ABACUS/src/XXX_VOA/XXX_h0_v2.cc

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

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

Copyright (c) J.-S. Caux.

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

File: XXX_h0_v2.cc

Purpose: Defines all class procedures used for the XXX chain in zero field.
        Aims at calculating the full k, omega dependence in one go.

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

#include "ABACUS.h"

using namespace std;

namespace ABACUS {


  DP Direct_J_integral (int Npts_p, DP req_prec, I_table Itable)
  {
    stringstream outfile_stringstream;
    string outfile_string;
    outfile_stringstream << "SF_4p_Np_" << Npts_p << "_prec_" << req_prec << ".raw";
    outfile_string = outfile_stringstream.str();
    const char* outfile_Cstr = outfile_string.c_str();

    ofstream outfile;
    outfile.open(outfile_Cstr);
    outfile.precision(16);

    stringstream src_stringstream;
    string src_string;
    src_stringstream << "SF_4p_Np_" << Npts_p << "_prec_" << req_prec << ".src";
    src_string = src_stringstream.str();
    const char* src_Cstr = src_string.c_str();

    ofstream srcfile;
    srcfile.open(src_Cstr);
    srcfile.precision(16);

    Vect_DP p(4);
    DP J_fn_cont = 0.0;
    DP sum_J_fn = 0.0;
    for (int ip0 = 0; ip0 < Npts_p; ++ip0) {
      p[0] = - (ip0 + 0.5) * PI/Npts_p;
      for (int ip1 = ip0 + 1; ip1 < Npts_p; ++ip1) {
	p[1] = - (ip1 + 0.5) * PI/Npts_p;
	for (int ip2 = ip1 + 1; ip2 < Npts_p; ++ip2) {
	  p[2] = - (ip2 + 0.5) * PI/Npts_p;
	  for (int ip3 = ip2 + 1; ip3 < Npts_p; ++ip3) {
	    p[3] = - (ip3 + 0.5) * PI/Npts_p;
	    J_fn_cont = J_fn (p, req_prec, Itable);
	    sum_J_fn += J_fn_cont;
	    if (p[0] > 0 || p[1] > 1 || p[2] > 2 || p[3] > 3) outfile << endl;
	    outfile << p << "\t" << J_fn_cont;
	  }
	}
      }
    }

    DP integral_J = Compute_C4 (req_prec) * 24.0 * sum_J_fn * pow(PI/Npts_p, 4.0);
    // 24:  from using ordered p's

    srcfile << integral_J << "\t" << integral_J/(4.0 * PI * PI) << "\t" << integral_J/(PI * PI) << endl;

    outfile.close();
    srcfile.close();

    return(integral_J);
  }

  void Smoothen_raw_SF_4p (int Npts_p, int Npts_o, DP req_prec, DP width)
  {
    stringstream rawfile_stringstream;
    string rawfile_string;
    rawfile_stringstream << "SF_4p_Np_" << Npts_p << "_No_" << Npts_o << "_prec_" << req_prec << ".raw";
    rawfile_string = rawfile_stringstream.str();
    const char* rawfile_Cstr = rawfile_string.c_str();

    ifstream rawfile;
    rawfile.open(rawfile_Cstr);

    stringstream smfile_stringstream;
    string smfile_string;
    smfile_stringstream << "SF_4p_Np_" << Npts_p << "_No_" << Npts_o << "_prec_" << req_prec << "_w_" << width << ".dat";
    smfile_string = smfile_stringstream.str();
    const char* smfile_Cstr = smfile_string.c_str();

    ofstream smfile;
    smfile.open(smfile_Cstr);
    smfile.precision(16);

    DP* SF_4p_raw = new DP[(Npts_p + 1) * Npts_o];
    DP* SF_4p_sm = new DP[(Npts_p + 1) * Npts_o];

    for (int iw = 0; iw < Npts_o; ++iw)
      for (int ik = 0; ik <= Npts_p; ++ik)
	rawfile >> SF_4p_raw[Npts_o * ik + iw];

    rawfile.close();

    // We now broaden to a Gaussian:

    int iw_half_window = int(width/(2.0 * PI/Npts_o));
    if (iw_half_window == 0) ABACUSerror("width too small in Smoothen_raw_SF_4p");

    int iwstart, iwstop;
    DP domega_sq_over_width_sq = pow(2.0 * PI/(Npts_o * width), 2.0);
    DP exp_factor;

    for (int iw = 0; iw < Npts_o; ++iw) {
      iwstart = ABACUS::max(0, iw - 10 * iw_half_window);
      iwstop = ABACUS::min(Npts_o, iw + 10 * iw_half_window);

      for (int iwraw = iwstart; iwraw <= iwstop; ++iwraw) {
	exp_factor = exp(-(iwraw - iw) * (iwraw - iw) * domega_sq_over_width_sq);
	for (int ik = 0; ik <= Npts_p; ++ik)
	  {
	    SF_4p_sm[Npts_o * ik + iw] += SF_4p_raw[Npts_o * ik + iwraw] * exp_factor;
	  }
      }
    }

    // Reset normalization from delta function and output data

    DP prefactor = 1.0/(sqrt(PI) * width);
    for (int iw = 0; iw < Npts_o; ++iw) {
      for (int ik = 0; ik <= Npts_p; ++ik)
	smfile << SF_4p_sm[Npts_o * ik + iw] * prefactor << "\t";
      smfile << endl;
    }

    smfile.close();
  }

  DP Direct_J_integral_bin (int Npts_p, int Npts_o, DP req_prec, I_table Itable)
  {
    // Produces binned file for J

    stringstream rawfile_stringstream;
    string rawfile_string;
    rawfile_stringstream << "SF_4p_Np_" << Npts_p << "_No_" << Npts_o << "_prec_" << req_prec << ".raw";
    rawfile_string = rawfile_stringstream.str();
    const char* rawfile_Cstr = rawfile_string.c_str();

    ofstream rawfile;
    rawfile.open(rawfile_Cstr);
    rawfile.precision(16);

    stringstream src_stringstream;
    string src_string;
    src_stringstream << "SF_4p_Np_" << Npts_p << "_No_" << Npts_o << "_prec_" << req_prec << ".src";
    src_string = src_stringstream.str();
    const char* src_Cstr = src_string.c_str();

    ofstream srcfile;
    srcfile.open(src_Cstr);
    srcfile.precision(16);

    Vect_DP p(4);
    DP J_fn_cont = 0.0;
    DP sum_J_fn = 0.0;

    DP* SF_4p_raw = new DP[(Npts_p + 1) * Npts_o];
    // labelling:  index is Npts_o * ik + iomega

    DP omegamax = 2.0 * PI;

    Write_K_File (Npts_p, 0, Npts_p);
    Write_Omega_File (Npts_o, 0.0, omegamax);

    int ik;
    DP omega;
    int iomega;
    DP sinp0, sinp1, sinp2;

    for (int ip0 = 0; ip0 < Npts_p; ++ip0) {
      p[0] = - (ip0 + 0.5) * PI/Npts_p;
      sinp0 = sin(p[0]);
      for (int ip1 = ip0 + 1; ip1 < Npts_p; ++ip1) {
	p[1] = - (ip1 + 0.5) * PI/Npts_p;
	sinp1 = sin(p[1]);
	for (int ip2 = ip1 + 1; ip2 < Npts_p; ++ip2) {
	  p[2] = - (ip2 + 0.5) * PI/Npts_p;
	  sinp2 = sin(p[2]);
	  for (int ip3 = ip2 + 1; ip3 < Npts_p; ++ip3) {
	    p[3] = - (ip3 + 0.5) * PI/Npts_p;

	    ik = ip0 + ip1 + ip2 + ip3;
	    if (ik > 2 * Npts_p) ik -= 2*Npts_p;  // guarantees 0 <= ik < 2Npts

	    if (ik <= Npts_p) {

	      omega = -0.5 * PI * (sinp0 + sinp1 + sinp2 + sin(p[3]));
	      iomega = int(omega * Npts_o/omegamax);

	      J_fn_cont = J_fn (p, req_prec, Itable);
	      sum_J_fn += (ik == Npts_p ? 1.0 : 2.0) * J_fn_cont;

	      SF_4p_raw[Npts_o * ik + iomega] += J_fn_cont;
	    }
	  }
	}
      }
    }

    DP prefactor = Compute_C4 (req_prec) * 24.0 * pow(PI/Npts_p, 4.0);
    // 24:  from using ordered p's

    DP integral_J = prefactor * sum_J_fn;

    // Output raw file
    for (int iw = 0; iw < Npts_o; ++iw) {
      for (int iK = 0; iK <= Npts_p; ++iK) rawfile << prefactor * SF_4p_raw[Npts_o * iK + iw] << "\t";
      rawfile << endl;
    }

    srcfile << integral_J << "\t" << integral_J/(4.0 * PI * PI) << "\t" << integral_J/(PI * PI) << endl;

    rawfile.close();
    srcfile.close();

    delete[] SF_4p_raw;

    return(integral_J);
  }

} // namespace ABACUS