problem

class StoppingCriteria

Bases: ABC

Abstract base class for iteration stopping criteria

abstract satisfied(previous_iterate, current_iterate)

Specifies if criteria is satisfied. :param current_iterate: :param previous_iterate: :return:

Parameters

• previous_iterate (ndarray) –

• current_iterate (ndarray) –

Return type

bool

class ResidualNormStoppingCriteria(tol=1e-09)

Bases: StoppingCriteria

__init__(tol=1e-09)

Stopping criteria based on the relative residual between two iterations is less than a given tolerance :param tol: tolerance for residual

property tol

satisfied(previous_iterate, current_iterate)

Returns true if

\[\frac{\|X_{\text{prev}} - X_{\text{curr}}\||_{F}}{\|X_{\text{prev}}\|_{F}} < tol.\]

Parameters

• previous_iterate (ndarray) – \(X_{\text{prev}\)

• current_iterate (ndarray) – \(X_{\text{curr}\)

Returns

class Problem(measurement_operator, data, indexing_order=None, input_shape=None)

Bases: object

Parameters

• measurement_operator (Union[LinearOperator, ndarray, csr_matrix, MatrixOperator]) –

• data (array) –

• indexing_order (IndexingOrder) –

• input_shape (Tuple[int, int]) –

__init__(measurement_operator, data, indexing_order=None, input_shape=None)

Description for a rank minimization problem

\[\min_{x \in \mathbb{C}^{d_1 \times d_2}} \operatorname{rank}(x), \text{s.t.} \Phi(x) = y,\]

Parameters

• measurement_operator (Union[LinearOperator, ndarray, csr_matrix, MatrixOperator]) –

• data (array) –

• indexing_order (IndexingOrder) –

• input_shape (Tuple[int, int]) –

solve(schatten_p_parameter, max_iter=1000, rank_estimate=None, regularization_rule=None, weighted_least_squares_solver=<hmirls.weighted_least_squares.ScipyCgWeightedLeastSquaresSolver object>, stopping_criteria=<hmirls.problem.ResidualNormStoppingCriteria object>)

Parameters

• schatten_p_parameter –

• max_iter –

• rank_estimate (int) –

• regularization_rule (RegularizationRule) –

• weighted_least_squares_solver (WeightedLeastSquaresSolver) –

• stopping_criteria (StoppingCriteria) –

Returns