# Sensitivity analysis¶

## The package sensitivity¶

Capabilities to run a sensitivity analysis.

This package contains:

## The base class SensitivityAnalysis¶

Abstract class for the computation and analysis of sensitivity indices.

The purpose of a sensitivity analysis is to qualify or quantify how the model’s uncertain inputs impact its outputs.

This analysis relies on SensitivityAnalysis computed from a MDODiscipline representing the model, a ParameterSpace describing the uncertain parameters and options associated with a particular concrete class inheriting from SensitivityAnalysis which is an abstract one.

class gemseo.uncertainty.sensitivity.analysis.SensitivityAnalysis(disciplines, parameter_space, n_samples=None, output_names=None, algo=None, algo_options=None, formulation='MDF', **formulation_options)[source]

Sensitivity analysis.

The SensitivityAnalysis class provides both the values of SensitivityAnalysis.indices and their graphical representations, from either the SensitivityAnalysis.plot() method, the SensitivityAnalysis.plot_radar() method or the SensitivityAnalysis.plot_bar() method.

It is also possible to use SensitivityAnalysis.sort_parameters() to get the parameters sorted according to SensitivityAnalysis.main_method. The SensitivityAnalysis.main_indices are indices computed with the latter.

Lastly, the SensitivityAnalysis.plot_comparison() method allows to compare the current SensitivityAnalysis with another one.

Parameters
• disciplines (Collection[MDODiscipline]) – The discipline or disciplines to use for the analysis.

• parameter_space (ParameterSpace) – A parameter space.

• n_samples (int | None) –

A number of samples. If None, the number of samples is computed by the algorithm.

By default it is set to None.

• output_names (Iterable[str]) –

The disciplines’ outputs to be considered for the analysis. If None, use all the outputs.

By default it is set to None.

• algo (str | None) –

The name of the DOE algorithm. If None, use the SensitivityAnalysis.DEFAULT_DRIVER.

By default it is set to None.

• algo_options (Mapping[str, DOELibraryOptionType] | None) –

The options of the DOE algorithm.

By default it is set to None.

• formulation (str) –

The name of the MDOFormulation to sample the disciplines.

By default it is set to MDF.

• **formulation_options (Any) – The options of the MDOFormulation.

Return type

None

compute_indices(outputs=None)[source]

Compute the sensitivity indices.

Parameters

outputs (Sequence[str] | None) –

The outputs for which to display sensitivity indices. If None, use the default outputs, that are all the discipline outputs.

By default it is set to None.

Returns

The sensitivity indices.

With the following structure:

{
"method_name": {
"output_name": [
{
"input_name": data_array,
}
]
}
}


Return type

dict[str, IndicesType]

export_to_dataset()[source]

Convert SensitivityAnalysis.indices into a Dataset.

Returns

The sensitivity indices.

Return type

Dataset

plot(output, inputs=None, title=None, save=True, show=False, file_path=None, file_format=None)[source]

Plot the sensitivity indices.

Parameters
• output (str | tuple[str, int]) – The output for which to display sensitivity indices, either a name or a tuple of the form (name, component). If name, its first component is considered.

• inputs (Iterable[str] | None) –

The inputs to display. If None, display all.

By default it is set to None.

• title (str | None) –

The title of the plot. If None, no title.

By default it is set to None.

• save (bool) –

If True, save the figure.

By default it is set to True.

• show (bool) –

If True, show the figure.

By default it is set to False.

• file_path (str | Path | None) –

A file path. Either a complete file path, a directory name or a file name. If None, use a default file name and a default directory. The file extension is inferred from filepath extension, if any.

By default it is set to None.

• file_format (str | None) –

A file format, e.g. ‘png’, ‘pdf’, ‘svg’, … Used when file_path does not have any extension. If None, use a default file extension.

By default it is set to None.

Return type

None

plot_bar(outputs, inputs=None, standardize=False, title=None, save=True, show=False, file_path=None, directory_path=None, file_name=None, file_format=None, **options)[source]

Plot the sensitivity indices on a bar chart.

This method may consider one or more outputs, as well as all inputs (default behavior) or a subset.

Parameters
• outputs (OutputsType) – The outputs for which to display sensitivity indices, either a name, a list of names, a (name, component) tuple, a list of such tuples or a list mixing such tuples and names. When a name is specified, all its components are considered. If None, use the default outputs.

• inputs (Iterable[str] | None) –

The inputs to display. If None, display all.

By default it is set to None.

• standardize (bool) –

If True, standardize the indices between 0 and 1 for each output.

By default it is set to False.

• title (str | None) –

The title of the plot. If None, no title.

By default it is set to None.

• save (bool) –

If True, save the figure.

By default it is set to True.

• show (bool) –

If True, show the figure.

By default it is set to False.

• file_path (str | Path | None) –

The path of the file to save the figures. If the extension is missing, use file_extension. If None, create a file path from directory_path, file_name and file_extension.

By default it is set to None.

• directory_path (str | Path | None) –

The path of the directory to save the figures. If None, use the current working directory.

By default it is set to None.

• file_name (str | None) –

The name of the file to save the figures. If None, use a default one generated by the post-processing.

By default it is set to None.

• file_format (str | None) –

A file extension, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.

By default it is set to None.

• **options (int) –

Returns

A bar chart representing the sensitivity indices.

Return type

BarPlot

plot_comparison(indices, output, inputs=None, title=None, use_bar_plot=True, save=True, show=False, file_path=None, directory_path=None, file_name=None, file_format=None, **options)[source]

Plot a comparison between the current sensitivity indices and other ones.

This method allows to use either a bar chart (default option) or a radar one.

Parameters
• indices (list[SensitivityAnalysis]) – The sensitivity indices.

• output (str | tuple[str, int]) – The output for which to display sensitivity indices, either a name or a tuple of the form (name, component). If name, its first component is considered.

• inputs (Iterable[str] | None) –

The inputs to display. If None, display all.

By default it is set to None.

• title (str | None) –

The title of the plot. If None, no title.

By default it is set to None.

• use_bar_plot (bool) –

The type of graph. If True, use a bar plot. Otherwise, use a radar chart.

By default it is set to True.

• save (bool) –

If True, save the figure.

By default it is set to True.

• show (bool) –

If True, show the figure.

By default it is set to False.

• file_path (str | Path | None) –

The path of the file to save the figures. If None, create a file path from directory_path, file_name and file_format.

By default it is set to None.

• directory_path (str | Path | None) –

The path of the directory to save the figures. If None, use the current working directory.

By default it is set to None.

• file_name (str | None) –

The name of the file to save the figures. If None, use a default one generated by the post-processing.

By default it is set to None.

• file_format (str | None) –

A file format, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.

By default it is set to None.

• **options (bool) – The options passed to the underlying DatasetPlot.

Returns

A graph comparing sensitivity indices.

Return type
plot_field(output, mesh=None, inputs=None, standardize=False, title=None, save=True, show=False, file_path=None, directory_path=None, file_name=None, file_format=None, properties=None)[source]

Plot the sensitivity indices related to a 1D or 2D functional output.

The output is considered as a 1D or 2D functional variable, according to the shape of the mesh on which it is represented.

Parameters
• output (str | tuple[str, int]) – The output for which to display sensitivity indices, either a name or a tuple of the form (name, component) where (name, component) is used to sort the inputs. If name, its first component is considered.

• mesh (ndarray | None) –

The mesh on which the p-length output is represented. Either a p-length array for a 1D functional output or a (p, 2) array for a 2D one. If None, assume a 1D functional output.

By default it is set to None.

• inputs (Iterable[str] | None) –

The inputs to display. If None, display all inputs.

By default it is set to None.

• standardize (bool) –

If True, standardize the indices between 0 and 1 for each output.

By default it is set to False.

• title (str | None) –

The title of the plot. If None, no title is displayed.

By default it is set to None.

• save (bool) –

If True, save the figure.

By default it is set to True.

• show (bool) –

If True, show the figure.

By default it is set to False.

• file_path (str | Path | None) –

The path of the file to save the figures. If None, create a file path from directory_path, file_name and file_extension.

By default it is set to None.

• directory_path (str | Path | None) –

The path of the directory to save the figures. If None, use the current working directory.

By default it is set to None.

• file_name (str | None) –

The name of the file to save the figures. If None, use a default one generated by the post-processing.

By default it is set to None.

• file_format (str | None) –

A file extension, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.

By default it is set to None.

• properties (Mapping[str, DatasetPlotPropertyType]) –

The general properties of a DatasetPlot.

By default it is set to None.

Returns

A bar plot representing the sensitivity indices.

Raises

NotImplementedError – If the dimension of the mesh is greater than 2.

Return type
plot_radar(outputs, inputs=None, standardize=False, title=None, save=True, show=False, file_path=None, directory_path=None, file_name=None, file_format=None, min_radius=None, max_radius=None, **options)[source]

Plot the sensitivity indices on a radar chart.

This method may consider one or more outputs, as well as all inputs (default behavior) or a subset.

For visualization purposes, it is also possible to change the minimum and maximum radius values.

Parameters
• outputs (OutputsType) – The outputs for which to display sensitivity indices, either a name, a list of names, a (name, component) tuple, a list of such tuples or a list mixing such tuples and names. When a name is specified, all its components are considered. If None, use the default outputs.

• inputs (Iterable[str] | None) –

The inputs to display. If None, display all.

By default it is set to None.

• standardize (bool) –

If True, standardize the indices between 0 and 1 for each output.

By default it is set to False.

• title (str | None) –

The title of the plot. If None, no title.

By default it is set to None.

• save (bool) –

If True, save the figure.

By default it is set to True.

• show (bool) –

If True, show the figure.

By default it is set to False.

• file_path (str | Path | None) –

The path of the file to save the figures. If the extension is missing, use file_extension. If None, create a file path from directory_path, file_name and file_extension.

By default it is set to None.

• directory_path (str | Path | None) –

The path of the directory to save the figures. If None, use the current working directory.

By default it is set to None.

• file_name (str | None) –

The name of the file to save the figures. If None, use a default one generated by the post-processing.

By default it is set to None.

• file_format (str | None) –

A file extension, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.

By default it is set to None.

• min_radius (float | None) –

The minimal radial value. If None, from data.

By default it is set to None.

• max_radius (float | None) –

The maximal radial value. If None, from data.

By default it is set to None.

• **options (bool) –

Returns

A radar chart representing the sensitivity indices.

Return type

RadarChart

sort_parameters(output)[source]

Return the parameters sorted in descending order.

Parameters

output (str | tuple[str, int]) – An output of the form (name, component), where name is the output name and component is the output component. If a string is passed, the tuple (name, 0) will be considered corresponding to the first component of the output name.

Returns

The input parameters sorted in descending order.

Return type

list[str]

static standardize_indices(indices)[source]

Standardize the sensitivity indices for each output component.

Each index is replaced by its absolute value divided by the largest index. Thus, the standardized indices belong to the interval $$[0,1]$$.

Parameters

indices (Dict[str, List[Dict[str, numpy.ndarray]]]) – The indices to be standardized.

Returns

The standardized indices.

Return type

Dict[str, List[Dict[str, numpy.ndarray]]]

dataset: gemseo.core.dataset.Dataset

The dataset containing the discipline evaluations.

default_output: list[str]

The default outputs of interest.

property indices: dict[str, Dict[str, List[Dict[str, numpy.ndarray]]]]

The sensitivity indices.

With the following structure:

{
"method_name": {
"output_name": [
{
"input_name": data_array,
}
]
}
}

property inputs_names: list[str]

The names of the inputs.

property main_indices: Dict[str, List[Dict[str, numpy.ndarray]]]

The main sensitivity indices.

With the following structure:

{
"output_name": [
{
"input_name": data_array,
}
]
}

property main_method: str

The name of the main method.