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diff --git a/src/Persistence_representations/include/gudhi/Persistence_landscape.h b/src/Persistence_representations/include/gudhi/Persistence_landscape.h new file mode 100644 index 00000000..b819ccb6 --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Persistence_landscape.h @@ -0,0 +1,1371 @@ +/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. + * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. + * Author(s): Pawel Dlotko + * + * Copyright (C) 2016 Inria + * + * Modification(s): + * - YYYY/MM Author: Description of the modification + */ + +#ifndef PERSISTENCE_LANDSCAPE_H_ +#define PERSISTENCE_LANDSCAPE_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> + +// standard include +#include <cmath> +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <string> +#include <utility> +#include <functional> + +namespace Gudhi { +namespace Persistence_representations { + +// pre declaration +class Persistence_landscape; +template <typename operation> +Persistence_landscape operation_on_pair_of_landscapes(const Persistence_landscape& land1, + const Persistence_landscape& land2); + +/** + * \class Persistence_landscape Persistence_landscape.h gudhi/Persistence_landscape.h + * \brief A class implementing persistence landscapes data structures. + * + * \ingroup Persistence_representations + * + * \details + * For theoretical description, please consult <i>Statistical topological data analysis using persistence + * landscapes</i>\cite bubenik_landscapes_2015 , and for details of algorithms, + * <i>A persistence landscapes toolbox for topological statistics</i>\cite bubenik_dlotko_landscapes_2016. + * + * Persistence landscapes allow vectorization, 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 rounding errors during the construction of persistence landscapes, 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. + * +**/ +class Persistence_landscape { + public: + /** + * Default constructor. + **/ + Persistence_landscape() { this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); } + + /** + * Constructor that takes as an input a vector of birth-death pairs. + **/ + Persistence_landscape(const std::vector<std::pair<double, double> >& p, + size_t number_of_levels = std::numeric_limits<size_t>::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. + **/ + Persistence_landscape(const char* filename, size_t dimension = std::numeric_limits<unsigned>::max(), + size_t number_of_levels = std::numeric_limits<size_t>::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; + + /** + * This function compute integral of the 'level'-level of a landscape. + **/ + double compute_integral_of_a_level_of_a_landscape(size_t level) const; + + /** + * This function compute integral of the landscape p-th power of a landscape (defined formally as sum of integrals + *on R of p-th powers of all landscape functions) + **/ + double compute_integral_of_landscape(double p) const; // this function compute integral of p-th power of landscape. + + /** + * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned + *level and double x. + * The procedure will compute the value of the level-landscape at the point x. + **/ + double compute_value_at_a_given_point(unsigned level, double x) const; + + /** + * Writing landscape into a stream. A i-th level landscape starts with a string "lambda_i". Then the discontinuity + *points of the landscapes follows. + * Shall those points be joined with lines, we will obtain the i-th landscape function. + **/ + friend std::ostream& operator<<(std::ostream& out, Persistence_landscape& land); + + template <typename operation> + friend Persistence_landscape operation_on_pair_of_landscapes(const Persistence_landscape& land1, + const Persistence_landscape& land2); + + /** + *\private A function that compute sum of two landscapes. + **/ + friend Persistence_landscape add_two_landscapes(const Persistence_landscape& land1, + const Persistence_landscape& land2) { + return operation_on_pair_of_landscapes<std::plus<double> >(land1, land2); + } + + /** + *\private A function that compute difference of two landscapes. + **/ + friend Persistence_landscape subtract_two_landscapes(const Persistence_landscape& land1, + const Persistence_landscape& land2) { + return operation_on_pair_of_landscapes<std::minus<double> >(land1, land2); + } + + /** + * An operator +, that compute sum of two landscapes. + **/ + friend Persistence_landscape operator+(const Persistence_landscape& first, const Persistence_landscape& second) { + return add_two_landscapes(first, second); + } + + /** + * An operator -, that compute difference of two landscapes. + **/ + friend Persistence_landscape operator-(const Persistence_landscape& first, const Persistence_landscape& second) { + return subtract_two_landscapes(first, second); + } + + /** + * An operator * that allows multiplication of a landscape by a real number. + **/ + friend Persistence_landscape operator*(const Persistence_landscape& first, double con) { + return first.multiply_lanscape_by_real_number_not_overwrite(con); + } + + /** + * An operator * that allows multiplication of a landscape by a real number (order of parameters swapped). + **/ + friend Persistence_landscape operator*(double con, const Persistence_landscape& first) { + return first.multiply_lanscape_by_real_number_not_overwrite(con); + } + + /** + * Operator +=. The second parameter is persistence landscape. + **/ + Persistence_landscape operator+=(const Persistence_landscape& rhs) { + *this = *this + rhs; + return *this; + } + + /** + * Operator -=. The second parameter is a persistence landscape. + **/ + Persistence_landscape operator-=(const Persistence_landscape& rhs) { + *this = *this - rhs; + return *this; + } + + /** + * Operator *=. The second parameter is a real number by which the y values of all landscape functions are multiplied. + *The x-values remain unchanged. + **/ + Persistence_landscape operator*=(double x) { + *this = *this * x; + return *this; + } + + /** + * Operator /=. The second parameter is a real number. + **/ + Persistence_landscape operator/=(double x) { + if (x == 0) throw("In operator /=, division by 0. Program terminated."); + *this = *this * (1 / x); + return *this; + } + + /** + * An operator to compare two persistence landscapes. + **/ + bool operator==(const Persistence_landscape& rhs) const; + + /** + * An operator to compare two persistence landscapes. + **/ + bool operator!=(const Persistence_landscape& rhs) const { return !((*this) == rhs); } + + /** + * Computations of maximum (y) value of landscape. + **/ + double compute_maximum() const { + double maxValue = 0; + if (this->land.size()) { + maxValue = -std::numeric_limits<int>::max(); + for (size_t i = 0; i != this->land[0].size(); ++i) { + if (this->land[0][i].second > maxValue) maxValue = this->land[0][i].second; + } + } + return maxValue; + } + + /** + *\private Computations of minimum (y) value of landscape. + **/ + double compute_minimum() const { + double minValue = 0; + if (this->land.size()) { + minValue = std::numeric_limits<int>::max(); + for (size_t i = 0; i != this->land[0].size(); ++i) { + if (this->land[0][i].second < minValue) minValue = this->land[0][i].second; + } + } + return minValue; + } + + /** + *\private Computations of a \f$L^i\f$ norm of landscape, where i is the input parameter. + **/ + double compute_norm_of_landscape(double i) { + Persistence_landscape l; + if (i < std::numeric_limits<double>::max()) { + return compute_distance_of_landscapes(*this, l, i); + } else { + return compute_max_norm_distance_of_landscapes(*this, l); + } + } + + /** + * An operator to compute the value of a landscape in the level 'level' at the argument 'x'. + **/ + double operator()(unsigned level, double x) const { return this->compute_value_at_a_given_point(level, x); } + + /** + *\private Computations of \f$L^{\infty}\f$ distance between two landscapes. + **/ + friend double compute_max_norm_distance_of_landscapes(const Persistence_landscape& first, + const Persistence_landscape& second); + + /** + *\private Computations of \f$L^{p}\f$ distance between two landscapes. p is the parameter of the procedure. + **/ + friend double compute_distance_of_landscapes(const Persistence_landscape& first, const Persistence_landscape& second, + double p); + + /** + * Function to compute absolute value of a PL function. The representation of persistence landscapes allow to store + *general PL-function. When computing distance between two landscapes, we compute difference between + * them. In this case, a general PL-function with negative value can appear as a result. Then in order to compute + *distance, we need to take its absolute value. This is the purpose of this procedure. + **/ + Persistence_landscape abs(); + + Persistence_landscape* new_abs(); + + /** + * Computes the number of landscape functions. + **/ + size_t size() const { return this->land.size(); } + + /** + * Compute maximal value of lambda-level landscape. + **/ + double find_max(unsigned lambda) const; + + /** + *\private Function to compute inner (scalar) product of two landscapes. + **/ + friend double compute_inner_product(const Persistence_landscape& l1, const Persistence_landscape& l2); + + // Implementations of functions for various concepts. + + /** + * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an + *integral of i-th landscape function over whole R. + * This function is required by the Real_valued_topological_data concept. + * At the moment this function is not tested, since it is quite likely to be changed in the future. Given this, when + *using it, keep in mind that it + * will be most likely changed in the next versions. + **/ + double project_to_R(int number_of_function) const { + return this->compute_integral_of_a_level_of_a_landscape((size_t)number_of_function); + } + + /** + * The function gives the number of possible projections to R. This function is required by the + *Real_valued_topological_data concept. + **/ + size_t number_of_projections_to_R() const { return this->number_of_functions_for_projections_to_reals; } + + /** + * This function produce a vector of doubles based on a landscape. It is required in a concept + * Vectorized_topological_data + */ + std::vector<double> vectorize(int number_of_function) const { + // TODO(PD) think of something smarter over here + std::vector<double> v; + if ((size_t)number_of_function > this->land.size()) { + return v; + } + v.reserve(this->land[number_of_function].size()); + for (size_t i = 0; i != this->land[number_of_function].size(); ++i) { + v.push_back(this->land[number_of_function][i].second); + } + return v; + } + /** + * This function return the number of functions that allows vectorization of persistence landscape. It is required in + *a concept Vectorized_topological_data. + **/ + size_t number_of_vectorize_functions() const { return this->number_of_functions_for_vectorization; } + + /** + * A function to compute averaged persistence landscape, based on vector of persistence landscapes. + * This function is required by Topological_data_with_averages concept. + **/ + void compute_average(const std::vector<Persistence_landscape*>& to_average) { + bool dbg = false; + + if (dbg) { + std::cerr << "to_average.size() : " << to_average.size() << std::endl; + } + + std::vector<Persistence_landscape*> nextLevelMerge(to_average.size()); + for (size_t i = 0; i != to_average.size(); ++i) { + nextLevelMerge[i] = to_average[i]; + } + bool is_this_first_level = true; // in the loop, we will create dynamically a number of intermediate complexes. We + // have to clean that up, but we cannot erase the initial landscapes we have + // to average. In this case, we simply check if the nextLevelMerge are the input landscapes or the ones created in + // that loop by using this extra variable. + + while (nextLevelMerge.size() != 1) { + if (dbg) { + std::cerr << "nextLevelMerge.size() : " << nextLevelMerge.size() << std::endl; + } + std::vector<Persistence_landscape*> nextNextLevelMerge; + nextNextLevelMerge.reserve(to_average.size()); + for (size_t i = 0; i < nextLevelMerge.size(); i = i + 2) { + if (dbg) { + std::cerr << "i : " << i << std::endl; + } + Persistence_landscape* l = new Persistence_landscape; + if (i + 1 != nextLevelMerge.size()) { + (*l) = (*nextLevelMerge[i]) + (*nextLevelMerge[i + 1]); + } else { + (*l) = *nextLevelMerge[i]; + } + nextNextLevelMerge.push_back(l); + } + if (dbg) { + std::cerr << "After this iteration \n"; + getchar(); + } + + if (!is_this_first_level) { + // deallocate the memory if the vector nextLevelMerge do not consist of the initial landscapes + for (size_t i = 0; i != nextLevelMerge.size(); ++i) { + delete nextLevelMerge[i]; + } + } + is_this_first_level = false; + nextLevelMerge.swap(nextNextLevelMerge); + } + (*this) = (*nextLevelMerge[0]); + (*this) *= 1 / static_cast<double>(to_average.size()); + } + + /** + * A function to compute distance between persistence landscape. + * The parameter of this function is a Persistence_landscape. + * This function is required in Topological_data_with_distances concept. + * For max norm distance, set power to std::numeric_limits<double>::max() + **/ + double distance(const Persistence_landscape& second, double power = 1) const { + if (power < std::numeric_limits<double>::max()) { + return compute_distance_of_landscapes(*this, second, power); + } else { + return compute_max_norm_distance_of_landscapes(*this, second); + } + } + + /** + * A function to compute scalar product of persistence landscapes. + * The parameter of this function is a Persistence_landscape. + * This function is required in Topological_data_with_scalar_product concept. + **/ + double compute_scalar_product(const Persistence_landscape& second) const { + return compute_inner_product((*this), second); + } + // end of implementation of functions needed for concepts. + + /** + * This procedure returns y-range of a given level persistence landscape. If a default value is used, the y-range + * of 0th level landscape is given (and this range contains the ranges of all other landscapes). + **/ + std::pair<double, double> get_y_range(size_t level = 0) const { + std::pair<double, double> result; + if (level < this->land.size()) { + double maxx = this->compute_maximum(); + double minn = this->compute_minimum(); + result = std::make_pair(minn, maxx); + } else { + result = std::make_pair(0, 0); + } + return result; + } + + // a function used to create a gnuplot script for visualization of landscapes + void plot(const char* filename, double xRangeBegin = std::numeric_limits<double>::max(), + double xRangeEnd = std::numeric_limits<double>::max(), + double yRangeBegin = std::numeric_limits<double>::max(), + double yRangeEnd = std::numeric_limits<double>::max(), int from = std::numeric_limits<int>::max(), + int to = std::numeric_limits<int>::max()); + + protected: + std::vector<std::vector<std::pair<double, double> > > land; + size_t number_of_functions_for_vectorization; + size_t number_of_functions_for_projections_to_reals; + + void construct_persistence_landscape_from_barcode(const std::vector<std::pair<double, double> >& p, + size_t number_of_levels = std::numeric_limits<size_t>::max()); + Persistence_landscape multiply_lanscape_by_real_number_not_overwrite(double x) const; + void multiply_lanscape_by_real_number_overwrite(double x); + friend double compute_maximal_distance_non_symmetric(const Persistence_landscape& pl1, + const Persistence_landscape& pl2); + + void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals() { + // warning, this function can be only called after filling in the intervals vector. + this->number_of_functions_for_vectorization = this->land.size(); + this->number_of_functions_for_projections_to_reals = this->land.size(); + } +}; + +Persistence_landscape::Persistence_landscape(const char* filename, size_t dimension, size_t number_of_levels) { + std::vector<std::pair<double, double> > barcode; + if (dimension < std::numeric_limits<double>::max()) { + barcode = read_persistence_intervals_in_one_dimension_from_file(filename, dimension); + } else { + barcode = read_persistence_intervals_in_one_dimension_from_file(filename); + } + this->construct_persistence_landscape_from_barcode(barcode, number_of_levels); + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); +} + +bool operatorEqualDbg = false; +bool Persistence_landscape::operator==(const Persistence_landscape& rhs) const { + if (this->land.size() != rhs.land.size()) { + if (operatorEqualDbg) std::cerr << "1\n"; + return false; + } + for (size_t level = 0; level != this->land.size(); ++level) { + if (this->land[level].size() != rhs.land[level].size()) { + if (operatorEqualDbg) std::cerr << "this->land[level].size() : " << this->land[level].size() << "\n"; + if (operatorEqualDbg) std::cerr << "rhs.land[level].size() : " << rhs.land[level].size() << "\n"; + if (operatorEqualDbg) std::cerr << "2\n"; + return false; + } + for (size_t i = 0; i != this->land[level].size(); ++i) { + if (!(almost_equal(this->land[level][i].first, rhs.land[level][i].first) && + almost_equal(this->land[level][i].second, rhs.land[level][i].second))) { + if (operatorEqualDbg) + std::cerr << "this->land[level][i] : " << this->land[level][i].first << " " << this->land[level][i].second + << "\n"; + if (operatorEqualDbg) + std::cerr << "rhs.land[level][i] : " << rhs.land[level][i].first << " " << rhs.land[level][i].second << "\n"; + if (operatorEqualDbg) std::cerr << "3\n"; + return false; + } + } + } + return true; +} + +Persistence_landscape::Persistence_landscape(const std::vector<std::pair<double, double> >& p, + size_t number_of_levels) { + this->construct_persistence_landscape_from_barcode(p, number_of_levels); + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); +} + +void Persistence_landscape::construct_persistence_landscape_from_barcode( + const std::vector<std::pair<double, double> >& p, size_t number_of_levels) { + bool dbg = false; + if (dbg) { + std::cerr << "Persistence_landscape::Persistence_landscape( const std::vector< std::pair< double , double > >& p )" + << std::endl; + } + + // this is a general algorithm to construct persistence landscapes. + std::vector<std::pair<double, double> > bars; + bars.insert(bars.begin(), p.begin(), p.end()); + std::sort(bars.begin(), bars.end(), compare_points_sorting); + + if (dbg) { + std::cerr << "Bars : \n"; + for (size_t i = 0; i != bars.size(); ++i) { + std::cerr << bars[i].first << " " << bars[i].second << "\n"; + } + getchar(); + } + + std::vector<std::pair<double, double> > characteristicPoints(p.size()); + for (size_t i = 0; i != bars.size(); ++i) { + characteristicPoints[i] = + std::make_pair((bars[i].first + bars[i].second) / 2.0, (bars[i].second - bars[i].first) / 2.0); + } + std::vector<std::vector<std::pair<double, double> > > Persistence_landscape; + size_t number_of_levels_in_the_landscape = 0; + while (!characteristicPoints.empty()) { + if (dbg) { + for (size_t i = 0; i != characteristicPoints.size(); ++i) { + std::cout << "(" << characteristicPoints[i].first << " " << characteristicPoints[i].second << ")\n"; + } + std::cin.ignore(); + } + + std::vector<std::pair<double, double> > lambda_n; + lambda_n.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0)); + lambda_n.push_back(std::make_pair(minus_length(characteristicPoints[0]), 0)); + lambda_n.push_back(characteristicPoints[0]); + + if (dbg) { + std::cerr << "1 Adding to lambda_n : (" << -std::numeric_limits<int>::max() << " " << 0 << ") , (" + << minus_length(characteristicPoints[0]) << " " << 0 << ") , (" << characteristicPoints[0].first << " " + << characteristicPoints[0].second << ") \n"; + } + + size_t i = 1; + std::vector<std::pair<double, double> > newCharacteristicPoints; + while (i < characteristicPoints.size()) { + size_t p = 1; + if ((minus_length(characteristicPoints[i]) >= minus_length(lambda_n[lambda_n.size() - 1])) && + (birth_plus_deaths(characteristicPoints[i]) > birth_plus_deaths(lambda_n[lambda_n.size() - 1]))) { + if (minus_length(characteristicPoints[i]) < birth_plus_deaths(lambda_n[lambda_n.size() - 1])) { + std::pair<double, double> point = std::make_pair( + (minus_length(characteristicPoints[i]) + birth_plus_deaths(lambda_n[lambda_n.size() - 1])) / 2, + (birth_plus_deaths(lambda_n[lambda_n.size() - 1]) - minus_length(characteristicPoints[i])) / 2); + lambda_n.push_back(point); + if (dbg) { + std::cerr << "2 Adding to lambda_n : (" << point.first << " " << point.second << ")\n"; + } + + if (dbg) { + std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i + p].first << " " + << characteristicPoints[i + p].second << "\n"; + std::cerr << "point : " << point.first << " " << point.second << "\n"; + getchar(); + } + + while ((i + p < characteristicPoints.size()) && + (almost_equal(minus_length(point), minus_length(characteristicPoints[i + p]))) && + (birth_plus_deaths(point) <= birth_plus_deaths(characteristicPoints[i + p]))) { + newCharacteristicPoints.push_back(characteristicPoints[i + p]); + if (dbg) { + std::cerr << "3.5 Adding to newCharacteristicPoints : (" << characteristicPoints[i + p].first << " " + << characteristicPoints[i + p].second << ")\n"; + getchar(); + } + ++p; + } + + newCharacteristicPoints.push_back(point); + if (dbg) { + std::cerr << "4 Adding to newCharacteristicPoints : (" << point.first << " " << point.second << ")\n"; + } + + while ((i + p < characteristicPoints.size()) && + (minus_length(point) <= minus_length(characteristicPoints[i + p])) && + (birth_plus_deaths(point) >= birth_plus_deaths(characteristicPoints[i + p]))) { + newCharacteristicPoints.push_back(characteristicPoints[i + p]); + if (dbg) { + std::cerr << "characteristicPoints[i+p] : " << characteristicPoints[i + p].first << " " + << characteristicPoints[i + p].second << "\n"; + std::cerr << "point : " << point.first << " " << point.second << "\n"; + std::cerr << "characteristicPoints[i+p] birth and death : " << minus_length(characteristicPoints[i + p]) + << " , " << birth_plus_deaths(characteristicPoints[i + p]) << "\n"; + std::cerr << "point birth and death : " << minus_length(point) << " , " << birth_plus_deaths(point) + << "\n"; + + std::cerr << "3 Adding to newCharacteristicPoints : (" << characteristicPoints[i + p].first << " " + << characteristicPoints[i + p].second << ")\n"; + getchar(); + } + ++p; + } + + } else { + lambda_n.push_back(std::make_pair(birth_plus_deaths(lambda_n[lambda_n.size() - 1]), 0)); + lambda_n.push_back(std::make_pair(minus_length(characteristicPoints[i]), 0)); + if (dbg) { + std::cerr << "5 Adding to lambda_n : (" << birth_plus_deaths(lambda_n[lambda_n.size() - 1]) << " " << 0 + << ")\n"; + std::cerr << "5 Adding to lambda_n : (" << minus_length(characteristicPoints[i]) << " " << 0 << ")\n"; + } + } + lambda_n.push_back(characteristicPoints[i]); + if (dbg) { + std::cerr << "6 Adding to lambda_n : (" << characteristicPoints[i].first << " " + << characteristicPoints[i].second << ")\n"; + } + } else { + newCharacteristicPoints.push_back(characteristicPoints[i]); + if (dbg) { + std::cerr << "7 Adding to newCharacteristicPoints : (" << characteristicPoints[i].first << " " + << characteristicPoints[i].second << ")\n"; + } + } + i = i + p; + } + lambda_n.push_back(std::make_pair(birth_plus_deaths(lambda_n[lambda_n.size() - 1]), 0)); + lambda_n.push_back(std::make_pair(std::numeric_limits<int>::max(), 0)); + + characteristicPoints = newCharacteristicPoints; + + lambda_n.erase(std::unique(lambda_n.begin(), lambda_n.end()), lambda_n.end()); + this->land.push_back(lambda_n); + + ++number_of_levels_in_the_landscape; + if (number_of_levels == number_of_levels_in_the_landscape) { + break; + } + } +} + +// this function find maximum of lambda_n +double Persistence_landscape::find_max(unsigned lambda) const { + if (this->land.size() < lambda) return 0; + double maximum = -std::numeric_limits<int>::max(); + for (size_t i = 0; i != this->land[lambda].size(); ++i) { + if (this->land[lambda][i].second > maximum) maximum = this->land[lambda][i].second; + } + return maximum; +} + +double Persistence_landscape::compute_integral_of_landscape() const { + double result = 0; + for (size_t i = 0; i != this->land.size(); ++i) { + for (size_t nr = 2; nr != this->land[i].size() - 1; ++nr) { + // it suffices to compute every planar integral and then sum them up for each lambda_n + result += 0.5 * (this->land[i][nr].first - this->land[i][nr - 1].first) * + (this->land[i][nr].second + this->land[i][nr - 1].second); + } + } + return result; +} + +double Persistence_landscape::compute_integral_of_a_level_of_a_landscape(size_t level) const { + double result = 0; + if (level >= this->land.size()) { + // this landscape function is constantly equal 0, so is the integral. + return result; + } + // also negative landscapes are assumed to be zero. + if (level < 0) return 0; + + for (size_t nr = 2; nr != this->land[level].size() - 1; ++nr) { + // it suffices to compute every planar integral and then sum them up for each lambda_n + result += 0.5 * (this->land[level][nr].first - this->land[level][nr - 1].first) * + (this->land[level][nr].second + this->land[level][nr - 1].second); + } + + return result; +} + +double Persistence_landscape::compute_integral_of_landscape(double p) const { + bool dbg = false; + double result = 0; + for (size_t i = 0; i != this->land.size(); ++i) { + for (size_t nr = 2; nr != this->land[i].size() - 1; ++nr) { + if (dbg) std::cout << "nr : " << nr << "\n"; + // In this interval, the landscape has a form f(x) = ax+b. We want to compute integral of (ax+b)^p = 1/a * + // (ax+b)^{p+1}/(p+1) + std::pair<double, double> coef = compute_parameters_of_a_line(this->land[i][nr], this->land[i][nr - 1]); + double a = coef.first; + double b = coef.second; + + if (dbg) + std::cout << "(" << this->land[i][nr].first << "," << this->land[i][nr].second << ") , " + << this->land[i][nr - 1].first << "," << this->land[i][nr].second << ")" << std::endl; + if (this->land[i][nr].first == this->land[i][nr - 1].first) continue; + if (a != 0) { + result += 1 / (a * (p + 1)) * + (pow((a * this->land[i][nr].first + b), p + 1) - pow((a * this->land[i][nr - 1].first + b), p + 1)); + } else { + result += (this->land[i][nr].first - this->land[i][nr - 1].first) * (pow(this->land[i][nr].second, p)); + } + if (dbg) { + std::cout << "a : " << a << " , b : " << b << std::endl; + std::cout << "result : " << result << std::endl; + } + } + } + return result; +} + +// this is O(log(n)) algorithm, where n is number of points in this->land. +double Persistence_landscape::compute_value_at_a_given_point(unsigned level, double x) const { + bool compute_value_at_a_given_pointDbg = false; + // in such a case lambda_level = 0. + if (level >= this->land.size()) return 0; + + // we know that the points in this->land[level] are ordered according to x coordinate. Therefore, we can find the + // point by using bisection: + unsigned coordBegin = 1; + unsigned coordEnd = this->land[level].size() - 2; + + if (compute_value_at_a_given_pointDbg) { + std::cerr << "Here \n"; + std::cerr << "x : " << x << "\n"; + std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n"; + std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n"; + } + + // in this case x is outside the support of the landscape, therefore the value of the landscape is 0. + if (x <= this->land[level][coordBegin].first) return 0; + if (x >= this->land[level][coordEnd].first) return 0; + + if (compute_value_at_a_given_pointDbg) std::cerr << "Entering to the while loop \n"; + + while (coordBegin + 1 != coordEnd) { + if (compute_value_at_a_given_pointDbg) { + std::cerr << "coordBegin : " << coordBegin << "\n"; + std::cerr << "coordEnd : " << coordEnd << "\n"; + std::cerr << "this->land[level][coordBegin].first : " << this->land[level][coordBegin].first << "\n"; + std::cerr << "this->land[level][coordEnd].first : " << this->land[level][coordEnd].first << "\n"; + } + + unsigned newCord = (unsigned)floor((coordEnd + coordBegin) / 2.0); + + if (compute_value_at_a_given_pointDbg) { + std::cerr << "newCord : " << newCord << "\n"; + std::cerr << "this->land[level][newCord].first : " << this->land[level][newCord].first << "\n"; + std::cin.ignore(); + } + + if (this->land[level][newCord].first <= x) { + coordBegin = newCord; + if (this->land[level][newCord].first == x) return this->land[level][newCord].second; + } else { + coordEnd = newCord; + } + } + + if (compute_value_at_a_given_pointDbg) { + std::cout << "x : " << x << " is between : " << this->land[level][coordBegin].first << " a " + << this->land[level][coordEnd].first << "\n"; + std::cout << "the y coords are : " << this->land[level][coordBegin].second << " a " + << this->land[level][coordEnd].second << "\n"; + std::cerr << "coordBegin : " << coordBegin << "\n"; + std::cerr << "coordEnd : " << coordEnd << "\n"; + std::cin.ignore(); + } + return function_value(this->land[level][coordBegin], this->land[level][coordEnd], x); +} + +std::ostream& operator<<(std::ostream& out, Persistence_landscape& land) { + for (size_t level = 0; level != land.land.size(); ++level) { + out << "Lambda_" << level << ":" << std::endl; + for (size_t i = 0; i != land.land[level].size(); ++i) { + if (land.land[level][i].first == -std::numeric_limits<int>::max()) { + out << "-inf"; + } else { + if (land.land[level][i].first == std::numeric_limits<int>::max()) { + out << "+inf"; + } else { + out << land.land[level][i].first; + } + } + out << " , " << land.land[level][i].second << std::endl; + } + } + return out; +} + +void Persistence_landscape::multiply_lanscape_by_real_number_overwrite(double x) { + for (size_t dim = 0; dim != this->land.size(); ++dim) { + for (size_t i = 0; i != this->land[dim].size(); ++i) { + this->land[dim][i].second *= x; + } + } +} + +bool AbsDbg = false; +Persistence_landscape Persistence_landscape::abs() { + Persistence_landscape result; + for (size_t level = 0; level != this->land.size(); ++level) { + if (AbsDbg) { + std::cout << "level: " << level << std::endl; + } + std::vector<std::pair<double, double> > lambda_n; + lambda_n.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0)); + for (size_t i = 1; i != this->land[level].size(); ++i) { + if (AbsDbg) { + std::cout << "this->land[" << level << "][" << i << "] : " << this->land[level][i].first << " " + << this->land[level][i].second << std::endl; + } + // if a line segment between this->land[level][i-1] and this->land[level][i] crosses the x-axis, then we have to + // add one landscape point t o result + if ((this->land[level][i - 1].second) * (this->land[level][i].second) < 0) { + double zero = + find_zero_of_a_line_segment_between_those_two_points(this->land[level][i - 1], this->land[level][i]); + + lambda_n.push_back(std::make_pair(zero, 0)); + lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second))); + if (AbsDbg) { + std::cout << "Adding pair : (" << zero << ",0)" << std::endl; + std::cout << "In the same step adding pair : (" << this->land[level][i].first << "," + << fabs(this->land[level][i].second) << ") " << std::endl; + std::cin.ignore(); + } + } else { + lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second))); + if (AbsDbg) { + std::cout << "Adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second) + << ") " << std::endl; + std::cin.ignore(); + } + } + } + result.land.push_back(lambda_n); + } + return result; +} + +Persistence_landscape* Persistence_landscape::new_abs() { + Persistence_landscape* result = new Persistence_landscape(*this); + for (size_t level = 0; level != this->land.size(); ++level) { + if (AbsDbg) { + std::cout << "level: " << level << std::endl; + } + std::vector<std::pair<double, double> > lambda_n; + lambda_n.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0)); + for (size_t i = 1; i != this->land[level].size(); ++i) { + if (AbsDbg) { + std::cout << "this->land[" << level << "][" << i << "] : " << this->land[level][i].first << " " + << this->land[level][i].second << std::endl; + } + // if a line segment between this->land[level][i-1] and this->land[level][i] crosses the x-axis, then we have to + // add one landscape point t o result + if ((this->land[level][i - 1].second) * (this->land[level][i].second) < 0) { + double zero = + find_zero_of_a_line_segment_between_those_two_points(this->land[level][i - 1], this->land[level][i]); + + lambda_n.push_back(std::make_pair(zero, 0)); + lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second))); + if (AbsDbg) { + std::cout << "Adding pair : (" << zero << ",0)" << std::endl; + std::cout << "In the same step adding pair : (" << this->land[level][i].first << "," + << fabs(this->land[level][i].second) << ") " << std::endl; + std::cin.ignore(); + } + } else { + lambda_n.push_back(std::make_pair(this->land[level][i].first, fabs(this->land[level][i].second))); + if (AbsDbg) { + std::cout << "Adding pair : (" << this->land[level][i].first << "," << fabs(this->land[level][i].second) + << ") " << std::endl; + std::cin.ignore(); + } + } + } + result->land.push_back(lambda_n); + } + return result; +} + +Persistence_landscape Persistence_landscape::multiply_lanscape_by_real_number_not_overwrite(double x) const { + std::vector<std::vector<std::pair<double, double> > > result(this->land.size()); + for (size_t dim = 0; dim != this->land.size(); ++dim) { + std::vector<std::pair<double, double> > lambda_dim(this->land[dim].size()); + for (size_t i = 0; i != this->land[dim].size(); ++i) { + lambda_dim[i] = std::make_pair(this->land[dim][i].first, x * this->land[dim][i].second); + } + result[dim] = lambda_dim; + } + Persistence_landscape res; + // CHANGE + // res.land = result; + res.land.swap(result); + return res; +} // multiply_lanscape_by_real_number_overwrite + +void Persistence_landscape::print_to_file(const char* filename) const { + std::ofstream write; + write.open(filename); + for (size_t dim = 0; dim != this->land.size(); ++dim) { + write << "#lambda_" << dim << std::endl; + for (size_t i = 1; i != this->land[dim].size() - 1; ++i) { + write << this->land[dim][i].first << " " << this->land[dim][i].second << std::endl; + } + } + write.close(); +} + +void Persistence_landscape::load_landscape_from_file(const char* filename) { + bool dbg = false; + // removing the current content of the persistence landscape. + this->land.clear(); + + // this constructor reads persistence landscape form a file. This file have to be created by this software before head + std::ifstream in; + in.open(filename); + if (!in.good()) { + std::cerr << "The file : " << filename << " do not exist. The program will now terminate \n"; + throw "The persistence landscape file do not exist. The program will now terminate \n"; + } + + std::string line; + std::vector<std::pair<double, double> > landscapeAtThisLevel; + + bool isThisAFirsLine = true; + while (in.good()) { + getline(in, line); + if (!(line.length() == 0 || line[0] == '#')) { + std::stringstream lineSS; + lineSS << line; + double beginn, endd; + lineSS >> beginn; + lineSS >> endd; + landscapeAtThisLevel.push_back(std::make_pair(beginn, endd)); + if (dbg) { + std::cerr << "Reading a point : " << beginn << " , " << endd << std::endl; + } + } else { + if (dbg) { + std::cout << "IGNORE LINE\n"; + getchar(); + } + if (!isThisAFirsLine) { + landscapeAtThisLevel.push_back(std::make_pair(std::numeric_limits<int>::max(), 0)); + this->land.push_back(landscapeAtThisLevel); + std::vector<std::pair<double, double> > newLevelOdLandscape; + landscapeAtThisLevel.swap(newLevelOdLandscape); + } + landscapeAtThisLevel.push_back(std::make_pair(-std::numeric_limits<int>::max(), 0)); + isThisAFirsLine = false; + } + } + if (landscapeAtThisLevel.size() > 1) { + // seems that the last line of the file is not finished with the newline sign. We need to put what we have in + // landscapeAtThisLevel to the constructed landscape. + landscapeAtThisLevel.push_back(std::make_pair(std::numeric_limits<int>::max(), 0)); + this->land.push_back(landscapeAtThisLevel); + } + + in.close(); +} + +template <typename T> +Persistence_landscape operation_on_pair_of_landscapes(const Persistence_landscape& land1, + const Persistence_landscape& land2) { + bool operation_on_pair_of_landscapesDBG = false; + if (operation_on_pair_of_landscapesDBG) { + std::cout << "operation_on_pair_of_landscapes\n"; + std::cin.ignore(); + } + Persistence_landscape result; + std::vector<std::vector<std::pair<double, double> > > land(std::max(land1.land.size(), land2.land.size())); + result.land = land; + T oper; + + if (operation_on_pair_of_landscapesDBG) { + for (size_t i = 0; i != std::min(land1.land.size(), land2.land.size()); ++i) { + std::cerr << "land1.land[" << i << "].size() : " << land1.land[i].size() << std::endl; + std::cerr << "land2.land[" << i << "].size() : " << land2.land[i].size() << std::endl; + } + getchar(); + } + + for (size_t i = 0; i != std::min(land1.land.size(), land2.land.size()); ++i) { + std::vector<std::pair<double, double> > lambda_n; + size_t p = 0; + size_t q = 0; + while ((p + 1 < land1.land[i].size()) && (q + 1 < land2.land[i].size())) { + if (operation_on_pair_of_landscapesDBG) { + std::cerr << "p : " << p << "\n"; + std::cerr << "q : " << q << "\n"; + std::cerr << "land1.land.size() : " << land1.land.size() << std::endl; + std::cerr << "land2.land.size() : " << land2.land.size() << std::endl; + std::cerr << "land1.land[" << i << "].size() : " << land1.land[i].size() << std::endl; + std::cerr << "land2.land[" << i << "].size() : " << land2.land[i].size() << std::endl; + std::cout << "land1.land[i][p].first : " << land1.land[i][p].first << "\n"; + std::cout << "land2.land[i][q].first : " << land2.land[i][q].first << "\n"; + } + + if (land1.land[i][p].first < land2.land[i][q].first) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "first \n"; + std::cout << " function_value(land2.land[i][q-1],land2.land[i][q],land1.land[i][p].first) : " + << function_value(land2.land[i][q - 1], land2.land[i][q], land1.land[i][p].first) << "\n"; + } + lambda_n.push_back( + std::make_pair(land1.land[i][p].first, + oper(static_cast<double>(land1.land[i][p].second), + function_value(land2.land[i][q - 1], land2.land[i][q], land1.land[i][p].first)))); + ++p; + continue; + } + if (land1.land[i][p].first > land2.land[i][q].first) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "Second \n"; + std::cout << "function_value(" << land1.land[i][p - 1].first << " " << land1.land[i][p - 1].second << " ," + << land1.land[i][p].first << " " << land1.land[i][p].second << ", " << land2.land[i][q].first + << " ) : " << function_value(land1.land[i][p - 1], land1.land[i][p - 1], land2.land[i][q].first) + << "\n"; + std::cout << "oper( " << function_value(land1.land[i][p], land1.land[i][p - 1], land2.land[i][q].first) << "," + << land2.land[i][q].second << " : " + << oper(land2.land[i][q].second, + function_value(land1.land[i][p], land1.land[i][p - 1], land2.land[i][q].first)) + << "\n"; + } + lambda_n.push_back(std::make_pair( + land2.land[i][q].first, oper(function_value(land1.land[i][p], land1.land[i][p - 1], land2.land[i][q].first), + land2.land[i][q].second))); + ++q; + continue; + } + if (land1.land[i][p].first == land2.land[i][q].first) { + if (operation_on_pair_of_landscapesDBG) std::cout << "Third \n"; + lambda_n.push_back( + std::make_pair(land2.land[i][q].first, oper(land1.land[i][p].second, land2.land[i][q].second))); + ++p; + ++q; + } + if (operation_on_pair_of_landscapesDBG) { + std::cout << "Next iteration \n"; + } + } + while ((p + 1 < land1.land[i].size()) && (q + 1 >= land2.land[i].size())) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "New point : " << land1.land[i][p].first + << " oper(land1.land[i][p].second,0) : " << oper(land1.land[i][p].second, 0) << std::endl; + } + lambda_n.push_back(std::make_pair(land1.land[i][p].first, oper(land1.land[i][p].second, 0))); + ++p; + } + while ((p + 1 >= land1.land[i].size()) && (q + 1 < land2.land[i].size())) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "New point : " << land2.land[i][q].first + << " oper(0,land2.land[i][q].second) : " << oper(0, land2.land[i][q].second) << std::endl; + } + lambda_n.push_back(std::make_pair(land2.land[i][q].first, oper(0, land2.land[i][q].second))); + ++q; + } + lambda_n.push_back(std::make_pair(std::numeric_limits<int>::max(), 0)); + // CHANGE + // result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + if (land1.land.size() > std::min(land1.land.size(), land2.land.size())) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "land1.land.size() > std::min( land1.land.size() , land2.land.size() )" << std::endl; + } + for (size_t i = std::min(land1.land.size(), land2.land.size()); i != std::max(land1.land.size(), land2.land.size()); + ++i) { + std::vector<std::pair<double, double> > lambda_n(land1.land[i]); + for (size_t nr = 0; nr != land1.land[i].size(); ++nr) { + lambda_n[nr] = std::make_pair(land1.land[i][nr].first, oper(land1.land[i][nr].second, 0)); + } + // CHANGE + // result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + } + if (land2.land.size() > std::min(land1.land.size(), land2.land.size())) { + if (operation_on_pair_of_landscapesDBG) { + std::cout << "( land2.land.size() > std::min( land1.land.size() , land2.land.size() ) ) " << std::endl; + } + for (size_t i = std::min(land1.land.size(), land2.land.size()); i != std::max(land1.land.size(), land2.land.size()); + ++i) { + std::vector<std::pair<double, double> > lambda_n(land2.land[i]); + for (size_t nr = 0; nr != land2.land[i].size(); ++nr) { + lambda_n[nr] = std::make_pair(land2.land[i][nr].first, oper(0, land2.land[i][nr].second)); + } + // CHANGE + // result.land[i] = lambda_n; + result.land[i].swap(lambda_n); + } + } + if (operation_on_pair_of_landscapesDBG) { + std::cout << "operation_on_pair_of_landscapes END\n"; + std::cin.ignore(); + } + return result; +} // operation_on_pair_of_landscapes + +double compute_maximal_distance_non_symmetric(const Persistence_landscape& pl1, const Persistence_landscape& pl2) { + bool dbg = false; + if (dbg) std::cerr << " compute_maximal_distance_non_symmetric \n"; + // this distance is not symmetric. It compute ONLY distance between inflection points of pl1 and pl2. + double maxDist = 0; + size_t minimalNumberOfLevels = std::min(pl1.land.size(), pl2.land.size()); + for (size_t level = 0; level != minimalNumberOfLevels; ++level) { + if (dbg) { + std::cerr << "Level : " << level << std::endl; + std::cerr << "PL1 : \n"; + for (size_t i = 0; i != pl1.land[level].size(); ++i) { + std::cerr << "(" << pl1.land[level][i].first << "," << pl1.land[level][i].second << ") \n"; + } + std::cerr << "PL2 : \n"; + for (size_t i = 0; i != pl2.land[level].size(); ++i) { + std::cerr << "(" << pl2.land[level][i].first << "," << pl2.land[level][i].second << ") \n"; + } + std::cin.ignore(); + } + + int p2Count = 0; + // In this case, I consider points at the infinity + for (size_t i = 1; i != pl1.land[level].size() - 1; ++i) { + while (true) { + if ((pl1.land[level][i].first >= pl2.land[level][p2Count].first) && + (pl1.land[level][i].first <= pl2.land[level][p2Count + 1].first)) + break; + p2Count++; + } + double val = + fabs(function_value(pl2.land[level][p2Count], pl2.land[level][p2Count + 1], pl1.land[level][i].first) - + pl1.land[level][i].second); + if (maxDist <= val) maxDist = val; + + if (dbg) { + std::cerr << pl1.land[level][i].first << "in [" << pl2.land[level][p2Count].first << "," + << pl2.land[level][p2Count + 1].first << "] \n"; + std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl; + std::cerr << "function_value( pl2[level][p2Count] , pl2[level][p2Count+1] , pl1[level][i].first ) : " + << function_value(pl2.land[level][p2Count], pl2.land[level][p2Count + 1], pl1.land[level][i].first) + << std::endl; + std::cerr << "val : " << val << std::endl; + std::cin.ignore(); + } + } + } + + if (dbg) std::cerr << "minimalNumberOfLevels : " << minimalNumberOfLevels << std::endl; + + if (minimalNumberOfLevels < pl1.land.size()) { + for (size_t level = minimalNumberOfLevels; level != pl1.land.size(); ++level) { + for (size_t i = 0; i != pl1.land[level].size(); ++i) { + if (dbg) std::cerr << "pl1[level][i].second : " << pl1.land[level][i].second << std::endl; + if (maxDist < pl1.land[level][i].second) maxDist = pl1.land[level][i].second; + } + } + } + return maxDist; +} + +double compute_distance_of_landscapes(const Persistence_landscape& first, const Persistence_landscape& second, + double p) { + bool dbg = false; + // This is what we want to compute: (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p). We will do it one step at a + // time: + + // first-second : + Persistence_landscape lan = first - second; + + //| first-second |: + lan = lan.abs(); + + if (dbg) { + std::cerr << "Abs of difference ; " << lan << std::endl; + getchar(); + } + + if (p < std::numeric_limits<double>::max()) { + // \int_{- \infty}^{+\infty}| first-second |^p + double result; + if (p != 1) { + if (dbg) std::cerr << "Power != 1, compute integral to the power p\n"; + result = lan.compute_integral_of_landscape(p); + } else { + if (dbg) std::cerr << "Power = 1, compute integral \n"; + result = lan.compute_integral_of_landscape(); + } + // (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p) + return pow(result, 1.0 / p); + } else { + // p == infty + if (dbg) std::cerr << "Power = infty, compute maximum \n"; + return lan.compute_maximum(); + } +} + +double compute_max_norm_distance_of_landscapes(const Persistence_landscape& first, + const Persistence_landscape& second) { + return std::max(compute_maximal_distance_non_symmetric(first, second), + compute_maximal_distance_non_symmetric(second, first)); +} + +bool comparePairsForMerging(std::pair<double, unsigned> first, std::pair<double, unsigned> second) { + return (first.first < second.first); +} + +double compute_inner_product(const Persistence_landscape& l1, const Persistence_landscape& l2) { + bool dbg = false; + double result = 0; + + for (size_t level = 0; level != std::min(l1.size(), l2.size()); ++level) { + if (dbg) { + std::cerr << "Computing inner product for a level : " << level << std::endl; + getchar(); + } + auto&& l1_land_level = l1.land[level]; + auto&& l2_land_level = l2.land[level]; + + if (l1_land_level.size() * l2_land_level.size() == 0) continue; + + // endpoints of the interval on which we will compute the inner product of two locally linear functions: + double x1 = -std::numeric_limits<int>::max(); + double x2; + if (l1_land_level[1].first < l2_land_level[1].first) { + x2 = l1_land_level[1].first; + } else { + x2 = l2_land_level[1].first; + } + + // iterators for the landscapes l1 and l2 + size_t l1It = 0; + size_t l2It = 0; + + while ((l1It < l1_land_level.size() - 1) && (l2It < l2_land_level.size() - 1)) { + // compute the value of a inner product on a interval [x1,x2] + + double a, b, c, d; + + if (l1_land_level[l1It + 1].first != l1_land_level[l1It].first) { + a = (l1_land_level[l1It + 1].second - l1_land_level[l1It].second) / + (l1_land_level[l1It + 1].first - l1_land_level[l1It].first); + } else { + a = 0; + } + b = l1_land_level[l1It].second - a * l1_land_level[l1It].first; + if (l2_land_level[l2It + 1].first != l2_land_level[l2It].first) { + c = (l2_land_level[l2It + 1].second - l2_land_level[l2It].second) / + (l2_land_level[l2It + 1].first - l2_land_level[l2It].first); + } else { + c = 0; + } + d = l2_land_level[l2It].second - c * l2_land_level[l2It].first; + + double contributionFromThisPart = (a * c * x2 * x2 * x2 / 3 + (a * d + b * c) * x2 * x2 / 2 + b * d * x2) - + (a * c * x1 * x1 * x1 / 3 + (a * d + b * c) * x1 * x1 / 2 + b * d * x1); + + result += contributionFromThisPart; + + if (dbg) { + std::cerr << "[l1_land_level[l1It].first,l1_land_level[l1It+1].first] : " << l1_land_level[l1It].first + << " , " << l1_land_level[l1It + 1].first << std::endl; + std::cerr << "[l2_land_level[l2It].first,l2_land_level[l2It+1].first] : " << l2_land_level[l2It].first + << " , " << l2_land_level[l2It + 1].first << std::endl; + std::cerr << "a : " << a << ", b : " << b << " , c: " << c << ", d : " << d << std::endl; + std::cerr << "x1 : " << x1 << " , x2 : " << x2 << std::endl; + std::cerr << "contributionFromThisPart : " << contributionFromThisPart << std::endl; + std::cerr << "result : " << result << std::endl; + getchar(); + } + + // we have two intervals in which functions are constant: + // [l1_land_level[l1It].first , l1_land_level[l1It+1].first] + // and + // [l2_land_level[l2It].first , l2_land_level[l2It+1].first] + // We also have an interval [x1,x2]. Since the intervals in the landscapes cover the whole R, then it is clear + // that x2 + // is either l1_land_level[l1It+1].first of l2_land_level[l2It+1].first or both. Lets test it. + if (x2 == l1_land_level[l1It + 1].first) { + if (x2 == l2_land_level[l2It + 1].first) { + // in this case, we increment both: + ++l2It; + if (dbg) { + std::cerr << "Incrementing both \n"; + } + } else { + if (dbg) { + std::cerr << "Incrementing first \n"; + } + } + ++l1It; + } else { + // in this case we increment l2It + ++l2It; + if (dbg) { + std::cerr << "Incrementing second \n"; + } + } + + if ( l1It + 1 >= l1_land_level.size() )break; + if ( l2It + 1 >= l2_land_level.size() )break; + + // Now, we shift x1 and x2: + x1 = x2; + if (l1_land_level[l1It + 1].first < l2_land_level[l2It + 1].first) { + x2 = l1_land_level[l1It + 1].first; + } else { + x2 = l2_land_level[l2It + 1].first; + } + } + } + return result; +} + +void Persistence_landscape::plot(const char* filename, double xRangeBegin, double xRangeEnd, double yRangeBegin, + double yRangeEnd, int from, int to) { + // this program create a gnuplot script file that allows to plot persistence diagram. + std::ofstream out; + + std::ostringstream gnuplot_script; + gnuplot_script << filename << "_GnuplotScript"; + out.open(gnuplot_script.str().c_str()); + + if ((xRangeBegin != std::numeric_limits<double>::max()) || (xRangeEnd != std::numeric_limits<double>::max()) || + (yRangeBegin != std::numeric_limits<double>::max()) || (yRangeEnd != std::numeric_limits<double>::max())) { + out << "set xrange [" << xRangeBegin << " : " << xRangeEnd << "]" << std::endl; + out << "set yrange [" << yRangeBegin << " : " << yRangeEnd << "]" << std::endl; + } + + if (from == std::numeric_limits<int>::max()) { + from = 0; + } + if (to == std::numeric_limits<int>::max()) { + to = this->land.size(); + } + + out << "plot "; + for (size_t lambda = std::min((size_t)from, this->land.size()); lambda != std::min((size_t)to, this->land.size()); + ++lambda) { + // out << " '-' using 1:2 title 'l" << lambda << "' with lp"; + out << " '-' using 1:2 notitle with lp"; + if (lambda + 1 != std::min((size_t)to, this->land.size())) { + out << ", \\"; + } + out << std::endl; + } + + for (size_t lambda = std::min((size_t)from, this->land.size()); lambda != std::min((size_t)to, this->land.size()); + ++lambda) { + for (size_t i = 1; i != this->land[lambda].size() - 1; ++i) { + out << this->land[lambda][i].first << " " << this->land[lambda][i].second << std::endl; + } + out << "EOF" << std::endl; + } + std::cout << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'" + << gnuplot_script.str().c_str() << "\'\"" << std::endl; +} + +} // namespace Persistence_representations +} // namespace Gudhi + +#endif // PERSISTENCE_LANDSCAPE_H_ |