Scipy Optimizer for ROOT

Scipy


Description

Implementation for Scipy minimizer in ROOT math libraries. This is an interface written in C++ using Python C-API and the plugin system implemented in the meth libraries in ROOT. This is under active development and hopefully It will be integrated to ROOT in the future.

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 and Scipy documentation

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

See Minuit2 Guide
See Minuit2 Tutorial
See Minimizer class
for more info on the ROOT minimization algorithms.

You can find some code benchmarking minimizers here

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

  • Integrated to the plugin system in ROOT
  • Support to pass jacobian and Hessian
  • It does not support constraints (Under development)

Many features that can be implemented coming soon!