Scipy Optimizer for ROOT

Scipy


Description

Implementation for Scipy minimizer in ROOT math libraries.

TODO

See Scipy doc from more info on the Scipy minimization algorithms.

Installation

To install ROOT please read first.

To install scipy

pip3 install numpy scipy

Download code from github in the branch scipy

https://github.com/omazapa/root/tree/scipy

to enable it in ROOT just add -Dscipy in the cmake command

cmake -Dscipy=ON ..

ROOT Scipy documentation

TODO

Example

This is an example of minimization of the Rosenbrok function using multiple algoritms.

#include "Math/ScipyMinimizer.h"
#include "Math/Functor.h"
#include <string>

double RosenBrock(const double *xx )
{
  const Double_t x = xx[0];
  const Double_t y = xx[1];
  const Double_t tmp1 = y-x*x;
  const Double_t tmp2 = 1-x;
  return 100*tmp1*tmp1+tmp2*tmp2;
}

////"Newton-CG", "dogleg", "trust-ncg","trust-exact","trust-krylov"
using namespace std;
int scipy()
{ 
   
   std::string methods[]={"Nelder-Mead","L-BFGS-B","Powell","CG","BFGS","TNC","COBYLA","SLSQP","trust-constr"};
   // Choose method upon creation between:

   for(const std::string &text : methods)
   {
   ROOT::Math::Experimental::ScipyMinimizer minimizer(text.c_str());
   minimizer.SetMaxFunctionCalls(1000000);
   minimizer.SetMaxIterations(100000);
   minimizer.SetTolerance(0.001);
    
   ROOT::Math::Functor f(&RosenBrock,2); 
   double step[2] = {0.01,0.01};
   double variable[2] = { 0.1,1.2};
 
   minimizer.SetFunction(f);
 
   // Set the free variables to be minimized!
   minimizer.SetVariable(0,"x",variable[0], step[0]);
   minimizer.SetVariable(1,"y",variable[1], step[1]);
 
   minimizer.Minimize(); 
 
   const double *xs = minimizer.X();
   cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): " 
        << RosenBrock(xs) << endl;
   cout << endl << "===============" << endl;
   }
   return 0;
}

Output

ozapatam@tuxito:~/tmp/root_scipy_tests$ root -l -q scipy.C 

Processing scipy.C...
=== Scipy Minimization
=== Method: Nelder-Mead
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully.
=== Function calls: 164
Minimum: f(0.999984,0.999969): 2.91866e-10

===============
=== Scipy Minimization
=== Method: L-BFGS-B
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
=== Function calls: 81
Minimum: f(0.999997,0.999994): 1.17739e-11

===============
=== Scipy Minimization
=== Method: Powell
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully.
=== Function calls: 213
Minimum: f(1,1): 2.32911e-28

===============
=== Scipy Minimization
=== Method: CG
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully.
=== Function calls: 120
Minimum: f(1,1): 2.47448e-13

===============
=== Scipy Minimization
=== Method: BFGS
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully.
=== Function calls: 96
Minimum: f(0.999996,0.999991): 2.00488e-11

===============
=== Scipy Minimization
=== Method: TNC
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Converged (|f_n-f_(n-1)| ~= 0)
=== Function calls: 192
Minimum: f(0.999991,0.999983): 7.99587e-11

===============
=== Scipy Minimization
=== Method: COBYLA
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully.
=== Function calls: 387
Minimum: f(1.08352,1.17468): 0.00701966

===============
=== Scipy Minimization
=== Method: SLSQP
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: Optimization terminated successfully
=== Function calls: 70
Minimum: f(1.00002,1.00004): 2.20434e-09

===============
=== Scipy Minimization
=== Method: trust-constr
=== Initial value: (0.1,1.2)
=== Status: 0
=== Message: `gtol` termination condition is satisfied.
=== Function calls: 105
Minimum: f(0.999996,0.999991): 2.00614e-11

===============
(int) 0

Current Status and Supported Features

This a basic prototype, it does not support constraints and many features that can be implemented!