exampleFunction.py File Reference

Detailed Description

Example of using Python functions as inputs to numerical algorithms using the ROOT Functor class.

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Use Functor1D for wrapping one-dimensional function and compute integral of f(x) = x^2-1
integral-1D value =  5.999999999999999
 
 
Use Functor for wrapping a multi-dimensional function, the Rosenbrock Function r(x,y) and find its minimum
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =    1.687e-08
NDf                       =            0
Edm                       =  1.68896e-08
NCalls                    =          146
Par_0                     =     0.999952   +/-   1.00372     
Par_1                     =     0.999892   +/-   2.00986     
 
 
Use GradFunctor1D for making a function object implementing f(x) and f'(x)
Found root value x0 : f(x0) = 0  :   1.0
 
 
Use GradFunctor for making a function object implementing f(x,y) and df(x,y)/dx and df(x,y)/dy
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =  2.72222e-08
NDf                       =            0
Edm                       =  2.72448e-08
NCalls                    =           76
Par_0                     =     0.999954   +/-   1.00444     
Par_1                     =     0.999892   +/-   2.01131     

 
import ROOT
import array
try:
    import numpy as np
except:
    print("Failed to import numpy.")
    exit()
 
## example 1D function
 
def f(x):
   return x*x -1
 
func = ROOT.Math.Functor1D(f)
 
#example of using the integral
 
print("Use Functor1D for wrapping one-dimensional function and compute integral of f(x) = x^2-1")
 
ig = ROOT.Math.Integrator()
ig.SetFunction(func)
 
value = ig.Integral(0, 3)
print("integral-1D value = ", value)
expValue = 6
if (not ROOT.TMath.AreEqualRel(value, expValue, 1.E-15)) :
   print("Error computing integral - computed value - different than expected, diff = ", value - expValue)
   
# example multi-dim function
 
print("\n\nUse Functor for wrapping a multi-dimensional function, the Rosenbrock Function r(x,y) and find its minimum")
 
def RosenbrockFunction(xx):
  x = xx[0]
  y = xx[1]
  tmp1 = y-x*x
  tmp2 = 1-x
  return 100*tmp1*tmp1+tmp2*tmp2
 
 
func2D = ROOT.Math.Functor(RosenbrockFunction,2)
 
### minimize multi-dim function using fitter class
 
fitter = ROOT.Fit.Fitter()
#use a numpy array to pass initial parameter array 
initialParams = np.array([0.,0.], dtype='d')
fitter.FitFCN(func2D, initialParams)
fitter.Result().Print(ROOT.std.cout)
if (not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(0), 1, 1.E-3) or not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(1), 1, 1.E-3)) :
   print("Error minimizing Rosenbrock function ")
 
## example 1d grad function
## derivative of f(x)= x**2-1
 
print("\n\nUse GradFunctor1D for making a function object implementing f(x) and f'(x)")
 
def g(x): return 2 * x
 
gradFunc = ROOT.Math.GradFunctor1D(f, g)
 
#check if ROOT has mathmore
prevLevel = ROOT.gErrorIgnoreLevel
ROOT.gErrorIgnoreLevel=ROOT.kFatal
ret = ROOT.gSystem.Load("libMathMore") 
ROOT.gErrorIgnoreLevel=prevLevel
if (ret < 0) :
   print("ROOT has not Mathmore")
   print("derivative value at x = 1", gradFunc.Derivative(1) )
 
else :
   rf = ROOT.Math.RootFinder(ROOT.Math.RootFinder.kGSL_NEWTON)
   rf.SetFunction(gradFunc, 3)
   rf.Solve()
   value = rf.Root()
   print("Found root value x0 : f(x0) = 0  :  ", value)
   if (value != 1):
      print("Error finding a ROOT of function f(x)=x^2-1")
 
 
print("\n\nUse GradFunctor for making a function object implementing f(x,y) and df(x,y)/dx and df(x,y)/dy")
 
def RosenbrockDerivatives(xx, icoord):
  x = xx[0]
  y = xx[1]
  #derivative w.r.t x 
  if (icoord == 0) :
    return 2*(200*x*x*x-200*x*y+x-1)
  else : 
    return 200 * (y - x * x)
    
gradFunc2d = ROOT.Math.GradFunctor(RosenbrockFunction, RosenbrockDerivatives, 2)
 
fitter = ROOT.Fit.Fitter()
#here we use a python array to pass initial parameters
initialParams = array.array('d',[0.,0.])
fitter.FitFCN(gradFunc2d, initialParams)
fitter.Result().Print(ROOT.std.cout)
if (not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(0), 1, 1.E-3) or not ROOT.TMath.AreEqualRel(fitter.Result().Parameter(1), 1, 1.E-3)) :
   print("Error minimizing Rosenbrock function ")

Author

Lorenzo Moneta

Definition in file exampleFunction.py.