set_stabilizer.h

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/*
 * set_stabilizer.h
 *
 *  Created on: Jun 27, 2021
 *      Author: betten
 */
 
#ifndef SRC_LIB_GROUP_ACTIONS_SET_STABILIZER_SET_STABILIZER_H_
#define SRC_LIB_GROUP_ACTIONS_SET_STABILIZER_SET_STABILIZER_H_
 
namespace orbiter {
 
namespace layer4_classification {
 
 
 
// ####################################################################################
// compute_stabilizer.cpp
// ####################################################################################
 
 
class compute_stabilizer {
 
public:
 
 
    substructure_stats_and_selection *SubSt;
 
    actions::action *A_on_the_set;
        // only used to print the induced action on the set
        // of the set stabilizer
 
    groups::sims *Stab; // the stabilizer of the original set
 
 
    ring_theory::longinteger_object stab_order, new_stab_order;
    int nb_times_orbit_count_does_not_match_up;
    int backtrack_nodes_first_time;
    int backtrack_nodes_total_in_loop;
 
    stabilizer_orbits_and_types *Stab_orbits;
 
 
 
 
 
 
 
    actions::action *A_induced; // the action on Stab_orbits->interesting_points[]
 
    ring_theory::longinteger_object induced_go, K_go;
 
    int *transporter_witness;
    int *transporter1;
    int *transporter2;
    int *T1, *T1v;
    int *T2;
 
    groups::sims *Kernel_original;
    groups::sims *K; // kernel for building up Stab
 
 
 
    groups::sims *Aut;
    groups::sims *Aut_original;
    ring_theory::longinteger_object ago;
    ring_theory::longinteger_object ago1;
    ring_theory::longinteger_object target_go;
 
 
    //union_find_on_k_subsets *U;
 
 
    long int *Canonical_form_input; // [nb_interesting_subsets_reduced * reduced_set_size]
    long int *Canonical_forms; // [nb_interesting_subsets_reduced * reduced_set_size]
    int *Canonical_form_transporter; // [nb_interesting_subsets_reduced * A_induced->elt_size_in_int]
 
    int nb_interesting_subsets_rr;
    long int *interesting_subsets_rr;
 
 
    compute_stabilizer();
    ~compute_stabilizer();
 
    void null();
    void freeself();
    void init(
            substructure_stats_and_selection *SubSt,
            long int *canonical_pts,
            int verbose_level);
    void compute_automorphism_group(int verbose_level);
    void compute_automorphism_group_handle_case(int cnt2, int verbose_level);
    void setup_stabilizer(groups::sims *Stab0, int verbose_level);
    void restricted_action_on_interesting_points(int verbose_level);
    void compute_canonical_form(int verbose_level);
    void compute_canonical_form_handle_case(int cnt, int verbose_level);
    void compute_canonical_set(long int *set_in, long int *set_out, int sz,
            int *transporter, int verbose_level);
    void compute_canonical_set_and_group(long int *set_in, long int *set_out, int sz,
            int *transporter, groups::sims *&stab, int verbose_level);
    void update_stabilizer(int verbose_level);
    void add_automorphism(int verbose_level);
    void retrieve_automorphism(int verbose_level);
    void make_canonical_second_set(int verbose_level);
    void report(std::ostream &ost);
    void print_canonical_sets();
 
};
 
 
 
 
 
 
// #############################################################################
// stabilizer_orbits_and_types.cpp
// #############################################################################
 
 
 
 
 
 
 
class stabilizer_orbits_and_types {
 
public:
    compute_stabilizer *CS;
 
    groups::strong_generators *selected_set_stab_gens;
    groups::sims *selected_set_stab;
 
 
    int reduced_set_size; // = set_size - level
 
 
 
 
    long int *reduced_set1; // [set_size]
    long int *reduced_set2; // [set_size]
    long int *reduced_set1_new_labels; // [set_size]
    long int *reduced_set2_new_labels; // [set_size]
    long int *canonical_set1; // [set_size]
    long int *canonical_set2; // [set_size]
 
    int *elt1, *Elt1, *Elt1_inv, *new_automorphism, *Elt4;
    int *elt2, *Elt2;
    int *transporter0; // = elt1 * elt2
 
    ring_theory::longinteger_object go_G;
 
    groups::schreier *Schreier;
    int nb_orbits;
    int *orbit_count1; // [nb_orbits]
    int *orbit_count2; // [nb_orbits]
 
 
    int minimal_orbit_pattern_idx;
    int nb_interesting_subsets_reduced;
    long int *interesting_subsets_reduced;
 
    int *Orbit_patterns; // [nb_interesting_subsets * nb_orbits]
 
 
    int *orbit_to_interesting_orbit; // [nb_orbits]
 
    int nb_interesting_orbits;
    int *interesting_orbits; // [nb_interesting_orbits]
 
    int nb_interesting_points; // sum of orbit length of interesting orbits
    long int *interesting_points; // [nb_interesting_points]
    // Note: Interesting points are sorted within each orbit.
    // Otherwise, it would not be possible to compute a canonical form.
 
    int *interesting_orbit_first; // [nb_interesting_orbits]
    int *interesting_orbit_len; // [nb_interesting_orbits]
 
    int local_idx1, local_idx2;
 
 
 
    stabilizer_orbits_and_types();
    ~stabilizer_orbits_and_types();
    void init(compute_stabilizer *CS, int verbose_level);
    void compute_stabilizer_orbits_and_find_minimal_pattern(int verbose_level);
    // uses selected_set_stab_gens to compute orbits on points in action A2
    void save_interesting_subsets_reduced(int stage, int verbose_level);
    void find_orbit_pattern(int cnt, int *transp, int verbose_level);
    // computes transporter to transp
    void find_interesting_orbits(int verbose_level);
    void compute_local_labels(long int *set_in, long int *set_out, int sz, int verbose_level);
    void map_subset_and_compute_local_labels(int cnt, int verbose_level);
    void map_reduced_set_and_do_orbit_counting(int cnt,
            long int subset_idx, int *transporter, int verbose_level);
        // computes orbit_count1[]
    int check_orbit_count();
    void print_orbit_count(int f_both);
    void print_minimal_orbit_pattern();
 
};
 
 
// #############################################################################
// substructure_classifier.cpp
// #############################################################################
 
 
 
 
 
 
 
class substructure_classifier {
public:
 
 
    std::string fname_base_out;
    int substructure_size;
 
    poset_classification::poset_classification *PC;
    poset_classification::poset_classification_control *Control;
    actions::action *A;
    actions::action *A2;
    poset_classification::poset_with_group_action *Poset;
    int nb_orbits;
 
 
    substructure_classifier();
    ~substructure_classifier();
    void classify_substructures(
            std::string &fname_base_out,
            actions::action *A,
            actions::action *A2,
            groups::strong_generators *gens,
            int substructure_size,
            int verbose_level);
    void set_stabilizer_in_any_space(
            actions::action *A, actions::action *A2,
            groups::strong_generators *Strong_gens,
            int intermediate_subset_size,
            std::string &fname_mask, int nb, std::string &column_label,
            std::string &fname_out,
            int verbose_level);
    void set_stabilizer_of_set(
            std::string &fname_out,
            int cnt, int nb, int row,
            long int *pts,
            int nb_pts,
            long int *canonical_pts,
            int verbose_level);
    void handle_orbit(
            substructure_stats_and_selection *SubSt,
            long int *canonical_pts,
            int *transporter_to_canonical_form,
            groups::strong_generators *&Gens_stabilizer_original_set,
            int verbose_level);
 
 
};
 
 
 
 
 
// #############################################################################
// substructure_stats_and_selection.cpp
// #############################################################################
 
 
 
 
 
 
 
class substructure_stats_and_selection {
public:
 
    std::string fname_case_out;
 
    substructure_classifier *SubC;
 
    long int *Pts;
    int nb_pts;
 
 
    // computed by SubC->PC->trace_all_k_subsets_and_compute_frequencies:
    int nCk;
    int *isotype; // [nCk]
    int *orbit_frequencies; // [nb_orbits]
    int nb_orbits;
    data_structures::tally *T;
 
 
    data_structures::set_of_sets *SoS;
    int *types;
    int nb_types;
    int selected_type;
    int selected_orbit;
    int selected_frequency;
 
    long int *interesting_subsets; // [selected_frequency]
    int nb_interesting_subsets;
        // interesting_subsets are the lvl-subsets of the given set
        // which are of the chosen type.
        // There is nb_interesting_subsets of them.
 
    groups::strong_generators *gens; // generators for the selected canonical subset
    //int *transporter_to_canonical_form;
    //strong_generators *Gens_stabilizer_original_set;
 
 
    substructure_stats_and_selection();
    ~substructure_stats_and_selection();
    void init(
            std::string &fname_case_out,
            substructure_classifier *SubC,
            long int *Pts,
            int nb_pts,
            int verbose_level);
 
};
 
 
 
 
}}
 
 
 
 
 
#endif /* SRC_LIB_GROUP_ACTIONS_SET_STABILIZER_SET_STABILIZER_H_ */