Need for smearing_calculations

Following is data for wilson loop beta=6.285 on 32,32,32,8 lattice

which can be found using awk, : awk '/Node: 0 Length= 1, Height= 30 /' wloop_node_0.txt

Node: 0 Length= 1, Height= 30 Wilson Loop: 2.567015352675811e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.914770814506352e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.768784740426048e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.098661656593434e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 9.057358599632912e-06
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.997806682024679e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 7.782634272675470e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.665314973379971e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.459902135745133e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.128350037402911e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.683015982628285e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.396152754096264e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.185907726430353e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.308039085350023e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.438313228716247e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.442639234365787e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.164617608714710e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.464968083615682e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 8.607658831328689e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.812756071518225e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.664334659827624e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.147830077412605e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.080703457666121e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.938179867246578e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.889561564543357e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.642831365973704e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.075626797442896e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.212595116758000e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.031975137942869e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.400626594278798e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.821838791883293e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.447822916830705e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.637143241244728e-06
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.356316413555416e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.912108472351451e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 7.953150013453430e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.051184619204976e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.308272380393049e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.140582908327933e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.178895557489912e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.207311254453190e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -5.741287306488892e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.316325206289341e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.214568608323840e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.710571212037848e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.097255192109906e-06
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.267600297553899e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.053633721318727e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.321938595216655e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.321938595216655e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.043613121336567e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -5.030258424594720e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.518137091218735e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -8.558429267720741e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.050352180963939e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.063199502197674e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.389235038435609e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.511893148045371e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 6.462631669257534e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.860742816853972e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.309569008801895e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 7.426849236096201e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.056850233445717e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.277951817494587e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.744464241684993e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -9.055252161937739e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.294170880862620e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.860726511640821e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.839928548630954e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.341045298975313e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.630828112185127e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 8.305318558852574e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 8.757129423588105e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.490709332328876e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.666427580130028e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.279360735146734e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.790120244629647e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.453113525355797e-06
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.891458894040707e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.622214424246126e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -9.352098007152346e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.097704476720261e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.808903921882951e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.783256298624873e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.803212000801308e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.571873406883432e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.215518540865490e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.735269770515687e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.244922359216196e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.863987233909952e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.170110818917077e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.710628903591808e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.133235246988412e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.319838428956831e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.450556038409269e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.450556038409269e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.786898939879330e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.949190334650842e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -8.137168380800727e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 8.573194841887194e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.151191356303037e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.089129919661425e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.158189106469293e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.486057941626101e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.514233394333279e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.037508655184175e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.341149680205718e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.166184869972801e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.115023176465101e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.314951607903459e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.334985058647927e-06
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.430668365504054e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.315345151914156e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.071440670198996e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.663830125758392e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.121602293651510e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -8.970846782106340e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.085778532735297e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.067498943743315e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.092447518528666e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.401931229348676e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.036472044916892e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.974357707448981e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.171932130420899e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 6.461296564018079e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.426154106670574e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.628177984061113e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.429197824943244e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.050811560541842e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.090134103856610e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.819312644416578e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.405961396075782e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.793004549731907e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.591922558471531e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.403802994099602e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -7.674296510840546e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.687276818270501e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.636763882069715e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.286018094783993e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.203229426224354e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.979683818435650e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.868829940483742e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.564222055752754e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 4.529735543652615e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.564236837591317e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.388017324095270e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.218928847728193e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.041464101918160e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.633754702677698e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.943722345811375e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.084764983085855e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.162337402929435e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.525420235630572e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.171813147633796e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.497950908418444e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.157886424970265e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.037658169599625e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.427163868120934e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.297661810771653e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.619274983666983e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.789218046116992e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 8.526494907014909e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.819967548331837e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.686877418523764e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.731869990946625e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.911977758827849e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.087239571989107e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.871046464756074e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 6.612495167726932e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.125398352935490e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 9.225952049871024e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.390644366936524e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.096552610247381e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.525380015461658e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.986728468125699e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.517128140702911e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 3.016208464371333e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.296499778848649e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.079714228763677e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -6.733829460089073e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.413414523940404e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.187432595546523e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.025933659695180e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.003123042169340e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.676024656646595e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 6.905920844591658e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.269067814800894e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.665029304022166e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.185249237619415e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -7.485117940645552e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 2.088893977098022e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -3.029428418369882e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.884477873895178e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -4.788693289192631e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: 1.899306680908747e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -2.271088324558872e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -8.292079431188700e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: 5.731838858208898e-05
Node: 0 Length= 1, Height= 30 Wilson Loop: -5.643817133968173e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.754670943702678e-04
Node: 0 Length= 1, Height= 30 Wilson Loop: -1.427911567354273e-04

The average can be found: awk '/Node: 0 Length= 1, Height= 30 /{total+= $NF} END { print "Average=" total/201}' wloop_node_0.txt

Average=3.05987e-06

These are all done to improve the signal to noise ratio (or to get better signal), In below link you can see that the wilson loop value for some node of gpu (try20 ,l32f21b6285), we get average value less then the actual value. i.e. signal is lost in fluctuations. To get rid of it we follow the technique of smearing.

Data node0