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diff --git a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h b/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h deleted file mode 100644 index d29a51ab..00000000 --- a/src/Gudhi_stat/include/gudhi/concretizations/Persistence_landscape_on_grid.h +++ /dev/null @@ -1,1363 +0,0 @@ -/* This file is part of the Gudhi Library. The Gudhi library - * (Geometric Understanding in Higher Dimensions) is a generic C++ - * library for computational topology. - *h - * 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 <unistd.h> -#include <cmath> - - -//gudhi include - -#include <gudhi/read_persitence_from_file.h> -#include <gudhi/common_gudhi_stat.h> - - - -namespace Gudhi -{ -namespace Gudhi_stat -{ - - -//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 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_ , size_t dimension_ = 0 ); - - /** - * 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 remaning parameters are - * calculated based on data. - **/ - Persistence_landscape_on_grid(const char* filename , size_t number_of_points ); - - - /** - * 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; - } - - - /** - * 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; - } - - - /** - *\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 L^i 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 L^{\infty} 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 L^{p} 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. - **/ - 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[ 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_ ); - 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 ); - 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_ ) -{ - 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_ << std::endl; - //getchar(); - 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_min_ == std::numeric_limits<double>::max()) ) - { - //in this case, we need to find grid_min_ and grid_min_ based - } - - 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; - } - 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 ) - { - 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; - } - } - - //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 char* filename , double grid_min_, double grid_max_ , size_t number_of_points_ , size_t dimension ) -{ - //standard file with barcode - std::vector< std::pair< double , double > > p = read_standard_file( filename ); - //gudhi file with barcode - //std::vector< std::pair< double , double > > p = read_gudhi_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 , size_t number_of_points_ ) -{ - //standard file with barcode - std::vector< std::pair< double , double > > p = read_standard_file( filename ); - //gudhi file with barcode - //std::vector< std::pair< double , double > > p = read_gudhi_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_ ); -} - -void Persistence_landscape_on_grid::load_landscape_from_file( const char* filename ) -{ - //check if the file exist. - 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::ifstream in; - in.open( filename ); - - 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 |