src.DGCG

General controller of the DGCG algorithm package.

Module Contents

Functions

set_model_parameters(alpha, beta, time_samples, H_dimensions, test_func, grad_test_func)	Set the the fundamental parameters of the model.
solve(data, **kwargs)	Solve the given dynamic inverse problem for input data.

src.DGCG.set_model_parameters(alpha, beta, time_samples, H_dimensions, test_func, grad_test_func)

Set the the fundamental parameters of the model.

Parameters

alpha, beta: float

Regularization parameter of the regularization problem, must be positive.

time_samples: numpy.ndarray

Ordered array of values between 0 and 1, with time_samples[0] = 0 and time_samples[-1] = 1.

H_dimension: list[int]

List of dimensions of the considered Hilbert spaces H_t.

test_funccallable[[int, numpy.ndarray], numpy.ndarray]

Function φ that defines the forward measurements. The first input is time, the second input is a list of elements in the domain Ω. It maps into a list of elements in H_t. See Notes for further reference.

grad_test_funccallable[[int, numpy.ndarray], numpy.ndarray]

The gradient of the input function test_func. The inputs of the gradient are the same of those of the original function. Returns a tuple with each partial derivative.

Returns

None

Notes

It is required to set this values prior to defining atoms or taking measurements. This is because the input values fix the set of extremal points of the Benomou-Brenier energy, and the given kernels define the Forward and Backward measurement operators.

The test_func φ is the funciton that defines the forward measurements. The first input is a time sample in [0, 1, ..., T-1], with T the total number of time samples. The second input is a list of N elements in Ω, expressed as a (N,2) numpy.ndarray (Ω is of dimension 2).

The output of φ is a list of N elements in H_t, since the dimension of H_t is input with H_dimensions, then the output of φ(t, x) is a (N, H_dimensions[t]) numpy.ndarray

The function grad_test_func ∇φ has the same input, but the output is a (2, N, H_dimensions[t]) tuple representing the two partial derivatives ∂_x and ∂_y respectively.

src.DGCG.solve(data, **kwargs)

Solve the given dynamic inverse problem for input data.

This function will apply the Dynamic Generalized Conditional Gradient (DGCG) algorithm.

Parameters

datanumpy.ndarray

Array of T entries, each a numpy.ndarray of size H_dimensions[t] for each t. See notes for further reference.

initial_measuresrc.classes.measure, optional

Initial guess for the DGCG algorithm. Default value is None corresponding the the zero measure.

use_ffmmpegbool, optional

To indicate the use of the ffmpeg library. If set to false, matplotlib won’t be able to save the output videos as videos files. Nonetheless, it is possible to animate the measures with the DGCG.classes.measure.animate method.

insertion_max_restartsint, optional

Hard limit on the number of allowed restarts for the multistart gradient descent at each iteration. Default 1000.

insertion_min_restartsint, optional

Hard limit on the number of allowed restarts for the multistart gradient descent at each iteration. Default 20.

results_folderstr, optional

name of the folder that will be created to save the simulation results. Default ‘results’.

multistart_early_stopcallable[[int,int], int] optional

function to stop early as a function of the found stationary points. Default lambda n,m: np.inf.

multistart_pooling_numint, optional

When insertion random curves, the algorithm will realize this given number of curves and then choose the one with best F(γ) value. The higher the value of this parameter, the more one samples on the best initial curves to descent. The drawback is that it slows down the proposition of random curves.

log_outputbool, optional

Save the output of shell into a .txt inside the results folder. default False, to be improved. <+TODO+>

Returns

solutionsrc.classes.measure

The computed solution.

exit_flagtuple[int, str]

Tuple with a numeric indicator and a string with a brief description. <+TODO+> check this, add dual_gap exit value.

Notes

The data input corresponds to the gathered data with the defined forward operator when running src.DGCG.set_model_parameters(). Each entry of this array correspond to the measurement at each time sample. Therefore, the size of that entry will correspond to the respective H_t space.