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diff --git a/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h new file mode 100644 index 00000000..68bce336 --- /dev/null +++ b/src/Persistence_representations/include/gudhi/Persistence_landscape_on_grid.h @@ -0,0 +1,1335 @@ +/* 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_ON_GRID_H_ +#define PERSISTENCE_LANDSCAPE_ON_GRID_H_ + +// gudhi include +#include <gudhi/read_persistence_from_file.h> +#include <gudhi/common_persistence_representations.h> + +// standard include +#include <iostream> +#include <vector> +#include <limits> +#include <fstream> +#include <sstream> +#include <algorithm> +#include <cmath> +#include <functional> +#include <utility> +#include <string> +#include <cstdint> + +namespace Gudhi { +namespace Persistence_representations { + +// pre declaration +class Persistence_landscape_on_grid; +template <typename operation> +Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid(const Persistence_landscape_on_grid& land1, + const Persistence_landscape_on_grid& land2); + +/** + * \class Persistence_landscape_on_grid Persistence_landscape_on_grid.h gudhi/Persistence_landscape_on_grid.h + * \brief A class implementing persistence landscapes by approximating them on a collection of grid points. + * + * \ingroup Persistence_representations + * + * \details + * Persistence landscapes on grid allows 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 on a grid, + * elements which are different by 0.000005 are considered the same. If the scale in your persistence diagrams + * is comparable to this value, please rescale them before use this code. +**/ + +// this class implements the following concepts: Vectorized_topological_data, Topological_data_with_distances, +// Real_valued_topological_data, Topological_data_with_averages, Topological_data_with_scalar_product +class Persistence_landscape_on_grid { + public: + /** + * Default constructor. + **/ + Persistence_landscape_on_grid() { + this->set_up_numbers_of_functions_for_vectorization_and_projections_to_reals(); + this->grid_min = this->grid_max = 0; + } + + /** + * Constructor that takes as an input a vector of birth-death pairs. + **/ + Persistence_landscape_on_grid(const std::vector<std::pair<double, double> >& p, double grid_min_, double grid_max_, + size_t number_of_points_); + + /** + * Constructor that takes as an input a vector of birth-death pairs, parameters of the grid and number of + *landscape function to be created. + **/ + Persistence_landscape_on_grid(const std::vector<std::pair<double, double> >& p, double grid_min_, double grid_max_, + size_t number_of_points_, unsigned number_of_levels_of_landscape); + + /** + * Constructor that reads persistence intervals from file and creates persistence landscape. The format of the + *input file is the following: in each line we put birth-death pair. Last line is assumed + * to be empty. Even if the points within a line are not ordered, they will be ordered while the input is read. + *The additional parameters of this procedure are: ranges of grid, resolution of a grid + * number of landscape functions to be created and the dimension of intervals that are need to be read from a file + *(in case of Gudhi format files). + **/ + Persistence_landscape_on_grid(const char* filename, double grid_min_, double grid_max_, size_t number_of_points_, + unsigned number_of_levels_of_landscape, + uint16_t dimension_ = std::numeric_limits<uint16_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. The + *additional parameters of this procedure are: ranges of grid, resolution 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_, + uint16_t dimension_ = std::numeric_limits<uint16_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. + *The additional parameter is the resolution of a grid and the number of landscape + * functions to be created. The remaining parameters are calculated based on data. + **/ + Persistence_landscape_on_grid(const char* filename, size_t number_of_points, unsigned number_of_levels_of_landscape, + uint16_t dimension = std::numeric_limits<uint16_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. The + *additional parameter is the resolution of a grid. The last parameter is the dimension + * of a persistence to read from the file. If your file contains only persistence pair in a single dimension, please + *set it up to std::numeric_limits<unsigned>::max(). + * The remaining parameters are calculated based on data. + **/ + Persistence_landscape_on_grid(const char* filename, size_t number_of_points, + uint16_t dimension = std::numeric_limits<uint16_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 { + 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) / static_cast<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) / static_cast<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 << "result : " << 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) / static_cast<double>(land.values_of_landscapes.size() - 1); + double x = land.grid_min; + for (size_t i = 0; i != land.values_of_landscapes.size(); ++i) { + out << x << " : "; + for (size_t j = 0; j != land.values_of_landscapes[i].size(); ++j) { + out << land.values_of_landscapes[i][j] << " "; + } + out << std::endl; + x += dx; + } + return out; + } + + template <typename oper> + friend Persistence_landscape_on_grid operation_on_pair_of_landscapes_on_grid( + const Persistence_landscape_on_grid& land1, const Persistence_landscape_on_grid& land2); + + /** + * A function that computes the value of a landscape at a given point. The parameters of the function are: unsigned + *level and double x. + * The procedure will compute the value of the level-landscape at the point x. + **/ + double compute_value_at_a_given_point(unsigned level, double x) const { + bool dbg = false; + if ((x < this->grid_min) || (x > this->grid_max)) return 0; + + // find a position of a vector closest to x: + double dx = (this->grid_max - this->grid_min) / static_cast<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 << "position : " << position << std::endl; + } + // check if we are not exactly 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 { + line = compute_parameters_of_a_line( + std::make_pair(position * dx + this->grid_min, 0), + std::make_pair((position + 1) * dx + this->grid_min, this->values_of_landscapes[position + 1][level])); + } + } else { + return 0; + } + } + // compute the value of the linear function parametrized by line on a point x: + return line.first * x + line.second; + } + + public: + /** + *\private A function that compute sum of two landscapes. + **/ + friend Persistence_landscape_on_grid add_two_landscapes(const Persistence_landscape_on_grid& land1, + const Persistence_landscape_on_grid& land2) { + return operation_on_pair_of_landscapes_on_grid<std::plus<double> >(land1, land2); + } + + /** + *\private A function that compute difference of two landscapes. + **/ + friend Persistence_landscape_on_grid subtract_two_landscapes(const Persistence_landscape_on_grid& land1, + const Persistence_landscape_on_grid& land2) { + return operation_on_pair_of_landscapes_on_grid<std::minus<double> >(land1, land2); + } + + /** + * An operator +, that compute sum of two landscapes. + **/ + friend Persistence_landscape_on_grid operator+(const Persistence_landscape_on_grid& first, + const Persistence_landscape_on_grid& second) { + return add_two_landscapes(first, second); + } + + /** + * An operator -, that compute difference of two landscapes. + **/ + friend Persistence_landscape_on_grid operator-(const Persistence_landscape_on_grid& first, + const Persistence_landscape_on_grid& second) { + return subtract_two_landscapes(first, second); + } + + /** + * An operator * that allows multiplication 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 multiplication 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 persistence landscape. + **/ + Persistence_landscape_on_grid operator+=(const Persistence_landscape_on_grid& rhs) { + *this = *this + rhs; + return *this; + } + + /** + * Operator -=. The second parameter is persistence landscape. + **/ + 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 incompatible 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); + } + + /** + * 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(); } + + /** + * This function computes maximal lambda for which lambda-level landscape is nonzero. + **/ + size_t number_of_nonzero_levels() const { + size_t result = 0; + for (size_t i = 0; i != this->values_of_landscapes.size(); ++i) { + if (this->values_of_landscapes[i].size() > result) result = this->values_of_landscapes[i].size(); + } + return result; + } + + /** + * Computations of a \f$L^i\f$ norm of landscape, where i is the input parameter. + **/ + double compute_norm_of_landscape(double i) const { + std::vector<std::pair<double, double> > p; + Persistence_landscape_on_grid l(p, this->grid_min, this->grid_max, this->values_of_landscapes.size() - 1); + + if (i < std::numeric_limits<double>::max()) { + return compute_distance_of_landscapes_on_grid(*this, l, i); + } else { + return compute_max_norm_distance_of_landscapes(*this, l); + } + } + + /** + * An operator to compute the value of a landscape in the level 'level' at the argument 'x'. + **/ + double operator()(unsigned level, double x) const { return this->compute_value_at_a_given_point(level, x); } + + /** + * Computations of \f$L^{\infty}\f$ distance between two landscapes. + **/ + friend double compute_max_norm_distance_of_landscapes(const Persistence_landscape_on_grid& first, + const Persistence_landscape_on_grid& second); + + /** + * 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. + **/ + 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(); } + + /** + * Compute 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) / static_cast<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 integral 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 i.e. : " << previous_x << " is : " + << a * c / 3 * previous_x * previous_x * previous_x + (a * d + b * c) / 2 * previous_x * previous_x + + b * d * previous_x + << std::endl; + std::cerr << "Value of the integral on the right end i.e. : " << current_x << " is " + << a * c / 3 * current_x * current_x * current_x + (a * d + b * c) / 2 * current_x * current_x + + b * d * current_x + << std::endl; + } + + result += added_value; + + if (dbg) { + std::cerr << "added_value : " << added_value << std::endl; + std::cerr << "result : " << result << std::endl; + getchar(); + } + + previous_x = current_x; + previous_y_l1 = current_y_l1; + previous_y_l2 = current_y_l2; + } + return result; + } + + /** + * Computations of \f$L^{p}\f$ distance between two landscapes on a grid. p is the parameter of the procedure. + * FIXME: Note that, due to the grid representation, the method below may give non--accurate results in case when the + *landscape P and Q the difference of which we want to compute + * are intersecting. 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(p); + if (dbg) { + std::cerr << "integral : " << result << std::endl; + getchar(); + } + } else { + result = lan.compute_integral_of_landscape(); + if (dbg) { + std::cerr << "integral, without power : " << result << std::endl; + getchar(); + } + } + // (\int_{- \infty}^{+\infty}| first-second |^p)^(1/p) + return pow(result, 1.0 / p); + } else { + // p == infty + return lan.compute_maximum(); + } + } + + // Functions that are needed for that class to implement the concept. + + /** + * The number of projections to R is defined to the number of nonzero landscape functions. I-th projection is an + *integral of i-th landscape function over whole R. + * This function is required by the Real_valued_topological_data concept. + * At the moment this function is not tested, since it is quite 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_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(PD) think of something smarter over here + if ((number_of_function < 0) || ((size_t)number_of_function >= this->values_of_landscapes.size())) { + throw "Wrong number of function\n"; + } + std::vector<double> v(this->values_of_landscapes.size()); + for (size_t i = 0; i != this->values_of_landscapes.size(); ++i) { + v[i] = 0; + if (this->values_of_landscapes[i].size() > (size_t)number_of_function) { + v[i] = this->values_of_landscapes[i][number_of_function]; + } + } + return v; + } + + /** + * This function return the number of functions that allows vectorization of persistence landscape. 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 average, 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 arithmetic 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] /= static_cast<double>(to_average.size()); + } + } + } // compute_average + + /** + * A function to compute distance between persistence landscape on a grid. + * The parameter of this function is 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 function is 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 landscapes. It can be used for visualization + **/ + 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 default values for min and + *max are std::numeric_limits<double>::max(). If the procedure detect those + * values, it will determine the range so that the whole landscape is supported there. If at least one min or max value + *is different from std::numeric_limits<double>::max(), then the values + * provided by the user will be used. + **/ + void plot(const char* filename, size_t from_, size_t to_) const { + this->plot(filename, std::numeric_limits<double>::max(), std::numeric_limits<double>::max(), + std::numeric_limits<double>::max(), std::numeric_limits<double>::max(), from_, to_); + } + + /** + * function used to create a gnuplot script for visualization of landscapes. Over here we can restrict also x and y + *range of the landscape. + **/ + void plot(const char* filename, double min_x = std::numeric_limits<double>::max(), + double max_x = std::numeric_limits<double>::max(), double min_y = std::numeric_limits<double>::max(), + double max_y = std::numeric_limits<double>::max(), size_t from_ = std::numeric_limits<size_t>::max(), + size_t to_ = std::numeric_limits<size_t>::max()) const; + + protected: + double grid_min; + double grid_max; + std::vector<std::vector<double> > values_of_landscapes; + size_t number_of_functions_for_vectorization; + size_t number_of_functions_for_projections_to_reals; + + void set_up_numbers_of_functions_for_vectorization_and_projections_to_reals() { + // warning, this function can be only called after filling in the values_of_landscapes vector. + this->number_of_functions_for_vectorization = this->values_of_landscapes.size(); + this->number_of_functions_for_projections_to_reals = this->values_of_landscapes.size(); + } + void set_up_values_of_landscapes(const std::vector<std::pair<double, double> >& p, double grid_min_, double grid_max_, + size_t number_of_points_, + unsigned number_of_levels = std::numeric_limits<unsigned>::max()); + Persistence_landscape_on_grid multiply_lanscape_by_real_number_not_overwrite(double x) const; +}; + +void Persistence_landscape_on_grid::set_up_values_of_landscapes(const std::vector<std::pair<double, double> >& p, + double grid_min_, double grid_max_, + size_t number_of_points_, unsigned number_of_levels) { + bool dbg = false; + if (dbg) { + std::cerr << "Here is the procedure : set_up_values_of_landscapes. The parameters are : grid_min_ : " << grid_min_ + << ", grid_max_ : " << grid_max_ << ", number_of_points_ : " << number_of_points_ + << ", number_of_levels: " << number_of_levels << std::endl; + std::cerr << "Here are the intervals at our disposal : \n"; + for (size_t i = 0; i != p.size(); ++i) { + std::cerr << p[i].first << " , " << p[i].second << std::endl; + } + } + + if ((grid_min_ == std::numeric_limits<double>::max()) || (grid_max_ == std::numeric_limits<double>::max())) { + // in this case, we need to find grid_min_ and grid_min_ based on the data. + double min = std::numeric_limits<double>::max(); + double max = std::numeric_limits<double>::min(); + for (size_t i = 0; i != p.size(); ++i) { + if (p[i].first < min) min = p[i].first; + if (p[i].second > max) max = p[i].second; + } + if (grid_min_ == std::numeric_limits<double>::max()) { + grid_min_ = min; + } else { + // in this case grid_max_ == std::numeric_limits<double>::max() + grid_max_ = max; + } + } + + // if number_of_levels == std::numeric_limits<size_t>::max(), then we will have all the nonzero values of landscapes, + // and will store them in a vector + // if number_of_levels != std::numeric_limits<size_t>::max(), then we will use those vectors as heaps. + this->values_of_landscapes = std::vector<std::vector<double> >(number_of_points_ + 1); + + this->grid_min = grid_min_; + this->grid_max = grid_max_; + + if (grid_max_ <= grid_min_) { + throw "Wrong parameters of grid_min and grid_max given to the procedure. The program will now terminate.\n"; + } + + double dx = (grid_max_ - grid_min_) / static_cast<double>(number_of_points_); + // for every interval in the diagram: + for (size_t int_no = 0; int_no != p.size(); ++int_no) { + size_t grid_interval_begin = (p[int_no].first - grid_min_) / dx; + size_t grid_interval_end = (p[int_no].second - grid_min_) / dx; + size_t grid_interval_midpoint = (size_t)(0.5 * (grid_interval_begin + grid_interval_end)); + + if (dbg) { + std::cerr << "Considering an interval : " << p[int_no].first << "," << p[int_no].second << std::endl; + + std::cerr << "grid_interval_begin : " << grid_interval_begin << std::endl; + std::cerr << "grid_interval_end : " << grid_interval_end << std::endl; + std::cerr << "grid_interval_midpoint : " << grid_interval_midpoint << std::endl; + } + + double landscape_value = dx; + for (size_t i = grid_interval_begin + 1; i < grid_interval_midpoint; ++i) { + if (dbg) { + std::cerr << "Adding landscape value (going up) for a point : " << i << " equal : " << landscape_value + << std::endl; + } + if (number_of_levels != std::numeric_limits<unsigned>::max()) { + // we have a heap of no more that number_of_levels values. + // Note that if we are using heaps, we want to know the shortest distance in the heap. + // This is achieved by putting -distance to the heap. + if (this->values_of_landscapes[i].size() >= number_of_levels) { + // in this case, the full heap is build, and we need to check if the landscape_value is not larger than the + // smallest element in the heap. + if (-landscape_value < this->values_of_landscapes[i].front()) { + // if it is, we remove the largest value in the heap, and move on. + std::pop_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + this->values_of_landscapes[i][this->values_of_landscapes[i].size() - 1] = -landscape_value; + std::push_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + } + } else { + // in this case we are still filling in the array. + this->values_of_landscapes[i].push_back(-landscape_value); + if (this->values_of_landscapes[i].size() == number_of_levels - 1) { + // this->values_of_landscapes[i].size() == number_of_levels + // in this case we need to create the heap. + std::make_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + } + } + } else { + // we have vector of all values + this->values_of_landscapes[i].push_back(landscape_value); + } + landscape_value += dx; + } + for (size_t i = grid_interval_midpoint; i <= grid_interval_end; ++i) { + if (landscape_value > 0) { + if (number_of_levels != std::numeric_limits<unsigned>::max()) { + // we have a heap of no more that number_of_levels values + if (this->values_of_landscapes[i].size() >= number_of_levels) { + // in this case, the full heap is build, and we need to check if the landscape_value is not larger than the + // smallest element in the heap. + if (-landscape_value < this->values_of_landscapes[i].front()) { + // if it is, we remove the largest value in the heap, and move on. + std::pop_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + this->values_of_landscapes[i][this->values_of_landscapes[i].size() - 1] = -landscape_value; + std::push_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + } + } else { + // in this case we are still filling in the array. + this->values_of_landscapes[i].push_back(-landscape_value); + if (this->values_of_landscapes[i].size() == number_of_levels - 1) { + // this->values_of_landscapes[i].size() == number_of_levels + // in this case we need to create the heap. + std::make_heap(this->values_of_landscapes[i].begin(), this->values_of_landscapes[i].end()); + } + } + } else { + this->values_of_landscapes[i].push_back(landscape_value); + } + + if (dbg) { + std::cerr << "Adding landscape value (going down) for a point : " << i << " equal : " << landscape_value + << std::endl; + } + } + landscape_value -= dx; + } + } + + if (number_of_levels != std::numeric_limits<unsigned>::max()) { + // in this case, vectors are used as heaps. And, since we want to have the smallest element at the top of + // each heap, we store minus distances. To get if right at the end, we need to multiply each value + // in the heap by -1 to get real vector of distances. + for (size_t pt = 0; pt != this->values_of_landscapes.size(); ++pt) { + for (size_t j = 0; j != this->values_of_landscapes[pt].size(); ++j) { + this->values_of_landscapes[pt][j] *= -1; + } + } + } + + // and now we need to sort the values: + for (size_t pt = 0; pt != this->values_of_landscapes.size(); ++pt) { + std::sort(this->values_of_landscapes[pt].begin(), this->values_of_landscapes[pt].end(), std::greater<double>()); + } +} // set_up_values_of_landscapes + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const std::vector<std::pair<double, double> >& p, + double grid_min_, double grid_max_, + size_t number_of_points_) { + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_); +} // Persistence_landscape_on_grid + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const std::vector<std::pair<double, double> >& p, + double grid_min_, double grid_max_, + size_t number_of_points_, + unsigned number_of_levels_of_landscape) { + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_, number_of_levels_of_landscape); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename, double grid_min_, double grid_max_, + size_t number_of_points_, uint16_t dimension) { + std::vector<std::pair<double, double> > p; + if (dimension == std::numeric_limits<uint16_t>::max()) { + p = read_persistence_intervals_in_one_dimension_from_file(filename); + } else { + p = read_persistence_intervals_in_one_dimension_from_file(filename, dimension); + } + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename, double grid_min_, double grid_max_, + size_t number_of_points_, + unsigned number_of_levels_of_landscape, + uint16_t dimension) { + std::vector<std::pair<double, double> > p; + if (dimension == std::numeric_limits<uint16_t>::max()) { + p = read_persistence_intervals_in_one_dimension_from_file(filename); + } else { + p = read_persistence_intervals_in_one_dimension_from_file(filename, dimension); + } + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_, number_of_levels_of_landscape); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename, size_t number_of_points_, + uint16_t dimension) { + std::vector<std::pair<double, double> > p; + if (dimension == std::numeric_limits<uint16_t>::max()) { + p = read_persistence_intervals_in_one_dimension_from_file(filename); + } else { + p = read_persistence_intervals_in_one_dimension_from_file(filename, dimension); + } + double grid_min_ = std::numeric_limits<double>::max(); + double grid_max_ = -std::numeric_limits<double>::max(); + for (size_t i = 0; i != p.size(); ++i) { + if (p[i].first < grid_min_) grid_min_ = p[i].first; + if (p[i].second > grid_max_) grid_max_ = p[i].second; + } + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_); +} + +Persistence_landscape_on_grid::Persistence_landscape_on_grid(const char* filename, size_t number_of_points_, + unsigned number_of_levels_of_landscape, + uint16_t dimension) { + std::vector<std::pair<double, double> > p; + if (dimension == std::numeric_limits<uint16_t>::max()) { + p = read_persistence_intervals_in_one_dimension_from_file(filename); + } else { + p = read_persistence_intervals_in_one_dimension_from_file(filename, dimension); + } + double grid_min_ = std::numeric_limits<double>::max(); + double grid_max_ = -std::numeric_limits<double>::max(); + for (size_t i = 0; i != p.size(); ++i) { + if (p[i].first < grid_min_) grid_min_ = p[i].first; + if (p[i].second > grid_max_) grid_max_ = p[i].second; + } + this->set_up_values_of_landscapes(p, grid_min_, grid_max_, number_of_points_, number_of_levels_of_landscape); +} + +void Persistence_landscape_on_grid::load_landscape_from_file(const char* filename) { + std::ifstream in; + in.open(filename); + // check if the file exist. + if (!in.good()) { + std::cerr << "The file : " << filename << " do not exist. The program will now terminate \n"; + throw "The persistence landscape file do not exist. The program will now terminate \n"; + } + + size_t number_of_points_in_the_grid = 0; + in >> this->grid_min >> this->grid_max >> number_of_points_in_the_grid; + + std::vector<std::vector<double> > v(number_of_points_in_the_grid); + std::string line; + std::getline(in, line); + double number; + for (size_t i = 0; i != number_of_points_in_the_grid; ++i) { + // read a line of a file and convert it to a vector. + std::vector<double> vv; + std::getline(in, line); + std::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 gnuplot_script; + gnuplot_script << filename << "_GnuplotScript"; + out.open(gnuplot_script.str().c_str()); + + 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) / static_cast<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 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 << "To visualize, install gnuplot and type the command: gnuplot -persist -e \"load \'" + << gnuplot_script.str().c_str() << "\'\"" << 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 perform 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 Persistence_representations +} // namespace Gudhi + +#endif // PERSISTENCE_LANDSCAPE_ON_GRID_H_ |