# TSpline::GetCoeff delivers wrong results (factor 2)

Hi,

i am reading a *.csv into a TTree, then I plot a graph from it.
I then make the TSpline on this graph, which works fine.
Then I call TSpline->GetCoeff, and write those values in an array for each node. I then plot the arrays I want to see.

What puzzles me, is that “c”, the second coefficient, always seems to be missing factor 2.
So when I make .csv-files with numerical defined x^2, 2x^2 and x^3, I get 1, 2, and 3*x for “c”.

This is true for both TSpline3 and TSpline5.

This is, what the source-file says about the coefficient:

``Double_t fC; // second order expansion coefficient : fC*2! is the second derivative at x``

What am I missing?

Greetings,
Stephan

Here is a snippet that resembles the problem.
The fourth column in the output is the one I mistrust.

``````{
TF1 *f1 = new TF1("f1","x*x",0,2);
Double_t *a = new Double_t[5];
Double_t *b = new Double_t[5];

a[0]=0;
a[1]=0.5;
a[2]=1;
a[3]=1.5;
a[4]=2;

for (Int_t i=0; i<5; i++){b[i] = f1->Eval(a[i]);}

TGraph *g = new TGraph(5,a,b);
TSpline3 *s = new TSpline3("spline",g);

for (Int_t i=0; i<4; i++){
Double_t *x = new Double_t;
Double_t *y = new Double_t;
Double_t *b = new Double_t;
Double_t *c = new Double_t;
Double_t *d = new Double_t;

s->GetCoeff(i,*x,*y,*b,*c,*d);
printf("%e,%e,%e,%e,%e\n",*x,*y,*b,*c,*d);
}
}``````

Hey folks,

i even get bad results for the third derivative of TSpline.
For x^3 i get 1 where it should be 6, for 2x^3 I get 2 where it should be 12.

If I get it right (ROOT newbe), than the method BuildCoeff() is the point, where the math happens.

Is there anybody into this?

regards,
Stephan

Hi,

The coefficients are defined as documented in root.cern.ch/root/html/TSplinePoly3.html.

2!*C is the second derivative and 3! * D is the third derivative. So the value you are getting seems to me what is expected.

Sorry for the late reply.

Best Regards

Lorenzo