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makeikk.cc

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// makeikk.cc
// A simple program to generate the Kramers-Kronig transform of a normalized
// SIS DC IV curve, such as generated by makeiv.cc. It gives good results
// most of the time; Examine a plot of the output to ensure that there are
// no discontinuities introduced by numerical artifacts.
//
// An input file name must be included on the command line;
// the output will be written to the standard output stream.

#include "supermix.h"
#include "numerical.h"

const char *comment = "#";

// ---------------------------------------------------------------------------
// Some parameters you can adjust to control the integration (see integrate.h):

unsigned   ORDER   = 3;        // the order of the Rhomberg extrapolation (min 1)
double     ABS_TOL = 1.0e-9;   // absolute error tolerance
double     REL_TOL = 1.0e-10;  // relative error tolerance

// Lowering the tolerances to ~ 1.0e-7 may generate the results more quickly, but
// will only work well if the DC IV curve is not very sharp at the gap. Lowering
// ORDER to 1 may help, but often will not. If you run into convergence
// problems, this condition will usually be indicated by an error message like
// "WARNING: Recursion limit reached in adaptive interpolator build."
// Ensure that you carefully examine the output in this case; if the input IV
// curve is very sharp, the output may be just fine, even though the warning was
// output. 
// If you do have convergence problems, try reducing ORDER and tightening the
// error tolerances.
// ---------------------------------------------------------------------------

real_interp IDC;
double Vo;
double idc(double v) { return (v < 0.0) ? -IDC(-v) : IDC(v); }

struct F {
  double x;
  F(double xx): x(xx) { }
  double operator()(double v) const
    { return (idc(v+x) + idc(v-x) - 2*idc(v))/v; }
};
 
integrator<double> In;
double ikk_f(double x)
{
  F f(x);
  return (In.open()(f, 0, Vo/3) + In.exp()(f, Vo/3, 1000))/Pi;
}

int main(int argc, char **argv) 
{
  if(argc < 2) {
    cerr << "Usage: " << argv[0] << " <idc_file>" << endl;
    return 1;
  }

  const char * name = argv[1];
  IDC.file(name).quiet();
  Vo = IDC.x(IDC.size()-1);     // max voltage in the table

  // Set the integrator control parameters:
  In.order = ORDER;
  In.abs_tolerance  = ABS_TOL;
  In.rel_tolerance = REL_TOL;

  interpolation ikk;
  ikk.left_slope(0);

  // Don't set accuracies any tighter in the following, or you may see
  // convergence problems. Note that we generate the transform values
  // out to voltages double those in the DC IV data set.
  adaptive_fill(ikk, ikk_f, 0, 2*Vo, 1e-6, 1e-3);

  cout << fixed << setprecision(10);
  cout << comment << " Normalized SIS Kramers-Kronig IV characteristic curve" << endl;
  cout << comment << " The DC IV file for this data:  " << name << endl;
  cout << comment << endl;
  cout << comment << " V:         " << "\t" << "I:" << endl;

  for (unsigned i = 0; i < ikk.size(); ++i)
    cout << ikk.x(i) << "\t" << ikk[i] << endl;
  return 0;
}

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