ABACUS/dev/BETHE/Base.cc

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

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

Copyright (c) J.-S. Caux.

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

File:  src/BETHE/Base.cc

Purpose:  defines functions in Base class,
          providing a unified base object for all
          Bethe Ansatz integrable models.

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

#include "ABACUS.h"

using namespace std;

namespace ABACUS {

  // Function definitions:  class Base

  Base::Base () : Charge(0), Nrap(Vect<int>()), Nraptot(0), Ix2_infty(Vect<DP>()),
		  Ix2_max(Vect<int>()), id(0LL) {}

  Base::Base (int N) : Charge(N), Nrap(Vect<int>(N,1)), Nraptot(N), Ix2_infty(Vect<DP>(1.0e+100,1)),
		       Ix2_max(Vect<int>(LONG_LONG_MAX, 1)), id(N) {}

  Base::Base (const Base& RefBase)  // copy constructor
    : Charge(RefBase.Charge), Nrap(Vect<int>(RefBase.Nrap.size())), Nraptot(RefBase.Nraptot),
      Ix2_infty(Vect<DP>(RefBase.Ix2_infty.size())),
      Ix2_max(Vect<int>(RefBase.Ix2_max.size())), id(RefBase.id)
  {
    for (int i = 0; i < Nrap.size(); ++i) {
      Nrap[i] = RefBase.Nrap[i];
      Ix2_infty[i] = RefBase.Ix2_infty[i];
      Ix2_max[i] = RefBase.Ix2_max[i];
    }
  }

  Base::Base (const Heis_Chain& RefChain, const Vect<int>& Nrapidities)
    : Charge(0), Nrap(Nrapidities), Nraptot(0), Ix2_infty(Vect<DP>(RefChain.Nstrings)),
      Ix2_max(Vect<int>(RefChain.Nstrings)),
      id (0LL)
  {
    // Check consistency of Nrapidities vector with RefChain
    if (RefChain.Nstrings != Nrapidities.size())
      ABACUSerror("Incompatible Nrapidities vector used in Base constructor.");

    int Mcheck = 0;
    for (int i = 0; i < RefChain.Nstrings; ++i) Mcheck += RefChain.Str_L[i] * Nrap[i];
    Charge = Mcheck;

    Nraptot = 0;
    for (int i = 0; i < RefChain.Nstrings; ++i) Nraptot += Nrap[i];

    // Compute id
    id += Nrapidities[0];
    long long int factor = 100000LL;
    for (int i = 1; i < RefChain.Nstrings; ++i) {
      id += factor * Nrapidities[i];
      factor *= 100LL;
    }

    // Now compute the Ix2_infty numbers
    (*this).Compute_Ix2_limits(RefChain);
  }

  Base::Base (const Heis_Chain& RefChain, long long int id_ref)
    : Charge(0), Nrap(Vect<int>(RefChain.Nstrings)), Nraptot(0),
      Ix2_infty(Vect<DP>(RefChain.Nstrings)), Ix2_max(Vect<int>(RefChain.Nstrings)),
      id (id_ref)
  {
    // Build Nrapidities vector from id_ref

    long long int factor = pow_ulli (10LL, 2* RefChain.Nstrings + 1);
    long long int id_eff = id_ref;
    for (int i = 0; i < RefChain.Nstrings - 1; ++i) {
      Nrap[RefChain.Nstrings - 1 - i] = id_eff/factor;
      id_eff -= factor * Nrap[RefChain.Nstrings - 1 - i];
      factor /= 100LL;
    }
    Nrap[0] = id_eff;

    int Mcheck = 0;
    for (int i = 0; i < RefChain.Nstrings; ++i) Mcheck += RefChain.Str_L[i] * Nrap[i];
    Charge = Mcheck;

    Nraptot = 0;
    for (int i = 0; i < RefChain.Nstrings; ++i) Nraptot += Nrap[i];

    // Now compute the Ix2_infty numbers
    (*this).Compute_Ix2_limits(RefChain);
  }


  Base& Base::operator= (const Base& RefBase)
  {
    if (this != & RefBase) {
      Charge = RefBase.Charge;
      Nrap = RefBase.Nrap;
      Nraptot = RefBase.Nraptot;
      Ix2_infty = RefBase.Ix2_infty;
      Ix2_max = RefBase.Ix2_max;
      id = RefBase.id;
    }
    return(*this);
  }

  bool Base::operator== (const Base& RefBase)
  {
    bool answer = (Nrap == RefBase.Nrap);

    return (answer);
  }

  bool Base::operator!= (const Base& RefBase)
  {
    bool answer = (Nrap != RefBase.Nrap);

    return (answer);
  }

  void Base::Compute_Ix2_limits (const Heis_Chain& RefChain)
  {

    if ((RefChain.Delta > 0.0) && (RefChain.Delta < 1.0)) {

      // Compute the Ix2_infty numbers

      DP sum1 = 0.0;
      DP sum2 = 0.0;

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	sum1 = 0.0;

	for (int k = 0; k < RefChain.Nstrings; ++k) {

	  sum2 = 0.0;

	  sum2 += (RefChain.Str_L[j] == RefChain.Str_L[k]) ? 0.0 :
	    2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
			   - 0.5 * fabs(RefChain.Str_L[j] - RefChain.Str_L[k]) * RefChain.anis));
	  sum2 += 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
				 - 0.5 * (RefChain.Str_L[j] + RefChain.Str_L[k]) * RefChain.anis));

	  for (int a = 1; a < ABACUS::min(RefChain.Str_L[j], RefChain.Str_L[k]); ++a)
	    sum2 += 2.0 * 2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j] * RefChain.par[k])
					 - 0.5 * (fabs(RefChain.Str_L[j] - RefChain.Str_L[k])
						  + 2.0*a) * RefChain.anis));

	  sum1 += (Nrap[k] - ((j == k) ? 1 : 0)) * sum2;
	}

	Ix2_infty[j] = (1.0/PI) * fabs(RefChain.Nsites *
				       2.0 * atan(tan(0.25 * PI * (1.0 + RefChain.par[j])
						      - 0.5 * RefChain.Str_L[j] * RefChain.anis)) - sum1);

      }  // The Ix2_infty are now set.

      // Now compute the Ix2_max limits

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	Ix2_max[j] = int(floor(Ix2_infty[j]));  // sets basic integer

	// Reject formally infinite rapidities (i.e. if Delta is root of unity)

	//cout << "Ix2_infty - Ix2_max = " << Ix2_infty[j] - Ix2_max[j] << endl;
	//if (Ix2_infty[j] == Ix2_max[j]) {
	//Ix2_max[j] -= 2;
	//}
	// If Nrap is even, Ix2_max must be odd.  If odd, then even.

	if (!((Nrap[j] + Ix2_max[j]) % 2)) Ix2_max[j] -= 1;

	while (Ix2_max[j] > RefChain.Nsites) {
	  Ix2_max[j] -= 2;
	}
      }
    } // if XXZ gapless

    else if (RefChain.Delta == 1.0) {

      // Compute the Ix2_infty numbers

      int sum1 = 0;

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	sum1 = 0;

	for (int k = 0; k < RefChain.Nstrings; ++k) {

	  sum1 += Nrap[k] * (2 * ABACUS::min(RefChain.Str_L[j], RefChain.Str_L[k]) - ((j == k) ? 1 : 0));
	}

	//Ix2_infty[j] = (RefChain.Nsites - 1.0 + 2.0 * RefChain.Str_L[j] - sum1);
	Ix2_infty[j] = (RefChain.Nsites + 1.0 - sum1); // to get counting right...

      }  // The Ix2_infty are now set.

      // Now compute the Ix2_max limits

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	Ix2_max[j] = int(floor(Ix2_infty[j]));  // sets basic integer

	// Give the correct parity to Ix2_max

	// If Nrap is even, Ix2_max must be odd.  If odd, then even.

	if (!((Nrap[j] + Ix2_max[j]) % 2)) Ix2_max[j] -= 1;

	// If Ix2_max equals Ix2_infty, we reduce it by 2:

	if (Ix2_max[j] == int(Ix2_infty[j])) Ix2_max[j] -= 2;

	while (Ix2_max[j] > RefChain.Nsites) {
	  Ix2_max[j] -= 2;
	}
      }

    } // if XXX AFM

    else if (RefChain.Delta > 1.0) {

      // Compute the Ix2_infty numbers

      int sum1 = 0;

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	sum1 = 0;

	for (int k = 0; k < RefChain.Nstrings; ++k) {

	  sum1 += Nrap[k] * (2 * ABACUS::min(RefChain.Str_L[j], RefChain.Str_L[k]) - ((j == k) ? 1 : 0));
	}

	Ix2_infty[j] = (RefChain.Nsites - 1 + 2 * RefChain.Str_L[j] - sum1);

      }  // The Ix2_infty are now set.

      // Now compute the Ix2_max limits

      for (int j = 0; j < RefChain.Nstrings; ++j) {

	Ix2_max[j] = int(floor(Ix2_infty[j]));  // sets basic integer

	// Give the correct parity to Ix2_max

	// If Nrap is even, Ix2_max must be odd.  If odd, then even.

	if (!((Nrap[j] + Ix2_max[j]) % 2)) Ix2_max[j] -= 1;

	// If Ix2_max equals Ix2_infty, we reduce it by 2:

	//if (Ix2_max[j] == Ix2_infty[j]) Ix2_max[j] -= 2;

	while (Ix2_max[j] > RefChain.Nsites) {
	  Ix2_max[j] -= 2;
	}

      }

    } // if XXZ_gpd

  }


} // namespace ABACUS