Integral with log binning

Hello ROOT crew,

Just a comment: the Integral method provided with TGraph seems not to work with logarithmic binning (so in the end I wrote something myself). It would be nice to have an alternative method prodived (e.g. simple trapezoidal approximation) to do 2D integration for binnings other than linear.

Cheers, Till

Can you be a be more precise ? TGraph has no “binning”. TGraph can be drawn in log scales but that purely graphics… So what do you mean by “log binning” ?

Hello couet,

You are right, my initial description was was not very precise. Actually, the idea with the log binning was a guess (and at a second look nonsense - sorry).

I had a look in the method in question: Double_t TGraph::Integral(Int_t first, Int_t last) const (v5.27.04).
And I found out that disagreement what I got for the integral was due to the fact that when I called the method the loop inside ( “for(Int_t i=first;i<=last;i++)” ) was adding as last element: “(fY[last]+fY[first])*(fX[first]-fX[last])” which to my mind it shouldn’t!!! So by changing in the source the loop to: “for(Int_t i=first;i<last;i++)” the integral is correct.

T

Hi,

I think the TGraph::Integral method is correct. You have to use the TGraph indexing convention, the index starts from 0 and the index for the n-th point is n-1.

Lorenzo

Yes, I know. Actually, inside the method it is checked that we don’t get out-of-bound with the indices (e.g.: “if(last >= fNpoints) last = fNpoints-1;”). But regardless if I integrate “from 0 to fNpoints-1” or “from 0 to fNpoints-2”, etc, the indices of the last term in the sum are i=last and j=first - which shouldn’t be!

Check out this small piece of python code:

from array import array
from ROOT import TGraph

TESTgr=TGraph( 3, array('f',[1,2,3]) , array('f',[1,1,1]) )
print 'TEST integral:',TESTgr.Integral()

The integral should be 2. Instead the output I get is:

If I cout the variables of the loop of TGraph::Integral method I get:

i=0 j=1 fX[i]=1 fX[j]=2 sum term:2
i=1 j=2 fX[i]=2 fX[j]=3 sum term:2
i=2 j=0 fX[i]=3 fX[j]=1 sum term:-4

… which is then divided by 2: (2+2-4)/2=0. Obviously the last sum term is wrong as I described before!

Cheers, T

Hi,

TGraph::Integral returns the integral of a closed polygon. So in your specific example it is right to return 0 since the TGraph is not closed. To get the value you expect you should use the TGraph with :

double x[] = { 1,2,3,4,5}
double y[] = { 1,1,1,0,0}

Lorenzo

Ok, I guess I skipped this - it’s actually written in the method description - I was just assuming that the method does what one would expect. Thanks for noting!
Anyways, wouldn’t it be nice to have a method to give the area between a series of points and the x-axis without the need to modify your graph? It could be quite useful - for example, to estimate the impact of a cut parameter.

Cheers, Till