431 lines
9.5 KiB
C++
431 lines
9.5 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "permutation.h"
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#include <stdio.h>
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#include <string.h>
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namespace LA {
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template <typename T>
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void NRPerm<T>::identity()
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{
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T n=this->size();
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#ifdef DEBUG
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if(n<0) laerror("invalid permutation size");
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#endif
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if(n==0) return;
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this->copyonwrite();
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for(T i=1; i<=n; ++i) (*this)[i]=i;
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}
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template <typename T>
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bool NRPerm<T>::is_identity() const
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{
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T n=this->size();
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#ifdef DEBUG
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if(n<0) laerror("invalid permutation size");
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#endif
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if(n==0) return 1;
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for(T i=1; i<=n; ++i) if((*this)[i]!=i) return 0;
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return 1;
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}
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template <typename T>
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bool NRPerm<T>::is_valid() const
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{
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T n = this->size();
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if(n<0) return 0;
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NRVec_from1<T> used(n);
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used.clear();
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for(T i=1; i<=n; ++i)
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{
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T x= (*this)[i];
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if(x<1||x>n) return 0;
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used[x] += 1;
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}
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for(T i=1; i<=n; ++i) if(used[i]!=1) return 0;
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return 1;
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}
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template <typename T>
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NRPerm<T> NRPerm<T>::inverse() const
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{
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#ifdef DEBUG
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if(!this->is_valid()) laerror("inverse of invalid permutation");
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#endif
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NRPerm<T> q(this->size());
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for(T i=1; i<=this->size(); ++i) q[(*this)[i]]=i;
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return q;
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}
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template <typename T>
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NRPerm<T> NRPerm<T>::operator*(const NRPerm<T> q) const
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{
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#ifdef DEBUG
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if(!this->is_valid() || !q.is_valid()) laerror("multiplication of invalid permutation");
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#endif
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T n=this->size();
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if(n!=q.size()) laerror("product of incompatible permutations");
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NRPerm<T> r(n);
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for(T i=1; i<=n; ++i) r[i] = (*this)[q[i]];
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return r;
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}
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template <typename T>
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NRPerm<T> NRPerm<T>::conjugate_by(const NRPerm<T> q) const
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{
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#ifdef DEBUG
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if(!this->is_valid() || !q.is_valid()) laerror("multiplication of invalid permutation");
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#endif
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T n=this->size();
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if(n!=q.size()) laerror("product of incompatible permutations");
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NRPerm<T> qi=q.inverse();
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NRPerm<T> r(n);
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for(T i=1; i<=n; ++i) r[i] = qi[(*this)[q[i]]];
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return r;
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}
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template <typename T>
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int NRPerm<T>::parity() const
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{
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if(!this->is_valid()) return 0;
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T n=this->size();
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if(n==1) return 1;
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T count=0;
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for(T i=2;i<=n;i++) for(T j=1;j<i;j++) if((*this)[j]>(*this)[i]) count++;
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return (count&1)? -1:1;
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}
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template <typename T>
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NRPerm<T>::NRPerm(const CyclePerm<T> &rhs, const int n)
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{
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#ifdef DEBUG
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if(!rhs.is_valid()) laerror("invalid cycle permutation");
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#endif
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int m;
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if(n) m=n; else m=rhs.max();
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this->resize(m);
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identity();
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T ncycles=rhs.size();
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for(T j=1; j<=ncycles; ++j)
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{
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T length= rhs[j].size();
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for(T i=1; i<=length; ++i) (*this)[rhs[j][i]] = rhs[j][i%length+1];
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}
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#ifdef DEBUG
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if(!is_valid()) laerror("internal error in NRPerm constructor from CyclePerm");
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#endif
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}
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template <typename T>
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void NRPerm<T>::randomize(void)
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{
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int n=this->size();
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if(n<=0) laerror("cannot randomize empty permutation");
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this->copyonwrite();
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this->identity();
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for(int i=n-1; i>=1; --i)
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{
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int j= random()%(i+1);
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T tmp = (*this)[i+1];
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(*this)[i+1]=(*this)[j+1];
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(*this)[j+1]=tmp;
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}
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}
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////////////////////////////////////////////////////////
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template <typename T>
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CyclePerm<T>:: CyclePerm(const NRPerm<T> &p)
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{
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#ifdef DEBUG
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if(!p.is_valid()) laerror("invalid permutation");
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#endif
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T n=p.size();
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NRVec_from1<T> used(0,n),tmp(n);
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T firstunused=1;
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T currentcycle=0;
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std::list<NRVec_from1<T> > cyclelist={};
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do
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{
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//find a cycle starting with first unused element
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T cyclelength=0;
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T next = firstunused;
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do
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{
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++cyclelength;
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used[next]=1;
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tmp[cyclelength] = next;
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next = p[next];
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}
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while(used[next]==0);
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if(cyclelength>1) //nontrivial cycle
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{
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NRVec_from1<T> cycle(&tmp[1],cyclelength);
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cyclelist.push_front(cycle);
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++currentcycle;
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}
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while(used[firstunused]) {++firstunused; if(firstunused>n) break;} //find next unused element
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}
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while(firstunused<=n);
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//convert list to NRVec
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this->resize(currentcycle);
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T i=1;
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for(auto l=cyclelist.begin(); l!=cyclelist.end(); ++l) (*this)[i++] = *l;
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}
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template <typename T>
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bool CyclePerm<T>::is_valid() const
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{
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for(T i=1; i<=this->size(); ++i)
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{
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T n=(*this)[i].size();
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if(n<=0) return false;
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for(T j=1; j<=n; ++j)
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{
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T x=(*this)[i][j];
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if(x<=0) return false;
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//now check for illegal duplicity of numbers withis a cycle or across cycles
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for(T ii=i; ii<=this->size(); ++ii)
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{
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T nn=(*this)[ii].size();
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for(T jj=(ii==i?j+1:1); jj<=nn; ++jj)
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{
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T xx=(*this)[ii][jj];
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if(x==xx) return false;
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}
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}
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}
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}
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return true;
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}
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template <typename T>
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bool CyclePerm<T>::is_identity() 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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for(T i=1; i<=this->size(); ++i) if((*this)[i].size()>1) return false; //at least one nontrivial cycle
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return true;
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}
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template <typename T>
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CyclePerm<T> CyclePerm<T>::inverse() 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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CyclePerm<T> r;
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T ncycles=this->size();
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r.resize(ncycles);
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for(T i=1; i<=ncycles; ++i)
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{
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T length=(*this)[i].size();
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r[i].resize(length);
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//reverse order in cycles (does not matter in cycle lengths 1 and 2 anyway)
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for(T j=1; j<=length; ++j) r[i][j] = (*this)[i][length-j+1];
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}
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return r;
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}
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//multiplication via NRPerm - could there be a more efficient direct algorithm?
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template <typename T>
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CyclePerm<T> CyclePerm<T>::operator*(const CyclePerm q) const
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{
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int m=this->max();
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int mm=q.max();
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if(mm>m) mm=m;
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NRPerm<T> qq(q,m);
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NRPerm<T> pp(*this,m);
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NRPerm<T> rr=pp*qq;
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return CyclePerm<T>(rr);
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}
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template <typename T>
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int CyclePerm<T>::parity() 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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int n_even_cycles=0;
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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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T length=(*this)[i].size();
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if((length&1)==0) ++n_even_cycles;
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}
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return (n_even_cycles&1)?-1:1;
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}
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template <typename T>
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Partition<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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T ncycles=this->size();
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for(T i=1; i<=ncycles; ++i)
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{
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T length=(*this)[i].size();
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if(length<=0||length>n) laerror("unexpected cycle length in permutation");
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r[length]++;
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}
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//fill in trivial cycles of length one
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r[1] += n - r.sum();
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if(r[1]<0) laerror("inconsistent cycle lengths in CyclePerm::cycles");
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return r;
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}
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//auxiliary function for input of a permutation in cycle format
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//returns pointer after closing bracket or NULL if no cycle found
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//or input error
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template <typename T>
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const char *read1cycle(NRVec_from1<T> &c, const char *p)
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{
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if(*p==0) return NULL;
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const char *openbracket = strchr(p,'(');
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if(!openbracket) return NULL;
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const char *closebracket = strchr(openbracket+1,')');
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if(!closebracket) return NULL;
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const char *s = openbracket+1;
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int r;
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int length=0;
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std::list<T> cycle;
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do {
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long int tmp;
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int nchar;
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if(*s==',') ++s;
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r = sscanf(s,"%ld%n",&tmp,&nchar);
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if(r==1)
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{
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++length;
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s += nchar;
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cycle.push_back((T)tmp);
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}
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}
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while(r==1 && s<closebracket);
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//make vector from list
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c.resize(length);
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int i=0;
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for(auto l=cycle.begin(); l!=cycle.end(); ++l) c[++i] = *l;
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return closebracket+1;
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}
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template <typename T>
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void CyclePerm<T>::readfrom(const std::string &line)
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{
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const char *p=line.c_str();
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std::list<NRVec<T> > cyclelist={};
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int ncycles=0;
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int count=0;
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NRVec_from1<T> c;
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while(p=read1cycle(c,p))
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{
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//printf("cycle %d of length %d read\n",count,c.size());
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if(c.size()!=0) //store a nonempty cycle
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{
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++count;
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cyclelist.push_back(c);
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}
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}
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//convert list to vector
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this->resize(count);
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T i=0;
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for(auto l=cyclelist.begin(); l!=cyclelist.end(); ++l) (*this)[++i] = *l;
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#ifdef DEBUG
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if(!this->is_valid()) laerror("readfrom received input of invalid CyclePerm");
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#endif
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}
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template <typename T>
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std::istream & operator>>(std::istream &s, CyclePerm<T> &x)
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{
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std::string l;
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getline(s,l);
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x.readfrom(l);
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return s;
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}
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template <typename T>
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std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x)
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{
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for(int i=1; i<=x.size(); ++i)
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{
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s<<"(";
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for(int j=1; j<=x[i].size(); ++j)
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{
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s<<x[i][j];
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if(j<x[i].size()) s<<" ";
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}
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s<<")";
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}
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return s;
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}
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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 Partition<int>;
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#define INSTANTIZE(T) \
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template std::istream & operator>>(std::istream &s, CyclePerm<T> &x); \
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template std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x); \
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INSTANTIZE(int)
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}//namespace
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