Example Multi Root

Example of using multiroot finder based on GSL algorithm. Find the root of Rosenbrock system of equations: f1(x,y) = a(1-x) f2(x,y) = b(y-x^2) with: a = 1, b=10

The MultiRootFinder is based on GSL and it requires the MathMore library installed

Usage:

>.x exampleMultiRoot.C()

>.x exampleMultiRoot(algoname,printlevel)

where algoname is for an algorithm not using the derivatives: hybridS (default) , hybrid, dnewton, broyden

Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer (Beta) from the macro found in the ROOT repository on Thursday, January 19, 2017 at 04:32 PM.



In [1]:

    
%%cpp -d
#include "RConfigure.h"

#ifdef R__HAS_MATHMORE
#include "Math/MultiRootFinder.h"
#endif
#include "Math/WrappedMultiTF1.h"
#include "TF2.h"
#include "TError.h"

Example of using multi root finder based on gsl need to use an algorithm not requiring the derivative like hybrids (default), hybrid, dnewton, broyden



In [2]:

    
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace ROOT::Math;

Arguments are defined.



In [3]:

    
const char * algo = 0;
int printlevel = 1;



In [4]:

    
#ifndef R__HAS_MATHMORE
Error("exampleMultiRoot","libMathMore is not available - cannot run this tutorial");
return;
#endif

ROOT::Math::MultiRootFinder r(algo);

Defining the function use Rosenbrock functions



In [5]:

    
TF2 * f1 = new TF2("f1","[0]*(1-x)+[1]*y");
TF2 * f2 = new TF2("f2","[0]*(y-x*x)");
f1->SetParameters(1,0);
f2->SetParameter(0,10);

Wrap the functions



In [6]:

    
ROOT::Math::WrappedMultiTF1 g1(*f1,2);
ROOT::Math::WrappedMultiTF1 g2(*f2,2);
r.AddFunction(g1);
r.AddFunction(g2);
r.SetPrintLevel(printlevel);

Starting point



In [7]:

    
double x0[2]={-1,-1};
r.Solve(x0);









    



GSLMultiRootFinder::Solve:hybrids max iterations 100 and  tolerance 1e-06
GSL Algorithm used is :  hybrids
Number of iterations  =  19
Root values     = x[0] =            1   x[1] =            1   
Function values = f[0] =            0   f[1] = -6.17162e-11   






    



Info in <ROOT::Math::GSLMultiRootFinder::Solve>: The iteration converged