progressing on partitions
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4be6df3317
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88628fb306
125
permutation.cc
125
permutation.cc
@ -603,12 +603,12 @@ return (n_even_cycles&1)?-1:1;
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template <typename T>
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Partition<T> CyclePerm<T>::cycles(const T n) const
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CompressedPartition<T> CyclePerm<T>::cycles(const T n) const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("operation with an invalid cycleperm");
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#endif
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Partition<T> r(n); r.clear();
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CompressedPartition<T> r(n); r.clear();
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T ncycles=this->size();
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for(T i=1; i<=ncycles; ++i)
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{
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@ -718,12 +718,133 @@ return s;
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///////////////////////////////////////////////////////
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template <typename T>
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PERM_RANK_TYPE CompressedPartition<T>::Sn_class_size() const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("operation with an invalid partition");
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#endif
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int n=this->size();
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PERM_RANK_TYPE r=factorial(n);
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for(int i=1; i<=n; ++i)
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{
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T m=(*this)[i];
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if(i>1 && m>0) r/=ipow(i,m);
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if(m>1) r/=factorial(m);
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}
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return r;
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}
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template <typename T>
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PERM_RANK_TYPE Partition<T>::Sn_irrep_dim() const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("operation with an invalid partition");
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#endif
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int n=this->size();
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PERM_RANK_TYPE prod=1;
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Partition<T> adj=this->adjoint();
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//hook length formula
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for(int i=1; i<=adj[1]; ++i) //rows
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for(int j=1; j<= (*this)[i]; ++j) //cols
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prod *= (*this)[i]-j+adj[j]-i+1;
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return factorial(n)/prod;
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}
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template <typename T>
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Partition<T> Partition<T>::adjoint() const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("operation with an invalid partition");
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#endif
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int n=this->size();
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Partition<T> r(n);
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r.clear();
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for(int i=1;i<=n;++i)
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{
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int j;
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for(j=1; j<=n&&(*this)[j]>=i; ++j);
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r[i]=j-1;
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}
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return r;
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}
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PERM_RANK_TYPE ipow(PERM_RANK_TYPE x, int i)
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{
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if(i<0) return 0;
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PERM_RANK_TYPE y=1;
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do
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{
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if(i&1) y *= x;
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i >>= 1;
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if(i) x *= x;
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}
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while(i);
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return y ;
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}
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//aux for the recursive procedure
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static PERM_RANK_TYPE partitioncount;
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template <typename T> static void (*_pcallback)(const Partition<T>&);
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static int partitiontyp;
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static int partitiontypabs;
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template <typename T> static Partition<T> *partition;
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template <typename T>
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void partgen(int remain, int pos)
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{
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int hi,lo;
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if(remain==0) {++partitioncount; (*_pcallback<T>)(*partition<T>); return;}
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if(partitiontyp) lo=(remain+partitiontypabs-pos)/(partitiontypabs-pos+1); else lo=1;
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hi=remain;
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if(partitiontyp>0) hi -= partitiontypabs-pos;
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if(pos>1 && (*partition<T>)[pos-1] < hi) hi= (*partition<T>)[pos-1];
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for((*partition<T>)[pos]=hi; (*partition<T>)[pos]>=lo; --(*partition<T>)[pos]) partgen<T>(remain-(*partition<T>)[pos],pos+1);
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(*partition<T>)[pos]=0;
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}
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template <typename T>
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PERM_RANK_TYPE Partition<T>::generate_all(void (*callback)(const Partition<T>&), int nparts)
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{
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int n=this->size();
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if(n==0) return 0;
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if(nparts>0 && n<nparts) return 0;
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this->copyonwrite();
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this->clear();
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partitioncount=0;
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_pcallback<T> =callback;
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partitiontyp=nparts;
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partition<T> = this;
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partitiontypabs= nparts>=0?nparts:-nparts;
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partgen<T>(n,1);
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return partitioncount;
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}
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template <typename T>
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YoungTableaux<T>::YoungTableaux(const Partition<T> &frame)
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: NRVec_from1<NRVec_from1<T> >()
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{
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#ifdef DEBUG
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if(!frame.is_valid()) laerror("invalid partition used as young frame");
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#endif
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int nlines=frame.nparts();
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this->resize(nlines);
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for(int i=1; i<=nlines; ++i) (*this)[i].resize(frame[i]);
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}
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/***************************************************************************//**
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* forced instantization in the corresponding object file
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******************************************************************************/
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template class NRPerm<int>;
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template class CyclePerm<int>;
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template class CompressedPartition<int>;
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template class Partition<int>;
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#define INSTANTIZE(T) \
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@ -33,6 +33,7 @@ namespace LA {
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template <typename T> class NRVec_from1;
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template <typename T> class CyclePerm;
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template <typename T> class Partition;
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template <typename T> class CompressedPartition;
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template <typename T>
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class NRPerm : public NRVec_from1<T> {
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@ -64,6 +65,7 @@ public:
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};
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extern PERM_RANK_TYPE factorial(const int n);
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extern PERM_RANK_TYPE ipow(PERM_RANK_TYPE x, int i);
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//permutations represented in the cycle format
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template <typename T>
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@ -78,9 +80,10 @@ public:
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CyclePerm inverse() const; //reverse all cycles
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int parity() const; //negative if having odd number of even-length cycles
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T max() const {T m=0; for(int i=1; i<=this->size(); ++i) {T mm= (*this)[i].max(); if(mm>m) m=mm;} return m;}
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Partition<T> cycles(const T n) const;
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CompressedPartition<T> cycles(const T n) const;
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void readfrom(const std::string &line);
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CyclePerm operator*(const CyclePerm q) const; //q is rhs and applied first, this applied second
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//@@@order = lcm of cycle lengths
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};
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@ -92,24 +95,54 @@ std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x);
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//partitions stored as #of 1s, #of 2s, etc.
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//compressed partitions stored as #of 1s, #of 2s, etc.
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template <typename T>
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class CompressedPartition : public NRVec_from1<T> {
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public:
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CompressedPartition(): NRVec_from1<T>() {};
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CompressedPartition(const int n) : NRVec_from1<T>(n) {};
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T sum() const {T s=0; for(int i=1; i<=this->size(); ++i) s += i*(*this)[i]; return s;}
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T nparts() const {T s=0; for(int i=1; i<=this->size(); ++i) s += (*this)[i]; return s;}
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T nclasses() const {T s=0; for(int i=1; i<=this->size(); ++i) if((*this)[i]) ++s; return s;}
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bool is_valid() const {return this->size() == this->sum();}
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explicit CompressedPartition(const Partition<T> &rhs) : NRVec_from1<T>(rhs.size()) {this->clear(); for(int i=1; i<=rhs.size(); ++i) if(!rhs[i]) break; else (*this)[rhs[i]]++; }
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PERM_RANK_TYPE Sn_class_size() const;
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//@@@output formatted as in the group character table
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};
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template <typename T>
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class Partition : public NRVec_from1<T> {
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public:
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Partition(): NRVec_from1<T>() {};
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Partition(const int n) : NRVec_from1<T>(n) {};
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T sum() const {T s=0; for(T i=1; i<=this->size(); ++i) s += i*(*this)[i]; return s;}
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T nparts() const {T s=0; for(T i=1; i<=this->size(); ++i) s += (*this)[i]; return s;}
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T nclasses() const {T s=0; for(T i=1; i<=this->size(); ++i) if((*this)[i]) ++s; return s;}
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bool is_valid() const {return this->size() == this->sum();}
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Partition(): NRVec_from1<T>() {};
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Partition(const int n) : NRVec_from1<T>(n) {};
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T nparts() const {T s=0; for(int i=1; i<=this->size(); ++i) if((*this)[i]) ++s; return s;}
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bool is_valid() const {if(this->size() != this->sum()) return false; for(int i=2; i<=this->size(); ++i) if((*this)[i]>(*this)[i-1]) return false; return true; }
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explicit Partition(const CompressedPartition<T> &rhs) : NRVec_from1<T>(rhs.size()) {this->clear(); int ithru=0; for(int i=rhs.size(); i>=1; --i) for(int j=0; j<rhs[i]; ++j) (*this)[++ithru]=i; }
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Partition adjoint() const;
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PERM_RANK_TYPE Sn_irrep_dim() const;
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PERM_RANK_TYPE generate_all(void (*callback)(const Partition<T>&), int nparts=0); //nparts <0 means at most to -nparts
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//@@@generate all partitions,
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//@@@enumerator of partitions of n to r parts and total
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//@@@adjoint partition,
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//@@@output formatted as in the group character table
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//@@@Sn character table computation
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//@@@yamanouchi symbol
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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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public:
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YoungTableaux() : NRVec_from1<NRVec_from1<T> >() {};
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explicit YoungTableaux(const Partition<T> &frame);
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bool is_valid() const; //@@@shape forms a partition
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bool filled_correctly() const; //is it filled correctly
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};
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//@@@enumerator of partitions of n to r parts and total from expr
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//@@@Sn character table computation from young - young frame filling
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}//namespace
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#endif
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24
t.cc
24
t.cc
@ -68,6 +68,17 @@ for(int i=0; i<4; ++i)
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}
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}
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void pprintme(const Partition<int> &p)
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{
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cout<<p;
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Partition<int> q=p.adjoint();
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cout<<"IR dim "<<p.Sn_irrep_dim()<<endl;
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cout <<q;
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CompressedPartition qc(q);
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cout<<"Class size "<<qc.Sn_class_size()<<endl;
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}
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int main()
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{
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@ -2085,7 +2096,7 @@ cout <<p;
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}while(p.next());
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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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@ -2094,4 +2105,15 @@ int tot=p.generate_all_lex(printme);
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cout <<"generated "<<tot<<endl;
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}
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if(1)
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{
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int n;
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cin >>n;
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Partition<int> p(n);
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int tot=p.generate_all(pprintme,0);
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cout <<"generated "<<tot<<endl;
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}
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}
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