JPolynome1D.cc

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#include <string>
#include <iostream>
#include <sstream>
#include <iomanip>
#include <map>

#include "TRandom3.h"

#include "JLang/JException.hh"
#include "JMath/JPolynome.hh"
#include "JTools/JFunction1D_t.hh"
#include "JTools/JGrid.hh"
#include "JTools/JQuantile.hh"
#include "JTools/JToolsToolkit.hh"

#include "Jeep/JPrint.hh"
#include "Jeep/JParser.hh"
#include "Jeep/JMessage.hh"

namespace {

  using JTOOLS::JQuantile;

  struct JABC {

    JABC(const char* title) :
      f (title),
      fp(title),
      v (title)
    {}

    JQuantile f;
    JQuantile fp;
    JQuantile v;
  };


  struct JPrecision_t {

    JPrecision_t() :
      f (0.0),
      fp(0.0),
      v (0.0)
    {}

    JPrecision_t(const double f,
                 const double fp,
                 const double v) :
      f (f),
      fp(fp),
      v (v)
    {}
    
    friend std::istream& operator>>(std::istream& in, JPrecision_t& object)
    {
      return in >> object.f >> object.fp >> object.v;
    }

    friend std::ostream& operator<<(std::ostream& out, const JPrecision_t& object)
    {
      return out << object.f << ' ' << object.fp << ' ' << object.v;
    }

    double f;
    double fp;
    double v;
  };
}


/**
 * \file
 *
 * Example program to test 1D interpolation of a polynome.
 * \author mdejong
 */
int main(int argc, char **argv)
{
  using namespace std;
  using namespace JPP;

  typedef map<string, JPrecision_t> map_type;

  unsigned int  numberOfEvents;
  unsigned int  numberOfBins;
  JPolynome     f1;
  map_type      precision;
  int           debug;

  precision["spline"]  = JPrecision_t(1.0e-3,  1.0e-1,  1.0e-4);
  precision["hermite"] = JPrecision_t(1.0e-3,  1.0e-1,  1.0e-4);
  precision["grid"]    = JPrecision_t(1.0e-3,  1.0e-1,  1.0e-4);
  precision["polint"]  = JPrecision_t(1.0e-14, 1.0e-12, 1.0e-14);

  try {

    JParser<> zap("Example program to test 1D interpolation of a polynome.");

    zap['n'] = make_field(numberOfEvents)   =  0;
    zap['N'] = make_field(numberOfBins)     = 21;
    zap['P'] = make_field(f1);
    zap['e'] = make_field(precision)        = JPARSER::initialised();
    zap['d'] = make_field(debug)            =  3;

    zap(argc, argv);
  }
  catch(const exception &error) {
    FATAL(error.what() << endl);
  }


  const int N = 3;                        // fixed degree of polynomial interpolation
  
  JSplineFunction1S_t         spline;
  JHermiteSplineFunction1S_t  hermite;
  JGridSplineFunction1S_t     grid;
  JPolintFunction1H_t< N >    polint;
  JPolintFunction1D_t<N+1>    Polint;     // integrand of polint

  const double xmin = -1.0;
  const double xmax = +1.0;  

  spline .configure(make_grid(numberOfBins, xmin, xmax), f1);
  hermite.configure(make_grid(numberOfBins, xmin, xmax), f1);
  grid   .configure(make_grid(numberOfBins, xmin, xmax), f1);
  polint .configure(make_grid(numberOfBins, xmin, xmax), f1);

  spline .compile();
  hermite.compile();
  grid   .compile();
  polint .compile();
  
  integrate(polint, Polint);

  Polint.compile();
    
  if (numberOfEvents != 0) {

    JABC Qspline ("spline");
    JABC Qhermite("hermite");
    JABC Qgrid   ("grid");
    JABC Qpolint ("polint");
    
    for (unsigned int i = 0; i != numberOfEvents; ++i) {
      
      const double x  = gRandom->Uniform(xmin, xmax);
      
      const double y1 = f1.getValue(x);
      const double fp = f1.getDerivative(x);
      const double F1 = f1.getIntegral(x) - f1.getIntegral(xmin);
      
      Qspline .f .put(y1 - spline (x).f);
      Qhermite.f .put(y1 - hermite(x).f);
      Qgrid   .f .put(y1 - grid   (x).f);
      Qpolint .f .put(y1 - polint (x).f);

      Qspline .fp.put(fp - spline (x).fp);
      Qhermite.fp.put(fp - hermite(x).fp);
      Qgrid   .fp.put(fp - grid   (x).fp);
      Qpolint .fp.put(fp - polint (x).fp);

      Qspline .v .put(F1 - spline (x).v);
      Qhermite.v .put(F1 - hermite(x).v);
      Qgrid   .v .put(F1 - grid   (x).v);
      Qpolint .v .put(F1 - Polint (x));
    }

    if (debug >= debug_t) {
    
      cout << "RMS:         f          f'         F     " << endl;
      cout << "_________________________________________" << endl;
      
      cout << "spline  "
           << SCIENTIFIC(10,3) << Qspline .f .getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qspline .fp.getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qspline .v .getSTDev() << endl;

      cout << "hermite "
           << SCIENTIFIC(10,3) << Qhermite.f .getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qhermite.fp.getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qhermite.v .getSTDev() << endl;
      
      cout << "grid    "
           << SCIENTIFIC(10,3) << Qgrid   .f .getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qgrid   .fp.getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qgrid   .v .getSTDev() << endl;
      
      cout << "polint  "
           << SCIENTIFIC(10,3) << Qpolint .f .getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qpolint .fp.getSTDev() << ' '
           << SCIENTIFIC(10,3) << Qpolint .v .getSTDev() << endl;
    }

    ASSERT(Qspline .f .getSTDev() <= precision["spline"].f);
    ASSERT(Qspline .fp.getSTDev() <= precision["spline"].fp);
    ASSERT(Qspline .v .getSTDev() <= precision["spline"].v);

    ASSERT(Qhermite.f .getSTDev() <= precision["hermite"].f);
    ASSERT(Qhermite.fp.getSTDev() <= precision["hermite"].fp);
    ASSERT(Qhermite.v .getSTDev() <= precision["hermite"].v);

    ASSERT(Qgrid   .f .getSTDev() <= precision["grid"].f);
    ASSERT(Qgrid   .fp.getSTDev() <= precision["grid"].fp);
    ASSERT(Qgrid   .v .getSTDev() <= precision["grid"].v);

    ASSERT(Qpolint .f .getSTDev() <= precision["polint"].f);
    ASSERT(Qpolint .fp.getSTDev() <= precision["polint"].fp);
    ASSERT(Qpolint .v .getSTDev() <= precision["polint"].v);

  } else {

    for ( ; ; ) {
        
      string buffer;
      
      cout << "> " << flush;

      getline(cin, buffer);
      
      if (buffer != "") {
        
        try {

          double x;
          
          istringstream(buffer) >> x;

          cout << "f1          " << f1     (x)   << endl;
          cout << "spline      " << spline (x).f << endl;
          cout << "hermite     " << hermite(x).f << endl;
          cout << "grid spline " << grid   (x).f << endl;
          cout << "polynomial  " << polint (x).f << endl;
        }
        catch(const JException& exception) {
          cout << exception.what() << endl;
        }

      } else {
        break;
      }
    }
  }

  return 0;
}