diff options
Diffstat (limited to 'include/gudhi/Persistence_landscape_on_grid.h')
| -rw-r--r-- | include/gudhi/Persistence_landscape_on_grid.h | 1348 |
1 files changed, 0 insertions, 1348 deletions
diff --git a/include/gudhi/Persistence_landscape_on_grid.h b/include/gudhi/Persistence_landscape_on_grid.h deleted file mode 100644 index fd8a181c..00000000 --- a/include/gudhi/Persistence_landscape_on_grid.h +++ /dev/null @@ -1,1348 +0,0 @@ -/** This file is part of the Gudhi Library. The Gudhi library - * (Geometric Understanding in Higher Dimensions) is a generic C++ - * library for computational topology. - * - * Author(s): Pawel Dlotko - * - * Copyright (C) 2016 Inria - * - * This program is free software: you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation, either version 3 of the License, or - * (at your option) any later version. - * - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with this program. If not, see <http://www.gnu.org/licenses/>. - **/ - -#ifndef PERSISTENCE_LANDSCAPE_ON_GRID_H_ -#define PERSISTENCE_LANDSCAPE_ON_GRID_H_ - -// 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_ |