root > .x binomial.C
root > .x binomial.C+ with ACLIC
Author: Federico Carminati
This notebook tutorial was automatically generated with ROOTBOOK-izer (Beta) from the macro found in the ROOT repository on Thursday, January 19, 2017 at 04:31 PM.
In [1]:
%%cpp -d
#include <TMath.h>
#include <TRandom.h>
A helper function is created:
In [2]:
%%cpp -d
void binomialSimple() {
//
// Simple test for the binomial distribution
//
printf("\nTMath::Binomial simple test\n");
printf("Build the Tartaglia triangle\n");
printf("============================\n");
const Int_t max=13;
Int_t j;
for(Int_t i=0;i<max;i++) {
printf("n=%2d",i);
for(j=0;j<(max-i);j++) printf(" ");
for(j=0;j<i+1;j++) printf("%4d",TMath::Nint(TMath::Binomial(i,j)));
printf("\n");
}
}
A helper function is created:
In [3]:
%%cpp -d
void binomialFancy() {
Double_t x;
Double_t y;
Double_t res1;
Double_t res2;
Double_t err;
Double_t serr=0;
const Int_t nmax=10000;
printf("\nTMath::Binomial fancy test\n");
printf("Verify Newton formula for (x+y)^n\n");
printf("x,y in [-2,2] and n from 0 to 9 \n");
printf("=================================\n");
TRandom r;
for(Int_t i=0; i<nmax; i++) {
do {
x=2*(1-2*r.Rndm());
y=2*(1-2*r.Rndm());
} while (TMath::Abs(x+y)<0.75); //Avoid large cancellations
for(Int_t j=0; j<10; j++) {
res1=TMath::Power(x+y,j);
res2=0;
for(Int_t k=0; k<=j; k++)
res2+=TMath::Power(x,k)*TMath::Power(y,j-k)*TMath::Binomial(j,k);
if((err=TMath::Abs(res1-res2)/TMath::Abs(res1))>1e-10)
printf("res1=%e res2=%e x=%e y=%e err=%e j=%d\n",res1,res2,x,y,err,j);
serr +=err;
}
}
printf("Average Error = %e\n",serr/nmax);
}
In [4]:
binomialSimple();
binomialFancy();