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)[source]

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)[source]

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)[source]

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

evaluate(mus, return_all_values=False)[source]

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

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)[source]

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)[source]

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.