0.25938249 0.7748299 2.90415618] [ 0.52613643 0.29141252 0.10113694 0.25809425 0.76434541 2.88053633] [ 0.53547462 0.28284952 0.10039518 0.26156713 0.78074846 2.88881516] [ 0.51207517 0.30263246 0.10329707 0.25290701 0.74425839 2.79765602] [ 0.51932192 0.29424221 0.10427114 0.25701422 0.74680324 2.77705229] [ 0.52353799 0.29177549 0.10256016 0.25852323 0.75915739 2.8007608 ] [ 0.53626072 0.28216612 0.10002232 0.26239601 0.78175651 2.87218951] [ 0.54335492 0.27570022 0.09990248 0.26711556 0.78762436 2.91036416] [ 0.53290065 0.2852575 0.10058848 0.25921837 0.77955401 2.88348864] [ 0.52966454 0.28630061 0.10191681 0.25959944 0.76869958 2.80506264] [ 0.52995182 0.28801748 0.10050156 0.25909631 0.77327462 2.87026801] [ 0.52462449 0.2916509 0.10206677 0.25968986 0.76147529 2.8420703 ] [ 0.52626663 0.28992931 0.10212287 0.25598621 0.76406966 2.83177282] [ 0.5314022 0.28518124 0.10153422 0.25901152 0.76990543 2.82820822] [ 0.53514724 0.28358058 0.10026963 0.26217446 0.77908047 2.91383668] [ 0.54021153 0.27902076 0.09963488 0.26466671 0.78602682 2.91029274] [ 0.52631236 0.28962128 0.10203791 0.25766403 0.76500781 2.80874601] [ 0.53135073 0.28577744 0.10138922 0.25971111 0.77285375 2.86126198] [ 5.53815397e-02 6.55200883e-01 1.97030904e-01 4.90872381e-04 3.55016718e-01 1.67696556e+00] [ 0.06047273 0.66468842 0.18372529 0.0076017 0.37682861 1.77308566] [ 0.52650951 0.29005838 0.10187643 0.25840044 0.76354558 2.85389674] [ 0.52383816 0.29304972 0.10147191 0.2558826 0.76653852 2.84860134] [ 0.52629906 0.28915372 0.1022692 0.25878042 0.76478413 2.79118329] [ 0.54146982 0.27708553 0.10013525 0.26291674 0.78715824 2.88658484] [ 0.5302259 0.28774642 0.10068224 0.25768992 0.77023269 2.88175257] [ 0.52705981 0.28787175 0.10294846 0.2609854 0.76081044 2.79474982] [ 0.53128097 0.2847741 0.10188783 0.25848762 0.76889865 2.81433624] [ 0.52789196 0.28689955 0.1030597 0.25897885 0.75988912 2.78947764] [ 0.53523871 0.28388554 0.09972998 0.26262631 0.78105307 2.90081029] [ 0.52025471 0.29464691 0.10347461 0.25627509 0.75313263 2.82714192] [ 0.50981867 0.30381556 0.1039395 0.25286274 0.73852865 2.7682182 ] [ 0.53059919 0.28549288 0.10197556 0.2623071 0.76617136 2.822803 ] [ 0.52890471 0.28755573 0.10190838 0.25986983 0.76452265 2.84737313] [ 0.52133391 0.29398937 0.10279122 0.25626093 0.75276751 2.81370615] [ 0.53702904 0.28001525 0.10141963 0.26339281 0.77730615 2.85323598] [ 0.515332 0.29890542 0.1037906 0.25407251 0.74766359 2.79011739] [ 0.52743209 0.28920702 0.10162935 0.25880255 0.7684052 2.83473272] [ 0.51946858 0.29638948 0.10230223 0.25368213 0.75726451 2.82024381] [ 0.53537141 0.28350969 0.10007002 0.26300454 0.77894133 2.91216582] [ 0.52447764 0.29021592 0.10333389 0.25826259 0.75509951 2.80339906] [ 0.52377007 0.29119375 0.10319841 0.25919138 0.75641308 2.81250339] [ 0.53015267 0.28567887 0.1020989 0.26106416 0.7674984 2.80959837] [ 0.52105089 0.29466429 0.10250292 0.25652888 0.75796965 2.82611744] [ 0.52659688 0.28971927 0.10201916 0.2596975 0.76373477 2.83595144] [ 0.52374074 0.29301149 0.10161118 0.25590681 0.76328724 2.84501041] [ 0.51572952 0.2978281 0.104165 0.25486238 0.74612119 2.77060481] [ 0.5212491 0.29460213 0.10229842 0.25820289 0.75402349 2.82110067] [ 0.54282331 0.27770118 0.09862896 0.26670425 0.79290162 2.94102635] [ 0.52184584 0.29367881 0.10257391 0.25459714 0.75779103 2.81340756] [ 0.52281197 0.29157578 0.10340297 0.2571364 0.75701685 2.78406993] [ 0.52894696 0.28760709 0.1019015 0.26041544 0.7674272 2.84463154] [ 0.52825362 0.28891156 0.10139311 0.26005646 0.76901035 2.86038072] [ 0.52599575 0.2914053 0.10140808 0.25812336 0.76463355 2.88324601] [ 0.53338401 0.28424363 0.10091121 0.26258757 0.77290848 2.86619671] [ 0.5276119 0.28782597 0.10259367 0.2572721 0.76539106 2.80453567] [ 0.5184783 0.2957683 0.10342041 0.25637218 0.7482443 2.77971043] [ 0.53659265 0.28030156 0.10145713 0.26350625 0.77644914 2.84416036] [ 0.52694306 0.29077124 0.10095033 0.25709491 0.77148102 2.88062678] [ 0.28553821 0.53179726 0.10127819 0.77293691 0.25916142 2.86268261] [ 0.52372652 0.29231586 0.10192659 0.25675985 0.75929218 2.81675714] [ 0.52945158 0.28572226 0.10299203 0.2603878 0.76284122 2.8131133 ] [ 0.5253707 0.28999668 0.10260932 0.25689112 0.76092178 2.81321853] [ 0.5264749 0.29116517 0.10099802 0.25768648 0.77019861 2.87666189] [ 0.52310969 0.29066315 0.10381287 0.2582183 0.75501916 2.76364245] [ 0.53266301 0.28664493 0.09972338 0.26140692 0.77815279 2.91808681] [ 0.51056008 0.29889078 0.10714799 0.25334157 0.73187801 2.65665704] [ 0.52433398 0.29049999 0.10295249 0.2572683 0.76025743 2.78871038] [ 0.52280189 0.29384601 0.10179031 0.25781456 0.7628629 2.84316288] [-0.09903585 0.53423213 0.28573782 -2.92513577 0.25998532 0.78325647] [ 0.52662097 0.28966623 0.10194027 0.2600913 0.76253476 2.83711918] [ 0.5404545 0.27882959 0.09957485 0.26202269 0.78780722 2.90529225] [ 0.53499006 0.28428914 0.09943003 0.26028216 0.78665838 2.90018619] [ 0.52669982 0.2899472 0.1019965 0.25756968 0.76566932 2.86029138] [ 0.52794014 0.28873458 0.10151457 0.25957832 0.76898957 2.83290662] [ 0.54665545 0.27445685 0.09819111 0.26639772 0.80070413 2.95890864] [ 0.53331102 0.28331178 0.10183197 0.2598207 0.77072812 2.8446211 ] [ 0.52368535 0.29091266 0.10319056 0.25840195 0.75704727 2.78181437] [ 0.53196822 0.28615115 0.10033134 0.26012755 0.77848085 2.86873238] [ 0.51508429 0.29869972 0.10412343 0.25587249 0.74280934 2.78437295] [ 0.53048054 0.28767698 0.1010155 0.258298 0.77402527 2.9151582 ] [ 0.52723301 0.28909623 0.10208045 0.25947213 0.76387878 2.84482814] [ 0.51952128 0.29482193 0.10359579 0.25777492 0.74882693 2.79011241] [ 0.52774811 0.28777904 0.10246343 0.26054284 0.76366758 2.80559247] [ 0.5378767 0.2797172 0.10096237 0.26429494 0.77727673 2.86542553] [ 0.52307405 0.29490564 0.10092164 0.25701665 0.76687642 2.89826955] [ 0.53419988 0.28435263 0.10011964 0.26226619 0.77947872 2.88386018] [ 0.53479144 0.28381697 0.10005226 0.26214838 0.78063353 2.88663129] [ 0.53176359 0.28704789 0.10006367 0.25738494 0.77882709 2.90250584] [ 0.51848826 0.29505421 0.10358523 0.25605531 0.749569 2.73974511] [ 0.52872309 0.28751982 0.10184708 0.25876996 0.76906045 2.82476911] [ 0.5328173 0.28680079 0.09928413 0.26158681 0.78266858 2.91994046] [ 0.52954946 0.28854867 0.10056727 0.25842205 0.77371554 2.88445499] [ 0.53299132 0.28459707 0.10087991 0.26124063 0.77310905 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2.80910863] [ 0.51903925 0.29496634 0.10380951 0.25711047 0.7477453 2.78131318] [ 0.52996665 0.28564034 0.10269081 0.26058744 0.76563393 2.81871834] [ 0.5232814 0.29233003 0.10234962 0.25657373 0.76216445 2.80553468] [ 0.525067 0.29164771 0.10146471 0.25836773 0.76254295 2.83605328] [ 0.52719783 0.28780352 0.10292461 0.25895767 0.76091071 2.79527354] [ 0.28994156 0.52647026 0.10191106 0.76467163 0.25734877 2.83532559] [ 0.52305178 0.29276585 0.10230685 0.25773615 0.75914243 2.82465874] [ 0.52856778 0.28758365 0.10192365 0.25875467 0.76763803 2.81783934] [ 0.5350429 0.28129477 0.10157757 0.25915126 0.77431688 2.81486369] [ 0.52612738 0.28956853 0.10224016 0.25835704 0.7656402 2.81205138] [ 0.53569545 0.2809378 0.10191666 0.26402413 0.77507526 2.85004431] [ 0.52438866 0.29168881 0.10220149 0.25730003 0.76026928 2.82954001] [ 0.52607397 0.28898986 0.10293108 0.26076329 0.75927632 2.80316181] [ 0.53507216 0.28228208 0.10119367 0.26129212 0.77567952 2.86382607] [ 0.51642385 0.29821004 0.1030096 0.2549652 0.74708293 2.78117826] [ 0.52640228 0.28826635 0.10333974 0.25980036 0.75742296 2.80288408] [ 0.52673795 0.29085399 0.10096923 0.25781478 0.76650165 2.86763364] [ 0.52837807 0.28867083 0.10116793 0.25973546 0.76965702 2.84072463] [ 0.52951983 0.28977408 0.09983996 0.25807791 0.77361383 2.92773712] [ 0.52938713 0.28647018 0.10201331 0.26161254 0.76588621 2.80339881] [ 0.52719761 0.2894341 0.10169525 0.25986704 0.76863853 2.84140025] [ 0.52874729 0.28989953 0.10035751 0.25774511 0.77590238 2.90620945] [ 0.52364376 0.29169641 0.10271022 0.25757595 0.75760172 2.81361837] [ 0.53277783 0.28450754 0.10100162 0.25928133 0.77421227 2.84583602] [ 0.52487636 0.29113294 0.1021706 0.25707876 0.76215313 2.82205077] [ 0.5254636 0.28980422 0.10280162 0.25750867 0.75951288 2.80969842] [ 0.52610468 0.29208697 0.10051673 0.25904634 0.76676938 2.88687345] [ 0.53461879 0.2842938 0.09994383 0.25982865 0.77981368 2.90050598] [ 0.53510774 0.28375294 0.09991674 0.26307639 0.78175061 2.89679988] [ 0.52736783 0.28809469 0.10260757 0.2604621 0.76135155 2.81194392] [ 0.52821214 0.28765387 0.10256923 0.26031367 0.76295723 2.8416404 ] [ 0.52506549 0.29079562 0.10221593 0.25699163 0.76293997 2.81741952] [ 0.52870852 0.29026068 0.10003274 0.25717336 0.77726506 2.91387298] [ 0.53718538 0.2821047 0.09975597 0.26392809 0.7826301 2.91899689] [ 0.06411115 0.64693944 0.19710945 0.00882075 0.3591072 1.68544595] [ 0.52251679 0.29284517 0.10275755 0.25546459 0.75793656 2.81654554] [ 0.52971348 0.28783831 0.10090017 0.25978563 0.765848 2.86418954] [ 0.53120602 0.28811871 0.09974228 0.26016694 0.78018173 2.91866383] [ 0.06118524 0.64596084 0.20060582 0.0092168 0.35818457 1.66325411] [ 0.52571433 0.28937013 0.10279786 0.25887424 0.76167658 2.79739084] [ 0.5282447 0.29033558 0.10041073 0.25740496 0.77441622 2.9026712 ] [ 0.53607734 0.28063875 0.10142577 0.26189281 0.77754531 2.82979831] [ 0.52442863 0.2910469 0.10242241 0.25818444 0.76107777 2.79656025] [ 0.52547131 0.29074083 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2.94174237] [ 0.52650822 0.29025492 0.10137817 0.25762226 0.76369918 2.83892077] [ 0.52337322 0.29063413 0.10344697 0.25726244 0.75779065 2.75972312] [ 0.52598605 0.29006452 0.10211042 0.25907657 0.76343466 2.82290879] [ 0.52813618 0.28860162 0.10189258 0.26104123 0.76746272 2.85927847] [ 0.28049229 0.53853096 0.09973483 0.78503468 0.2622274 2.89719719] [ 0.52544327 0.29076398 0.10204194 0.25836822 0.76310707 2.8313018 ] [ 0.52026506 0.29354963 0.10395558 0.25723144 0.74965528 2.77420767] [ 0.5247171 0.29069113 0.102528 0.25828391 0.75921436 2.81286479] [ 0.52684543 0.28971534 0.10164376 0.25721073 0.76559197 2.83531795] [ 0.52594202 0.29017062 0.10228079 0.25635112 0.76428463 2.84107937] [ 0.5289056 0.28949642 0.1002741 0.25858292 0.77251406 2.88825832] [ 0.51852037 0.29562303 0.1037344 0.25563593 0.75178676 2.78908453] [ 0.52902934 0.28678077 0.10213886 0.26072167 0.76444062 2.81521856] [ 0.52208917 0.29202554 0.10358605 0.25726925 0.75349076 2.77173279] [ 0.53333743 0.28419871 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0.10192849 0.25847128 0.76607563 2.84421587] [ 0.52633143 0.29082167 0.10167129 0.25737656 0.76284037 2.8838062 ] [ 0.53635476 0.28247545 0.10003128 0.26186494 0.78080359 2.90495958] [ 0.52749402 0.28834402 0.10202937 0.26051953 0.76400516 2.8064462 ] [ 0.52058258 0.29535858 0.10249066 0.25638029 0.75613788 2.84344334] [ 0.53413695 0.28451886 0.10018444 0.26260983 0.78055003 2.89469616] [ 0.5270811 0.28912213 0.10204762 0.25884922 0.76443884 2.82596262] [ 0.53243049 0.28590178 0.10040012 0.25971708 0.77828005 2.88631051] [ 0.53477592 0.28277539 0.1011187 0.26044755 0.77476631 2.87433358] [ 0.531574 0.28615107 0.10089461 0.26284967 0.77296706 2.8726847 ] [ 0.53514495 0.28245102 0.1008908 0.26148377 0.7774131 2.86311392] [ 0.52887099 0.28700813 0.10232011 0.26080608 0.76858139 2.82641204] [ 0.53095095 0.28504814 0.10219777 0.26122541 0.76752809 2.83304513] [ 0.52764703 0.28943312 0.10151056 0.25770116 0.76991665 2.86268701] [ 0.52732566 0.28934728 0.10184708 0.25935151 0.76565845 2.85207019] [ 0.52075785 0.29397804 0.10300018 0.25724217 0.75390347 2.78676032] [ 0.54104297 0.27801781 0.09967893 0.26392303 0.785561 2.90081829] [ 0.54122072 0.27867505 0.09921965 0.26297255 0.78704108 2.93502006] [ 0.51981025 0.29565301 0.10265215 0.25733669 0.75262626 2.81066119] [ 0.5257059 0.28951124 0.10287315 0.25763764 0.76209253 2.80884421] [ 0.53544919 0.28251666 0.10085514 0.2617638 0.77714038 2.8873489 ] [ 0.53657106 0.28315327 0.09930474 0.25767675 0.78696961 2.92468905] [ 0.53211439 0.28520003 0.10115161 0.26126171 0.77318652 2.86362067] [ 0.53242889 0.28743979 0.09940946 0.26051327 0.78129282 2.94545026] [ 0.5158112 0.29742653 0.10452968 0.25352688 0.74061523 2.76664581] [ 0.52120104 0.29699407 0.10066399 0.25498771 0.7681264 2.89223579] [ 0.52420961 0.29246375 0.10154315 0.2574962 0.76364781 2.83413036] [ 0.52613427 0.29019937 0.10181884 0.25784719 0.76490984 2.82343037] [ 0.52866367 0.28801314 0.10170721 0.25991643 0.76762924 2.84165497] [ 0.51654817 0.29631759 0.10440188 0.25508265 0.75034952 2.72990728] [ 0.52701223 0.28884805 0.1022939 0.26008116 0.76301071 2.82320506] [ 0.53355981 0.28484854 0.1004711 0.26095633 0.77883573 2.89585338] [ 0.53374491 0.2835389 0.10123559 0.25985232 0.77715042 2.85762167] [ 0.52466884 0.28957782 0.10353714 0.25796679 0.75615711 2.78022428] [ 0.52567286 0.29039021 0.10232599 0.25956768 0.75817252 2.84134323] [ 0.52238719 0.2931687 0.1026264 0.25631929 0.75612964 2.82445974] [ 0.52781149 0.28815127 0.10239217 0.25755458 0.7636327 2.83875035] [ 0.5220532 0.29134438 0.10417585 0.25777312 0.7496721 2.75297225] [ 0.5341324 0.28191199 0.1020713 0.26158702 0.77188596 2.81690617] [ 0.53486646 0.28398245 0.09979077 0.26164167 0.78464975 2.88958711] [ 0.53368001 0.28576518 0.09965746 0.26289935 0.77890475 2.92783336] [ 0.52999564 0.28781035 0.10065017 0.25948127 0.77450136 2.86497161] [ 0.52606389 0.28896949 0.10270894 0.25887797 0.76165403 2.78918733] [ 0.52931996 0.29004159 0.09972038 0.25985084 0.77367586 2.9263604 ] 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0.26049541 0.76598475 2.82699308] [ 0.52233499 0.29431153 0.10210225 0.25559321 0.76151078 2.86995981] [ 0.53204485 0.28457431 0.10170409 0.26164345 0.77099163 2.84022704] [ 0.52598751 0.28960733 0.10254337 0.25939281 0.76120657 2.81144073] [ 0.53362831 0.28323645 0.10141269 0.26299079 0.77155283 2.84137372] [ 0.52308717 0.29183088 0.10283795 0.25571515 0.75924073 2.78437989] [ 0.52687315 0.28948162 0.10206935 0.25793478 0.76332563 2.84560029] [ 0.53314429 0.28465924 0.10101663 0.26369414 0.77415568 2.88625619] [ 0.53248988 0.28713785 0.09949612 0.25843999 0.77939191 2.93087451] [ 0.52374514 0.28986893 0.1040107 0.25766334 0.75407075 2.76477429] [ 0.52885533 0.28711043 0.10215746 0.25886441 0.76536886 2.824698 ] [ 0.52627639 0.29142438 0.10109022 0.2575209 0.76731071 2.88723357] [ 0.53429284 0.28365149 0.10060417 0.26212082 0.77839625 2.87476986] [ 0.53182771 0.28515975 0.10139914 0.26232739 0.77397888 2.85049865] [ 0.51910333 0.29508097 0.10374835 0.25408495 0.75232274 2.79300236] [ 0.53861625 0.28003905 0.10011604 0.26205505 0.78542464 2.89358245] [ 0.52809341 0.28796043 0.10171989 0.25807632 0.76707552 2.80648627] [ 0.5256959 0.29187513 0.10084523 0.25738993 0.76971408 2.86035592] [ 0.52899238 0.28809258 0.10127235 0.25977672 0.76827747 2.84726761] [ 0.52351903 0.29084111 0.10339811 0.25756215 0.75655937 2.77664849] [ 0.52718497 0.28925749 0.10192159 0.25791794 0.76396465 2.84315096] [ 0.52270635 0.29367338 0.10186355 0.25463222 0.75940764 2.83664674] [ 0.52822077 0.28821158 0.10176434 0.25980682 0.76584135 2.82933031] [ 0.52131217 0.29247369 0.10396257 0.25721006 0.74998565 2.77623242] [ 0.53308514 0.28547414 0.10015266 0.26098515 0.78072016 2.89127547] [ 0.51145489 0.30123013 0.10441562 0.25276369 0.74202611 2.72586251] [ 0.52929645 0.28793194 0.10125864 0.25869101 0.76911369 2.86126487] [ 0.53320016 0.28489256 0.10044565 0.26159278 0.78034917 2.87307599] [ 0.52574764 0.29001368 0.10225555 0.25921034 0.75901415 2.81562831] [ 0.09923129 0.63191703 0.17771703 0.006538 0.39395246 1.78767132] [ 0.53595576 0.28208098 0.1005969 0.26373088 0.77891398 2.87849982] [ 0.51861492 0.29290955 0.10551099 0.2567067 0.74147035 2.70432719] [ 0.53107854 0.2876433 0.10005808 0.25938022 0.77827878 2.89729478] [ 0.52160072 0.29316155 0.10335265 0.25581587 0.75296115 2.80704465] [ 0.52931247 0.28933322 0.0999779 0.25871824 0.7811064 2.88256764] [ 0.53189274 0.28527411 0.10125389 0.26048375 0.77451064 2.85818027] [ 0.52505319 0.28827716 0.10401935 0.25898918 0.75466654 2.74698268] [ 0.5272063 0.28732839 0.10334876 0.25948526 0.75886962 2.78702641] [ 0.55246005 0.26936611 0.09770425 0.27064095 0.80881942 2.97680152] [ 0.52519719 0.28989871 0.10297964 0.25969375 0.75782237 2.81245431] [ 0.53107077 0.28673764 0.10075112 0.259777 0.77344787 2.87324688] [ 0.53115574 0.28546159 0.10160448 0.2594502 0.77234232 2.83708493] [ 0.51304958 0.30010488 0.10431147 0.25397149 0.73695949 2.74941105] [ 0.53352586 0.28494921 0.09985331 0.25923154 0.77903195 2.86761321] [ 0.52420379 0.292961 0.10111229 0.25608682 0.76413228 2.85347801] [ 0.52190528 0.29545194 0.10120687 0.25680649 0.76202454 2.86485705] [ 0.52909481 0.28743565 0.10168576 0.25968323 0.76850044 2.83454126] [ 0.53780743 0.28121152 0.09994042 0.26124006 0.7848882 2.90835116] [ 0.52272554 0.29193173 0.10341721 0.25652327 0.75352027 2.80313395] [ 0.53241043 0.2852567 0.1006502 0.26014953 0.77836583 2.85377275] [ 0.52891899 0.28692587 0.10207505 0.25959672 0.76660916 2.80869195] [ 0.53238862 0.28656514 0.10023172 0.26177933 0.77792251 2.9276921 ] [ 0.53692457 0.28225425 0.09947964 0.26236346 0.78533564 2.89328815] [ 0.52245262 0.29374118 0.10233715 0.25652127 0.75987964 2.84551507] [ 0.53101422 0.28647761 0.10096178 0.2608076 0.77328269 2.86003905] [ 0.05360153 0.65885247 0.19530218 0.00218887 0.36141223 1.67993716] [ 0.52726841 0.28895852 0.10199427 0.25863356 0.76334161 2.83589025] [ 0.52991631 0.28390608 0.10350774 0.26124459 0.7610519 2.74745654] [ 0.52173123 0.29321271 0.10322528 0.256943 0.75493732 2.81408761] [ 0.52162905 0.2944627 0.10198822 0.2581943 0.75642664 2.82308231] [ 0.52214334 0.29456905 0.10167859 0.25698458 0.76296321 2.84677689] [ 0.53243442 0.28435989 0.10156694 0.26144974 0.76773697 2.84141831] [ 0.53284569 0.28645369 0.09949677 0.2603123 0.77723518 2.90539385] [ 0.53075179 0.28670695 0.10108942 0.2607481 0.77106256 2.8687915 ] [ 0.52380489 0.29071546 0.10305983 0.25697863 0.75569504 2.77106681] [ 0.51884316 0.29577501 0.10333893 0.25516526 0.75238539 2.80103642] [ 0.52672915 0.28715923 0.10345992 0.2585589 0.75985149 2.75218791] [ 0.53809955 0.28234155 0.09895372 0.26092183 0.789505 2.95919072] [ 0.53298905 0.28295349 0.10205402 0.25996167 0.77015286 2.81386848] [ 0.53401301 0.28241364 0.10172916 0.26204168 0.77324848 2.82896724] [ 0.52207708 0.29524382 0.10118795 0.25607316 0.75923036 2.85955849] [ 0.532236 0.28641943 0.10025189 0.26201998 0.77508753 2.90828479] [ 0.54498154 0.27454505 0.0993426 0.26735828 0.79345859 2.91277922] [ 0.53025333 0.28553496 0.1022792 0.26117691 0.76833141 2.81534693] [ 0.5237447 0.29099602 0.10286065 0.25835123 0.75446608 2.78058381] [ 0.53130749 0.28418171 0.10226511 0.26084131 0.76920612 2.79318655] [ 0.52346536 0.29247875 0.10245293 0.257052 0.76057591 2.83331464] [ 0.52749952 0.28943064 0.10138779 0.25810906 0.7685576 2.84991901] [ 0.52460689 0.28961883 0.10338292 0.2579294 0.75641959 2.7752487 ] [ 0.53049637 0.28757866 0.10042928 0.26002384 0.77501618 2.87001052] [ 0.51269169 0.2981811 0.106362 0.25476857 0.73514336 2.70900314] [ 0.52793748 0.28731116 0.10243957 0.26005414 0.76144354 2.78799071] [ 0.52818181 0.28897068 0.1013893 0.25869743 0.76554969 2.86506956] [ 0.51343212 0.2988521 0.10519421 0.25393952 0.73801555 2.73992285] [ 4.13080399e-02 6.70485838e-01 1.96231718e-01 6.31740808e-04 3.49224325e-01 1.67197417e+00] [ 0.52675856 0.28956004 0.10191284 0.25997235 0.76291699 2.8319394 ] [ 0.52990742 0.28674604 0.10174946 0.26050306 0.76762552 2.84425034] [ 0.52613824 0.28918352 0.10269816 0.25919657 0.75898253 2.80395193] [ 0.07297242 0.64914119 0.18641418 0.00368508 0.37736454 1.74551483] [ 0.53048232 0.28639512 0.10123356 0.26086265 0.771392 2.82953222] [ 0.52682657 0.28953115 0.10183149 0.2593706 0.76584836 2.83651067] [ 0.52001559 0.29649103 0.10180931 0.25644917 0.75595258 2.83988232] [ 0.51987594 0.29725182 0.10127206 0.25504363 0.7573217 2.84998559] [ 0.52515752 0.29002971 0.10306119 0.25753806 0.76015993 2.81779325] [ 0.52095674 0.29464644 0.10273816 0.25600956 0.75566799 2.83238229] [ 0.52171042 0.29172417 0.10422897 0.25848012 0.75098926 2.77008969] [ 0.53106304 0.28657384 0.10094881 0.25642551 0.77362385 2.86853104] [ 0.52939777 0.28689257 0.10180248 0.25772 0.7669455 2.82138191] [ 0.5290277 0.28661431 0.10210206 0.26136866 0.76673154 2.79329181] [ 0.52622888 0.29030698 0.10193191 0.2599442 0.7628199 2.85264796] [ 0.53108094 0.28498935 0.10206505 0.26108525 0.76655213 2.8185568 ] [ 0.53969012 0.27912758 0.09985401 0.26516029 0.78539057 2.88975334] [ 0.53615892 0.28073735 0.10124902 0.26337014 0.77829377 2.83208267] [ 0.51798147 0.29571245 0.10407169 0.25614846 0.74593199 2.77239561] [ 0.52881264 0.28737848 0.10207795 0.25968972 0.76527222 2.82989608] [ 0.52793704 0.2872948 0.10272804 0.25821711 0.7636653 2.79467031] [ 0.52768682 0.28851781 0.10208945 0.25925678 0.76451799 2.82981063] [ 0.52401751 0.2922806 0.10190711 0.25824111 0.76297853 2.82913342] [ 0.52679015 0.28924567 0.10217381 0.25967567 0.76357449 2.83131173] [ 0.55001739 0.27176231 0.09767767 0.26564112 0.80451578 2.97421032] [ 0.52979756 0.2891404 0.09986536 0.26078733 0.77485417 2.89794845] [ 0.52285424 0.29288532 0.10234173 0.25543113 0.76000584 2.81330011] [ 0.52865048 0.28671545 0.10263745 0.2595323 0.76476118 2.80708651] [ 0.52460395 0.28935336 0.10371485 0.25829875 0.75329096 2.76957825] [ 0.53427092 0.28169435 0.10221843 0.26366424 0.77122693 2.82288857] [ 0.51422612 0.30016796 0.10356888 0.25322885 0.74374909 2.80116524] [ 0.5323394 0.28457222 0.10160385 0.26168386 0.76978613 2.85672118] [ 0.52805262 0.28830913 0.10186172 0.25929803 0.76670731 2.82849115] [ 0.53060005 0.28694093 0.10112127 0.25945773 0.771722 2.87198922] [ 0.53244154 0.28472573 0.10133471 0.26434208 0.77029992 2.86152347] [ 0.51625968 0.29808631 0.10343518 0.254273 0.74382004 2.78450317] [ 0.51821657 0.29532528 0.10422085 0.25623564 0.74581779 2.77491566] [ 0.52868774 0.28827435 0.10158974 0.26033228 0.76664923 2.85880036] [ 0.51961659 0.29496647 0.10341704 0.25480578 0.75324005 2.79967155] [ 0.2909476 0.52545472 0.10197925 0.76500725 0.25777484 2.84552246] [ 0.52610665 0.28859887 0.10314306 0.25999585 0.75910705 2.79058506] [ 0.52533108 0.28915992 0.10353545 0.25920943 0.7566486 2.80105423] [ 0.52393791 0.29045989 0.10361454 0.25774485 0.75802754 2.7912884 ] [ 0.53551165 0.28285012 0.10034351 0.26526277 0.77769391 2.88108454] [ 0.53523471 0.28328106 0.10041258 0.26258546 0.77654018 2.9043921 ] [ 0.53389848 0.28333288 0.10107988 0.25984264 0.77595677 2.84971588] [ 0.53086532 0.28748015 0.10041897 0.25866336 0.77499882 2.88875793] [ 0.53077808 0.28614478 0.10149339 0.26129196 0.77151297 2.85019515] [ 0.53419325 0.28425821 0.10039426 0.26154175 0.77947484 2.89694274] [ 0.53008394 0.28814815 0.10062697 0.26139131 0.77151043 2.89619598] [ 0.51513122 0.30006099 0.10293536 0.25438952 0.74807127 2.81379943] [ 0.52865669 0.28737083 0.10218947 0.25928435 0.76444029 2.83006383] [ 0.53399964 0.28299112 0.10110487 0.26012129 0.77913145 2.83365457] [ 0.53078003 0.28641964 0.10120639 0.25863946 0.77165946 2.85219154] [ 0.52911696 0.28759665 0.10170686 0.26150076 0.76456735 2.85061307] [ 0.52700242 0.29165372 0.10026302 0.25884108 0.77067618 2.90340925] [ 0.53113105 0.28728562 0.10031662 0.25946382 0.77379825 2.88847715] [ 0.53469981 0.28321628 0.10075448 0.26046006 0.77689576 2.88137561] [ 0.52103504 0.29396709 0.10286256 0.25600074 0.75591739 2.79510413] [ 0.52218041 0.29306682 0.10278659 0.25784315 0.75456945 2.80530246] [ 0.53488979 0.28456274 0.09961068 0.2609477 0.78219402 2.93018205] [ 0.5353003 0.28289292 0.10013739 0.2636142 0.77959224 2.86250979] [ 0.53145148 0.28666708 0.10057358 0.26123714 0.77494858 2.88312511] [ 0.53348079 0.28490948 0.10045029 0.26348002 0.77483923 2.89405823] [ 0.53430312 0.28329864 0.100852 0.26173564 0.77772964 2.85608802] [ 0.53166226 0.28823415 0.09953981 0.26102529 0.78341687 2.95366331] [ 0.53732096 0.28041206 0.10077841 0.26262079 0.77934805 2.87108249] [ 0.52610854 0.29067848 0.10172096 0.25949741 0.76224694 2.86219681] [ 0.52676134 0.28962629 0.1020867 0.25971637 0.76263121 2.849982 ] [ 0.53096013 0.28599651 0.10132206 0.26102624 0.7733681 2.83904765] [ 0.53295435 0.28550362 0.1001244 0.25935821 0.78119616 2.87742617] [ 0.52911002 0.28912229 0.10025344 0.25713488 0.77551707 2.87747989] [ 0.52565747 0.29070289 0.10185273 0.25756771 0.76286919 2.83515279] [ 0.53157627 0.2870114 0.10018012 0.25702632 0.77541539 2.89112248] [ 0.52771203 0.28719687 0.10299977 0.25861102 0.76124833 2.79532915] [ 7.13864084e-02 6.43552443e-01 1.92243668e-01 9.90038755e-04 3.62271221e-01 1.66563598e+00] [ 0.52841079 0.28881544 0.10116992 0.26066672 0.76957296 2.85255336] [ 0.53748314 0.28281583 0.09890411 0.26384694 0.78806422 2.94016195] [ 0.53089353 0.28424391 0.10266871 0.26077172 0.76497477 2.79377089] [ 0.52468294 0.29323155 0.10080495 0.25844071 0.7644761 2.88374157] [ 0.52856263 0.28666958 0.10266642 0.26124391 0.76189338 2.80060798] [ 0.52187814 0.2926676 0.10338985 0.25749876 0.75390421 2.79575108] [ 0.53252939 0.28597645 0.10038814 0.26282542 0.77588385 2.90147454] [ 0.5236712 0.29368162 0.10124636 0.25723466 0.76587674 2.86500493] [ 0.52529396 0.29074346 0.10214809 0.25883767 0.75988511 2.83021831] [ 0.52675731 0.29060069 0.10132859 0.25975769 0.76651393 2.87892118] [ 0.53325516 0.28638121 0.09934416 0.26117588 0.78309773 2.91472751] [ 0.52988921 0.2887574 0.10028533 0.25948238 0.77706472 2.90311953] [ 0.53795289 0.27963987 0.10109944 0.26416497 0.77907 2.88032623] [ 0.51906123 0.29431499 0.10409717 0.25489278 0.74868064 2.75130043] [ 0.53938137 0.27905109 0.10026632 0.26602141 0.78126996 2.88866107] [ 0.53254 0.28582747 0.10029792 0.26027107 0.77663162 2.88362016] [ 0.53242062 0.28467651 0.10130878 0.25990816 0.77414209 2.85301061] [ 0.52672878 0.2898127 0.10169636 0.25845187 0.76750841 2.83622944] [ 0.52692607 0.28736549 0.1035058 0.25961257 0.7600043 2.77858015] [ 0.53338757 0.28473032 0.10056772 0.26040871 0.77881532 2.88164688] [ 0.53455009 0.28315956 0.10090712 0.2618802 0.77516591 2.87521866] [ 0.52401699 0.29190515 0.10250628 0.2580886 0.75989484 2.83981721] [ 0.53616127 0.28270729 0.10006049 0.26381802 0.78136094 2.9122556 ] [ 0.54207776 0.27813236 0.09856762 0.26356645 0.79211254 2.92114314] [ 0.5258879 0.28963515 0.10255799 0.25922681 0.75963392 2.82025446] [ 0.52983933 0.28835302 0.10044129 0.25937693 0.77086135 2.87822085] [ 0.51856872 0.29657675 0.10310135 0.2541727 0.75207935 2.81897886] [ 0.52592707 0.29050379 0.10194356 0.25875737 0.76343657 2.84094004] [ 0.52858308 0.28851164 0.10118884 0.25931086 0.76619205 2.84450938] [ 0.53097776 0.28561953 0.1017676 0.25954643 0.77320758 2.84213667] [ 0.52124465 0.29370989 0.10290339 0.25732938 0.75631952 2.79946241] [ 0.52458588 0.29162825 0.10149375 0.25622207 0.76406089 2.81208125] [ 0.52578693 0.28989576 0.10253662 0.25910238 0.76178743 2.81893128] [ 0.54169812 0.27808933 0.09946962 0.2637004 0.78960884 2.94172628] [ 0.53094338 0.28803627 0.10002704 0.26163979 0.77390157 2.91589849] [ 0.52833051 0.28835288 0.10162424 0.25842743 0.76902444 2.83721103] [ 0.52796721 0.29001763 0.10097134 0.25913759 0.76917688 2.9024221 ] [ 0.52763328 0.28898571 0.10170951 0.25887647 0.76697375 2.84096154] [ 0.53048754 0.28724643 0.10089604 0.26098032 0.77225632 2.87122151] [ 0.53258068 0.28317182 0.10232105 0.26200757 0.76709755 2.81519185] [ 0.52673862 0.28950797 0.10210245 0.25768315 0.76052414 2.83918912] [ 0.52436905 0.2913004 0.10257355 0.2591361 0.76126523 2.82585915] [ 0.53142045 0.28625123 0.10084861 0.26068265 0.77464387 2.86613393] [ 0.53097593 0.2874495 0.10025114 0.25984928 0.7767134 2.8859161 ] [ 0.52425067 0.29471028 0.10030069 0.25802118 0.76675389 2.93328853] [ 0.53047763 0.28586576 0.10199251 0.26104112 0.76701649 2.83060097] [ 0.52351259 0.29151098 0.10303191 0.25564088 0.75701715 2.80374168] [ 0.52923131 0.28841511 0.10083273 0.25731952 0.77331325 2.86363404] [ 0.52855331 0.29133154 0.09921841 0.25643501 0.77753993 2.93603201] [ 0.52497109 0.2910064 0.10210152 0.25526823 0.76105129 2.82413231] [ 0.29282152 0.52397429 0.10150452 0.76390521 0.25686506 2.8406086 ] [ 0.526921 0.28955753 0.10193746 0.26100734 0.76351418 2.84183106] [ 0.54045158 0.27866262 0.09963642 0.26624963 0.78911339 2.90315597] [ 0.52568445 0.29094665 0.10211989 0.2576108 0.76472948 2.86544976] [ 0.5331346 0.28419945 0.1009209 0.26316389 0.77219107 2.84872529] [ 0.52105294 0.29345024 0.10348245 0.25775431 0.75140411 2.79487489] [ 0.53705216 0.28002126 0.10119789 0.26103897 0.77797736 2.84522076] [ 0.53445606 0.28415627 0.09993353 0.26163676 0.77793596 2.88199432] [ 0.51999391 0.29439693 0.10366078 0.25701904 0.74963335 2.79831749] [ 0.52150788 0.29458529 0.10234917 0.25616219 0.75616095 2.84570527] [ 0.52046679 0.29362527 0.10376618 0.25595748 0.75014522 2.78747685] [ 0.52444354 0.29133581 0.10230412 0.25760216 0.76423008 2.81468826] [ 0.53308721 0.28400382 0.10140704 0.26111285 0.77332075 2.84666406]
Now let's create arrays of the fluctuations of the best fit parameters popti around the true solution popt0¶
In [13]:
omegas1 = np.array(omegas1) - w10
omegas2 = np.array(omegas2) - w20
omegas3 = np.array(omegas3) - w30
omegas4 = np.array(omegas4) - w40
sigmas1 = np.array(sigmas1) - s10
sigmas2 = np.array(sigmas2) - s20
sigmas3 = np.array(sigmas3) - s30
In [14]:
## now computing the standard deviation of the best-fit parameters population
stdw1, stdw2,stdw3,stdw4,stds1,stds2,stds3 = omegas1.std(), omegas2.std(), omegas3.std(),omegas4.std(), sigmas1.std(),sigmas2.std(),sigmas3.std()
print "Bootstrap errors in w1,w2,w3,w4,s1,s2,s3 are:", stdw1, stdw2,stdw3,stdw4,stds1,stds2,stds3
Bootstrap errors in w1,w2,w3,w4,s1,s2,s3 are: 0.0772531005887 0.0610754089333 0.0149780096104 0.00644211083616 0.121609755555 0.0840172033095 0.192045426395
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