young tableaux and young operator
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2a6e79520e
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d3215e46fd
178
permutation.cc
178
permutation.cc
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@ -817,7 +817,7 @@ template <typename T>
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Partition<T>::Partition(const YoungTableaux<T> &x)
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{
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#ifdef DEBUG
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if(x.is_valid()) laerror("operation with an invalid tableaux");
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if(!x.is_valid()) laerror("operation with an invalid tableaux");
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#endif
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int nparts=x.size();
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int n=0;
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@ -1095,6 +1095,7 @@ if(!is_valid()) laerror("invalid young frame");
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if(!is_standard()) laerror("nonstandardly filled young frame");
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#endif
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if(!ncyc) ncyc=max(); //number of types of applied points
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NRVec_from1<T> onxlines(0,ncyc);
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@ -1116,6 +1117,10 @@ for(int i=1;i<=ncyc;i++) contrib += ((onxlines[i]&1)^1);
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return (1-2*(contrib&1)); //add it to the character +1 for even no. of odd apl., -1 for odd no. of odd apl.
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}
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static bool _callyoung;
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template <typename T>
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static void (*_young_callback)(const YoungTableaux<T>&);
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template <typename T>
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static T _character;
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@ -1243,7 +1248,15 @@ template <typename T>
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void nextapply(T ncyc)
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{
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_nowapplying<T>++;
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if(ncyc> _ncycles<T>) _character<T> += _tchi<T>->character_contribution(_ncycles<T>);
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if(ncyc> _ncycles<T>)
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{
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if(_callyoung)
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{
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_young_callback<T>(*_tchi<T>);
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_character<T> ++;
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}
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else _character<T> += _tchi<T>->character_contribution(_ncycles<T>);
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}
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else regulapply(ncyc,(*_aplnumbers<T>)[ncyc]);
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_nowapplying<T>--;
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}
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@ -1279,22 +1292,175 @@ if(aplnumbers[k]==1)
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//prepare static variables for the recursive procedure and generate all regular applications
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YoungTableaux<T> y(irrep);
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//y.clear(); //already done in the constructor
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_callyoung=false;
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_ncycles<T> =ncycles;
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_tchi<T> = &y;
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_nn<T> = n;
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_nowapplying<T> =0;
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_aplnumbers<T> = &aplnumbers;
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_character<T> =0;
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_oclin<T> = new Partition<T>(n);
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_occol<T> = new Partition<T>(n);
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Partition<T> oclin(n);
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_oclin<T> = &oclin;
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Partition<T> occol(n);
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_occol<T> = &occol;
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for(int i=1; i<=n; ++i) (*_oclin<T>)[i]= (*_occol<T>)[i]= 1;
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nextapply<T>(1);
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delete _occol<T>;
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delete _oclin<T>;
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return _character<T>;
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}
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template <typename T>
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PERM_RANK_TYPE YoungTableaux<T>::generate_all_standard(void (*callback)(const YoungTableaux<T>&))
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("invalid young frame");
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#endif
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//prepare numbers to apply to the tableaux
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T n=this->sum();
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T ncycles=n;
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NRVec_from1<T> aplnumbers(n);
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for(T i=1; i<=n; ++i) aplnumbers[i]=1;
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//prepare static variables for the recursive procedure and generate all regular applications
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this->clear();
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_callyoung=true;
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_young_callback<T> =callback;
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_ncycles<T> =ncycles;
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_tchi<T> = this;
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_nn<T> = n;
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_nowapplying<T> =0;
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_aplnumbers<T> = &aplnumbers;
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_character<T> =0;
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Partition<T> oclin(n);
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_oclin<T> = &oclin;
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Partition<T> occol(n);
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_occol<T> = &occol;
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for(int i=1; i<=n; ++i) (*_oclin<T>)[i]= (*_occol<T>)[i]= 1;
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nextapply<T>(1);
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return _character<T>;
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}
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////generation of the young operator
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template <typename T>
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void (*_young_operator_callback)(const NRPerm<T>&p, const T parity, const PERM_RANK_TYPE nterms);
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template <typename T>
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static NRPerm<T> _aperm;
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template <typename T>
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static NRPerm<T> _sperm;
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template <typename T>
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static const YoungTableaux<T> *_tyou;
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template <typename T>
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static const Partition<T> *_tyou_cols;
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template <typename T>
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static const Partition<T> *_tyou_rows;
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static PERM_RANK_TYPE _nyoungterms, _expectterms;
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template <typename T>
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static T _antparity;
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template <typename T>
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void symetr(T ilin, T iel)
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{
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if(ilin > (*_tyou_cols<T>)[1])
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{
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++_nyoungterms;
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(*_young_operator_callback<T>)(_aperm<T>*_sperm<T>,_antparity<T>,_expectterms);
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}
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else if(iel > (*_tyou_rows<T>)[ilin]) symetr(ilin+1,1);
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else
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{
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int i;
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for(i=1;i<=(*_tyou_rows<T>)[ilin];i++)
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if(!_sperm<T>[(*_tyou<T>)[ilin][i]])
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{
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_sperm<T>[(*_tyou<T>)[ilin][i]]= (*_tyou<T>)[ilin][iel];
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symetr(ilin,iel+1);
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_sperm<T>[(*_tyou<T>)[ilin][i]]=0;
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}
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}
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}
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template <typename T>
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void antisym(T icol,T iel)
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{
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if(icol > (*_tyou_rows<T>)[1])
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{
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_antparity<T> = _aperm<T>.parity();
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symetr<T>(1,1);
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}
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else
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if(iel > (*_tyou_cols<T>)[icol]) antisym(icol+1,1);
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else
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{
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int i;
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for(i=1;i<=(*_tyou_cols<T>)[icol];i++)
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if(!_aperm<T>[(*_tyou<T>)[i][icol]])
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{
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_aperm<T>[(*_tyou<T>)[i][icol]]= (*_tyou<T>)[iel][icol];
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antisym(icol,iel+1);
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_aperm<T>[(*_tyou<T>)[i][icol]]=0;
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}
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}
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}
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template <typename T>
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PERM_RANK_TYPE YoungTableaux<T>::young_operator(void (*callback)(const NRPerm<T>&p, const T parity, const PERM_RANK_TYPE nterms)) const
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{
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#ifdef DEBUG
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if(!this->is_standard()) laerror("young_operator called for non-standard tableaux");
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#endif
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_young_operator_callback<T> = callback;
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_nyoungterms =0;
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_tyou<T> = this;
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Partition<T> rows=Partition<T>(*this);
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Partition<T> cols=rows.adjoint();
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_tyou_rows<T> = &rows;
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_tyou_cols<T> = &cols;
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T n=rows.sum();
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_aperm<T>.resize(n); _aperm<T>.clear();
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_sperm<T>.resize(n); _sperm<T>.clear();
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_expectterms=1;
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for(int i=1;i<=cols[1];i++) _expectterms *= factorial(rows[i]);
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for(int i=1;i<=rows[1];i++) _expectterms *= factorial(cols[i]);
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antisym<T>(1,1);
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if(_nyoungterms!=_expectterms) laerror("youngconstruct: inconsistent number of terms");
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return _nyoungterms;
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}
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template <typename T>
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static NRVec_from1<CompressedPartition<T> > *_irreps;
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@ -162,6 +162,15 @@ public:
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};
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template <typename T>
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extern T Sn_character(const Partition<T> &irrep, const Partition<T> &cclass);
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template <typename T>
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inline T Sn_character(const CompressedPartition<T> &irrep, const CompressedPartition<T> &cclass)
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{
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return Sn_character(Partition<T>(irrep),Partition<T>(cclass));
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}
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template <typename T>
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class YoungTableaux : public NRVec_from1<NRVec_from1<T> > {
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@ -177,8 +186,9 @@ public:
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T max() const; //get back highest number filled in
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NRVec_from1<T> yamanouchi() const; //yamanouchi symbol
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T character_contribution(int ncyc=0) const; //contribution of filled tableaux to Sn character
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PERM_RANK_TYPE generate_all_standard(void (*callback)(const YoungTableaux<T>&));
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PERM_RANK_TYPE young_operator(void (*callback)(const NRPerm<T>&p, const T parity, const PERM_RANK_TYPE nterms)) const; //generate young operator for a standard tableaux
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//@@@ ??>young operator as a linear comb of permutations - maybe a class for itself, i.e. element of the Sn group algebra? or maybe as a vector with index being the rank of the permutation(n! length) or as a sparsemat thereof or maybe a list???
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};
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template <typename T>
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@ -187,15 +197,6 @@ std::ostream & operator<<(std::ostream &s, const YoungTableaux<T> &x);
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extern PERM_RANK_TYPE partitions(int n, int k= -1); //enumerate partitions to k parts; k== -1 for total # of partitions
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template <typename T>
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extern T Sn_character(const Partition<T> &irrep, const Partition<T> &cclass);
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template <typename T>
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inline T Sn_character(const CompressedPartition<T> &irrep, const CompressedPartition<T> &cclass)
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{
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return Sn_character(Partition<T>(irrep),Partition<T>(cclass));
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}
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//Sn character table
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template <typename T>
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25
t.cc
25
t.cc
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@ -71,13 +71,30 @@ for(int i=0; i<4; ++i)
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static int unitary_n;
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static PERM_RANK_TYPE space_dim;
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void yyprintme(const NRPerm<int>&p, const int parity, const PERM_RANK_TYPE nterms)
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{
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cout<< parity<<"/"<<nterms<<" "<<p;
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}
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void yprintme(const YoungTableaux<int>&y)
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{
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cout <<y;
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if(!y.is_standard()) laerror("internal error in young");
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y.young_operator(yyprintme);
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}
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void pprintme(const Partition<int> &p)
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{
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CompressedPartition pc(p);
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cout<<'['<<pc<<"] ";
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CompressedPartition<int> pc(p);
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cout<<'['<<pc<<"]\n";
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YoungTableaux<int> y(p);
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PERM_RANK_TYPE dim=y.generate_all_standard(yprintme);
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Partition<int> q=p.adjoint();
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PERM_RANK_TYPE snd=p.Sn_irrep_dim();
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cout<<"IR dim "<<snd<<endl;
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if(dim!=snd) laerror("inconsistency in standard tableaux generation");
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PERM_RANK_TYPE und=p.Un_irrep_dim(unitary_n);
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cout<<"U("<<unitary_n<<") ir dim "<<und<<endl;
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space_dim += und*snd;
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@ -2129,7 +2146,7 @@ int tot=p.generate_all_lex(printme);
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cout <<"generated "<<tot<<endl;
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}
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if(0)
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if(1)
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{
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int n;
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cin >>n >>unitary_n;
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@ -2141,7 +2158,7 @@ if(tot!=partitions(n)) laerror("internal error in partition generation or enumer
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if(space_dim!=longpow(unitary_n,n)) {cout<<space_dim<<" "<<ipow(unitary_n,n)<<endl;laerror("integer overflow or internal error in space dimensions");}
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}
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if(1)
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if(0)
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{
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int n;
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cin >>n ;
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