exampleMultiRoot.C File Reference

Detailed Description

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()

or

>.x exampleMultiRoot(algoname,printlevel)

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

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] =  2.61797e-10   

 
#include "RConfigure.h"
 
#ifdef R__HAS_MATHMORE
#include "Math/MultiRootFinder.h"
#else
#error libMathMore is not available - cannot run this tutorial
#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
 
using namespace ROOT::Math;
void exampleMultiRoot(const char * algo = nullptr, int printlevel = 1) {
   ROOT::Math::MultiRootFinder r(algo);
   //defining the function
   // use Rosenbrock functions
   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
   ROOT::Math::WrappedMultiTF1 g1(*f1,2);
   ROOT::Math::WrappedMultiTF1 g2(*f2,2);
   r.AddFunction(g1);
   r.AddFunction(g2);
   r.SetPrintLevel(printlevel);
 
   // starting point
   double x0[2]={-1,-1};
   r.Solve(x0);
}

Author

Lorenzo Moneta

Definition in file exampleMultiRoot.C.