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binomial.C File Reference

## Detailed Description

tutorial illustrating the use of TMath::Binomial can be run with:

root > .x binomial.C
root > .x binomial.C+ with ACLIC
TMath::Binomial simple test
Build the Tartaglia triangle
============================
n= 0 1
n= 1 1 1
n= 2 1 2 1
n= 3 1 3 3 1
n= 4 1 4 6 4 1
n= 5 1 5 10 10 5 1
n= 6 1 6 15 20 15 6 1
n= 7 1 7 21 35 35 21 7 1
n= 8 1 8 28 56 70 56 28 8 1
n= 9 1 9 36 84 126 126 84 36 9 1
n=10 1 10 45 120 210 252 210 120 45 10 1
n=11 1 11 55 165 330 462 462 330 165 55 11 1
n=12 1 12 66 220 495 792 924 792 495 220 66 12 1
TMath::Binomial fancy test
Verify Newton formula for (x+y)^n
x,y in [-2,2] and n from 0 to 9
=================================
Average Error = 1.060390e-13
#include <TMath.h>
#include <TRandom.h>
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");
}
}
void binomialFancy() {
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");
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++)
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);
}
void binomial () {
binomialSimple();
binomialFancy();
}
ROOT::R::TRInterface & r
Definition Object.C:4
#define e(i)
Definition RSha256.hxx:103
int Int_t
Definition RtypesCore.h:45
double Double_t
Definition RtypesCore.h:59
This is the base class for the ROOT Random number generators.
Definition TRandom.h:27
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17
Int_t Nint(T x)
Round to nearest integer. Rounds half integers to the nearest even integer.
Definition TMath.h:713
Double_t Binomial(Int_t n, Int_t k)
Calculate the binomial coefficient n over k.
Definition TMath.cxx:2083
LongDouble_t Power(LongDouble_t x, LongDouble_t y)
Definition TMath.h:735
Short_t Abs(Short_t d)
Definition TMathBase.h:120

Definition in file binomial.C.