Re: Seeking further guidance on implementing a user defined equation in ROOT (More)

ROOT considers that the fit fails (despite computing good parameters) because your data points do not have correct errors associated with each bin. By the way, when you do not fix alpha_k you get a better fit.

Rene Brun

Russell Leslie wrote:
> Dear Rene,
>
> Thank you very much for the scripted fitting function and the advice
> to check the equation (in the definition of function "fint" the
> parameter "Lambdas" had been replaced with parameter "lambda_k" ).
>
> Your advice to fix one or more parameters was well taken. The
> parameters alpha_k and econst are fixed for any individual case
> (varying only between cases). I also set upper and lower bounds for
> the non-fixed parameters (as none of the parameters can take negative
> values).
>
> One thing that puzzles me is that the end result of the fit looks
> pretty well perfect, the values of the various parameters are
> physically plausible and the curves appear to match well, but root
> gave the following message:
>
> Warning in <TH1F::Fit>: Abnormal termination of minimization.
> FCN=0.0598415 FROM MIGRAD STATUS=FAILED 458 CALLS
> 459 TOTAL
> EDM=0.000252546 STRATEGY= 1 ERR MATRIX
> NOT POS-DEF
> EXT PARAMETER APPROXIMATE STEP FIRST
> NO. NAME VALUE ERROR SIZE DERIVATIVE
> 1 alpha_k 2.21243e-01 fixed
> 2 gamma 4.86939e-02 2.20292e-01 -0.00000e+00 -1.76568e-02
> 3 lambda_k 2.54645e-01 4.59892e-02 -0.00000e+00 -2.42907e-01
> 4 tau_c 5.79966e-02 3.65613e-01 0.00000e+00 -8.21423e-02
> 5 econst 1.00000e+00 fixed
> 6 Lambdas 7.83294e-02 1.37364e-01 -0.00000e+00 3.41404e-02
>
> Should I worry that root considers the fit a failure - or should I
> just accept the results of the fit.
>
> Regards
>
> Russell Leslie
> Nuclear Physics
> R.S.Phys.S.E.
> ANU
>
>
> ----- Original Message -----
> From: Rene Brun <Rene.Brun_at_cern.ch>
> Date: Saturday, February 21, 2009 12:51 am
> Subject: Re: [ROOT] Seeking further uidance on implementing a user
> defined equation in ROOT (More)
> To: Russell Leslie <u4504546_at_anu.edu.au>
> Cc: roottalk_at_lxbuild091.cern.ch
>
> > In my previouis mail I forgot to mention 2 problems
> > -you should provide a good error estimate for the bin
> > contents of your
> > histogram. The default being to use the sqrt(bin content) does
> > not make
> > much sense in your case. I used the option "w" that means use
> > same
> > weight=1 for all bins.
> >
> > -you should fix a few parameters. In my previous mail, all
> > parameters
> > were free. in the attachment
> > you will find an example where one of your parameters is fixed,
> > you can
> > add more.
> >
> > Rene Brun
> >
> > Russell Leslie wrote:
> > > Dear Rene,
> > >
> > > I seem to be missing some vital step in using a user defined
> > equation
> > > to fit to a histogram.
> > >
> > > I am trying to use the function gks from the script gks.C
> > (that you
> > > produced for me) as a fitting function for the Monte Carlo
> > data that
> > > we produce from a FORTRAN program. I have attached a
> > copy of a root
> > > file containing a typical set of such data (file MCGcalc.root).
> > >
> > > I have compiled your script (using the command ".x gks.C+")
> > and
> > > produced a shared object gks_C.so.
> > >
> > > I have loaded gks_C.so (using the command ".L gks_C.so") and
> > then
> > > tried to fit using various permutations of commands such as
> > >
> > > G2values.Fit("gks") but everything I have tried so far gives
> > rise to
> > > messages similar to "Unknown function: gks" (with the
> > occasional seg
> > > fault).
> > >
> > > I have been similarly unsuccessful using the FitPanel GUI.
> > >
> > > Any guidance you can give on what I might be doing wrong would
> > be
> > > greatly appreciated.
> > >
> > > Regards
> > >
> > > Russell Leslie
> > > Nuclear Physics
> > > R.S.Phys.S.E.
> > > ANU
> > >
> > >
> > > ----- Original Message -----
> > > From: Russell Leslie <russell.leslie_at_gmail.com>
> > > Date: Friday, February 20, 2009 8:07 pm
> > > Subject: Fwd: [ROOT] Seeking guidance on implementing a user
> > defined
> > > equation in ROOT
> > > To: u4504546_at_anu.edu.au
> > >
> > > >
> > > >
> > > > ---------- Forwarded message ----------
> > > > From: *Rene Brun* <Rene.Brun_at_cern.ch>
> > > > Date: Thu, Feb 19, 2009 at 7:16 PM
> > > > Subject: Re: [ROOT] Seeking guidance on implementing a user
> > defined
> > > equation in ROOT
> > > > To: Russell Leslie <u4504546_at_anu.edu.au
> > > <javascript:main.compose('new', 't=u4504546_at_anu.edu.au')>>
> > > > Cc: roottalk_at_lxbuild091.cern.ch
> > <javascript:main.compose('new',
> > > 't=roottalk_at_lxbuild091.cern.ch')>
> > > >
> > > >
> > > > Try the function gks.C in attachment
> > > > To run do:
> > > > root > .x gks.C+
> > > >
> > > > Rene Brun
> > > >
> > > > Russell Leslie wrote:
> > >
> > > > Dear all,
> > > > NOTE - message resent because
> > I sent this originally from
> > > another account and it did not turn up
> > on the roottalk list.
> > > > I am still feeling my way
> > forward on ROOT, but I have found it
> > > to be a very useful tool-set.
> > > > One problem I am currently working
> > on is to try to implement the
> > > following equations in ROOT (LaTex
> > form of the equations below).
> > > >
> > > > $$
> > > > G_{k}(t) = e^{-\Lambda^{*}
> > t}G_{k}^{(fluct.)}(t)+ \int_{0}^{t}
> > > \Lambda^{*} G_{k}^{(fluct.)}(t')\cdotp
> > e^{-\Lambda^{*}
> > > t'}G_{k}^{(stat.)} (t-t')dt'
> > > > $$
> > > > Where Gk(stat) is give by the
> > following equation
> > > > $$
> > > > G_{k}^{(stat.)} (t) = \left\langle
> > \alpha_{k} \right\rangle + (
> > > 1 - \left\langle
> > \alpha_{k}\right\rangle )e^{- \Gamma t}
> > > > $$
> > > > and Gk(fluct) is given by the
> > this equation
> > > > $$
> > > > G_{k}^{(fluct.)}(t) = ( 1 -
> > \lambda_{k}\tau_{c} )e^{ - \lambda
> > > _{k} t }
> > > > $$
> > > > The equations are from the
> > manual for the Coulex code GOSIA and
> > > I want to use them as the fitting
> > function for the output of a
> > > Monte Carlo simulation that we use.
> > > > I have had no problems
> > producing the curves for Gk(stat) and
> > > Gk(fluct) - but I have not been able
> > to implement the integral
> > > term in the Gk equation (the first
> > equation above). The code I
> > > have so far is given below
> > > > {
> > > > //Calculate Gks
> > > > //parameter[0] = alpha_k
> > > > //parameter[1] = gamma
> > > > TF1 *Gks = new
> > TF1("Gks","[0]+(1-[0])*exp(-[1]*x)",0,15);
> > > > Gks-
> > >SetParameters(0.221243,0.4);>
> > > //Calculate Gkf
> > > > //parameter[0] =
> > lambda_k> >
> > //parameter[1] = tau_c
> > > > TF1 *Gkf = new
> > TF1("Gkf","(1-[0]*[1])*exp(-[0]*x)",0,15);
> > > > Gkf-
> > >SetParameters(0.172,0.5);>
> > > //Calculate expLamba*t
> > > > //parameter[0] =
> > 1 //parameter[1] = Lambda*
> > > > TF1 *eLst = new
> > TF1("eLst","[0]*exp(-[1]*x)",0,15);
> > > > eLst-
> > >SetParameters(1,0.0345);>
> > > //Combine Gks and Gkf to for Gkcalc
> > > > TF1 *Gkcalc = new
> > TF1("Gkcalc","Gkf*eLst*[0]*[1]",0,15); //
> > > This is the bit I can't get!!!!!!!!
> > > >
> > //Create a canvas to draw Gkcalc
> > > > TCanvas *Gkcalc1 = new
> > >
> > TCanvas("Gkcalc1","Gkcalc1",10,10,1400,1200);> > //Draw and
> format Gkcalc
> > > > Gkcalc->Draw();
> > > > Gkcalc-
> > >SetLineWidth(2.0);> >
> > Gkcalc->SetLineColor(kBlue);
> > > > Gkcalc->GetXaxis()-
> > >SetTitle("time");> >
> > Gkcalc->GetYaxis()->SetTitle("G_{k}(t)");
> > > > Gkcalc-
> > >SetTitle("G_{k}(t) = e^{-#Lambda^{*}
> > > t}G_{k}^{(fluct.)}(t)+ #int_{0}^{t}
> > #Lambda^{*}> G_{k}^{(fluct.)}(t').e^{-
> > #Lambda^{*} t'}G_{k}^{(stat.)} (t-t')dt' ");
> > > > Gkcalc->GetYaxis()-
> > >SetLabelFont(22);> >
> > Gkcalc->GetYaxis()->SetTitleFont(22);
> > > > Gkcalc->GetXaxis()-
> > >SetLabelFont(22);> >
> > Gkcalc->GetXaxis()->SetTitleFont(22);
> > > > //Add other lines
> > > > Gks->Draw("same");
> > > > Gks-
> > >SetLineWidth(2.0);> >
> > Gks->SetLineColor(kRed);
> > > > Gkf->Draw("same");
> > > > Gkf-
> > >SetLineWidth(2.0);> >
> > Gkf->SetLineColor(kGreen);
> > > > eLst->Draw("same");
> > > > eLst-
> > >SetLineWidth(2.0);> >
> > eLst->SetLineColor(kMagenta);
> > > > TLegend *legend =
> > new TLegend(.75,.80,.95,.95);
> > > > legend-
> > >AddEntry(Gkcalc,"G_{k}(t)");>
> > > legend->AddEntry(Gks,"G_{k}^{(stat)}(t)");
> > > > legend-
> > >AddEntry(Gkf,"G_{k}^{(fluct)}(t)");>
> > > legend->AddEntry(Gks,"e^{-#Lambda^{*} t}");
> > > > legend->Draw();
> > > > }
> > > > My root details as as follows ROOT
> > 5.18/00b> (branches/v5-18-00-
> > patches_at_22563 <mailto:branches
> > > <javascript:main.compose('new',
> > > 't=branches')>/v5-18-00-
> > patches_at_22563>, Oct 19 2008, 22:04:00 on
> > > linuxx8664gcc4.3)
> > >
> > > > Any help or guidance you can
> > give on this would be greatly
> > > appreciated.
> > > > Russell Leslie
> > > > Nuclear Physics
> > > > R.S.Phys.S.E.
> > > > ANU
> > >
> > > >
> > > >
> > >
> > >
> > > Russell Leslie
> > > Nuclear Physics
> > > R.S.Phys.S.E.
> > > ANU
> >
>
> Russell Leslie
> Nuclear Physics
> R.S.Phys.S.E.
> ANU
Received on Mon Feb 23 2009 - 08:59:34 CET