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diff --git a/src/Gudhi_stat/include/gudhi/persistence_representations/Persistence_landscape.h b/src/Gudhi_stat/include/gudhi/persistence_representations/Persistence_landscape.h new file mode 100644 index 00000000..c71eb3d2 --- /dev/null +++ b/src/Gudhi_stat/include/gudhi/persistence_representations/Persistence_landscape.h @@ -0,0 +1,1492 @@ +/* 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): Pawel Dlotko + * + * Copyright (C) 2015 INRIA (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 Persistence_landscapes_H +#define Persistence_landscapes_H + +//standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <unistd.h> + + +//gudhi include +#include <gudhi/read_persitence_from_file.h> +#include <gudhi/common_gudhi_stat.h> + + + + +namespace Gudhi +{ +namespace Gudhi_stat +{ + + + + + + +/** + * A clas implementing persistence landascpes data structures. For theroretical desciritpion, please consult a paper ''Statistical topological data analysis using persistence landscapes'' by Peter Bubenik. + * For details of algorithms, please consult ''A persistence landscapes toolbox for topological statistics'' by Peter Bubenik and Pawel Dlotko. + * Persistence landscapes allow vertorization, computations of distances, computations of projections to Real, computations of averages and scalar products. Therefore they implement suitable interfaces. + * It implements the following concepts: Vectorized_topological_data, Topological_data_with_distances, Real_valued_topological_data, Topological_data_with_averages, Topological_data_with_scalar_product +**/ +class Persistence_landscape +{ +public: + /** + * Default constructor. + **/ + Persistence_landscape() + { + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); + } + + /** + * Constructor that takes as an input a vector of birth-death pairs. + **/ + Persistence_landscape( const std::vector< std::pair< double , double > >& p ); + + /** + * Constructor that reads persistence intervals from file and creates persistence landscape. The format of the input file is the following: in each line we put birth-death pair. Last line is assumed + * to be empty. Even if the points within a line are not ordered, they will be ordered while the input is read. + **/ + Persistence_landscape(const char* filename , size_t dimension = 0); + + + + /** + * This procedure loads a landscape from file. It erase all the data that was previously stored in this landscape. + **/ + void load_landscape_from_file( const char* filename ); + + + /** + * The procedure stores a landscape to a file. The file can be later used by a procedure load_landscape_from_file. + **/ + void print_to_file( const char* filename )const; + + + + /** + * This function compute integral of the landscape (defined formally as sum of integrals on R of all landscape functions) + **/ + double compute_integral_of_landscape()const; + + + /** + * This function compute integral of the 'level'-level of a landscape. + **/ + double compute_integral_of_a_level_of_a_landscape( size_t level )const; + + + /** + * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals on R of p-th powers of all landscape functions) + **/ + double compute_integral_of_landscape( double p )const;//this function compute integral of p-th power of landscape. + + + /** + * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned level and double x. + * The procedure will compute the value of the level-landscape at the point x. + **/ + double compute_value_at_a_given_point( unsigned level , double x )const; + + /** + * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity points of the landscapes follows. + * Shall those points be joined with lines, we will obtain the i-th landscape function. + **/ + friend std::ostream& operator<<(std::ostream& out, Persistence_landscape& land ); + + + + + + /** + *\private A function that compute sum of two landscapes. + **/ + friend Persistence_landscape add_two_landscapes ( const Persistence_landscape& land1 , const Persistence_landscape& land2 ) + { + return operation_on_pair_of_landscapes< std::plus<double> >(land1,land2); + } + + /** + *\private A function that compute difference of two landscapes. + **/ + friend Persistence_landscape subtract_two_landscapes ( const Persistence_landscape& land1 , const Persistence_landscape& land2 ) + { + return operation_on_pair_of_landscapes< std::minus<double> >(land1,land2); + } + + /** + * An operator +, that compute sum of two landscapes. + **/ + friend Persistence_landscape operator+( const Persistence_landscape& first , const Persistence_landscape& second ) + { + return add_two_landscapes( first,second ); + } + + /** + * An operator -, that compute difference of two landscapes. + **/ + friend Persistence_landscape operator-( const Persistence_landscape& first , const Persistence_landscape& second ) + { + return subtract_two_landscapes( first,second ); + } + + /** + * An operator * that allows multipilication of a landscape by a real number. + **/ + friend Persistence_landscape operator*( const Persistence_landscape& first , double con ) + { + return first.multiply_lanscape_by_real_number_not_overwrite(con); + } + + /** + * An operator * that allows multipilication of a landscape by a real number (order of parameters swapped). + **/ + friend Persistence_landscape operator*( double con , const Persistence_landscape& first ) + { + return first.multiply_lanscape_by_real_number_not_overwrite(con); + } + + /** + * Operator +=. The second parameter is persistence landscape. + **/ + Persistence_landscape operator += ( const Persistence_landscape& rhs ) + { + *this = *this + rhs; + return *this; + } + + /** + * Operator -=. The second parameter is a persistence landscape. + **/ + Persistence_landscape operator -= ( const Persistence_landscape& rhs ) + { + *this = *this - rhs; + return *this; + } + + + /** + * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. The x-values remain unchanged. + **/ + Persistence_landscape operator *= ( double x ) + { + *this = *this*x; + return *this; + } + + /** + * Operator /=. The second parameter is a real number. + **/ + Persistence_landscape operator /= ( double x ) + { + if ( x == 0 )throw( "In operator /=, division by 0. Program terminated." ); + *this = *this * (1/x); + return *this; + } + + /** + * An operator to compare two persistence landscapes. + **/ + bool operator == ( const Persistence_landscape& rhs )const; + + + /** + * An operator to compare two persistence landscapes. + **/ + bool operator != ( const Persistence_landscape& rhs )const + { + return !((*this) == rhs); + } + + + /** + * Computations of maximum (y) value of landscape. + **/ + double compute_maximum()const + { + double maxValue = 0; + if ( this->land.size() ) + { + maxValue = -std::numeric_limits<int>::max(); + for ( size_t i = 0 ; i != this->land[0].size() ; ++i ) + { + if ( this->land[0][i].second > maxValue )maxValue = this->land[0][i].second; + } + } + return maxValue; + } + + + /** + *\private Computations of minimum (y) value of landscape. + **/ + double compute_minimum()const + { + double minValue = 0; + if ( this->land.size() ) + { + minValue = std::numeric_limits<int>::max(); + for ( size_t i = 0 ; i != this->land[0].size() ; ++i ) + { + if ( this->land[0][i].second < minValue )minValue = this->land[0][i].second; + } + } + return minValue; + } + + /** + *\private Computations of a L^i norm of landscape, where i is the input parameter. + **/ + double compute_norm_of_landscape( double i ) + { + Persistence_landscape l; + if ( i < std::numeric_limits< double >::max() ) + { + return compute_distance_of_landscapes(*this,l,i); + } + else + { + return compute_max_norm_distance_of_landscapes(*this,l); + } + } + + /** + * An operator to compute the value of a landscape in the level 'level' at the argument 'x'. + **/ + double operator()(unsigned level,double x)const{return this->compute_value_at_a_given_point(level,x);} + + /** + *\private Computations of L^{\infty} distance between two landscapes. + **/ + friend double compute_max_norm_distance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second ); + //friend double compute_max_norm_distance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , unsigned& nrOfLand , double&x , double& y1, double& y2 ); + + + /** + *\private Computations of L^{p} distance between two landscapes. p is the parameter of the procedure. + **/ + friend double compute_distance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , double p ); + + + + /** + * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store general PL-function. When computing distance betwen two landscapes, we compute difference between + * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute distance, we need to take its absolute value. This is the purpose of this procedure. + **/ + Persistence_landscape abs(); + + /** + * Computes the number of landscape functions. + **/ + size_t size()const{return this->land.size(); } + + /** + * Computate maximal value of lambda-level landscape. + **/ + double find_max( unsigned lambda )const; + + /** + *\private Function to compute inner (scalar) product of two landscapes. + **/ + friend double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 ); + + + + + + + + + + + + + + + + //Implementations of functions for various concepts. + + /** + * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an integral of i-th landscape function over whole R. + * This function is required by the Real_valued_topological_data concept. + **/ + double project_to_R( int number_of_function )const + { + return this->compute_integral_of_a_level_of_a_landscape( (size_t)number_of_function ); + } + + /** + * The function gives the number of possible projections to R. This function is required by the Real_valued_topological_data concept. + **/ + size_t number_of_projections_to_R()const + { + return this->number_of_functions_for_projections_to_reals; + } + + /** + * This function produce a vector of doubles based on a landscape. It is required in a concept Vectorized_topological_data + */ + std::vector<double> vectorize( int number_of_function )const + { + //TODO, think of something smarter over here + std::vector<double> v; + if ( (size_t)number_of_function > this->land.size() ) + { + return v; + } + v.reserve( this->land[number_of_function].size() ); + for ( size_t i = 0 ; i != this->land[number_of_function].size() ; ++i ) + { + v.push_back( this->land[number_of_function][i].second ); + } + return v; + } + /** + * This function return the number of functions that allows vectorization of persistence laandscape. It is required in a concept Vectorized_topological_data. + **/ + size_t number_of_vectorize_functions()const + { + return this->number_of_functions_for_vectorization; + } + + /** + * A function to compute averaged persistence landscape, based on vector of persistence landscapes. + * This function is required by Topological_data_with_averages concept. + **/ + void compute_average( const std::vector< Persistence_landscape* >& to_average ) + { + bool dbg = false; + + if ( dbg ){std::cerr << "to_average.size() : " << to_average.size() << std::endl;} + + std::vector< Persistence_landscape* > nextLevelMerge( to_average.size() ); + for ( size_t i = 0 ; i != to_average.size() ; ++i ) + { + nextLevelMerge[i] = to_average[i]; + } + bool is_this_first_level = true;//in the loop, we will create dynamically a unmber of intermediate complexes. We have to clean that up, but we cannot erase the initial andscapes we have + //to average. In this case, we simply check if the nextLevelMerge are the input landscapes or the ones created in that loop by usig this extra variable. + + while ( nextLevelMerge.size() != 1 ) + { + if ( dbg ){std::cerr << "nextLevelMerge.size() : " << nextLevelMerge.size() << std::endl;} + std::vector< Persistence_landscape* > nextNextLevelMerge; + nextNextLevelMerge.reserve( to_average.size() ); + for ( size_t i = 0 ; i < nextLevelMerge.size() ; i=i+2 ) + { + if ( dbg ){std::cerr << "i : " << i << std::endl;} + Persistence_landscape* l = new Persistence_landscape; + if ( i+1 != nextLevelMerge.size() ) + { + (*l) = (*nextLevelMerge[i])+(*nextLevelMerge[i+1]); + } + else + { + (*l) = *nextLevelMerge[i]; + } + nextNextLevelMerge.push_back( l ); + } + if ( dbg ){std::cerr << "After this iteration \n";getchar();} + + if ( !is_this_first_level ) + { + //deallocate the memory if the vector nextLevelMerge do not consist of the initial landscapes + for ( size_t i = 0 ; i != nextLevelMerge.size() ; ++i ) + { + delete nextLevelMerge[i]; + } + } + is_this_first_level = false; + nextLevelMerge.swap(nextNextLevelMerge); + } + (*this) = (*nextLevelMerge[0]); + (*this) *= 1/( (double)to_average.size() ); + } + + + /** + * A function to compute distance between persistence landscape. + * The parameter of this functionis a Persistence_landscape. + * This function is required in Topological_data_with_distances concept. + * For max norm distance, set power to std::numeric_limits<double>::max() + **/ + double distance( const Persistence_landscape& second , double power = 1 )const + { + if ( power < std::numeric_limits<double>::max() ) + { + return compute_distance_of_landscapes( *this , second , power ); + } + else + { + return compute_max_norm_distance_of_landscapes( *this , second ); + } + } + + + /** + * A function to compute scalar product of persistence landscapes. + * The parameter of this functionis a Persistence_landscape. + * This function is required in Topological_data_with_scalar_product concept. + **/ + double compute_scalar_product( const Persistence_landscape& second )const + { + return compute_inner_product( (*this) , second ); + } + //end of implementation of functions needed for concepts. + + + /** + * This procedure returns x-range of a given level persistence landscape. If a default value is used, the x-range + * of 0th level landscape is given (and this range contains the ranges of all other landscapes). + **/ + std::pair< double , double > get_x_range( size_t level = 0 )const + { + std::pair< double , double > result; + if ( level < this->land.size() ) + { + result = std::make_pair( this->land[level][1].first , this->land[level][ this->land[level].size() - 2 ].first ); + } + else + { + result = std::make_pair( 0,0 ); + } + return result; + } + + /** + * This procedure returns y-range of a given level persistence landscape. If a default value is used, the y-range + * of 0th level landscape is given (and this range contains the ranges of all other landscapes). + **/ + std::pair< double , double > get_y_range( size_t level = 0 )const + { + std::pair< double , double > result; + if ( level < this->land.size() ) + { + double maxx = this->compute_maximum(); + double minn = this->compute_minimum(); + result = std::make_pair( minn , maxx ); + } + else + { + result = std::make_pair( 0,0 ); + } + return result; + } + + + + //a function used to create a gnuplot script for visualization of landscapes + void plot( const char* filename, double xRangeBegin = std::numeric_limits<double>::max() , double xRangeEnd = std::numeric_limits<double>::max() , + double yRangeBegin = std::numeric_limits<double>::max() , double yRangeEnd = std::numeric_limits<double>::max(), + int from = std::numeric_limits<int>::max(), int to = std::numeric_limits<int>::max() ); + + +protected: + std::vector< std::vector< std::pair<double,double> > > land; + size_t number_of_functions_for_vectorization; + size_t number_of_functions_for_projections_to_reals; + + void construct_persistence_landscape_from_barcode( const std::vector< std::pair< double , double > > & p ); + Persistence_landscape multiply_lanscape_by_real_number_not_overwrite( double x )const; + void multiply_lanscape_by_real_number_overwrite( double x ); + template < typename oper > friend Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 , const Persistence_landscape& land2 ); + friend double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 ); + + void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals() + { + //warning, this function can be only called after filling in the intervals vector. + this->number_of_functions_for_vectorization = this->land.size(); + this->number_of_functions_for_projections_to_reals = this->land.size(); + } +}; + + + + + + + + +Persistence_landscape::Persistence_landscape(const char* filename , size_t dimension) +{ + bool dbg = false; + + if ( dbg ) + { + std::cerr << "Using constructor : Persistence_landscape(char* filename)" << std::endl; + } + //standard file with barcode + //std::vector< std::pair< double , double > > barcode = read_standard_file( filename ); + //gudhi file with barcode + std::vector< std::pair< double , double > > barcode = read_gudhi_file( filename , dimension ); + this->construct_persistence_landscape_from_barcode( barcode ); + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); +} + + +bool operatorEqualDbg = false; +bool Persistence_landscape::operator == ( const Persistence_landscape& rhs )const +{ + if ( this->land.size() != rhs.land.size() ) + { + if (operatorEqualDbg)std::cerr << "1\n"; + return false; + } + for ( size_t level = 0 ; level != this->land.size() ; ++level ) + { + if ( this->land[level].size() != rhs.land[level].size() ) + { + if (operatorEqualDbg)std::cerr << "this->land[level].size() : " << this->land[level].size() << "\n"; + if (operatorEqualDbg)std::cerr << "rhs.land[level].size() : " << rhs.land[level].size() << "\n"; + if (operatorEqualDbg)std::cerr << "2\n"; + return false; + } + for ( size_t i = 0 ; i != this->land[level].size() ; ++i ) + { + if ( !( almost_equal(this->land[level][i].first , rhs.land[level][i].first) && almost_equal(this->land[level][i].second , rhs.land[level][i].second) ) ) + { + //std::cerr<< this->land[level][i].first << " , " << rhs.land[level][i].first << " and " << this->land[level][i].second << " , " << rhs.land[level][i].second << std::endl; + if (operatorEqualDbg)std::cerr << "this->land[level][i] : " << this->land[level][i].first << " " << this->land[level][i].second << "\n"; + if (operatorEqualDbg)std::cerr << "rhs.land[level][i] : " << rhs.land[level][i].first << " " << rhs.land[level][i].second << "\n"; + if (operatorEqualDbg)std::cerr << "3\n"; + return false; + } + } + } + return true; +} + + + + +Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > > & p ) +{ + this->construct_persistence_landscape_from_barcode( p ); + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); +} + + +void Persistence_landscape::construct_persistence_landscape_from_barcode( const std::vector< std::pair< double , double > > & p ) +{ + bool dbg = false; + if ( dbg ){std::cerr << "Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > >& p )" << std::endl;} + + //this is a general algorithm to construct persistence landscapes. + std::vector< std::pair<double,double> > bars; + bars.insert( bars.begin() , p.begin() , p.end() ); + std::sort( bars.begin() , bars.end() , compare_points_sorting ); + + if (dbg) + { + std::cerr << "Bars : \n"; + for ( size_t i = 0 ; i != bars.size() ; ++i ) + { + std::cerr << bars[i].first << " " << bars[i].second << "\n"; + } + getchar(); + } + + std::vector< std::pair<double,double> > characteristicPoints(p.size()); + for ( size_t i = 0 ; i != bars.size() ; ++i ) + { + characteristicPoints[i] = std::make_pair((bars[i].first+bars[i].second)/2.0 , (bars[i].second - bars[i].first)/2.0); + } + std::vector< std::vector< std::pair<double,double> > > Persistence_landscape; + while ( !characteristicPoints.empty() ) + { + if(dbg) + { + for ( size_t i = 0 ; i != characteristicPoints.size() ; ++i ) + { + std::cout << "(" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n"; + } + std::cin.ignore(); + } + + std::vector< std::pair<double,double> > lambda_n; + lambda_n.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) ); + lambda_n.push_back( std::make_pair(minus_length(characteristicPoints[0]),0) ); + lambda_n.push_back( characteristicPoints[0] ); + + if (dbg) + { + std::cerr << "1 Adding to lambda_n : (" << -std::numeric_limits<int>::max() << " " << 0 << ") , (" << minus_length(characteristicPoints[0]) << " " << 0 << ") , (" << characteristicPoints[0].first << " " << characteristicPoints[0].second << ") \n"; + } + + size_t i = 1; + std::vector< std::pair<double,double> > newCharacteristicPoints; + while ( i < characteristicPoints.size() ) + { + size_t p = 1; + if ( (minus_length(characteristicPoints[i]) >= minus_length(lambda_n[lambda_n.size()-1])) && (birth_plus_deaths(characteristicPoints[i]) > birth_plus_deaths(lambda_n[lambda_n.size()-1])) ) + { + if ( minus_length(characteristicPoints[i]) < birth_plus_deaths(lambda_n[lambda_n.size()-1]) ) + { + std::pair<double,double> point = std::make_pair( (minus_length(characteristicPoints[i])+birth_plus_deaths(lambda_n[lambda_n.size()-1]))/2 , (birth_plus_deaths(lambda_n[lambda_n.size()-1])-minus_length(characteristicPoints[i]))/2 ); + lambda_n.push_back( point ); + if (dbg) + { + std::cerr << "2 Adding to lambda_n : (" << point.first << " " << point.second << ")\n"; + } + + + if ( dbg ) + { + std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n"; + std::cerr << "point : " << point.first << " " << point.second << "\n"; + getchar(); + } + + while ( (i+p < characteristicPoints.size() ) && ( almost_equal(minus_length(point),minus_length(characteristicPoints[i+p])) ) && ( birth_plus_deaths(point) <= birth_plus_deaths(characteristicPoints[i+p]) ) ) + { + newCharacteristicPoints.push_back( characteristicPoints[i+p] ); + if (dbg) + { + std::cerr << "3.5 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n"; + getchar(); + } + ++p; + } + + + newCharacteristicPoints.push_back( point ); + if (dbg) + { + std::cerr << "4 Adding to newCharacteristicPoints : (" << point.first << " " << point.second << ")\n"; + } + + + while ( (i+p < characteristicPoints.size() ) && ( minus_length(point) <= minus_length(characteristicPoints[i+p]) ) && (birth_plus_deaths(point)>=birth_plus_deaths(characteristicPoints[i+p])) ) + { + newCharacteristicPoints.push_back( characteristicPoints[i+p] ); + if (dbg) + { + std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << "\n"; + std::cerr << "point : " << point.first << " " << point.second << "\n"; + std::cerr << "characteristicPoints[i+p] birth and death : " << minus_length(characteristicPoints[i+p]) << " , " << birth_plus_deaths(characteristicPoints[i+p]) << "\n"; + std::cerr << "point birth and death : " << minus_length(point) << " , " << birth_plus_deaths(point) << "\n"; + + std::cerr << "3 Adding to newCharacteristicPoints : (" << characteristicPoints[i+p].first << " " << characteristicPoints[i+p].second << ")\n"; + getchar(); + } + ++p; + } + + } + else + { + lambda_n.push_back( std::make_pair( birth_plus_deaths(lambda_n[lambda_n.size()-1]) , 0 ) ); + lambda_n.push_back( std::make_pair( minus_length(characteristicPoints[i]) , 0 ) ); + if (dbg) + { + std::cerr << "5 Adding to lambda_n : (" << birth_plus_deaths(lambda_n[lambda_n.size()-1]) << " " << 0 << ")\n"; + std::cerr << "5 Adding to lambda_n : (" << minus_length(characteristicPoints[i]) << " " << 0 << ")\n"; + } + } + lambda_n.push_back( characteristicPoints[i] ); + if (dbg) + { + std::cerr << "6 Adding to lambda_n : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n"; + } + } + else + { + newCharacteristicPoints.push_back( characteristicPoints[i] ); + if (dbg) + { + std::cerr << "7 Adding to newCharacteristicPoints : (" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n"; + } + } + i = i+p; + } + lambda_n.push_back( std::make_pair(birth_plus_deaths(lambda_n[lambda_n.size()-1]),0) ); + lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) ); + + characteristicPoints = newCharacteristicPoints; + + lambda_n.erase(std::unique(lambda_n.begin(), lambda_n.end()), lambda_n.end()); + this->land.push_back( lambda_n ); + } +} + + + +//this function find maximum of lambda_n +double Persistence_landscape::find_max( unsigned lambda )const +{ + if ( this->land.size() < lambda )return 0; + double maximum = -std::numeric_limits<int>::max(); + for ( size_t i = 0 ; i != this->land[lambda].size() ; ++i ) + { + if ( this->land[lambda][i].second > maximum )maximum = this->land[lambda][i].second; + } + return maximum; +} + + +double Persistence_landscape::compute_integral_of_landscape()const +{ + double result = 0; + for ( size_t i = 0 ; i != this->land.size() ; ++i ) + { + for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr ) + { + //it suffices to compute every planar integral and then sum them ap for each lambda_n + result += 0.5*( this->land[i][nr].first - this->land[i][nr-1].first )*(this->land[i][nr].second + this->land[i][nr-1].second); + } + } + return result; +} + +double Persistence_landscape::compute_integral_of_a_level_of_a_landscape( size_t level )const +{ + double result = 0; + if ( level >= this->land.size() ) + { + //this landscape function is constantly equal 0, so is the intergral. + return result; + } + //also negative landscapes are assumed to be zero. + if ( level < 0 )return 0; + + for ( size_t nr = 2 ; nr != this->land[ level ].size()-1 ; ++nr ) + { + //it suffices to compute every planar integral and then sum them ap for each lambda_n + result += 0.5*( this->land[ level ][nr].first - this->land[ level ][nr-1].first )*(this->land[ level ][nr].second + this->land[ level ][nr-1].second); + } + + return result; +} + + +double Persistence_landscape::compute_integral_of_landscape( double p )const +{ + bool dbg = false; + double result = 0; + for ( size_t i = 0 ; i != this->land.size() ; ++i ) + { + for ( size_t nr = 2 ; nr != this->land[i].size()-1 ; ++nr ) + { + if (dbg)std::cout << "nr : " << nr << "\n"; + //In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * (ax+b)^{p+1}/(p+1) + std::pair<double,double> coef = compute_parameters_of_a_line( this->land[i][nr] , this->land[i][nr-1] ); + double a = coef.first; + double b = coef.second; + + if (dbg)std::cout << "(" << this->land[i][nr].first << "," << this->land[i][nr].second << ") , " << this->land[i][nr-1].first << "," << this->land[i][nr].second << ")" << std::endl; + if ( this->land[i][nr].first == this->land[i][nr-1].first )continue; + if ( a != 0 ) + { + result += 1/(a*(p+1)) * ( pow((a*this->land[i][nr].first+b),p+1) - pow((a*this->land[i][nr-1].first+b),p+1)); + } + else + { + result += ( this->land[i][nr].first - this->land[i][nr-1].first )*( pow(this->land[i][nr].second,p) ); + } + if ( dbg ) + { + std::cout << "a : " <<a << " , b : " << b << std::endl; + std::cout << "result : " << result << std::endl; + } + } + //if (compute_integral_of_landscapeDbg) std::cin.ignore(); + } + return result; +} + + +//this is O(log(n)) algorithm, where n is number of points in this->land. +double Persistence_landscape::compute_value_at_a_given_point( unsigned level , double x )const +{ + bool compute_value_at_a_given_pointDbg = false; + //in such a case lambda_level = 0. + if ( level > this->land.size() ) return 0; + + //we know that the points in this->land[level] are ordered according to x coordinate. Therefore, we can find the point by using bisection: + unsigned coordBegin = 1; + unsigned coordEnd = this->land[level].size()-2; + + if ( compute_value_at_a_given_pointDbg ) + { + std::cerr << "Here \n"; + std::cerr << "x : " << x << "\n"; + std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n"; + std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n"; + } + + //in this case x is outside the support of the landscape, therefore the value of the landscape is 0. + if ( x <= this->land[level][coordBegin].first )return 0; + if ( x >= this->land[level][coordEnd].first )return 0; + + if (compute_value_at_a_given_pointDbg)std::cerr << "Entering to the while loop \n"; + + while ( coordBegin+1 != coordEnd ) + { + if (compute_value_at_a_given_pointDbg) + { + std::cerr << "coordBegin : " << coordBegin << "\n"; + std::cerr << "coordEnd : " << coordEnd << "\n"; + std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n"; + std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n"; + } + + + unsigned newCord = (unsigned)floor((coordEnd+coordBegin)/2.0); + + if (compute_value_at_a_given_pointDbg) + { + std::cerr << "newCord : " << newCord << "\n"; + std::cerr << "this->land[level][newCord].first : " << this->land[level][newCord].first << "\n"; + std::cin.ignore(); + } + + if ( this->land[level][newCord].first <= x ) + { + coordBegin = newCord; + if ( this->land[level][newCord].first == x )return this->land[level][newCord].second; + } + else + { + coordEnd = newCord; + } + } + + if (compute_value_at_a_given_pointDbg) + { + std::cout << "x : " << x << " is between : " << this->land[level][coordBegin].first << " a " << this->land[level][coordEnd].first << "\n"; + std::cout << "the y coords are : " << this->land[level][coordBegin].second << " a " << this->land[level][coordEnd].second << "\n"; + std::cerr << "coordBegin : " << coordBegin << "\n"; + std::cerr << "coordEnd : " << coordEnd << "\n"; + std::cin.ignore(); + } + return function_value( this->land[level][coordBegin] , this->land[level][coordEnd] , x ); +} + +std::ostream& operator<<(std::ostream& out, Persistence_landscape& land ) +{ + for ( size_t level = 0 ; level != land.land.size() ; ++level ) + { + out << "Lambda_" << level << ":" << std::endl; + for ( size_t i = 0 ; i != land.land[level].size() ; ++i ) + { + if ( land.land[level][i].first == -std::numeric_limits<int>::max() ) + { + out << "-inf"; + } + else + { + if ( land.land[level][i].first == std::numeric_limits<int>::max() ) + { + out << "+inf"; + } + else + { + out << land.land[level][i].first; + } + } + out << " , " << land.land[level][i].second << std::endl; + } + } + return out; +} + + + + +void Persistence_landscape::multiply_lanscape_by_real_number_overwrite( double x ) +{ + for ( size_t dim = 0 ; dim != this->land.size() ; ++dim ) + { + for ( size_t i = 0 ; i != this->land[dim].size() ; ++i ) + { + this->land[dim][i].second *= x; + } + } +} + +bool AbsDbg = false; +Persistence_landscape Persistence_landscape::abs() +{ + Persistence_landscape result; + for ( size_t level = 0 ; level != this->land.size() ; ++level ) + { + if ( AbsDbg ){ std::cout << "level: " << level << std::endl; } + std::vector< std::pair<double,double> > lambda_n; + lambda_n.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) ); + for ( size_t i = 1 ; i != this->land[level].size() ; ++i ) + { + if ( AbsDbg ){std::cout << "this->land[" << level << "][" << i << "] : " << this->land[level][i].first << " " << this->land[level][i].second << std::endl;} + //if a line segment between this->land[level][i-1] and this->land[level][i] crosses the x-axis, then we have to add one landscape point t oresult + if ( (this->land[level][i-1].second)*(this->land[level][i].second) < 0 ) + { + double zero = find_zero_of_a_line_segment_between_those_two_points( this->land[level][i-1] , this->land[level][i] ); + + lambda_n.push_back( std::make_pair(zero , 0) ); + lambda_n.push_back( std::make_pair(this->land[level][i].first , fabs(this->land[level][i].second)) ); + if ( AbsDbg ) + { + std::cout << "Adding pair : (" << zero << ",0)" << std::endl; + std::cout << "In the same step adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second) << ") " << std::endl; + std::cin.ignore(); + } + } + else + { + lambda_n.push_back( std::make_pair(this->land[level][i].first , fabs(this->land[level][i].second)) ); + if ( AbsDbg ) + { + std::cout << "Adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second) << ") " << std::endl; + std::cin.ignore(); + } + } + } + result.land.push_back( lambda_n ); + } + return result; +} + + +Persistence_landscape Persistence_landscape::multiply_lanscape_by_real_number_not_overwrite( double x )const +{ + std::vector< std::vector< std::pair<double,double> > > result(this->land.size()); + for ( size_t dim = 0 ; dim != this->land.size() ; ++dim ) + { + std::vector< std::pair<double,double> > lambda_dim( this->land[dim].size() ); + for ( size_t i = 0 ; i != this->land[dim].size() ; ++i ) + { + lambda_dim[i] = std::make_pair( this->land[dim][i].first , x*this->land[dim][i].second ); + } + result[dim] = lambda_dim; + } + Persistence_landscape res; + //CHANGE + //res.land = result; + res.land.swap(result); + return res; +}//multiply_lanscape_by_real_number_overwrite + + +void Persistence_landscape::print_to_file( const char* filename )const +{ + std::ofstream write; + write.open(filename); + for ( size_t dim = 0 ; dim != this->land.size() ; ++dim ) + { + write << "#lambda_" << dim << std::endl; + for ( size_t i = 1 ; i != this->land[dim].size()-1 ; ++i ) + { + write << this->land[dim][i].first << " " << this->land[dim][i].second << std::endl; + } + } + write.close(); +} + +void Persistence_landscape::load_landscape_from_file( const char* filename ) +{ + bool dbg = false; + //removing the current content of the persistence landscape. + this->land.clear(); + + + //this constructor reads persistence landscape form a file. This file have to be created by this software beforehead + std::ifstream in; + in.open( filename ); + if ( !( access( filename, F_OK ) != -1 ) ) + { + std::cerr << "The file : " << filename << " do not exist. The program will now terminate \n"; + throw "The file from which you are trying to read the persistence landscape do not exist. The program will now terminate \n"; + } + + std::string line; + std::vector< std::pair<double,double> > landscapeAtThisLevel; + + bool isThisAFirsLine = true; + while ( !in.eof() ) + { + getline(in,line); + if ( !(line.length() == 0 || line[0] == '#') ) + { + std::stringstream lineSS; + lineSS << line; + double beginn, endd; + lineSS >> beginn; + lineSS >> endd; + landscapeAtThisLevel.push_back( std::make_pair( beginn , endd ) ); + if (dbg){std::cerr << "Reading a pont : " << beginn << " , " << endd << std::endl;} + } + else + { + if (dbg) + { + std::cout << "IGNORE LINE\n"; + getchar(); + } + if ( !isThisAFirsLine ) + { + landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) ); + this->land.push_back(landscapeAtThisLevel); + std::vector< std::pair<double,double> > newLevelOdLandscape; + landscapeAtThisLevel.swap(newLevelOdLandscape); + } + landscapeAtThisLevel.push_back( std::make_pair( -std::numeric_limits<int>::max() , 0 ) ); + isThisAFirsLine = false; + } + } + if ( landscapeAtThisLevel.size() > 1 ) + { + //seems that the last line of the file is not finished with the newline sign. We need to put what we have in landscapeAtThisLevel to the constructed landscape. + landscapeAtThisLevel.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) ); + this->land.push_back(landscapeAtThisLevel); + } + + in.close(); +} + + +template < typename T > +Persistence_landscape operation_on_pair_of_landscapes ( const Persistence_landscape& land1 , const Persistence_landscape& land2 ) +{ + bool operation_on_pair_of_landscapesDBG = false; + if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes\n";std::cin.ignore();} + Persistence_landscape result; + std::vector< std::vector< std::pair<double,double> > > land( std::max( land1.land.size() , land2.land.size() ) ); + result.land = land; + T oper; + + if ( operation_on_pair_of_landscapesDBG ) + { + for ( size_t i = 0 ; i != std::min( land1.land.size() , land2.land.size() ) ; ++i ) + { + std::cerr << "land1.land[" << i << "].size() : " << land1.land[i].size() << std::endl; + std::cerr << "land2.land[" << i << "].size() : " << land2.land[i].size() << std::endl; + } + getchar(); + } + + for ( size_t i = 0 ; i != std::min( land1.land.size() , land2.land.size() ) ; ++i ) + { + std::vector< std::pair<double,double> > lambda_n; + size_t p = 0; + size_t q = 0; + while ( (p+1 < land1.land[i].size()) && (q+1 < land2.land[i].size()) ) + { + if ( operation_on_pair_of_landscapesDBG ) + { + std::cerr << "p : " << p << "\n"; + std::cerr << "q : " << q << "\n"; + std::cerr << "land1.land.size() : " << land1.land.size() << std::endl; + std::cerr << "land2.land.size() : " << land2.land.size() << std::endl; + std::cerr << "land1.land[" << i << "].size() : " << land1.land[i].size() << std::endl; + std::cerr << "land2.land[" << i << "].size() : " << land2.land[i].size() << std::endl; + std::cout << "land1.land[i][p].first : " << land1.land[i][p].first << "\n"; + std::cout << "land2.land[i][q].first : " << land2.land[i][q].first << "\n"; + //getchar(); + } + + if ( land1.land[i][p].first < land2.land[i][q].first ) + { + if ( operation_on_pair_of_landscapesDBG ) + { + std::cout << "first \n"; + std::cout << " function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) : "<< function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << "\n"; + //std::cout << "oper( " << land1.land[i][p].second <<"," << function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) << " : " << oper( land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) << "\n"; + } + lambda_n.push_back( + std::make_pair( + land1.land[i][p].first , + oper( (double)land1.land[i][p].second , function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) ) + ) + ); + ++p; + continue; + } + if ( land1.land[i][p].first > land2.land[i][q].first ) + { + if ( operation_on_pair_of_landscapesDBG ) + { + std::cout << "Second \n"; + std::cout << "function_value("<< land1.land[i][p-1].first << " " << land1.land[i][p-1].second <<" ,"<< land1.land[i][p].first << " " << land1.land[i][p].second <<", " << land2.land[i][q].first<<" ) : " << function_value( land1.land[i][p-1] , land1.land[i][p-1] ,land2.land[i][q].first ) << "\n"; + std::cout << "oper( " << function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) <<"," << land2.land[i][q].second <<" : " << oper( land2.land[i][q].second , function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) ) << "\n"; + } + lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( function_value( land1.land[i][p] , land1.land[i][p-1] ,land2.land[i][q].first ) , land2.land[i][q].second ) ) ); + ++q; + continue; + } + if ( land1.land[i][p].first == land2.land[i][q].first ) + { + if (operation_on_pair_of_landscapesDBG)std::cout << "Third \n"; + lambda_n.push_back( std::make_pair( land2.land[i][q].first , oper( land1.land[i][p].second , land2.land[i][q].second ) ) ); + ++p;++q; + } + if (operation_on_pair_of_landscapesDBG){std::cout << "Next iteration \n";} + } + while ( (p+1 < land1.land[i].size())&&(q+1 >= land2.land[i].size()) ) + { + if (operation_on_pair_of_landscapesDBG) + { + std::cout << "New point : " << land1.land[i][p].first << " oper(land1.land[i][p].second,0) : " << oper(land1.land[i][p].second,0) << std::endl; + } + lambda_n.push_back( std::make_pair(land1.land[i][p].first , oper(land1.land[i][p].second,0) ) ); + ++p; + } + while ( (p+1 >= land1.land[i].size())&&(q+1 < land2.land[i].size()) ) + { + if (operation_on_pair_of_landscapesDBG) + { + std::cout << "New point : " << land2.land[i][q].first << " oper(0,land2.land[i][q].second) : " << oper(0,land2.land[i][q].second) << std::endl; + } + lambda_n.push_back( std::make_pair(land2.land[i][q].first , oper(0,land2.land[i][q].second) ) ); + ++q; + } + lambda_n.push_back( std::make_pair( std::numeric_limits<int>::max() , 0 ) ); + //CHANGE + //result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + if ( land1.land.size() > std::min( land1.land.size() , land2.land.size() ) ) + { + if (operation_on_pair_of_landscapesDBG){std::cout << "land1.land.size() > std::min( land1.land.size() , land2.land.size() )" << std::endl;} + for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i ) + { + std::vector< std::pair<double,double> > lambda_n( land1.land[i] ); + for ( size_t nr = 0 ; nr != land1.land[i].size() ; ++nr ) + { + lambda_n[nr] = std::make_pair( land1.land[i][nr].first , oper( land1.land[i][nr].second , 0 ) ); + } + //CHANGE + //result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + } + if ( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) ) + { + if (operation_on_pair_of_landscapesDBG){std::cout << "( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) ) " << std::endl;} + for ( size_t i = std::min( land1.land.size() , land2.land.size() ) ; i != std::max( land1.land.size() , land2.land.size() ) ; ++i ) + { + std::vector< std::pair<double,double> > lambda_n( land2.land[i] ); + for ( size_t nr = 0 ; nr != land2.land[i].size() ; ++nr ) + { + lambda_n[nr] = std::make_pair( land2.land[i][nr].first , oper( 0 , land2.land[i][nr].second ) ); + } + //CHANGE + //result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + } + if ( operation_on_pair_of_landscapesDBG ){std::cout << "operation_on_pair_of_landscapes END\n";std::cin.ignore();} + return result; +}//operation_on_pair_of_landscapes + + + +double compute_maximal_distance_non_symmetric( const Persistence_landscape& pl1, const Persistence_landscape& pl2 ) +{ + bool dbg = false; + if (dbg)std::cerr << " compute_maximal_distance_non_symmetric \n"; + //this distance is not symmetric. It compute ONLY distance between inflection points of pl1 and pl2. + double maxDist = 0; + size_t minimalNumberOfLevels = std::min( pl1.land.size() , pl2.land.size() ); + for ( size_t level = 0 ; level != minimalNumberOfLevels ; ++ level ) + { + if (dbg) + { + std::cerr << "Level : " << level << std::endl; + std::cerr << "PL1 : \n"; + for ( size_t i = 0 ; i != pl1.land[level].size() ; ++i ) + { + std::cerr << "(" <<pl1.land[level][i].first << "," << pl1.land[level][i].second << ") \n"; + } + std::cerr << "PL2 : \n"; + for ( size_t i = 0 ; i != pl2.land[level].size() ; ++i ) + { + std::cerr << "(" <<pl2.land[level][i].first << "," << pl2.land[level][i].second << ") \n"; + } + std::cin.ignore(); + } + + int p2Count = 0; + for ( size_t i = 1 ; i != pl1.land[level].size()-1 ; ++i ) //w tym przypadku nie rozwarzam punktow w nieskocznosci + { + while ( true ) + { + if ( (pl1.land[level][i].first>=pl2.land[level][p2Count].first) && (pl1.land[level][i].first<=pl2.land[level][p2Count+1].first) )break; + p2Count++; + } + double val = fabs( function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) - pl1.land[level][i].second); + if ( maxDist <= val )maxDist = val; + + if (dbg) + { + std::cerr << pl1.land[level][i].first <<"in [" << pl2.land[level][p2Count].first << "," << pl2.land[level][p2Count+1].first <<"] \n"; + std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl; + std::cerr << "function_value( pl2[level][p2Count] , pl2[level][p2Count+1] , pl1[level][i].first ) : " << function_value( pl2.land[level][p2Count] , pl2.land[level][p2Count+1] , pl1.land[level][i].first ) << std::endl; + std::cerr << "val : " << val << std::endl; + std::cin.ignore(); + } + } + } + + if (dbg)std::cerr << "minimalNumberOfLevels : " << minimalNumberOfLevels << std::endl; + + if ( minimalNumberOfLevels < pl1.land.size() ) + { + for ( size_t level = minimalNumberOfLevels ; level != pl1.land.size() ; ++ level ) + { + for ( size_t i = 0 ; i != pl1.land[level].size() ; ++i ) + { + if (dbg)std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl; + if ( maxDist < pl1.land[level][i].second )maxDist = pl1.land[level][i].second; + } + } + } + return maxDist; +} + + + + +double compute_distance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second , double p ) +{ + bool dbg = false; + //This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a time: + + //first-second : + Persistence_landscape lan = first-second; + + //| first-second |: + lan = lan.abs(); + + if ( dbg ){std::cerr << "Abs of difference ; " << lan << std::endl;getchar();} + + if ( p < std::numeric_limits<double>::max() ) + { + //\int_{- \infty}^{+\infty}| first-second |^p + double result; + if ( p != 1 ) + { + if ( dbg )std::cerr << "Power != 1, compute integral to the power p\n"; + result = lan.compute_integral_of_landscape( (double)p ); + } + else + { + if ( dbg )std::cerr << "Power = 1, compute integral \n"; + result = lan.compute_integral_of_landscape(); + } + //(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p) + return pow( result , 1/(double)p ); + } + else + { + //p == infty + if ( dbg )std::cerr << "Power = infty, compute maximum \n"; + return lan.compute_maximum(); + } +} + +double compute_max_norm_distance_of_landscapes( const Persistence_landscape& first, const Persistence_landscape& second ) +{ + return std::max( compute_maximal_distance_non_symmetric(first,second) , compute_maximal_distance_non_symmetric(second,first) ); +} + + +bool comparePairsForMerging( std::pair< double , unsigned > first , std::pair< double , unsigned > second ) +{ + return (first.first < second.first); +} + + + + +double compute_inner_product( const Persistence_landscape& l1 , const Persistence_landscape& l2 ) +{ + bool dbg = false; + double result = 0; + + for ( size_t level = 0 ; level != std::min( l1.size() , l2.size() ) ; ++level ) + { + if ( dbg ){std::cerr << "Computing inner product for a level : " << level << std::endl;getchar();} + if ( l1.land[level].size() * l2.land[level].size() == 0 )continue; + + //endpoints of the interval on which we will compute the inner product of two locally linear functions: + double x1 = -std::numeric_limits<int>::max(); + double x2; + if ( l1.land[level][1].first < l2.land[level][1].first ) + { + x2 = l1.land[level][1].first; + } + else + { + x2 = l2.land[level][1].first; + } + + //iterators for the landscapes l1 and l2 + size_t l1It = 0; + size_t l2It = 0; + + while ( (l1It < l1.land[level].size()-1) && (l2It < l2.land[level].size()-1) ) + { + //compute the value of a inner product on a interval [x1,x2] + + double a,b,c,d; + + if ( l1.land[level][l1It+1].first != l1.land[level][l1It].first ) + { + a = (l1.land[level][l1It+1].second - l1.land[level][l1It].second)/(l1.land[level][l1It+1].first - l1.land[level][l1It].first); + } + else + { + a = 0; + } + b = l1.land[level][l1It].second - a*l1.land[level][l1It].first; + if ( l2.land[level][l2It+1].first != l2.land[level][l2It].first ) + { + c = (l2.land[level][l2It+1].second - l2.land[level][l2It].second)/(l2.land[level][l2It+1].first - l2.land[level][l2It].first); + } + else + { + c = 0; + } + d = l2.land[level][l2It].second - c*l2.land[level][l2It].first; + + double contributionFromThisPart + = + (a*c*x2*x2*x2/3 + (a*d+b*c)*x2*x2/2 + b*d*x2) - (a*c*x1*x1*x1/3 + (a*d+b*c)*x1*x1/2 + b*d*x1); + + result += contributionFromThisPart; + + if ( dbg ) + { + std::cerr << "[l1.land[level][l1It].first,l1.land[level][l1It+1].first] : " << l1.land[level][l1It].first << " , " << l1.land[level][l1It+1].first << std::endl; + std::cerr << "[l2.land[level][l2It].first,l2.land[level][l2It+1].first] : " << l2.land[level][l2It].first << " , " << l2.land[level][l2It+1].first << std::endl; + std::cerr << "a : " << a << ", b : " << b << " , c: " << c << ", d : " << d << std::endl; + std::cerr << "x1 : " << x1 << " , x2 : " << x2 << std::endl; + std::cerr << "contributionFromThisPart : " << contributionFromThisPart << std::endl; + std::cerr << "result : " << result << std::endl; + getchar(); + } + + //we have two intervals in which functions are constant: + //[l1.land[level][l1It].first , l1.land[level][l1It+1].first] + //and + //[l2.land[level][l2It].first , l2.land[level][l2It+1].first] + //We also have an interval [x1,x2]. Since the intervals in the landscapes cover the whole R, then it is clear that x2 + //is either l1.land[level][l1It+1].first of l2.land[level][l2It+1].first or both. Lets test it. + if ( x2 == l1.land[level][l1It+1].first ) + { + if ( x2 == l2.land[level][l2It+1].first ) + { + //in this case, we increment both: + ++l2It; + if ( dbg ){std::cerr << "Incrementing both \n";} + } + else + { + if ( dbg ){std::cerr << "Incrementing first \n";} + } + ++l1It; + } + else + { + //in this case we increment l2It + ++l2It; + if ( dbg ){std::cerr << "Incrementing second \n";} + } + //Now, we shift x1 and x2: + x1 = x2; + if ( l1.land[level][l1It+1].first < l2.land[level][l2It+1].first ) + { + x2 = l1.land[level][l1It+1].first; + } + else + { + x2 = l2.land[level][l2It+1].first; + } + + } + + } + return result; +} + + +void Persistence_landscape::plot( const char* filename, double xRangeBegin , double xRangeEnd , double yRangeBegin , double yRangeEnd , int from , int to ) +{ + //this program create a gnuplot script file that allows to plot persistence diagram. + std::ofstream out; + + std::ostringstream nameSS; + nameSS << filename << "_GnuplotScript"; + std::string nameStr = nameSS.str(); + out.open( nameStr ); + + if ( (xRangeBegin != std::numeric_limits<double>::max()) || (xRangeEnd != std::numeric_limits<double>::max()) || (yRangeBegin != std::numeric_limits<double>::max()) || (yRangeEnd != std::numeric_limits<double>::max()) ) + { + out << "set xrange [" << xRangeBegin << " : " << xRangeEnd << "]" << std::endl; + out << "set yrange [" << yRangeBegin << " : " << yRangeEnd << "]" << std::endl; + } + + if ( from == std::numeric_limits<int>::max() ){from = 0;} + if ( to == std::numeric_limits<int>::max() ){to = this->land.size();} + + out << "plot "; + for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda ) + { + //out << " '-' using 1:2 title 'l" << lambda << "' with lp"; + out << " '-' using 1:2 notitle with lp"; + if ( lambda+1 != std::min((size_t)to,this->land.size()) ) + { + out << ", \\"; + } + out << std::endl; + } + + for ( size_t lambda= std::min((size_t)from,this->land.size()) ; lambda != std::min((size_t)to,this->land.size()) ; ++lambda ) + { + for ( size_t i = 1 ; i != this->land[lambda].size()-1 ; ++i ) + { + out << this->land[lambda][i].first << " " << this->land[lambda][i].second << std::endl; + } + out << "EOF" << std::endl; + } + std::cout << "Gnuplot script to visualize persistence diagram written to the file: " << nameStr << ". Type load '" << nameStr << "' in gnuplot to visualize." << std::endl; +} + + + + +}//namespace gudhi stat +}//namespace gudhi + + +#endif |