ABACUS/src/UTILS/State_Label.cc

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

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

Copyright (c) J.-S. Caux.

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

File:  src/UTILS/State_Label.cc

Purpose:  universal implementation of state labels for ABACUS

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

#include "ABACUS.h"

using namespace std;
using namespace ABACUS;

namespace ABACUS {

  // The label of a state is built as follows:

  // M0[|type1:M1|type2:M2...]_nexc0[|nexc1|nexc2...]_type0Ix2old@type0Ix2new[:...][|type1Ix2old@type1Ix2new...]

  // A label is always relative to another label reference state, in practice
  // the seed state used in the scanning for correlations (or otherwise by default: the ground state).

  // The first part of the label (before the first _ ) labels the particle content (the "base").
  // The second part (between the two _ ) specifies the number of quantum numbers
  // excited to a position different from the configuration of the label reference state.
  // The third part gives, for each excitation, the moved quantum number, and
  // (after the @) the quantum number it has been moved to.

  // The second part is redundant (it could be read off the third part), but is kept since it is human-readable.

  // Example:

  // 300|2:23|5:4_3|2|1_-21@-43:11@-21:299@341|0@-24:4@12|5@35

  // labels a state with
  // 300 particles of type 0, 23 of type 2 and 4 of type 5
  // 3 type 0 particles displaced (Ix2 = -21 displaced to Ix2 = -43, 11 to -21 and 299 at 341)
  // 2 type 2 particles displaced (Ix2 = 0 to -24 and 4 to 12)
  // 1 type 5 particle displaced (Ix2 = 5 displaced to Ix2 = 35).



  string Extract_Base_Label (string label)
  {
    string::size_type i1 = label.find(LABELSEP);

    string baselabel = label.substr(0, i1);

    return(baselabel);
  }

  string Extract_nexc_Label (string label)
  {
    string::size_type i1 = label.find(LABELSEP);
    string::size_type i2 = label.rfind(LABELSEP);

    return(label.substr(i1+1, i2-i1-1));
  }

  // For compressed labels: conversions between integers and char/strings.
  // This is done according to the following data (in ABACUS_Scan.h): look for ABACUScoding.

  string Convert_POSINT_to_STR (int int_to_convert)
  {
    // Converts a positive integer into a string according to the coding defined by global constant array ABACUScoding.
    if (int_to_convert < 0) ABACUSerror("Trying to convert a negative integer to a string.");

    int remainder = int_to_convert;
    stringstream result_strstrm;
    do {
      result_strstrm << ABACUScoding[remainder - ABACUScodingsize * (remainder/ABACUScodingsize)];
      remainder /= ABACUScodingsize;
    } while (remainder > 0);

    return(result_strstrm.str());
  }

  int Convert_CHAR_to_POSINT (char char_to_convert)
  {
    // Converts a char into an int according to the coding defined by global constant array ABACUScoding.
    for (int i = 0; i < ABACUScodingsize; ++i)
      if (char_to_convert == ABACUScoding[i]) return(i);
    cout << "char to convert: " << char_to_convert << endl;
    ABACUSerror("Failed to convert char to posint: char not in ABACUScoding set.");
    return(-1);
  }

  int Convert_STR_to_POSINT (string str_to_convert)
  {
    // Converts a string into a positive integer according to the coding defined by global constant array ABACUScoding.
    int result = 0;
    for (unsigned int i = 0; i < str_to_convert.size(); ++i) {
      result = ABACUScodingsize * result + Convert_CHAR_to_POSINT(str_to_convert[str_to_convert.size() - 1 - i]);
    }
    return(result);
  }


  // For reading only the base part of a label:
  State_Label_Data Read_Base_Label (string label)
  {
    // Converts a given label into the appropriate State_Label_Data

    // Split label into base, nexc and q#exc parts:
    // these are divided by the two LABELSEP characters in the label.

    string::size_type i1 = label.find(LABELSEP);
    string::size_type i2 = label.rfind(LABELSEP);

    string baselabel = label.substr(0, i1);
    string nexclabel = label.substr(i1+1, i2-i1-1);
    string Ix2exclabel = label.substr(i2+1);

    // Read off the base label: count the number of TYPESEP in baselabel
    int nbar = 0;
    for (unsigned int i = 0; i < baselabel.length(); ++i) if (baselabel[i] == TYPESEP) nbar++;

    // There are now nbar + 1 base label data:
    int ntypes = nbar + 1;

    Vect<int> type(ntypes); // integer type labels of the types present
    type[0] = 0; // always the case by convention
    Vect<int> M(ntypes); // how many particles of each type

    if (ntypes == 1) { // Only one type to read off
      istringstream M0buffer(baselabel);
      M0buffer >> M[0];
    }

    else { // ntypes > 1
      // Read off M[0]:
      string::size_type i1 = baselabel.find(TYPESEP); // M0 is always present, without type specifier
      string M0 = baselabel.substr(0, i1);
      istringstream M0buffer(M0);
      M0buffer >> M[0];

      // Read off M[1 ... ntypes - 2]
      string baselabelremaining = baselabel;
      for (int itype = 1; itype < ntypes - 1; ++itype) {
	// Remove everything up to leftmost TYPESEP in baselabelremaining
	string::size_type i1 = baselabelremaining.find(TYPESEP); // M0 is always present, without type specifier
	baselabelremaining = baselabelremaining.substr(i1+1);
	string::size_type i2 = baselabelremaining.find(EXCSEP);
	string::size_type i3 = baselabelremaining.find(TYPESEP);
	string typeread = baselabelremaining.substr(0, i2);
	string Mread = baselabelremaining.substr(i2+1,i3-i2-1);
	istringstream typereadbuffer (typeread);
	typereadbuffer >> type[itype];
	istringstream Mreadbuffer (Mread);
	Mreadbuffer >> M[itype];
      }

      // Read off M[ntypes - 1]
      {
	string::size_type i1 = baselabelremaining.find(TYPESEP); // M0 is always present, without type specifier
	baselabelremaining = baselabelremaining.substr(i1+1);
	string::size_type i2 = baselabelremaining.find(EXCSEP);
	string typeread = baselabelremaining.substr(0, i2);
	string Mread = baselabelremaining.substr(i2+1);
	istringstream typereadbuffer (typeread);
	typereadbuffer >> type[ntypes - 1];
	istringstream Mreadbuffer (Mread);
	Mreadbuffer >> M[ntypes - 1];
      }

    } // else if ntypes > 1

    // baselabel is now completely read

    // Define some dud nex, Ix2old, Ix2exc:
    Vect<int> nexc(ntypes); // how many excitations as compared to the OriginState
    Vect<Vect<int> > Ix2old(ntypes); // which Ix2 will be excited
    Vect<Vect<int> > Ix2exc(ntypes); // which Ix2 the excitation has shifted to

    State_Label_Data labeldata (type, M, nexc, Ix2old, Ix2exc);

    return(labeldata);
  }



  State_Label_Data Read_State_Label (string label, const Vect<Vect<int> >& OriginIx2)
  {
    // Converts a given label into the appropriate State_Label_Data

    // Split label into base, nexc and q#exc parts:
    // these are divided by the two LABELSEP characters in the label.

    string::size_type i1 = label.find(LABELSEP);
    string::size_type i2 = label.rfind(LABELSEP);

    string baselabel = label.substr(0, i1);
    string nexclabel = label.substr(i1+1, i2-i1-1);
    string Ix2exclabel = label.substr(i2+1);


    // Read off the base label: count the number of TYPESEP in baselabel
    int nbar = 0;
    for (unsigned int i = 0; i < baselabel.length(); ++i) if (baselabel[i] == TYPESEP) nbar++;

    // There are now nbar + 1 base label data:
    int ntypes = nbar + 1;

    Vect<int> type(ntypes); // integer type labels of the types present
    type[0] = 0; // always the case by convention
    Vect<int> M(ntypes); // how many particles of each type

    if (ntypes == 1) { // Only one type to read off
      istringstream M0buffer(baselabel);
      M0buffer >> M[0];
    }

    else { // ntypes > 1
      // Read off M[0]:
      string::size_type i1 = baselabel.find(TYPESEP); // M0 is always present, without type specifier
      string M0 = baselabel.substr(0, i1);
      istringstream M0buffer(M0);
      M0buffer >> M[0];

      // Read off M[1 ... ntypes - 2]
      string baselabelremaining = baselabel;
      for (int itype = 1; itype < ntypes - 1; ++itype) {
	// Remove everything up to leftmost TYPESEP in baselabelremaining
	string::size_type i1 = baselabelremaining.find(TYPESEP); // M0 is always present, without type specifier
	baselabelremaining = baselabelremaining.substr(i1+1);
	string::size_type i2 = baselabelremaining.find(EXCSEP);
	string::size_type i3 = baselabelremaining.find(TYPESEP);
	string typeread = baselabelremaining.substr(0, i2);
	string Mread = baselabelremaining.substr(i2+1,i3-i2-1);
	istringstream typereadbuffer (typeread);
	typereadbuffer >> type[itype];
	istringstream Mreadbuffer (Mread);
	Mreadbuffer >> M[itype];
      }

      // Read off M[ntypes - 1]
      {
	string::size_type i1 = baselabelremaining.find(TYPESEP); // M0 is always present, without type specifier
	baselabelremaining = baselabelremaining.substr(i1+1);
	string::size_type i2 = baselabelremaining.find(EXCSEP);
	string typeread = baselabelremaining.substr(0, i2);
	string Mread = baselabelremaining.substr(i2+1);
	istringstream typereadbuffer (typeread);
	typereadbuffer >> type[ntypes - 1];
	istringstream Mreadbuffer (Mread);
	Mreadbuffer >> M[ntypes - 1];
      }

    } // else if ntypes > 1

    // baselabel is now completely read

    // Read off the nexc vector:
    Vect<int> nexc(ntypes); // how many excitations as compared to the OriginState

    if (ntypes == 1) { // Only one type to read off
      istringstream exc0buffer(nexclabel);
      exc0buffer >> nexc[0];
    }

    else { // ntypes > 1
      // Read off nexc[0]:
      string::size_type i1 = nexclabel.find(TYPESEP);
      string nexc0 = nexclabel.substr(0, i1);
      istringstream nexc0buffer(nexc0);
      nexc0buffer >> nexc[0];

      // Read off nexc[1 ... ntypes - 2]
      string nexclabelremaining = nexclabel;
      for (int itype = 1; itype < ntypes - 1; ++itype) {
	// Remove everything up to leftmost TYPESEP in nexclabelremaining
	string::size_type i1 = nexclabelremaining.find(TYPESEP);
	nexclabelremaining = nexclabelremaining.substr(i1+1);
	string::size_type i2 = nexclabelremaining.find(TYPESEP);
	string nexcread = nexclabelremaining.substr(0, i2);
	istringstream nexcreadbuffer (nexcread);
	nexcreadbuffer >> nexc[itype];
      }

      // Read off nexc[ntypes - 1]
      {
	string::size_type i1 = nexclabelremaining.find(TYPESEP);
	nexclabelremaining = nexclabelremaining.substr(i1+1);
	istringstream nexcreadbuffer (nexclabelremaining);
	nexcreadbuffer >> nexc[ntypes - 1];
      }

    } // else if ntypes > 1

    // nexc is now completely read


    // Now read off the (compressed) jexc and Ix2exc vectors of vectors:
    Vect<Vect<int> > Ix2old(ntypes); // which Ix2 will be excited
    Vect<Vect<int> > Ix2exc(ntypes); // which Ix2 the excitation has shifted to

    for (int itype = 0; itype < ntypes; ++itype) {
      Ix2old[itype] = Vect<int> (ABACUS::max(nexc[itype],1));
      Ix2exc[itype] = Vect<int> (ABACUS::max(nexc[itype],1));
    }

    string Ix2exclabelremaining = Ix2exclabel;
    for (int itype = 0; itype < ntypes - 1; ++itype) {
      // Read off the Ix2old, Ix2exc:
      if (nexc[itype] == 0) { // careful here, need to remove a TYPESEP
	string::size_type i2 = Ix2exclabelremaining.find(TYPESEP);
	Ix2exclabelremaining = Ix2exclabelremaining.substr(i2+1);
      }
      for (int iexc = 0; iexc < nexc[itype]; ++iexc) {
	//string::size_type i1 = Ix2exclabelremaining.find(INEXCSEP);
	string::size_type i2 = (iexc < nexc[itype] - 1 ? Ix2exclabelremaining.find(EXCSEP)
				: Ix2exclabelremaining.find(TYPESEP)); // careful here!
	string Ix2excIDread = Ix2exclabelremaining.substr(0,i2);
	int Ix2excID = Convert_STR_to_POSINT(Ix2excIDread);
	Ix2old[itype][iexc] = OriginIx2[type[itype] ][Ix2excID - M[itype] * (Ix2excID/M[itype])];
	// index is remainder w/r to nr of strings of this type
	// Convention: if remainder is even, moving left. If odd, moving right.
	// 0 means move one unit left, 1 means move one unit right, etc.
	Ix2exc[itype][iexc] = Ix2old[itype][iexc] + (Ix2excID/M[itype] % 2 ? 2 : -2)
	  * (Ix2excID/(2 * M[itype]) + 1); // ABACUS++T_8 onwards

	// Remove everything up to index i2 in Ix2exclabelremaining
	Ix2exclabelremaining = Ix2exclabelremaining.substr(i2+1);
      }
    }

    // Now read off the Ix2old, Ix2exc of the last type: this is always done
    for (int iexc = 0; iexc < nexc[ntypes - 1] - 1; ++iexc) {
      string::size_type i2 = Ix2exclabelremaining.find(EXCSEP);
      string Ix2excIDread = Ix2exclabelremaining.substr(0,i2);
      int Ix2excID = Convert_STR_to_POSINT(Ix2excIDread);
      Ix2old[ntypes - 1][iexc] = OriginIx2[type[ntypes - 1] ][Ix2excID - M[ntypes - 1] * (Ix2excID/M[ntypes - 1])];
      // index is remainder w/r to nr of strings of this type
      // Convention: if remainder is even, moving left. If odd, moving right.
      Ix2exc[ntypes - 1][iexc] = Ix2old[ntypes - 1][iexc] + (Ix2excID/M[ntypes - 1] % 2 ? 2 : -2)
	* (Ix2excID/(2 * M[ntypes - 1]) + 1); // ABACUS++T_8 onwards

      // Remove everything up to index i2 in Ix2exclabelremaining
      Ix2exclabelremaining = Ix2exclabelremaining.substr(i2+1);
    }

    // Now read off the last pair:
    int Ix2excID = Convert_STR_to_POSINT(Ix2exclabelremaining);
    Ix2old[ntypes - 1][ABACUS::max(nexc[ntypes - 1] - 1,0)] =
      OriginIx2[type[ntypes - 1] ][Ix2excID - M[ntypes - 1] * (Ix2excID/M[ntypes - 1])];
    // index is remainder w/r to nr of strings of this type
    // Convention: if remainder is even, moving left. If odd, moving right.
    Ix2exc[ntypes - 1][ABACUS::max(nexc[ntypes - 1] - 1,0)] = Ix2old[ntypes - 1][nexc[ntypes - 1] - 1]
      + (Ix2excID/M[ntypes - 1] % 2 ? 2 : -2) * (Ix2excID/(2 * M[ntypes - 1]) + 1); // ABACUS++T_8 onwards

    State_Label_Data labeldata (type, M, nexc, Ix2old, Ix2exc);

    return(labeldata);
  }

  State_Label_Data Read_State_Label (string label, const Vect<int>& OriginIx2)
  {
    Vect<Vect<int> > OriginIx2here(1);
    OriginIx2here[0] = OriginIx2;
    return(Read_State_Label (label, OriginIx2here));
  }

  string Return_State_Label (State_Label_Data data, const Vect<Vect<int> >& OriginIx2)
  {
    // This function produces a compressed label.

    string label;

    // Write the base:
    // First, particles of type 0:
    stringstream M0out;
    M0out << data.M[0];
    label += M0out.str();

    for (int itype = 1; itype < data.M.size(); ++itype) {
      if (data.M[itype] > 0) {
	label += TYPESEP;
	stringstream typeout;
	typeout << data.type[itype];
	label += typeout.str();
	label += EXCSEP;
	stringstream Mout;
	Mout << data.M[itype];
	label += Mout.str();
      }
    }
    label += LABELSEP;

    // Now the nexc:
    stringstream nexc0out;
    nexc0out << data.nexc[0];
    label += nexc0out.str();
    for (int iexc = 1; iexc < data.nexc.size(); ++iexc) {
      label += TYPESEP;
      stringstream nexcout;
      nexcout << data.nexc[iexc];
      label += nexcout.str();
    }
    label += LABELSEP;

    // Now the displacements:
    // The conventions are as follows.
    // For each excitation, an integer number ID is given according to the following rules:
    // ID % data.M[itype] gives the index of the hole position in OriginIx2.
    // We now define remainder1 == ID - (ID % data.M[itype]).
    // remainder1 is interpreted as: remainder1 even/odd means displacement to left/right
    // remainder1/2 + 1 gives then the displacement in units of quantum nr.
    // The +1 is to start labeling displacement from 0 (so 0 means displace by one unit).
    for (int itype = 0; itype < data.M.size(); ++itype) {
      if (itype > 0) label += TYPESEP;
      for (int iexc = 0; iexc < data.nexc[itype]; ++iexc) {
	if (iexc > 0) label += EXCSEP;
	int excID = abs(data.Ix2exc[itype][iexc] - data.Ix2old[itype][iexc]) - 2; // necessarily even and >= 0
	if (data.Ix2exc[itype][iexc] > data.Ix2old[itype][iexc]) excID += 1; // make odd if displacement is to the right
	int holeindex = -1;
	do {
	  holeindex++;
	} while (OriginIx2[data.type[itype] ][holeindex] != data.Ix2old[itype][iexc]
		 && holeindex < OriginIx2[data.type[itype] ].size() - 1);
	if (holeindex == OriginIx2[data.type[itype] ].size())
	  ABACUSerror("Going out of bounds in Compress_Label.");
	excID = excID * data.M[itype] + holeindex;
	label += Convert_POSINT_to_STR(excID);
      } // for iexc
    } // for itype

    return(label);
  }

  string Return_State_Label (State_Label_Data data, const Vect<int>& OriginIx2)
  {
    Vect<Vect<int> > OriginIx2here(1);
    OriginIx2here[0] = OriginIx2;
    return(Return_State_Label (data, OriginIx2here));
  }

  string Return_State_Label (const Vect<Vect<int> >& ScanIx2, const Vect<Vect<int> >& OriginIx2)
  {
    // This function does not assume any ordering of the Ix2.

    if (ScanIx2.size() != OriginIx2.size())
      ABACUSerror("ScanIx2.size() != OriginIx2.size() in Find_Label.");
    for (int i = 0; i < ScanIx2.size(); ++i)
      if (ScanIx2[i].size() != OriginIx2[i].size())
	ABACUSerror("ScanIx2[i].size() != OriginIx2[i].size() in Find_Label.");

    // Set the state ulabel:
    // Count the number of types present:
    int ntypespresent = 0;
    for (int is = 0; is < ScanIx2.size(); ++is)
      if (is == 0 || ScanIx2[is].size() > 0) ntypespresent++; // type 0 is by default always present

    Vect<int> type_ref(ntypespresent);
    Vect<int> M_ref(ntypespresent);
    Vect<int> nexc_ref(0, ntypespresent);

    // Define type_ref and M_ref:
    int ntypespresentcheck = 0;
    for (int is = 0; is < ScanIx2.size(); ++is) if (is == 0 || ScanIx2[is].size() > 0) { // type 0 is by default always present
	type_ref[ntypespresentcheck] = is;
	M_ref[ntypespresentcheck++] = ScanIx2[is].size();
      }
    if (ntypespresentcheck != ntypespresent) ABACUSerror("Counting types present wrong in Return_Label.");

    // Count nr of particle-holes:
    for (int it = 0; it < ntypespresent; ++it)
      for (int i = 0; i < M_ref[it]; ++i) if (!OriginIx2[type_ref[it] ].includes(ScanIx2[type_ref[it] ][i])) nexc_ref[it] += 1;
    Vect<Vect<int> > Ix2old_ref(ntypespresent);
    Vect<Vect<int> > Ix2exc_ref(ntypespresent);
    for (int it = 0; it < ntypespresent; ++it) Ix2old_ref[it] = Vect<int>(ABACUS::max(nexc_ref[it],1));
    for (int it = 0; it < ntypespresent; ++it) Ix2exc_ref[it] = Vect<int>(ABACUS::max(nexc_ref[it],1));
    for (int it = 0; it < ntypespresent; ++it) {
      int nexccheck = 0;
      for (int i = 0; i < M_ref[it]; ++i)
	if (!OriginIx2[type_ref[it] ].includes(ScanIx2[type_ref[it] ][i]))
	  Ix2exc_ref[it][nexccheck++] = ScanIx2[type_ref[it] ][i];
      if (nexccheck != nexc_ref[it])
	ABACUSerror("Counting excitations wrong (1) in Return_State_Label");
      nexccheck = 0;
      for (int i = 0; i < M_ref[it]; ++i)
	if (!ScanIx2[type_ref[it] ].includes(OriginIx2[type_ref[it] ][i]))
	  Ix2old_ref[it][nexccheck++] = OriginIx2[type_ref[it] ][i];
      if (nexccheck != nexc_ref[it]) {
	cout << OriginIx2 << endl;
	cout << ScanIx2 << endl;
	cout << nexc_ref[it] << endl;
	cout << Ix2exc_ref[it] << endl;
	ABACUSerror("Counting excitations wrong (2) in Return_State_Label");
      }
      // Now order the Ix2old_ref and Ix2exc_ref:
      Ix2old_ref[it].QuickSort();
      Ix2exc_ref[it].QuickSort();
    } // for it

    State_Label_Data labeldata(type_ref, M_ref, nexc_ref, Ix2old_ref, Ix2exc_ref);

    return(Return_State_Label (labeldata, OriginIx2));
  }

  string Return_State_Label (const Vect<int>& ScanIx2, const Vect<int>& OriginIx2)
  {
    Vect<Vect<int> > ScanIx2here(1);
    ScanIx2here[0] = ScanIx2;
    Vect<Vect<int> > OriginIx2here(1);
    OriginIx2here[0] = OriginIx2;
    return(Return_State_Label (ScanIx2here, OriginIx2here));
  }



  Vect<Vect<int> > Return_Ix2_from_Label (string label_ref, const Vect<Vect<int> >& OriginIx2)
  {
    // ASSUMPTIONS:
    // OriginIx2 is ordered.

    Vect<Vect<int> > Ix2 = OriginIx2; // this will fail if the sizes are incompatible

    State_Label_Data labeldata = Read_State_Label (label_ref, OriginIx2);

    // Now set the excitations:
    for (int it = 0; it < labeldata.type.size(); ++it)
      for (int iexc = 0; iexc < labeldata.nexc[it]; ++iexc)
	for (int i = 0; i < labeldata.M[it]; ++i)
	  if (Ix2[labeldata.type[it] ][i] == labeldata.Ix2old[it][iexc]) {
	    Ix2[labeldata.type[it] ][i] = labeldata.Ix2exc[it][iexc];
	  }

    // Now reorder the Ix2 to follow convention:
    for (int il = 0; il < Ix2.size(); ++il) Ix2[il].QuickSort();

    return(Ix2);
  }

  Vect<int> Return_Ix2_from_Label (string label_ref, const Vect<int>& OriginIx2)
  {
    Vect<Vect<int> > OriginIx2here(1);
    OriginIx2here[0] = OriginIx2;

    return(Return_Ix2_from_Label(label_ref, OriginIx2here)[0]);
  }


} // namespace ABACUS