diff options
author | Travis Galoppo <tjg2107@columbia.edu> | 2015-02-06 10:26:51 -0800 |
---|---|---|
committer | Xiangrui Meng <meng@databricks.com> | 2015-02-06 10:26:51 -0800 |
commit | 9ad56ad2a2a51df449040c4f4b7c66b104883312 (patch) | |
tree | 5b86feec8fba10c96f786bf5a7eaa89697eac358 | |
parent | 37d35ab53b82916e4bf0eeb788044bfc33f329df (diff) | |
download | spark-9ad56ad2a2a51df449040c4f4b7c66b104883312.tar.gz spark-9ad56ad2a2a51df449040c4f4b7c66b104883312.tar.bz2 spark-9ad56ad2a2a51df449040c4f4b7c66b104883312.zip |
[SPARK-5013] [MLlib] Added documentation and sample data file for GaussianMixture
Simple description and code samples (and sample data) for GaussianMixture
Author: Travis Galoppo <tjg2107@columbia.edu>
Closes #4401 from tgaloppo/spark-5013 and squashes the following commits:
c9ff9a5 [Travis Galoppo] Fixed link in mllib-clustering.md Added Gaussian mixture and power iteration as available clustering techniques in mllib-guide
2368690 [Travis Galoppo] Minor fixes
3eb41fa [Travis Galoppo] [SPARK-5013] Added documentation and sample data file for GaussianMixture
-rw-r--r-- | data/mllib/gmm_data.txt | 2000 | ||||
-rw-r--r-- | docs/mllib-clustering.md | 131 | ||||
-rw-r--r-- | docs/mllib-guide.md | 2 |
3 files changed, 2130 insertions, 3 deletions
diff --git a/data/mllib/gmm_data.txt b/data/mllib/gmm_data.txt new file mode 100644 index 0000000000..934ee4a83a --- /dev/null +++ b/data/mllib/gmm_data.txt @@ -0,0 +1,2000 @@ + 2.59470454e+00 2.12298217e+00 + 1.15807024e+00 -1.46498723e-01 + 2.46206638e+00 6.19556894e-01 + -5.54845070e-01 -7.24700066e-01 + -3.23111426e+00 -1.42579084e+00 + 3.02978115e+00 7.87121753e-01 + 1.97365907e+00 1.15914704e+00 + -6.44852101e+00 -3.18154314e+00 + 1.30963349e+00 1.62866434e-01 + 4.26482541e+00 2.15547996e+00 + 3.79927257e+00 1.50572445e+00 + 4.17452609e-01 -6.74032760e-01 + 4.21117627e-01 4.45590255e-01 + -2.80425571e+00 -7.77150554e-01 + 2.55928797e+00 7.03954218e-01 + 1.32554059e+00 -9.46663152e-01 + -3.39691439e+00 -1.49005743e+00 + -2.26542270e-01 3.60052515e-02 + 1.04994198e+00 5.29825685e-01 + -1.51566882e+00 -1.86264432e-01 + -3.27928172e-01 -7.60859110e-01 + -3.18054866e-01 3.97719805e-01 + 1.65579418e-01 -3.47232033e-01 + 6.47162333e-01 4.96059961e-02 + -2.80776647e-01 4.79418757e-01 + 7.45069752e-01 1.20790281e-01 + 2.13604102e-01 1.59542555e-01 + -3.08860224e+00 -1.43259870e+00 + 8.97066497e-01 1.10206801e+00 + -2.23918874e-01 -1.07267267e+00 + 2.51525708e+00 2.84761973e-01 + 9.98052532e-01 1.08333783e+00 + 1.76705588e+00 8.18866778e-01 + 5.31555163e-02 -1.90111151e-01 + -2.17405059e+00 7.21854582e-02 + -2.13772505e+00 -3.62010387e-01 + 2.95974057e+00 1.31602381e+00 + 2.74053561e+00 1.61781757e+00 + 6.68135448e-01 2.86586009e-01 + 2.82323739e+00 1.74437257e+00 + 8.11540288e-01 5.50744478e-01 + 4.10050897e-01 5.10668402e-03 + 9.58626136e-01 -3.49633680e-01 + 4.66599798e+00 1.49964894e+00 + 4.94507794e-01 2.58928077e-01 + -2.36029742e+00 -1.61042909e+00 + -4.99306804e-01 -8.04984769e-01 + 1.07448510e+00 9.39605828e-01 + -1.80448949e+00 -1.05983264e+00 + -3.22353821e-01 1.73612093e-01 + 1.85418702e+00 1.15640643e+00 + 6.93794163e-01 6.59993560e-01 + 1.99399102e+00 1.44547123e+00 + 3.38866124e+00 1.23379290e+00 + -4.24067720e+00 -1.22264282e+00 + 6.03230201e-02 2.95232729e-01 + -3.59341813e+00 -7.17453726e-01 + 4.87447372e-01 -2.00733911e-01 + 1.20149195e+00 4.07880197e-01 + -2.13331464e+00 -4.58518077e-01 + -3.84091083e+00 -1.71553950e+00 + -5.37279250e-01 2.64822629e-02 + -2.10155227e+00 -1.32558103e+00 + -1.71318897e+00 -7.12098563e-01 + -1.46280695e+00 -1.84868337e-01 + -3.59785325e+00 -1.54832434e+00 + -5.77528081e-01 -5.78580857e-01 + 3.14734283e-01 5.80184639e-01 + -2.71164714e+00 -1.19379432e+00 + 1.09634489e+00 7.20143887e-01 + -3.05527722e+00 -1.47774064e+00 + 6.71753586e-01 7.61350020e-01 + 3.98294144e+00 1.54166484e+00 + -3.37220384e+00 -2.21332064e+00 + 1.81222914e+00 7.41212752e-01 + 2.71458282e-01 1.36329078e-01 + -3.97815359e-01 1.16766886e-01 + -1.70192814e+00 -9.75851571e-01 + -3.46803804e+00 -1.09965988e+00 + -1.69649627e+00 -5.76045801e-01 + -1.02485636e-01 -8.81841246e-01 + -3.24194667e-02 2.55429276e-01 + -2.75343168e+00 -1.51366320e+00 + -2.78676702e+00 -5.22360489e-01 + 1.70483164e+00 1.19769805e+00 + 4.92022579e-01 3.24944706e-01 + 2.48768464e+00 1.00055363e+00 + 4.48786400e-01 7.63902870e-01 + 2.93862696e+00 1.73809968e+00 + -3.55019305e+00 -1.97875558e+00 + 1.74270784e+00 6.90229224e-01 + 5.13391994e-01 4.58374016e-01 + 1.78379499e+00 9.08026381e-01 + 1.75814147e+00 7.41449784e-01 + -2.30687792e-01 3.91009729e-01 + 3.92271353e+00 1.44006290e+00 + 2.93361679e-01 -4.99886375e-03 + 2.47902690e-01 -7.49542503e-01 + -3.97675355e-01 1.36824887e-01 + 3.56535953e+00 1.15181329e+00 + 3.22425301e+00 1.28702383e+00 + -2.94192478e-01 -2.42382557e-01 + 8.02068864e-01 -1.51671475e-01 + 8.54133530e-01 -4.89514885e-02 + -1.64316316e-01 -5.34642346e-01 + -6.08485405e-01 -2.10332352e-01 + -2.18940059e+00 -1.07024952e+00 + -1.71586960e+00 -2.83333492e-02 + 1.70200448e-01 -3.28031178e-01 + -1.97210346e+00 -5.39948532e-01 + 2.19500160e+00 1.05697170e+00 + -1.76239935e+00 -1.09377438e+00 + 1.68314744e+00 6.86491164e-01 + -2.99852288e+00 -1.46619067e+00 + -2.23769560e+00 -9.15008355e-01 + 9.46887516e-01 5.58410503e-01 + 5.02153123e-01 1.63851235e-01 + -9.70297062e-01 3.14625374e-01 + -1.29405593e+00 -8.20994131e-01 + 2.72516079e+00 7.85839947e-01 + 1.45788024e+00 3.37487353e-01 + -4.36292749e-01 -5.42150480e-01 + 2.21304711e+00 1.25254042e+00 + -1.20810271e-01 4.79632898e-01 + -3.30884511e+00 -1.50607586e+00 + -6.55882455e+00 -1.94231256e+00 + -3.17033630e+00 -9.94678930e-01 + 1.42043617e+00 7.28808957e-01 + -1.57546099e+00 -1.10320497e+00 + -3.22748754e+00 -1.64174579e+00 + 2.96776017e-03 -3.16191512e-02 + -2.25986054e+00 -6.13123197e-01 + 2.49434243e+00 7.73069183e-01 + 9.08494049e-01 -1.53926853e-01 + -2.80559090e+00 -1.37474221e+00 + 4.75224286e-01 2.53153674e-01 + 4.37644006e+00 8.49116998e-01 + 2.27282959e+00 6.16568202e-01 + 1.16006880e+00 1.65832798e-01 + -1.67163193e+00 -1.22555386e+00 + -1.38231118e+00 -7.29575504e-01 + -3.49922750e+00 -2.26446675e+00 + -3.73780110e-01 -1.90657869e-01 + 1.68627679e+00 1.05662987e+00 + -3.28891792e+00 -1.11080334e+00 + -2.59815798e+00 -1.51410198e+00 + -2.61203309e+00 -6.00143552e-01 + 6.58964943e-01 4.47216094e-01 + -2.26711381e+00 -7.26512923e-01 + -5.31429009e-02 -1.97925341e-02 + 3.19749807e+00 9.20425476e-01 + -1.37595787e+00 -6.58062732e-01 + 8.09900278e-01 -3.84286160e-01 + -5.07741280e+00 -1.97683808e+00 + -2.99764250e+00 -1.50753777e+00 + -9.87671815e-01 -4.63255889e-01 + 1.65390765e+00 6.73806615e-02 + 5.51252659e+00 2.69842267e+00 + -2.23724309e+00 -4.77624004e-01 + 4.99726228e+00 1.74690949e+00 + 1.75859162e-01 -1.49350995e-01 + 4.13382789e+00 1.31735161e+00 + 2.69058117e+00 4.87656923e-01 + 1.07180318e+00 1.01426954e+00 + 3.37216869e+00 1.05955377e+00 + -2.95006781e+00 -1.57048303e+00 + -2.46401648e+00 -8.37056374e-01 + 1.19012962e-01 7.54702770e-01 + 3.34142539e+00 4.81938295e-01 + 2.92643913e+00 1.04301050e+00 + 2.89697751e+00 1.37551442e+00 + -1.03094242e+00 2.20903962e-01 + -5.13914589e+00 -2.23355387e+00 + -8.81680780e-01 1.83590000e-01 + 2.82334775e+00 1.26650464e+00 + -2.81042540e-01 -3.26370240e-01 + 2.97995487e+00 8.34569452e-01 + -1.39857135e+00 -1.15798385e+00 + 4.27186506e+00 9.04253702e-01 + 6.98684517e-01 7.91167305e-01 + 3.52233095e+00 1.29976473e+00 + 2.21448029e+00 2.73213379e-01 + -3.13505683e-01 -1.20593774e-01 + 3.70571571e+00 1.06220876e+00 + 9.83881041e-01 5.67713803e-01 + -2.17897705e+00 2.52925205e-01 + 1.38734039e+00 4.61287066e-01 + -1.41181602e+00 -1.67248955e-02 + -1.69974639e+00 -7.17812071e-01 + -2.01005793e-01 -7.49662056e-01 + 1.69016336e+00 3.24687979e-01 + -2.03250179e+00 -2.76108460e-01 + 3.68776848e-01 4.12536941e-01 + 7.66238259e-01 -1.84750637e-01 + -2.73989147e-01 -1.72817250e-01 + -2.18623745e+00 -2.10906798e-01 + -1.39795625e-01 3.26066094e-02 + -2.73826912e-01 -6.67586097e-02 + -1.57880654e+00 -4.99395900e-01 + 4.55950908e+00 2.29410489e+00 + -7.36479631e-01 -1.57861857e-01 + 1.92082888e+00 1.05843391e+00 + 4.29192810e+00 1.38127810e+00 + 1.61852879e+00 1.95871986e-01 + -1.95027403e+00 -5.22448168e-01 + -1.67446281e+00 -9.41497162e-01 + 6.07097859e-01 3.44178029e-01 + -3.44004683e+00 -1.49258461e+00 + 2.72114752e+00 6.00728991e-01 + 8.80685522e-01 -2.53243336e-01 + 1.39254928e+00 3.42988512e-01 + 1.14194836e-01 -8.57945694e-02 + -1.49387332e+00 -7.60860481e-01 + -1.98053285e+00 -4.86039865e-01 + 3.56008568e+00 1.08438692e+00 + 2.27833961e-01 1.09441881e+00 + -1.16716710e+00 -6.54778242e-01 + 2.02156613e+00 5.42075758e-01 + 1.08429178e+00 -7.67420693e-01 + 6.63058455e-01 4.61680991e-01 + -1.06201537e+00 1.38862846e-01 + 3.08701875e+00 8.32580273e-01 + -4.96558108e-01 -2.47031257e-01 + 7.95109987e-01 7.59314147e-02 + -3.39903524e-01 8.71565566e-03 + 8.68351357e-01 4.78358641e-01 + 1.48750819e+00 7.63257420e-01 + -4.51224101e-01 -4.44056898e-01 + -3.02734750e-01 -2.98487961e-01 + 5.46846609e-01 7.02377629e-01 + 1.65129778e+00 3.74008231e-01 + -7.43336512e-01 3.95723531e-01 + -5.88446605e-01 -6.47520211e-01 + 3.58613167e+00 1.95024937e+00 + 3.11718883e+00 8.37984715e-01 + 1.80919244e+00 9.62644986e-01 + 5.43856371e-02 -5.86297543e-01 + -1.95186766e+00 -1.02624212e-01 + 8.95628057e-01 5.91812281e-01 + 4.97691627e-02 5.31137156e-01 + -1.07633113e+00 -2.47392788e-01 + -1.17257986e+00 -8.68528265e-01 + -8.19227665e-02 5.80579434e-03 + -2.86409787e-01 1.95812924e-01 + 1.10582671e+00 7.42853240e-01 + 4.06429774e+00 1.06557476e+00 + -3.42521792e+00 -7.74327139e-01 + 1.28468671e+00 6.20431661e-01 + 6.01201008e-01 -1.16799728e-01 + -1.85058727e-01 -3.76235293e-01 + 5.44083324e+00 2.98490868e+00 + 2.69273070e+00 7.83901153e-01 + 1.88938036e-01 -4.83222152e-01 + 1.05667256e+00 -2.57003165e-01 + 2.99711662e-01 -4.33131912e-01 + 7.73689216e-02 -1.78738364e-01 + 9.58326279e-01 6.38325706e-01 + -3.97727049e-01 2.27314759e-01 + 3.36098175e+00 1.12165237e+00 + 1.77804871e+00 6.46961933e-01 + -2.86945546e+00 -1.00395518e+00 + 3.03494815e+00 7.51814612e-01 + -1.43658194e+00 -3.55432244e-01 + -3.08455105e+00 -1.51535106e+00 + -1.55841975e+00 3.93454820e-02 + 7.96073412e-01 -3.11036969e-01 + -9.84125401e-01 -1.02064649e+00 + -7.75688143e+00 -3.65219926e+00 + 1.53816429e+00 7.65926670e-01 + -4.92712738e-01 2.32244240e-02 + -1.93166919e+00 -1.07701304e+00 + 2.03029875e-02 -7.54055699e-01 + 2.52177489e+00 1.01544979e+00 + 3.65109048e-01 -9.48328494e-01 + -1.28849143e-01 2.51947174e-01 + -1.02428075e+00 -9.37767116e-01 + -3.04179748e+00 -9.97926994e-01 + -2.51986980e+00 -1.69117413e+00 + -1.24900838e+00 -4.16179917e-01 + 2.77943992e+00 1.22842327e+00 + -4.37434557e+00 -1.70182693e+00 + -1.60019319e+00 -4.18345639e-01 + -1.67613646e+00 -9.44087262e-01 + -9.00843245e-01 8.26378089e-02 + 3.29770621e-01 -9.07870444e-01 + -2.84650535e+00 -9.00155396e-01 + 1.57111705e+00 7.07432268e-01 + 1.24948552e+00 1.04812849e-01 + 1.81440558e+00 9.53545082e-01 + -1.74915794e+00 -1.04606288e+00 + 1.20593269e+00 -1.12607147e-02 + 1.36004919e-01 -1.09828044e+00 + 2.57480693e-01 3.34941541e-01 + 7.78775385e-01 -5.32494732e-01 + -1.79155126e+00 -6.29994129e-01 + -1.75706839e+00 -8.35100126e-01 + 4.29512012e-01 7.81426910e-02 + 3.08349370e-01 -1.27359861e-01 + 1.05560329e+00 4.55150640e-01 + 1.95662574e+00 1.17593217e+00 + 8.77376632e-01 6.57866662e-01 + 7.71311255e-01 9.15134334e-02 + -6.36978275e+00 -2.55874241e+00 + -2.98335339e+00 -1.59567024e+00 + -3.67104587e-01 1.85315291e-01 + 1.95347407e+00 -7.15503113e-02 + 8.45556363e-01 6.51256415e-02 + 9.42868521e-01 3.56647624e-01 + 2.99321875e+00 1.07505254e+00 + -2.91030538e-01 -3.77637183e-01 + 1.62870918e+00 3.37563671e-01 + 2.05773173e-01 3.43337416e-01 + -8.40879199e-01 -1.35600767e-01 + 1.38101624e+00 5.99253495e-01 + -6.93715607e+00 -2.63580662e+00 + -1.04423404e+00 -8.32865050e-01 + 1.33448476e+00 1.04863475e+00 + 6.01675207e-01 1.98585194e-01 + 2.31233993e+00 7.98628331e-01 + 1.85201313e-01 -1.76070247e+00 + 1.92006354e+00 8.45737582e-01 + 1.06320415e+00 2.93426068e-01 + -1.20360141e+00 -1.00301288e+00 + 1.95926629e+00 6.26643532e-01 + 6.04483978e-02 5.72643059e-01 + -1.04568563e+00 -5.91021496e-01 + 2.62300678e+00 9.50997831e-01 + -4.04610275e-01 3.73150879e-01 + 2.26371902e+00 8.73627529e-01 + 2.12545313e+00 7.90640352e-01 + 7.72181917e-03 1.65718952e-02 + 1.00422340e-01 -2.05562936e-01 + -1.22989802e+00 -1.01841681e-01 + 3.09064082e+00 1.04288010e+00 + 5.18274167e+00 1.34749259e+00 + -8.32075153e-01 -1.97592029e-01 + 3.84126764e-02 5.58171345e-01 + 4.99560727e-01 -4.26154438e-02 + 4.79071151e+00 2.19728942e+00 + -2.78437968e+00 -1.17812590e+00 + -2.22804226e+00 -4.31174255e-01 + 8.50762292e-01 -1.06445261e-01 + 1.10812830e+00 -2.59118812e-01 + -2.91450155e-01 6.42802679e-01 + -1.38631532e-01 -5.88585623e-01 + -5.04120983e-01 -2.17094915e-01 + 3.41410820e+00 1.67897767e+00 + -2.23697326e+00 -6.62735244e-01 + -3.55961064e-01 -1.27647226e-01 + -3.55568274e+00 -2.49011369e+00 + -8.77586408e-01 -9.38268065e-03 + 1.52382384e-01 -5.62155760e-01 + 1.55885574e-01 1.07617069e-01 + -8.37129973e-01 -5.22259081e-01 + -2.92741750e+00 -1.35049428e+00 + -3.54670781e-01 5.69205952e-02 + 2.21030255e+00 1.34689986e+00 + 1.60787722e+00 5.75984706e-01 + 1.32294221e+00 5.31577509e-01 + 7.05672928e-01 3.34241244e-01 + 1.41406179e+00 1.15783408e+00 + -6.92172228e-01 -2.84817896e-01 + 3.28358655e-01 -2.66910083e-01 + 1.68013644e-01 -4.28016549e-02 + 2.07365974e+00 7.76496211e-01 + -3.92974907e-01 2.46796730e-01 + -5.76078636e-01 3.25676963e-01 + -1.82547204e-01 -5.06410543e-01 + 3.04754906e+00 1.16174496e+00 + -3.01090632e+00 -1.09195183e+00 + -1.44659696e+00 -6.87838682e-01 + 2.11395861e+00 9.10495785e-01 + 1.40962871e+00 1.13568678e+00 + -1.66653234e-01 -2.10012503e-01 + 3.17456029e+00 9.74502922e-01 + 2.15944820e+00 8.62807189e-01 + -3.45418719e+00 -1.33647548e+00 + -3.41357732e+00 -8.47048920e-01 + -3.06702448e-01 -6.64280634e-01 + -2.86930714e-01 -1.35268264e-01 + -3.15835557e+00 -5.43439253e-01 + 2.49541440e-01 -4.71733570e-01 + 2.71933912e+00 4.13308399e-01 + -2.43787038e+00 -1.08050547e+00 + -4.90234490e-01 -6.64069865e-01 + 8.99524451e-02 5.76180541e-01 + 5.00500404e+00 2.12125521e+00 + -1.73107940e-01 -2.28506575e-02 + 5.44938858e-01 -1.29523352e-01 + 5.13526842e+00 1.68785993e+00 + 1.70228304e+00 1.02601138e+00 + 3.58957507e+00 1.54396196e+00 + 1.85615738e+00 4.92916197e-01 + 2.55772147e+00 7.88438908e-01 + -1.57008279e+00 -4.17377300e-01 + -1.42548604e+00 -3.63684860e-01 + -8.52026118e-01 2.72052686e-01 + -5.10563077e+00 -2.35665994e+00 + -2.95517031e+00 -1.84945297e+00 + -2.91947959e+00 -1.66016784e+00 + -4.21462387e+00 -1.41131535e+00 + 6.59901121e-01 4.87156314e-01 + -9.75352532e-01 -4.50231285e-01 + -5.94084444e-01 -1.16922670e+00 + 7.50554615e-01 -9.83692552e-01 + 1.07054926e+00 2.77143030e-01 + -3.88079578e-01 -4.17737309e-02 + -9.59373733e-01 -8.85454886e-01 + -7.53560665e-02 -5.16223870e-02 + 9.84108158e-01 -5.89290700e-02 + 1.87272961e-01 -4.34238391e-01 + 6.86509981e-01 -3.15116460e-01 + -1.07762538e+00 6.58984161e-02 + 6.09266592e-01 6.91808473e-02 + -8.30529954e-01 -7.00454791e-01 + -9.13179464e-01 -6.31712891e-01 + 7.68744851e-01 1.09840676e+00 + -1.07606690e+00 -8.78390282e-01 + -1.71038184e+00 -5.73606033e-01 + 8.75982765e-01 3.66343143e-01 + -7.04919009e-01 -8.49182590e-01 + -1.00274668e+00 -7.99573611e-01 + -1.05562848e+00 -5.84060076e-01 + 4.03490015e+00 1.28679206e+00 + -3.53484804e+00 -1.71381255e+00 + 2.31527363e-01 1.04179397e-01 + -3.58592392e-02 3.74895739e-01 + 3.92253428e+00 1.81852726e+00 + -7.27384249e-01 -6.45605128e-01 + 4.65678097e+00 2.41379899e+00 + 1.16750534e+00 7.60718205e-01 + 1.15677059e+00 7.96225550e-01 + -1.42920261e+00 -4.66946295e-01 + 3.71148192e+00 1.88060191e+00 + 2.44052407e+00 3.84472199e-01 + -1.64535035e+00 -8.94530036e-01 + -3.69608753e+00 -1.36402754e+00 + 2.24419208e+00 9.69744889e-01 + 2.54822427e+00 1.22613039e+00 + 3.77484909e-01 -5.98521878e-01 + -3.61521175e+00 -1.11123912e+00 + 3.28113127e+00 1.52551775e+00 + -3.51030902e+00 -1.53913980e+00 + -2.44874505e+00 -6.30246005e-01 + -3.42516153e-01 -5.07352665e-01 + 1.09110502e+00 6.36821628e-01 + -2.49434967e+00 -8.02827146e-01 + 1.41763139e+00 -3.46591820e-01 + 1.61108619e+00 5.93871102e-01 + 3.97371717e+00 1.35552499e+00 + -1.33437177e+00 -2.83908670e-01 + -1.41606483e+00 -1.76402601e-01 + 2.23945322e-01 -1.77157065e-01 + 2.60271569e+00 2.40778251e-01 + -2.82213895e-02 1.98255474e-01 + 4.20727940e+00 1.31490863e+00 + 3.36944889e+00 1.57566635e+00 + 3.53049396e+00 1.73579350e+00 + -1.29170202e+00 -1.64196290e+00 + 9.27295604e-01 9.98808036e-01 + 1.75321843e-01 -2.83267817e-01 + -2.19069578e+00 -1.12814358e+00 + 1.66606031e+00 7.68006933e-01 + -7.13826035e-01 5.20881684e-02 + -3.43821888e+00 -2.36137021e+00 + -5.93210310e-01 1.21843813e-01 + -4.09800822e+00 -1.39893953e+00 + 2.74110954e+00 1.52728606e+00 + 1.72652512e+00 -1.25435113e-01 + 1.97722357e+00 6.40667481e-01 + 4.18635780e-01 3.57018509e-01 + -1.78303569e+00 -2.11864764e-01 + -3.52809366e+00 -2.58794450e-01 + -4.72407090e+00 -1.63870734e+00 + 1.73917807e+00 8.73251829e-01 + 4.37979356e-01 8.49210569e-01 + 3.93791881e+00 1.76269490e+00 + 2.79065411e+00 1.04019042e+00 + -8.47426142e-01 -3.40136892e-01 + -4.24389181e+00 -1.80253120e+00 + -1.86675870e+00 -7.64558265e-01 + 9.46212675e-01 -7.77681445e-02 + -2.82448462e+00 -1.33592449e+00 + -2.57938567e+00 -1.56554690e+00 + -2.71615767e+00 -6.27667233e-01 + -1.55999166e+00 -5.81013466e-01 + -4.24696864e-01 -7.44673250e-01 + 1.67592970e+00 7.68164292e-01 + 8.48455216e-01 -6.05681126e-01 + 6.12575454e+00 1.65607584e+00 + 1.38207327e+00 2.39261863e-01 + 3.13364450e+00 1.17154698e+00 + 1.71694858e+00 1.26744905e+00 + -1.61746367e+00 -8.80098073e-01 + -8.52196756e-01 -9.27299728e-01 + -1.51562462e-01 -8.36552490e-02 + -7.04792753e-01 -1.24726713e-02 + -3.35265757e+00 -1.82176312e+00 + 3.32173170e-01 -1.33405580e-01 + 4.95841013e-01 4.58292712e-01 + 1.57713955e+00 7.79272991e-01 + 2.09743109e+00 9.23542557e-01 + 3.90450311e-03 -8.42873164e-01 + 2.59519038e+00 7.56479591e-01 + -5.77643976e-01 -2.36401904e-01 + -5.22310654e-01 1.34187830e-01 + -2.22096086e+00 -7.75507719e-01 + 1.35907831e+00 7.80197510e-01 + 3.80355868e+00 1.16983476e+00 + 3.82746596e+00 1.31417718e+00 + 3.30451183e+00 1.55398159e+00 + -3.42917814e-01 -8.62281222e-02 + -2.59093020e+00 -9.29883526e-01 + 1.40928562e+00 1.08398346e+00 + 1.54400137e-01 3.35881092e-01 + 1.59171586e+00 1.18855802e+00 + -5.25164002e-01 -1.03104220e-01 + 2.20067959e+00 1.37074713e+00 + 6.97860830e-01 6.27718548e-01 + -4.59743507e-01 1.36061163e-01 + -1.04691963e-01 -2.16271727e-01 + -1.08905573e+00 -5.95510769e-01 + -1.00826983e+00 -5.38509162e-02 + -3.16402719e+00 -1.33414216e+00 + 1.47870874e-01 1.75234619e-01 + -2.57078234e-01 7.03316889e-02 + 1.81073945e+00 4.26901462e-01 + 2.65476530e+00 6.74217273e-01 + 1.27539811e+00 6.22914081e-01 + -3.76750499e-01 -1.20629449e+00 + 1.00177595e+00 -1.40660091e-01 + -2.98919265e+00 -1.65145013e+00 + -2.21557682e+00 -8.11123452e-01 + -3.22635378e+00 -1.65639056e+00 + -2.72868553e+00 -1.02812087e+00 + 1.26042797e+00 8.49005248e-01 + -9.38318534e-01 -9.87588651e-01 + 3.38013194e-01 -1.00237461e-01 + 1.91175691e+00 8.48716369e-01 + 4.30244344e-01 6.05539915e-02 + 2.21783435e+00 3.03268204e-01 + 1.78019576e+00 1.27377108e+00 + 1.59733274e+00 4.40674687e-02 + 3.97428484e+00 2.20881566e+00 + -2.41108677e+00 -6.01410418e-01 + -2.50796499e+00 -5.71169866e-01 + -3.71957427e+00 -1.38195726e+00 + -1.57992670e+00 1.32068593e-01 + -1.35278851e+00 -6.39349270e-01 + 1.23075932e+00 2.40445409e-01 + 1.35606530e+00 4.33180078e-01 + 9.60968518e-02 2.26734255e-01 + 6.22975063e-01 5.03431915e-02 + -1.47624851e+00 -3.60568238e-01 + -2.49337808e+00 -1.15083052e+00 + 2.15717792e+00 1.03071559e+00 + -3.07814376e-02 1.38700314e-02 + 4.52049499e-02 -4.86409775e-01 + 2.58231061e+00 1.14327809e-01 + 1.10999138e+00 -5.18568405e-01 + -2.19426443e-01 -5.37505538e-01 + -4.44740298e-01 6.78099955e-01 + 4.03379080e+00 1.49825720e+00 + -5.13182408e-01 -4.90201950e-01 + -6.90139716e-01 1.63875126e-01 + -8.17281461e-01 2.32155064e-01 + -2.92357619e-01 -8.02573544e-01 + -1.80769841e+00 -7.58907326e-01 + 2.16981590e+00 1.06728873e+00 + 1.98995203e-01 -6.84176682e-02 + -2.39546753e+00 -2.92873789e-01 + -4.24251021e+00 -1.46255564e+00 + -5.01411291e-01 -5.95712813e-03 + 2.68085809e+00 1.42883780e+00 + -4.13289873e+00 -1.62729388e+00 + 1.87957843e+00 3.63341638e-01 + -1.15270744e+00 -3.03563774e-01 + -4.43994248e+00 -2.97323905e+00 + -7.17067733e-01 -7.08349542e-01 + -3.28870393e+00 -1.19263863e+00 + -7.55325944e-01 -5.12703329e-01 + -2.07291938e+00 -2.65025085e-01 + -7.50073814e-01 -1.70771041e-01 + -8.77381404e-01 -5.47417325e-01 + -5.33725862e-01 5.15837119e-01 + 8.45056431e-01 2.82125560e-01 + -1.59598637e+00 -1.38743235e+00 + 1.41362902e+00 1.06407789e+00 + 1.02584504e+00 -3.68219466e-01 + -1.04644488e+00 -1.48769392e-01 + 2.66990191e+00 8.57633492e-01 + -1.84251857e+00 -9.82430175e-01 + 9.71404204e-01 -2.81934209e-01 + -2.50177989e+00 -9.21260335e-01 + -1.31060074e+00 -5.84488113e-01 + -2.12129400e-01 -3.06244708e-02 + -5.28933882e+00 -2.50663129e+00 + 1.90220541e+00 1.08662918e+00 + -3.99366086e-02 -6.87178973e-01 + -4.93417342e-01 4.37354182e-01 + 2.13494486e+00 1.37679569e+00 + 2.18396765e+00 5.81023868e-01 + -3.07866587e+00 -1.45384974e+00 + 6.10894119e-01 -4.17050124e-01 + -1.88766952e+00 -8.86160058e-01 + 3.34527253e+00 1.78571260e+00 + 6.87769059e-01 -5.01157336e-01 + 2.60470837e+00 1.45853560e+00 + -6.49315691e-01 -9.16112805e-01 + -1.29817687e+00 -2.15924339e-01 + -1.20100409e-03 -4.03137422e-01 + -1.36471594e+00 -6.93266356e-01 + 1.38682062e+00 7.15131598e-01 + 2.47830103e+00 1.24862305e+00 + -2.78288147e+00 -1.03329235e+00 + -7.33443403e-01 -6.11041652e-01 + -4.12745671e-01 -5.96133390e-02 + -2.58632336e+00 -4.51557058e-01 + -1.16570367e+00 -1.27065510e+00 + 2.76187104e+00 2.21895451e-01 + -3.80443767e+00 -1.66319902e+00 + 9.84658633e-01 6.81475569e-01 + 9.33814584e-01 -4.89335563e-02 + -4.63427997e-01 1.72989539e-01 + 1.82401546e+00 3.60164021e-01 + -5.36521077e-01 -8.08691351e-01 + -1.37367030e+00 -1.02126160e+00 + -3.70310682e+00 -1.19840844e+00 + -1.51894242e+00 -3.89510223e-01 + -3.67347940e-01 -3.25540516e-02 + -1.00988595e+00 1.82802194e-01 + 2.01622795e+00 7.86367901e-01 + 1.02440231e+00 8.79780360e-01 + -3.05971480e+00 -8.40901527e-01 + 2.73909457e+00 1.20558628e+00 + 2.39559056e+00 1.10786694e+00 + 1.65471544e+00 7.33824651e-01 + 2.18546787e+00 6.41168955e-01 + 1.47152266e+00 3.91839132e-01 + 1.45811155e+00 5.21820495e-01 + -4.27531469e-02 -3.52343068e-03 + -9.54948010e-01 -1.52313876e-01 + 7.57151215e-01 -5.68728854e-03 + -8.46205751e-01 -7.54580229e-01 + 4.14493548e+00 1.45532780e+00 + 4.58688968e-01 -4.54012803e-02 + -1.49295381e+00 -4.57471758e-01 + 1.80020351e+00 8.13724973e-01 + -5.82727738e+00 -2.18269581e+00 + -2.09017809e+00 -1.18305177e+00 + -2.31628303e+00 -7.21600235e-01 + -8.09679091e-01 -1.49101752e-01 + 8.88005605e-01 8.57940857e-01 + -1.44148219e+00 -3.10926299e-01 + 3.68828186e-01 -3.08848059e-01 + -6.63267389e-01 -8.58950139e-02 + -1.14702569e+00 -6.32147854e-01 + -1.51741715e+00 -8.53330564e-01 + -1.33903718e+00 -1.45875547e-01 + 4.12485387e+00 1.85620435e+00 + -2.42353639e+00 -2.92669850e-01 + 1.88708583e+00 9.35984730e-01 + 2.15585179e+00 6.30469051e-01 + -1.13627973e-01 -1.62554045e-01 + 2.04540494e+00 1.36599834e+00 + 2.81591381e+00 1.60897941e+00 + 3.02736260e-02 3.83255815e-03 + 7.97634013e-02 -2.82035099e-01 + -3.24607473e-01 -5.30065956e-01 + -3.91862894e+00 -1.94083334e+00 + 1.56360901e+00 7.93882743e-01 + -1.03905772e+00 6.25590229e-01 + 2.54746492e+00 1.64233560e+00 + -4.80774423e-01 -8.92298032e-02 + 9.06979990e-02 1.05020427e+00 + -2.47521290e+00 -1.78275982e-01 + -3.91871729e-01 3.80285423e-01 + 1.00658382e+00 4.58947483e-01 + 4.68102941e-01 1.02992741e+00 + 4.44242568e-01 2.89870239e-01 + 3.29684452e+00 1.44677474e+00 + -2.24983007e+00 -9.65574499e-01 + -3.54453926e-01 -3.99020325e-01 + -3.87429665e+00 -1.90079739e+00 + 2.02656674e+00 1.12444894e+00 + 3.77011621e+00 1.43200852e+00 + 1.61259275e+00 4.65417399e-01 + 2.28725434e+00 6.79181395e-01 + 2.75421009e+00 2.27327345e+00 + -2.40894409e+00 -1.03926359e+00 + 1.52996651e-01 -2.73373046e-02 + -2.63218977e+00 -7.22802821e-01 + 2.77688169e+00 1.15310186e+00 + 1.18832341e+00 4.73457165e-01 + -2.35536326e+00 -1.08034554e+00 + -5.84221627e-01 1.03505984e-02 + 2.96730300e+00 1.33478306e+00 + -8.61947692e-01 6.09137051e-02 + 8.22343921e-01 -8.14155286e-02 + 1.75809015e+00 1.07921470e+00 + 1.19501279e+00 1.05309972e+00 + -1.75901792e+00 9.75320161e-02 + 1.64398635e+00 9.54384323e-01 + -2.21878052e-01 -3.64847144e-01 + -2.03128968e+00 -8.57866419e-01 + 1.86750633e+00 7.08524487e-01 + 8.03972976e-01 3.47404314e-01 + 3.41203749e+00 1.39810900e+00 + 4.22397681e-01 -6.41440488e-01 + -4.88493360e+00 -1.58967816e+00 + -1.67649284e-01 -1.08485915e-01 + 2.11489023e+00 1.50506158e+00 + -1.81639929e+00 -3.85542192e-01 + 2.24044819e-01 -1.45100577e-01 + -3.39262411e+00 -1.44394324e+00 + 1.68706599e+00 2.29199618e-01 + -1.94093257e+00 -1.65975814e-01 + 8.28143367e-01 5.92109281e-01 + -8.29587998e-01 -9.57130831e-01 + -1.50011401e+00 -8.36802092e-01 + 2.40770449e+00 9.32820177e-01 + 7.41391309e-02 3.12878473e-01 + 1.87745264e-01 6.19231425e-01 + 9.57622692e-01 -2.20640033e-01 + 3.18479243e+00 1.02986233e+00 + 2.43133846e+00 8.41302677e-01 + -7.09963834e-01 1.99718943e-01 + -2.88253498e-01 -3.62772094e-01 + 5.14052574e+00 1.79304595e+00 + -3.27930993e+00 -1.29177973e+00 + -1.16723536e+00 1.29519656e-01 + 1.04801056e+00 3.41508300e-01 + -3.99256195e+00 -2.51176471e+00 + -7.62824318e-01 -6.84242153e-01 + 2.71524986e-02 5.35157164e-02 + 3.26430102e+00 1.34887262e+00 + -1.72357766e+00 -4.94524388e-01 + -3.81149536e+00 -1.28121944e+00 + 3.36919354e+00 1.10672075e+00 + -3.14841757e+00 -7.10713767e-01 + -3.16463676e+00 -7.58558435e-01 + -2.44745969e+00 -1.08816514e+00 + 2.79173264e-01 -2.19652051e-02 + 4.15309883e-01 6.07502790e-01 + -9.51007417e-01 -5.83976336e-01 + -1.47929839e+00 -8.39850409e-01 + 2.38335703e+00 6.16055149e-01 + -7.47749031e-01 -5.56164928e-01 + -3.65643622e-01 -5.06684411e-01 + -1.76634163e+00 -7.86382097e-01 + 6.76372222e-01 -3.06592181e-01 + -1.33505058e+00 -1.18301441e-01 + 3.59660179e+00 2.00424178e+00 + -7.88912762e-02 8.71956146e-02 + 1.22656397e+00 1.18149583e+00 + 4.24919729e+00 1.20082355e+00 + 2.94607456e+00 1.00676505e+00 + 7.46061275e-02 4.41761753e-02 + -2.47738025e-02 1.92737701e-01 + -2.20509316e-01 -3.79163193e-01 + -3.50222190e-01 3.58727299e-01 + -3.64788014e+00 -1.36107312e+00 + 3.56062799e+00 9.27032742e-01 + 1.04317289e+00 6.08035970e-01 + 4.06718718e-01 3.00628051e-01 + 4.33158086e+00 2.25860714e+00 + 2.13917145e-01 -1.72757967e-01 + -1.40637998e+00 -1.14119465e+00 + 3.61554872e+00 1.87797348e+00 + 1.01726871e+00 5.70255097e-01 + -7.04902551e-01 2.16444147e-01 + -2.51492186e+00 -8.52997369e-01 + 1.85097530e+00 1.15124496e+00 + -8.67569714e-01 -3.05682432e-01 + 8.07550858e-01 5.88901608e-01 + 1.85186755e-01 -1.94589367e-01 + -1.23378238e+00 -7.84128347e-01 + -1.22713161e+00 -4.21218235e-01 + 2.97751165e-01 2.81055275e-01 + 4.77703554e+00 1.66265524e+00 + 2.51549669e+00 7.49980674e-01 + 2.76510822e-01 1.40456909e-01 + 1.98740905e+00 -1.79608212e-01 + 9.35429145e-01 8.44344180e-01 + -1.20854492e+00 -5.00598453e-01 + 2.29936219e+00 8.10236668e-01 + 6.92555544e-01 -2.65891331e-01 + -1.58050994e+00 2.31237821e-01 + -1.50864880e+00 -9.49661690e-01 + -1.27689206e+00 -7.18260016e-01 + -3.12517127e+00 -1.75587113e+00 + 8.16062912e-02 -6.56551804e-01 + -5.02479939e-01 -4.67162543e-01 + -5.47435788e+00 -2.47799576e+00 + 1.95872901e-02 5.80874076e-01 + -1.59064958e+00 -6.34554756e-01 + -3.77521478e+00 -1.74301790e+00 + 5.89628224e-01 8.55736553e-01 + -1.81903543e+00 -7.50011008e-01 + 1.38557775e+00 3.71490991e-01 + 9.70032652e-01 -7.11356016e-01 + 2.63539625e-01 -4.20994771e-01 + 2.12154222e+00 8.19081400e-01 + -6.56977937e-01 -1.37810098e-01 + 8.91309581e-01 2.77864361e-01 + -7.43693195e-01 -1.46293770e-01 + 2.24447769e+00 4.00911438e-01 + -2.25169262e-01 2.04148801e-02 + 1.68744684e+00 9.47573007e-01 + 2.73086373e-01 3.30877195e-01 + 5.54294414e+00 2.14198009e+00 + -8.49238733e-01 3.65603298e-02 + 2.39685712e+00 1.17951039e+00 + -2.58230528e+00 -5.52116673e-01 + 2.79785277e+00 2.88833717e-01 + -1.96576188e-01 1.11652123e+00 + -4.69383301e-01 1.96496282e-01 + -1.95011845e+00 -6.15235169e-01 + 1.03379890e-02 2.33701239e-01 + 4.18933607e-01 2.77939814e-01 + -1.18473337e+00 -4.10051126e-01 + -7.61499744e-01 -1.43658094e+00 + -1.65586092e+00 -3.41615303e-01 + -5.58523700e-02 -5.21837080e-01 + -2.40331088e+00 -2.64521583e-01 + 2.24925206e+00 6.79843335e-02 + 1.46360479e+00 1.04271443e+00 + -3.09255443e+00 -1.82548953e+00 + 2.11325841e+00 1.14996627e+00 + -8.70657797e-01 1.02461839e-01 + -5.71056521e-01 9.71232588e-02 + -3.37870752e+00 -1.54091877e+00 + 1.03907189e+00 -1.35661392e-01 + 8.40057486e-01 6.12172413e-02 + -1.30998234e+00 -1.34077226e+00 + 7.53744974e-01 1.49447350e-01 + 9.13995056e-01 -1.81227962e-01 + 2.28386229e-01 3.74498520e-01 + 2.54829151e-01 -2.88802704e-01 + 1.61709009e+00 2.09319193e-01 + -1.12579380e+00 -5.95955338e-01 + -2.69610726e+00 -2.76222736e-01 + -2.63773329e+00 -7.84491970e-01 + -2.62167427e+00 -1.54792874e+00 + -4.80639856e-01 -1.30582102e-01 + -1.26130891e+00 -8.86841840e-01 + -1.24951950e+00 -1.18182622e+00 + -1.40107574e+00 -9.13695575e-01 + 4.99872179e-01 4.69014702e-01 + -2.03550193e-02 -1.48859738e-01 + -1.50189069e+00 -2.97714278e-02 + -2.07846113e+00 -7.29937809e-01 + -5.50576792e-01 -7.03151525e-01 + -3.88069238e+00 -1.63215295e+00 + 2.97032988e+00 6.43571144e-01 + -1.85999273e-01 1.18107620e+00 + 1.79249709e+00 6.65356160e-01 + 2.68842472e+00 1.35703255e+00 + 1.07675417e+00 1.39845588e-01 + 8.01226349e-01 2.11392275e-01 + 9.64329379e-01 3.96146195e-01 + -8.22529511e-01 1.96080831e-01 + 1.92481841e+00 4.62985744e-01 + 3.69756927e-01 3.77135799e-01 + 1.19807835e+00 8.87715050e-01 + -1.01363587e+00 -2.48151636e-01 + 8.53071010e-01 4.96887868e-01 + -3.41120553e+00 -1.35401843e+00 + -2.64787381e+00 -1.08690563e+00 + -1.11416759e+00 -4.43848915e-01 + 1.46242648e+00 6.17106076e-02 + -7.52968881e-01 -9.20972209e-01 + -1.22492228e+00 -5.40327617e-01 + 1.08001827e+00 5.29593785e-01 + -2.58706464e-01 1.13022085e-01 + -4.27394011e-01 1.17864354e-02 + -3.20728413e+00 -1.71224737e-01 + 1.71398530e+00 8.68885893e-01 + 2.12067866e+00 1.45092772e+00 + 4.32782616e-01 -3.34117769e-01 + 7.80084374e-01 -1.35100217e-01 + -2.05547729e+00 -4.70217750e-01 + 2.38379736e+00 1.09186058e+00 + -2.80825477e+00 -1.03320187e+00 + 2.63434576e+00 1.15671733e+00 + -1.60936214e+00 1.91843035e-01 + -5.02298769e+00 -2.32820708e+00 + 1.90349195e+00 1.45215416e+00 + 3.00232888e-01 3.24412586e-01 + -2.46503943e+00 -1.19550010e+00 + 1.06304233e+00 2.20136246e-01 + -2.99101388e+00 -1.58299318e+00 + 2.30071719e+00 1.12881362e+00 + -2.37587247e+00 -8.08298336e-01 + 7.27006308e-01 3.80828984e-01 + 2.61199061e+00 1.56473491e+00 + 8.33936357e-01 -1.42189425e-01 + 3.13291605e+00 1.77771210e+00 + 2.21917371e+00 5.68427075e-01 + 2.38867649e+00 9.06637262e-01 + -6.92959466e+00 -3.57682881e+00 + 2.57904824e+00 5.93959108e-01 + 2.71452670e+00 1.34436199e+00 + 4.39988761e+00 2.13124672e+00 + 5.71783077e-01 5.08346173e-01 + -3.65399429e+00 -1.18192861e+00 + 4.46176453e-01 3.75685594e-02 + -2.97501495e+00 -1.69459236e+00 + 1.60855728e+00 9.20930014e-01 + -1.44270290e+00 -1.93922306e-01 + 1.67624229e+00 1.66233866e+00 + -1.42579598e+00 -1.44990145e-01 + 1.19923176e+00 4.58490278e-01 + -9.00068460e-01 5.09701825e-02 + -1.69391694e+00 -7.60070300e-01 + -1.36576440e+00 -5.24244256e-01 + -1.03016748e+00 -3.44625878e-01 + 2.40519313e+00 1.09947587e+00 + 1.50365433e+00 1.06464802e+00 + -1.07609727e+00 -3.68897187e-01 + 2.44969069e+00 1.28486192e+00 + -1.25610307e+00 -1.14644789e+00 + 2.05962899e+00 4.31162369e-01 + -7.15886908e-01 -6.11587804e-02 + -6.92354119e-01 -7.85019920e-01 + -1.63016508e+00 -5.96944975e-01 + 1.90352536e+00 1.28197457e+00 + -4.01535243e+00 -1.81934488e+00 + -1.07534435e+00 -2.10544784e-01 + 3.25500866e-01 7.69603661e-01 + 2.18443365e+00 6.59773335e-01 + 8.80856790e-01 6.39505913e-01 + -2.23956372e-01 -4.65940132e-01 + -1.06766519e+00 -5.38388505e-03 + 7.25556863e-01 -2.91123488e-01 + -4.69451411e-01 7.89182650e-02 + 2.58146587e+00 1.29653243e+00 + 1.53747468e-01 7.69239075e-01 + -4.61152262e-01 -4.04151413e-01 + 1.48183517e+00 8.10079506e-01 + -1.83402614e+00 -1.36939322e+00 + 1.49315501e+00 7.95225425e-01 + 1.41922346e+00 1.05582774e-01 + 1.57473493e-01 9.70795657e-01 + -2.67603254e+00 -7.48562280e-01 + -8.49156216e-01 -6.05762529e-03 + 1.12944274e+00 3.67741591e-01 + 1.94228071e-01 5.28188141e-01 + -3.65610158e-01 4.05851838e-01 + -1.98839111e+00 -1.38452764e+00 + 2.73765752e+00 8.24150530e-01 + 7.63728641e-01 3.51617707e-01 + 5.78307267e+00 1.68103612e+00 + 2.27547227e+00 3.60876164e-01 + -3.50681697e+00 -1.74429984e+00 + 4.01241184e+00 1.26227829e+00 + 2.44946343e+00 9.06119057e-01 + -2.96638941e+00 -9.01532322e-01 + 1.11267643e+00 -3.43333381e-01 + -6.61868994e-01 -3.44666391e-01 + -8.34917179e-01 5.69478372e-01 + -1.91888454e+00 -3.03791075e-01 + 1.50397636e+00 8.31961240e-01 + 6.12260198e+00 2.16851807e+00 + 1.34093127e+00 8.86649385e-01 + 1.48748519e+00 8.26273697e-01 + 7.62243068e-01 2.64841396e-01 + -2.17604986e+00 -3.54219958e-01 + 2.64708640e-01 -4.38136718e-02 + 1.44725372e+00 1.18499914e-01 + -6.71259446e-01 -1.19526851e-01 + 2.40134595e-01 -8.90042323e-02 + -3.57238199e+00 -1.23166201e+00 + -3.77626645e+00 -1.19533443e+00 + -3.81101035e-01 -4.94160532e-01 + -3.02758757e+00 -1.18436066e+00 + 2.59116298e-01 1.38023047e+00 + 4.17900116e+00 1.12065959e+00 + 1.54598848e+00 2.89806755e-01 + 1.00656475e+00 1.76974511e-01 + -4.15730234e-01 -6.22681694e-01 + -6.00903565e-01 -1.43256959e-01 + -6.03652508e-01 -5.09936379e-01 + -1.94096658e+00 -9.48789544e-01 + -1.74464105e+00 -8.50491590e-01 + 1.17652544e+00 1.88118317e+00 + 2.35507776e+00 1.44000205e+00 + 2.63067924e+00 1.06692988e+00 + 2.88805386e+00 1.23924715e+00 + 8.27595008e-01 5.75364692e-01 + 3.91384216e-01 9.72781920e-02 + -1.03866816e+00 -1.37567768e+00 + -1.34777969e+00 -8.40266025e-02 + -4.12904508e+00 -1.67618340e+00 + 1.27918111e+00 3.52085961e-01 + 4.15361174e-01 6.28896189e-01 + -7.00539496e-01 4.80447955e-02 + -1.62332639e+00 -5.98236485e-01 + 1.45957300e+00 1.00305154e+00 + -3.06875603e+00 -1.25897545e+00 + -1.94708176e+00 4.85143006e-01 + 3.55744156e+00 -1.07468822e+00 + 1.21602223e+00 1.28768827e-01 + 1.89093098e+00 -4.70835659e-01 + -6.55759125e+00 2.70114082e+00 + 8.96843535e-01 -3.98115252e-01 + 4.13450429e+00 -2.32069236e+00 + 2.37764218e+00 -1.09098890e+00 + -1.11388901e+00 6.27083097e-01 + -6.34116929e-01 4.62816387e-01 + 2.90203079e+00 -1.33589143e+00 + 3.17457598e+00 -5.13575945e-01 + -1.76362299e+00 5.71820693e-01 + 1.66103362e+00 -8.99466249e-01 + -2.53947433e+00 8.40084780e-01 + 4.36631397e-01 7.24234261e-02 + -1.87589394e+00 5.08529113e-01 + 4.49563965e+00 -9.43365992e-01 + 1.78876299e+00 -1.27076149e+00 + -1.16269107e-01 -4.55078316e-01 + 1.92966079e+00 -8.05371385e-01 + 2.20632583e+00 -9.00919345e-01 + 1.52387824e+00 -4.82391996e-01 + 8.04004564e-01 -2.73650595e-01 + -7.75326067e-01 1.07469566e+00 + 1.83226282e+00 -4.52173344e-01 + 1.25079758e-01 -3.52895417e-02 + -9.90957437e-01 8.55993130e-01 + 1.71623322e+00 -7.08691667e-01 + -2.86175924e+00 6.75160955e-01 + -8.40817853e-01 -1.00361809e-01 + 1.33393000e+00 -4.65788123e-01 + 5.29394114e-01 -5.44881619e-02 + -8.07435599e-01 8.27353370e-01 + -4.33165824e+00 1.97299638e+00 + 1.26452422e+00 -8.34070486e-01 + 1.45996394e-02 2.97736043e-01 + -1.64489287e+00 6.72839598e-01 + -5.74234578e+00 3.20975117e+00 + 2.13841341e-02 3.64514015e-01 + 6.68084924e+00 -2.27464254e+00 + -3.22881590e+00 8.01879324e-01 + 3.02534313e-01 -4.56222796e-01 + -5.84520734e+00 1.95678162e+00 + 2.81515232e+00 -1.72101318e+00 + -2.39620908e-01 2.69145522e-01 + -7.41669691e-01 -2.30283281e-01 + -2.15682714e+00 3.45313021e-01 + 1.23475788e+00 -7.32276553e-01 + -1.71816113e-01 1.20419560e-02 + 1.89174235e+00 2.27435901e-01 + -3.64511114e-01 1.72260361e-02 + -3.24143860e+00 6.50125817e-01 + -2.25707409e+00 5.66970751e-01 + 1.03901456e+00 -1.00588433e+00 + -5.09159710e+00 1.58736109e+00 + 1.45534075e+00 -5.83787452e-01 + 4.28879587e+00 -1.58006866e+00 + 8.52384427e-01 -1.11042299e+00 + 4.51431615e+00 -2.63844265e+00 + -4.33042648e+00 1.86497078e+00 + -2.13568046e+00 5.82559743e-01 + -4.42568887e+00 1.26131214e+00 + 3.15821315e+00 -1.61515905e+00 + -3.14125204e+00 8.49604386e-01 + 6.54152300e-01 -2.04624711e-01 + -3.73374317e-01 9.94187820e-02 + -3.96177282e+00 1.27245623e+00 + 9.59825199e-01 -1.15547861e+00 + 3.56902055e+00 -1.46591091e+00 + 1.55433633e-02 6.93544345e-01 + 1.15684646e+00 -4.99836352e-01 + 3.11824573e+00 -4.75900506e-01 + -8.61706369e-01 -3.50774059e-01 + 9.89057391e-01 -7.16878802e-01 + -4.94787870e+00 2.09137481e+00 + 1.37777347e+00 -1.34946349e+00 + -1.13161577e+00 8.05114754e-01 + 8.12020675e-01 -1.04849421e+00 + 4.73783881e+00 -2.26718812e+00 + 8.99579366e-01 -8.89764451e-02 + 4.78524868e+00 -2.25795843e+00 + 1.75164590e+00 -1.73822209e-01 + 1.30204590e+00 -7.26724717e-01 + -7.26526403e-01 -5.23925361e-02 + 2.01255351e+00 -1.69965366e+00 + 9.87852740e-01 -4.63577220e-01 + 2.45957762e+00 -1.29278962e+00 + -3.13817948e+00 1.64433038e+00 + -1.76302159e+00 9.62784302e-01 + -1.91106331e+00 5.81460008e-01 + -3.30883001e+00 1.30378978e+00 + 5.54376450e-01 3.78814272e-01 + 1.09982111e+00 -1.47969612e+00 + -2.61300705e-02 -1.42573464e-01 + -2.22096157e+00 7.75684440e-01 + 1.70319323e+00 -2.89738444e-01 + -1.43223842e+00 6.39284281e-01 + 2.34360959e-01 -1.64379268e-01 + -2.67147991e+00 9.46548086e-01 + 1.51131425e+00 -4.91594395e-01 + -2.48446856e+00 1.01286123e+00 + 1.50534658e-01 -2.94620246e-01 + -1.66966792e+00 1.67755508e+00 + -1.50094241e+00 3.30163095e-01 + 2.27681194e+00 -1.08064317e+00 + 2.05122965e+00 -1.15165939e+00 + -4.23509309e-01 -6.56906167e-02 + 1.80084023e+00 -1.07228556e+00 + -2.65769521e+00 1.18023206e+00 + 2.02852676e+00 -8.06793574e-02 + -4.49544185e+00 2.68200163e+00 + -7.50043216e-01 1.17079331e+00 + 6.80060893e-02 3.99055351e-01 + -3.83634635e+00 1.38406887e+00 + 3.24858545e-01 -9.25273218e-02 + -2.19895100e+00 1.47819500e+00 + -3.61569522e-01 -1.03188739e-01 + 1.12180375e-01 -9.52696354e-02 + -1.31477803e+00 1.79900570e-01 + 2.39573628e+00 -6.09739269e-01 + -1.00135700e+00 6.02837296e-01 + -4.11994589e+00 2.49599192e+00 + -1.54196236e-01 -4.84921951e-01 + 5.92569908e-01 -1.87310359e-01 + 3.85407741e+00 -1.50979925e+00 + 5.17802528e+00 -2.26032607e+00 + -1.37018916e+00 1.87111822e-01 + 8.46682996e-01 -3.56676331e-01 + -1.17559949e+00 5.29057734e-02 + -5.56475671e-02 6.79049243e-02 + 1.07851745e+00 -5.14535101e-01 + -2.71622446e+00 1.00151846e+00 + -1.08477208e+00 8.81391054e-01 + 5.50755824e-01 -5.20577727e-02 + 4.70885495e+00 -2.04220397e+00 + -1.87375336e-01 -6.16962830e-02 + 3.52097100e-01 2.21163550e-01 + 7.07929984e-01 -1.75827590e-01 + -1.22149219e+00 1.83084346e-01 + 2.58247412e+00 -6.15914898e-01 + -6.01206182e-01 -2.29832987e-01 + 9.83360449e-01 -3.75870060e-01 + -3.20027685e+00 1.35467480e+00 + 1.79178978e+00 -1.38531981e+00 + -3.30376867e-01 -1.16250192e-01 + -1.89053055e+00 5.68463567e-01 + -4.20604849e+00 1.65429681e+00 + -1.01185529e+00 1.92801240e-01 + -6.18819882e-01 5.42206996e-01 + -5.08091672e+00 2.61598591e+00 + -2.62570344e+00 2.51590658e+00 + 3.05577906e+00 -1.49090609e+00 + 2.77609677e+00 -1.37681378e+00 + -7.93515301e-02 4.28072744e-01 + -2.08359471e+00 8.94334295e-01 + 2.20163801e+00 4.01127167e-02 + -1.18145785e-01 -2.06822464e-01 + -2.74788298e-01 2.96250607e-01 + 1.59613555e+00 -3.87246203e-01 + -3.82971472e-01 -3.39716093e-02 + -4.20311307e-02 3.88529510e-01 + 1.52128574e+00 -9.33138876e-01 + -9.06584458e-01 -2.75016094e-02 + 3.56216834e+00 -9.99384622e-01 + 2.11964220e+00 -9.98749118e-02 + 4.01203480e+00 -2.03032745e+00 + -1.24171557e+00 1.97596725e-01 + -1.57230455e+00 4.14126609e-01 + -1.85484741e+00 5.40041563e-01 + 1.76329831e+00 -6.95967734e-01 + -2.29439232e-01 5.08669245e-01 + -5.45124276e+00 2.26907549e+00 + -5.71364288e-02 5.04476476e-01 + 3.12468018e+00 -1.46358879e+00 + 8.20017359e-01 6.51949028e-01 + -1.33977500e+00 2.83634232e-04 + -1.83311685e+00 1.23947117e+00 + 6.31205922e-01 1.19792164e-02 + -2.21967834e+00 6.94056232e-01 + -1.41693842e+00 9.93526233e-01 + -7.58885703e-01 6.78547347e-01 + 3.60239086e+00 -1.08644935e+00 + 6.72217073e-02 3.00036011e-02 + -3.42680958e-01 -3.48049352e-01 + 1.87546079e+00 -4.78018246e-01 + 7.00485821e-01 -3.52905383e-01 + -8.54580948e-01 8.17330861e-01 + 8.19123706e-01 -5.73927281e-01 + 2.70855639e-01 -3.08940052e-01 + -1.05059952e+00 3.27873168e-01 + 1.08282999e+00 4.84559349e-02 + -7.89899220e-01 1.22291138e+00 + -2.87939816e+00 7.17403497e-01 + -2.08429452e+00 8.87409226e-01 + 1.58409232e+00 -4.74123532e-01 + 1.26882735e+00 1.59162510e-01 + -2.53782993e+00 6.18253491e-01 + -8.92757445e-01 3.35979011e-01 + 1.31867900e+00 -1.17355054e+00 + 1.14918879e-01 -5.35184038e-01 + -1.70288738e-01 5.35868087e-02 + 4.21355121e-01 5.41848690e-02 + 2.07926943e+00 -5.72538144e-01 + 4.08788970e-01 3.77655777e-01 + -3.39631381e+00 9.84216764e-01 + 2.94170163e+00 -1.83120916e+00 + -7.94798752e-01 7.39889052e-01 + 1.46555463e+00 -4.62275563e-01 + 2.57255955e+00 -1.04671434e+00 + 8.45042540e-01 -1.96952892e-01 + -3.23526646e+00 1.60049846e+00 + 3.21948565e+00 -8.88376674e-01 + 1.43005104e+00 -9.21561086e-01 + 8.82360506e-01 2.98403872e-01 + -8.91168097e-01 1.01319072e+00 + -5.13215241e-01 -2.47182649e-01 + -1.35759444e+00 7.07450608e-02 + -4.04550983e+00 2.23534867e+00 + 1.39348883e+00 3.81637747e-01 + -2.85676418e+00 1.53240862e+00 + -1.37183120e+00 6.37977425e-02 + -3.88195859e+00 1.73887145e+00 + 1.19509776e+00 -6.25013512e-01 + -2.80062734e+00 1.79840585e+00 + 1.96558429e+00 -4.70997234e-01 + 1.93111352e+00 -9.70318441e-01 + 3.57991190e+00 -1.65065116e+00 + 2.12831714e+00 -1.11531708e+00 + -3.95661018e-01 -8.54339904e-02 + -2.41630441e+00 1.65166304e+00 + 7.55412624e-01 -1.53453579e-01 + -1.77043450e+00 1.39928715e+00 + -9.32631260e-01 8.73649199e-01 + 1.53342205e+00 -8.39569765e-01 + -6.29846924e-02 1.25023084e-01 + 3.31509049e+00 -1.10733235e+00 + -2.18957109e+00 3.07376993e-01 + -2.35740747e+00 6.47437564e-01 + -2.22142438e+00 8.47318938e-01 + -6.51401147e-01 3.48398562e-01 + 2.75763095e+00 -1.21390708e+00 + 1.12550484e+00 -5.61412847e-01 + -5.65053161e-01 6.74365205e-02 + 1.68952456e+00 -6.57566096e-01 + 8.95598401e-01 3.96738993e-01 + -1.86537066e+00 9.44129208e-01 + -2.59933294e+00 2.57423247e-01 + -6.59598267e-01 1.91828851e-02 + -2.64506676e+00 8.41783205e-01 + -1.25911802e+00 5.52425066e-01 + -1.39754507e+00 3.73689222e-01 + 5.49550729e-02 1.35071215e+00 + 3.31874811e+00 -1.05682424e+00 + 3.63159604e+00 -1.42864695e+00 + -4.45944617e+00 1.42889446e+00 + 5.87314342e-01 -4.88892988e-01 + -7.26130820e-01 1.51936106e-01 + -1.79246441e+00 6.05888105e-01 + -5.50948207e-01 6.21443081e-01 + -3.17246063e-01 1.77213880e-01 + -2.00098937e+00 1.23799074e+00 + 4.33790961e+00 -1.08490465e+00 + -2.03114114e+00 1.31613237e+00 + -6.29216542e+00 1.92406317e+00 + -1.60265624e+00 8.87947500e-01 + 8.64465062e-01 -8.37416270e-01 + -2.14273937e+00 8.05485900e-01 + -2.36844256e+00 6.17915124e-01 + -1.40429636e+00 6.78296866e-01 + 9.99019988e-01 -5.84297572e-01 + 7.38824546e-01 1.68838678e-01 + 1.45681238e+00 3.04641461e-01 + 2.15914949e+00 -3.43089227e-01 + -1.23895930e+00 1.05339864e-01 + -1.23162264e+00 6.46629863e-01 + 2.28183862e+00 -9.24157063e-01 + -4.29615882e-01 5.69130863e-01 + -1.37449121e+00 -9.12032183e-01 + -7.33890904e-01 -3.91865471e-02 + 8.41400661e-01 -4.76002200e-01 + -1.73349274e-01 -6.84143467e-02 + 3.16042891e+00 -1.32651856e+00 + -3.78244609e+00 2.38619718e+00 + -3.69634380e+00 2.22368561e+00 + 1.83766344e+00 -1.65675953e+00 + -1.63206002e+00 1.19484469e+00 + 3.68480064e-01 -5.70764494e-01 + 3.61982479e-01 1.04274409e-01 + 2.48863048e+00 -1.13285542e+00 + -2.81896488e+00 9.47958768e-01 + 5.74952901e-01 -2.75959392e-01 + 3.72783275e-01 -3.48937848e-01 + 1.95935716e+00 -1.06750415e+00 + 5.19357531e+00 -2.32070803e+00 + 4.09246149e+00 -1.89976700e+00 + -3.36666087e-01 8.17645057e-02 + 1.85453493e-01 3.76913151e-01 + -3.06458262e+00 1.34106402e+00 + -3.13796566e+00 7.00485099e-01 + 1.42964058e+00 -1.35536932e-01 + -1.23440423e-01 4.60094177e-02 + -2.86753037e+00 -5.21724160e-02 + 2.67113726e+00 -1.83746924e+00 + -1.35335062e+00 1.28238073e+00 + -2.43569899e+00 1.25998539e+00 + 1.26036740e-01 -2.35416844e-01 + -1.35725745e+00 7.37788491e-01 + -3.80897538e-01 3.30757889e-01 + 6.58694434e-01 -1.07566603e+00 + 2.11273640e+00 -9.02260632e-01 + 4.00755057e-01 -2.49229150e-02 + -1.80095812e+00 9.73099742e-01 + -2.68408372e+00 1.63737364e+00 + -2.66079826e+00 7.47289412e-01 + -9.92321439e-02 -1.49331396e-01 + 4.45678251e+00 -1.80352394e+00 + 1.35962915e+00 -1.31554389e+00 + -7.76601417e-01 -9.66173523e-02 + 1.68096348e+00 -6.27235133e-01 + 1.53081227e-01 -3.54216830e-01 + -1.54913095e+00 3.43689269e-01 + 5.29187357e-02 -6.73916964e-01 + -2.06606084e+00 8.34784242e-01 + 1.73701179e+00 -6.06467340e-01 + 1.55856757e+00 -2.58642780e-01 + 1.04349101e+00 -4.43027348e-01 + -1.02397719e+00 1.01308824e+00 + -2.13860204e-01 -4.73347361e-01 + -2.59004955e+00 1.43367853e+00 + 7.98457679e-01 2.18621627e-02 + -1.32974762e+00 4.61802208e-01 + 3.21419359e-01 2.30723316e-02 + 2.87201888e-02 6.24566672e-02 + -1.22261418e+00 6.02340363e-01 + 1.28750335e+00 -3.34839548e-02 + -9.67952623e-01 4.34470505e-01 + 2.02850324e+00 -9.05160255e-01 + -4.13946010e+00 2.33779091e+00 + -4.47508806e-01 3.06440495e-01 + -3.91543394e+00 1.68251022e+00 + -6.45193001e-01 5.29781162e-01 + -2.15518916e-02 5.07278355e-01 + -2.83356868e+00 1.00670227e+00 + 1.82989749e+00 -1.37329222e+00 + -1.09330213e+00 1.08560688e+00 + 1.90533722e+00 -1.28905879e+00 + 2.33986084e+00 2.30642626e-02 + 8.01940220e-01 -1.63986962e+00 + -4.23415165e+00 2.07530423e+00 + 9.33382522e-01 -7.62917211e-01 + -1.84033954e+00 1.07469401e+00 + -2.81938669e+00 1.07342024e+00 + -7.05169988e-01 2.13124943e-01 + 5.09598137e-01 1.32725493e-01 + -2.34558226e+00 8.62383168e-01 + -1.70322072e+00 2.70893796e-01 + 1.23652660e+00 -7.53216034e-02 + 2.84660646e+00 -3.48178304e-02 + 2.50250128e+00 -1.27770855e+00 + -1.00279469e+00 8.77194218e-01 + -4.34674121e-02 -2.12091350e-01 + -5.84151289e-01 1.50382340e-01 + -1.79024013e+00 4.24972808e-01 + -1.23434666e+00 -8.85546570e-02 + 1.36575412e+00 -6.42639880e-01 + -1.98429947e+00 2.27650336e-01 + 2.36253589e+00 -1.51340773e+00 + 8.79157643e-01 6.84142159e-01 + -2.18577755e+00 2.76526200e-01 + -3.55473434e-01 8.29976561e-01 + 1.16442595e+00 -5.97699411e-01 + -7.35528097e-01 2.40318183e-01 + -1.73702631e-01 7.33788663e-02 + -1.40451745e+00 3.24899628e-01 + -2.05434385e+00 5.68123738e-01 + 8.47876642e-01 -5.74224294e-01 + -6.91955602e-01 1.26009087e+00 + 2.56574498e+00 -1.15602581e+00 + 3.93306545e+00 -1.38398209e+00 + -2.73230251e+00 4.89062581e-01 + -1.04315474e+00 6.06335547e-01 + 1.23231431e+00 -4.46675065e-01 + -3.93035285e+00 1.43287651e+00 + -1.02132111e+00 9.58919791e-01 + -1.49425352e+00 1.06456165e+00 + -6.26485337e-01 1.03791402e+00 + -6.61772998e-01 2.63275425e-01 + -1.80940386e+00 5.70767403e-01 + 9.83720450e-01 -1.39449756e-01 + -2.24619662e+00 9.01044870e-01 + 8.94343014e-01 5.31038678e-02 + 1.95518199e-01 -2.81343295e-01 + -2.30533019e-01 -1.74478106e-01 + -2.01550361e+00 5.55958010e-01 + -4.36281469e+00 1.94374226e+00 + -5.18530457e+00 2.89278357e+00 + 2.67289101e+00 -2.98511449e-01 + -1.53566179e+00 -1.00588944e-01 + -6.09943217e-02 -1.56986047e-01 + -5.22146452e+00 1.66209208e+00 + -3.69777478e+00 2.26154873e+00 + 2.24607181e-01 -4.86934960e-01 + 2.49909450e+00 -1.03033370e+00 + -1.07841120e+00 8.22388054e-01 + -3.20697089e+00 1.09536143e+00 + 3.43524232e+00 -1.47289362e+00 + -5.65784134e-01 4.60365175e-01 + -1.76714734e+00 1.57752346e-01 + -7.77620365e-01 5.60153443e-01 + 6.34399352e-01 -5.22339836e-01 + 2.91011875e+00 -9.72623380e-01 + -1.19286824e+00 6.32370253e-01 + -2.18327609e-01 8.23953181e-01 + 3.42430842e-01 1.37098055e-01 + 1.28658034e+00 -9.11357320e-01 + 2.06914465e+00 -6.67556382e-01 + -6.69451020e-01 -6.38605102e-01 + -2.09312398e+00 1.16743634e+00 + -3.63778357e+00 1.91919157e+00 + 8.74685911e-01 -1.09931208e+00 + -3.91496791e+00 1.00808357e+00 + 1.29621330e+00 -8.32239802e-01 + 9.00222045e-01 -1.31159793e+00 + -1.12242062e+00 1.98517079e-01 + -3.71932852e-01 1.31667093e-01 + -2.23829610e+00 1.26328346e+00 + -2.08365062e+00 9.93385336e-01 + -1.91082720e+00 7.45866855e-01 + 4.38024917e+00 -2.05901118e+00 + -2.28872886e+00 6.85279335e-01 + 1.01274497e-01 -3.26227153e-01 + -5.04447572e-01 -3.18619513e-01 + 1.28537006e+00 -1.04573551e+00 + -7.83175212e-01 1.54791645e-01 + -3.89239175e+00 1.60017929e+00 + -8.87877111e-01 -1.04968005e-01 + 9.32215179e-01 -5.58691113e-01 + -6.44977127e-01 -2.23018375e-01 + 1.10141900e+00 -1.00666432e+00 + 2.92755687e-01 -1.45480350e-01 + 7.73580681e-01 -2.21150567e-01 + -1.40873709e+00 7.61548044e-01 + -8.89031805e-01 -3.48542923e-01 + 4.16844267e-01 -2.39914494e-01 + -4.64265832e-01 7.29581138e-01 + 1.99835179e+00 -7.70542813e-01 + 4.20523191e-02 -2.18783563e-01 + -6.32611758e-01 -3.09926115e-01 + 6.82912198e-02 -8.48327050e-01 + 1.92425229e+00 -1.37876951e+00 + 3.49461782e+00 -1.88354255e+00 + -3.25209026e+00 1.49809395e+00 + 6.59273182e-01 -2.37435654e-01 + -1.15517300e+00 8.46134387e-01 + 1.26756151e+00 -4.58988026e-01 + -3.99178418e+00 2.04153008e+00 + 7.05687841e-01 -6.83433306e-01 + -1.61997342e+00 8.16577004e-01 + -3.89750399e-01 4.29753250e-01 + -2.53026432e-01 4.92861432e-01 + -3.16788324e+00 4.44285524e-01 + -7.86248901e-01 1.12753716e+00 + -3.02351433e+00 1.28419015e+00 + -1.30131355e+00 1.71226678e+00 + -4.08843475e+00 1.62063214e+00 + -3.09209403e+00 1.19958520e+00 + 1.49102271e+00 -1.11834864e+00 + -3.18059348e+00 5.74587042e-01 + 2.06054867e+00 3.25797860e-03 + -3.50999200e+00 2.02412428e+00 + -8.26610023e-01 3.46528211e-01 + 2.00546034e+00 -4.07333110e-01 + -9.69941653e-01 4.80953753e-01 + 4.47925660e+00 -2.33127314e+00 + 2.03845790e+00 -9.90439915e-01 + -1.11349191e+00 4.31183918e-01 + -4.03628396e+00 1.68509679e+00 + -1.48177601e+00 7.74322088e-01 + 3.07369385e+00 -9.57465886e-01 + 2.39011286e+00 -6.44506921e-01 + 2.91561991e+00 -8.78627328e-01 + 1.10212733e+00 -4.21637388e-01 + 5.31985231e-01 -6.17445696e-01 + -6.82340929e-01 -2.93529716e-01 + 1.94290679e+00 -4.64268634e-01 + 1.92262116e+00 -7.93142835e-01 + 4.73762800e+00 -1.63654174e+00 + -3.17848641e+00 8.05791391e-01 + 4.08739432e+00 -1.80816807e+00 + -7.60648826e-01 1.24216138e-01 + -2.24716400e+00 7.90020937e-01 + 1.64284052e+00 -7.18784070e-01 + 1.04410012e-01 -7.11195880e-02 + 2.18268225e+00 -7.01767831e-01 + 2.06218013e+00 -8.70251746e-01 + -1.35266581e+00 7.08456358e-01 + -1.38157779e+00 5.14401086e-01 + -3.28326008e+00 1.20988399e+00 + 8.85358917e-01 -8.12213495e-01 + -2.34067500e+00 3.67657353e-01 + 3.96878127e+00 -1.66841450e+00 + 1.36518053e+00 -8.33436812e-01 + 5.25771988e-01 -5.06121987e-01 + -2.25948361e+00 1.30663765e+00 + -2.57662070e+00 6.32114628e-01 + -3.43134685e+00 2.38106008e+00 + 2.31571924e+00 -1.56566818e+00 + -2.95397202e+00 1.05661888e+00 + -1.35331242e+00 6.76383411e-01 + 1.40977132e+00 -1.17775938e+00 + 1.52561996e+00 -9.83147176e-01 + 2.26550832e+00 -2.10464123e-02 + 6.23371684e-01 -5.30768122e-01 + -4.42356624e-01 9.72226986e-01 + 2.31517901e+00 -1.08468105e+00 + 1.97236640e+00 -1.42016619e+00 + 3.18618687e+00 -1.45056343e+00 + -2.75880360e+00 5.40254980e-01 + -1.92916581e+00 1.45029864e-01 + 1.90022524e+00 -6.03805754e-01 + -1.05446211e+00 5.74361752e-01 + 1.45990390e+00 -9.28233993e-01 + 5.14960557e+00 -2.07564096e+00 + -7.53104842e-01 1.55876958e-01 + 8.09490983e-02 -8.58886384e-02 + -1.56894969e+00 4.53497227e-01 + 1.36944658e-01 5.60670875e-01 + -5.32635329e-01 4.40309945e-01 + 1.32507853e+00 -5.83670099e-01 + 1.20676031e+00 -8.02296831e-01 + -3.65023422e+00 1.17211368e+00 + 1.53393850e+00 -6.17771312e-01 + -3.99977129e+00 1.71415137e+00 + 5.70705058e-01 -4.60771539e-01 + -2.20608002e+00 1.07866596e+00 + -1.09040244e+00 6.77441076e-01 + -5.09886482e-01 -1.97282128e-01 + -1.58062785e+00 6.18333697e-01 + -1.53295020e+00 4.02168701e-01 + -5.18580598e-01 2.25767177e-01 + 1.59514316e+00 -2.54983617e-01 + -5.91938655e+00 2.68223782e+00 + 2.84200509e+00 -1.04685313e+00 + 1.31298664e+00 -1.16672614e+00 + -2.36660033e+00 1.81359460e+00 + 6.94163290e-02 3.76658816e-01 + 2.33973934e+00 -8.33173023e-01 + -8.24640389e-01 7.83717285e-01 + -1.02888281e+00 1.04680766e+00 + 1.34750745e+00 -5.89568160e-01 + -2.48761231e+00 7.44199284e-01 + -1.04501559e+00 4.72326911e-01 + -3.14610089e+00 1.89843692e+00 + 2.13003416e-01 5.76633620e-01 + -1.69239608e+00 5.66070021e-01 + 1.80491280e+00 -9.31701080e-01 + -6.94362572e-02 6.96026587e-01 + 1.36502578e+00 -6.85599000e-02 + -7.76764337e-01 3.64328661e-01 + -2.67322167e+00 6.80150021e-01 + 1.84338485e+00 -1.18487494e+00 + 2.88009231e+00 -1.25700411e+00 + 1.17114433e+00 -7.69727080e-01 + 2.11576167e+00 2.81502116e-01 + -1.51470088e+00 2.61553540e-01 + 1.18923669e-01 -1.17890202e-01 + 4.48359786e+00 -1.81427466e+00 + -1.27055948e+00 9.92388998e-01 + -8.00276606e-01 9.11326621e-02 + 7.51764024e-01 -1.03676498e-01 + 1.35769348e-01 -2.11470084e-01 + 2.50731332e+00 -1.12418270e+00 + -2.49752781e-01 7.81224033e-02 + -6.23037902e-01 3.16599691e-01 + -3.93772902e+00 1.37195391e+00 + 1.74256361e+00 -1.12363582e+00 + -1.49737281e+00 5.98828310e-01 + 7.75592115e-01 -4.64733802e-01 + -2.26027693e+00 1.36991118e+00 + -1.62849836e+00 7.36899107e-01 + 2.36850751e+00 -9.32126872e-01 + 5.86169745e+00 -2.49342512e+00 + -5.37092226e-01 1.23821274e+00 + 2.80535867e+00 -1.93363302e+00 + -1.77638106e+00 9.10050276e-01 + 3.02692018e+00 -1.60774676e+00 + 1.97833084e+00 -1.50636531e+00 + 9.09168906e-01 -8.83799359e-01 + 2.39769655e+00 -7.56977869e-01 + 1.47283981e+00 -1.06749890e+00 + 2.92060943e-01 -6.07040605e-01 + -2.09278201e+00 7.71858590e-01 + 7.10015905e-01 -5.42768432e-01 + -2.16826169e-01 1.56897896e-01 + 4.56288247e+00 -2.08912680e+00 + -6.63374020e-01 6.67325183e-01 + 1.80564442e+00 -9.76366134e-01 + 3.28720168e+00 -4.66575145e-01 + -1.60463695e-01 -2.58428153e-01 + 1.78590750e+00 -3.96427146e-01 + 2.75950306e+00 -1.82102856e+00 + -1.18234310e+00 6.28073320e-01 + 4.11415835e+00 -2.33551216e+00 + 1.38721004e+00 -2.77450622e-01 + -2.94903545e+00 1.74813352e+00 + 8.67290400e-01 -6.51667894e-01 + 2.70022274e+00 -8.11832480e-01 + -2.06766146e+00 8.24047249e-01 + 3.90717142e+00 -1.20155758e+00 + -2.95102809e+00 1.36667968e+00 + 6.08815147e+00 -2.60737974e+00 + 2.78576476e+00 -7.86628755e-01 + -3.26258407e+00 1.09302450e+00 + 1.59849422e+00 -1.09705202e+00 + -2.50600710e-01 1.63243175e-01 + -4.90477087e-01 -4.57729572e-01 + -1.24837181e+00 3.22157840e-01 + -2.46341049e+00 1.06517849e+00 + 9.62880751e-01 4.56962496e-01 + 3.99964487e-01 2.07472802e-01 + 6.36657705e-01 -3.46400942e-02 + 4.91231407e-02 -1.40289235e-02 + -4.66683524e-02 -3.72326100e-01 + -5.22049702e-01 -1.70440260e-01 + 5.27062938e-01 -2.32628395e-01 + -2.69440318e+00 1.18914874e+00 + 3.65087539e+00 -1.53427267e+00 + -1.16546364e-01 4.93245392e-02 + 7.55931384e-01 -3.02980139e-01 + 2.06338745e+00 -6.24841225e-01 + 1.31177908e-01 7.29338183e-01 + 1.48021784e+00 -6.39509896e-01 + -5.98656707e-01 2.84525503e-01 + -2.18611080e+00 1.79549812e+00 + -2.91673624e+00 2.15772237e-01 + -8.95591350e-01 7.68250538e-01 + 1.36139762e+00 -1.93845144e-01 + 5.45730414e+00 -2.28114404e+00 + 3.22747247e-01 9.33582332e-01 + -1.46384504e+00 1.12801186e-01 + 4.26728166e-01 -2.33481242e-01 + -1.41327270e+00 8.16103740e-01 + -2.53998067e-01 1.44906646e-01 + -1.32436467e+00 1.87556361e-01 + -3.77313086e+00 1.32896038e+00 + 3.77651731e+00 -1.76548043e+00 + -2.45297093e+00 1.32571926e+00 + -6.55900588e-01 3.56921462e-01 + 9.25558722e-01 -4.51988954e-01 + 1.20732231e+00 -3.02821614e-01 + 3.72660154e-01 -1.89365208e-01 + -1.77090939e+00 9.18087975e-01 + 3.01127567e-01 2.67965829e-01 + -1.76708900e+00 4.62069259e-01 + -2.71812099e+00 1.57233508e+00 + -5.35297633e-01 4.99231535e-01 + 1.50507631e+00 -9.85763646e-01 + 3.00424787e+00 -1.29837562e+00 + -4.99311105e-01 3.91086482e-01 + 1.30125207e+00 -1.26247924e-01 + 4.01699483e-01 -4.46909391e-01 + -1.33635257e+00 5.12068703e-01 + 1.39229757e+00 -9.10974858e-01 + -1.74229508e+00 1.49475978e+00 + -1.21489414e+00 4.04193753e-01 + -3.36537605e-01 -6.74335427e-01 + -2.79186828e-01 8.48314720e-01 + -2.03080140e+00 1.66599815e+00 + -3.53064281e-01 -7.68582906e-04 + -5.30305657e+00 2.91091546e+00 + -1.20049972e+00 8.26578358e-01 + 2.95906989e-01 2.40215920e-01 + -1.42955534e+00 4.63480310e-01 + -1.87856619e+00 8.21459385e-01 + -2.71124720e+00 1.80246843e+00 + -3.06933780e+00 1.22235760e+00 + 5.21935582e-01 -1.27298218e+00 + -1.34175797e+00 7.69018937e-01 + -1.81962785e+00 1.15528991e+00 + -3.99227550e-01 2.93821598e-01 + 1.22533179e+00 -4.73846323e-01 + -2.08068359e-01 -1.75039817e-01 + -2.03068526e+00 1.50370503e+00 + -3.27606113e+00 1.74906330e+00 + -4.37802587e-01 -2.26956048e-01 + -7.69774213e-02 -3.54922468e-01 + 6.47160749e-02 -2.07334721e-01 + -1.37791524e+00 4.43766709e-01 + 3.29846803e+00 -1.04060799e+00 + -3.63704046e+00 1.05800226e+00 + -1.26716116e+00 1.13077353e+00 + 1.98549075e+00 -1.31864807e+00 + 1.85159500e+00 -5.78629560e-01 + -1.55295206e+00 1.23655857e+00 + 6.76026255e-01 9.18824125e-02 + 1.23418960e+00 -4.68162027e-01 + 2.43186642e+00 -9.22422440e-01 + -3.18729701e+00 1.77582673e+00 + -4.02945613e+00 1.14303496e+00 + -1.92694576e-01 1.03301431e-01 + 1.89554730e+00 -4.60128096e-01 + -2.55626581e+00 1.16057084e+00 + 6.89144365e-01 -9.94982900e-01 + -4.44680606e+00 2.19751983e+00 + -3.15196193e+00 1.18762993e+00 + -1.17434977e+00 1.04534656e+00 + 8.58386984e-02 -1.03947487e+00 + 3.33354973e-01 5.54813610e-01 + -9.37631808e-01 3.33450150e-01 + -2.50232471e+00 5.39720635e-01 + 1.03611949e+00 -7.16304095e-02 + -2.05556816e-02 -3.28992265e-01 + -2.24176201e+00 1.13077506e+00 + 4.53583688e+00 -1.10710212e+00 + 4.77389762e-01 -8.99445512e-01 + -2.69075551e+00 6.83176866e-01 + -2.21779724e+00 1.16916849e+00 + -1.09669056e+00 2.10044765e-01 + -8.45367920e-01 -8.45951423e-02 + 4.37558941e-01 -6.95904256e-01 + 1.84884195e+00 -1.71205136e-01 + -8.36371957e-01 5.62862478e-01 + 1.27786531e+00 -1.33362147e+00 + 2.90684492e+00 -7.49892184e-01 + -3.38652716e+00 1.51180670e+00 + -1.30945978e+00 7.09261928e-01 + -7.50471924e-01 -5.24637889e-01 + 1.18580718e+00 -9.97943971e-04 + -7.55395645e+00 3.19273590e+00 + 1.72822535e+00 -1.20996962e+00 + 5.67374320e-01 6.19573416e-01 + -2.99163781e+00 1.79721534e+00 + 1.49862187e+00 -6.05631846e-02 + 1.79503506e+00 -4.90419706e-01 + 3.85626054e+00 -1.95396324e+00 + -9.39188410e-01 7.96498057e-01 + 2.91986664e+00 -1.29392724e+00 + -1.54265750e+00 6.40727933e-01 + 1.14919794e+00 1.20834257e-01 + 2.00936817e+00 -1.53728359e+00 + 3.72468420e+00 -1.38704612e+00 + -1.27794802e+00 3.48543179e-01 + 3.63294077e-01 5.70623314e-01 + 1.49381016e+00 -6.04500534e-01 + 2.98912256e+00 -1.72295726e+00 + -1.80833817e+00 2.94907625e-01 + -3.19669622e+00 1.31888700e+00 + 1.45889401e+00 -8.88448639e-01 + -2.80045388e+00 1.01207060e+00 + -4.78379567e+00 1.48646520e+00 + 2.25510003e+00 -7.13372461e-01 + -9.74441433e-02 -2.17766373e-01 + 2.64468496e-01 -3.60842698e-01 + -5.98821713e+00 3.20197892e+00 + 2.67030213e-01 -5.36386416e-01 + 2.24546960e+00 -8.13464649e-01 + -4.89171414e-01 3.86255031e-01 + -7.45713706e-01 6.29800380e-01 + -3.30460503e-01 3.85127284e-01 + -4.19588147e+00 1.52793198e+00 + 5.42078582e-01 -2.61642741e-02 + 4.24938513e-01 -5.72936751e-01 + 2.82717288e+00 -6.75355024e-01 + -1.44741788e+00 5.03578028e-01 + -1.65547573e+00 7.76444277e-01 + 2.20361170e+00 -1.40835680e+00 + -3.69540235e+00 2.32953767e+00 + -1.41909357e-01 2.28989778e-01 + 1.92838879e+00 -8.72525737e-01 + 1.40708100e+00 -6.81849638e-02 + 1.24988112e+00 -1.39470590e-01 + -2.39435855e+00 7.26587655e-01 + 7.03985028e-01 4.85403277e-02 + 4.05214529e+00 -9.16928318e-01 + 3.74198837e-01 -5.04192358e-01 + -8.43374127e-01 2.36064018e-01 + -3.32253349e-01 7.47840055e-01 + -6.03725210e+00 1.95173337e+00 + 4.60829865e+00 -1.51191309e+00 + -1.46247098e+00 1.11140916e+00 + -9.60111157e-01 -1.23189114e-01 + -7.49613187e-01 4.53614129e-01 + -5.77838219e-01 2.07366469e-02 + 8.07652950e-01 -5.16272662e-01 + -6.02556049e-01 5.05318649e-01 + -1.28712445e-01 2.57836512e-01 + -5.27662820e+00 2.11790737e+00 + 5.40819308e+00 -2.15366022e+00 + 9.37742513e-02 -1.60221751e-01 + 4.55902865e+00 -1.24646307e+00 + -9.06582589e-01 1.92928110e-01 + 2.99928996e+00 -8.04301218e-01 + -3.24317381e+00 1.80076061e+00 + 3.20421743e-01 8.76524679e-01 + -5.29606705e-01 -3.16717696e-01 + -1.77264560e+00 7.52686776e-01 + -1.51706824e+00 8.43755103e-01 + 1.52759111e+00 -7.86814243e-01 + 4.74845617e-01 4.21319700e-01 + 6.97829149e-01 -8.15664881e-01 + 3.09564973e+00 -1.06202469e+00 + 2.95320379e+00 -1.98963943e+00 + -4.23033224e+00 1.41013338e+00 + 1.48576206e+00 8.02908511e-02 + 4.52041627e+00 -2.04620399e+00 + 6.58403922e-01 -7.60781799e-01 + 2.10667543e-01 1.15241731e-01 + 1.77702583e+00 -8.10271859e-01 + 2.41277385e+00 -1.46972042e+00 + 1.50685525e+00 -1.99272545e-01 + 7.61665522e-01 -4.11276152e-01 + 1.18352312e+00 -9.59908608e-01 + -3.32031305e-01 8.07500132e-02 + 1.16813118e+00 -1.73095194e-01 + 1.18363346e+00 -5.41565052e-01 + 5.17702179e-01 -7.62442035e-01 + 4.57401006e-01 -1.45951115e-02 + 1.49377115e-01 2.99571605e-01 + 1.40399453e+00 -1.30160353e+00 + 5.26231567e-01 3.52783752e-01 + -1.91136514e+00 4.24228635e-01 + 1.74156701e+00 -9.92076776e-01 + -4.89323391e+00 2.32483507e+00 + 2.54011209e+00 -8.80366295e-01 + -5.56925706e-01 1.48842026e-01 + -2.35904668e+00 9.60474853e-01 + 1.42216971e+00 -4.67062761e-01 + -1.10809680e+00 7.68684300e-01 + 4.09674726e+00 -1.90795680e+00 + -2.23048923e+00 9.03812542e-01 + 6.57025763e-01 1.36514871e-01 + 2.10944145e+00 -9.78897838e-02 + 1.22552525e+00 -2.50303867e-01 + 2.84620103e-01 -5.30164020e-01 + -2.13562585e+00 1.03503056e+00 + 1.32414902e-01 -8.14190240e-03 + -5.82433561e-01 3.21020292e-01 + -5.06473247e-01 3.11530419e-01 + 1.57162465e+00 -1.20763919e+00 + -1.43155284e+00 -2.51203698e-02 + -1.47093713e+00 -1.39620999e-01 + -2.65765643e+00 1.06091403e+00 + 2.45992927e+00 -5.88815836e-01 + -1.28440162e+00 -1.99377398e-01 + 6.11257504e-01 -3.73577401e-01 + -3.46606103e-01 6.06081290e-01 + 3.76687505e+00 -8.80181424e-01 + -1.03725103e+00 1.45177517e+00 + 2.76659936e+00 -1.09361320e+00 + -3.61311296e+00 9.75032455e-01 + 3.22878655e+00 -9.69497365e-01 + 1.43560379e+00 -5.52524585e-01 + 2.94042153e+00 -1.79747037e+00 + 1.30739580e+00 2.47989248e-01 + -4.05056982e-01 1.22831715e+00 + -2.25827421e+00 2.30604626e-01 + 3.69262926e-01 4.32714650e-02 + -5.52064063e-01 6.07806340e-01 + 7.03325987e+00 -2.17956730e+00 + -2.37823835e-01 -8.28068639e-01 + -4.84279888e-01 5.67765194e-01 + -3.15863410e+00 1.02241617e+00 + -3.39561593e+00 1.36876374e+00 + -2.78482934e+00 6.81641104e-01 + -4.37604334e+00 2.23826340e+00 + -2.54049692e+00 8.22676745e-01 + 3.73264822e+00 -9.93498732e-01 + -3.49536064e+00 1.84771519e+00 + 9.81801604e-01 -5.21278776e-01 + 1.52996831e+00 -1.27386206e+00 + -9.23490293e-01 5.29099482e-01 + -2.76999461e+00 9.24831872e-01 + -3.30029834e-01 -2.49645555e-01 + -1.71156166e+00 5.44940854e-01 + -2.37009487e+00 5.83826982e-01 + -3.03216865e+00 1.04922722e+00 + -2.19539936e+00 1.37558730e+00 + 1.15350207e+00 -6.15318535e-01 + 4.62011792e+00 -2.46714517e+00 + 1.52627952e-02 -1.00618283e-01 + -1.10399342e+00 4.87413533e-01 + 3.55448194e+00 -9.10394190e-01 + -5.21890321e+00 2.44710745e+00 + 1.54289749e+00 -6.54269311e-01 + 2.67935674e+00 -9.92758863e-01 + 1.05801310e+00 2.60054285e-02 + 1.52509097e+00 -4.08768600e-01 + 3.27576917e+00 -1.28769406e+00 + 1.71008412e-01 -2.68739994e-01 + -9.83351344e-04 7.02495897e-02 + -7.60795056e-03 1.61968285e-01 + -1.80620472e+00 4.24934471e-01 + 2.32023297e-02 -2.57284559e-01 + 3.98219478e-01 -4.65361935e-01 + 6.63476988e-01 -3.29823196e-02 + 4.00154707e+00 -1.01792211e+00 + -1.50286870e+00 9.46875359e-01 + -2.22717585e+00 7.50636195e-01 + -3.47381508e-01 -6.51596975e-01 + 2.08076453e+00 -8.22800165e-01 + 2.05099963e+00 -4.00868250e-01 + 3.52576988e-02 -2.54418565e-01 + 1.57342042e+00 -7.62166492e-02 + -1.47019722e+00 3.40861172e-01 + -1.21156090e+00 3.21891246e-01 + 3.79729047e+00 -1.54350764e+00 + 1.26459678e-02 6.99203693e-01 + 1.53974177e-01 4.68643204e-01 + -1.73923561e-01 -1.26229768e-01 + 4.54644993e+00 -2.13951783e+00 + 1.46022547e-01 -4.57084165e-01 + 6.50048037e+00 -2.78872609e+00 + -1.51934912e+00 1.03216768e+00 + -3.06483575e+00 1.81101446e+00 + -2.38212125e+00 9.19559042e-01 + -1.81319611e+00 8.10545112e-01 + 1.70951294e+00 -6.10712680e-01 + 1.67974156e+00 -1.51241453e+00 + -5.94795113e+00 2.56893813e+00 + 3.62633110e-01 -7.46965304e-01 + -2.44042594e+00 8.52761797e-01 + 3.32412550e+00 -1.28439899e+00 + 4.74860766e+00 -1.72821964e+00 + 1.29072541e+00 -8.24872902e-01 + -1.69450702e+00 4.09600876e-01 + 1.29705411e+00 1.22300809e-01 + -2.63597613e+00 8.55612913e-01 + 9.28467301e-01 -2.63550114e-02 + 2.44670264e+00 -4.10123002e-01 + 1.06408206e+00 -5.03361942e-01 + 5.12384049e-02 -1.27116595e-02 + -1.06731272e+00 -1.76205029e-01 + -9.45454582e-01 3.74404917e-01 + 2.54343689e+00 -7.13810545e-01 + -2.54460335e+00 1.31590265e+00 + 1.89864233e+00 -3.98436339e-01 + -1.93990133e+00 6.01474630e-01 + -1.35938824e+00 4.00751788e-01 + 2.38567018e+00 -6.13904880e-01 + 2.18748050e-01 2.62631712e-01 + -2.01388788e+00 1.41474031e+00 + 2.74014581e+00 -1.27448105e+00 + -2.13828583e+00 1.13616144e+00 + 5.98730932e+00 -2.53430080e+00 + -1.72872795e+00 1.53702057e+00 + -2.53263962e+00 1.27342410e+00 + 1.34326968e+00 -1.99395088e-01 + 3.83352666e-01 -1.25683065e-01 + -2.35630657e+00 5.54116983e-01 + -1.94900838e+00 5.76270178e-01 + -1.36699108e+00 -3.40904824e-01 + -2.34727346e+00 -1.93054940e-02 + -3.82779777e+00 1.83025664e+00 + -4.31602080e+00 9.21605705e-01 + 5.54098133e-01 2.33991419e-01 + -4.53591188e+00 1.99833353e+00 + -3.92715909e+00 1.83231482e+00 + 3.91344440e-01 -1.11355111e-01 + 3.48576363e+00 -1.41379449e+00 + -1.42858690e+00 3.84532286e-01 + 1.79519859e+00 -9.23486448e-01 + 8.49691242e-01 -1.76551084e-01 + 1.53618138e+00 8.23835015e-02 + 5.91476520e-02 3.88296940e-02 + 1.44837346e+00 -7.24097604e-01 + -6.79008418e-01 4.04078097e-01 + 2.87555510e+00 -9.51825076e-01 + -1.12379101e+00 2.93457714e-01 + 1.45263980e+00 -6.01960544e-01 + -2.55741621e-01 9.26233518e-01 + 3.54570714e+00 -1.41521877e+00 + -1.61542388e+00 6.57844512e-01 + -3.22844269e-01 3.02823546e-01 + 1.03523913e+00 -6.92730711e-01 + 1.11084909e+00 -3.50823642e-01 + 3.41268693e+00 -1.90865862e+00 + 7.67062858e-01 -9.48792160e-01 + -5.49798016e+00 1.71139960e+00 + 1.14865798e+00 -6.12669150e-01 + -2.18256680e+00 7.78634462e-01 + 4.78857389e+00 -2.55555085e+00 + -1.85555569e+00 8.04311615e-01 + -4.22278799e+00 2.01162524e+00 + -1.56556149e+00 1.54353907e+00 + -3.11527864e+00 1.65973526e+00 + 2.66342611e+00 -1.20449402e+00 + 1.57635314e+00 -1.48716308e-01 + -6.35606865e-01 2.59701180e-01 + 1.02431976e+00 -6.76929904e-01 + 1.12973772e+00 1.49473892e-02 + -9.12758116e-01 2.21533933e-01 + -2.98014470e+00 1.71651189e+00 + 2.74016965e+00 -9.47893923e-01 + -3.47830591e+00 1.34941430e+00 + 1.74757562e+00 -3.72503752e-01 + 5.55820383e-01 -6.47992466e-01 + -1.19871928e+00 9.82429151e-01 + -2.53040133e+00 2.10671307e+00 + -1.94085605e+00 1.38938137e+00 diff --git a/docs/mllib-clustering.md b/docs/mllib-clustering.md index 413b824e36..1e9ef345b7 100644 --- a/docs/mllib-clustering.md +++ b/docs/mllib-clustering.md @@ -16,9 +16,12 @@ often used for exploratory analysis and/or as a component of a hierarchical supervised learning pipeline (in which distinct classifiers or regression models are trained for each cluster). -MLlib supports -[k-means](http://en.wikipedia.org/wiki/K-means_clustering) clustering, one of -the most commonly used clustering algorithms that clusters the data points into +MLlib supports the following models: + +### k-means + +[k-means](http://en.wikipedia.org/wiki/K-means_clustering) is one of the +most commonly used clustering algorithms that clusters the data points into a predefined number of clusters. The MLlib implementation includes a parallelized variant of the [k-means++](http://en.wikipedia.org/wiki/K-means%2B%2B) method called [kmeans||](http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf). @@ -34,6 +37,20 @@ a given dataset, the algorithm returns the best clustering result). * *initializationSteps* determines the number of steps in the k-means\|\| algorithm. * *epsilon* determines the distance threshold within which we consider k-means to have converged. +### Gaussian mixture + +A [Gaussian Mixture Model](http://en.wikipedia.org/wiki/Mixture_model#Multivariate_Gaussian_mixture_model) +represents a composite distribution whereby points are drawn from one of *k* Gaussian sub-distributions, +each with its own probability. The MLlib implementation uses the +[expectation-maximization](http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm) + algorithm to induce the maximum-likelihood model given a set of samples. The implementation +has the following parameters: + +* *k* is the number of desired clusters. +* *convergenceTol* is the maximum change in log-likelihood at which we consider convergence achieved. +* *maxIterations* is the maximum number of iterations to perform without reaching convergence. +* *initialModel* is an optional starting point from which to start the EM algorithm. If this parameter is omitted, a random starting point will be constructed from the data. + ### Power Iteration Clustering Power iteration clustering is a scalable and efficient algorithm for clustering points given pointwise mutual affinity values. Internally the algorithm: @@ -56,6 +73,8 @@ Example outputs for a dataset inspired by the paper - but with five clusters ins ### Examples +#### k-means + <div class="codetabs"> <div data-lang="scala" markdown="1"> The following code snippets can be executed in `spark-shell`. @@ -168,6 +187,112 @@ print("Within Set Sum of Squared Error = " + str(WSSSE)) </div> +#### GaussianMixture + +<div class="codetabs"> +<div data-lang="scala" markdown="1"> +In the following example after loading and parsing data, we use a +[GaussianMixture](api/scala/index.html#org.apache.spark.mllib.clustering.GaussianMixture) +object to cluster the data into two clusters. The number of desired clusters is passed +to the algorithm. We then output the parameters of the mixture model. + +{% highlight scala %} +import org.apache.spark.mllib.clustering.GaussianMixture +import org.apache.spark.mllib.linalg.Vectors + +// Load and parse the data +val data = sc.textFile("data/mllib/gmm_data.txt") +val parsedData = data.map(s => Vectors.dense(s.trim.split(' ').map(_.toDouble))).cache() + +// Cluster the data into two classes using GaussianMixture +val gmm = new GaussianMixture().setK(2).run(parsedData) + +// output parameters of max-likelihood model +for (i <- 0 until gmm.k) { + println("weight=%f\nmu=%s\nsigma=\n%s\n" format + (gmm.weights(i), gmm.gaussians(i).mu, gmm.gaussians(i).sigma)) +} + +{% endhighlight %} +</div> + +<div data-lang="java" markdown="1"> +All of MLlib's methods use Java-friendly types, so you can import and call them there the same +way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the +Spark Java API uses a separate `JavaRDD` class. You can convert a Java RDD to a Scala one by +calling `.rdd()` on your `JavaRDD` object. A self-contained application example +that is equivalent to the provided example in Scala is given below: + +{% highlight java %} +import org.apache.spark.api.java.*; +import org.apache.spark.api.java.function.Function; +import org.apache.spark.mllib.clustering.GaussianMixture; +import org.apache.spark.mllib.clustering.GaussianMixtureModel; +import org.apache.spark.mllib.linalg.Vector; +import org.apache.spark.mllib.linalg.Vectors; +import org.apache.spark.SparkConf; + +public class GaussianMixtureExample { + public static void main(String[] args) { + SparkConf conf = new SparkConf().setAppName("GaussianMixture Example"); + JavaSparkContext sc = new JavaSparkContext(conf); + + // Load and parse data + String path = "data/mllib/gmm_data.txt"; + JavaRDD<String> data = sc.textFile(path); + JavaRDD<Vector> parsedData = data.map( + new Function<String, Vector>() { + public Vector call(String s) { + String[] sarray = s.trim().split(" "); + double[] values = new double[sarray.length]; + for (int i = 0; i < sarray.length; i++) + values[i] = Double.parseDouble(sarray[i]); + return Vectors.dense(values); + } + } + ); + parsedData.cache(); + + // Cluster the data into two classes using GaussianMixture + GaussianMixtureModel gmm = new GaussianMixture().setK(2).run(parsedData.rdd()); + + // Output the parameters of the mixture model + for(int j=0; j<gmm.k(); j++) { + System.out.println("weight=%f\nmu=%s\nsigma=\n%s\n", + gmm.weights()[j], gmm.gaussians()[j].mu(), gmm.gaussians()[j].sigma()); + } + } +} +{% endhighlight %} +</div> + +<div data-lang="python" markdown="1"> +In the following example after loading and parsing data, we use a +[GaussianMixture](api/python/pyspark.mllib.html#pyspark.mllib.clustering.GaussianMixture) +object to cluster the data into two clusters. The number of desired clusters is passed +to the algorithm. We then output the parameters of the mixture model. + +{% highlight python %} +from pyspark.mllib.clustering import GaussianMixture +from numpy import array + +# Load and parse the data +data = sc.textFile("data/mllib/gmm_data.txt") +parsedData = data.map(lambda line: array([float(x) for x in line.strip().split(' ')])) + +# Build the model (cluster the data) +gmm = GaussianMixture.train(parsedData, 2) + +# output parameters of model +for i in range(2): + print ("weight = ", gmm.weights[i], "mu = ", gmm.gaussians[i].mu, + "sigma = ", gmm.gaussians[i].sigma.toArray()) + +{% endhighlight %} +</div> + +</div> + In order to run the above application, follow the instructions provided in the [Self-Contained Applications](quick-start.html#self-contained-applications) section of the Spark diff --git a/docs/mllib-guide.md b/docs/mllib-guide.md index 73728bb35e..7779fbc9c4 100644 --- a/docs/mllib-guide.md +++ b/docs/mllib-guide.md @@ -25,6 +25,8 @@ filtering, dimensionality reduction, as well as underlying optimization primitiv * alternating least squares (ALS) * [Clustering](mllib-clustering.html) * k-means + * Gaussian mixture + * power iteration * [Dimensionality reduction](mllib-dimensionality-reduction.html) * singular value decomposition (SVD) * principal component analysis (PCA) |