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] | None) –

    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.

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

static load(file_path)[source]

Load a sensitivity analysis from the disk.

Parameters:

file_path (str | Path) – The path to the file.

Returns:

The sensitivity analysis.

Return type:

SensitivityAnalysis

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:

BarPlot | RadarChart

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:

Curves | Surfaces

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

save(file_path)[source]

Save the current sensitivity analysis on the disk.

Parameters:

file_path (str | Path) – The path to the file.

Return type:

None

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: 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, 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.

Examples