pymor.algorithms.error

Module Contents

Functions

reduction_error_analysis	Analyze the model reduction error.
_compute_errors

pymor.algorithms.error.reduction_error_analysis(rom, fom, reductor, test_mus, basis_sizes=0, error_estimator=True, condition=False, error_norms=(), error_norm_names=None, error_estimator_norm_index=0, custom=(), plot=False, plot_custom_logarithmic=True, pool=dummy_pool)

Analyze the model reduction error.

The maximum model reduction error is estimated by solving the reduced Model for given random Parameters.

Parameters

rom

The reduced Model.

fom

The high-dimensional Model.

reductor

The reductor which has created rom.

test_mus

List of Parameters to compute the errors for.

basis_sizes

Either a list of reduced basis dimensions to consider, or the number of dimensions (which are then selected equidistantly, always including the maximum reduced space dimension). The dimensions are input for the dim-Parameter of reductor.reduce().

error_estimator

If True evaluate the error estimator of rom on the test Parameters.

condition

If True, compute the condition of the reduced system matrix for the given test Parameters (can only be specified if rom is an instance of StationaryModel and rom.operator is linear).

error_norms

List of norms in which to compute the model reduction error.

error_norm_names

Names of the norms given by error_norms. If None, the name attributes of the given norms are used.

error_estimator_norm_index

When error_estimator is True and error_norms are specified, this is the index of the norm in error_norms w.r.t. which to compute the effectivity of the error estimator.

custom

List of custom functions which are evaluated for each test parameter values and basis size. The functions must have the signature

def custom_value(rom, fom, reductor, mu, dim):
    pass

plot

If True, generate a plot of the computed quantities w.r.t. the basis size.

plot_custom_logarithmic

If True, use a logarithmic y-axis to plot the computed custom values.

pool

If not None, the WorkerPool to use for parallelization.

Returns

Dict with the following fields

mus

The test Parameters which have been considered.

basis_sizes

The reduced basis dimensions which have been considered.

norms

NumPy array of the norms of the high-dimensional solutions w.r.t. all given test Parameters, reduced basis dimensions and norms in error_norms. (Only present when error_norms has been specified.)

max_norms

Maxima of norms over the given test Parameters.

max_norm_mus

Parameters corresponding to max_norms.

errors

NumPy array of the norms of the model reduction errors w.r.t. all given test Parameters, reduced basis dimensions and norms in error_norms. (Only present when error_norms has been specified.)

max_errors

Maxima of errors over the given test Parameters.

max_error_mus

Parameters corresponding to max_errors.

rel_errors

errors divided by norms. (Only present when error_norms has been specified.)

max_rel_errors

Maxima of rel_errors over the given test Parameters.

max_rel_error_mus

Parameters corresponding to max_rel_errors.

error_norm_names

Names of the given error_norms. (Only present when error_norms has been specified.)

error_estimates

NumPy array of the model reduction error estimates w.r.t. all given test Parameters and reduced basis dimensions. (Only present when error_estimator is True.)

max_error_estimate

Maxima of error_estimates over the given test Parameters.

max_error_estimate_mus

Parameters corresponding to max_error_estimates.

effectivities

errors divided by error_estimates. (Only present when error_estimator is True and error_norms has been specified.)

min_effectivities

Minima of effectivities over the given test Parameters.

min_effectivity_mus

Parameters corresponding to min_effectivities.

max_effectivities

Maxima of effectivities over the given test Parameters.

max_effectivity_mus

Parameters corresponding to max_effectivities.

errors

NumPy array of the reduced system matrix conditions w.r.t. all given test Parameters and reduced basis dimensions. (Only present when conditions is True.)

max_conditions

Maxima of conditions over the given test Parameters.

max_condition_mus

Parameters corresponding to max_conditions.

custom_values

NumPy array of custom function evaluations w.r.t. all given test Parameters, reduced basis dimensions and functions in custom. (Only present when custom has been specified.)

max_custom_values

Maxima of custom_values over the given test Parameters.

max_custom_values_mus

Parameters corresponding to max_custom_values.

time

Time (in seconds) needed for the error analysis.

summary

String containing a summary of all computed quantities for the largest (last) considered basis size.

figure

The figure containing the generated plots. (Only present when plot is True.)

pymor.algorithms.error._compute_errors(mu, fom, reductor, error_estimator, error_norms, condition, custom, basis_sizes)