[74a91c9] | 1 | /* |
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| 2 | * gfan_symmetry.h |
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| 3 | * |
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| 4 | * Created on: Oct 22, 2010 |
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| 5 | * Author: anders |
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| 6 | */ |
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| 7 | |
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| 8 | #ifndef GFANLIB_SYMMETRY_H_INCLUDED |
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| 9 | #define GFANLIB_SYMMETRY_H_INCLUDED |
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| 10 | |
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| 11 | #include <set> |
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| 12 | #include "gfanlib_vector.h" |
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| 13 | #include "gfanlib_matrix.h" |
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| 14 | |
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| 15 | namespace gfan{ |
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| 16 | |
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| 17 | /** |
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| 18 | * The permutation class represents an element in the symmetric group S_n. |
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| 19 | */ |
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| 20 | class Permutation:public IntVector |
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| 21 | { |
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| 22 | // IntVector data; |
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| 23 | public: |
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| 24 | /** |
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| 25 | * Returns true if a contains the elements from 0 up to a.size()-1. |
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| 26 | */ |
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| 27 | static bool isPermutation(IntVector const &a); |
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| 28 | /** |
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| 29 | * Generates the identity permutation on n elements. |
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| 30 | */ |
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| 31 | Permutation(int n): |
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| 32 | IntVector(n) |
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| 33 | { |
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| 34 | for(int i=0;i<n;i++)(*this)[i]=i; |
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| 35 | } |
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| 36 | /** |
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| 37 | * Generates a permutation from the vector v. The ith entry of v tells |
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| 38 | * If the check flag is set to true, then it is checked whether the vector represents |
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| 39 | * a permutation. If not, the code fails with an assertion. |
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| 40 | */ |
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| 41 | Permutation(IntVector const &v, bool check=true): |
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| 42 | IntVector(v) |
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| 43 | { |
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| 44 | if(check)assert(isPermutation(v)); |
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| 45 | } |
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| 46 | |
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| 47 | static Permutation transposition(int n, int i, int j) |
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| 48 | { |
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| 49 | IntVector ret(n); |
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| 50 | for(int k=0;k<n;k++)ret[k]=k; |
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| 51 | ret[i]=j; |
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| 52 | ret[j]=i; |
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| 53 | return Permutation(ret); |
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| 54 | } |
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| 55 | static Permutation cycle(int n) |
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| 56 | { |
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| 57 | IntVector a(n); |
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| 58 | for(int i=0;i<n-1;i++)a[i]=i+1; |
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| 59 | a[n-1]=0; |
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| 60 | return Permutation(a); |
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| 61 | } |
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| 62 | IntVector toIntVector()const |
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| 63 | { |
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| 64 | return IntVector(*this); |
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| 65 | } |
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| 66 | |
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| 67 | int sizeOfBaseSet()const |
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| 68 | { |
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| 69 | return size(); |
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| 70 | } |
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| 71 | Permutation inverse()const; |
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| 72 | |
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| 73 | /** |
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| 74 | * Apply the permutation |
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| 75 | */ |
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| 76 | Permutation apply(Permutation const &p)const; |
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| 77 | IntVector apply(IntVector const &v)const; |
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| 78 | ZVector apply(ZVector const &v)const; |
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| 79 | ZMatrix apply(ZMatrix const &m)const; |
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| 80 | Permutation applyInverse(Permutation const &p)const; |
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| 81 | IntVector applyInverse(IntVector const &v)const; |
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| 82 | ZVector applyInverse(ZVector const &v)const; |
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| 83 | ZMatrix applyInverse(ZMatrix const &m)const; |
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| 84 | |
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| 85 | /** |
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| 86 | The set of vectors which are not improved lexicographically when |
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| 87 | perm is applied to them is convex. Its closure is a |
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| 88 | halfspace. This routine returns the inner normal of this |
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| 89 | halfspace. The only exception is if perm is the identity then the |
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| 90 | zero vector is returned. |
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| 91 | */ |
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| 92 | ZVector fundamentalDomainInequality()const; |
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| 93 | }; |
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| 94 | |
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| 95 | /** |
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| 96 | * This object represents a subgroup of the symmetric group S_n. |
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| 97 | */ |
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| 98 | |
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| 99 | class SymmetryGroup{ |
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| 100 | // unsigned char *byteTable; |
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| 101 | int byteTableHeight; |
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| 102 | class Trie *trie; |
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| 103 | public: |
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| 104 | typedef std::set<Permutation/*,LexicographicTermOrder*/> ElementContainer; |
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| 105 | ElementContainer elements;//Make this private |
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| 106 | int size()const |
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| 107 | { |
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| 108 | return elements.size(); |
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| 109 | } |
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| 110 | int sizeOfBaseSet()const; |
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| 111 | /** |
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| 112 | The set of vectors which cannot be improved lexicographically by |
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| 113 | applying an element from the group is a convex set. Its closure |
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| 114 | is a polyhedral cone. This routine returns a set of inequalities |
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| 115 | The returned list does not contain the zero vector. |
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| 116 | */ |
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| 117 | ZMatrix fundamentalDomainInequalities()const; |
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| 118 | SymmetryGroup(int n); |
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| 119 | void computeClosure(Permutation const &v); |
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[c4d065] | 120 | void computeClosure(IntMatrix const &l); |
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| 121 | IntMatrix getGenerators()const; |
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[74a91c9] | 122 | int orbitSize(ZVector const &stable)const; |
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| 123 | bool isTrivial()const; |
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| 124 | /** |
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| 125 | The symmetry group acts on vectors by permuting the entries. The |
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| 126 | following routine returns a unique representative for the orbit |
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| 127 | containing v. This makes it easy to check if two elements are in |
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| 128 | the same orbit. The permutation used to get this representative |
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| 129 | is stored in *usedPermutation (if pointer not 0). |
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| 130 | */ |
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| 131 | ZVector orbitRepresentative(ZVector const &v, Permutation *usedPermutation=0)const; |
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| 132 | /** |
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| 133 | This routine works as orbitRepresentative() except that the |
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| 134 | symmetry group considered is only the subgroup keeping the vector |
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| 135 | fixed fixed. |
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| 136 | */ |
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| 137 | ZVector orbitRepresentativeFixing(ZVector const &v, ZVector const &fixed)const; |
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| 138 | |
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| 139 | // Methods for highly optimized symmetry group computations: |
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| 140 | // void createByteTable();//Can only be called once. SymmetryGroup is not allowed to be changed afterwards or to be copied. Leaks memory at destruction. |
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| 141 | void createTrie(); |
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| 142 | // unsigned char *getByteTable()const; |
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| 143 | // int getByteTableHeight()const; |
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| 144 | }; |
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| 145 | /** |
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| 146 | * Sorts v and returns the number of swaps performed. |
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| 147 | */ |
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| 148 | int mergeSort(IntVector &v); |
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| 149 | } |
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| 150 | |
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| 151 | |
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| 152 | |
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| 153 | |
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| 154 | #endif /* GFAN_SYMMETRY_H_ */ |
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