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diff --git a/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h new file mode 100644 index 00000000..cd4a2bcc --- /dev/null +++ b/src/Persistent_cohomology/include/gudhi/Persistent_cohomology.h @@ -0,0 +1,772 @@ + /* This file is part of the Gudhi Library. The Gudhi library + * (Geometric Understanding in Higher Dimensions) is a generic C++ + * library for computational topology. + * + * Author(s): Clément Maria + * + * Copyright (C) 2014 INRIA Sophia Antipolis-Méditerranée (France) + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see <http://www.gnu.org/licenses/>. + */ + +#ifndef _PERSISTENCECOMPUTATION_SIMPLEXTREE_ +#define _PERSISTENCECOMPUTATION_SIMPLEXTREE_ + +#include <boost/tuple/tuple.hpp> +#include <boost/intrusive/set.hpp> +#include <boost/pending/disjoint_sets.hpp> +#include <boost/intrusive/list.hpp> +#include <boost/pool/object_pool.hpp> +#include "gudhi/Persistent_cohomology/Persistent_cohomology_column.h" +#include "gudhi/Persistent_cohomology/Field_Zp.h" + +namespace Gudhi{ + +/** \defgroup persistent_cohomology Persistent Cohomology Package + * + * Computation of persistent cohomology using the algorithm of + * \cite DBLP:journals/dcg/SilvaMV11 and \cite DBLP:journals/corr/abs-1208-5018 + * and the Compressed Annotation Matrix + * implementation of \cite DBLP:conf/esa/BoissonnatDM13 + * + * + * + + The theory of homology consists in attaching to a topological space a sequence of + (homology) groups, + capturing global topological features + like connected components, holes, cavities, etc. Persistent homology studies the evolution + -- birth, life and death -- of + these features when the topological space is changing. Consequently, the theory is essentially + composed of three elements: + topological spaces, their homology groups and an evolution scheme. + + <DT>Topological Spaces:</DT> + Topological spaces are represented by simplicial complexes. + Let \f$V = \{1, \cdots ,|V|\}\f$ be a set of <EM>vertices</EM>. + A <EM>simplex</EM> \f$\sigma\f$ is a subset of vertices + \f$\sigma \subseteq V\f$. A <EM>simplicial complex</EM> \f$\mathbf{K}\f$ + on \f$V\f$ is a collection of simplices \f$\{\sigma\}\f$, + \f$\sigma \subseteq V\f$, such that \f$\tau \subseteq \sigma \in \mathbf{K} + \Rightarrow \tau \in \mathbf{K}\f$. The dimension \f$n=|\sigma|-1\f$ of \f$\sigma\f$ + is its number of elements minus 1. A <EM>filtration</EM> of a simplicial complex is + a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying \f$f(\tau)\leq + f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. + + We define the concept FilteredComplex which enumerates the requirements for a class + to represent a filtered complex from which persistent homology may be computed. + We use the vocabulary of simplicial complexes, but the concept + is valid for any type of cell complex. The main requirements + are the definition of: + \li type <CODE>Indexing_tag</CODE>, which is a model of the concept + <CODE>IndexingTag</CODE>, + describing the nature of the indexing scheme, + \li type Simplex_handle to manipulate simplices, + \li method <CODE>int dimension(Simplex_handle)</CODE> returning + the dimension of a simplex, + \li type and method <CODE>Boundary_simplex_range + boundary_simplex_range(Simplex_handle)</CODE> that returns + a range giving access to the codimension 1 subsimplices of the + input simplex, as-well-as the coefficients \f$(-1)^i\f$ in the + definition of the operator \f$\partial\f$. The iterators have + value type <CODE>Simplex_handle</CODE>, + \li type and method + <CODE>Filtration_simplex_range filtration_simplex_range ()</CODE> + that returns a range giving + access to all the simplices of the complex read in the order + assigned by the indexing scheme, + \li type and method + <CODE>Filtration_value filtration (Simplex_handle)</CODE> that returns the value of + the filtration on the simplex represented by the handle. + + <DT>Homology:</DT> + For a ring \f$\mathcal{R}\f$, the group of <EM>n-chains</EM>, + denoted \f$\mathbf{C}_n(\mathbf{K},\mathcal{R})\f$, of \f$\mathbf{K}\f$ is the + group of formal sums of + n-simplices with \f$\mathcal{R}\f$ coefficients. The <EM>boundary operator</EM> is a + linear operator + \f$\partial_n: \mathbf{C}_n(\mathbf{K},\mathcal{R}) \rightarrow \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R})\f$ + such that \f$\partial_n \sigma = \partial_n [v_0, \cdots , v_n] = + \sum_{i=0}^n (-1)^{i}[v_0,\cdots ,\widehat{v_i}, \cdots,v_n]\f$, + where \f$\widehat{v_i}\f$ means \f$v_i\f$ is omitted from the list. The chain + groups form a sequence: + + \f[\cdots \ \ \mathbf{C}_n(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_n\ } \mathbf{C}_{n-1}(\mathbf{K},\mathcal{R}) + \xrightarrow{\partial_{n-1}} \cdots \xrightarrow{\ \partial_2 \ } + \mathbf{C}_1(\mathbf{K},\mathcal{R}) \xrightarrow{\ \partial_1 \ } \mathbf{C}_0(\mathbf{K},\mathcal{R}) \f] + + of finitely many groups \f$\mathbf{C}_n(\mathbf{K},\mathcal{R})\f$ and homomorphisms + \f$\partial_n\f$, indexed by the dimension \f$n \geq 0\f$. + The boundary operators satisfy the property \f$\partial_n \circ \partial_{n+1}=0\f$ + for every \f$n > 0\f$ + and we define the homology groups: + + \f[\mathbf{H}_n(\mathbf{K},\mathcal{R}) = \ker \partial_n / \mathrm{im} \ \partial_{n+1}\f] + + We refer to \cite Munkres-elementsalgtop1984 for an introduction to homology + theory and to \cite DBLP:books/daglib/0025666 for an introduction to persistent homology. + + <DT>Indexing Scheme:</DT> + "Changing" a simplicial complex consists in applying a simplicial map. + An <EM>indexing scheme</EM> is a directed graph together with a traversal + order, such that two + consecutive nodes in the graph are connected by an arrow (either forward or backward). + The nodes represent simplicial complexes and the directed edges simplicial maps. + + From the computational point of view, there are two types of indexing schemes of + interest + in persistent homology: <EM>linear</EM> ones + \f$\bullet \longrightarrow \bullet \longrightarrow \cdots \longrightarrow \bullet + \longrightarrow \bullet\f$ + in persistent homology \cite DBLP:journals/dcg/ZomorodianC05 , + and <EM>zigzag</EM> ones + \f$\bullet \longrightarrow \bullet \longleftarrow \cdots + \longrightarrow \bullet + \longleftarrow \bullet \f$ in zigzag persistent + homology \cite DBLP:journals/focm/CarlssonS10. + These indexing schemes have a natural left-to-right traversal order, and we + describe them with ranges and iterators. + In the current release of the Gudhi library, only the linear case is implemented. + + In the following, we consider the case where the indexing scheme is induced + by a filtration. + Ordering the simplices + by increasing filtration values (breaking ties so as a simplex appears after + its subsimplices of same filtration value) provides an indexing scheme. + + + + <DT>Implementations:</DT> + We use the <EM>Compressed Annotation Matrix</EM> of \cite DBLP:conf/esa/BoissonnatDM13 to + implement the + persistent cohomology algorithm of \cite DBLP:journals/dcg/SilvaMV11 + and \cite DBLP:conf/compgeom/DeyFW14 for persistence in the class Persistent_cohomology. + + The coefficient fields available as models of CoefficientField are Field_Zp + for \f$\mathbb{Z}_p\f$ (for any prime p) and Multi_field for the multi-field persistence algorithm + -- computing persistence simultaneously in various coefficient fields -- described + in \cite boissonnat:hal-00922572. + + + \author Clément Maria + \version 1.0 + \date 2014 + \copyright GNU General Public License v3. + @{ + */ + +/** \brief Computes the persistent cohomology of a filtered complex. +* +* The computation is implemented with a Compressed Annotation Matrix +* (CAM)\cite DBLP:conf/esa/BoissonnatDM13, +* and is adapted to the computation of Multi-Field Persistent Homology (MF) +* \cite boissonnat:hal-00922572 . +* +* \implements PersistentHomology +* +*/ +//Memory allocation policy: classic, use a mempool, etc.*/ + template < class FilteredComplex + , class CoefficientField + > //to do mem allocation policy: classic, mempool, etc. + class Persistent_cohomology { + public: + + typedef FilteredComplex Complex_ds; + // Data attached to each simplex to interface with a Property Map. + typedef typename Complex_ds::Simplex_key Simplex_key; + typedef typename Complex_ds::Simplex_handle Simplex_handle; + typedef typename Complex_ds::Filtration_value Filtration_value; + typedef typename CoefficientField::Element Arith_element; +// Compressed Annotation Matrix types: + // Column type + typedef Persistent_cohomology_column < Simplex_key + , Arith_element + > Column; // contains 1 set_hook + // Cell type + typedef typename Column::Cell Cell; // contains 2 list_hooks + // Remark: constant_time_size must be false because base_hook_cam_h has auto_unlink link_mode + typedef boost::intrusive::list < Cell + , boost::intrusive::constant_time_size<false> + , boost::intrusive::base_hook< base_hook_cam_h > + > Hcell; + + typedef boost::intrusive::set < Column + , boost::intrusive::constant_time_size<false> + > Cam; +// Sparse column type for the annotation of the boundary of an element. + typedef std::vector< std::pair<Simplex_key + , Arith_element > > A_ds_type; +// Persistent interval type. The Arith_element field is used for the multi-field framework. + typedef boost::tuple< Simplex_handle + , Simplex_handle + , Arith_element > Persistent_interval; + +/** \brief Initializes the Persistent_cohomology class. + * + * @param[in] cpx Complex for which the persistent homology is compiuted. + cpx is a model of FilteredComplex + * + * @param[in] persistence_dim_max if true, the persistent homology for the maximal dimension in the + * complex is computed. If false, it is ignored. Default is false. + */ +Persistent_cohomology ( Complex_ds & cpx + , bool persistence_dim_max = false ) +: cpx_ (&cpx) +, dim_max_(cpx.dimension()) // upper bound on the dimension of the simplices +, coeff_field_() // initialize the field coefficient structure. +, ds_rank_ (cpx_->num_simplices()) // union-find +, ds_parent_(cpx_->num_simplices()) // union-find +, ds_repr_ (cpx_->num_simplices(),NULL) // union-find -> annotation vectors +, dsets_(&ds_rank_[0],&ds_parent_[0]) // union-find +, cam_() // collection of annotation vectors +, zero_cocycles_() // union-find -> Simplex_key of creator for 0-homology +, transverse_idx_() // key -> row +, persistent_pairs_() +, interval_length_policy(&cpx,0) +, column_pool_(new boost::object_pool< Column > ()) // memory pools for the CAM +, cell_pool_(new boost::object_pool< Cell > ()) +{ + if( persistence_dim_max ) { ++dim_max_; } + Simplex_key idx_fil = 0; + for(auto & sh : cpx_->filtration_simplex_range()) + { + cpx_->assign_key(sh,idx_fil); ++idx_fil; + dsets_.make_set(cpx_->key(sh)); + } +} + +~Persistent_cohomology() +{ +//Clean the remaining columns in the matrix. + for(auto & cam_ref : cam_) { cam_ref.col_.clear(); } +//Clean the transversal lists + for( auto & transverse_ref : transverse_idx_ ) + { transverse_ref.second.row_->clear(); delete transverse_ref.second.row_; } +//Clear the memory pools + delete column_pool_; + delete cell_pool_; +} + +private: +struct length_interval { + length_interval ( Complex_ds * cpx + , Filtration_value min_length) + : cpx_(cpx) + , min_length_(min_length) {} + + bool operator()(Simplex_handle sh1, Simplex_handle sh2) + { return cpx_->filtration(sh2) - cpx_->filtration(sh1) > min_length_; } + + void set_length(Filtration_value new_length) { min_length_ = new_length; } + + Complex_ds * cpx_; + Filtration_value min_length_; +}; + + +public: +/** \brief Initializes the coefficient field.*/ +void init_coefficients( int charac ) { coeff_field_.init(charac); } +/** \brief Initializes the coefficient field for multi-field persistent homology.*/ +void init_coefficients( int charac_min + , int charac_max ) { coeff_field_.init(charac_min,charac_max); } + +/** \brief Compute the persistent homology of the filtered simplicial + * complex. + * + * @param[in] min_interval_length the computation disgards all intervals of length + * less or equal than min_interval_length + * + * Assumes that the filtration provided by the simplicial complex is + * valid. Undefined behavior otherwise. */ +void compute_persistent_cohomology ( Filtration_value min_interval_length = 0 ) +{ + interval_length_policy.set_length(min_interval_length); + // Compute all finite intervals + for( auto sh : cpx_->filtration_simplex_range() ) + { + int dim_simplex = cpx_->dimension(sh); + switch(dim_simplex) { + case 0 : break; + case 1 : update_cohomology_groups_edge( sh ) ; break; + default: update_cohomology_groups( sh, dim_simplex ); break; + } + } + // Compute infinite intervals of dimension 0 + Simplex_key key; + for(auto v_sh : cpx_->skeleton_simplex_range(0)) //for all 0-dimensional simplices + { + key = cpx_->key(v_sh); + + if( ds_parent_[key] == key //root of its tree + && zero_cocycles_.find(key) == zero_cocycles_.end() ) + { + persistent_pairs_.push_back( Persistent_interval ( cpx_->simplex(key) + , cpx_->null_simplex() + , coeff_field_.characteristic() ) + ); + } + } + for( auto zero_idx : zero_cocycles_ ) + { + persistent_pairs_.push_back( Persistent_interval ( cpx_->simplex(zero_idx.second) + , cpx_->null_simplex() + , coeff_field_.characteristic() ) + ); + } +// Compute infinite interval of dimension > 0 + for(auto cocycle : transverse_idx_) + { + persistent_pairs_.push_back( Persistent_interval ( cpx_->simplex (cocycle.first) + , cpx_->null_simplex() + , cocycle.second.characteristics_ ) ); + } +} + + + +private: +/** \brief Update the cohomology groups under the insertion of an edge. + * + * The 0-homology is maintained with a simple Union-Find data structure, which + * explains the existance of a specific function of edge insertions. */ +void update_cohomology_groups_edge ( Simplex_handle sigma ) +{ + Simplex_handle u,v; + boost::tie(u,v) = cpx_->endpoints(sigma); + + Simplex_key ku = dsets_.find_set( cpx_->key(u) ); + Simplex_key kv = dsets_.find_set( cpx_->key(v) ); + + if(ku != kv ) { // Destroy a connected component + dsets_.link(ku,kv); + // Keys of the simplices which created the connected components containing + // respectively u and v. + Simplex_key idx_coc_u, idx_coc_v; + auto map_it_u = zero_cocycles_.find(ku); + // If the index of the cocycle representing the class is already ku. + if (map_it_u == zero_cocycles_.end()) { idx_coc_u = ku; } + else { idx_coc_u = map_it_u->second; } + + auto map_it_v = zero_cocycles_.find(kv); + // If the index of the cocycle representing the class is already kv. + if (map_it_v == zero_cocycles_.end()) { idx_coc_v = kv; } + else { idx_coc_v = map_it_v->second; } + + if(cpx_->filtration(cpx_->simplex(idx_coc_u)) + < cpx_->filtration(cpx_->simplex(idx_coc_v)) ) // Kill cocycle [idx_coc_v], which is younger. + { + if(interval_length_policy(cpx_->simplex(idx_coc_v),sigma)) { + persistent_pairs_.push_back ( Persistent_interval ( cpx_->simplex(idx_coc_v) + , sigma + , coeff_field_.characteristic() + ) + ); + } + // Maintain the index of the 0-cocycle alive. + if( kv != idx_coc_v ) { zero_cocycles_.erase( map_it_v ); } + if( kv == dsets_.find_set(kv) ) { + if( ku != idx_coc_u ) { zero_cocycles_.erase( map_it_u ); } + zero_cocycles_[kv] = idx_coc_u; + } + } + else // Kill cocycle [idx_coc_u], which is younger. + { + if(interval_length_policy(cpx_->simplex(idx_coc_u),sigma)) { + persistent_pairs_.push_back ( Persistent_interval ( cpx_->simplex(idx_coc_u) + , sigma + , coeff_field_.characteristic() + ) + ); + } + // Maintain the index of the 0-cocycle alive. + if( ku != idx_coc_u ) { zero_cocycles_.erase( map_it_u ); } + if( ku == dsets_.find_set(ku) ) { + if( kv != idx_coc_v ) { zero_cocycles_.erase( map_it_v ); } + zero_cocycles_[ku] = idx_coc_v; + } + } + cpx_->assign_key(sigma,cpx_->null_key()); + } + else { // If ku == kv, same connected component: create a 1-cocycle class. + create_cocycle( sigma, coeff_field_.multiplicative_identity(), coeff_field_.characteristic() ); + } +} + +/* + * Compute the annotation of the boundary of a simplex. + */ +void annotation_of_the_boundary(std::map< Simplex_key, Arith_element > & map_a_ds + , Simplex_handle sigma + , int dim_sigma ) +{ + // traverses the boundary of sigma, keeps track of the annotation vectors, + // with multiplicity, in a map. + std::map < Column *, int > annotations_in_boundary; + std::pair < typename std::map< Column *, int >::iterator + , bool > result_insert_bound; + int sign = 1 - 2 * (dim_sigma % 2); // \in {-1,1} provides the sign in the + // alternate sum in the boundary. + Simplex_key key; Column * curr_col; + + for( auto sh : cpx_->boundary_simplex_range(sigma) ) + { + key = cpx_->key(sh); + if( key != cpx_->null_key() ) // A simplex with null_key is a killer, and have null annotation + { // vector. + // Find its annotation vector + curr_col = ds_repr_[ dsets_.find_set(key) ]; + if( curr_col != NULL ) + { // and insert it in annotations_in_boundary with multyiplicative factor "sign". + result_insert_bound = + annotations_in_boundary.insert(std::pair<Column *,int>(curr_col,sign)); + if( !(result_insert_bound.second) ) { result_insert_bound.first->second += sign; } + } + } + sign = -sign; + } + // Sum the annotations with multiplicity, using a map<key,coeff> + // to represent a sparse vector. + std::pair < typename std::map < Simplex_key, Arith_element >::iterator + , bool > result_insert_a_ds; + + for( auto ann_ref : annotations_in_boundary ) + { + if(ann_ref.second != coeff_field_.additive_identity()) // For all columns in the boundary, + { + for( auto cell_ref : ann_ref.first->col_ ) // insert every cell in map_a_ds with multiplicity + { + Arith_element w_y = + coeff_field_.times(cell_ref.coefficient_ , ann_ref.second); //coefficient * multiplicity + + if( w_y != coeff_field_.additive_identity() ) // if != 0 + { + result_insert_a_ds = map_a_ds.insert(std::pair< Simplex_key + , Arith_element >(cell_ref.key_ , w_y)); + if( !(result_insert_a_ds.second) ) //if cell_ref.key_ already a Key in map_a_ds + { + coeff_field_.plus_equal(result_insert_a_ds.first->second, w_y); + if(result_insert_a_ds.first->second == coeff_field_.additive_identity()) + { map_a_ds.erase(result_insert_a_ds.first); } + } + } + } + } + } +} + +/* + * Update the cohomology groups under the insertion of a simplex. + */ +void update_cohomology_groups ( Simplex_handle sigma + , int dim_sigma ) +{ +//Compute the annotation of the boundary of sigma: + std::map< Simplex_key, Arith_element > map_a_ds; + annotation_of_the_boundary(map_a_ds, sigma, dim_sigma ); +// Update the cohomology groups: + if( map_a_ds.empty() ) { // sigma is a creator in all fields represented in coeff_field_ + if(dim_sigma < dim_max_) { create_cocycle ( sigma + , coeff_field_.multiplicative_identity() + , coeff_field_.characteristic() );} + } + else { // sigma is a destructor in at least a field in coeff_field_ + // Convert map_a_ds to a vector + A_ds_type a_ds; //admits reverse iterators + for ( auto map_a_ds_ref : map_a_ds ) + { + a_ds.push_back( std::pair< Simplex_key + , Arith_element> ( map_a_ds_ref.first + , map_a_ds_ref.second )); + } + + + Arith_element inv_x, charac; + Arith_element prod = coeff_field_.characteristic(); // Product of characteristic of the fields + for( auto a_ds_rit = a_ds.rbegin(); + (a_ds_rit != a_ds.rend()) && (prod != coeff_field_.multiplicative_identity()); + ++a_ds_rit ) + { + std::tie(inv_x,charac) = coeff_field_.inverse ( a_ds_rit->second + , prod ); + + if( inv_x != coeff_field_.additive_identity() ) + { + destroy_cocycle ( sigma + , a_ds + , a_ds_rit->first + , inv_x + , charac ); + prod /= charac; + } + } + if( prod != coeff_field_.multiplicative_identity() && dim_sigma < dim_max_ ) + { create_cocycle( sigma , coeff_field_.multiplicative_identity(prod), prod ); } + } +} + +/* \brief Create a new cocycle class. + * + * The class is created by the insertion of the simplex sigma. + * The methods adds a cocycle, representing the new cocycle class, + * to the matrix representing the cohomology groups. + * The new cocycle has value 0 on every simplex except on sigma + * where it worths 1.*/ +void create_cocycle ( Simplex_handle sigma + , Arith_element x + , Arith_element charac ) +{ + Simplex_key key = cpx_->key(sigma); + // Create a column containing only one cell, + Column * new_col = column_pool_->construct(Column(key)); + Cell * new_cell = cell_pool_->construct(Cell (key, x, new_col)); + new_col->col_.push_back(*new_cell); + // and insert it in the matrix, in constant time thanks to the hint cam_.end(). + // Indeed *new_col has the biggest lexicographic value because key is the + // biggest key used so far. + cam_.insert (cam_.end(), *new_col); + // Update the disjoint sets data structure. + Hcell * new_hcell = new Hcell; + new_hcell->push_back(*new_cell); + transverse_idx_[key] = cocycle(charac,new_hcell); //insert the new row + ds_repr_[key] = new_col; +} + +/* \brief Destroy a cocycle class. + * + * The cocycle class is destroyed by the insertion of sigma. + * The methods proceeds to a reduction of the matrix representing + * the cohomology groups using Gauss pivoting. The reduction zeros-out + * the row containing the cell with highest key in + * a_ds, the annotation of the boundary of simplex sigma. This key + * is "death_key".*/ +void destroy_cocycle ( Simplex_handle sigma + , A_ds_type const& a_ds + , Simplex_key death_key + , Arith_element inv_x + , Arith_element charac ) +{ + // Create a finite persistent interval + if(interval_length_policy(cpx_->simplex(death_key),sigma)) { + persistent_pairs_.push_back ( Persistent_interval ( cpx_->simplex(death_key) //creator + , sigma //destructor + , charac ) //fields + ); // for which the interval exists + } + + auto death_key_row = transverse_idx_.find(death_key); // Find the beginning of the row. + std::pair< typename Cam::iterator, bool > result_insert_cam; + + auto row_cell_it = death_key_row->second.row_->begin(); + + while( row_cell_it != death_key_row->second.row_->end() ) // Traverse all cells in + { // the row at index death_key. + Arith_element w = coeff_field_.times_minus( inv_x , row_cell_it->coefficient_ ); + + if( w != coeff_field_.additive_identity() ) + { + Column * curr_col = row_cell_it->self_col_; ++row_cell_it; + // Disconnect the column from the rows in the CAM. + for( auto col_cell_it = curr_col->col_.begin(); + col_cell_it != curr_col->col_.end(); ++col_cell_it ) + { col_cell_it->base_hook_cam_h::unlink(); } + + // Remove the column from the CAM before modifying its value + cam_.erase( cam_.iterator_to(*curr_col) ); + // Proceed to the reduction of the column + plus_equal_column(*curr_col, a_ds, w); + + if( curr_col->col_.empty() ) // If the column is null + { + ds_repr_[ curr_col->class_key_ ] = NULL; + column_pool_->free(curr_col); //delete curr_col; + } + else + { + // Find whether the column obtained is already in the CAM + result_insert_cam = cam_.insert( *curr_col ); + if ( result_insert_cam.second ) // If it was not in the CAM before: insertion has succeeded + { + for ( auto col_cell_it = curr_col->col_.begin(); + col_cell_it != curr_col->col_.end(); ++col_cell_it ) //re-establish the row links + { transverse_idx_[ col_cell_it->key_ ].row_->push_front(*col_cell_it); } + } + else // There is already an identical column in the CAM: + { // merge two disjoint sets. + dsets_.link ( curr_col->class_key_ , + result_insert_cam.first->class_key_ ); + + Simplex_key key_tmp = dsets_.find_set( curr_col->class_key_ ); + ds_repr_[ key_tmp ] = &(*(result_insert_cam.first)); + result_insert_cam.first->class_key_ = key_tmp; + column_pool_->free(curr_col); //delete curr_col; + } + } + } + else { ++row_cell_it; } // If w == 0, pass. + } + + // Because it is a killer simplex, set the data of sigma to null_key(). + if(charac == coeff_field_.characteristic()) { cpx_->assign_key( sigma, cpx_->null_key() ); } + if(death_key_row->second.characteristics_ == charac) + { + delete death_key_row->second.row_; + transverse_idx_.erase(death_key_row); + } + else { death_key_row->second.characteristics_ /= charac; } +} + +/* + * Assign: target <- target + w * other. + */ +void plus_equal_column ( Column & target + , A_ds_type const& other //value_type is pair<Simplex_key,Arith_element> + , Arith_element w ) +{ + auto target_it = target.col_.begin(); auto other_it = other.begin(); + while ( target_it != target.col_.end() && other_it != other.end() ) + { + if(target_it->key_ < other_it->first) { ++target_it; } + else { + if(target_it->key_ > other_it->first) + { + Cell * cell_tmp = cell_pool_->construct(Cell( other_it->first //key + , coeff_field_.additive_identity() + , &target)); + + coeff_field_.plus_times_equal(cell_tmp->coefficient_, other_it->second, w); + + target.col_.insert( target_it, *cell_tmp ); + + ++other_it; + } + else { //it1->key == it2->key + //target_it->coefficient_ <- target_it->coefficient_ + other_it->second * w + coeff_field_.plus_times_equal( target_it->coefficient_ , other_it->second , w); + if( target_it->coefficient_ == coeff_field_.additive_identity() ) + { + auto tmp_it = target_it; + ++target_it; ++other_it; // iterators remain valid + Cell * tmp_cell_ptr = &(*tmp_it); + target.col_.erase(tmp_it); // removed from column + + coeff_field_.clear_coefficient(tmp_cell_ptr->coefficient_); + cell_pool_->free(tmp_cell_ptr); // delete from memory + } + else { ++target_it; ++other_it; } + } + } + } + while(other_it != other.end()) + { + Cell * cell_tmp = cell_pool_->construct(Cell( other_it->first //key + , coeff_field_.additive_identity() + , &target)); + + coeff_field_.plus_times_equal(cell_tmp->coefficient_, other_it->second, w); + + target.col_.insert( target.col_.end(), *cell_tmp ); + + ++other_it; + } +} + +/* + * Compare two intervals by length. + */ +struct cmp_intervals_by_length { + cmp_intervals_by_length( Complex_ds * sc ) : sc_ (sc) {} + bool operator() ( Persistent_interval & p1 + , Persistent_interval & p2 ) + { + return ( sc_->filtration( get<1>(p1) ) - sc_->filtration( get<0>(p1) ) + > sc_->filtration( get<1>(p2) ) - sc_->filtration( get<0>(p2) ) ); + } + Complex_ds * sc_; +}; + +public: +/** \brief Output the persistence diagram in ostream. + * + * The file format is the following: + * p1*...*pr dim b d + * + * where "dim" is the dimension of the homological feature, + * b and d are respectively the birth and death of the feature and + * p1*...*pr is the product of prime numbers pi such that the homology + * feature exists in homology with Z/piZ coefficients. + */ +void output_diagram(std::ostream& ostream = std::cout) +{ + cmp_intervals_by_length cmp( cpx_ ); + persistent_pairs_.sort( cmp ); + for(auto pair : persistent_pairs_) + { + ostream << get<2>(pair) << " " + << cpx_->dimension(get<0>(pair)) << " " + << cpx_->filtration(get<0>(pair)) << " " + << cpx_->filtration(get<1>(pair)) << " " + << std::endl; + } +} + +private: +/* + * Structure representing a cocycle. + */ +struct cocycle { + cocycle() {} + cocycle( Arith_element characteristics + , Hcell * row ) + : row_(row), characteristics_(characteristics) {} + + Hcell * row_; //points to the corresponding row in the CAM + Arith_element characteristics_; //product of field characteristics for which the cocycle exist +}; + +public: + Complex_ds * cpx_; + int dim_max_; + CoefficientField coeff_field_; + +/* Disjoint sets data structure to link the model of FilteredComplex + * with the compressed annotation matrix. + * ds_rank_ is a property map Simplex_key -> int, ds_parent_ is a property map + * Simplex_key -> simplex_key_t */ + std::vector< int > ds_rank_; + std::vector< Simplex_key > ds_parent_; + std::vector< Column * > ds_repr_; + boost::disjoint_sets< int *, Simplex_key * > dsets_; +/* The compressed annotation matrix fields.*/ + Cam cam_; +/* Dictionary establishing the correspondance between the Simplex_key of + * the root vertex in the union-find ds and the Simplex_key of the vertex which + * created the connected component as a 0-dimension homology feature.*/ + std::map<Simplex_key,Simplex_key> zero_cocycles_; +/* Key -> row. */ + std::map< Simplex_key , cocycle > transverse_idx_; +/* Persistent intervals. */ + std::list< Persistent_interval > persistent_pairs_; + length_interval interval_length_policy; + + boost::object_pool< Column > * column_pool_; + boost::object_pool< Cell > * cell_pool_; +}; + +/** @} */ //end defgroup persistent_cohomology + +} // namespace GUDHI + +#endif // _PERSISTENCECOMPUTATION_SIMPLEXTREE_ |