R/constants.R

In stla/tanhsinh: Numerical Integration with the tanh-sinh Quadrature

halfpi <- 1.5707963267948966192

layerSizes <- c(3L, 3L, 6L, 12L, 24L, 48L, 96L, 192L, 384L, 768L)
nEvaluations <- 1L + cumsum(layerSizes)

Abcissas <- list(
  # 1st layer abcissas: transformed 1, 2, 3
  c(
    0.95136796407274694573,
    0.99997747719246159286,
    0.99999999999995705839
  ),
  # 2nd layer abcissas: transformed 1/2, 3/2, 5/2
  c(
    0.67427149224843582608,
    0.99751485645722438683,
    0.99999998887566488198
  ),
  # 3rd layer abcissas: transformed 1/4, 3/4, ...
  c(
    0.37720973816403417379,
    0.85956905868989663517,
    0.98704056050737689169,
    0.99968826402835320905,
    0.99999920473711471266,
    0.99999999995285644818
  ),
  # 4th layer abcissas: transformed 1/8, 3/8, ...
  c(
    0.19435700332493543161,
    0.53914670538796776905,
    0.78060743898320029925,
    0.91487926326457461091,
    0.97396686819567744856,
    0.99405550663140214329,
    0.99906519645578584642,
    0.99990938469514399984,
    0.99999531604122052843,
    0.99999989278161241838,
    0.99999999914270509218,
    0.99999999999823216531
  ),
  # 5th layer abcissa: transformed 1/16, 3/16, ...
  c(
    0.097923885287832333262,
    0.28787993274271591456,
    0.46125354393958570440,
    0.61027365750063894488,
    0.73101803479256151149,
    0.82331700550640237006,
    0.88989140278426019808,
    0.93516085752198468323,
    0.96411216422354729193,
    0.98145482667733517003,
    0.99112699244169880223,
    0.99610866543750854254,
    0.99845420876769773751,
    0.99945143443527460584,
    0.99982882207287494166,
    0.99995387100562796075,
    0.99998948201481850361,
    0.99999801714059543208,
    0.99999969889415261122,
    0.99999996423908091534,
    0.99999999678719909830,
    0.99999999978973286224,
    0.99999999999039393352,
    0.99999999999970809734
  ),
  # 6th layer abcissas: transformed 1/32, 3/32, ...
  c(
    0.049055967305077886315,
    0.14641798429058794053,
    0.24156631953888365838,
    0.33314226457763809244,
    0.41995211127844715849,
    0.50101338937930910152,
    0.57558449063515165995,
    0.64317675898520470128,
    0.70355000514714201566,
    0.75669390863372994941,
    0.80279874134324126576,
    0.84221924635075686382,
    0.87543539763040867837,
    0.90301328151357387064,
    0.92556863406861266645,
    0.94373478605275715685,
    0.95813602271021369012,
    0.96936673289691733517,
    0.97797623518666497298,
    0.98445883116743083087,
    0.98924843109013389601,
    0.99271699719682728538,
    0.99517602615532735426,
    0.99688031812819187372,
    0.99803333631543375402,
    0.99879353429880589929,
    0.99928111192179195541,
    0.99958475035151758732,
    0.99976797159956083506,
    0.99987486504878034648,
    0.99993501992508242369,
    0.99996759306794345976,
    0.99998451990227082442,
    0.99999293787666288565,
    0.99999693244919035751,
    0.99999873547186590954,
    0.99999950700571943689,
    0.99999981889371276701,
    0.99999993755407837378,
    0.99999997987450320175,
    0.99999999396413420165,
    0.99999999832336194826,
    0.99999999957078777261,
    0.99999999989927772326,
    0.99999999997845533741,
    0.99999999999582460688,
    0.99999999999927152627,
    0.99999999999988636130
  ),
  # 7th layer abcissas: transformed 1/64, 3/64, ...
  c(
    0.024539763574649160379,
    0.073525122985671294475,
    0.12222912220155764235,
    0.17046797238201051811,
    0.21806347346971200463,
    0.26484507658344795046,
    0.31065178055284596083,
    0.35533382516507453330,
    0.39875415046723775644,
    0.44078959903390086627,
    0.48133184611690504422,
    0.52028805069123015958,
    0.55758122826077823080,
    0.59315035359195315880,
    0.62695020805104287950,
    0.65895099174335012438,
    0.68913772506166767176,
    0.71750946748732412721,
    0.74407838354734739913,
    0.76886868676824658459,
    0.79191549237614211447,
    0.81326360850297385168,
    0.83296629391941087564,
    0.85108400798784873261,
    0.86768317577564598669,
    0.88283498824466895513,
    0.89661425428007602579,
    0.90909831816302043511,
    0.92036605303195280235,
    0.93049693799715340631,
    0.93957022393327475539,
    0.94766419061515309734,
    0.95485549580502268541,
    0.96121861515111640753,
    0.96682537031235585284,
    0.97174454156548730892,
    0.97604156025657673933,
    0.97977827580061576265,
    0.98301279148110110558,
    0.98579936302528343597,
    0.98818835380074264243,
    0.99022624046752774694,
    0.99195566300267761562,
    0.99341551316926403900,
    0.99464105571251119672,
    0.99566407681695316965,
    0.99651305464025377317,
    0.99721334704346870224,
    0.99778739195890653083,
    0.99825491617199629344,
    0.99863314864067747762,
    0.99893703483351217373,
    0.99917944893488591716,
    0.99937140114093768690,
    0.99952223765121720422,
    0.99963983134560036519,
    0.99973076151980848263,
    0.99980048143113838630,
    0.99985347277311141171,
    0.99989338654759256426,
    0.99992317012928932869,
    0.99994518061445869309,
    0.99996128480785666613,
    0.99997294642523223656,
    0.99998130127012072679,
    0.99998722128200062811,
    0.99999136844834487344,
    0.99999423962761663478,
    0.99999620334716617675,
    0.99999752962380516793,
    0.99999841381096473542,
    0.99999899541068996962,
    0.99999937270733536947,
    0.99999961398855024275,
    0.99999976602333243312,
    0.99999986037121459941,
    0.99999991800479471056,
    0.99999995264266446185,
    0.99999997311323594362,
    0.99999998500307631173,
    0.99999999178645609907,
    0.99999999558563361584,
    0.99999999767323673790,
    0.99999999879798350040,
    0.99999999939177687583,
    0.99999999969875436925,
    0.99999999985405611550,
    0.99999999993088839501,
    0.99999999996803321674,
    0.99999999998556879008,
    0.99999999999364632387,
    0.99999999999727404948,
    0.99999999999886126543,
    0.99999999999953722654,
    0.99999999999981720098,
    0.99999999999992987953
  ),
  # 8th layer abcissas: transformed 1/128, 3/128, ...
  c(
    0.012271355118082202032,
    0.036802280950025085015,
    0.061297889413659975774,
    0.085734754877651055756,
    0.11008962993262801258,
    0.13433951528767223660,
    0.15846172828929950397,
    0.18243396969028915021,
    0.20623438831102876939,
    0.22984164325436075370,
    0.25323496335600023568,
    0.27639420357617861412,
    0.29929989806396047268,
    0.32193330965336916623,
    0.34427647557970491862,
    0.36631224923490408186,
    0.38802433781211774759,
    0.40939733572152948913,
    0.43041675369143706433,
    0.45106904350045199477,
    0.47134161831799846569,
    0.49122286866081148740,
    0.51070217400255814206,
    0.52976991010177455839,
    0.54841745213979235465,
    0.56663717378501885805,
    0.58442244232266394166,
    0.60176761000963345902,
    0.61866800183272806126,
    0.63511989986442183612,
    0.65112052442430422952,
    0.66666801226573768132,
    0.68176139201642731255,
    0.69640055710845920729,
    0.71058623643800578665,
    0.72431996299740748037,
    0.73760404072282524490,
    0.75044150979924043507,
    0.76283611066139236881,
    0.77479224692443536981,
    0.78631494747181960601,
    0.79740982792031224702,
    0.80808305167333853750,
    0.81834129076409782795,
    0.82819168667935709927,
    0.83764181134360002466,
    0.84669962843146369636,
    0.85537345516427153090,
    0.86367192473410523488,
    0.87160394948637771882,
    0.87917868497938937025,
    0.88640549502697870181,
    0.89329391781821098233,
    0.89985363319617013142,
    0.90609443116640420057,
    0.91202618169448681916,
    0.91765880584154933982,
    0.92300224827655440350,
    0.92806645119455512621,
    0.93286132966124005414,
    0.93739674839571913814,
    0.94168249999576933549,
    0.94572828460263224006,
    0.94954369099593635964,
    0.95313817910339380265,
    0.95652106390458093039,
    0.95970150070333660918,
    0.96268847173907826997,
    0.96549077410362047309,
    0.96811700892685631619,
    0.97057557179190042034,
    0.97287464433796388157,
    0.97502218700730634954,
    0.97702593289105795751,
    0.97889338262749402910,
    0.98063180030544870501,
    0.98224821032494106506,
    0.98374939516673124534,
    0.98514189402239802876,
    0.98643200223660844634,
    0.98762577151351068435,
    0.98872901083960236189,
    0.98974728807598709630,
    0.99068593217361507217,
    0.99155003596589173475,
    0.99234445949391817544,
    0.99307383382058443126,
    0.99374256529076161081,
    0.99435484019592089004,
    0.99491462980263887160,
    0.99542569570562280669,
    0.99589159546710020146,
    0.99631568850566092522,
    0.99670114219891260513,
    0.99705093816560912953,
    0.99736787869423543437,
    0.99765459328637785930,
    0.99791354528457702658,
    0.99814703855574842560,
    0.99835722420266376422,
    0.99854610727741271669,
    0.99871555347220884299,
    0.99886729576436380530,
    0.99900294099372885851,
    0.99912397635238982898,
    0.99923177576789885198,
    0.99932760616282995392,
    0.99941263357495257907,
    0.99948792912382330712,
    0.99955447481109673980,
    0.99961316914334685811,
    0.99966483256766467736,
    0.99971021271175103442,
    0.99974998942164885873,
    0.99978477959165116588,
    0.99981514178227306105,
    0.99984158062348206873,
    0.99986455100163506866,
    0.99988446202976620436,
    0.99990168080200286945,
    0.99991653593395122902,
    0.99992932089188418878,
    0.99994029711447937461,
    0.99994969693168930040,
    0.99995772628607798188,
    0.99996456726262607664,
    0.99997038043358927568,
    0.99997530702549203764,
    0.99997947091575155638,
    0.99998298046675659624,
    0.99998593020547479250,
    0.99998840235683319386,
    0.99999046823921387747,
    0.99999218953043364608,
    0.99999361941253889148,
    0.99999480360364887637,
    0.99999578128492849272,
    0.99999658593057078966,
    0.99999724604842617839,
    0.99999778583863522997,
    0.99999822577731137616,
    0.99999858313198448720,
    0.99999887241516193488,
    0.99999910578199579973,
    0.99999929337766848039,
    0.99999944363972887688,
    0.99999956356023190916,
    0.99999965891215931916,
    0.99999973444423295616,
    0.99999979404787605819,
    0.99999984089973594587,
    0.99999987758285510663,
    0.99999990618926848870,
    0.99999992840651414318,
    0.99999994559027295118,
    0.99999995882510149025,
    0.99999996897499024115,
    0.99999997672526713495,
    0.99999998261717346246,
    0.99999998707626477497,
    0.99999999043563278590,
    0.99999999295480449194,
    0.99999999483505072428,
    0.99999999623172700257,
    0.99999999726417374584,
    0.99999999802361943187,
    0.99999999857945803645,
    0.99999999898420990121,
    0.99999999927742199320,
    0.99999999948871830533,
    0.99999999964017294488,
    0.99999999974814637755,
    0.99999999982469852250,
    0.99999999987867018949,
    0.99999999991650604925,
    0.99999999994287733973,
    0.99999999996115031400,
    0.99999999997373657262,
    0.99999999998235350022,
    0.99999999998821670168,
    0.99999999999218131937,
    0.99999999999484516360,
    0.99999999999662349854,
    0.99999999999780292553,
    0.99999999999857995263,
    0.99999999999908841992,
    0.99999999999941886937,
    0.99999999999963213209,
    0.99999999999976879311,
    0.99999999999985573828,
    0.99999999999991065033,
    0.99999999999994507432
  ),
  # 9th layer abcissas: transformed 1/256, 3/256, ...
  c(
    0.0061358617516650178814,
    0.018406111784085708219,
    0.030671942524894121251,
    0.042930411515166562798,
    0.055178581893721422800,
    0.067413524625259240925,
    0.079632320717575212711,
    0.091832063424763596168,
    0.10400986043336450719,
    0.11616283602844130979,
    0.12828813323662109188,
    0.14038291594318142574,
    0.15244437098032358168,
    0.16446971018383541009,
    0.17645617241541602985,
    0.18840102554800904050,
    0.20030156841157097484,
    0.21215513269678687602,
    0.22395908481433495113,
    0.23571082770739694138,
    0.24740780261520986439,
    0.25904749078555782190,
    0.27062741513420931274,
    0.28214514184941562342,
    0.29359828193969905643,
    0.30498449272327566428,
    0.31630147925757544403,
    0.32754699570744326916,
    0.33871884665072584729,
    0.34981488832007334726,
    0.36083302977990869183,
    0.37177123403764251926,
    0.38262751908833713856,
    0.39339995889214810289,
    0.40408668428399697422,
    0.41468588381505312637,
    0.42519580452572571828,
    0.43561475264998895758,
    0.44594109425098417131,
    0.45617325578796071895,
    0.46630972461473414973,
    0.47634904940995395966,
    0.48628984053958459490,
    0.49613077035211174288,
    0.50587057340709122954,
    0.51550804663775979469,
    0.52504204944852545662,
    0.53447150374824992649,
    0.54379539392032643232,
    0.55301276673064321799,
    0.56212273117460576583,
    0.57112445826446934049,
    0.58001718075830766952,
    0.58880019283201338272,
    0.59747284969579116223,
    0.60603456715666535917,
    0.61448482112858007525,
    0.62282314709172137065,
    0.63104913950273833533,
    0.63916245115758225988,
    0.64716279250872108501,
    0.65504993093851973101,
    0.66282368999060585703,
    0.67048394856106513423,
    0.67803064005133030637,
    0.68546375148464423725,
    0.69278332258798889792,
    0.69998944484137992602,
    0.70708226049643010513,
    0.71406196156608497922,
    0.72092878878742995892,
    0.72768303055946082421,
    0.73432502185769861571,
    0.74085514312751567708,
    0.74727381915802220779,
    0.75358151793834225843,
    0.75977874949808480237,
    0.76586606473378950117,
    0.77184405422309820529,
    0.77771334702837225158,
    0.78347460949144239550,
    0.78912854402114290586,
    0.79467588787524411191,
    0.80011741193835868395,
    0.80545391949735630489,
    0.81068624501577930534,
    0.81581525290870844055,
    0.82084183631948343254,
    0.82576691589963733151,
    0.83059143859335730879,
    0.83531637642773731913,
    0.83994272531004029663,
    0.84447150383313930808,
    0.84890375209025850480,
    0.85324053050008591216,
    0.85748291864328119013,
    0.86163201411135260184,
    0.86568893136882864543,
    0.86965480062960124023,
    0.87353076674826910732,
    0.87731798812726213751,
    0.88101763564048018352,
    0.88463089157413292692,
    0.88815894858542133016,
    0.89160300867965575926,
    0.89496428220636121818,
    0.89824398687487633108,
    0.90144334678990979803,
    0.90456359150747608261,
    0.90760595511159111085,
    0.91057167531206880986,
    0.91346199256372042654,
    0.91627814920722077271,
    0.91902138863186886845,
    0.92169295446043492392,
    0.92429408975625122784,
    0.92682603625267131361,
    0.92929003360498976160,
    0.93168731866488417548,
    0.93401912477741124496,
    0.93628668110056037790,
    0.93849121194734114784,
    0.94063393615035475377,
    0.94271606644877481894,
    0.94473880889763915403,
    0.94670336229933156357,
    0.94861091765711136911,
    0.95046265765052803931,
    0.95225975613253913851,
    0.95400337764813170972,
    0.95569467697423017357,
    0.95733479868065782749,
    0.95892487671190404575,
    0.96046603398943528309,
    0.96195938203427494801,
    0.96340602060956510705,
    0.96480703738281178154,
    0.96616350760750527355,
    0.96747649382379748051,
    0.96874704557790949658,
    0.96997619915993492615,
    0.97116497735969721881,
    0.97231438924031294800,
    0.97342542992910726586,
    0.97449908042552274702,
    0.97553630742565845311,
    0.97653806316307228042,
    0.97750528526547646574,
    0.97843889662695349307,
    0.97933980529531753782,
    0.98020890437424498044,
    0.98104707193979638954,
    0.98185517097095169208,
    0.98263404929377998936,
    0.98338453953886561754,
    0.98410745911161256927,
    0.98480361017505026315,
    0.98547377964476485168,
    0.98611873919558177283,
    0.98673924527962705695,
    0.98733603915539697995,
    0.98790984692746798695,
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  #10th layer: transformed 1/512, 3/512, ...
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  )
)

Weights <- list(
  # 1st layer weights
  c(
    0.230022394514788685,
    0.00026620051375271690866,
    1.3581784274539090834e-12
  ),
  # 2nd layer weights
  c(
    0.96597657941230114801,
    0.018343166989927842087,
    2.1431204556943039358e-7
  ),
  # 3rd layer weights
  c(
    1.3896147592472563229,
    0.53107827542805397476,
    0.076385743570832304188,
    0.0029025177479013135936,
    0.000011983701363170720047,
    1.1631165814255782766e-9
  ),
  # 4th layer weights
  c(
    1.5232837186347052132,
    1.1934630258491569639,
    0.73743784836154784136,
    0.36046141846934367417,
    0.13742210773316772341,
    0.039175005493600779072,
    0.0077426010260642407123,
    0.00094994680428346871691,
    0.000062482559240744082891,
    1.8263320593710659699e-6,
    1.8687282268736410132e-8,
    4.9378538776631926964e-11
  ),
  #  5th layer weights
  c(
    1.5587733555333301451,
    1.466014426716965781,
    1.297475750424977998,
    1.0816349854900704074,
    0.85017285645662006895,
    0.63040513516474369106,
    0.44083323627385823707,
    0.290240679312454185,
    0.17932441211072829296,
    0.10343215422333290062,
    0.055289683742240583845,
    0.027133510013712003219,
    0.012083543599157953493,
    0.0048162981439284630173,
    0.0016908739981426396472,
    0.00051339382406790336017,
    0.00013205234125609974879,
    0.000028110164327940134749,
    4.8237182032615502124e-6,
    6.4777566035929719908e-7,
    6.5835185127183396672e-8,
    4.8760060974240625869e-9,
    2.5216347918530148572e-10,
    8.6759314149796046502e-12
  ),
  # 6th layer weights
  c(
    1.5677814313072218572,
    1.5438811161769592204,
    1.4972262225410362896,
    1.4300083548722996676,
    1.3452788847662516615,
    1.2467012074518577048,
    1.1382722433763053734,
    1.0240449331118114483,
    0.90787937915489531693,
    0.79324270082051671787,
    0.68306851634426375464,
    0.57967810308778764708,
    0.48475809121475539287,
    0.39938474152571713515,
    0.32408253961152890402,
    0.258904639514053516,
    0.20352399885860174519,
    0.15732620348436615027,
    0.11949741128869592428,
    0.089103139240941462841,
    0.065155533432536205042,
    0.046668208054846613644,
    0.032698732726609031113,
    0.022379471063648476483,
    0.014937835096050129696,
    0.0097072237393916892692,
    0.0061300376320830301252,
    0.0037542509774318343023,
    0.0022250827064786427022,
    0.0012733279447082382027,
    0.0007018595156842422708,
    0.00037166693621677760301,
    0.00018856442976700318572,
    0.000091390817490710122732,
    0.000042183183841757600604,
    0.000018481813599879217116,
    7.6595758525203162562e-6,
    2.9916615878138787094e-6,
    1.0968835125901264732e-6,
    3.7595411862360630091e-7,
    1.1992442782902770219e-7,
    3.5434777171421953043e-8,
    9.6498888961089633609e-9,
    2.4091773256475940779e-9,
    5.482835779709497755e-10,
    1.1306055347494680536e-10,
    2.0989335404511469109e-11,
    3.4841937670261059685e-12
  ),
  # 7th layer weights
  c(
    1.5700420292795931467,
    1.5640214037732320999,
    1.5520531698454121192,
    1.5342817381543034316,
    1.5109197230741697127,
    1.48224329788553807,
    1.4485862549613225916,
    1.4103329714462590129,
    1.3679105116808964881,
    1.3217801174437728579,
    1.2724283455378627082,
    1.2203581095793582207,
    1.1660798699324345766,
    1.1101031939653403796,
    1.0529288799552666556,
    0.99504180404613271514,
    0.93690461274566793366,
    0.87895234555278212039,
    0.82158803526696470334,
    0.7651792989089561367,
    0.71005590120546898385,
    0.65650824613162753076,
    0.60478673057840362158,
    0.55510187800363350959,
    0.5076251588319080997,
    0.4624903980553677613,
    0.41979566844501548066,
    0.37960556938665160999,
    0.3419537959230168323,
    0.30684590941791694932,
    0.27426222968906810637,
    0.24416077786983990868,
    0.21648020911729617038,
    0.19114268413342749532,
    0.16805663794826916233,
    0.14711941325785693248,
    0.12821973363120098675,
    0.11123999898874453035,
    0.096058391865189467849,
    0.082550788110701737654,
    0.070592469906866999352,
    0.060059642358636300319,
    0.05083075757257047107,
    0.042787652157725676034,
    0.035816505604196436523,
    0.029808628117310126969,
    0.024661087314753282511,
    0.020277183817500123926,
    0.016566786254247575375,
    0.013446536605285730674,
    0.010839937168255907211,
    0.0086773307495391815854,
    0.0068957859690660035329,
    0.0054388997976239984331,
    0.0042565295990178580165,
    0.0033044669940348302363,
    0.0025440657675291729678,
    0.0019418357759843675814,
    0.0014690143599429791058,
    0.0011011261134519383862,
    0.00081754101332469493115,
    0.00060103987991147422573,
    0.00043739495615911687786,
    0.00031497209186021200274,
    0.00022435965205008549104,
    0.00015802788400701191949,
    0.00011002112846666697224,
    0.000075683996586201477788,
    0.000051421497447658802092,
    0.0000344921247593431977,
    0.000022832118109036146591,
    0.000014908514031870608449,
    9.5981941283784710776e-6,
    6.0899100320949039256e-6,
    3.8061983264644899045e-6,
    2.3421667208528096843e-6,
    1.4183067155493917523e-6,
    8.4473756384859863469e-7,
    4.9458288702754198508e-7,
    2.8449923659159806339e-7,
    1.6069394579076224911e-7,
    8.9071395140242387124e-8,
    4.8420950198072369669e-8,
    2.579956822953589238e-8,
    1.3464645522302038796e-8,
    6.8784610955899001111e-9,
    3.4371856744650090511e-9,
    1.6788897682161906807e-9,
    8.0099784479729665356e-10,
    3.7299501843052790038e-10,
    1.6939457789411646876e-10,
    7.4967397573818224522e-11,
    3.230446433325236576e-11,
    1.3542512912336274432e-11,
    5.5182369468174885821e-12,
    2.1835922099233609052e-12
  ),
  # 8th layer weigths
  c(
    1.5706077165382752221,
    1.5690996953516691278,
    1.5660882389174613672,
    1.5615824934918106191,
    1.5555961146316604222,
    1.5481471912355573327,
    1.5392581453118818324,
    1.5289556083545807159,
    1.5172702754050546803,
    1.5042367380636772129,
    1.4898932978832971219,
    1.4742817617280797281,
    1.4574472208125486663,
    1.4394378152464069775,
    1.4203044859996911837,
    1.4001007162694446514,
    1.3788822642731375177,
    1.3567068895156054675,
    1.3336340745757561354,
    1.3097247444374397383,
    1.2850409853467272312,
    1.2596457651166706021,
    1.2336026567219467108,
    1.2069755669313082254,
    1.1798284716173337423,
    1.1522251592625474295,
    1.1242289840506032581,
    1.0959026297929722120,
    1.0673078857975038741,
    1.0385054356373923292,
    1.0095546596294298182,
    0.98051345168085502518,
    0.95143805101635270871,
    0.92238288915245514551,
    0.89340045234719599827,
    0.86454115961966899850,
    0.83585325630826713063,
    0.80738272301876303826,
    0.77917319970479798076,
    0.75126592452435685914,
    0.72369968702683029320,
    0.69651079514654688482,
    0.66973305541029099784,
    0.64339776570825285563,
    0.61753371992990889984,
    0.59216722372820694936,
    0.56732212064673871784,
    0.54301982782484286720,
    0.51927938048424633085,
    0.49611748439731621395,
    0.47354857554061400458,
    0.45158488614754491438,
    0.43023651638978897817,
    0.40951151093819363437,
    0.38941593967921202783,
    0.36995398189211387219,
    0.35112801322442524717,
    0.33293869483774779538,
    0.31538506413267813526,
    0.29846462649944498395,
    0.28217344757959610491,
    0.26650624556313516142,
    0.25145648308451039820,
    0.23701645831941898916,
    0.22317739492218458777,
    0.20992953048020753663,
    0.19726220319743719884,
    0.18516393655277551537,
    0.17362252171163130317,
    0.16262509749938432420,
    0.15215822777419972033,
    0.14220797606340183124,
    0.13275997735244552638,
    0.12379950693841296101,
    0.11531154628093733739,
    0.10728084580255643429,
    0.099691984607788577667,
    0.092529427105778463901,
    0.085777576535268189773,
    0.079420825403008155143,
    0.073443602857638774779,
    0.067830419030657966461,
    0.062565906384455108313,
    0.057634858114654726990,
    0.053022263660287178655,
    0.048713341380701431455,
    0.044693568462765533523,
    0.040948708125867302498,
    0.037464834195628972796,
    0.034228353120175696600,
    0.031226023505331741095,
    0.028444973247334237421,
    0.025872714343617644485,
    0.023497155463988527331,
    0.021306612366126070466,
    0.019289816240845601468,
    0.017435920073977461260,
    0.015734503113059796502,
    0.014175573528330460202,
    0.012749569358731162696,
    0.011447357834799756253,
    0.010260233171410768905,
    0.0091799129243109016820,
    0.0081985330052611999147,
    0.0073086414513132480273,
    0.0065031910442825794570,
    0.0057755308768065491406,
    0.0051193969614537818670,
    0.0045289019791562891247,
    0.0039985242627335310487,
    0.0035230961104429863210,
    0.0030977915233008206567,
    0.0027181134583502264180,
    0.0023798806881004382465,
    0.0020792143540086661490,
    0.0018125242991288642651,
    0.0015764952619105560467,
    0.0013680730096097039552,
    0.0011844504858902772191,
    0.0010230540429745410946,
    0.00088152982417297002263,
    0.00075773035782735921074,
    0.00064970141867429037385,
    0.00055566920742578558188,
    0.00047402789401816719609,
    0.00040332756454954092911,
    0.00034226260646297688095,
    0.00028966056108877174343,
    0.00024447146728689162442,
    0.00020575771467998818629,
    0.00017268441988592922811,
    0.00014451033429094586468,
    0.00012057928729056996115,
    0.00010031216460112420171,
    0.000083199417240036480655,
    0.000068794093113496376995,
    0.000056705379853932877470,
    0.000046592644630494618702,
    0.000038159954120245760316,
    0.000031151055677448352881,
    0.000025344798968850110020,
    0.000020550975944934244592,
    0.000016606555976508335934,
    0.000013372292284532372637,
    0.000010729675406852340659,
    8.5782093537079082475e-6,
    6.8329862774218506793e-6,
    5.4225358918240331875e-6,
    4.2869264939998226801e-6,
    3.3760952348055109687e-6,
    2.6483862254043410593e-6,
    2.0692761257364670911e-6,
    1.6102680094507650587e-6,
    1.2479355121177451928e-6,
    9.6310052117659252623e-7,
    7.4012893490908614245e-7,
    5.6633028402050775175e-7,
    4.3144825587165380567e-7,
    3.2723037330517558940e-7,
    2.4706624511249700701e-7,
    1.8568491370025132364e-7,
    1.3890286996035952957e-7,
    1.0341528040745607125e-7,
    7.6623873974817584699e-8,
    5.6495763871670621475e-8,
    4.1448233558505383940e-8,
    3.0255196464899467189e-8,
    2.1971648917089349871e-8,
    1.5872978090968232626e-8,
    1.1406465554850482081e-8,
    8.1527464828576537675e-9,
    5.7953495730966064130e-9,
    4.0967579139685198005e-9,
    2.8797013464471104655e-9,
    2.0126210218867172874e-9,
    1.3984414312565442026e-9,
    9.6594851858099300536e-10,
    6.6320863470162099804e-10,
    4.5257576104153821952e-10,
    3.0692702078723328679e-10,
    2.0684203539029217545e-10,
    1.3850287525834145109e-10,
    9.2140564226518884083e-11,
    6.0893387064380670509e-11,
    3.9973389519930269589e-11,
    2.6061960502805293348e-11,
    1.6874519343915025229e-11,
    1.0849161834337120075e-11,
    6.9255280152681382343e-12,
    4.3888651899779304013e-12,
    2.7608587671398283608e-12,
    1.7237644036042717645e-12
  ),
  # 9th layer weights
  c(
    1.5707491719879868670,
    1.5703719873556768426,
    1.5696179050632321482,
    1.5684874986536598326,
    1.5669816274390033181,
    1.5651014352998765110,
    1.5628483490889917265,
    1.5602240766422204348,
    1.5572306044015889561,
    1.5538701946554600872,
    1.5501453824019834955,
    1.5460589718427099541,
    1.5416140325140545443,
    1.5368138950650593777,
    1.5316621466906448410,
    1.5261626262302476185,
    1.5203194189424217018,
    1.5141368509666232913,
    1.5076194834840101126,
    1.5007721065896585393,
    1.4935997328891365303,
    1.4861075908328653880,
    1.4783011178021575554,
    1.4701859529612300633,
    1.4617679298898629774,
    1.4530530690116986020,
    1.4440475698334597700,
    1.4347578030106039672,
    1.4251903022551241386,
    1.4153517561013568268,
    1.4052489995457639699,
    1.3948890055767165918,
    1.3842788766103272462,
    1.3734258358483540805,
    1.3623372185741335854,
    1.3510204634023924088,
    1.3394831034986421479,
    1.3277327577836759685,
    1.3157771221384635807,
    1.3036239606244829463,
    1.2912810967342346503,
    1.2787564046863597594,
    1.2660578007794259311,
    1.2531932348180613123,
    1.2401706816247032241,
    1.2269981326497906832,
    1.2136835876927683985,
    1.2002350467457870035,
    1.1866605019714819433,
    1.1729679298256936659,
    1.1591652833354566018,
    1.1452604845420359018,
    1.1312614171182310504,
    1.1171759191685963111,
    1.1030117762206514528,
    1.0887767144145743283,
    1.0744783938982815087,
    1.0601244024342162190,
    1.0457222492235760467,
    1.0312793589531280908,
    1.0168030660691780503,
    1.0023006092826838472,
    0.98777912630893529415,
    0.97324564884466050503,
    0.95870709778486862046,
    0.94417027868119827023,
    0.92964187744301325924,
    0.91512845628197237358,
    0.90063644990030001346,
    0.88617216192249953086,
    0.87174176156978255715,
    0.85735128057603603424,
    0.84300661034371480914,
    0.82871349933763212692,
    0.81447755071422368377,
    0.80030422018348351975,
    0.78619881410041229658,
    0.77216648778248069519,
    0.75821224404929297812,
    0.74434093198033831648,
    0.73055724588644032821,
    0.71686572449025839510,
    0.70327075031095763330,
    0.68977654924794773605,
    0.67638719035839408023,
    0.66310658582302722283,
    0.64993849109461889452,
    0.63688650522335345611,
    0.62395407135320311049,
    0.61114447738331250341,
    0.59846085678831321130,
    0.58590618959142047847,
    0.57348330348411287398,
    0.56119487508615970949,
    0.54904343133974048642,
    0.53703135103139470026,
    0.52516086643554837842,
    0.51343406507338511096,
    0.50185289158086338400,
    0.49041914967972807121,
    0.47913450424542130009,
    0.46800048346586590713,
    0.45701848108517265006,
    0.44618975872640957844,
    0.43551544828766780536,
    0.42499655440576170783,
    0.41463395698201265702,
    0.40442841376468309748,
    0.39438056298275152591,
    0.38449092602584804738,
    0.37475991016530410924,
    0.36518781131140814498,
    0.35577481680210063614,
    0.34652100821848697149,
    0.33742636422269392132,
    0.32849076341374504347,
    0.31971398719728140973,
    0.31109572266510622162,
    0.30263556548068473010,
    0.29433302276688396389,
    0.28618751599238970640,
    0.27819838385339056653,
    0.27036488514727050929,
    0.26268620163520151706,
    0.25516144089067683242,
    0.24778963913117220092,
    0.24056976403026742128,
    0.23350071750770307761,
    0.22658133849498734824,
    0.21981040567430505739,
    0.21318664018861547385,
    0.20670870832095660306,
    0.20037522414110171927,
    0.19418475211783851608,
    0.18813580969526240792,
    0.18222686983159309843,
    0.17645636349913746971,
    0.17082268214413207645,
    0.16532418010530500733,
    0.15995917699009956997,
    0.15472596000760114762,
    0.14962278625730366024,
    0.14464788497294334691,
    0.13979945972071508801,
    0.13507569055127023365,
    0.13047473610497493816,
    0.12599473566998436676,
    0.12163381119276089656,
    0.11739006924073364439,
    0.11326160291686239001,
    0.10924649372593130391,
    0.10534281339245691773,
    0.10154862563015058282,
    0.097861987862928342230,
    0.094280952897510792686,
    0.090803570547702237912,
    0.087427889210482337848,
    0.084151957394084648378,
    0.080973825198275032243,
    0.077891545747079015548,
    0.074903176574240877821,
    0.072006780961728709867,
    0.069200429231628965648,
    0.066482199991801284855,
    0.063850181335689683677,
    0.061302471996709713442,
    0.058837182457652979731,
    0.056452436015570605966,
    0.054146369802615920783,
    0.051917135763343950906,
    0.049762901588981311018,
    0.047681851609194896719,
    0.045672187641901500150,
    0.043732129801673170945,
    0.041859917267304924762,
    0.040053809009122340888,
    0.038312084476616768333,
    0.036633044247005351234,
    0.035015010635321959873,
    0.033456328266653439147,
    0.031955364611143423500,
    0.030510510482393373013,
    0.029120180499897511822,
    0.027782813516155044781,
    0.026496873009109434199,
    0.025260847440570673572,
    0.024073250581282433026,
    0.022932621803301700282,
    0.021837526340364125707,
    0.020786555516913719867,
    0.019778326946480862353,
    0.018811484700097772288,
    0.017884699445445670647,
    0.016996668557432835032,
    0.016146116200907607620,
    0.015331793386215161806,
    0.014552477998311454233,
    0.013806974800152274673,
    0.013094115411079641920,
    0.012412758260931961771,
    0.011761788520608343053,
    0.011140118009821236899,
    0.010546685082775098308,
    0.0099804544925120407716,
    0.0094404172346684363446,
    0.0089255903713890752917,
    0.0084350168361478109482,
    0.0079677652202255452721,
    0.0075229295415979270042,
    0.0070996289969862053723,
    0.0066970076978252759670,
    0.0063142343909030402249,
    0.0059505021644247449235,
    0.0056050281402549431807,
    0.0052770531530880947233,
    0.0049658414172965731218,
    0.0046706801822019453601,
    0.0043908793765118104475,
    0.0041257712426602067776,
    0.0038747099617846028287,
    0.0036370712700667552538,
    0.0034122520671582377174,
    0.0031996700174042010132,
    0.0029987631445709109736,
    0.0028089894207738193637,
    0.0026298263502933513555,
    0.0024607705489552414753,
    0.0023013373197411215180,
    0.0021510602252831654917,
    0.0020094906578839381334,
    0.0018761974076891881384,
    0.0017507662296271914383,
    0.0016327994097134032928,
    0.0015219153313036434549,
    0.0014177480418628420560,
    0.0013199468207995439703,
    0.0012281757488989378826,
    0.0011421132798691774485,
    0.0010614518144972326850,
    0.00098589727789148932638,
    0.00091516870026884378211,
    0.00084899780172416501201,
    0.00078712858139975734579,
    0.00072931691145190687140,
    0.00067533013619077670724,
    0.00062494667674888259701,
    0.00057795564161218005883,
    0.00053415644332647867146,
    0.00049335842167051929336,
    0.00045538047356565755744,
    0.00042005068997074326257,
    0.00038720599998952137839,
    0.00035669182239675682166,
    0.00032836172476835170079,
    0.00030207709038002909555,
    0.00027770679301874915105,
    0.00025512687983094738985,
    0.00023422026231198611745,
    0.00021487641552193022335,
    0.00019699108559393917236,
    0.00018046600558324598413,
    0.00016520861968690764912,
    0.00015113181584729341827,
    0.00013815366673565885884,
    0.00012619717909616295649,
    0.00011519005141534857511,
    0.00010506443986744615644,
    0.000095756732471896669582,
    0.000087207331386239617687,
    0.000079360443244989556631,
    0.000072163877443341326837,
    0.000065568852253508373584,
    0.000059529808651215570139,
    0.000054004231720340450412,
    0.000048952479494924501614,
    0.000044337619089756241767,
    0.000040125269963454656640,
    0.000036283454151447103274,
    0.000032782453300429480882,
    0.000029594672330805491693,
    0.000026694509549211148607,
    0.000024058233029523270026,
    0.000021663863077707567906,
    0.000019491060593462360815,
    0.000017521021139835606671,
    0.000015736374530812084255,
    0.000014121089746259110537,
    0.000012660384983556994662,
    0.000011340642655697374147,
    0.000010149329146580734980,
    9.0749191356552313384e-6,
    8.1068243058833635771e-6,
    7.2353262512717953341e-6,
    6.4515134028230726030e-6,
    5.7472217947367057478e-6,
    5.1149794959715616576e-6,
    4.5479545358526086843e-6,
    4.0399061562339582625e-6,
    3.5851392267885450747e-6,
    3.1784616642549782756e-6,
    2.8151447009070830738e-6,
    2.4908858520952395048e-6,
    2.2017744374155040559e-6,
    1.9442595148683221211e-6,
    1.7151200922500854451e-6,
    1.5114374849556247656e-6,
    1.3305696943368536786e-6,
    1.1701276857422685078e-6,
    1.0279534503351376288e-6,
    9.0209973973748510226e-7,
    7.9081136745612998086e-7,
    6.9250797590107209327e-7,
    6.0576817259164900077e-7,
    5.2931494384959360264e-7,
    4.6200225888908339552e-7,
    4.0280278172197425763e-7,
    3.5079661269270778067e-7,
    3.0516098573406334675e-7,
    2.6516085158528664228e-7,
    2.3014028123251661035e-7,
    1.9951462771321869584e-7,
    1.7276338816784555664e-7,
    1.4942371162043472222e-7,
    1.2908450142342646044e-7,
    1.1138106460956361386e-7,
    9.5990263554991129462e-8,
    8.2626128372976771067e-8,
    7.1035891328037911616e-8,
    6.0996407287279811489e-8,
    5.2310926811556165406e-8,
    4.4806190936256643373e-8,
    3.8329819003135151088e-8,
    3.2747963084014261628e-8,
    2.7943204588154729649e-8,
    2.3812670571556689663e-8,
    2.0266349072681384170e-8,
    1.7225584489453884533e-8,
    1.4621735591476706307e-8,
    1.2394980233805252414e-8,
    1.0493252209132055506e-8,
    8.8712969485578800659e-9,
    7.4898339620602365150e-9,
    6.3148150030487657305e-9,
    5.3167679517209510567e-9,
    4.4702173439306598649e-9,
    3.7531733304974860033e-9,
    3.1466816407521673072e-9,
    2.6344278479469008343e-9,
    2.2023898971398184530e-9,
    1.8385334623264711836e-9,
    1.5325452528211614182e-9,
    1.2755998929109107770e-9,
    1.0601564571736536696e-9,
    8.7978115996081491351e-10,
    7.2899307461385486313e-10,
    6.0313009906543121763e-10,
    4.9823269244974207011e-10,
    4.1094318492683283837e-10,
    3.3841871266064447048e-10,
    2.7825605416745889022e-10,
    2.2842684530022966801e-10,
    1.8722183003303799710e-10,
    1.5320296488988400140e-10,
    1.2516233811367523428e-10,
    1.0208699215038266985e-10,
    8.3128851257354343301e-11,
    6.7579056439360266466e-11,
    5.4846098761534411501e-11,
    4.4437220566829488131e-11,
    3.5942623316732204732e-11,
    2.9022081662082772449e-11,
    2.3393616830994292629e-11,
    1.8823929305161791659e-11,
    1.5120331779356425993e-11,
    1.2123959225436894588e-11,
    9.7040641098719717837e-12,
    7.7532319801952814800e-12,
    6.1833762231947121145e-12,
    4.9223912374418986849e-12,
    3.9113609401922142931e-12,
    3.1022347868423332255e-12,
    2.4558966249420161528e-12,
    1.9405630045850719514e-12,
    1.5304572620310973620e-12
  ),
  # 10th layer weights
  c(
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    1.5706902305819748303,
    1.5705016337811934634,
    1.5702187834268734376,
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