// @(#)root/mlp:$Id$
// Author: Christophe.Delaere@cern.ch   20/07/03

/*************************************************************************
 * Copyright (C) 1995-2003, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

///////////////////////////////////////////////////////////////////////////
//
// TNeuron
//
// This class decribes an elementary neuron, which is the basic
// element for a Neural Network.
// A network is built connecting neurons by synapses.
// There are different types of neurons: linear (a+bx),
// sigmoid (1/(1+exp(-x)), tanh or gaussian.
// An external function can also be used, together with its derivative.
// In a Multi Layer Perceptron, the input layer is made of
// inactive neurons (returning the normalized input) and output neurons
// are linear. Hidden neurons may be anything, the default being sigmoids.
//
// This implementation contains several methods to compute the value,
// the derivative, the DeDw, ...
// Values are stored in local buffers. The SetNewEvent() method is
// there to inform buffered values are outdated.
//
///////////////////////////////////////////////////////////////////////////

#include "TSynapse.h"
#include "TNeuron.h"
#include "TTree.h"
#include "TTreeFormula.h"
#include "TFormula.h"
#include "TBranch.h"
#include "TCanvas.h"
#include "TROOT.h"
#include "TH1D.h"
#include "TRegexp.h"
#include "TMath.h"
#include "Riostream.h"

ClassImp(TNeuron)

//______________________________________________________________________________
TNeuron::TNeuron(TNeuron::ENeuronType type /*= kSigmoid*/,
                 const char* name /*= ""*/, const char* title /*= ""*/,
                 const char* extF /*= ""*/, const char* extD  /*= ""*/ )
   :TNamed(name, title)
{
   // Usual constructor
   fpre.SetOwner(false);
   fpost.SetOwner(false);
   flayer.SetOwner(false);
   fWeight = 0.;
   fNorm[0] = 1.;
   fNorm[1] = 0.;
   fType = type;
   fNewInput = true;
   fNewValue = true;
   fNewDeriv = true;
   fNewDeDw = true;
   fFormula = 0;
   fDeDw  = 0;
   fDEDw  = 0;
   fValue = 0;
   fExtF  = 0;
   fExtD  = 0;
   fIndex = 0;
   fDerivative = 0;
   fInput = 0;
   if(fType==kExternal) {
      fExtF = (TFormula*)gROOT->FindObject(extF);
      fExtD = (TFormula*)gROOT->FindObject(extD);
   }
}

//______________________________________________________________________________
Double_t TNeuron::Sigmoid(Double_t x) const
{
   // The Sigmoid.
   // Fast computation of the values of the sigmoid function.
   // Uses values of the function up  to the seventh order
   // tabulated at 700 points.
   // Values were computed in long double precision (16 bytes,
   // precision to about 37 digits) on a hp computer.
   // Some values were checked with Mathematica.
   // Result should be correct to ~ 15 digits (about double
   // precision)
   //
   // From the mlpfit package (J.Schwindling   20-Jul-1999)

   static Double_t sigval[7000] = {
   -3.500000e+01, 6.30511676014698530e-16, 6.30511676014698130e-16, 3.15255838007348670e-16, 1.05085279335782620e-16, 2.62713198339455210e-17, 5.25426396678905190e-18, 8.75710661131491060e-19, 1.25101523018779380e-19, 1.56376903773461590e-20,
   -3.490000e+01, 6.96823167838580650e-16, 6.96823167838580160e-16, 3.48411583919289640e-16, 1.16137194639762880e-16, 2.90342986599405540e-17, 5.80685973198804710e-18, 9.67809955331319670e-19, 1.38258565047325200e-19, 1.72823206309141090e-20,
   -3.480000e+01, 7.70108700136546340e-16, 7.70108700136545750e-16, 3.85054350068272280e-16, 1.28351450022757030e-16, 3.20878625056890590e-17, 6.41757250113773230e-18, 1.06959541685626250e-18, 1.52799345265172810e-19, 1.90999181581447200e-20,
   -3.470000e+01, 8.51101739147945470e-16, 8.51101739147944780e-16, 4.25550869573971650e-16, 1.41850289857990070e-16, 3.54625724644972780e-17, 7.09251449289935940e-18, 1.18208574881652770e-18, 1.68869392688066160e-19, 2.11086740860059710e-20,
   -3.460000e+01, 9.40612890429916560e-16, 9.40612890429915770e-16, 4.70306445214957000e-16, 1.56768815071651720e-16, 3.91922037679126390e-17, 7.83844075358240950e-18, 1.30640679226369560e-18, 1.86629541751945290e-19, 2.33286927189903510e-20,
   -3.450000e+01, 1.03953801167022100e-15, 1.03953801167021980e-15, 5.19769005835108810e-16, 1.73256335278368870e-16, 4.33140838195918600e-17, 8.66281676391822790e-18, 1.44380279398632340e-18, 2.06257541998032470e-19, 2.57821927497506280e-20,
   -3.440000e+01, 1.14886717873211280e-15, 1.14886717873211140e-15, 5.74433589366054410e-16, 1.91477863122017240e-16, 4.78694657805038730e-17, 9.57389315610059860e-18, 1.59564885935004120e-18, 2.27949837049989100e-19, 2.84937296312444480e-20,
   -3.430000e+01, 1.26969459466634980e-15, 1.26969459466634820e-15, 6.34847297333172530e-16, 2.11615765777723080e-16, 5.29039414444302330e-17, 1.05807882888858320e-17, 1.76346471481423380e-18, 2.51923530687727210e-19, 3.14904413359607800e-20,
   -3.420000e+01, 1.40322954086308920e-15, 1.40322954086308720e-15, 7.01614770431541630e-16, 2.33871590143845880e-16, 5.84678975359608160e-17, 1.16935795071919010e-17, 1.94892991786522940e-18, 2.78418559695007730e-19, 3.48023199618697190e-20,
   -3.410000e+01, 1.55080847994653150e-15, 1.55080847994652920e-15, 7.75404239973262210e-16, 2.58468079991085760e-16, 6.46170199977706390e-17, 1.29234039995538080e-17, 2.15390066659219480e-18, 3.07700095227425790e-19, 3.84625119034205930e-20,
   -3.400000e+01, 1.71390843154201000e-15, 1.71390843154200710e-15, 8.56954215771000580e-16, 2.85651405256998220e-16, 7.14128513142485820e-17, 1.42825702628493230e-17, 2.38042837714142370e-18, 3.40061196734451790e-19, 4.25076495917971450e-20,
   -3.390000e+01, 1.89416175478487890e-15, 1.89416175478487530e-15, 9.47080877392433920e-16, 3.15693625797475610e-16, 7.89234064493677060e-17, 1.57846812898730630e-17, 2.63078021497868450e-18, 3.75825744996909330e-19, 4.69782181246022790e-20,
   -3.380000e+01, 2.09337248551938710e-15, 2.09337248551938240e-15, 1.04668624275968680e-15, 3.48895414253226000e-16, 8.72238535633050470e-17, 1.74447707126604240e-17, 2.90746178544320960e-18, 4.15351683634688560e-19, 5.19189604543221620e-20,
   -3.370000e+01, 2.31353439169574760e-15, 2.31353439169574210e-15, 1.15676719584786570e-15, 3.85589065282618330e-16, 9.63972663206527960e-17, 1.92794532641298470e-17, 3.21324221068806990e-18, 4.59034601526799130e-19, 5.73793251908329070e-20,
   -3.360000e+01, 2.55685092766997700e-15, 2.55685092766997070e-15, 1.27842546383497880e-15, 4.26141821278321860e-16, 1.06535455319578300e-16, 2.13070910639147860e-17, 3.55118184398550770e-18, 5.07311691997846610e-19, 6.34139614997100740e-20,
   -3.350000e+01, 2.82575728711560320e-15, 2.82575728711559530e-15, 1.41287864355778950e-15, 4.70959547852591190e-16, 1.17739886963145140e-16, 2.35479773926279630e-17, 3.92466289877097270e-18, 5.60666128395751820e-19, 7.00832660494436280e-20,
   -3.340000e+01, 3.12294477526050570e-15, 3.12294477526049620e-15, 1.56147238763023820e-15, 5.20490795876739570e-16, 1.30122698969181640e-16, 2.60245397938350280e-17, 4.33742329897207160e-18, 6.19631899853029210e-19, 7.74539874815976920e-20,
   -3.330000e+01, 3.45138774437420440e-15, 3.45138774437419260e-15, 1.72569387218708450e-15, 5.75231290729020130e-16, 1.43807822682251060e-16, 2.87615645364486300e-17, 4.79359408940757550e-18, 6.84799155629502340e-19, 8.55998944536499720e-20,
   -3.320000e+01, 3.81437336208505550e-15, 3.81437336208504050e-15, 1.90718668104250570e-15, 6.35728893680825560e-16, 1.58932223420201530e-16, 3.17864446840383680e-17, 5.29774078067241470e-18, 7.56820111524445930e-19, 9.46025139405095430e-20,
   -3.310000e+01, 4.21553451045883940e-15, 4.21553451045882130e-15, 2.10776725522939290e-15, 7.02589085076452470e-16, 1.75647271269107180e-16, 3.51294542538190670e-17, 5.85490904230238850e-18, 8.36415577471544070e-19, 1.04551947183886600e-19,
   -3.300000e+01, 4.65888614510337560e-15, 4.65888614510335430e-15, 2.32944307255165550e-15, 7.76481024183870600e-16, 1.94120256045960400e-16, 3.88240512091891920e-17, 6.47067520153056710e-18, 9.24382171646948210e-19, 1.15547771455799630e-19,
   -3.290000e+01, 5.14886547819381740e-15, 5.14886547819379060e-15, 2.57443273909686890e-15, 8.58144246365605200e-16, 2.14536061591392470e-16, 4.29072123182749640e-17, 7.15120205304464960e-18, 1.02160029329175600e-18, 1.27700036661385360e-19,
   -3.280000e+01, 5.69037638758347510e-15, 5.69037638758344200e-15, 2.84518819379168870e-15, 9.48396064597207920e-16, 2.37099016149291180e-16, 4.74198032298539250e-17, 7.90330053830754850e-18, 1.12904293404352430e-18, 1.41130366755337750e-19,
   -3.270000e+01, 6.28883849646157640e-15, 6.28883849646153690e-15, 3.14441924823072900e-15, 1.04813974941021660e-15, 2.62034937352540980e-16, 5.24069874705029230e-17, 8.73449791174873020e-18, 1.24778541596360200e-18, 1.55973176995324680e-19,
   -3.260000e+01, 6.95024141476392120e-15, 6.95024141476387310e-15, 3.47512070738188800e-15, 1.15837356912726370e-15, 2.89593392281799860e-16, 5.79186784563535330e-17, 9.65311307605677590e-18, 1.37901615372178300e-18, 1.72377019215069530e-19,
   -3.250000e+01, 7.68120468520203540e-15, 7.68120468520197700e-15, 3.84060234260092930e-15, 1.28020078086693710e-15, 3.20050195216714590e-16, 6.40100390433350520e-17, 1.06683398405532210e-17, 1.52404854864971080e-18, 1.90506068581026560e-19,
   -3.240000e+01, 8.48904403387170610e-15, 8.48904403387163350e-15, 4.24452201693574420e-15, 1.41484067231186670e-15, 3.53710168077942670e-16, 7.07420336155789230e-17, 1.17903389359266190e-17, 1.68433413370288750e-18, 2.10541766712632160e-19,
   -3.230000e+01, 9.38184458849859670e-15, 9.38184458849850840e-15, 4.69092229424916660e-15, 1.56364076474966340e-15, 3.90910191187386470e-16, 7.81820382374655680e-17, 1.30303397062403500e-17, 1.86147710089036070e-18, 2.32684637611015680e-19,
   -3.220000e+01, 1.03685417971139710e-14, 1.03685417971138640e-14, 5.18427089855682470e-15, 1.72809029951886980e-15, 4.32022574879681600e-16, 8.64045149759219900e-17, 1.44007524959822210e-17, 2.05725035656752340e-18, 2.57156294570599160e-19,
   -3.210000e+01, 1.14590108570221770e-14, 1.14590108570220460e-14, 5.72950542851089130e-15, 1.90983514283687630e-15, 4.77458785709175300e-16, 9.54917571418175490e-17, 1.59152928569637550e-17, 2.27361326527886920e-18, 2.84201658159441780e-19,
   -3.200000e+01, 1.26641655490940160e-14, 1.26641655490938570e-14, 6.33208277454676750e-15, 2.11069425818214890e-15, 5.27673564545483790e-16, 1.05534712909075370e-16, 1.75891188181721000e-17, 2.51273125973683490e-18, 3.14091407466595250e-19,
   -3.190000e+01, 1.39960674665542220e-14, 1.39960674665540250e-14, 6.99803373327681690e-15, 2.33267791109214150e-15, 5.83169477772970090e-16, 1.16633895554567910e-16, 1.94389825924192790e-17, 2.77699751320026640e-18, 3.47124689149411470e-19,
   -3.180000e+01, 1.54680467314603800e-14, 1.54680467314601400e-14, 7.73402336572983000e-15, 2.57800778857645030e-15, 6.44501947144032790e-16, 1.28900389428774660e-16, 2.14833982381184800e-17, 3.06905689115674430e-18, 3.83632111393833500e-19,
   -3.170000e+01, 1.70948354070450830e-14, 1.70948354070447900e-14, 8.54741770352210300e-15, 2.84913923450717270e-15, 7.12284808626695750e-16, 1.42456961725300190e-16, 2.37428269542037130e-17, 3.39183242202539070e-18, 4.23979052752246120e-19,
   -3.160000e+01, 1.88927149411560280e-14, 1.88927149411556710e-14, 9.44635747057747730e-15, 3.14878582352558780e-15, 7.87196455881277930e-16, 1.57439291176208010e-16, 2.62398818626854730e-17, 3.74855455180767740e-18, 4.68569318974826550e-19,
   -3.150000e+01, 2.08796791164589010e-14, 2.08796791164584650e-14, 1.04398395582287960e-14, 3.47994651940930800e-15, 8.69986629852181640e-16, 1.73997325970378200e-16, 2.89995543283769920e-17, 4.14279347547689150e-18, 5.17849184433227460e-19,
   -3.140000e+01, 2.30756141382617880e-14, 2.30756141382612580e-14, 1.15378070691300960e-14, 3.84593568970967660e-15, 9.61483922427241660e-16, 1.92296784485377340e-16, 3.20494640808725600e-17, 4.57849486868931840e-18, 5.72311858584474310e-19,
   -3.130000e+01, 2.55024976623420620e-14, 2.55024976623414120e-14, 1.27512488311700560e-14, 4.25041627705625120e-15, 1.06260406926384610e-15, 2.12520813852682500e-16, 3.54201356420848460e-17, 5.06001937743243370e-18, 6.32502422176989520e-19,
   -3.120000e+01, 2.81846187547126010e-14, 2.81846187547118060e-14, 1.40923093773551080e-14, 4.69743645911783960e-15, 1.17435911477919500e-15, 2.34871822955733110e-16, 3.91453038259202140e-17, 5.59218626083565740e-18, 6.99023282601935360e-19,
   -3.110000e+01, 3.11488209847576830e-14, 3.11488209847567110e-14, 1.55744104923773830e-14, 5.19147016412514760e-15, 1.29786754103096350e-15, 2.59573508206063350e-16, 4.32622513676341070e-17, 6.18032162393540810e-18, 7.72540202988845880e-19,
   -3.100000e+01, 3.44247710846985810e-14, 3.44247710846973950e-14, 1.72123855423475110e-14, 5.73746184744838010e-15, 1.43436546186170000e-15, 2.86873092372182000e-16, 4.78121820619776690e-17, 6.83031172312461810e-18, 8.53788965386815150e-19,
   -3.090000e+01, 3.80452558642202530e-14, 3.80452558642188080e-14, 1.90226279321079550e-14, 6.34087597736835340e-15, 1.58521899434160580e-15, 3.17043798868128200e-16, 5.28406331446237000e-17, 7.54866187778500530e-18, 9.43582734718530590e-19,
   -3.080000e+01, 4.20465103518829610e-14, 4.20465103518811940e-14, 2.10232551759388270e-14, 7.00775172531176340e-15, 1.75193793132735160e-15, 3.50387586265234630e-16, 5.83979310441271980e-17, 8.34256157771000690e-18, 1.04282019720813850e-18,
   -3.070000e+01, 4.64685804474675720e-14, 4.64685804474654130e-14, 2.32342902237305450e-14, 7.74476340790874180e-15, 1.93619085197646560e-15, 3.87238170395005280e-16, 6.45396950657382470e-17, 9.21995643793518570e-18, 1.15249455473504320e-18,
   -3.060000e+01, 5.13557237147994640e-14, 5.13557237147968260e-14, 2.56778618573957750e-14, 8.55928728579683310e-15, 2.13982182144832910e-15, 4.27964364289314180e-16, 7.13273940481018150e-17, 1.01896277211239110e-17, 1.27370346513211610e-18,
   -3.050000e+01, 5.67568523263239960e-14, 5.67568523263207780e-14, 2.83784261631571670e-14, 9.45947538771690840e-15, 2.36486884692815310e-15, 4.72973769385201140e-16, 7.88289615640570200e-17, 1.12612802233958120e-17, 1.40766002791425000e-18,
   -3.040000e+01, 6.27260225925671670e-14, 6.27260225925632420e-14, 3.13630112962776830e-14, 1.04543370987566040e-14, 2.61358427468783960e-15, 5.22716854937043290e-16, 8.71194758226656970e-17, 1.24456394031879920e-17, 1.55570492538600840e-18,
   -3.030000e+01, 6.93229759758606750e-14, 6.93229759758558660e-14, 3.46614879879231310e-14, 1.15538293293045040e-14, 2.88845733232452430e-15, 5.77691466464264150e-16, 9.62819110771637780e-17, 1.37545587252480860e-17, 1.71931984064075470e-18,
   -3.020000e+01, 7.66137370029775430e-14, 7.66137370029716740e-14, 3.83068685014799680e-14, 1.27689561671560770e-14, 3.19223904178706240e-15, 6.38447808356629930e-16, 1.06407968059177450e-16, 1.52011382940936700e-17, 1.90014228674307500e-18,
   -3.010000e+01, 8.46712740607860540e-14, 8.46712740607788850e-14, 4.23356370303822730e-14, 1.41118790101226440e-14, 3.52796975252827130e-15, 7.05593950504698390e-16, 1.17598991750464440e-16, 1.67998559642610260e-17, 2.09998199550986870e-18,
   -3.000000e+01, 9.35762296883929890e-14, 9.35762296883842290e-14, 4.67881148441833550e-14, 1.55960382813886140e-14, 3.89900957034423470e-15, 7.79801914067679430e-16, 1.29966985677557410e-16, 1.85667122395398620e-17, 2.32083902991468430e-18,
   -2.990000e+01, 1.03417727674778080e-13, 1.03417727674767390e-13, 5.17088638373729960e-14, 1.72362879457838680e-14, 4.30907198644240230e-15, 8.61814397287054390e-16, 1.43635732880700410e-16, 2.05193904113928150e-17, 2.56492380139014880e-18,
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   2.940000e+01, 9.99999999999829470e-01, 1.70507007384838220e-13, -8.52535036923900290e-14, 2.84178345641106270e-14, -7.10445864101796640e-15, 1.42089172819971680e-15, -2.36815288031994070e-16, 3.38307554327728270e-17, -4.22884442900430890e-18,
   2.950000e+01, 9.99999999999845680e-01, 1.54281120319141160e-13, -7.71405601595467770e-14, 2.57135200531663900e-14, -6.42838001328366320e-15, 1.28567600265355900e-15, -2.14279333774535300e-16, 3.06113333960599290e-17, -3.82641667443192610e-18,
   2.960000e+01, 9.99999999999860440e-01, 1.39599330561269830e-13, -6.97996652806154250e-14, 2.32665550935254810e-14, -5.81663877337487480e-15, 1.16332775467237650e-15, -1.93887959111196630e-16, 2.76982798727806240e-17, -3.46228498403571140e-18,
   2.970000e+01, 9.99999999999873660e-01, 1.26314697824611900e-13, -6.31573489122899990e-14, 2.10524496374193610e-14, -5.26311240934952190e-15, 1.05262248186777700e-15, -1.75437080310587040e-16, 2.50624400441669680e-17, -3.13280500547021870e-18,
   2.980000e+01, 9.99999999999885760e-01, 1.14294265039617650e-13, -5.71471325197957610e-14, 1.90490441732565420e-14, -4.76226104330978190e-15, 9.52452208660214540e-16, -1.58742034776121860e-16, 2.26774335392800970e-17, -2.83467919236854260e-18,
   2.990000e+01, 9.99999999999896530e-01, 1.03417727674766650e-13, -5.17088638373726360e-14, 1.72362879457837450e-14, -4.30907198644237150e-15, 8.61814397287048370e-16, -1.43635732880699370e-16, 2.05193904113926700e-17, -2.56492380139013070e-18,
   3.000000e+01, 9.99999999999906410e-01, 9.35762296883842290e-14, -4.67881148441833610e-14, 1.55960382813886140e-14, -3.89900957034423470e-15, 7.79801914067679530e-16, -1.29966985677557410e-16, 1.85667122395398650e-17, -2.32083902991468430e-18,
   3.010000e+01, 9.99999999999915290e-01, 8.46712740607782790e-14, -4.23356370303819700e-14, 1.41118790101225430e-14, -3.52796975252824600e-15, 7.05593950504693360e-16, -1.17598991750463600e-16, 1.67998559642609060e-17, -2.09998199550985370e-18,
   3.020000e+01, 9.99999999999923390e-01, 7.66137370029714090e-14, -3.83068685014798350e-14, 1.27689561671560310e-14, -3.19223904178705130e-15, 6.38447808356627660e-16, -1.06407968059177070e-16, 1.52011382940936180e-17, -1.90014228674306770e-18,
   3.030000e+01, 9.99999999999930720e-01, 6.93229759758561190e-14, -3.46614879879232510e-14, 1.15538293293045450e-14, -2.88845733232453450e-15, 5.77691466464266220e-16, -9.62819110771641100e-17, 1.37545587252481340e-17, -1.71931984064076160e-18,
   3.040000e+01, 9.99999999999937270e-01, 6.27260225925628000e-14, -3.13630112962774620e-14, 1.04543370987565300e-14, -2.61358427468782110e-15, 5.22716854937039650e-16, -8.71194758226650810e-17, 1.24456394031879060e-17, -1.55570492538599900e-18,
   3.050000e+01, 9.99999999999943270e-01, 5.67568523263207840e-14, -2.83784261631571700e-14, 9.45947538771690840e-15, -2.36486884692815350e-15, 4.72973769385201240e-16, -7.88289615640570320e-17, 1.12612802233958130e-17, -1.40766002791424940e-18,
   3.060000e+01, 9.99999999999948600e-01, 5.13557237147964600e-14, -2.56778618573955920e-14, 8.55928728579677160e-15, -2.13982182144831410e-15, 4.27964364289311180e-16, -7.13273940481013100e-17, 1.01896277211238390e-17, -1.27370346513210690e-18,
   3.070000e+01, 9.99999999999953480e-01, 4.64685804474652490e-14, -2.32342902237304630e-14, 7.74476340790871500e-15, -1.93619085197645890e-15, 3.87238170395003900e-16, -6.45396950657380130e-17, 9.21995643793515330e-18, -1.15249455473503900e-18,
   3.080000e+01, 9.99999999999957920e-01, 4.20465103518813390e-14, -2.10232551759388990e-14, 7.00775172531178780e-15, -1.75193793132735770e-15, 3.50387586265235810e-16, -5.83979310441273950e-17, 8.34256157771003620e-18, -1.04282019720814140e-18,
   3.090000e+01, 9.99999999999961920e-01, 3.80452558642185360e-14, -1.90226279321078230e-14, 6.34087597736830850e-15, -1.58521899434159470e-15, 3.17043798868125930e-16, -5.28406331446233300e-17, 7.54866187778495290e-18, -9.43582734718524040e-19,
   3.100000e+01, 9.99999999999965580e-01, 3.44247710846973950e-14, -1.72123855423475140e-14, 5.73746184744838090e-15, -1.43436546186170020e-15, 2.86873092372182050e-16, -4.78121820619776750e-17, 6.83031172312461890e-18, -8.53788965386815540e-19,
   3.110000e+01, 9.99999999999968800e-01, 3.11488209847564900e-14, -1.55744104923772730e-14, 5.19147016412511060e-15, -1.29786754103095420e-15, 2.59573508206061480e-16, -4.32622513676337930e-17, 6.18032162393536420e-18, -7.72540202988840200e-19,
   3.120000e+01, 9.99999999999971800e-01, 2.81846187547117050e-14, -1.40923093773550570e-14, 4.69743645911782230e-15, -1.17435911477919090e-15, 2.34871822955732270e-16, -3.91453038259200720e-17, 5.59218626083563660e-18, -6.99023282601933050e-19,
   3.130000e+01, 9.99999999999974460e-01, 2.55024976623415030e-14, -1.27512488311701020e-14, 4.25041627705626620e-15, -1.06260406926384980e-15, 2.12520813852683260e-16, -3.54201356420849750e-17, 5.06001937743245150e-18, -6.32502422176991450e-19,
   3.140000e+01, 9.99999999999976910e-01, 2.30756141382610940e-14, -1.15378070691300150e-14, 3.84593568970964980e-15, -9.61483922427234960e-16, 1.92296784485376010e-16, -3.20494640808723390e-17, 4.57849486868928600e-18, -5.72311858584469210e-19,
   3.150000e+01, 9.99999999999979130e-01, 2.08796791164584650e-14, -1.04398395582287960e-14, 3.47994651940930800e-15, -8.69986629852181640e-16, 1.73997325970378200e-16, -2.89995543283769920e-17, 4.14279347547689220e-18, -5.17849184433227650e-19,
   3.160000e+01, 9.99999999999981130e-01, 1.88927149411555350e-14, -9.44635747057741110e-15, 3.14878582352556530e-15, -7.87196455881272310e-16, 1.57439291176206870e-16, -2.62398818626852850e-17, 3.74855455180765200e-18, -4.68569318974822510e-19,
   3.170000e+01, 9.99999999999982900e-01, 1.70948354070447300e-14, -8.54741770352207300e-15, 2.84913923450716240e-15, -7.12284808626693180e-16, 1.42456961725299670e-16, -2.37428269542036270e-17, 3.39183242202537880e-18, -4.23979052752244240e-19,
   3.180000e+01, 9.99999999999984570e-01, 1.54680467314601930e-14, -7.73402336572985840e-15, 2.57800778857645970e-15, -6.44501947144035160e-16, 1.28900389428775130e-16, -2.14833982381185570e-17, 3.06905689115675550e-18, -3.83632111393834950e-19,
   3.190000e+01, 9.99999999999986010e-01, 1.39960674665539270e-14, -6.99803373327676720e-15, 2.33267791109212490e-15, -5.83169477772965950e-16, 1.16633895554567090e-16, -1.94389825924191410e-17, 2.77699751320024640e-18, -3.47124689149409350e-19,
   3.200000e+01, 9.99999999999987340e-01, 1.26641655490938550e-14, -6.33208277454676670e-15, 2.11069425818214850e-15, -5.27673564545483690e-16, 1.05534712909075360e-16, -1.75891188181721000e-17, 2.51273125973683490e-18, -3.14091407466594670e-19,
   3.210000e+01, 9.99999999999988560e-01, 1.14590108570219640e-14, -5.72950542851085020e-15, 1.90983514283686250e-15, -4.77458785709171850e-16, 9.54917571418168590e-17, -1.59152928569636410e-17, 2.27361326527885370e-18, -2.84201658159439420e-19,
   3.220000e+01, 9.99999999999989670e-01, 1.03685417971138640e-14, -5.18427089855682390e-15, 1.72809029951886960e-15, -4.32022574879681600e-16, 8.64045149759219900e-17, -1.44007524959822210e-17, 2.05725035656752380e-18, -2.57156294570599110e-19,
   3.230000e+01, 9.99999999999990560e-01, 9.38184458849850840e-15, -4.69092229424916660e-15, 1.56364076474966340e-15, -3.90910191187386520e-16, 7.81820382374655680e-17, -1.30303397062403490e-17, 1.86147710089036070e-18, -2.32684637611014280e-19,
   3.240000e+01, 9.99999999999991560e-01, 8.48904403387157360e-15, -4.24452201693571420e-15, 1.41484067231185670e-15, -3.53710168077940160e-16, 7.07420336155784300e-17, -1.17903389359265360e-17, 1.68433413370287570e-18, -2.10541766712631340e-19,
   3.250000e+01, 9.99999999999992340e-01, 7.68120468520197700e-15, -3.84060234260092930e-15, 1.28020078086693710e-15, -3.20050195216714640e-16, 6.40100390433350650e-17, -1.06683398405532220e-17, 1.52404854864971060e-18, -1.90506068581026700e-19,
   3.260000e+01, 9.99999999999993010e-01, 6.95024141476382340e-15, -3.47512070738186320e-15, 1.15837356912725540e-15, -2.89593392281797740e-16, 5.79186784563531140e-17, -9.65311307605670500e-18, 1.37901615372177360e-18, -1.72377019215068900e-19,
   3.270000e+01, 9.99999999999993670e-01, 6.28883849646153690e-15, -3.14441924823072860e-15, 1.04813974941021660e-15, -2.62034937352540930e-16, 5.24069874705029170e-17, -8.73449791174872870e-18, 1.24778541596360150e-18, -1.55973176995325000e-19,
   3.280000e+01, 9.99999999999994340e-01, 5.69037638758344200e-15, -2.84518819379168870e-15, 9.48396064597207920e-16, -2.37099016149291180e-16, 4.74198032298539190e-17, -7.90330053830754850e-18, 1.12904293404352410e-18, -1.41130366755338760e-19,
   3.290000e+01, 9.99999999999994890e-01, 5.14886547819375430e-15, -2.57443273909685070e-15, 8.58144246365599090e-16, -2.14536061591390950e-16, 4.29072123182746550e-17, -7.15120205304459720e-18, 1.02160029329174860e-18, -1.27700036661385190e-19,
   3.300000e+01, 9.99999999999995340e-01, 4.65888614510335430e-15, -2.32944307255165550e-15, 7.76481024183870600e-16, -1.94120256045960430e-16, 3.88240512091891920e-17, -6.47067520153056780e-18, 9.24382171646948020e-19, -1.15547771455798300e-19,
   3.310000e+01, 9.99999999999995780e-01, 4.21553451045879130e-15, -2.10776725522937790e-15, 7.02589085076447440e-16, -1.75647271269105920e-16, 3.51294542538188150e-17, -5.85490904230234690e-18, 8.36415577471538480e-19, -1.04551947183885770e-19,
   3.320000e+01, 9.99999999999996230e-01, 3.81437336208504050e-15, -1.90718668104250570e-15, 6.35728893680825560e-16, -1.58932223420201530e-16, 3.17864446840383680e-17, -5.29774078067241470e-18, 7.56820111524446220e-19, -9.46025139405087250e-20,
   3.330000e+01, 9.99999999999996560e-01, 3.45138774437419260e-15, -1.72569387218708430e-15, 5.75231290729020130e-16, -1.43807822682251060e-16, 2.87615645364486240e-17, -4.79359408940757470e-18, 6.84799155629502910e-19, -8.55998944536504290e-20,
   3.340000e+01, 9.99999999999996890e-01, 3.12294477526047450e-15, -1.56147238763022740e-15, 5.20490795876735930e-16, -1.30122698969180730e-16, 2.60245397938348490e-17, -4.33742329897204160e-18, 6.19631899853024490e-19, -7.74539874815976800e-20,
   3.350000e+01, 9.99999999999997220e-01, 2.82575728711559530e-15, -1.41287864355778950e-15, 4.70959547852591190e-16, -1.17739886963145140e-16, 2.35479773926279630e-17, -3.92466289877097200e-18, 5.60666128395752110e-19, -7.00832660494431820e-20,
   3.360000e+01, 9.99999999999997450e-01, 2.55685092766995250e-15, -1.27842546383496980e-15, 4.26141821278318850e-16, -1.06535455319577530e-16, 2.13070910639146380e-17, -3.55118184398548230e-18, 5.07311691997843240e-19, -6.34139614997088460e-20,
   3.370000e+01, 9.99999999999997670e-01, 2.31353439169574210e-15, -1.15676719584786570e-15, 3.85589065282618280e-16, -9.63972663206527840e-17, 1.92794532641298440e-17, -3.21324221068806990e-18, 4.59034601526799610e-19, -5.73793251908333040e-20,
   3.380000e+01, 9.99999999999997890e-01, 2.09337248551938240e-15, -1.04668624275968680e-15, 3.48895414253225950e-16, -8.72238535633050340e-17, 1.74447707126604210e-17, -2.90746178544320920e-18, 4.15351683634688900e-19, -5.19189604543224990e-20,
   3.390000e+01, 9.99999999999998110e-01, 1.89416175478486190e-15, -9.47080877392427420e-16, 3.15693625797473390e-16, -7.89234064493671520e-17, 1.57846812898729520e-17, -2.63078021497866600e-18, 3.75825744996906480e-19, -4.69782181246030610e-20,
   3.400000e+01, 9.99999999999998330e-01, 1.71390843154200710e-15, -8.56954215771000580e-16, 2.85651405256998220e-16, -7.14128513142485820e-17, 1.42825702628493230e-17, -2.38042837714142440e-18, 3.40061196734451400e-19, -4.25076495917978010e-20,
   3.410000e+01, 9.99999999999998450e-01, 1.55080847994651830e-15, -7.75404239973256690e-16, 2.58468079991083940e-16, -6.46170199977701830e-17, 1.29234039995537170e-17, -2.15390066659217940e-18, 3.07700095227423530e-19, -3.84625119034199790e-20,
   3.420000e+01, 9.99999999999998560e-01, 1.40322954086308700e-15, -7.01614770431541530e-16, 2.33871590143845830e-16, -5.84678975359608040e-17, 1.16935795071918990e-17, -1.94892991786522900e-18, 2.78418559695007630e-19, -3.48023199618701640e-20,
   3.430000e+01, 9.99999999999998780e-01, 1.26969459466634840e-15, -6.34847297333172530e-16, 2.11615765777723100e-16, -5.29039414444302390e-17, 1.05807882888858340e-17, -1.76346471481423380e-18, 2.51923530687728270e-19, -3.14904413359617250e-20,
   3.440000e+01, 9.99999999999998890e-01, 1.14886717873210330e-15, -5.74433589366050270e-16, 1.91477863122015880e-16, -4.78694657805035270e-17, 9.57389315610053080e-18, -1.59564885935003000e-18, 2.27949837049987270e-19, -2.84937296312450620e-20,
   3.450000e+01, 9.99999999999999000e-01, 1.03953801167021980e-15, -5.19769005835108810e-16, 1.73256335278368870e-16, -4.33140838195918600e-17, 8.66281676391822790e-18, -1.44380279398632340e-18, 2.06257541998031890e-19, -2.57821927497502700e-20,
   3.460000e+01, 9.99999999999999110e-01, 9.40612890429909060e-16, -4.70306445214953640e-16, 1.56768815071650610e-16, -3.91922037679123620e-17, 7.83844075358235410e-18, -1.30640679226368620e-18, 1.86629541751943390e-19, -2.33286927189902040e-20,
   3.470000e+01, 9.99999999999999110e-01, 8.51101739147944780e-16, -4.25550869573971700e-16, 1.41850289857990070e-16, -3.54625724644972780e-17, 7.09251449289935940e-18, -1.18208574881652830e-18, 1.68869392688066110e-19, -2.11086740860057180e-20,
   3.480000e+01, 9.99999999999999220e-01, 7.70108700136545650e-16, -3.85054350068272230e-16, 1.28351450022757000e-16, -3.20878625056890530e-17, 6.41757250113773230e-18, -1.06959541685626230e-18, 1.52799345265172830e-19, -1.90999181581443530e-20,
   3.490000e+01, 9.99999999999999330e-01, 6.96823167838575130e-16, -3.48411583919287070e-16, 1.16137194639762020e-16, -2.90342986599403450e-17, 5.80685973198800470e-18, -9.67809955331312550e-19, 1.38258565047323660e-19, -1.72823206309143410e-20 };

   Int_t i = (Int_t)(10*x+350.5);
   if(i<0)   return TMath::Exp(x);
   if(i>699) return 1;
   Double_t* basePoint = sigval+(10*i);
   Double_t res =  x - basePoint[0];
   res =        basePoint[1] + res * ( basePoint[2] + res * ( basePoint[3]
      + res * ( basePoint[4] + res * ( basePoint[5] + res * ( basePoint[6]
      + res * ( basePoint[7] + res * ( basePoint[8] )))))));
   /*
   if(x<-15) return TMath::Exp(x);
   if(x> 15) return 1;
   return (1/(1+TMath::Exp(-x)));
   */
   return res;
}

//______________________________________________________________________________
Double_t TNeuron::DSigmoid(Double_t x) const
{
   // The Derivative of the Sigmoid.

   //if (x>2.1972246) return x/(1+TMath::Exp(x));
   //Double_t a = Sigmoid(x);
   //return a-a*a;
   if (TMath::Abs(x) > 5)
      return TMath::Exp(-TMath::Abs(x));
   Double_t expmx = TMath::Exp(-x);
   return expmx / ((1 + expmx) * (1 + expmx));
}

//______________________________________________________________________________
void TNeuron::AddPre(TSynapse * pre)
{
   // Adds a synapse to the neuron as an input
   // This method is used by the TSynapse while
   // connecting two neurons.
   fpre.AddLast(pre);
   if (fpre.GetEntriesFast() == fpre.GetSize())
      fpre.Expand(2 * fpre.GetSize());
}

//______________________________________________________________________________
void TNeuron::AddPost(TSynapse * post)
{
   // Adds a synapse to the neuron as an output
   // This method is used by the TSynapse while
   // connecting two neurons.
   fpost.AddLast(post);
   if (fpost.GetEntriesFast() == fpost.GetSize())
      fpost.Expand(2 * fpost.GetSize());
}

//______________________________________________________________________________
void TNeuron::AddInLayer(TNeuron * nearP)
{
   // Tells a neuron which neurons form its layer (including itself).
   // This is needed for self-normalizing functions, like Softmax.
   flayer.AddLast(nearP);
   if (flayer.GetEntriesFast() == flayer.GetSize())
      flayer.Expand(2 * flayer.GetSize());
}

//______________________________________________________________________________
TNeuron::ENeuronType TNeuron::GetType() const
{
   // Returns the neuron type.
   return fType;
}

//______________________________________________________________________________
TTreeFormula* TNeuron::UseBranch(TTree* input, const char* formula)
{
   // Sets a formula that can be used to make the neuron an input.
   // The formula is automatically normalized to mean=0, RMS=1.
   // This normalisation is used by GetValue() (input neurons)
   // and GetError() (output neurons)
   if (fFormula) delete fFormula;
   // Set the formula
   // One checks for {}: defined as instance in TMultiLayerPerceptron
   // so that EvalInstance can be used. This allows to use arrays as
   // input, also in complex calculation, without detailed string parsing.
   TRegexp re("{[0-9]+}$");
   TString f(formula);
   Ssiz_t len = f.Length();
   Ssiz_t pos = re.Index(f,&len);
   if(pos==-1 || len<3)
      fFormula = new TTreeFormula(Form("NF%lu",(ULong_t)this),formula,input);
   else {
      TString newformula(formula,pos);
      TString val = f(pos+1,len-2);
      fFormula = new TTreeFormula(Form("NF%lu",(ULong_t)this),
                                  (const char*) newformula,input);
      fIndex = val.Atoi();
      f = newformula;
   }
   // Computes the default normalization
   TH1D tmp("tmpb", "tmpb", 1, -FLT_MAX, FLT_MAX);
   input->Draw(Form("%s>>tmpb",(const char*)f),"","goff");
   fNorm[0] = tmp.GetRMS();
   if(fNorm[0]<1e-15) fNorm[0]=1.;
   fNorm[1] = tmp.GetMean();
   // Check the dimensionality
   if(fFormula->GetNdata()>1 && fIndex==0)
      Warning("TNeuron::UseBranch()","all indices in arrays must be specified, otherwise the first element will be assumed.");
   return fFormula;
}

//______________________________________________________________________________
Double_t TNeuron::GetBranch() const
{
   // Returns the formula value.
   Double_t branch = fFormula->EvalInstance(fIndex);
   if (TMath::IsNaN(branch))
      branch = 0.;
   return branch;
}

//______________________________________________________________________________
Double_t TNeuron::GetInput() const
{
   // Returns neuron input
   if (!fNewInput) {
      return fInput;
   }
   ((TNeuron*)this)->fNewInput = false;
   Double_t input = 0.0;
   Int_t nEntries = fpre.GetEntriesFast();
   if (nEntries) {
      input = fWeight;
      for (Int_t i = 0; i < nEntries; i++) {
         TSynapse *preSynapse = (TSynapse*)fpre.UncheckedAt(i);
         input += preSynapse->GetValue();
      }
   }
   return (((TNeuron*)this)->fInput = input);
}

//______________________________________________________________________________
Double_t TNeuron::GetValue() const
{
   // Computes the output using the appropriate function and all
   // the weighted inputs, or uses the branch as input.
   // In that case, the branch normalisation is also used.
   if (!fNewValue) {
      return fValue;
   }
   ((TNeuron*)this)->fNewValue = false;
   Int_t nentries = fpre.GetEntriesFast();
   if (!nentries) {
      Double_t branch = GetBranch();
      return (((TNeuron*)this)->fValue = (branch - fNorm[1]) / fNorm[0]);
   } else {
      Double_t input = GetInput();
      Double_t value = 0;
      switch (fType) {
      case TNeuron::kOff: {
         value = 0;
         break;
      }
      case TNeuron::kLinear: {
         value = input;
         break;
      }
      case TNeuron::kSigmoid: {
         value =  Sigmoid(input);
         break;
      }
      case TNeuron::kTanh: {
         value = TMath::TanH(input);
         break;
      }
      case TNeuron::kGauss: {
         value = TMath::Exp(-input * input);
         break;
      }
      case TNeuron::kSoftmax: {
         Double_t normalization = 0.0;
         for (Int_t i = 0; i < flayer.GetEntriesFast(); i++) {
            // this is not very efficient, as the same normalization
            // is calculated once per neuron instead of just once
            normalization += TMath::Exp(((TNeuron*) flayer.UncheckedAt(i))->GetInput());
         }
         if (normalization > 0.0) {
            // exp(a_k) / sum_k'[ exp(a_k') ]
            value = TMath::Exp(input) / normalization;
         } else {
            // all neurons have output = 0 ?
            value = 1.0 / flayer.GetEntriesFast();
         }
         break;
      }
      case TNeuron::kExternal: {
         value = fExtF->Eval(input);
         break;
      }
      }
      return (((TNeuron*)this)->fValue = value);
   }
}

//______________________________________________________________________________
Double_t TNeuron::GetDerivative() const
{
   // computes the derivative for the appropriate function
   // at the working point
   if (!fNewDeriv)
      return fDerivative;
   ((TNeuron*)this)->fNewDeriv = false;
   Int_t nentries = fpre.GetEntriesFast();
   Double_t input = fWeight;
   for (Int_t i=0;i<nentries;i++) {
      TSynapse *preSynapse = (TSynapse*)fpre.UncheckedAt(i);
      input += preSynapse->GetValue();
   }
   Double_t derivative = 0;
   switch (fType) {
      case TNeuron::kOff: {
         derivative = 0;
         break;
      }
      case TNeuron::kLinear: {
         derivative = 1;
         break;
      }
      case TNeuron::kSigmoid: {
         derivative = DSigmoid(input);
         break;
      }
      case TNeuron::kTanh: {
         derivative = (1 - (TMath::TanH(input) * TMath::TanH(input)));
         break;
      }
      case TNeuron::kGauss: {
         derivative = (-2) * input * TMath::Exp(-input * input);
         break;
      }
      case TNeuron::kSoftmax: {
         // actually this is not the derivative, as the Softmax function needs
         // exp(activation) of all the neurons in the layer for the normalization.
         // it will be smartly taken care of in GetDeDw()
         derivative = GetValue();
         break;
      }
      case TNeuron::kExternal: {
         derivative = fExtD->Eval(input);
         break;
      }
   }
   return (((TNeuron*)this)->fDerivative = derivative);
}

//______________________________________________________________________________
Double_t TNeuron::GetError() const
{
   // Computes the error for output neurons.
   // Returns 0 for other neurons.
   if (!fpost.GetEntriesFast())
      return (GetValue() - (GetBranch() - fNorm[1]) / fNorm[0]);
   return 0;
}

//______________________________________________________________________________
Double_t TNeuron::GetTarget() const
{
   // Computes the normalized target pattern for output neurons.
   // Returns 0 for other neurons.
   if (!fpost.GetEntriesFast())
      return ((GetBranch() - fNorm[1]) / fNorm[0]);
   return 0;
}

//______________________________________________________________________________
Double_t TNeuron::GetDeDw() const
{
   // Computes the derivative of the error wrt the neuron weight.
   if (!fNewDeDw)
      return fDeDw;
   ((TNeuron*)this)->fNewDeDw = false;
   // Output units DeDw is just the error for these cases:
   //  - linear output,  with sum-of-squares error
   //  - sigmoid output, with binary cross-entropy
   //  - softmax output, with 1-of-c cross entropy
   Int_t nEntries = fpost.GetEntriesFast();
   if (nEntries == 0) {
      // output neuron
      ((TNeuron*)this)->fDeDw = GetError();
   } else {
      // hidden nuron
      ((TNeuron*)this)->fDeDw = 0.0;
      if (fType != TNeuron::kSoftmax) {
         // non-softmax
         for (Int_t i = 0; i < nEntries; i++) {
            TSynapse *postSynapse = (TSynapse*)fpost.UncheckedAt(i);
            ((TNeuron*)this)->fDeDw +=
              postSynapse->GetWeight() *
              postSynapse->GetPost()->GetDeDw();
         }
      } else {
         // softmax derivative can be taken care of correcting the forward weight
         for (Int_t i = 0; i < nEntries; i++) {
            TSynapse *postSynapse = (TSynapse*)fpost.UncheckedAt(i);
            ((TNeuron*)this)->fDeDw +=
              (postSynapse->GetWeight() - postSynapse->GetPost()->GetInput()) *
              postSynapse->GetPost()->GetDeDw();
         }
      }
      ((TNeuron*)this)->fDeDw *= GetDerivative();
   }
   return fDeDw;
}

//______________________________________________________________________________
void TNeuron::ForceExternalValue(Double_t value)
{
   // Uses the branch type to force an external value.
   fNewValue = false;
   fValue = (value - fNorm[1]) / fNorm[0];
}

//______________________________________________________________________________
void TNeuron::SetNormalisation(Double_t mean, Double_t RMS)
{
   // Sets the normalization variables.
   // Any input neuron will return (branch-mean)/RMS.
   // When UseBranch is called, mean and RMS are automatically set
   // to the actual branch mean and RMS.
   fNorm[0] = RMS;
   fNorm[1] = mean;
}

//______________________________________________________________________________
void TNeuron::SetWeight(Double_t w)
{
   // Sets the neuron weight to w.
   // The neuron weight corresponds to the bias in the
   // linear combination of the inputs.
   fWeight = w;
}

//______________________________________________________________________________
void TNeuron::SetNewEvent() const
{
   // Inform the neuron that inputs of the network have changed,
   // so that the buffered values have to be recomputed.
   ((TNeuron*)this)->fNewInput = true;
   ((TNeuron*)this)->fNewValue = true;
   ((TNeuron*)this)->fNewDeriv = true;
   ((TNeuron*)this)->fNewDeDw = true;
}

//______________________________________________________________________________
void TNeuron::SetDEDw(Double_t in)
{
   // Sets the derivative of the total error wrt the neuron weight.
   fDEDw = in;
}