Piece-wise polynomial fitting

Newbie
1

Hi,

So I am having some issues regarding fitting a section of data sets. It seems it doesn’t fit the last few data sets. I have tried using code similar to

TF1 *f4= new TF1("f4", "(pol3)*(x<500)+(pol3)*(x>=500 && x<=600)+(pol4)*(x>600 && x<=1510)+(pol3)*(x>1510 && x<=2000)",-1,2000);

However, it doesn’t respect ranges and the fits don’t come out well. I have attached the picture and code below for reference. I have tried various combinations of pol as well as range however the best one is shown in the image.

image
image1588×801 7.56 KB

double numbers3[14]={ 20,	40,	100,	200,	375,	500,	750,	825,	1000,	1250,	1500,	2000,	2500,	3000};
double numbers5[14]={ 0,	0,	5.00E-05,	0.0002,	0.0004,	0.0004,	0.0002,	0.00045,	0.00020001,	0.0002,	0.0002,	0,	0,	0 };
double numbers6[14]={0,	0,	5.00E-05,	1.00E-04,	0.000141393,	0.000141393,	1.00E-04,	0.000149966,	1.00E-04,	1.00E-04,	1.00E-04,	0,	0,	0};

   TGraphErrors *g = new TGraphErrors();
   for(int i=0;i<14;i++){            
   g->SetPoint(i, numbers3[i],numbers5[i]);
   g->SetPointError(i,0,numbers6[i]);
   }

  g->Draw("AP");
  g->SetMarkerStyle(20);
  g->SetFillColor(6);
  g->SetFillStyle(3005);
  g->GetXaxis()->SetLimits(0,3100);
  g->GetYaxis()->SetLimits(-10,0.07195);
  
  
TF1 *f1= new TF1("f5", "(pol4)*(x<=750)",-1,750);
TF1 *f2= new TF1("f4", "(pol3)*(x>=749 && x<=1001)",749,1001);
TF1 *f3= new TF1("f6", "(pol3)*(x>=999 && x<=1501)",999,1501);
TF1 *f4= new TF1("f7", "(pol1)*(x>=1499 && x<=2001)",1499,2001);

g->Fit(f1,"R+");
g->Fit(f2,"R+"); 
g->Fit(f3,"R+");
g->Fit(f4,"R+");

Thank you for your help!

2

Perhaps @moneta or @StephanH can help?

3

This here:

Cannot work because the pol3 for the left part and the pol3 for the middle part have the same parameters. You need to write down the polynomials yourself, and give them different parameters:

(x[0]*1 + x[1]*x + x[2]*x*x) * (cut) + (x[3]*1 + ...) * (cut)

Note how I numbered the coefficients such that the polynomials are not the same.

4

Hi,

I tried your suggestion, here is the code snippet:
TF1 *f4= new TF1("f4", "([0]*x*x*x+[1]*x*x+[2]*x+[3])*(x<=750)+([4]*x*x*x+[5]*x*x+[6]*x+[7])*(x>=750 && x<=1000)+([8]*x*x*x+[9]*x*x+[10]*x+[11])*(x>=1000 && x<=1500)",-1,1500);

The graph created, however, isn’t very smooth, here is the image

image
image1548×768 7.05 KB

5

Hi,

Try to incrust the number of function points used to draw, by calling for example
`f4->SetNpx(10000)

Lorenzo

6

Hi, I tried the suggestion however the graph changed very little.