gemseo.uncertainty.sensitivity.correlation_analysis module#

Class for the estimation of various correlation coefficients.

class CorrelationAnalysis(samples='')[source]#

Bases: BaseSensitivityAnalysis

Sensitivity analysis based on indices using correlation measures.

Examples

>>> from numpy import pi
>>> from gemseo import create_discipline, create_parameter_space
>>> from gemseo.uncertainty.sensitivity.correlation_analysis import (
...     CorrelationAnalysis,
... )
>>>
>>> expressions = {"y": "sin(x1)+7*sin(x2)**2+0.1*x3**4*sin(x1)"}
>>> discipline = create_discipline(
...     "AnalyticDiscipline", expressions=expressions
... )
>>>
>>> parameter_space = create_parameter_space()
>>> parameter_space.add_random_variable(
...     "x1", "OTUniformDistribution", minimum=-pi, maximum=pi
... )
>>> parameter_space.add_random_variable(
...     "x2", "OTUniformDistribution", minimum=-pi, maximum=pi
... )
>>> parameter_space.add_random_variable(
...     "x3", "OTUniformDistribution", minimum=-pi, maximum=pi
... )
>>>
>>> analysis = CorrelationAnalysis()
>>> analysis.compute_samples([discipline], parameter_space, n_samples=1000)
>>> indices = analysis.compute_indices()
Parameters:

samples (IODataset | str | Path) --

The samples for the estimation of the sensitivity indices, either as an IODataset or as a pickle file path generated from the IODataset.to_pickle method. If empty, use compute_samples().

By default it is set to "".

class Method(value)[source]#

Bases: StrEnum

The names of the sensitivity methods.

KENDALL = 'Kendall'#

The Kendall rank correlation coefficient.

PCC = 'PCC'#

The partial correlation coefficient.

PEARSON = 'Pearson'#

The Pearson coefficient.

PRCC = 'PRCC'#

The partial rank correlation coefficient.

SPEARMAN = 'Spearman'#

The Spearman coefficient.

SRC = 'SRC'#

The standard regression coefficient.

SRRC = 'SRRC'#

The standard rank regression coefficient.

SSRC = 'SSRC'#

The squared standard regression coefficient.

class SensitivityIndices(kendall: 'FirstOrderIndicesType' = <factory>, pcc: 'FirstOrderIndicesType' = <factory>, pearson: 'FirstOrderIndicesType' = <factory>, prcc: 'FirstOrderIndicesType' = <factory>, spearman: 'FirstOrderIndicesType' = <factory>, src: 'FirstOrderIndicesType' = <factory>, srrc: 'FirstOrderIndicesType' = <factory>, ssrc: 'FirstOrderIndicesType' = <factory>)[source]#

Bases: object

Parameters:
kendall: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Kendall rank correlation coefficients.

pcc: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Partial Correlation Coefficients.

pearson: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Pearson coefficients.

prcc: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Partial Rank Correlation Coefficients.

spearman: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Spearman coefficients.

src: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Standard Regression Coefficients.

srrc: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Standard Rank Regression Coefficients.

ssrc: dict[str, list[dict[str, ndarray[Any, dtype[floating[Any]]]]]]#

The Squared Standard Regression Coefficients.

compute_indices(output_names=())[source]#

Compute the sensitivity indices.

Parameters:

output_names (str | Sequence[str]) --

The name(s) of the output(s) for which to compute the sensitivity indices. If empty, use the names of the outputs set at instantiation.

By default it is set to ().

Returns:

The sensitivity indices.

Given a sensitivity method, an input variable and an output variable, the sensitivity index which is a 1D NumPy array can be accessed through indices.method_name[output_name][output_component][input_name].

Return type:

SensitivityIndices

plot(output, input_names=(), title='', save=True, show=False, file_path='', directory_path='', file_name='', file_format='')[source]#

Plot the sensitivity indices.

Parameters:

  • output (VariableType) -- 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.

  • input_names (Iterable[str]) --

    The input variables for which to display the sensitivity indices. If empty, display all the input variables.

    By default it is set to ().

  • title (str) --

    The title of the plot, if any.

    By default it is set to "".

  • 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) --

    A file path. Either a complete file path, a directory name or a file name. If empty, 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 "".

  • directory_path (str | Path) --

    The path to the directory where to save the plots.

    By default it is set to "".

  • file_name (str) --

    The name of the file.

    By default it is set to "".

  • file_format (str) --

    A file format, e.g. 'png', 'pdf', 'svg', ... Used when file_path does not have any extension. If empty, use a default file extension.

    By default it is set to "".

Returns:

The plot figure.

Return type:

RadarChart

plot_radar(outputs=(), input_names=(), title='', save=True, show=False, file_path='', directory_path='', file_name='', file_format='', min_radius=-1.0, max_radius=1.0, **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 empty, use the default outputs.

    By default it is set to ().

  • input_names (Iterable[str]) --

    The input variables for which to display the sensitivity indices. If empty, display all the input variables.

    By default it is set to ().

  • title (str) --

    The title of the plot, if any.

    By default it is set to "".

  • 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) --

    The path of the file to save the figures. If the extension is missing, use file_extension. If empty, create a file path from directory_path, file_name and file_extension.

    By default it is set to "".

  • directory_path (str | Path) --

    The path of the directory to save the figures. If empty, use the current working directory.

    By default it is set to "".

  • file_name (str) --

    The name of the file to save the figures. If empty, use a default one generated by the post-processing.

    By default it is set to "".

  • file_format (str) --

    A file extension, e.g. 'png', 'pdf', 'svg', ... If empty, use a default file extension.

    By default it is set to "".

  • min_radius (float) --

    The minimal radial value. If None, from data.

    By default it is set to -1.0.

  • max_radius (float) --

    The maximal radial value. If None, from data.

    By default it is set to 1.0.

  • **options (bool) -- The description is missing.

Returns:

A radar chart representing the sensitivity indices.

Return type:

RadarChart

DEFAULT_DRIVER: ClassVar[str] = 'OT_MONTE_CARLO'#