quara.minimization_algorithm.projected_gradient_descent_backtracking module

class ProjectedGradientDescentBacktracking(func_proj=None)[source]

Bases: quara.minimization_algorithm.minimization_algorithm.MinimizationAlgorithm

Constructor

Parameters

func_proj (Callable[[np.ndarray], np.ndarray], optional) – function of projection, by default None

property func_proj: Callable[[numpy.ndarray], numpy.ndarray]

returns function of projection.

Returns

function of projection.

Return type

Callable[[np.ndarray], np.ndarray]

is_loss_and_option_sufficient()[source]

returns whether the loss and the option are sufficient.

Returns

whether the loss and the option are sufficient.

Return type

bool

is_loss_sufficient()[source]

returns whether the loss is sufficient.

Returns

whether the loss is sufficient.

Return type

bool

is_option_sufficient()[source]

returns whether the option is sufficient.

Returns

whether the option is sufficient.

Return type

bool

optimize(loss_function, loss_function_option, algorithm_option, on_iteration_history=False)[source]

optimizes using specified parameters.

Parameters

  • loss_function (LossFunction) – Loss Function

  • loss_function_option (LossFunctionOption) – Loss Function Option

  • algorithm_option (ProjectedGradientDescentBaseOption) – Projected Gradient Descent Base Algorithm Option

  • on_iteration_history (bool, optional) – whether to return iteration history, by default False

Returns

the result of the optimization.

Return type

ProjectedGradientDescentBaseResult

Raises

  • ValueError – when on_value of loss_function is False.

  • ValueError – when on_gradient of loss_function is False.

set_constraint_from_standard_qt_and_option(qt, option)[source]

sets constraint from StandardQTomography and Algorithm Option.

Parameters
Return type

None

class ProjectedGradientDescentBacktrackingOption(on_algo_eq_constraint=True, on_algo_ineq_constraint=True, var_start=None, mu=None, gamma=0.3, mode_stopping_criterion_gradient_descent='single_difference_loss', num_history_stopping_criterion_gradient_descent=1, mode_proj_order='eq_ineq', eps=None)[source]

Bases: quara.minimization_algorithm.minimization_algorithm.MinimizationAlgorithmOption

Constructor

Parameters

  • on_algo_eq_constraint (bool, optional) – whether this algorithm needs on algorithm equality constraint, by default True

  • on_algo_ineq_constraint (bool, optional) – whether this algorithm needs on algorithm inequality constraint, by default True

  • var_start (np.ndarray, optional) – initial variable for the algorithm, by default None

  • mu (float, optional) – algorithm option mu, by default None

  • gamma (float, optional) – algorithm option gamma, by default 0.3

  • mode_stopping_criterion_gradient_descent (str, optional) – mode of stopping criterion for gradient descent, by default “single_difference_loss”

  • num_history_stopping_criterion_gradient_descent (int, optional) – number of history to be used stopping criterion for gradient descent, by default 1 this must be a integer and greater than or equal to 1.

  • mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”.

  • eps (float, optional) – algorithm option epsilon, by default None

property eps: float

returns algorithm option eps.

Returns

algorithm option eps.

Return type

float

property gamma: float

returns algorithm option gamma.

Returns

algorithm option gamma.

Return type

float

property mode_proj_order: str

returns the order in which the projections are performed.

Returns

the order in which the projections are performed.

Return type

str

property mode_stopping_criterion_gradient_descent: str

returns mode of stopping criterion for gradient descent.

Returns

mode of stopping criterion for gradient descent.

Return type

str

property mu: float

returns algorithm option mu.

Returns

algorithm option mu.

Return type

float

property num_history_stopping_criterion_gradient_descent: int

returns number of history to be used stopping criterion for gradient descent.

Returns

number of history to be used stopping criterion for gradient descent.

Return type

int

class ProjectedGradientDescentBacktrackingResult(value, computation_time=None, k=None, fx=None, x=None, y=None, alpha=None, error_values=None)[source]

Bases: quara.minimization_algorithm.minimization_algorithm.MinimizationResult

Constructor

Parameters

  • value (np.ndarray) – the result of the minimization.

  • computation_time (float, optional) – computation time for the minimization, by default None

  • k (int) –

  • fx (List[numpy.ndarray]) –

  • x (List[numpy.ndarray]) –

  • y (List[numpy.ndarray]) –

  • alpha (List[float]) –

  • error_values (List[float]) –

property alpha: List[numpy.ndarray]

return the alpha per iteration.

Returns

the alpha per iteration.

Return type

List[np.ndarray]

property error_values: List[numpy.ndarray]

return the error_values per iteration.

Returns

the error_values per iteration.

Return type

List[np.ndarray]

property fx: List[numpy.ndarray]

return the value of f(x) per iteration.

Returns

the value of f(x) per iteration.

Return type

List[np.ndarray]

property k: int

returns the number of iterations.

Returns

the number of iterations.

Return type

int

property x: List[numpy.ndarray]

return the x per iteration.

Returns

the x per iteration.

Return type

List[np.ndarray]

property y: List[numpy.ndarray]

return the y per iteration.

Returns

the y per iteration.

Return type

List[np.ndarray]