nilpotent.hpp

/*
MIT License
Copyright (c) 2019 Xinzhe WU @ Maison de la Simulation, France
Copyright (c) 2019-2022, Xinzhe Wu @ Simulation and Data Laboratory Quantum 
                                     Materials,  Forschungszentrum Juelich GmbH.
                                     
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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*/
 
#ifndef __NILPOTENT_H__
#define __NILPOTENT_H__
 
 
#include "utils/utils.hpp"
 
 
template<typename S>
class Nilpotent
{
    private:
 
        S probSize;
 
        S degree;
 
        S offset;
 
        std::vector<S> indOfZeros; // a pair: index
 
    public:
 
        Nilpotent(S nbOne, S size);
 
        Nilpotent(S nbOne, S diag, S size);
 
        Nilpotent(std::vector<S> nilpvec, S size);
 
        Nilpotent(std::vector<S> nilpvec, S diag, S size);
        ~Nilpotent();
 
        S computeDegree(std::vector<S> nilpvec);
 
        S getProbSize(){return probSize;};
        S getDegree(){return degree;};
 
        S getOffset(){return offset;};
 
        std::vector<S> getIndOfZeros(){return indOfZeros;};
 
        void show();
 
};
 
 
 
template<typename S>
Nilpotent<S>::Nilpotent(S nbOne, S size){
 
    probSize = size;
    offset = 1; //in the default mode, the Nilpotent is generated with the diagonal of offset 1
    degree = nbOne + 1;
 
    if(nbOne > probSize - 1){
        try{
            throw 505;
        }catch(...){
            std::cout << "SMG2S]> Caught Exception: for Nilpotent, nbOne is too large" << std::endl;
        }
    }
 
    for(auto i = 0; i < probSize - 1; i++){
        if( (i + 1) % (nbOne + 1) == 0 ){
            indOfZeros.push_back(i);
        }
    }       
}
 
template<typename S>
Nilpotent<S>::Nilpotent(S nbOne, S diag, S size){
 
    probSize = size;
    offset = diag; //in the default mode, the Nilpotent is generated with the diagonal of offset 1
    //degree = nbOne + 1;
    
    if(nbOne > probSize - diag){
        try{
            throw 505;
        }catch(...){
            std::cout << "SMG2S]> Caught Exception: for Nilpotent, nbOne is too large" << std::endl;
        }
    }
 
    S length = probSize - diag;
 
    S cnt = 0;
 
    while (cnt < length){
        S l1 =  1 + (rand() % nbOne);
        S l2 =  1 + (rand() % nbOne);
 
        for(auto i = l1 + cnt; i < l1 + l2 + cnt; i++){
            if(i < length){
                indOfZeros.push_back(i);
            }
        }
 
        cnt += l1 + l2;
    }
 
    std::vector<S> nilpvec(length);
    std::fill(nilpvec.begin(), nilpvec.end(), 1);
    for(auto i = 0; i < indOfZeros.size(); i++){
        nilpvec[indOfZeros[i]] = 0;
    }
 
    degree = computeDegree(nilpvec);
 
}
 
template<typename S>
Nilpotent<S>::Nilpotent(std::vector<S> nilpvec, S size){
    probSize = size;
    offset = 1; 
    
    S nbOne = 0;
    S cnt = 0;
 
    if(nilpvec.size() < size - 1){
        try{
            throw 505;
        }catch(...){
            std::cout << "SMG2S]> Caught Exception: for Nilpotent, nilpvec size is not enough" << std::endl;
        }       
    }
    for(auto i = 0; i < size - 1; i++){
        if (nilpvec[i] != 0){
            cnt ++;
        }else if(nilpvec[i] == 0){
            indOfZeros.push_back(i);
            if (cnt > nbOne){
                nbOne = cnt;
            }
            cnt = 0;
        }
    }
 
    degree = nbOne + 1;    
}
        
template<typename S>
Nilpotent<S>::Nilpotent(std::vector<S> nilpvec, S diag, S size){
    probSize = size;
    offset = diag; 
 
    if(nilpvec.size() < size - offset){
        try{
            throw 505;
        }catch(...){
            std::cout << "SMG2S]> Caught Exception: for Nilpotent, nilpvec size is not enough" << std::endl;
        }  
    }
    for(auto i = 0; i < size - diag; i++){
        if(nilpvec[i] == 0){
            indOfZeros.push_back(i);
        }
    }
 
    std::vector<S> vec(nilpvec.begin(), nilpvec.begin() + size - offset);
    degree = computeDegree(vec);   
}
 
template<typename S>
S Nilpotent<S>::computeDegree(std::vector<S> nilpvec){
 
    std::vector<S> vectmps(nilpvec.begin(), nilpvec.end());
 
    S diag_offset = offset;
    degree = 1;
    S maxdegree = 80;
 
    while (degree <= maxdegree){
        for(auto i = 0; i < probSize - offset - diag_offset; i++){
            vectmps[i] = nilpvec[i] * vectmps[i+offset];
        }
 
        degree = degree + 1;
 
        bool zeros = std::all_of(vectmps.begin(), vectmps.begin() + probSize-offset - diag_offset, [](S i) { return i==0; });
        if(zeros){
            break;
        }
        diag_offset = diag_offset + offset;
    }
 
    return degree;
}
 
template<typename S>
void Nilpotent<S>::show(){
    std::cout << "Nilpotent: " << "Matrix Size = " << probSize << ", diag_offset = " << offset << "; degree = " << degree << std::endl;
}
 
template<typename S>
Nilpotent<S>::~Nilpotent(){
 
}
 // end of group3
 
#endif