added scipy.C macro in fit tutorial

Author: omazapa

tutorials/fit/scipy.C

@@ -0,0 +1,83 @@
+#include "Math/ScipyMinimizer.h"
+#include "Math/MultiNumGradFunction.h"
+#include <Fit/ParameterSettings.h>
+#include "Math/Functor.h"
+#include <string>
+#include "Math/MinimizerOptions.h"
+#include "TStopwatch.h"
+
+
+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;
+}
+
+double RosenBrockGrad(const double *x, unsigned int ipar)
+{
+   if (ipar == 0)
+      return -2 * (1 - x[0]) + 200 * (x[1] - x[0] * x[0]) * (-2 * x[0]);
+   else
+      return 200 * (x[1] - x[0] * x[0]);
+}
+
+bool RosenBrockHessian(const std::vector<double> &xx, double *hess)
+{
+   const double x = xx[0];
+   const double y = xx[1];
+   
+   hess[0] = 1200*x*x - 400*y + 2;
+   hess[1] = -400*x;
+   hess[2] = -400*x;
+   hess[3] = 200;
+   
+   return true;
+}
+
+// methods that requires hessian to work "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","Newton-CG", "dogleg", "trust-ncg","trust-exact","trust-krylov"};
+   TStopwatch t;
+   for(const std::string &text : methods)
+   {
+      ROOT::Math::Experimental::ScipyMinimizer minimizer(text.c_str());
+      minimizer.SetMaxFunctionCalls(1000000);
+      minimizer.SetMaxIterations(100000);
+      minimizer.SetTolerance(1e-3);
+      minimizer.SetExtraOption("gtol",1e-3);
+      ROOT::Math::GradFunctor f(&RosenBrock,&RosenBrockGrad,2); 
+      double step[2] = {0.01,0.01};
+      double variable[2] = { -1.2,1.0};
+   
+      minimizer.SetFunction(f);
+      minimizer.SetHessianFunction(RosenBrockHessian);
+   
+      // variables to be minimized!
+      minimizer.SetVariable(0,"x",variable[0], step[0]);
+      minimizer.SetVariable(1,"y",variable[1], step[1]);
+      minimizer.SetVariableLimits(0, -2.0, 2.0);
+      minimizer.SetVariableLimits(1, -2.0, 2.0);
+
+      t.Reset();
+      t.Start();
+      minimizer.Minimize(); 
+      t.Stop();
+      const double *xs = minimizer.X();
+      cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): " 
+         << RosenBrock(xs) << endl;
+      cout << "Cpu Time (sec) = " << t.CpuTime() <<endl<< "Real Time (sec) = " << t.RealTime() << endl;
+      cout << endl << "===============" << endl;
+   }
+   return 0;
+}
+
+int main()
+{
+  return scipy();
+}