pymor.algorithms.error
¶
Module Contents¶
Functions¶
Analyze the model reduction error. 

Plots the results from 

 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=(), custom_names=None, plot=False, plot_custom_logarithmic=True, pool=dummy_pool)[source]¶
Analyze the model reduction error.
The maximum model reduction error is estimated by solving the reduced
Model
for given randomParameters
.Parameters
 rom
The reduced
Model
. fom
The highdimensional
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 ofreductor.reduce()
. error_estimator
If
True
evaluate the error estimator ofrom
on the testParameters
. condition
If
True
, compute the condition of the reduced system matrix for the given testParameters
(can only be specified ifrom
is an instance ofStationaryModel
androm.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
. IfNone
, thename
attributes of the given norms are used. error_estimator_norm_index
When
error_estimator
isTrue
anderror_norms
are specified, this is the index of the norm inerror_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 signaturedef custom_value(rom, fom, reductor, mu, dim): pass
 custom_names
List of names to be used for plotting custom values.
 plot
If
True
, generate a plot of the computed quantities w.r.t. the basis size. plot_custom_logarithmic
If
True
, use a logarithmic yaxis to plot the computed custom values. pool
If not
None
, theWorkerPool
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 highdimensional solutions w.r.t. all given testParameters
and norms inerror_norms
. (Only present whenerror_norms
has been specified.) max_norms
Maxima of
norms
over the given testParameters
. max_norm_mus
Parameters
corresponding tomax_norms
. errors
NumPy array
of the norms of the model reduction errors w.r.t. all given testParameters
, reduced basis dimensions and norms inerror_norms
. (Only present whenerror_norms
has been specified.) max_errors
Maxima of
errors
over the given testParameters
. max_error_mus
Parameters
corresponding tomax_errors
. rel_errors
errors
divided bynorms
. (Only present whenerror_norms
has been specified.) max_rel_errors
Maxima of
rel_errors
over the given testParameters
. max_rel_error_mus
Parameters
corresponding tomax_rel_errors
. error_norm_names
Names of the given
error_norms
. (Only present whenerror_norms
has been specified.) error_estimates
NumPy array
of the model reduction error estimates w.r.t. all given testParameters
and reduced basis dimensions. (Only present whenerror_estimator
isTrue
.) max_error_estimate
Maxima of
error_estimates
over the given testParameters
. max_error_estimate_mus
Parameters
corresponding tomax_error_estimates
. effectivities
errors
divided byerror_estimates
. (Only present whenerror_estimator
isTrue
anderror_norms
has been specified.) min_effectivities
Minima of
effectivities
over the given testParameters
. min_effectivity_mus
Parameters
corresponding tomin_effectivities
. max_effectivities
Maxima of
effectivities
over the given testParameters
. max_effectivity_mus
Parameters
corresponding tomax_effectivities
. errors
NumPy array
of the reduced system matrix conditions w.r.t. all given testParameters
and reduced basis dimensions. (Only present whenconditions
isTrue
.) max_conditions
Maxima of
conditions
over the given testParameters
. max_condition_mus
Parameters
corresponding tomax_conditions
. custom_values
NumPy array
of custom function evaluations w.r.t. all given testParameters
, reduced basis dimensions and functions incustom
. (Only present whencustom
has been specified.) max_custom_values
Maxima of
custom_values
over the given testParameters
. max_custom_values_mus
Parameters
corresponding tomax_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.
 pymor.algorithms.error.plot_reduction_error_analysis(result, max_basis_size=None, plot_effectivities=True, plot_condition=True, plot_custom_logarithmic=True, plot_custom_with_errors=False)[source]¶
Plots the results from
reduction_error_analysis
.Parameters
 result
Dictionary with entries as returned by
reduction_error_analysis
. max_basis_size
Only plot results up to this basis size.
 plot_effectivities
If
True
, plot the effectivities of the a posteriori error estimate. plot_condition
If
True
, plot the condition of the reduced system matrix. plot_custom_logarithmic
If
True
, use a logarithmic yaxis to plot the computed custom values. plot_custom_with_errors
It
True
, plot errors and custom values in a single plot (otherwise in separate ones).