darsia.BeckmannBregmanSolver

class BeckmannBregmanSolver(grid, weight=None, options={})

Bases: BeckmannProblem

Class to determine the Wasserstein distance solved with the Bregman method.

Implements the darsia.BeckmannProblem interface by specifying the method darsia.BeckmannProblem.solve_beckmann_problem().

Initialise the Bregman solver.

Parameters:

griddarsia.Grid

Tensor grid associated with the images.

weightdarsia.Image, optional

Weight for the heterogeneous case.

optionsdict, optional

Solver options. Recognised keys, with defaults:

L (float)              1.0    penalty parameter (face mobility)
bregman_update         never  callable(iter) -> bool deciding
                              when to update the regularisation
num_iter (int)         100    max iterations
tol_residual (float)   inf    relative mass-conservation residual
tol_increment (float)  inf    relative aux/force increment
tol_distance (float)   inf    relative distance increment

Methods

broken_darcy_with_custom_flux_block(...)	Construct the broken Darcy operator with given flux-flux block.
cell_weighted_flux(cell_flux)	Compute the cell-weighted flux.
distance_matrix(images)	Compute the distance between each iteam of a list.
eliminate_flux(jacobian, residual)	Eliminate the flux block from the jacobian and residual.
eliminate_lagrange_multiplier(...)	Eliminate the lagrange multiplier from the reduced system.
exact_linearization(solution)	Compute the exact linearization of the constrained minimization problem.
flat_view(img)	Flatten the image to a vector.
flux_view(vector)	Extract the flux from the vector.
l1_dissipation(flat_flux)	Compute the l1 dissipation of the solution.
linear_solve(matrix, rhs[, ...])	Solve the linear system.
ndofs()	Return the total number of degrees of freedom.
optimality_conditions(solution, ...)	Evaluate optimality conditions of the constrained minimization problem.
pressure_view(vector)	Extract the pressure from the vector.
rescaled_flux_optimality_conditions(solution)	Evaluate scaled optimality conditions of the constrained minimization problem.
solve_beckmann_problem(flat_mass_diff)	Solve the Beckmann problem using the Bregman method.
transport_density(flat_flux[, weighted, flatten])	Compute the transport density from the solution.
transport_density_faces(flat_flux)	Compute the transport density from the solution.

Attributes

L	Penalty parameter for the Bregman iteration, associated to face mobility.
bregman_update	Function to determine whether/when to update the Bregman regularization.
convergence_criteria	Convergence criteria for the Bregman solver.
grid	darsia.Grid: grid
voxel_size	np.ndarray: voxel size
options	dict: options for the solver
regularization	float: regularization parameter
verbose	bool: verbosity
mobility_mode	str: mode for computing the mobility
weight	Weight defined on cells
callbacks	list: list of callbacks to be called during the optimization

solve_beckmann_problem(flat_mass_diff)

Solve the Beckmann problem using the Bregman method.

Parameters:

flat_mass_diffnp.ndarray

Difference of mass distributions.

Returns:

tuple

Distance, solution, info.

L

Penalty parameter for the Bregman iteration, associated to face mobility.

bregman_update

Function to determine whether/when to update the Bregman regularization.

convergence_criteria

Convergence criteria for the Bregman solver.