ABACUS/src/EXECS/LiebLin_Fourier_to_x_equal_...

/**********************************************************

This software is part of J.-S. Caux's ABACUS library.

Copyright (c) J.-S. Caux.

-----------------------------------------------------------

File:  LiebLin_Fourier_to_x_equal_t.cc

Purpose:  Fourier transform to static space correlator for LiebLin.

***********************************************************/

#include "ABACUS.h"

using namespace std;
using namespace ABACUS;


int main(int argc, char* argv[])
{
  if (argc != 9) { // provide some info

    cout << endl << "Welcome to ABACUS\t(copyright J.-S. Caux)." << endl;
    cout << endl << "Usage of LiebLin_Fourier_to_x_equal_t executable: " << endl;
    cout << endl << "Provide the following arguments:" << endl << endl;
    cout << "char whichDSF \t\t Which structure factor ?  Options are:  "
      "d for rho rho, g for psi psi{dagger}, o for psi{dagger} psi" << endl;
    cout << "DP c_int \t\t Value of the interaction parameter" << endl;
    cout << "DP L \t\t\t Length of the system" << endl;
    cout << "int N \t\t\t Number of particles" << endl;
    cout << "int iKmin" << endl << "int iKmax \t\t Min and max momentum integers scanned over" << endl;
    cout << "DP kBT \t\t Temperature" << endl;
    cout << "int Npts_x Number of points in space for the Fourier transform" << endl;
  }

  else { // (argc == 9), correct nr of arguments
    char whichDSF = *argv[1];
    DP c_int = atof(argv[2]);
    DP L = atof(argv[3]);
    int N = atoi(argv[4]);
    int iKmin = atoi(argv[5]);
    int iKmax = atoi(argv[6]);
    DP kBT = atof(argv[7]);
    int Npts_x = atoi(argv[8]);

    stringstream filenameprefix;
    Data_File_Name (filenameprefix, whichDSF, c_int, L, N, iKmin, iKmax, kBT, 0.0, "");
    string prefix = filenameprefix.str();

    stringstream RAW_stringstream;    string RAW_string;
    RAW_stringstream << prefix << ".raw";
    RAW_string = RAW_stringstream.str();    const char* RAW_Cstr = RAW_string.c_str();
    ifstream RAW_infile;
    RAW_infile.open(RAW_Cstr);
    if (RAW_infile.fail()) {
      cout << RAW_Cstr << endl;
      ABACUSerror("Could not open RAW_infile... ");
    }

    // We also read the f-sumrule file, to correct for missing intensity.
    stringstream FSR_stringstream;    string FSR_string;
    FSR_stringstream << prefix << ".fsr";
    FSR_string = FSR_stringstream.str();    const char* FSR_Cstr = FSR_string.c_str();
    ifstream FSR_infile;
    FSR_infile.open(FSR_Cstr);
    if (FSR_infile.fail()) {
      cout << FSR_Cstr << endl;
      ABACUSerror("Could not open FSR_infile... ");
    }

    stringstream SFT_stringstream;    string SFT_string;
    SFT_stringstream << prefix << ".sft";
    SFT_string = SFT_stringstream.str();    const char* SFT_Cstr = SFT_string.c_str();
    ofstream SFT_outfile;
    SFT_outfile.open(SFT_Cstr);
    if (SFT_outfile.fail()) ABACUSerror("Could not open SFT_outfile... ");

    // First compute the static structure factor from the RAW data:

    Vect_DP SSF(0.0, iKmax - iKmin + 1);

    DP omega;
    int iK;
    DP FF;
    DP dev;
    string label;

    while (RAW_infile.peek() != EOF) {
      RAW_infile >> omega >> iK >> FF >> dev >> label;
      if (iK >= iKmin && iK <= iKmax) {
	SSF[iK - iKmin] += FF * FF;
      }
    }
    RAW_infile.close();

    // Reset proper normalization:
    DP normalization = twoPI * L;
    for (int iK = 0; iK < iKmax - iKmin + 1; ++iK) SSF[iK] *= normalization/twoPI; // twoPI from integral over omega

    // We now refine the SSF in the following way.
    // First, we read off the f-sumrule saturation from the FSR file.
    // Then, we put back the missing weight, assuming that it lives
    // on the free k^2 dispersion relation (so the DSF is then simply 2\pi N/L \delta(\omega - k^2)).

    Vect_DP FSRsaturated(0.0, iKmax - iKmin + 1);
    int dummyint;
    DP dummy;
    for (int i = iKmin; i <= iKmax; ++i)
      FSR_infile >> dummyint >> FSRsaturated[i - iKmin] >> dummy;

    FSR_infile.close();

    // Now correct the SSF by the missing piece:
    //for (int iK = iKmin; iK <= iKmax; ++iK)
    //SSF[iK - iKmin] += (1.0 - FSRsaturated[iK - iKmin]) * N/L;

    //cout << FSRsaturated << endl;

    //cout << SSF << endl;

    // Now define real-space coordinates: between 0 and L
    Vect_DP xlattice(Npts_x);
    for (int i = 0; i < Npts_x; ++i) xlattice[i] = (i + 0.5) * L/Npts_x;

    // Now the correlation at x:
    Vect_DP FTre(0.0, Npts_x);
    Vect_DP FTim(0.0, Npts_x);

    DP twopioverL = twoPI/L;

    // Fourier transform:
    for (int ix = 0; ix < Npts_x; ++ix) {
      for (int iK = iKmin; iK <= iKmax; ++iK) {
	FTre[ix] += SSF[iK - iKmin] * cos(twopioverL * iK * xlattice[ix]);
	FTim[ix] += SSF[iK - iKmin] * sin(twopioverL * iK * xlattice[ix]);
      }
      // Reset proper normalization: 1/L from space FT,
      FTre[ix] /= L;
      FTim[ix] /= L;

      // Outside of window iKmin, iKmax, we take the DSF to be a constant with delta function
      // at free energy k^2, so DSF = 2\pi N/L \delta(\omega - k^2) (to fit f-sumrule)
      // so SSF becomes N/L.
      // We thus need to correct above by adding
      // \frac{1}{L} \sum_{-\infty}^{iKmin - 1} SSF e^{ikx} + \frac{1}{L} \sum_{iKmax + 1}^\infty SSF e^{ikx}
      // Resumming carefully:
      if (whichDSF == 'd') {
	FTre[ix] += (sin(twopioverL * (iKmin - 0.5) * xlattice[ix]) - sin(twopioverL * (iKmax + 0.5) * xlattice[ix]))
	  * N/(2.0 * L*L * sin(PI * xlattice[ix]/L));
	FTim[ix] += (-cos(twopioverL * (iKmin - 0.5) * xlattice[ix]) + cos(twopioverL * (iKmax + 0.5) * xlattice[ix]))
	  * N/(2.0 * L*L * sin(PI * xlattice[ix]/L));
      }
    }

    // Since iKmax and iKmin are finite, we need to average over an interval of
    // deltax such that (2\pi/L) iKmax deltax = 2\pi, with deltax == deltaix * L/Npts_x
    // so deltaix = (Npts_x/L) * (L/iKmax)
    /*
    int deltaix = 0*int(Npts_x/(2.0*iKmax));
    cout << "deltaix = " << deltaix << endl;

    Vect_DP FTreavg(0.0, Npts_x);
    Vect_DP FTimavg(0.0, Npts_x);
    for (int ix = 0; ix < Npts_x; ++ix) {
      for (int ix2 = -deltaix; ix2 < deltaix; ++ix2) {
	FTreavg[ix] += FTre[ABACUS::min(ABACUS::max(0, ix + ix2), Npts_x - 1)];
	FTimavg[ix] += FTim[ABACUS::min(ABACUS::max(0, ix + ix2), Npts_x - 1)];
      }
      FTreavg[ix] /= (2*deltaix + 1);
      FTimavg[ix] /= (2*deltaix + 1);
    }
    */
    if (whichDSF == 'd') cout << "g2(0) = dE0_dc/L = " << LiebLin_dE0_dc (c_int, L, N)/L
			      << "\t" << LiebLin_dE0_dc (c_int, 2.0*L, 2*N)/(2.0*L) << endl;

    // Output to file:
    for (int ix = 0; ix < Npts_x; ++ix) {
      if (ix > 0) SFT_outfile << endl;
      //SFT_outfile << xlattice[ix] << "\t" << FTre[ix] << "\t" << FTim[ix] << "\t" << FTreavg[ix] << "\t" << FTimavg[ix];
      SFT_outfile << xlattice[ix] << "\t" << FTre[ix] << "\t" << FTim[ix];
    }

    SFT_outfile.close();
  }

  return(0);

}