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

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

Copyright (c) J.-S. Caux.

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

File:  src/HEIS/Heis_Chem_Pot.cc

Purpose:  calculates the chemical potential.

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

#include "ABACUS.h"

using namespace std;

namespace ABACUS {

  DP Ezero (DP Delta, int N, int M)
  {
    // Returns the energy of the ground state with M down spins

    if (M < 0 || M > N/2) ABACUSerror("M out of bounds in Ezero.");

    DP E = -1.0; // sentinel value

    if (M == 0) E = N * Delta/4.0;

    else {

      Heis_Chain BD1(1.0, Delta, 0.0, N);

      Vect_INT Nrapidities_groundstate(0, BD1.Nstrings);

      Nrapidities_groundstate[0] = M;

      Heis_Base baseconfig_groundstate(BD1, Nrapidities_groundstate);

      if ((Delta > 0.0) && (Delta < 1.0)) {
	XXZ_Bethe_State groundstate(BD1, baseconfig_groundstate);
	groundstate.Compute_All(true);
	E = groundstate.E;
      }

      else if (Delta == 1.0) {
	XXX_Bethe_State groundstate(BD1, baseconfig_groundstate);
	groundstate.Compute_All(true);
	E = groundstate.E;
      }

      else if (Delta > 1.0) {
	XXZ_gpd_Bethe_State groundstate(BD1, baseconfig_groundstate);
	groundstate.Compute_All(true);
	E = groundstate.E;
      }

      else ABACUSerror("Anisotropy out of bounds in Ezero.");
    }

    return(E);
  }

  DP H_vs_M (DP Delta, int N, int M)
  {
    // Assumes dE/dM = 0 = dE_0/dM + h, with dE_0/dM = E_0(M) - E_0 (M - 1)

    DP H = 0.0;

    if (2*M == N) H = 0.0;

    else if (Delta <= 1.0) H = Ezero (Delta, N, M - 1) - Ezero (Delta, N, M);

    return(H);
  }

  DP HZmin (DP Delta, int N, int M, Vect_DP& Ezero_ref)
  {
    if (M < 0 || M > N/2 - 1) {
      cout << "M = " << M << endl;
      ABACUSerror("M out of bounds in HZmin.");
    }

    if (Ezero_ref[M] == -1.0) Ezero_ref[M] = Ezero(Delta, N, M);
    if (Ezero_ref[M + 1] == -1.0) Ezero_ref[M + 1] = Ezero(Delta, N, M + 1);

    return(Ezero_ref[M] - Ezero_ref[M + 1]);
  }

  int M_vs_H (DP Delta, int N, DP HZ)
  {
    // Returns the value of M for given field HZ

    if (HZ < 0.0) ABACUSerror("Please use a positive field in M_vs_H.");

    else if (HZ == 0.0) return(N/2);

    // Here, -1.0 is a sentinel value.
    Vect_DP Ezero(-1.0, N/2 + 1);  // contains the GSE[M].

    // We look for M s.t. HZmin[M] < HZ <= HZmin[M + 1]

    int M_actual = N/4; // start somewhere in middle
    int M_step = N/8 - 1; // step
    DP HZmin_actual = 0.0;
    DP HZmax_actual = 0.0;
    bool M_found = false;

    if (HZ >= 1.0 + Delta) M_actual = 0;  // saturation

    else {

      HZmin_actual = HZmin (Delta, N, M_actual, Ezero);
      HZmax_actual = HZmin (Delta, N, M_actual - 1, Ezero);

      while (!M_found) {

	if (HZmin_actual > HZ) M_actual += M_step;
	else if (HZmax_actual <= HZ) M_actual -= M_step;

	M_step = (M_step + 1)/2;

	HZmin_actual = HZmin (Delta, N, M_actual, Ezero);
	HZmax_actual = HZmin (Delta, N, M_actual - 1, Ezero);

	M_found = (HZmin_actual < HZ && HZ <= HZmax_actual);

	//cout << "M_actual = " << M_actual << "\tM_step = " << M_step
	//   << "\tHZmin_actual = " << HZmin_actual << "\tHZmax_actual = " << HZmax_actual << "\tHZ = " << HZ << "\t" << M_found << endl;
      }
    }
    //cout << "M found = " << M_actual << "\tHZmax = " << Ezero[M_actual] - Ezero[M_actual + 1] << "\tHZmin = " << Ezero[M_actual - 1] - Ezero[M_actual] << endl;

    return(M_actual);
  }

  DP Chemical_Potential (const Heis_Bethe_State& AveragingState)
  {
    return(-H_vs_M (AveragingState.chain.Delta, AveragingState.chain.Nsites, AveragingState.base.Mdown));  // - sign since E_{M+1} - E_M = -H
  }

}