test_fejer.java running
xmin=0.0  xmax=6.283185307179586  ymin=-0.5  ymax=0.5  yavg=0.0
FejerFit2.java step function -0.5 to +0.5 at x==Pi
y=a[1]*Math.cos(x)+b[1]*Math.sin(x);
for(int j=3; j<t; j=j+2)y=y+ /* t=12 for 11 terms */
((double)(t-j)/(double)(t-1))*a[j]*Math.cos((double)j*x)+
((double)(t-j)/(double)(t-1))*b[j]*Math.sin((double)j*x);
a[0]=0.009900990099009901  b[0]=0.0
a[1]=-0.02969339172855432  b[1]=-0.6359526045019362
a[2]=0.0098626850917543  b[2]=-9.23013482759155E-4
a[3]=-0.029616818771663826  b[3]=-0.21020744988429907
a[4]=0.00974791826461936  b[4]=-0.0018406670652063313
a[5]=-0.02946396910377735  b[5]=-0.12399991935119231
a[6]=0.009557133628163616  b[6]=-0.0027476146354994996
a[7]=-0.02923543407056648  b[7]=-0.08630851965124292
a[8]=0.009291069291082516  b[8]=-0.0036385375106818933
a[9]=-0.028932097829677917  b[9]=-0.06480165068676198
a[10]=0.008950754604608495  b[10]=-0.004508157779077944
a[11]=-0.02855513393009896  b[11]=-0.050664915280475994
a[12]=0.008537506180151939  b[12]=-0.005351251190779413
a[13]=-0.02810600077192567  b[13]=-0.04051089569053738
a[14]=0.008052922795585376  b[14]=-0.006162659436203268
a[15]=-0.0275864359640948  b[15]=-0.03276109487443378
a[16]=0.007498879209886233  b[16]=-0.00693730164404362
a[17]=-0.026998449601913912  b[17]=-0.026581789506526697
a[18]=0.006877518910055087  b[18]=-0.007670184918323214
a[19]=-0.026344316490392185  b[19]=-0.02149196538433525
a[20]=0.006191245818381357  b[20]=-0.008356413719008684
a[21]=-0.025626567343460374  b[21]=-0.01719528066144797
a[22]=0.005442714992136678  b[22]=-0.008991197871052648
a[23]=-0.02484797899313375  b[23]=-0.01349969251783979
a[24]=0.00463482235167183  b[24]=-0.009569858961608098
a[25]=-0.024011563646485302  b[25]=-0.010275656125105283
a[26]=0.0037706934766684633  b[26]=-0.010087834853099432
a[27]=-0.023120557232002563  b[27]=-0.007432895844583366
a[28]=0.0028536715138689057  b[28]=-0.010540681999063354
a[29]=-0.02217840688041251  b[29]=-0.00490678314237441
a[30]=0.0018873042431021027  b[30]=-0.010924075197586144
a[31]=-0.021188757588390995  b[31]=-0.002649983093693049
a[32]=8.753303516041746E-4  b[32]=-0.011233804350565653
a[33]=-0.020155438116798402  b[33]=-6.271347055830403E-4
a[34]=-1.783350302324868E-4  b[34]=-0.011465767711655478
a[35]=-0.019082446177928262  b[35]=0.0011886480844495557
a[36]=-0.0012696154757344403  b[36]=-0.01161596099557087
a[37]=-0.01797393296914374  b[37]=0.0028181432580826663
a[38]=-0.0023942890328629393  b[38]=-0.01168046157883261
a[39]=-0.016834187112701418  b[39]=0.004277661453369187
a[40]=-0.0035480045581117647  b[40]=-0.011655406836133617
a[41]=-0.015667618063906107  b[41]=0.00558020816332015
a[42]=-0.004726298550239962  b[42]=-0.011536965412707314
a[43]=-0.014478739051781498  b[43]=0.006736322840458532
a[44]=-0.005924612418698454  b[44]=-0.011321299911031386
a[45]=-0.013272149618263259  b[45]=0.007754695076078165
a[46]=-0.007138310119923118  b[46]=-0.0110045190412916
a[47]=-0.01205251782347245  b[47]=0.008642623918266314
a[48]=-0.008362696093286583  b[48]=-0.010582616709149065
a[49]=-0.010824562185888256  b[49]=0.009406364817913767
k=4   t=12
max_err=0.5865494698516713
approximation
x[0]=0.0  y[0]=-0.5  yf[0]=-0.08654946985166996
x[1]=0.06283185307179587  y[1]=-0.5  yf[1]=-0.20770800652112406
x[2]=0.12566370614359174  y[2]=-0.5  yf[2]=-0.309718291265228
x[3]=0.1884955592153876  y[3]=-0.5  yf[3]=-0.3865410135781407
x[4]=0.25132741228718347  y[4]=-0.5  yf[4]=-0.437169498561667
x[5]=0.3141592653589793  y[5]=-0.5  yf[5]=-0.4651450742820826
x[6]=0.3769911184307752  y[6]=-0.5  yf[6]=-0.47694370504833283
x[7]=0.4398229715025711  y[7]=-0.5  yf[7]=-0.4798424237600594
x[8]=0.5026548245743669  y[8]=-0.5  yf[8]=-0.4799778793798214
x[9]=0.5654866776461628  y[9]=-0.5  yf[9]=-0.4811562951012884
x[10]=0.6283185307179586  y[10]=-0.5  yf[10]=-0.4846428632075268
x[11]=0.6911503837897546  y[11]=-0.5  yf[11]=-0.4897893940189062
x[12]=0.7539822368615504  y[12]=-0.5  yf[12]=-0.4950940394129787
x[13]=0.8168140899333463  y[13]=-0.5  yf[13]=-0.4992133204775302
x[14]=0.8796459430051422  y[14]=-0.5  yf[14]=-0.5015665516298985
x[15]=0.942477796076938  y[15]=-0.5  yf[15]=-0.5024103785922892
x[16]=1.0053096491487339  y[16]=-0.5  yf[16]=-0.5025024114813029
x[17]=1.0681415022205298  y[17]=-0.5  yf[17]=-0.5026173736274316
x[18]=1.1309733552923256  y[18]=-0.5  yf[18]=-0.5031813872683566
x[19]=1.1938052083641215  y[19]=-0.5  yf[19]=-0.5041730257177225
x[20]=1.2566370614359172  y[20]=-0.5  yf[20]=-0.5052768100823618
x[21]=1.3194689145077132  y[21]=-0.5  yf[21]=-0.5061501441504646
x[22]=1.3823007675795091  y[22]=-0.5  yf[22]=-0.5066329584150543
x[23]=1.4451326206513049  y[23]=-0.5  yf[23]=-0.5067928055527329
x[24]=1.5079644737231008  y[24]=-0.5  yf[24]=-0.5068108003475693
x[25]=1.5707963267948968  y[25]=-0.5  yf[25]=-0.5068088712232217
x[26]=1.6336281798666925  y[26]=-0.5  yf[26]=-0.5067447525194784
x[27]=1.6964600329384885  y[27]=-0.5  yf[27]=-0.506447823044893
x[28]=1.7592918860102844  y[28]=-0.5  yf[28]=-0.5057710439890782
x[29]=1.8221237390820801  y[29]=-0.5  yf[29]=-0.504751395789986
x[30]=1.884955592153876  y[30]=-0.5  yf[30]=-0.5036545697039615
x[31]=1.9477874452256718  y[31]=-0.5  yf[31]=-0.5028433731924744
x[32]=2.0106192982974678  y[32]=-0.5  yf[32]=-0.5025210978939733
x[33]=2.0734511513692637  y[33]=-0.5  yf[33]=-0.5024977793908865
x[34]=2.1362830044410597  y[34]=-0.5  yf[34]=-0.5021477546161648
x[35]=2.199114857512855  y[35]=-0.5  yf[35]=-0.5006463456101535
x[36]=2.261946710584651  y[36]=-0.5  yf[36]=-0.4974207733532764
x[37]=2.324778563656447  y[37]=-0.5  yf[37]=-0.4925988738451449
x[38]=2.387610416728243  y[38]=-0.5  yf[38]=-0.48717322236587757
x[39]=2.450442269800039  y[39]=-0.5  yf[39]=-0.4826707543214066
x[40]=2.5132741228718345  y[40]=-0.5  yf[40]=-0.48031915548137477
x[41]=2.5761059759436304  y[41]=-0.5  yf[41]=-0.4799553879630343
x[42]=2.6389378290154264  y[42]=-0.5  yf[42]=-0.479115274458327
x[43]=2.7017696820872223  y[43]=-0.5  yf[43]=-0.4727743360867479
x[44]=2.7646015351590183  y[44]=-0.5  yf[44]=-0.45403783062727787
x[45]=2.8274333882308142  y[45]=-0.5  yf[45]=-0.4157469865337402
x[46]=2.8902652413026098  y[46]=-0.5  yf[46]=-0.35259848671754707
x[47]=2.9530970943744057  y[47]=-0.5  yf[47]=-0.26311450547827436
x[48]=3.0159289474462017  y[48]=-0.5  yf[48]=-0.15076801665439155
x[49]=3.0787608005179976  y[49]=-0.5  yf[49]=-0.02379567994885508
x[50]=3.1415926535897936  y[50]=0.5  yf[50]=0.10635145004969046
x[51]=3.204424506661589  y[51]=0.5  yf[51]=0.227509986719144
x[52]=3.267256359733385  y[52]=0.5  yf[52]=0.32952027146324797
x[53]=3.330088212805181  y[53]=0.5  yf[53]=0.4063429937761606
x[54]=3.392920065876977  y[54]=0.5  yf[54]=0.45697147875968697
x[55]=3.455751918948773  y[55]=0.5  yf[55]=0.48494705448010245
x[56]=3.518583772020569  y[56]=0.5  yf[56]=0.4967456852463525
x[57]=3.5814156250923643  y[57]=0.5  yf[57]=0.49964440395807935
x[58]=3.6442474781641603  y[58]=0.5  yf[58]=0.4997798595778414
x[59]=3.7070793312359562  y[59]=0.5  yf[59]=0.5009582752993081
x[60]=3.769911184307752  y[60]=0.5  yf[60]=0.5044448434055466
x[61]=3.832743037379548  y[61]=0.5  yf[61]=0.509591374216926
x[62]=3.8955748904513436  y[62]=0.5  yf[62]=0.5148960196109986
x[63]=3.9584067435231396  y[63]=0.5  yf[63]=0.51901530067555
x[64]=4.0212385965949355  y[64]=0.5  yf[64]=0.5213685318279183
x[65]=4.084070449666731  y[65]=0.5  yf[65]=0.5222123587903093
x[66]=4.1469023027385274  y[66]=0.5  yf[66]=0.5223043916793229
x[67]=4.209734155810323  y[67]=0.5  yf[67]=0.5224193538254516
x[68]=4.272566008882119  y[68]=0.5  yf[68]=0.5229833674663764
x[69]=4.335397861953915  y[69]=0.5  yf[69]=0.5239750059157424
x[70]=4.39822971502571  y[70]=0.5  yf[70]=0.5250787902803814
x[71]=4.461061568097507  y[71]=0.5  yf[71]=0.5259521243484843
x[72]=4.523893421169302  y[72]=0.5  yf[72]=0.5264349386130741
x[73]=4.586725274241099  y[73]=0.5  yf[73]=0.5265947857507526
x[74]=4.649557127312894  y[74]=0.5  yf[74]=0.5266127805455889
x[75]=4.71238898038469  y[75]=0.5  yf[75]=0.5266108514212416
x[76]=4.775220833456486  y[76]=0.5  yf[76]=0.5265467327174981
x[77]=4.838052686528282  y[77]=0.5  yf[77]=0.5262498032429128
x[78]=4.900884539600078  y[78]=0.5  yf[78]=0.5255730241870983
x[79]=4.9637163926718735  y[79]=0.5  yf[79]=0.524553375988006
x[80]=5.026548245743669  y[80]=0.5  yf[80]=0.5234565499019812
x[81]=5.089380098815465  y[81]=0.5  yf[81]=0.5226453533904943
x[82]=5.152211951887261  y[82]=0.5  yf[82]=0.5223230780919932
x[83]=5.215043804959057  y[83]=0.5  yf[83]=0.5222997595889064
x[84]=5.277875658030853  y[84]=0.5  yf[84]=0.5219497348141845
x[85]=5.340707511102649  y[85]=0.5  yf[85]=0.5204483258081732
x[86]=5.403539364174445  y[86]=0.5  yf[86]=0.5172227535512958
x[87]=5.46637121724624  y[87]=0.5  yf[87]=0.5124008540431647
x[88]=5.529203070318037  y[88]=0.5  yf[88]=0.506975202563897
x[89]=5.592034923389832  y[89]=0.5  yf[89]=0.5024727345194263
x[90]=5.6548667764616285  y[90]=0.5  yf[90]=0.5001211356793945
x[91]=5.717698629533424  y[91]=0.5  yf[91]=0.49975736816105415
x[92]=5.7805304826052195  y[92]=0.5  yf[92]=0.49891725465634645
x[93]=5.843362335677016  y[93]=0.5  yf[93]=0.4925763162847675
x[94]=5.906194188748811  y[94]=0.5  yf[94]=0.47383981082529797
x[95]=5.969026041820608  y[95]=0.5  yf[95]=0.43554896673176
x[96]=6.031857894892403  y[96]=0.5  yf[96]=0.37240046691556655
x[97]=6.094689747964199  y[97]=0.5  yf[97]=0.28291648567629424
x[98]=6.157521601035995  y[98]=0.5  yf[98]=0.1705699968524107
x[99]=6.220353454107791  y[99]=0.5  yf[99]=0.04359766014687523
x[100]=6.283185307179587  y[100]=0.5  yf[100]=-0.08654946985167133
nvert=6  npoly=5  ipoly=15
nvert=107  npoly=105  ipoly=315
write num_points=107
write num_polys=105
wrote test_fejer.dat