SALib.analyze.sobol module#

SALib.analyze.sobol.Si_list_to_dict(S_list, D: int, num_resamples: int, keep_resamples: bool, calc_second_order: bool)[source]#

Convert the parallel output into the regular dict format for printing/returning

SALib.analyze.sobol.Si_to_pandas_dict(S_dict)[source]#

Convert Si information into Pandas DataFrame compatible dict.

Examples

>>> X = saltelli.sample(problem, 512)
>>> Y = Ishigami.evaluate(X)
>>> Si = sobol.analyze(problem, Y, print_to_console=True)
>>> T_Si, first_Si, (idx, second_Si) = sobol.Si_to_pandas_dict(Si, problem)
Parameters:

S_dict (ResultDict) – Sobol sensitivity indices

See also

Si_list_to_dict

Returns:

tuple – Total and first order are dicts. Second order sensitivities contain a tuple of parameter name combinations for use as the DataFrame index and second order sensitivities. If no second order indices found, then returns tuple of (None, None)

Return type:

of total, first, and second order sensitivities.

SALib.analyze.sobol.analyze(problem, Y, calc_second_order=True, num_resamples=100, conf_level=0.95, print_to_console=False, parallel=False, n_processors=None, keep_resamples=False, seed=None)[source]#

Perform Sobol Analysis on model outputs.

Returns a dictionary with keys ‘S1’, ‘S1_conf’, ‘ST’, and ‘ST_conf’, where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file. If calc_second_order is True, the dictionary also contains keys ‘S2’ and ‘S2_conf’.

There are several approaches to estimating sensitivity indices. The general approach is described in [1]. The implementation offered here follows [2] for first and total order indices, whereas estimation of second order sensitivities follows [3]. A noteworthy point is the improvement to reduce error rates in sensitivity estimation is introduced in [4].

Notes

Compatible with:

saltelli : SALib.sample.saltelli.sample() sobol : SALib.sample.sobol.sample()

Examples

>>> X = saltelli.sample(problem, 512)
>>> Y = Ishigami.evaluate(X)
>>> Si = sobol.analyze(problem, Y, print_to_console=True)
Parameters:

  • problem (dict) – The problem definition

  • Y (numpy.array) – A NumPy array containing the model outputs

  • calc_second_order (bool) – Calculate second-order sensitivities (default True)

  • num_resamples (int) – The number of resamples (default 100)

  • conf_level (float) – The confidence interval level (default 0.95)

  • print_to_console (bool) – Print results directly to console (default False)

  • parallel (bool) – Perform analysis in parallel if True

  • n_processors (int) – Number of parallel processes (only used if parallel is True)

  • keep_resamples (bool) – Whether or not to store intermediate resampling results (default False)

  • seed (int) – Seed to generate a random number

References

  1. Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271-280, doi:10.1016/S0378-4754(00)00270-6.

  2. Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and S. Tarantola (2010). Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2):259-270, doi:10.1016/j.cpc.2009.09.018.

  3. Saltelli, A. (2002). Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2):280-297 doi:10.1016/S0010-4655(02)00280-1.

  4. Sobol’, I. M., Tarantola, S., Gatelli, D., Kucherenko, S. S., & Mauntz, W. (2007). Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering & System Safety, 92(7), 957-960. https://doi.org/10.1016/j.ress.2006.07.001

SALib.analyze.sobol.cli_action(args)[source]#
SALib.analyze.sobol.cli_parse(parser)[source]#
SALib.analyze.sobol.create_Si_dict(D: int, num_resamples: int, keep_resamples: bool, calc_second_order: bool)[source]#

initialize empty dict to store sensitivity indices

SALib.analyze.sobol.create_task_list(D, calc_second_order, n_processors)[source]#

Create list with one entry (key, parameter 1, parameter 2) per sobol index (+conf.). This is used to supply parallel tasks to multiprocessing.Pool

SALib.analyze.sobol.first_order(A, AB, B)[source]#

First order estimator following Saltelli et al. 2010 CPC, normalized by sample variance

SALib.analyze.sobol.second_order(A, ABj, ABk, BAj, B)[source]#

Second order estimator following Saltelli 2002

SALib.analyze.sobol.separate_output_values(Y, D, N, calc_second_order)[source]#
SALib.analyze.sobol.sobol_parallel(Z, A, AB, BA, B, r, tasks)[source]#
SALib.analyze.sobol.to_df(self)[source]#

Conversion method to Pandas DataFrame. To be attached to ResultDict.

Returns:

List

Return type:

of Pandas DataFrames in order of Total, First, Second

Examples

>>> Si = sobol.analyze(problem, Y, print_to_console=True)
>>> total_Si, first_Si, second_Si = Si.to_df()
SALib.analyze.sobol.total_order(A, AB, B)[source]#

Total order estimator following Saltelli et al. 2010 CPC, normalized by sample variance