Simultaneous fit

ROOT
1

Hi,

I have a question about simultaneous fit.
Example,
I have 2 data sets, a(x, y) and b(x, y).
and user defined function “func” with 3 parameters par(0), par(1), and par(2).
Then, fit of 2 data sets, and get best values of par(0), par(1), and par(2) and chi2/ndf.
This means that I get 2 fitting lines (for a and b data).
The par(0,1,2) are for both a and b data sets and chi2/ndf is for both a and b data sets.
Would you tell me how to do simultaneous multi graph fitting?

e.g.)

a_data = new TGraphErrors(10);
b_data = new TGraphErrors(15);

Double_t func(Double_t *x, Double_t *par);

void main()
{
…
TF1 *intfunc_a = new TF1(“intfunc_a”, func, 0.0, 1.0, 3);
a_data->Fit(“intfunc_a”);
…
TF1 *intfunc_b = new TF1(“intfunc_b”, func, 0.0, 1.0, 3);
b_data->Fit(“intfunc_b”);
…
}

  |
  |  *
  |  ------ *         a_data
  |    ---------  *
  |       -----------  *
Y|
  |  ----------------------       *
  |    +
  |  ---      +
  |  --------       +        b_data
  |     -------------      +
  |   -----------------------     +
  |
  +-------------------------------

------------------------ x

The above example is the independent fitting that means the fitting for a_data and fitting for b_data are separated.
And the parameters of a_data and the parameters of b_data are totally different, and chi2/ndf’s are different, too.
But, I want to get common parameters, means

par(0) for a_data = par(0) for b_data
par(1) for a_data = par(1) for b_data
par(2) for a_data = par(2) for b_data

and I want to know total chi2/ndf for (a_data + b_data).
So, this fitting is for minimizing total chi2.
The normalization constants (magnitude constant such as x 10, or x 100) are different for a_data and b_data.

I want to know how to do that.
Thank you!

2

see example in $ROOTSYS/tutorials/fit/fitMultiGraph.C

Rene

3

Hi,

Thank you for your reply, however, the fitMultiGraph.C example is only ONE fitting line for
3 data sets. I want to get TWO fitting lines for 2 data sets using same parameters except
normalization constants (magnitude constants). How should I do for that?

Thank you,

4

How can you pretend to get two different lines with exactly the same function coefficients?

Rene

5

Hi,

For example,

y = a * f(x); (for a_data set)
y = b * f(x); (for b_data set)
f(x) = f( x, par(0), par(1), par(2),… );

a and b are normalization constants (magnitude constants),
so, we can draw two lines and the f(x) is same function and same parameters.
(actually, the constant a and b are also parameters for the fitting)
That’s why I say “different normalization constants” in previous message.

Would you tell me how to do for that?
Thank you!

6

Dear friends,

Please let me continue this old thread.
Also I’m very interesting in Nobu-san’s questions.

I prepared instant samples as below, I would like to know how to extract normalization factor ‘a_0’ and ‘parameters’ using same function throughout simultaneous fit when we add two independent experimental data sets, for example.

In short, the point is to get ‘a_0’ which satisfies only one 2nd order polynomial shape for both data distributions simultaneously.

Carefully guessing, this kind analysis would be very popular, but I can’t solve it. Please let me share your wisdom.

Regards,
Ha


{

  // dummy data point
  double x1[5], y1[5], ye1[5];
  for (int i=0; i<5; i++){
    x1[i] = 2+i;
    y1[i] = log(2+i) / 1000.;
    ye1[i] = y1[i] / 3.;
  }

  double x2[5], y2[5], ye2[5];
  for (int i=0; i<5; i++){
    x2[i] = 5+i;
    y2[i] = sqrt(2+i);
    ye2[i] = y2[i] / 3.;
  }

  //
  TCanvas *c = new TCanvas("c", "", 0, 0, 900, 300);
  c.Divide(3,1);

  c.cd(1);
  TH2F *h1 = new TH2F("h1","", 2, 0.0, 10.0, 2, 0, 0.010);
  h1->SetXTitle("x  ");
  h1->SetYTitle("a_{0} f  ");
  h1->Draw();
  TGraphErrors *gr1 = new TGraphErrors(5, x1, y1, 0, ye1);
  gr1->SetMarkerColor(4);
  gr1->SetMarkerStyle(20);
  gr1->Draw("SP+");

  c.cd(2);
  TH2F *h2 = new TH2F("h2","", 2, 0.0, 10.0, 2, 0, 10);
  h2->SetXTitle("x  ");
  h2->SetYTitle("f  ");
  h2->Draw();
  TGraphErrors *gr2 = new TGraphErrors(5, x2, y2, 0, ye2);
  gr2->SetMarkerColor(2);
  gr2->SetMarkerStyle(23);
  gr2->Draw("SP+");  

  // combined simultaneous fit?
  // decide a_0, par[0], par[1], and par[2] 
  // throughout simultaneous fit
  c.cd(3);
  TH2F *h3 = new TH2F("h3","", 2, 0.0, 10.0, 2, 0, 10);
  h3->SetXTitle("x  ");
  h3->SetYTitle("f  ");
  h3->Draw();
  TMultiGraph *mg = new TMultiGraph("mg","");
  mg.Add(gr1);
  mg.Add(gr2);
  mg->Draw("SP+");

  //
  TF1 *ff = new TF1("ff", "[3] * ( [0] + [1]*x + [2]*x*x )");
  ff->SetParName(3,"a_{0}"); // norm

  //----??
  //mg.Fit("ff", "E", "", 0.0, 9.5);