diff options
Diffstat (limited to 'src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h')
-rw-r--r-- | src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h | 455 |
1 files changed, 150 insertions, 305 deletions
diff --git a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h index f2c753d9..b8887e71 100644 --- a/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h +++ b/src/Bitmap_cubical_complex/include/gudhi/Bitmap_cubical_complex.h @@ -34,7 +34,9 @@ namespace Cubical_complex { //global variable, was used just for debugging. -const bool globalDbg = false; +const bool globalDbg = false;
+
+template <typename T> class is_before_in_filtration; template <typename T = double> class Bitmap_cubical_complex : public Bitmap_cubical_complex_base<T> @@ -45,71 +47,8 @@ public: //*********************************************// friend class Simplex_handle; typedef size_t Simplex_key; - typedef T Filtration_value; - - -//*********************************************// -//Simplex handle class -//*********************************************// - /** - * Handle of a cell, required for compatibility with the function to compute persistence in Gudhi. - * Elements of this class are: the pointer to the bitmap B in which the considered cell is - * together with a position of this cell in B. Given this data, - * one can get all the information about the considered cell. - **/ - class Simplex_handle - { - public: - Simplex_handle() - { - if ( globalDbg ){cerr << "Simplex_handle()\n";} - this->b = 0; - this->position = 0; - } - - Simplex_handle(Bitmap_cubical_complex<T>* b) - { - if ( globalDbg ) - { - cerr << "Simplex_handle(Bitmap_cubical_complex<T>* b)\n"; - } - this->b = b; - this->position = 0; - } - - //Simplex_handle( const Simplex_handle& org ):b(org.b) - //{ - // if ( globalDbg ){cerr << "Simplex_handle( const Simplex_handle& org )\n";} - // this->position = org.position; - //} - - Simplex_handle operator = ( const Simplex_handle& rhs ) - { - if ( globalDbg ){cerr << "Simplex_handle operator = \n";} - this->position = rhs.position; - this->b = rhs.b; - return *this; - } - - Simplex_handle(Bitmap_cubical_complex<T>* b , Simplex_key position) - { - if ( globalDbg ) - { - cerr << "Simplex_handle(Bitmap_cubical_complex<T>* b , Simplex_key position)\n"; - cerr << "Position : " << position << endl; - } - this->b = b; - this->position = position; - } - friend class Bitmap_cubical_complex<T>; - private: - Bitmap_cubical_complex<T>* b; - Simplex_key position; - //Assumption -- field above always keep the REAL position of simplex in the bitmap, - //no matter what keys have been. - //to deal with the keys, the class Bitmap_cubical_complex have extra vectors: key_associated_to_simplex and - //simplex_associated_to_key that allow to move between actual cell and the key assigned to it. - }; + typedef T Filtration_value;
+ typedef Simplex_key Simplex_handle;
//*********************************************// @@ -125,39 +64,37 @@ public: * Constructor form a Perseus-style file. **/ Bitmap_cubical_complex( const char* perseus_style_file ): - Bitmap_cubical_complex_base<T>(perseus_style_file),key_associated_to_simplex(this->total_number_of_cells+1), - simplex_associated_to_key(this->total_number_of_cells+1) + Bitmap_cubical_complex_base<T>(perseus_style_file),key_associated_to_simplex(this->total_number_of_cells+1) { if ( globalDbg ){cerr << "Bitmap_cubical_complex( const char* perseus_style_file )\n";} for ( size_t i = 0 ; i != this->total_number_of_cells ; ++i ) { - this->key_associated_to_simplex[i] = this->simplex_associated_to_key[i] = i; + this->key_associated_to_simplex[i] = i; } - //we initialize this only once, in each constructor, when the bitmap is constructed. + //we initialize this only once, in each constructor, when the bitmap is constructed. //If the user decide to change some elements of the bitmap, then this procedure need //to be called again. - this->initialize_elements_ordered_according_to_filtration(); + this->initialize_simplex_associated_to_key(); } /** - * Constructor that requires vector of elements of type unsigned, which gives number of top dimensional cells + * Constructor that requires vector of elements of type unsigned, which gives number of top dimensional cells * in the following directions and vector of element of a type T * with filtration on top dimensional cells. **/ Bitmap_cubical_complex( std::vector<unsigned>& dimensions , std::vector<T>& top_dimensional_cells ): Bitmap_cubical_complex_base<T>(dimensions,top_dimensional_cells), - key_associated_to_simplex(this->total_number_of_cells+1), - simplex_associated_to_key(this->total_number_of_cells+1) + key_associated_to_simplex(this->total_number_of_cells+1) { for ( size_t i = 0 ; i != this->total_number_of_cells ; ++i ) { - this->key_associated_to_simplex[i] = this->simplex_associated_to_key[i] = i; + this->key_associated_to_simplex[i] = i; } - //we initialize this only once, in each constructor, when the bitmap is constructed. + //we initialize this only once, in each constructor, when the bitmap is constructed. //If the user decide to change some elements of the bitmap, then this procedure need //to be called again. - this->initialize_elements_ordered_according_to_filtration(); + this->initialize_simplex_associated_to_key(); } //*********************************************// @@ -174,15 +111,17 @@ public: /** * Returns a Simplex_handle to a cube that do not exist in this complex. **/ - Simplex_handle null_simplex() - { - return Simplex_handle(this,this->data.size()); - } + static Simplex_handle null_simplex() + {
+ if ( globalDbg ){cerr << "Simplex_handle null_simplex()\n";} + return std::numeric_limits<int>::max(); + }
+ /** * Returns dimension of the complex. **/ - size_t dimension() + inline size_t dimension()const { return this->sizes.size(); } @@ -190,10 +129,10 @@ public: /** * Return dimension of a cell pointed by the Simplex_handle. **/ - unsigned dimension(const Simplex_handle& sh) + inline unsigned dimension(const Simplex_handle& sh)const { if ( globalDbg ){cerr << "unsigned dimension(const Simplex_handle& sh)\n";} - if ( sh.position != this->data.size() ) return sh.b->get_dimension_of_a_cell( sh.position ); + if ( sh != std::numeric_limits<int>::max() ) return this->get_dimension_of_a_cell( sh ); return -1; } @@ -204,26 +143,30 @@ public: { if ( globalDbg ){cerr << "T filtration(const Simplex_handle& sh)\n";} //Returns the filtration value of a simplex. - if ( sh.position != this->data.size() ) return sh.b->data[ sh.position ]; + if ( sh != std::numeric_limits<int>::max() ) return this->data[sh]; return std::numeric_limits<int>::max(); } /** * Return a key which is not a key of any cube in the considered data structure. **/ - Simplex_key null_key() + static Simplex_key null_key() { if ( globalDbg ){cerr << "Simplex_key null_key()\n";} - return this->data.size(); + return std::numeric_limits<int>::max(); } /** * Return the key of a cube pointed by the Simplex_handle. **/ - Simplex_key key(const Simplex_handle& sh) + Simplex_key key(const Simplex_handle& sh)const { - if ( globalDbg ){cerr << "Simplex_key key(const Simplex_handle& sh)\n";} - return sh.b->key_associated_to_simplex[ sh.position ]; + if ( globalDbg ){cerr << "Simplex_key key(const Simplex_handle& sh)\n";}
+ if ( sh != std::numeric_limits<int>::max() )
+ {
+ return this->key_associated_to_simplex[sh];
+ } + return this->null_key(); } /** @@ -231,8 +174,12 @@ public: **/ Simplex_handle simplex(Simplex_key key) { - if ( globalDbg ){cerr << "Simplex_handle simplex(Simplex_key key)\n";} - return Simplex_handle( this , this->simplex_associated_to_key[ key ] ); + if ( globalDbg ){cerr << "Simplex_handle simplex(Simplex_key key)\n";}
+ if ( key != std::numeric_limits<int>::max() )
+ {
+ return this->simplex_associated_to_key[ key ];
+ } + return null_simplex(); } /** @@ -240,15 +187,29 @@ public: **/ void assign_key(Simplex_handle& sh, Simplex_key key) { - if ( globalDbg ){cerr << "void assign_key(Simplex_handle& sh, Simplex_key key)\n";} - this->key_associated_to_simplex[sh.position] = key; - this->simplex_associated_to_key[key] = sh.position; + if ( globalDbg ){cerr << "void assign_key(Simplex_handle& sh, Simplex_key key)\n";}
+
+
+
+
+
+
+
+
+if ( key == std::numeric_limits<int>::max() ) return;//TODO FAKE!!! CHEATING!!! +
+
+
+
+
+ this->key_associated_to_simplex[sh] = key; + this->simplex_associated_to_key[key] = sh; } /** * Function called from a constructor. It is needed for Filtration_simplex_iterator to work. **/ - void initialize_elements_ordered_according_to_filtration(); + void initialize_simplex_associated_to_key(); @@ -256,104 +217,42 @@ public: //Iterators //*********************************************// - /** - * Boundary_simplex_iterator class allows iteration on boundary of each cube. - **/ - class Boundary_simplex_range; - class Boundary_simplex_iterator : std::iterator< std::input_iterator_tag, Simplex_handle > - { - //Iterator on the simplices belonging to the boundary of a simplex. - //value_type must be 'Simplex_handle'. - public: - Boundary_simplex_iterator( Simplex_handle& sh ):sh(sh) - { - if ( globalDbg ){cerr << "Boundary_simplex_iterator( Simplex_handle& sh )\n";} - this->position = 0; - this->boundary_elements = this->sh.b->get_boundary_of_a_cell( this->sh.position ); - } - Boundary_simplex_iterator operator++() - { - if ( globalDbg ){cerr << "Boundary_simplex_iterator operator++()\n";} - ++this->position; - return *this; - } - Boundary_simplex_iterator operator++(int) - { - Boundary_simplex_iterator result = *this; - ++(*this); - return result; - } - Boundary_simplex_iterator operator =( const Boundary_simplex_iterator& rhs ) - { - if ( globalDbg ){cerr << "Boundary_simplex_iterator operator =\n";} - this->sh = rhs.sh; - this->boundary_elements.clear(); - this->boundary_elementsinsert - (this->boundary_elements.end(), rhs.boundary_elements.begin(), rhs.boundary_elements.end()); - } - bool operator == ( const Boundary_simplex_iterator& rhs ) - { - if ( globalDbg ){cerr << "bool operator ==\n";} - if ( this->position == rhs.position ) - { - if ( this->boundary_elements.size() != rhs.boundary_elements.size() )return false; - for ( size_t i = 0 ; i != this->boundary_elements.size() ; ++i ) - { - if ( this->boundary_elements[i] != rhs.boundary_elements[i] )return false; - } - return true; - } - return false; - } - - bool operator != ( const Boundary_simplex_iterator& rhs ) - { - if ( globalDbg ){cerr << "bool operator != \n";} - return !(*this == rhs); - } - Simplex_handle operator*() - { - if ( globalDbg ){cerr << "Simplex_handle operator*\n";} - return Simplex_handle( this->sh.b , this->boundary_elements[this->position] ); - } - - friend class Boundary_simplex_range; - private: - Simplex_handle sh; - std::vector< size_t > boundary_elements; - size_t position; - }; /** * Boundary_simplex_range class provides ranges for boundary iterators. - **/ + **/
+ typedef typename std::vector< Simplex_handle >::iterator Boundary_simplex_iterator; class Boundary_simplex_range { //Range giving access to the simplices in the boundary of a simplex. //.begin() and .end() return type Boundary_simplex_iterator. - public: - Boundary_simplex_range(const Simplex_handle& sh):sh(sh){}; - Boundary_simplex_iterator begin() - { - if ( globalDbg ){cerr << "Boundary_simplex_iterator begin\n";} - Boundary_simplex_iterator it( this->sh ); - return it; - } - Boundary_simplex_iterator end() - { - if ( globalDbg ){cerr << "Boundary_simplex_iterator end()\n";} - Boundary_simplex_iterator it( this->sh ); - it.position = it.boundary_elements.size(); - return it; - } - private: - Simplex_handle sh; - }; + public:
+ typedef Boundary_simplex_iterator const_iterator;
+ Boundary_simplex_range(const Simplex_handle& sh , Bitmap_cubical_complex<T>* CC_):sh(sh),CC(CC_)
+ {
+ this->boundary_elements = this->CC->get_boundary_of_a_cell( sh );
+ }
+ Boundary_simplex_iterator begin()
+ {
+ if ( globalDbg ){cerr << "Boundary_simplex_iterator begin\n";}
+ return this->boundary_elements.begin();
+
+ }
+ Boundary_simplex_iterator end()
+ {
+ if ( globalDbg ){cerr << "Boundary_simplex_iterator end()\n";}
+ return this->boundary_elements.end();
+ }
+ private:
+ Simplex_handle sh;
+ Bitmap_cubical_complex<T>* CC;
+ std::vector< Simplex_handle > boundary_elements;
+ };
/** - * Filtration_simplex_iterator class provides an iterator though the whole structure in the order of filtration. + * Filtration_simplex_iterator class provides an iterator though the whole structure in the order of filtration. * Secondary criteria for filtration are: * (1) Dimension of a cube (lower dimensional comes first). * (2) Position in the data structure (the ones that are earlies in the data structure comes first). @@ -385,17 +284,13 @@ public: this->b = rhs.b; this->position = rhs.position; } - bool operator == ( const Filtration_simplex_iterator& rhs ) + bool operator == ( const Filtration_simplex_iterator& rhs )const { if ( globalDbg ){cerr << "bool operator == ( const Filtration_simplex_iterator& rhs )\n";} - if ( this->position == rhs.position ) - { - return true; - } - return false; + return ( this->position == rhs.position ); } - bool operator != ( const Filtration_simplex_iterator& rhs ) + bool operator != ( const Filtration_simplex_iterator& rhs )const { if ( globalDbg ){cerr << "bool operator != ( const Filtration_simplex_iterator& rhs )\n";} return !(*this == rhs); @@ -403,7 +298,7 @@ public: Simplex_handle operator*() { if ( globalDbg ){cerr << "Simplex_handle operator*()\n";} - return Simplex_handle( this->b , this->b->elements_ordered_according_to_filtration[ this->position ] ); + return this->b->simplex_associated_to_key[ this->position ]; } friend class Filtration_simplex_range; @@ -420,7 +315,8 @@ public: { //Range over the simplices of the complex in the order of the filtration. //.begin() and .end() return type Filtration_simplex_iterator. - public: + public:
+ typedef Filtration_simplex_iterator const_iterator; Filtration_simplex_range(Bitmap_cubical_complex<T>* b):b(b){}; Filtration_simplex_iterator begin() { @@ -431,7 +327,7 @@ public: { if ( globalDbg ){cerr << "Filtration_simplex_iterator end()\n";} Filtration_simplex_iterator it( this->b ); - it.position = this->b->elements_ordered_according_to_filtration.size(); + it.position = this->b->simplex_associated_to_key.size(); return it; } private: @@ -443,19 +339,19 @@ public: //*********************************************// //Methods to access iterators from the container: /** - * boundary_simplex_range creates an object of a Boundary_simplex_range class + * boundary_simplex_range creates an object of a Boundary_simplex_range class * that provides ranges for the Boundary_simplex_iterator. **/ Boundary_simplex_range boundary_simplex_range(Simplex_handle& sh) { if ( globalDbg ){cerr << "Boundary_simplex_range boundary_simplex_range(Simplex_handle& sh)\n";} - //Returns a range giving access to all simplices of the boundary of a simplex, + //Returns a range giving access to all simplices of the boundary of a simplex, //i.e. the set of codimension 1 subsimplices of the Simplex. - return Boundary_simplex_range(sh); + return Boundary_simplex_range(sh,this); } /** - * filtration_simplex_range creates an object of a Filtration_simplex_range class + * filtration_simplex_range creates an object of a Filtration_simplex_range class * that provides ranges for the Filtration_simplex_iterator. **/ Filtration_simplex_range filtration_simplex_range() @@ -470,9 +366,9 @@ public: //*********************************************// //Elements which are in Gudhi now, but I (and in all the cases I asked also Marc) do not understand why they are there. - //TODO -- the file IndexingTag.h in the Gudhi library contains an empty structure, so + //TODO -- the file IndexingTag.h in the Gudhi library contains an empty structure, so //I understand that this is something that was planned (for simplicial maps?) - //but was never finished. The only idea I have here is to use the same empty structure from + //but was never finished. The only idea I have here is to use the same empty structure from //IndexingTag.h file, but only if the compiler needs it. If the compiler //do not need it, then I would rather not add here elements which I do not understand. //typedef Indexing_tag @@ -481,7 +377,7 @@ public: **/ std::pair<Simplex_handle, Simplex_handle> endpoints( Simplex_handle sh ) { - std::vector< size_t > bdry = this->get_boundary_of_a_cell( sh.position ); + std::vector< size_t > bdry = this->get_boundary_of_a_cell( sh ); if ( globalDbg ) { cerr << "std::pair<Simplex_handle, Simplex_handle> endpoints( Simplex_handle sh )\n"; @@ -490,7 +386,7 @@ public: //this method returns two first elements from the boundary of sh. if ( bdry.size() < 2 ) throw("Error in endpoints in Bitmap_cubical_complex class. The cell have less than two elements in the boundary."); - return std::make_pair( Simplex_handle(this,bdry[0]) , Simplex_handle(this,bdry[1]) ); + return std::make_pair( bdry[0] , bdry[1] ); } @@ -508,9 +404,9 @@ public: if ( globalDbg ){cerr << "Skeleton_simplex_iterator ( Bitmap_cubical_complex* b , size_t d )\n";} //find the position of the first simplex of a dimension d this->position = 0; - while ( - (this->position != b->data.size()) && - ( this->b->get_dimension_of_a_cell( this->position ) != this->dimension ) + while ( + (this->position != b->data.size()) && + ( this->b->get_dimension_of_a_cell( this->position ) != this->dimension ) ) { ++this->position; @@ -523,9 +419,9 @@ public: if ( globalDbg ){cerr << "Skeleton_simplex_iterator operator++()\n";} //increment the position as long as you did not get to the next element of the dimension dimension. ++this->position; - while ( - (this->position != this->b->data.size()) && - ( this->b->get_dimension_of_a_cell( this->position ) != this->dimension ) + while ( + (this->position != this->b->data.size()) && + ( this->b->get_dimension_of_a_cell( this->position ) != this->dimension ) ) { ++this->position; @@ -544,17 +440,13 @@ public: this->b = rhs.b; this->position = rhs.position; } - bool operator == ( const Skeleton_simplex_iterator& rhs ) + bool operator == ( const Skeleton_simplex_iterator& rhs )const { if ( globalDbg ){cerr << "bool operator ==\n";} - if ( this->position == rhs.position ) - { - return true; - } - return false; + return ( this->position == rhs.position ); } - bool operator != ( const Skeleton_simplex_iterator& rhs ) + bool operator != ( const Skeleton_simplex_iterator& rhs )const { if ( globalDbg ){cerr << "bool operator != ( const Skeleton_simplex_iterator& rhs )\n";} return !(*this == rhs); @@ -562,7 +454,7 @@ public: Simplex_handle operator*() { if ( globalDbg ){cerr << "Simplex_handle operator*() \n";} - return Simplex_handle( this->b , this->position ); + return this->position; } friend class Skeleton_simplex_range; @@ -578,7 +470,8 @@ public: { //Range over the simplices of the complex in the order of the filtration. //.begin() and .end() return type Filtration_simplex_iterator. - public: + public:
+ typedef Skeleton_simplex_iterator const_iterator; Skeleton_simplex_range(Bitmap_cubical_complex<T>* b , unsigned dimension):b(b),dimension(dimension){}; Skeleton_simplex_iterator begin() { @@ -606,107 +499,59 @@ public: return Skeleton_simplex_range( this , dimension ); } + friend class is_before_in_filtration<T>; -//*********************************************// -//functions used for debugging: - /** - * Function used for debugging purposes. - **/ - //void printkey_associated_to_simplex() - //{ - // for ( size_t i = 0 ; i != this->data.size() ; ++i ) - // { - // cerr << i << " -> " << this->simplex_associated_to_key[i] << endl; - // } - //} - - /** - * Function used for debugging purposes. - **/ - size_t printRealPosition( const Simplex_handle& sh ) - { - return sh.position; - } - -private: +protected: std::vector< size_t > key_associated_to_simplex; std::vector< size_t > simplex_associated_to_key; - std::vector< size_t > elements_ordered_according_to_filtration; - //filed above is needed by Filtration_simplex_iterator. If this iterator is not used, this field is not initialized. };//Bitmap_cubical_complex - +
template <typename T> -bool compare_elements_for_elements_ordered_according_to_filtration -( const std::pair< size_t , std::pair< T , char > >& f , const std::pair< size_t , std::pair< T , char > >& s ) +void Bitmap_cubical_complex<T>::initialize_simplex_associated_to_key() { - if ( globalDbg ){cerr << "compare_elements_for_elements_ordered_according_to_filtration\n";} - if ( f.second.first < s.second.first ) - { - return true; - } - else + if ( globalDbg ) { - if ( f.second.first > s.second.first ) - { - return false; - } - else - { - //in this case f.second.first == s.second.first, and we use dimension to compare: - if ( f.second.second < s.second.second ) - { - return true; - } - else - { - if ( f.second.second > s.second.second ) - { - return false; - } - else - { - //in this case, both the filtration value and the dimensions for those cells are the same. - //Since it may be nice to have a stable sorting procedure, in this case, - //we compare positions in the bitmap: - return ( f.first < s.first ); - } - } - } + cerr << "void Bitmap_cubical_complex<T>::initialize_elements_ordered_according_to_filtration() \n"; } + std::vector<size_t> data_of_elements_from_bitmap( this->data.size() ); + std::iota (std::begin(data_of_elements_from_bitmap), std::end(data_of_elements_from_bitmap), 0); + std::sort( data_of_elements_from_bitmap.begin() , + data_of_elements_from_bitmap.end() , + is_before_in_filtration<T>(this) ); + this->simplex_associated_to_key = data_of_elements_from_bitmap; } - +
+
template <typename T> -void Bitmap_cubical_complex<T>::initialize_elements_ordered_according_to_filtration() +class is_before_in_filtration { - if ( globalDbg ) - { - cerr << "void Bitmap_cubical_complex<T>::initialize_elements_ordered_according_to_filtration() \n"; - } - //( position , (filtration , dimension) ) - std::vector< std::pair< size_t , std::pair< T , char > > > data_of_elements_from_bitmap( this->data.size() ); - for ( size_t i = 0 ; i != this->data.size() ; ++i ) - { - //TODO -- this can be optimized by having a counter here. - //We do not need to re-compute the dimension for every cell from scratch - data_of_elements_from_bitmap[i] = - std::make_pair( i , std::make_pair( this->data[i] , this->get_dimension_of_a_cell(i) ) ); - } - std::sort( data_of_elements_from_bitmap.begin() , - data_of_elements_from_bitmap.end() , - compare_elements_for_elements_ordered_according_to_filtration<T> ); - - std::vector< size_t > - elements_ordered_according_to_filtration_then_to_dimension_then_to_position - ( this->data.size() ); - for ( size_t i = 0 ; i != data_of_elements_from_bitmap.size() ; ++i ) +public: + explicit is_before_in_filtration(Bitmap_cubical_complex<T> * CC) + : CC_(CC) { } + + bool operator()( const typename Bitmap_cubical_complex<T>::Simplex_handle sh1, const typename Bitmap_cubical_complex<T>::Simplex_handle sh2) const { - elements_ordered_according_to_filtration_then_to_dimension_then_to_position[i] - = data_of_elements_from_bitmap[i].first; - } - this->elements_ordered_according_to_filtration = - elements_ordered_according_to_filtration_then_to_dimension_then_to_position; -} + // Not using st_->filtration(sh1) because it uselessly tests for null_simplex. + T fil1 = CC_->data[sh1]; + T fil2 = CC_->data[sh2]; + if ( fil1 != fil2 ) + { + return fil1 < fil2; + } + //in this case they are on the same filtration level, so the dimension decide. + size_t dim1 = CC_->get_dimension_of_a_cell(sh1); + size_t dim2 = CC_->get_dimension_of_a_cell(sh2); + if ( dim1 != dim2 ) + { + return dim1 < dim2; + } + //in this case both filtration and dimensions of the considered cubes are the same. To have stable sort, we simply compare their positions in the bitmap: + return sh1 < sh2; + } +protected: + Bitmap_cubical_complex<T>* CC_; + }; //****************************************************************************************************************// @@ -716,4 +561,4 @@ void Bitmap_cubical_complex<T>::initialize_elements_ordered_according_to_filtrat } -}
\ No newline at end of file +}
|