JMultiFunction1D.cc

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#include <string>
#include <iostream>
#include <iomanip>
#include <cmath>

#include "TRandom3.h"
#include "TMath.h"

#include "JTools/JMapList.hh"
#include "JTools/JFunction1D_t.hh"
#include "JTools/JFunctionalMap_t.hh"
#include "JTools/JConstantFunction1D.hh"
#include "JTools/JMultiFunction.hh"
#include "JTools/JQuantile.hh"
#include "JTools/JToolsToolkit.hh"

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

namespace {

  using namespace JPP;

  /**
   * 5D test function.
   */
  inline double f5(const double x0,
                   const double x1,
                   const double x2,
                   const double x3,
                   const double x4)
  {
    return TMath::Gaus(x4, x0+x1+x2+x3, 1.0, kTRUE);
  }
}


/**
 * \file
 *
 * Example program to create 1D function interpolator from multi-dimensional interpolator.
 * \author mdejong
 */
int main(int argc, char **argv)
{
  using namespace std;
  using namespace JPP;

  int         numberOfEvents;
  int         numberOfBins;
  double      precision;
  int         debug;

  try {

    JParser<> zap("Example program to create 1D function interpolator from multi-dimensional interpolator.");

    zap['n'] = make_field(numberOfEvents)   = 1000;
    zap['N'] = make_field(numberOfBins)     = 11;
    zap['e'] = make_field(precision)        = 1.0e-14;
    zap['d'] = make_field(debug)            = 3;

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

  ASSERT(numberOfEvents > 0);

  const double xmin = -1.0;
  const double xmax = +1.0;
  const double dx   = (xmax - xmin) / (numberOfBins - 1);

  typedef JSplineFunction1D<JSplineElement2D<double, double>, JCollection> JFunction1D_t;
  typedef JFunction1D_t::abscissa_type                                     abscissa_type;
  typedef JFunction1D_t::value_type                                        value_type;

  typedef JConstantFunction1D<abscissa_type, JCollection<value_type> >     JCollection1D_t;

  typedef JMAPLIST<JPolint1FunctionalMap,
    JPolint1FunctionalMap,
    JPolint1FunctionalMap,
    JPolint1FunctionalMap>::maplist                         JMaplist_t;

  JMultiFunction<JFunction1D_t,   JMaplist_t>  g5;
  JMultiFunction<JCollection1D_t, JMaplist_t>  h5;

  for (double x0 = xmin; x0 < xmax + 0.5*dx; x0 += dx) {
    for (double x1 = xmin; x1 < xmax + 0.5*dx; x1 += dx) {
      for (double x2 = xmin; x2 < xmax + 0.5*dx; x2 += dx) {
        for (double x3 = xmin; x3 < xmax + 0.5*dx; x3 += dx) {
          for (double x4 = xmin; x4 < xmax + 0.5*dx; x4 += dx) {
            g5[x0][x1][x2][x3][x4] = f5(x0,x1,x2,x3,x4);
            h5[x0][x1][x2][x3][x4] = f5(x0,x1,x2,x3,x4);
          }
        }
      }
    }
  }

  g5.compile();
  h5.compile();


  const double x0 = +0.15;
  const double x1 = -0.25;
  const double x2 =  0.25;
  const double x3 = -0.15;
    
  JFunction1D_t g1;

  JTimer timer("4D interpolator");

  timer.start();

  for (int i = 0; i != 100; ++i) {
    copy(h5(x0,x1,x2,x3), g1);      // put interpolated data into 1D functional object
  }

  timer.stop();
  timer.print(cout, 1.0/100, micro_t);

  g1.compile();

  JTimer t1("1D interpolator");
  JTimer t5("5D interpolator");

  JQuantile Q1("1D interpolator");
  JQuantile Q5("5D interpolator");
    
  // mini buffer to reduce overhead in timer

  const int N = 100;

  double x[N];
  double y[N];
  double v[N];
  double w[N];

  for (int i = 0; i != numberOfEvents; ++i) {

    for (int __i = 0; __i != N; ++__i) {

      const double x4 = gRandom->Uniform(xmin, xmax);

      x[__i] = x4;
      y[__i] = f5(x0,x1,x2,x3,x4);
    }

    t1.start();

    for (int __i = 0; __i != N; ++__i) {
      v[__i] = g1(x[__i]);
    }

    t1.stop();

    t5.start();

    for (int __i = 0; __i != N; ++__i) {
      w[__i] = g5(x0,x1,x2,x3,x[__i]);
    }

    t5.stop();

    for (int __i = 0; __i != N; ++__i) {
      Q1.put(v[__i] - y[__i]);
      Q5.put(w[__i] - y[__i]);
    }
  }

  if (debug >= notice_t) {

    Q1.print(cout);
    Q5.print(cout, false);
      
    t1.print(cout, 1.0 / (N * numberOfEvents), nano_t);
    t5.print(cout, 1.0 / (N * numberOfEvents), nano_t);
  }

  ASSERT(fabs(Q1.getMean()  - Q5.getMean())  <= precision);
  ASSERT(fabs(Q1.getSTDev() - Q5.getSTDev()) <= precision);

  return 0;
}