src.config

General configuration file.

Summary

This module contains all the configuration parameters that define the details of the DGCG algorithm. Al parameters are set at execution of src.DGCG.solve() and then remain fixed.

Therefore, to modify any of these parameters, do it before executing src.DGCG.solve()

Module Contents

Functions

self_pickle(filename)

Function to pickle and save the variables in this module.

src.config.self_pickle(filename)

Function to pickle and save the variables in this module.

The pickled variables are saved into the folder set by src.config.results_folder

src.config.results_folder = results

str. By default, the algorithm stores at each iteration the iterate, graphs the convergence plots, dual gaps, found stationary points, etc. This variable indicates the name of the folder in which these are stored.

src.config.logger

src.log_mod.logger. The logger class is involved in all the logging activities, like plotting, pickling data, terminal printing, etc. A logger object is created and then accessed by all the modules here.

src.config.T = 51

int. The number of time samples of the problem.

src.config.time

numpy.ndarray.

The respective time samples of the problem.

src.config.time_weights

numpy.ndarray.

The associated weights to each time sample. By default, these are equally weighted summing up to 1. Relevant when dealing with different uncertainty values for each time sample.

src.config.alpha = 0.1

float. Regularization coefficient of the problem

src.config.beta = 0.1

float. Regularization coefficient of the problem

src.config.f_t

list[numpy.ndarray]. Input data in the problem, represents a list of elements in H_t for each t.

src.config.measure_coefficient_too_low = 1e-18

float. The measure class is a weighted sum of atoms. When the weight of an atom is lower than this threshold, it is automatically discarded.

src.config.full_max_iterations = 1000

int. Maximum number of iterations of the algorithm.

src.config.insertion_max_segments = 20

int. In the insertion step, during the multistart gradient descent, random curves are proposed for descense in insertion_mod.random_insertion The number of segments of the random curves is chosen at random, with this parameter defining the upper limit on the chosen segments.

src.config.rejection_sampling_epsilon = 0.05

float. When generating random curves for insertion at insertion_mod.random_insertion, once the time nodes of the curve is defined, the spatial positions are chosed via the rejection_sampling algorithm. This parameter is involved in the definition of used function. In principle, the higher is this number, the faster the rejection sampling algorithm will find a candidate. But simultaneously, it will miss possible candidates that have values barely above 0.

src.config.insertion_length_bound_factor = 1.1

float. When proposing curves to descend in insertion_mod.propose, it is known from the theory that any solution must not exceed a certain length that can be computed. If any proposed curve surpases this limit by a factor given by this parameter, it is automatically discarded.

src.config.multistart_pooling_num = 1000

int. When proposing random curves, many random curves are proposed and afterwards, before descending them, we choose the best one from this group The size of the generated random curves is defined by this parameter. The criteria to choose the best curve is one that has the least F(γ) value.

src.config.crossover_consecutive_inserts = 30

int. The proposing method at insertion_mod.propose switches between choosing a crossover curve or a random curve. For each N crossover propositions it does 1 random proposition. N here corresponds to this parameter.

src.config.crossover_search_attempts = 1000

int. To crossover curves the algorithm must look for curves that are close enough to crossover and then check if these have been crossover beforehand. This information is contained in the sort-of-dictionary object insertion_mod.ordered_list_of_lists, and to look for new pairs it will randomly access the entries to see if a crossover can be obtained. It will attempt this random entries the number given by the his parameters, if no crossover is found after this search, insertion_mod.propose will declare that there are no available crossovers and then will propose a random curve for descent.

src.config.crossover_child_F_threshold = 0.8

float. Obtained crossover curves will be proposed for descensen only if their energy F(γ) is close to the best known stationary curve. How close it has to be is modulated by this parameter, it must satisfy F(crossover_child) < crossover_child_F_threshold * F(best_curve), remember that the energies are negative.

src.config.crossover_max_distance = 0.05

float. Childs from two curves can be obtained only if at some point in time they get close one to another, this parameter indicates how close they need to get in H^1 norm for a crossover to happen.

src.config.insertion_eps = 1e-10

float. This is the tolenrance value to stop the algorithm. If the dual gap drops below it, the algorithm exits.

src.config.insertion_max_restarts = 20

int. The maximum number of restarts of the multistart algorithm.

src.config.insertion_min_restarts = 15

int. The minimum number of restarts of the multistart algorithm. This parameter is useful only in the case an early stop criteria is set via the multistart_early_stop parameter.

src.config.multistart_inter_iteration_checkup = 50

int. While descending a single curve during the multistart gradient descent, the code will routinely check if curve being descended is close to the any element of the stationary point set. If so, the descense is stopped and the curve is discarded. This parameter regulates how often this check is done. Precaution: The algorithm also is coded to “omit” the curves that got too fast too close to the stationary point set. By “omiting”, we mean that such a descented curve will not count towards the number of descented curves; “too fast” means that the curve got too close to the statonary set before the first checkup. A consequence of this is that if this checkup number is set too high, and there are a few stationary points, then (almost) all the descended curves will converge faster than the first checkup and as such, they will not count towards the number of attempted tries. Heavily slowing down the algorithm.

src.config.multistart_max_discarded_tries = 30

int. If more than multistart_max_discarded_tries curves are discarded consecutively. Then the algorithm will issue a warning to set multistart_inter_iteration_checkup higher and will add a counter to the number of restarts. This is a failsafe against a while true loop.

src.config.multistart_taboo_dist = 0.01

float. The distance, in H^1 norm, of a curve to an element of the stationary set to be discarded.

src.config.multistart_energy_dist = 0.01

float. Acceleration parameter to measure the distance between the descended curve with those of the stationary set. The stationary point set is ordered by their F(γ) value, which is also readily available in a list. Therefore by computing the F(γ) value of the descended curve, one can just compare the current curve with those around that value, this parameter defines that radius.

src.config.multistart_early_stop

callable[[int,int], int], default constant equal to infinite. This parameter allows to pass an early stop criteria to the multistart algorithm. The input is a two variable function whose first input is the number of attempted restarts, and the second parameter is the number of found stationary point. The multistart gradient descent will stop once it either reaches the insertion_max_restart value, or the value given by this function.

src.config.multistart_proposition_max_iter = 10000

int. Each proposed curve must start with negative energy, if it does not, it is discarded and another curve is proposed. This parameter sets a limit on how many attempts will be done.

src.config.multistart_descent_max_iter = 16000

int. This parameter limits the number of gradient descent steps that will be done on each descended curve.

src.config.multistart_descent_soft_max_iter = 5000

int. This is a soft maximum number of iterations. If the currently descended curve has done more than this number of iterations, and simultaneously its energy is not “good enough”, then the descense will be stopped.

src.config.multistart_descent_soft_max_threshold = 0.8

float. Sets the threshold to discard the current descended curve, the current descended curve has to be at least this ratio closer to the best known stationary curve.

src.config.multistart_descent_init_step = 10.0

float. The gradient descent uses an Armijo with backtracking descent. This parameter sets the intiial stepsize/

src.config.multistart_descent_limit_stepsize = 1e-20

float. The gradient descent stops when the stepsize becomes smaller than this value.

src.config.H1_tolerance = 1e-05

float. The quadratic optimization step will attempt to merge curves that are closer than this distance in H1 norm.

src.config.curves_list_length_lim = 1000

int. The quadratic optimization step will take at most this number of stationary point found in the insertion step.

src.config.curves_list_length_min = 10

int. In the optimization step after the insertion step, the inserted curves are the union of the already known curves, together with those found in the multistart descent. This parameter sets least number of stationary curves from the mutlistart descent that have to be added for optimization.

src.config.CVXOPT_TOL = 1e-25

float. CVXOPT is the used solver to tackle the quadratic optimization step. This parameter defines the considered tolerance value for both the relative and absolute errors.

src.config.slide_opt_max_iter = 100000

int. During the sliding step, this parameter modules the maximum number of iterations to execute.

src.config.slide_opt_in_between_iters = 100

int. During the sliding step, in between iterations, the weights of the measure are optomized via the optimization step. This parameter regulates how often this is done.

src.config.slide_init_step = 1.0

float. The initial stepsize of the Armijo with Backtracking gradient descent for the Sliding step.

src.config.slide_limit_stepsize = 1e-20

float, default 1e-20. During the sliding step, the descent stops once the stepsize reaches this size.

src.config.log_output = False

bool. Switch to log the convergence information into a .txt file into the results folder. WARNING: requires rework, too many useless lines are saved.

src.config.save_output_each_N = 1000

int. How often the saved logs will be saved. This parameter consider the number of lines of the file.

src.config.log_maximal_line_size = 10000

int. Maximum size of the logfile. If exceeded, the file is discarded.

src.config.use_ffmpeg = True

bool. Switch to enable/disable the use of the ffmpeg library <https://ffmpeg.org/>. If disabled, no videos can be saved.