1 | /* |
---|
2 | * gfan_symmetry.h |
---|
3 | * |
---|
4 | * Created on: Oct 22, 2010 |
---|
5 | * Author: anders |
---|
6 | */ |
---|
7 | |
---|
8 | #ifndef GFANLIB_SYMMETRY_H_INCLUDED |
---|
9 | #define GFANLIB_SYMMETRY_H_INCLUDED |
---|
10 | |
---|
11 | #include <set> |
---|
12 | #include "gfanlib_vector.h" |
---|
13 | #include "gfanlib_matrix.h" |
---|
14 | |
---|
15 | namespace gfan{ |
---|
16 | |
---|
17 | /** |
---|
18 | * The permutation class represents an element in the symmetric group S_n. |
---|
19 | */ |
---|
20 | class Permutation:public IntVector |
---|
21 | { |
---|
22 | // IntVector data; |
---|
23 | public: |
---|
24 | /** |
---|
25 | * Returns true if a contains the elements from 0 up to a.size()-1. |
---|
26 | */ |
---|
27 | static bool isPermutation(IntVector const &a); |
---|
28 | /** |
---|
29 | * Returns true if all rows of the matrix are pemutations |
---|
30 | */ |
---|
31 | static bool arePermutations(IntMatrix const &m); |
---|
32 | /** |
---|
33 | * Generates the identity permutation on n elements. |
---|
34 | */ |
---|
35 | Permutation(int n): |
---|
36 | IntVector(n) |
---|
37 | { |
---|
38 | for(int i=0;i<n;i++)(*this)[i]=i; |
---|
39 | } |
---|
40 | /** |
---|
41 | * Generates a permutation from the vector v. The ith entry of v tells |
---|
42 | * If the check flag is set to true, then it is checked whether the vector represents |
---|
43 | * a permutation. If not, the code fails with an assertion. |
---|
44 | */ |
---|
45 | Permutation(IntVector const &v, bool check=true): |
---|
46 | IntVector(v) |
---|
47 | { |
---|
48 | if(check)assert(isPermutation(v)); |
---|
49 | } |
---|
50 | |
---|
51 | static Permutation transposition(int n, int i, int j) |
---|
52 | { |
---|
53 | IntVector ret(n); |
---|
54 | for(int k=0;k<n;k++)ret[k]=k; |
---|
55 | ret[i]=j; |
---|
56 | ret[j]=i; |
---|
57 | return Permutation(ret); |
---|
58 | } |
---|
59 | static Permutation cycle(int n) |
---|
60 | { |
---|
61 | IntVector a(n); |
---|
62 | for(int i=0;i<n-1;i++)a[i]=i+1; |
---|
63 | a[n-1]=0; |
---|
64 | return Permutation(a); |
---|
65 | } |
---|
66 | IntVector toIntVector()const |
---|
67 | { |
---|
68 | return IntVector(*this); |
---|
69 | } |
---|
70 | |
---|
71 | int sizeOfBaseSet()const |
---|
72 | { |
---|
73 | return size(); |
---|
74 | } |
---|
75 | Permutation inverse()const; |
---|
76 | |
---|
77 | /** |
---|
78 | * Apply the permutation |
---|
79 | */ |
---|
80 | Permutation apply(Permutation const &p)const; |
---|
81 | IntVector apply(IntVector const &v)const; |
---|
82 | ZVector apply(ZVector const &v)const; |
---|
83 | ZMatrix apply(ZMatrix const &m)const; |
---|
84 | Permutation applyInverse(Permutation const &p)const; |
---|
85 | IntVector applyInverse(IntVector const &v)const; |
---|
86 | ZVector applyInverse(ZVector const &v)const; |
---|
87 | ZMatrix applyInverse(ZMatrix const &m)const; |
---|
88 | |
---|
89 | /** |
---|
90 | The set of vectors which are not improved lexicographically when |
---|
91 | perm is applied to them is convex. Its closure is a |
---|
92 | halfspace. This routine returns the inner normal of this |
---|
93 | halfspace. The only exception is if perm is the identity then the |
---|
94 | zero vector is returned. |
---|
95 | */ |
---|
96 | ZVector fundamentalDomainInequality()const; |
---|
97 | }; |
---|
98 | |
---|
99 | /** |
---|
100 | * This object represents a subgroup of the symmetric group S_n. |
---|
101 | */ |
---|
102 | |
---|
103 | class SymmetryGroup{ |
---|
104 | // unsigned char *byteTable; |
---|
105 | int byteTableHeight; |
---|
106 | class Trie *trie; |
---|
107 | public: |
---|
108 | typedef std::set<Permutation/*,LexicographicTermOrder*/> ElementContainer; |
---|
109 | ElementContainer elements;//Make this private |
---|
110 | int size()const |
---|
111 | { |
---|
112 | return elements.size(); |
---|
113 | } |
---|
114 | int sizeOfBaseSet()const; |
---|
115 | /** |
---|
116 | The set of vectors which cannot be improved lexicographically by |
---|
117 | applying an element from the group is a convex set. Its closure |
---|
118 | is a polyhedral cone. This routine returns a set of inequalities |
---|
119 | The returned list does not contain the zero vector. |
---|
120 | */ |
---|
121 | ZMatrix fundamentalDomainInequalities()const; |
---|
122 | SymmetryGroup(int n); |
---|
123 | void computeClosure(Permutation const &v); |
---|
124 | void computeClosure(IntMatrix const &l); |
---|
125 | IntMatrix getGenerators()const; |
---|
126 | int orbitSize(ZVector const &stable)const; |
---|
127 | bool isTrivial()const; |
---|
128 | /** |
---|
129 | The symmetry group acts on vectors by permuting the entries. The |
---|
130 | following routine returns a unique representative for the orbit |
---|
131 | containing v. This makes it easy to check if two elements are in |
---|
132 | the same orbit. The permutation used to get this representative |
---|
133 | is stored in *usedPermutation (if pointer not 0). |
---|
134 | */ |
---|
135 | ZVector orbitRepresentative(ZVector const &v, Permutation *usedPermutation=0)const; |
---|
136 | /** |
---|
137 | This routine works as orbitRepresentative() except that the |
---|
138 | symmetry group considered is only the subgroup keeping the vector |
---|
139 | fixed fixed. |
---|
140 | */ |
---|
141 | ZVector orbitRepresentativeFixing(ZVector const &v, ZVector const &fixed)const; |
---|
142 | |
---|
143 | // Methods for highly optimized symmetry group computations: |
---|
144 | // void createByteTable();//Can only be called once. SymmetryGroup is not allowed to be changed afterwards or to be copied. Leaks memory at destruction. |
---|
145 | void createTrie(); |
---|
146 | // unsigned char *getByteTable()const; |
---|
147 | // int getByteTableHeight()const; |
---|
148 | }; |
---|
149 | /** |
---|
150 | * Sorts v and returns the number of swaps performed. |
---|
151 | */ |
---|
152 | int mergeSort(IntVector &v); |
---|
153 | } |
---|
154 | |
---|
155 | |
---|
156 | |
---|
157 | |
---|
158 | #endif /* GFAN_SYMMETRY_H_ */ |
---|