pymor.algorithms.scm

Module for the successive constraints method.

Module Contents

class pymor.algorithms.scm.LBSuccessiveConstraintsFunctional(operator, constraint_parameters, coercivity_constants, bounds, linprog_method='highs', linprog_options={}, M=None)

Bases: pymor.parameters.functionals.ParameterFunctional

ParameterFunctional providing the lower bound from the successive constraints method.

See [HRSP07].

Parameters:

• operator – LincombOperator for which to provide a lower bound on the coercivity constant.

• constraint_parameters – List of Parameters used to construct the constraints.

• coercivity_constants – A list of coercivity constants for the constraint_parameters.

• bounds – List of tuples containing lower and upper bounds for the design variables, i.e. the unknowns in the linear program.

• linprog_method – Name of the algorithm to use for solving the linear program using scipy.optimize.linprog.

• linprog_options – Dictionary of additional solver options passed to scipy.optimize.linprog.

• M – Number of parameters to use for estimating the coercivity constant. The M closest parameters (with respect to the Euclidean distance) are chosen. If None, all parameters from constraint_parameters are used.

Methods

evaluate

Evaluate the functional for given parameter values mu.

evaluate(mu=None)

Evaluate the functional for given parameter values mu.

class pymor.algorithms.scm.SuccessiveConstraintsSurrogate(operator, initial_parameter, bounds, product=None, linprog_method='highs', linprog_options={}, M=None)

Bases: pymor.algorithms.greedy.WeakGreedySurrogate

Surrogate for constructing the functionals in a greedy algorithm.

This surrogate is used in a weak greedy algorithm to select the parameters used to compute the constraints for the lower and upper bounds derived by the successive constraints method.

Parameters:

• operator – LincombOperator for which to provide a bounds on the coercivity constant.

• initial_parameter – Parameter used to initialize the surrogate for the greedy algorithm.

• bounds – List of tuples containing lower and upper bounds for the design variables, i.e. the unknowns in the linear program.

• product – Product with respect to which the coercivity constant should be estimated.

• linprog_method – Name of the algorithm to use for solving the linear program using scipy.optimize.linprog.

• linprog_options – Dictionary of additional solver options passed to scipy.optimize.linprog.

• M – Number of parameters to use for estimating the coercivity constant. The M closest parameters (with respect to the Euclidean distance) are chosen. If None, all parameters are used.

Methods

evaluate	Evaluate the surrogate for given parameters.
extend	Extend the approximation basis.

evaluate(mus, return_all_values=False)

Evaluate the surrogate for given parameters.

Parameters:

• mus – List of parameters for which to estimate the approximation error. When parallelization is used, mus can be a RemoteObject.

• return_all_values – See below.

Returns:

• If return_all_values is True, an NumPy array of the estimated errors.

• If return_all_values is False, the maximum estimated error as first

• return value and the corresponding parameter as second return value.

extend(mu)

Extend the approximation basis.

Parameters:

mu – A parameter from the training_set for which to add the corresponding vector \(v_\mu\) to the approximation basis.

class pymor.algorithms.scm.UBSuccessiveConstraintsFunctional(operator, constraint_parameters, minimizers)

Bases: pymor.parameters.functionals.ParameterFunctional

ParameterFunctional providing the upper bound from the successive constraints method.

See [HRSP07].

Parameters:

• operator – LincombOperator for which to provide an upper bound on the coercivity constant.

• constraint_parameters – List of Parameters used to construct the constraints.

• minimizers – List of minimizers associated to the coercivity constants of the operators in operator.

Methods

evaluate

Evaluate the functional for given parameter values mu.

evaluate(mu=None)

Evaluate the functional for given parameter values mu.

pymor.algorithms.scm.construct_scm_functionals(operator, training_set, initial_parameter, atol=None, rtol=None, max_extensions=None, product=None, linprog_method='highs', linprog_options={}, M=None)

Method to construct lower and upper bounds using the successive constraints method.

Parameters:

• operator – LincombOperator for which to provide a bounds on the coercivity constant.

• training_set – Parameters used as training set for the greedy algorithm.

• initial_parameter – Parameter used to initialize the surrogate for the greedy algorithm.

• atol – If not None, stop the greedy algorithm if the maximum (estimated) error on the training set drops below this value.

• rtol – If not None, stop the greedy algorithm if the maximum (estimated) relative error on the training set drops below this value.

• max_extensions – If not None, stop the greedy algorithm after max_extensions extension steps.

• product – Product with respect to which the coercivity constant should be estimated.

• linprog_method – Name of the algorithm to use for solving the linear program using scipy.optimize.linprog.

• linprog_options – Dictionary of additional solver options passed to scipy.optimize.linprog.

• M – Number of parameters to use for estimating the coercivity constant. The M closest parameters (with respect to the Euclidean distance) are chosen. If None, all parameters selected in the greedy method are used.

Returns:

• Functional for a lower bound on the coercivity constant, functional

• for an upper bound on the coercivity constant, and the results returned

• by the weak greedy algorithm.