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diff --git a/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h new file mode 100644 index 00000000..5703163a --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h @@ -0,0 +1,1563 @@ +/** 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_landscape_on_grid_H_ +#define Persistence_landscape_on_grid_H_ + + +//standard include +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <cmath> +#include <limits> +#include <functional> +#include <functional> + + +//gudhi include + +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> + + + +namespace Gudhi +{ +namespace Persistence_representations +{ + +//predeclaration +class Persistence_landscape_on_grid; +template < typename operation > +Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid( const Persistence_landscape_on_grid& land1 , const Persistence_landscape_on_grid& land2 ); + +/** + * A clas implementing persistence landascpes by approximating them on a collection of grid points. * Persistence landscapes on grid 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 + * Note that at the moment, due to roundoff errors during the construction of persistence landscapes on a grid, elements which are different by 0.000005 are considered the same. If the scale in your persistence diagrams + * is comparable to this value, please rescale them before use this code. +**/ + +//this class 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_on_grid +{ +public: + /** + * Default constructor. + **/ + Persistence_landscape_on_grid() + { + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); + this->grid_min = this->grid_max = 0; + } + + /** + * Constructor that takes as an input a vector of birth-death pairs. + **/ + Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ ); + + + /** + * Constructor that takes as an input a vector of birth-death pairs, parameters of the grid and number of landscape function to be created. + **/ + Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ , unsigned number_of_levels_of_landscape ); + + /** + * 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. The additional parameters of this procedure are: ranges of grid, resoltion of a grid + * number of landscape functions to be created and the dimension of intervals that are need to be read from a file (in case of Gudhi format files). + **/ + Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , unsigned number_of_levels_of_landscape , unsigned short dimension_ = std::numeric_limits<unsigned short>::max() ); + + /** + * 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. The additional parameters of this procedure are: ranges of grid, resoltion of a grid + * and the dimension of intervals that are need to be read from a file (in case of Gudhi format files). + **/ + Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , unsigned short dimension_ = std::numeric_limits<unsigned short>::max() ); + + + /** + * 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. The additional parameter is the resoution of a grid and the number of landscape + * functions to be created. The remaning parameters are calculated based on data. + **/ + Persistence_landscape_on_grid(const char* filename , size_t number_of_points , unsigned number_of_levels_of_landscape , unsigned short dimension = std::numeric_limits<unsigned short>::max() ); + + /** + * 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. The additional parameter is the resoution of a grid. The last parameter is the dimension + * of a persistence to read from the file. If your file contains only persistence pair in a single dimension, please set it up to std::numeric_limits<unsigned>::max(). + * The remaning parameters are calculated based on data. + **/ + Persistence_landscape_on_grid(const char* filename , size_t number_of_points , unsigned short dimension = std::numeric_limits<unsigned short>::max() ); + + + /** + * 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 + { + size_t maximal_level = this->number_of_nonzero_levels(); + double result = 0; + for ( size_t i = 0 ; i != maximal_level ; ++i ) + { + result += this->compute_integral_of_landscape(i); + } + return result; + } + + + /** + * This function compute integral of the 'level'-level of a landscape. + **/ + double compute_integral_of_landscape( size_t level )const + { + bool dbg = false; + double result = 0; + double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1); + + if ( dbg ) + { + std::cerr << "this->grid_max : " << this->grid_max << std::endl; + std::cerr << "this->grid_min : " << this->grid_min << std::endl; + std::cerr << "this->values_of_landscapes.size() : " << this->values_of_landscapes.size() << std::endl; + getchar(); + } + + + double previous_x = this->grid_min-dx; + double previous_y = 0; + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + double current_x = previous_x + dx; + double current_y = 0; + if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level]; + + if ( dbg ) + { + std::cerr << "this->values_of_landscapes[i].size() : " << this->values_of_landscapes[i].size() << " , level : " << level << std::endl; + if ( this->values_of_landscapes[i].size() > level )std::cerr << "this->values_of_landscapes[i][level] : " << this->values_of_landscapes[i][level] << std::endl; + std::cerr << "previous_y : " << previous_y << std::endl; + std::cerr << "current_y : " << current_y << std::endl; + std::cerr << "dx : " << dx << std::endl; + std::cerr << "0.5*dx*( previous_y + current_y ); " << 0.5*dx*( previous_y + current_y ) << std::endl; + } + + result += 0.5*dx*( previous_y + current_y ); + previous_x = current_x; + previous_y = current_y; + } + return result; + } + + /** + * 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 + { + size_t maximal_level = this->number_of_nonzero_levels(); + double result = 0; + for ( size_t i = 0 ; i != maximal_level ; ++i ) + { + result += this->compute_integral_of_landscape(p,i); + } + return result; + } + + /** + * This function compute integral of the landscape p-th power of a level 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 , size_t level )const + { + bool dbg = false; + + double result = 0; + double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1); + double previous_x = this->grid_min; + double previous_y = 0; + if ( this->values_of_landscapes[0].size() > level )previous_y = this->values_of_landscapes[0][level]; + + if ( dbg ) + { + std::cerr << "dx : " << dx << std::endl; + std::cerr << "previous_x : " << previous_x << std::endl; + std::cerr << "previous_y : " << previous_y << std::endl; + std::cerr << "power : " << p << std::endl; + getchar(); + } + + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + double current_x = previous_x + dx; + double current_y = 0; + if ( this->values_of_landscapes[i].size() > level )current_y = this->values_of_landscapes[i][level]; + + if ( dbg )std::cerr << "current_y : " << current_y << std::endl; + + if ( current_y == previous_y )continue; + + std::pair<double,double> coef = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y ) , std::make_pair( current_x , current_y ) ); + double a = coef.first; + double b = coef.second; + + if ( dbg ) + { + std::cerr << "A line passing through points : (" << previous_x << "," << previous_y << ") and (" << current_x << "," << current_y << ") is : " << a << "x+" << b << std::endl; + } + + //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) + double value_to_add = 0; + if ( a != 0 ) + { + value_to_add = 1/(a*(p+1)) * ( pow((a*current_x+b),p+1) - pow((a*previous_x+b),p+1)); + } + else + { + value_to_add = ( current_x - previous_x )*( pow(b,p) ); + } + result += value_to_add; + if ( dbg ) + { + std::cerr << "Increasing result by : " << value_to_add << std::endl; + std::cerr << "restult : " << result << std::endl; + getchar(); + } + previous_x = current_x; + previous_y = current_y; + } + if ( dbg )std::cerr << "The total result is : " << result << std::endl; + return result; + } + + /** + * 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, const Persistence_landscape_on_grid& land ) + { + double dx = (land.grid_max - land.grid_min)/(double)(land.values_of_landscapes.size()-1); + double x = land.grid_min; + for ( size_t i = 0 ; i != land.values_of_landscapes.size() ; ++i ) + { + out << x << " : "; + for ( size_t j = 0 ; j != land.values_of_landscapes[i].size() ; ++j ) + { + out << land.values_of_landscapes[i][j] << " "; + } + out << std::endl; + x += dx; + } + return out; + } + + template < typename oper > + friend Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid( const Persistence_landscape_on_grid& land1 , const Persistence_landscape_on_grid& land2 ); + + + /** + * 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 + { + bool dbg = false; + if ( (x < this->grid_min) || (x > this->grid_max) )return 0; + + //find a position of a vector closest to x: + double dx = (this->grid_max - this->grid_min)/(double)(this->values_of_landscapes.size()-1); + size_t position = size_t((x-this->grid_min)/dx); + + if ( dbg ) + { + std::cerr << "This is a procedure compute_value_at_a_given_point \n"; + std::cerr << "level : " << level << std::endl; + std::cerr << "x : " << x << std::endl; + std::cerr << "psoition : " << position << std::endl; + } + //check if we are not exacly in the grid point: + if ( almost_equal( position*dx+ this->grid_min , x) ) + { + if ( this->values_of_landscapes[position].size() < level ) + { + return this->values_of_landscapes[position][level]; + } + else + { + return 0; + } + } + //in the other case, approximate with a line: + std::pair<double,double> line; + if ( (this->values_of_landscapes[position].size() > level) && (this->values_of_landscapes[position+1].size() > level) ) + { + line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) ); + } + else + { + if ( (this->values_of_landscapes[position].size() > level) || (this->values_of_landscapes[position+1].size() > level) ) + { + if ( (this->values_of_landscapes[position].size() > level) ) + { + line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , this->values_of_landscapes[position][level] ) , std::make_pair( (position+1)*dx+ this->grid_min , 0 ) ); + } + else + { + //(this->values_of_landscapes[position+1].size() > level) + line = compute_parameters_of_a_line( std::make_pair( position*dx+ this->grid_min , 0 ) , std::make_pair( (position+1)*dx+ this->grid_min , this->values_of_landscapes[position+1][level] ) ); + } + } + else + { + return 0; + } + } + //compute the value of the linear function parametrized by line on a point x: + return line.first*x+line.second; + } + + + public: + /** + *\private A function that compute sum of two landscapes. + **/ + friend Persistence_landscape_on_grid add_two_landscapes ( const Persistence_landscape_on_grid& land1 , const Persistence_landscape_on_grid& land2 ) + { + return operation_on_pair_of_landscapes_on_grid< std::plus<double> >(land1,land2); + } + + /** + *\private A function that compute difference of two landscapes. + **/ + friend Persistence_landscape_on_grid subtract_two_landscapes ( const Persistence_landscape_on_grid& land1 , const Persistence_landscape_on_grid& land2 ) + { + return operation_on_pair_of_landscapes_on_grid< std::minus<double> >(land1,land2); + } + + /** + * An operator +, that compute sum of two landscapes. + **/ + friend Persistence_landscape_on_grid operator+( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second ) + { + return add_two_landscapes( first,second ); + } + + /** + * An operator -, that compute difference of two landscapes. + **/ + friend Persistence_landscape_on_grid operator-( const Persistence_landscape_on_grid& first , const Persistence_landscape_on_grid& second ) + { + return subtract_two_landscapes( first,second ); + } + + /** + * An operator * that allows multipilication of a landscape by a real number. + **/ + friend Persistence_landscape_on_grid operator*( const Persistence_landscape_on_grid& 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_on_grid operator*( double con , const Persistence_landscape_on_grid& first ) + { + return first.multiply_lanscape_by_real_number_not_overwrite(con); + } + + friend bool check_if_defined_on_the_same_domain( const Persistence_landscape_on_grid& land1, const Persistence_landscape_on_grid& land2 ) + { + if ( land1.values_of_landscapes.size() != land2.values_of_landscapes.size() )return false; + if ( land1.grid_min != land2.grid_min )return false; + if ( land1.grid_max != land2.grid_max )return false; + return true; + } + + /** + * Operator +=. The second parameter is persistnece landwscape. + **/ + Persistence_landscape_on_grid operator += ( const Persistence_landscape_on_grid& rhs ) + { + *this = *this + rhs; + return *this; + } + + /** + * Operator -=. The second parameter is persistnece landwscape. + **/ + Persistence_landscape_on_grid operator -= ( const Persistence_landscape_on_grid& 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_on_grid operator *= ( double x ) + { + *this = *this*x; + return *this; + } + + /** + * Operator /=. The second parameter is a real number. + **/ + Persistence_landscape_on_grid 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_on_grid& rhs )const + { + bool dbg = true; + if ( this->values_of_landscapes.size() != rhs.values_of_landscapes.size() ) + { + if (dbg) std::cerr << "values_of_landscapes of incompatable sizes\n"; + return false; + } + if ( !almost_equal( this->grid_min , rhs.grid_min ) ) + { + if (dbg) std::cerr << "grid_min not equal\n"; + return false; + } + if ( !almost_equal(this->grid_max,rhs.grid_max ) ) + { + if (dbg) std::cerr << "grid_max not equal\n"; + return false; + } + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + for ( size_t aa = 0 ; aa != this->values_of_landscapes[i].size() ; ++aa ) + { + if ( !almost_equal( this->values_of_landscapes[i][aa] , rhs.values_of_landscapes[i][aa] ) ) + { + if (dbg) + { + std::cerr << "Problem in the position : " << i << " of values_of_landscapes. \n"; + std::cerr << this->values_of_landscapes[i][aa] << " " << rhs.values_of_landscapes[i][aa] << std::endl; + } + return false; + } + } + } + return true; + } + + + /** + * An operator to compare two persistence landscapes. + **/ + bool operator != ( const Persistence_landscape_on_grid& rhs )const + { + return !((*this) == rhs); + } + + + /** + * Computations of maximum (y) value of landscape. + **/ + double compute_maximum()const + { + //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays: + double max_value = -std::numeric_limits<double>::max(); + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + if ( this->values_of_landscapes[i].size() ) + { + if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0]; + if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ]; + } + } + return max_value; + } + + /** + * Computations of minimum and maximum value of landscape. + **/ + std::pair<double,double> compute_minimum_maximum()const + { + //since the function can only be entirely positive or negative, the maximal value will be an extremal value in the arrays: + double max_value = -std::numeric_limits<double>::max(); + double min_value = 0; + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + if ( this->values_of_landscapes[i].size() ) + { + if ( this->values_of_landscapes[i][0] > max_value )max_value = this->values_of_landscapes[i][0]; + if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] > max_value )max_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ]; + + if ( this->values_of_landscapes[i][0] < min_value )min_value = this->values_of_landscapes[i][0]; + if ( this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] < min_value )min_value = this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ]; + } + } + return std::make_pair(min_value , max_value); + } + + /** + * 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 + { + return std::make_pair( this->grid_min , this->grid_max ); + //std::pair< double , double > result; + //if ( level < this->land.size() ) + //{ + // double dx = (this->grid_max - this->grid_min)/(double)this->values_of_landscapes.size(); + // size_t first_nonzero = 0; + // while ( (first_nonzero != this->values_of_landscapes.size()) && (this->values_of_landscapes[level][first_nonzero] == 0) )++first_nonzero; + // + // if ( first_nonzero == 0 ) + // { + // return std::make_pair( 0,0 );//this landscape is empty. + // } + // + // size_t last_nonzero = 0; + // while ( (last_nonzero != 0) && (this->values_of_landscapes[level][last_nonzero] == 0) )--last_nonzero; + // + // result = std::make_pair( this->grid_min +first_nonzero*dx , this->grid_max - last_nonzero*dx ); + //} + //else + //{ + // result = std::make_pair( 0,0 ); + //} + //return result; + } + + /** + * This procedure returns y-range of a 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 + { + return this->compute_minimum_maximum(); + //std::pair< double , double > result; + //if ( level < this->land.size() ) + //{ + // result = this->compute_minimum_maximum() + //} + //else + //{ + // result = std::make_pair( 0,0 ); + //} + //return result; + } + + /** + * This function computes maximal lambda for which lambda-level landscape is nonzero. + **/ + size_t number_of_nonzero_levels()const + { + size_t result = 0; + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + if ( this->values_of_landscapes[i].size() > result )result = this->values_of_landscapes[i].size(); + } + return result; + } + + /** + * Computations of a \f$L^i\f$ norm of landscape, where i is the input parameter. + **/ + double compute_norm_of_landscape( double i )const + { + std::vector< std::pair< double , double > > p; + Persistence_landscape_on_grid l(p,this->grid_min,this->grid_max,this->values_of_landscapes.size()-1); + + if ( i < std::numeric_limits<double>::max() ) + { + return compute_distance_of_landscapes_on_grid(*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);} + + /** + * Computations of \f$L^{\infty}\f$ distance between two landscapes. + **/ + friend double compute_max_norm_distance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second ); + //friend double compute_max_norm_distance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second , unsigned& nrOfLand , double&x , double& y1, double& y2 ); + + + + + /** + * 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. + **/ + void abs() + { + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j ) + { + this->values_of_landscapes[i][j] = std::abs( this->values_of_landscapes[i][j] ); + } + } + } + + /** + * Computes the number of landscape functions. + **/ + size_t size()const{return this->number_of_nonzero_levels(); } + + /** + * Computate maximal value of lambda-level landscape. + **/ + double find_max( unsigned lambda )const + { + double max_value = -std::numeric_limits<double>::max(); + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + if ( this->values_of_landscapes[i].size() > lambda ) + { + if ( this->values_of_landscapes[i][lambda] > max_value )max_value = this->values_of_landscapes[i][lambda]; + } + } + return max_value; + } + + /** + * Function to compute inner (scalar) product of two landscapes. + **/ + friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 ) + { + if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate"; + size_t maximal_level = l1.number_of_nonzero_levels(); + double result = 0; + for ( size_t i = 0 ; i != maximal_level ; ++i ) + { + result += compute_inner_product(l1,l2,i); + } + return result; + } + + + + /** + * Function to compute inner (scalar) product of given levels of two landscapes. + **/ + friend double compute_inner_product( const Persistence_landscape_on_grid& l1 , const Persistence_landscape_on_grid& l2 , size_t level ) + { + bool dbg = false; + + if ( !check_if_defined_on_the_same_domain(l1,l2) )throw "Landscapes are not defined on the same grid, the program will now terminate"; + double result = 0; + + double dx = (l1.grid_max - l1.grid_min)/(double)(l1.values_of_landscapes.size()-1); + + double previous_x = l1.grid_min-dx; + double previous_y_l1 = 0; + double previous_y_l2 = 0; + for ( size_t i = 0 ; i != l1.values_of_landscapes.size() ; ++i ) + { + if ( dbg )std::cerr << "i : " << i << std::endl; + + double current_x = previous_x + dx; + double current_y_l1 = 0; + if ( l1.values_of_landscapes[i].size() > level )current_y_l1 = l1.values_of_landscapes[i][level]; + + double current_y_l2 = 0; + if ( l2.values_of_landscapes[i].size() > level )current_y_l2 = l2.values_of_landscapes[i][level]; + + if ( dbg ) + { + std::cerr << "previous_x : " << previous_x << std::endl; + std::cerr << "previous_y_l1 : " << previous_y_l1 << std::endl; + std::cerr << "current_y_l1 : " << current_y_l1 << std::endl; + std::cerr << "previous_y_l2 : " << previous_y_l2 << std::endl; + std::cerr << "current_y_l2 : " << current_y_l2 << std::endl; + } + + std::pair<double,double> l1_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l1 ) , std::make_pair( current_x , current_y_l1 ) ); + std::pair<double,double> l2_coords = compute_parameters_of_a_line( std::make_pair( previous_x , previous_y_l2 ) , std::make_pair( current_x , current_y_l2 ) ); + + //let us assume that the first line is of a form y = ax+b, and the second one is of a form y = cx + d. Then here are a,b,c,d: + double a = l1_coords.first; + double b = l1_coords.second; + + double c = l2_coords.first; + double d = l2_coords.second; + + if ( dbg ) + { + std::cerr << "Here are the formulas for a line: \n"; + std::cerr << "a : " << a << std::endl; + std::cerr << "b : " << b << std::endl; + std::cerr << "c : " << c << std::endl; + std::cerr << "d : " << d << std::endl; + } + + //now, to compute the inner product in this interval we need to compute the integral of (ax+b)(cx+d) = acx^2 + (ad+bc)x + bd in the interval from previous_x to current_x: + //The integal is ac/3*x^3 + (ac+bd)/2*x^2 + bd*x + + double added_value = (a*c/3*current_x*current_x*current_x + (a*d+b*c)/2*current_x*current_x + b*d*current_x)- + (a*c/3*previous_x*previous_x*previous_x + (a*d+b*c)/2*previous_x*previous_x + b*d*previous_x); + + if ( dbg ) + { + std::cerr << "Value of the integral on the left end ie : " << previous_x << " is : " << a*c/3*previous_x*previous_x*previous_x + (a*d+b*c)/2*previous_x*previous_x + b*d*previous_x << std::endl; + std::cerr << "Value of the integral on the right end i.e. : " << current_x << " is " << a*c/3*current_x*current_x*current_x + (a*d+b*c)/2*current_x*current_x + b*d*current_x << std::endl; + } + + result += added_value; + + if ( dbg ) + { + std::cerr << "added_value : " << added_value << std::endl; + std::cerr << "result : " << result << std::endl; + getchar(); + } + + + previous_x = current_x; + previous_y_l1 = current_y_l1; + previous_y_l2 = current_y_l2; + + } + return result; + } + + + /** + * Computations of \f$L^{p}\f$ distance between two landscapes on a grid. p is the parameter of the procedure. + * FIXME: Note that, due to the grid representation, the method below may give non--accurate results in case when the landscape P and Q the difference of which we want to compute + * are interxsecting. This is a consequence of a general way they are computed. In the future, an integral of absolute value of a difference of P and Q will be given as a separated + * function to fix that inaccuracy. + **/ + friend double compute_distance_of_landscapes_on_grid( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& 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: + + if ( dbg ) + { + std::cerr << "first : " << first << std::endl; + std::cerr << "second : " << second << std::endl; + getchar(); + } + + //first-second : + Persistence_landscape_on_grid lan = first-second; + + if ( dbg ) + { + std::cerr << "Difference : " << lan << std::endl; + } + + //| first-second |: + lan.abs(); + + if ( dbg ) + { + std::cerr << "Abs : " << lan << std::endl; + } + + if ( p < std::numeric_limits< double >::max() ) + { + //\int_{- \infty}^{+\infty}| first-second |^p + double result; + if ( p != 1 ) + { + if (dbg){std::cerr << "p : " << p << std::endl; getchar();} + result = lan.compute_integral_of_landscape( (double)p ); + if (dbg){std::cerr << "integral : " << result << std::endl;getchar();} + } + else + { + result = lan.compute_integral_of_landscape(); + if (dbg){std::cerr << "integral, wihtout power : " << result << std::endl;getchar();} + } + //(\int_{- \infty}^{+\infty}| first-second |^p)^(1/p) + return pow( result , 1/(double)p ); + } + else + { + //p == infty + return lan.compute_maximum(); + } + } + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + //Functions that are needed for that class to implement the concept. + + /** + * 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. + * At the moment this function is not tested, since it is quite likelly to be changed in the future. Given this, when using it, keep in mind that it + * will be most likelly changed in the next versions. + **/ + double project_to_R( int number_of_function )const + { + return this->compute_integral_of_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 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 + if ( ( number_of_function < 0 ) || ( (size_t)number_of_function >= this->values_of_landscapes.size() ) ) + { + throw "Wrong number of function\n"; + } + std::vector<double> v( this->values_of_landscapes.size() ); + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + v[i] = 0; + if ( this->values_of_landscapes[i].size() > (size_t)number_of_function ) + { + v[ i ] = this->values_of_landscapes[i][number_of_function]; + } + } + 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 number_of_functions_for_vectorization; + } + + + + + + /** + * A function to compute averaged persistence landscape on a grid, based on vector of persistence landscapes on grid. + * This function is required by Topological_data_with_averages concept. + **/ + void compute_average( const std::vector< Persistence_landscape_on_grid* >& to_average ) + { + + bool dbg = false; + //After execution of this procedure, the average is supposed to be in the current object. To make sure that this is the case, we need to do some cleaning first. + this->values_of_landscapes .clear(); + this->grid_min = this->grid_max = 0; + + //if there is nothing to averate, then the average is a zero landscape. + if ( to_average.size() == 0 )return; + + //now we need to check if the grids in all objects of to_average are the same: + for ( size_t i = 0 ; i != to_average.size() ; ++i ) + { + if ( !check_if_defined_on_the_same_domain(*(to_average[0]),*(to_average[i])) )throw "Two grids are not compatible"; + } + + this->values_of_landscapes = std::vector< std::vector<double> >( (to_average[0])->values_of_landscapes.size() ); + this->grid_min = (to_average[0])->grid_min; + this->grid_max = (to_average[0])->grid_max; + + if ( dbg ) + { + std::cerr << "Computations of average. The data from the current landscape have been cleared. We are ready to do the computations. \n"; + } + + //for every point in the grid: + for ( size_t grid_point = 0 ; grid_point != (to_average[0])->values_of_landscapes.size() ; ++grid_point ) + { + + //set up a vector of the correct size: + size_t maximal_size_of_vector = 0; + for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no ) + { + if ( (to_average[land_no])->values_of_landscapes[grid_point].size() > maximal_size_of_vector ) + maximal_size_of_vector = (to_average[land_no])->values_of_landscapes[grid_point].size(); + } + this->values_of_landscapes[grid_point] = std::vector<double>( maximal_size_of_vector ); + + if ( dbg ) + { + std::cerr << "We are considering the point : " << grid_point << " of the grid. In this point, there are at most : " << maximal_size_of_vector << " nonzero landscape functions \n"; + } + + //and compute an arythmetic average: + for ( size_t land_no = 0 ; land_no != to_average.size() ; ++land_no ) + { + //summing: + for ( size_t i = 0 ; i != (to_average[land_no])->values_of_landscapes[grid_point].size() ; ++i ) + { + //compute the average in a smarter way. + this->values_of_landscapes[grid_point][i] += (to_average[land_no])->values_of_landscapes[grid_point][i]; + } + } + //normalizing: + for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i ) + { + this->values_of_landscapes[grid_point][i] /= (double)to_average.size(); + } + } + }//compute_average + + + /** + * A function to compute distance between persistence landscape on a grid. + * The parameter of this functionis a Persistence_landscape_on_grid. + * 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_on_grid& second , double power = 1 )const + { + if ( power < std::numeric_limits<double>::max() ) + { + return compute_distance_of_landscapes_on_grid( *this , second , power ); + } + else + { + return compute_max_norm_distance_of_landscapes( *this , second ); + } + } + + /** + * A function to compute scalar product of persistence landscape on a grid. + * The parameter of this functionis a Persistence_landscape_on_grid. + * This function is required in Topological_data_with_scalar_product concept. + **/ + double compute_scalar_product( const Persistence_landscape_on_grid& second ) + { + return compute_inner_product( (*this) , second ); + } + + //end of implementation of functions needed for concepts. + + + + + + + + + + + + + + + + + + + + + /** + * A function that returns values of landsapes. It can be used for vizualization + **/ + std::vector< std::vector< double > > output_for_visualization()const + { + return this->values_of_landscapes; + } + + /** + * function used to create a gnuplot script for visualization of landscapes. Over here we need to specify which landscapes do we want to plot. + * In addition, the user may specify the range (min and max) where landscape is plot. The fefault values for min and max are std::numeric_limits<double>::max(). If the procedure detect those + * values, it will determine the range so that the whole landscape is supported there. If at least one min or max value is different from std::numeric_limits<double>::max(), then the values + * provided by the user will be used. + **/ + void plot( const char* filename , size_t from_ , size_t to_ )const + { + this->plot( filename , std::numeric_limits<double>::max() , std::numeric_limits<double>::max(), std::numeric_limits<double>::max() , std::numeric_limits<double>::max() , from_ , to_ ); + } + + /** + * function used to create a gnuplot script for visualization of landscapes. Over here we can restrict also x and y range of the landscape. + **/ + void plot( const char* filename, double min_x = std::numeric_limits<double>::max() , double max_x = std::numeric_limits<double>::max() , double min_y = std::numeric_limits<double>::max() , double max_y = std::numeric_limits<double>::max() , size_t from_ = std::numeric_limits<size_t>::max(), size_t to_= std::numeric_limits<size_t>::max() )const; + + +protected: + double grid_min; + double grid_max; + std::vector< std::vector< double > > values_of_landscapes; + size_t number_of_functions_for_vectorization; + size_t number_of_functions_for_projections_to_reals; + + void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals() + { + //warning, this function can be only called after filling in the values_of_landscapes vector. + this->number_of_functions_for_vectorization = this->values_of_landscapes.size(); + this->number_of_functions_for_projections_to_reals = this->values_of_landscapes.size(); + } + void set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ , unsigned number_of_levels = std::numeric_limits<unsigned>::max() ); + Persistence_landscape_on_grid multiply_lanscape_by_real_number_not_overwrite( double x )const; +}; + + +void Persistence_landscape_on_grid::set_up_values_of_landscapes( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_, unsigned number_of_levels ) +{ + bool dbg = false; + if ( dbg ) + { + std::cerr << "Here is the procedure : set_up_values_of_landscapes. The parameters are : grid_min_ : " << grid_min_ << ", grid_max_ : " << grid_max_ << ", number_of_points_ : " << number_of_points_ << ", number_of_levels: " << number_of_levels << std::endl; + std::cerr << "Here are the intervals at our disposal : \n"; + for ( size_t i = 0 ; i != p.size() ; ++i ) + { + std::cerr << p[i].first << " , " << p[i].second << std::endl; + } + } + + if ( (grid_min_ == std::numeric_limits<double>::max()) || (grid_max_ == std::numeric_limits<double>::max()) ) + { + //in this case, we need to find grid_min_ and grid_min_ based on the data. + double min = std::numeric_limits<double>::max(); + double max = std::numeric_limits<double>::min(); + for ( size_t i = 0 ; i != p.size() ; ++i ) + { + if ( p[i].first < min )min = p[i].first; + if ( p[i].second > max )max = p[i].second; + } + if ( grid_min_ == std::numeric_limits<double>::max() ) + { + grid_min_ = min; + } + else + { + //in this case grid_max_ == std::numeric_limits<double>::max() + grid_max_ = max; + } + } + + //if number_of_levels == std::numeric_limits<size_t>::max(), then we will have all the nonzero values of landscapes, and will store them in a vector + //if number_of_levels != std::numeric_limits<size_t>::max(), then we will use those vectors as heaps. + this->values_of_landscapes = std::vector< std::vector< double > >( number_of_points_+1 ); + + + this->grid_min = grid_min_; + this->grid_max = grid_max_; + + if ( grid_max_ <= grid_min_ ) + { + throw "Wrong parameters of grid_min and grid_max given to the procedure. THe grid have negative, or zero size. The program will now terminate.\n"; + } + + double dx = ( grid_max_ - grid_min_ )/(double)(number_of_points_); + //for every interval in the diagram: + for ( size_t int_no = 0 ; int_no != p.size() ; ++int_no ) + { + size_t grid_interval_begin = (p[int_no].first-grid_min_)/dx; + size_t grid_interval_end = (p[int_no].second-grid_min_)/dx; + size_t grid_interval_midpoint = (size_t)(0.5*(grid_interval_begin+grid_interval_end)); + + if ( dbg ) + { + std::cerr << "Considering an interval : " << p[int_no].first << "," << p[int_no].second << std::endl; + + std::cerr << "grid_interval_begin : " << grid_interval_begin << std::endl; + std::cerr << "grid_interval_end : " << grid_interval_end << std::endl; + std::cerr << "grid_interval_midpoint : " << grid_interval_midpoint << std::endl; + } + + double landscape_value = dx; + for ( size_t i = grid_interval_begin+1 ; i < grid_interval_midpoint ; ++i ) + { + if ( dbg ) + { + std::cerr << "Adding landscape value (going up) for a point : " << i << " equal : " << landscape_value << std::endl; + } + if ( number_of_levels != std::numeric_limits<unsigned>::max() ) + { + //we have a heap of no more that number_of_levels values. + //Note that if we are using heaps, we want to know the shortest distance in the heap. + //This is achieved by putting -distance to the heap. + if ( this->values_of_landscapes[i].size() >= number_of_levels ) + { + //in this case, the full heap is build, and we need to check if the landscape_value is not larger than the smallest element in the heap. + if ( -landscape_value < this->values_of_landscapes[i].front() ) + { + //if it is, we remove the largest value in the heap, and move on. + std::pop_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] = -landscape_value; + std::push_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + } + } + else + { + + //in this case we are still filling in the array. + this->values_of_landscapes[i].push_back( -landscape_value ); + if ( this->values_of_landscapes[i].size() == number_of_levels-1 ) + { + //this->values_of_landscapes[i].size() == number_of_levels + //in this case we need to create the heep. + std::make_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + } + } + } + else + { + //we have vector of all values + this->values_of_landscapes[i].push_back( landscape_value ); + } + landscape_value += dx; + } + for ( size_t i = grid_interval_midpoint ; i <= grid_interval_end ; ++i ) + { + if ( landscape_value > 0 ) + { + if ( number_of_levels != std::numeric_limits< unsigned >::max() ) + { + //we have a heap of no more that number_of_levels values + if ( this->values_of_landscapes[i].size() >= number_of_levels ) + { + //in this case, the full heap is build, and we need to check if the landscape_value is not larger than the smallest element in the heap. + if ( -landscape_value < this->values_of_landscapes[i].front() ) + { + //if it is, we remove the largest value in the heap, and move on. + std::pop_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + this->values_of_landscapes[i][ this->values_of_landscapes[i].size()-1 ] = -landscape_value; + std::push_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + } + } + else + { + + //in this case we are still filling in the array. + this->values_of_landscapes[i].push_back( -landscape_value ); + if ( this->values_of_landscapes[i].size() == number_of_levels-1 ) + { + //this->values_of_landscapes[i].size() == number_of_levels + //in this case we need to create the heep. + std::make_heap (this->values_of_landscapes[i].begin(),this->values_of_landscapes[i].end()); + } + } + } + else + { + this->values_of_landscapes[i].push_back( landscape_value ); + } + + + if ( dbg ) + { + std::cerr << "AAdding landscape value (going down) for a point : " << i << " equal : " << landscape_value << std::endl; + } + } + landscape_value -= dx; + } + } + + if ( number_of_levels != std::numeric_limits< unsigned >::max() ) + { + //in this case, vectors are used as heaps. And, since we want to have the smallest element at the top of + //each heap, we store mminus distances. To get if right at the end, we need to multiply each value + //in the heap by -1 to get real vector of distances. + for ( size_t pt = 0 ; pt != this->values_of_landscapes.size() ; ++pt ) + { + //std::cerr << this->values_of_landscapes[pt].size() <<std::endl; + for ( size_t j = 0 ; j != this->values_of_landscapes[pt].size() ; ++j ) + { + this->values_of_landscapes[pt][j] *= -1; + } + } + } + + //and now we need to sort the values: + for ( size_t pt = 0 ; pt != this->values_of_landscapes.size() ; ++pt ) + { + std::sort( this->values_of_landscapes[pt].begin() , this->values_of_landscapes[pt].end() , std::greater<double>() ); + } +}//set_up_values_of_landscapes + + + +Persistence_landscape_on_grid::Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ ) +{ + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ ); +}//Persistence_landscape_on_grid + + +Persistence_landscape_on_grid::Persistence_landscape_on_grid( const std::vector< std::pair< double , double > >& p , double grid_min_ , double grid_max_ , size_t number_of_points_ , unsigned number_of_levels_of_landscape ) +{ + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ , number_of_levels_of_landscape ); +} + + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , unsigned short dimension ) +{ + std::vector< std::pair< double , double > > p; + if ( dimension == std::numeric_limits<unsigned short>::max() ) + { + p = read_persistence_intervals_in_one_dimension_from_file( filename ); + } + else + { + p = read_persistence_intervals_in_one_dimension_from_file( filename , dimension ); + } + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ ); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , double grid_min_, double grid_max_ , size_t number_of_points_, unsigned number_of_levels_of_landscape, unsigned short dimension ) +{ + std::vector< std::pair< double , double > > p; + if ( dimension == std::numeric_limits<unsigned short>::max() ) + { + p = read_persistence_intervals_in_one_dimension_from_file( filename ); + } + else + { + p = read_persistence_intervals_in_one_dimension_from_file( filename , dimension ); + } + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ , number_of_levels_of_landscape ); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , size_t number_of_points_ , unsigned short dimension ) +{ + std::vector< std::pair< double , double > > p; + if ( dimension == std::numeric_limits<unsigned short>::max() ) + { + p = read_persistence_intervals_in_one_dimension_from_file( filename ); + } + else + { + p = read_persistence_intervals_in_one_dimension_from_file( filename , dimension ); + } + double grid_min_ = std::numeric_limits<double>::max(); + double grid_max_ = -std::numeric_limits<double>::max(); + for ( size_t i = 0 ; i != p.size() ; ++i ) + { + if ( p[i].first < grid_min_ )grid_min_ = p[i].first; + if ( p[i].second > grid_max_ )grid_max_ = p[i].second; + } + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ ); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename , size_t number_of_points_ , unsigned number_of_levels_of_landscape , unsigned short dimension ) +{ + std::vector< std::pair< double , double > > p; + if ( dimension == std::numeric_limits<unsigned short>::max() ) + { + p = read_persistence_intervals_in_one_dimension_from_file( filename ); + } + else + { + p = read_persistence_intervals_in_one_dimension_from_file( filename , dimension ); + } + double grid_min_ = std::numeric_limits<double>::max(); + double grid_max_ = -std::numeric_limits<double>::max(); + for ( size_t i = 0 ; i != p.size() ; ++i ) + { + if ( p[i].first < grid_min_ )grid_min_ = p[i].first; + if ( p[i].second > grid_max_ )grid_max_ = p[i].second; + } + this->set_up_values_of_landscapes( p , grid_min_ , grid_max_ , number_of_points_ , number_of_levels_of_landscape ); +} + + +void Persistence_landscape_on_grid::load_landscape_from_file( const char* filename ) +{ + std::ifstream in; + in.open( filename ); + //check if the file exist. + if ( !in.good() ) + { + 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"; + } + + size_t number_of_points_in_the_grid = 0; + in >> this->grid_min >> this->grid_max >> number_of_points_in_the_grid; + + std::vector< std::vector< double > > v(number_of_points_in_the_grid); + std::string line; + std::getline(in, line); + double number; + for ( size_t i = 0 ; i != number_of_points_in_the_grid ; ++i ) + { + //read a line of a file and convert it to a vector. + std::vector< double > vv; + std::getline(in, line); + //std::cerr << "Reading line : " << line << std::endl;getchar(); + std::istringstream stream(line); + while (stream >> number) + { + vv.push_back(number); + } + v[i] = vv; + } + this->values_of_landscapes = v; + in.close(); +} + +void Persistence_landscape_on_grid::print_to_file( const char* filename )const +{ + std::ofstream out; + out.open( filename ); + + //first we store the parameters of the grid: + out << grid_min << std::endl << grid_max << std::endl << this->values_of_landscapes.size() << std::endl; + + //and now in the following lines, the values of this->values_of_landscapes for the following arguments: + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + for ( size_t j = 0 ; j != this->values_of_landscapes[i].size() ; ++j ) + { + out << this->values_of_landscapes[i][j] << " "; + } + out << std::endl; + } + + out.close(); +} + +void Persistence_landscape_on_grid::plot( const char* filename, double min_x , double max_x , double min_y , double max_y, size_t from_ , size_t to_ )const +{ + //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 ( min_x == max_x ) + { + std::pair<double,double> min_max = compute_minimum_maximum(); + out << "set xrange [" << this->grid_min << " : " << this->grid_max << "]" << std::endl; + out << "set yrange [" << min_max.first << " : " << min_max.second << "]" << std::endl; + } + else + { + out << "set xrange [" << min_x << " : " << max_x << "]" << std::endl; + out << "set yrange [" << min_y << " : " << max_y << "]" << std::endl; + } + + size_t number_of_nonzero_levels = this->number_of_nonzero_levels(); + double dx = ( this->grid_max - this->grid_min )/((double)this->values_of_landscapes.size()-1); + + + size_t from = 0; + if ( from_ != std::numeric_limits<size_t>::max() ) + { + if ( from_ < number_of_nonzero_levels ) + { + from = from_; + } + else + { + return; + } + } + size_t to = number_of_nonzero_levels; + if ( to_ != std::numeric_limits<size_t>::max() ) + { + if ( to_ < number_of_nonzero_levels ) + { + to = to_; + } + } + + + out << "plot "; + for ( size_t lambda= from ; lambda != to ; ++lambda ) + { + //out << " '-' using 1:2 title 'l" << lambda << "' with lp"; + out << " '-' using 1:2 notitle with lp"; + if ( lambda+1 != to ) + { + out << ", \\"; + } + out << std::endl; + } + + for ( size_t lambda = from ; lambda != to ; ++lambda ) + { + double point = this->grid_min; + for ( size_t i = 0 ; i != this->values_of_landscapes.size() ; ++i ) + { + double value = 0; + if ( this->values_of_landscapes[i].size() > lambda ) + { + value = this->values_of_landscapes[i][lambda]; + } + out << point << " " << value << std::endl; + point += dx; + } + 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; +} + +template < typename T > +Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid ( const Persistence_landscape_on_grid& land1 , const Persistence_landscape_on_grid& land2 ) +{ + //first we need to check if the domains are the same: + if ( !check_if_defined_on_the_same_domain(land1,land2) )throw "Two grids are not compatible"; + + T oper; + Persistence_landscape_on_grid result; + result.values_of_landscapes = std::vector< std::vector< double > >( land1.values_of_landscapes.size() ); + result.grid_min = land1.grid_min; + result.grid_max = land1.grid_max; + + //now we perorm the operations: + for ( size_t grid_point = 0 ; grid_point != land1.values_of_landscapes.size() ; ++grid_point ) + { + result.values_of_landscapes[grid_point] = std::vector< double >( std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) ); + for ( size_t lambda = 0 ; lambda != std::max( land1.values_of_landscapes[grid_point].size() , land2.values_of_landscapes[grid_point].size() ) ; ++lambda ) + { + double value1 = 0; + double value2 = 0; + if ( lambda < land1.values_of_landscapes[grid_point].size() )value1 = land1.values_of_landscapes[grid_point][lambda]; + if ( lambda < land2.values_of_landscapes[grid_point].size() )value2 = land2.values_of_landscapes[grid_point][lambda]; + result.values_of_landscapes[grid_point][lambda] = oper( value1 , value2 ); + } + } + + return result; +} + +Persistence_landscape_on_grid Persistence_landscape_on_grid::multiply_lanscape_by_real_number_not_overwrite( double x )const +{ + Persistence_landscape_on_grid result; + result.values_of_landscapes = std::vector< std::vector< double > >( this->values_of_landscapes.size() ); + result.grid_min = this->grid_min; + result.grid_max = this->grid_max; + + for ( size_t grid_point = 0 ; grid_point != this->values_of_landscapes.size() ; ++grid_point ) + { + result.values_of_landscapes[grid_point] = std::vector< double >( this->values_of_landscapes[grid_point].size() ); + for ( size_t i = 0 ; i != this->values_of_landscapes[grid_point].size() ; ++i ) + { + result.values_of_landscapes[grid_point][i] = x*this->values_of_landscapes[grid_point][i]; + } + } + + return result; +} + +double compute_max_norm_distance_of_landscapes( const Persistence_landscape_on_grid& first, const Persistence_landscape_on_grid& second ) +{ + double result = 0; + + //first we need to check if first and second is defined on the same domain" + if ( !check_if_defined_on_the_same_domain(first, second) )throw "Two grids are not compatible"; + + for ( size_t i = 0 ; i != first.values_of_landscapes.size() ; ++i ) + { + for ( size_t j = 0 ; j != std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) ; ++j ) + { + if ( result < abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] ) ) + { + result = abs( first.values_of_landscapes[i][j] - second.values_of_landscapes[i][j] ); + } + } + if ( first.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) ) + { + for ( size_t j = first.values_of_landscapes[i].size() ; j != second.values_of_landscapes[i].size() ; ++j ) + { + if ( result < second.values_of_landscapes[i][j] )result = second.values_of_landscapes[i][j]; + } + } + if ( second.values_of_landscapes[i].size() == std::min( first.values_of_landscapes[i].size() , second.values_of_landscapes[i].size() ) ) + { + for ( size_t j = second.values_of_landscapes[i].size() ; j != first.values_of_landscapes[i].size() ; ++j ) + { + if ( result < first.values_of_landscapes[i][j] )result = first.values_of_landscapes[i][j]; + } + } + } + return result; +} + + + +}//namespace Gudhi_stat +}//namespace Gudhi + +#endif |