SALib.analyze package#

Submodules#

SALib.analyze.common_args module#

SALib.analyze.common_args.create(cli_parser=None)[source]#
SALib.analyze.common_args.run_cli(cli_parser, run_analysis, known_args=None)[source]#
SALib.analyze.common_args.setup(parser)[source]#

SALib.analyze.delta module#

SALib.analyze.delta.analyze(problem: Dict, X: ndarray, Y: ndarray, num_resamples: int = 100, conf_level: float = 0.95, print_to_console: bool = False, seed: Optional[int] = None) → Dict[source]#

Perform Delta Moment-Independent Analysis on model outputs.

Returns a dictionary with keys ‘delta’, ‘delta_conf’, ‘S1’, and ‘S1_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.

Notes

Compatible with:

all samplers

Examples

>>> X = latin.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = delta.analyze(problem, X, Y, print_to_console=True)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.matrix) – A NumPy matrix containing the model inputs

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

  • num_resamples (int) – The number of resamples when computing confidence intervals (default 100)

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

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

References

1

Borgonovo, E. (2007). “A new uncertainty importance measure.” Reliability Engineering & System Safety, 92(6):771-784, doi:10.1016/j.ress.2006.04.015.

2

Plischke, E., E. Borgonovo, and C. L. Smith (2013). “Global sensitivity measures from given data.” European Journal of Operational Research, 226(3):536-550, doi:10.1016/j.ejor.2012.11.047.

SALib.analyze.delta.bias_reduced_delta(Y, Ygrid, X, m, num_resamples, conf_level)[source]#

Plischke et al. 2013 bias reduction technique (eqn 30)

SALib.analyze.delta.calc_delta(Y, Ygrid, X, m)[source]#

Plischke et al. (2013) delta index estimator (eqn 26) for d_hat.

SALib.analyze.delta.cli_action(args)[source]#
SALib.analyze.delta.cli_parse(parser)[source]#
SALib.analyze.delta.sobol_first(Y, X, m)[source]#
SALib.analyze.delta.sobol_first_conf(Y, X, m, num_resamples, conf_level)[source]#

SALib.analyze.dgsm module#

SALib.analyze.dgsm.analyze(problem, X, Y, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None)[source]#

Calculates Derivative-based Global Sensitivity Measure on model outputs.

Returns a dictionary with keys ‘vi’, ‘vi_std’, ‘dgsm’, and ‘dgsm_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.

Notes

Compatible with:

finite_diff : SALib.sample.finite_diff.sample()

Examples

>>> X = finite_diff.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = dgsm.analyze(problem, Y, print_to_console=False)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.matrix) – The NumPy matrix containing the model inputs

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

  • num_resamples (int) – The number of resamples used to compute the confidence intervals (default 1000)

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

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

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

References

1

Sobol, I. M. and S. Kucherenko (2009). “Derivative based global sensitivity measures and their link with global sensitivity indices.” Mathematics and Computers in Simulation, 79(10):3009-3017, doi:10.1016/j.matcom.2009.01.023.

SALib.analyze.dgsm.calc_dgsm(base, perturbed, x_delta, bounds, num_resamples, conf_level)[source]#

v_i sensitivity measure following Sobol and Kucherenko (2009). For comparison, total order S_tot <= dgsm

SALib.analyze.dgsm.calc_vi_mean(base, perturbed, x_delta)[source]#

Calculate v_i mean.

Same as calc_vi_stats but only returns the mean.

SALib.analyze.dgsm.calc_vi_stats(base, perturbed, x_delta)[source]#

Calculate v_i mean and std.

v_i sensitivity measure following Sobol and Kucherenko (2009) For comparison, Morris mu* < sqrt(v_i)

Same as calc_vi_mean but returns standard deviation as well.

SALib.analyze.dgsm.cli_action(args)[source]#
SALib.analyze.dgsm.cli_parse(parser)[source]#

SALib.analyze.fast module#

SALib.analyze.fast.analyze(problem, Y, M=4, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None)[source]#

Perform extended Fourier Amplitude Sensitivity Test on model outputs

Returns a dictionary with keys ‘S1’ and ‘ST’, where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file.

Notes

Compatible with:

fast_sampler : SALib.sample.fast_sampler.sample()

Examples

>>> X = fast_sampler.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = fast.analyze(problem, Y, print_to_console=False)
Parameters

  • problem (dict) – The problem definition

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

  • M (int) – The interference parameter, i.e., the number of harmonics to sum in the Fourier series decomposition (default 4)

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

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

References

1

Cukier, R. I., C. M. Fortuin, K. E. Shuler, A. G. Petschek, and J. H. Schaibly (1973). “Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.” J. Chem. Phys., 59(8):3873-3878, doi:10.1063/1.1680571.

2

Saltelli, A., S. Tarantola, and K. P.-S. Chan (1999). “A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output.” Technometrics, 41(1):39-56, doi:10.1080/00401706.1999.10485594.

3

Pujol, G. (2006) fast99 - R sensitivity package https://github.com/cran/sensitivity/blob/master/R/fast99.R

SALib.analyze.fast.bootstrap(Y: ndarray, M: int, resamples: int, conf_level: float)[source]#

Compute CIs.

Infers N from results of sub-sample Y and re-estimates omega (ω) for the above N.

SALib.analyze.fast.cli_action(args)[source]#
SALib.analyze.fast.cli_parse(parser)[source]#

Add method specific options to CLI parser.

Parameters

parser (argparse object) –

Return type

Updated argparse object

SALib.analyze.fast.compute_orders(outputs: ndarray, N: int, M: int, omega: int)[source]#

SALib.analyze.ff module#

Created on 30 Jun 2015

@author: will2

SALib.analyze.ff.analyze(problem, X, Y, second_order=False, print_to_console=False, seed=None)[source]#

Perform a fractional factorial analysis

Returns a dictionary with keys ‘ME’ (main effect) and ‘IE’ (interaction effect). The techniques bulks out the number of parameters with dummy parameters to the nearest 2**n. Any results involving dummy parameters could indicate a problem with the model runs.

Notes

Compatible with:

ff : SALib.sample.ff.sample()

Examples

>>> X = sample(problem)
>>> Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
>>> analyze(problem, X, Y, second_order=True, print_to_console=True)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.matrix) – The NumPy matrix containing the model inputs

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

  • second_order (bool, default=False) – Include interaction effects

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

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

Returns

Si – A dictionary of sensitivity indices, including main effects ME, and interaction effects IE (if second_order is True)

Return type

dict

References

1

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. http://doi.org/10.1002/9780470725184

SALib.analyze.ff.cli_action(args)[source]#
SALib.analyze.ff.cli_parse(parser)[source]#
SALib.analyze.ff.interactions(problem, Y)[source]#

Computes the second order effects

Computes the second order effects (interactions) between all combinations of pairs of input factors

Parameters

  • problem (dict) – The problem definition

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

Returns

  • ie_names (list) – The names of the interaction pairs

  • IE (list) – The sensitivity indices for the pairwise interactions

SALib.analyze.ff.to_df(self)[source]#

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

Returns

main_effect, inter_effect – A tuple of DataFrames for main effects and interaction effects. The second element (for interactions) will be None if not available.

Return type

tuple

SALib.analyze.hdmr module#

SALib.analyze.hdmr.analyze(problem: Dict, X: ndarray, Y: ndarray, maxorder: int = 2, maxiter: int = 100, m: int = 2, K: int = 20, R: Optional[int] = None, alpha: float = 0.95, lambdax: float = 0.01, print_to_console: bool = False, seed: Optional[int] = None) → Dict[source]#

Compute global sensitivity indices using the meta-modeling technique known as High-Dimensional Model Representation (HDMR).

HDMR itself is not a sensitivity analysis method but a surrogate modeling approach. It constructs a map of relationship between sets of high dimensional inputs and output system variables [1]. This I/O relation can be constructed using different basis functions (orthonormal polynomials, splines, etc.). The model decomposition can be expressed as

\[\widehat{y} = \sum_{u \subseteq \{1, 2, ..., d \}} f_u\]

where u represents any subset including an empty set.

HDMR becomes extremely useful when the computational cost of obtaining sufficient Monte Carlo samples are prohibitive, as may be the case with Sobol’s method. It uses least-square regression to reduce the required number of samples and thus the number of function (model) evaluations. Another advantage of this method is that it can account for correlation among the model input. Unlike other variance-based methods, the main effects are the combination of structural (uncorrelated) and correlated contributions.

This method uses as input

  • a N x d matrix of N different d-vectors of model inputs (factors/parameters)

  • a N x 1 vector of corresponding model outputs

Notes

Compatible with:

all samplers

Sets an emulate method allowing re-use of the emulator.

Examples

 1sp = ProblemSpec({
 2    'names': ['X1', 'X2', 'X3'],
 3    'bounds': [[-np.pi, np.pi]] * 3,
 4    # 'groups': ['A', 'B', 'A'],
 5    'outputs': ['Y']
 6})
 7
 8(sp.sample_saltelli(2048)
 9    .evaluate(Ishigami.evaluate)
10    .analyze_hdmr()
11)
12
13sp.emulate()
Parameters

  • problem (dict) – The problem definition

  • X (numpy.matrix) – The NumPy matrix containing the model inputs, N rows by d columns

  • Y (numpy.array) – The NumPy array containing the model outputs for each row of X

  • maxorder (int (1-3, default: 2)) – Maximum HDMR expansion order

  • maxiter (int (1-1000, default: 100)) – Max iterations backfitting

  • m (int (2-10, default: 2)) – Number of B-spline intervals

  • K (int (1-100, default: 20)) – Number of bootstrap iterations

  • R (int (100-N/2, default: N/2)) – Number of bootstrap samples. Will be set to length of Y if K is set to 1.

  • alpha (float (0.5-1)) – Confidence interval F-test

  • lambdax (float (0-10, default: 0.01)) – Regularization term

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

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

Returns

Si – Sa : Uncorrelated contribution of a term

Sa_conf : Confidence interval of Sa

Sb : Correlated contribution of a term

Sb_conf : Confidence interval of Sb

STotal contribution of a particular term

Sum of Sa and Sb, representing first/second/third order sensitivity indices

S_conf : Confidence interval of S

ST : Total contribution of a particular dimension/parameter

ST_conf: Confidence interval of ST select: Number of selection (F-Test)

EmEmulator result set

C1: First order coefficient C2: Second order coefficient C3: Third Order coefficient

Return type

ResultDict,

References

1

Rabitz, H. and Aliş, Ö.F., “General foundations of high dimensional model representations”, Journal of Mathematical Chemistry 25, 197-233 (1999) https://doi.org/10.1023/A:1019188517934

2
Genyuan Li, H. Rabitz, P.E. Yelvington, O.O. Oluwole, F. Bacon,

C.E. Kolb, and J. Schoendorf,

“Global Sensitivity Analysis for Systems with Independent and/or

Correlated Inputs”,

Journal of Physical Chemistry A, Vol. 114 (19), pp. 6022 - 6032, 2010, https://doi.org/10.1021/jp9096919

SALib.analyze.hdmr.cli_action(args)[source]#
SALib.analyze.hdmr.cli_parse(parser)[source]#

SALib.analyze.morris module#

SALib.analyze.morris.analyze(problem: Dict, X: ndarray, Y: ndarray, num_resamples: int = 100, conf_level: float = 0.95, print_to_console: bool = False, num_levels: int = 4, seed=None) → Dict[source]#

Perform Morris Analysis on model outputs.

Returns a result set with keys mu, mu_star, sigma, and mu_star_conf, where each entry corresponds to the parameters defined in the problem spec or parameter file.

  • mu metric indicates the mean of the distribution

  • mu_star metric indicates the mean of the distribution of absolute

    values

  • sigma is the standard deviation of the distribution

Notes

When applied with groups, the mu metric is less reliable as the effect from parameters within a group become averaged out.

The mu_star metric avoids this issue as it indicates the mean of the absolute values. If the direction of effects is important, Campolongo et al., [2] suggest comparing mu_star with mu. If mu is low and mu_star is high, then the effects are of different signs.

sigma is used as an indicator of interactions between parameters, or groups of parameters.

Notes

Compatible with:

morris : SALib.sample.morris.sample()

Examples

>>> X = morris.sample(problem, 1000, num_levels=4)
>>> Y = Ishigami.evaluate(X)
>>> Si = morris.analyze(problem, X, Y, conf_level=0.95,
>>>                     print_to_console=True, num_levels=4)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.array) – The NumPy matrix containing the model inputs of dtype=float

  • Y (numpy.array) – The NumPy array containing the model outputs of dtype=float

  • num_resamples (int) – The number of resamples used to compute the confidence intervals (default 1000)

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

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

  • num_levels (int) – The number of grid levels, must be identical to the value passed to SALib.sample.morris (default 4)

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

Returns

Si – A dictionary of sensitivity indices containing the following entries.

  • mu - the mean elementary effect

  • mu_star - the absolute of the mean elementary effect

  • sigma - the standard deviation of the elementary effect

  • mu_star_conf - the bootstrapped confidence interval

  • names - the names of the parameters

Return type

dict

References

1
Morris, M. (1991).
“Factorial Sampling Plans for Preliminary

Computational Experiments.”

Technometrics, 33(2):161-174, doi:10.1080/00401706.1991.10484804.

2
Campolongo, F., J. Cariboni, and A. Saltelli (2007).
“An effective screening design for sensitivity analysis

of large models.”

Environmental Modelling & Software, 22(10):1509-1518, doi:10.1016/j.envsoft.2006.10.004.

SALib.analyze.morris.cli_action(args)[source]#
SALib.analyze.morris.cli_parse(parser)[source]#

SALib.analyze.pawn module#

SALib.analyze.pawn.analyze(problem: Dict, X: ndarray, Y: ndarray, S: int = 10, print_to_console: bool = False, seed: Optional[int] = None)[source]#

Performs PAWN sensitivity analysis.

The PAWN method [1] is a moment-independent approach to Global Sensitivity Analysis (GSA). It is described as producing robust results at relatively low sample sizes (see [2]) for the purpose of factor ranking and screening.

The distribution of model outputs is examined rather than their variation as is typical in other common GSA approaches. The PAWN method further distinguishes itself from other moment-independent approaches by characterizing outputs by their cumulative distribution function (CDF) as opposed to their probability distribution function. As the CDF for a given random variable is typically normally distributed, PAWN can be more appropriately applied when outputs are highly-skewed or multi-modal, for which variance-based methods may produce unreliable results.

PAWN characterizes the relationship between inputs and outputs by quantifying the variation in the output distributions after conditioning an input. A factor is deemed non-influential if distributions coincide at all S conditioning intervals. The Kolmogorov-Smirnov statistic is used as a measure of distance between the distributions.

This implementation reports the PAWN index at the min, mean, median, and max across the slides/conditioning intervals as well as the coefficient of variation (CV). The median value is the typically reported value. As the CV is (standard deviation / mean), it indicates the level of variability across the slides, with values closer to zero indicating lower variation.

Notes

Compatible with:

all samplers

This implementation ignores all NaNs.

When applied to grouped factors, the analysis is conducted on each factor individually, and the mean of their results are reported.

Examples

>>> X = latin.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = pawn.analyze(problem, X, Y, S=10, print_to_console=False)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.array) – A NumPy array containing the model inputs

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

  • S (int) – Number of slides; the conditioning intervals (default 10)

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

  • seed (int) – Seed value to ensure deterministic results

References

1

Pianosi, F., Wagener, T., 2015. A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. Environmental Modelling & Software 67, 1-11. https://doi.org/10.1016/j.envsoft.2015.01.004

2

Pianosi, F., Wagener, T., 2018. Distribution-based sensitivity analysis from a generic input-output sample. Environmental Modelling & Software 108, 197-207. https://doi.org/10.1016/j.envsoft.2018.07.019

3

Baroni, G., Francke, T., 2020. An effective strategy for combining variance- and distribution-based global sensitivity analysis. Environmental Modelling & Software, 134, 104851. https://doi.org/10.1016/j.envsoft.2020.104851

4

Baroni, G., Francke, T., 2020. GSA-cvd Combining variance- and distribution-based global sensitivity analysis https://github.com/baronig/GSA-cvd

SALib.analyze.pawn.cli_action(args)[source]#
SALib.analyze.pawn.cli_parse(parser)[source]#

SALib.analyze.rbd_fast module#

SALib.analyze.rbd_fast.analyze(problem, X, Y, M=10, num_resamples=100, conf_level=0.95, print_to_console=False, seed=None)[source]#

Performs the Random Balanced Design - Fourier Amplitude Sensitivity Test (RBD-FAST) on model outputs.

Returns a dictionary with keys ‘S1’, where each entry is a list of size D (the number of parameters) containing the indices in the same order as the parameter file.

Notes

Compatible with:

all samplers

Examples

>>> X = latin.sample(problem, 1000)
>>> Y = Ishigami.evaluate(X)
>>> Si = rbd_fast.analyze(problem, X, Y, print_to_console=False)
Parameters

  • problem (dict) – The problem definition

  • X (numpy.array) – A NumPy array containing the model inputs

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

  • M (int) – The interference parameter, i.e., the number of harmonics to sum in the Fourier series decomposition (default 10)

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

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

References

1

S. Tarantola, D. Gatelli and T. Mara (2006) “Random Balance Designs for the Estimation of First Order Global Sensitivity Indices”, Reliability Engineering and System Safety, 91:6, 717-727 https://doi.org/10.1016/j.ress.2005.06.003

2

Elmar Plischke (2010) “An effective algorithm for computing global sensitivity indices (EASI) Reliability Engineering & System Safety”, 95:4, 354-360. doi:10.1016/j.ress.2009.11.005

3

Jean-Yves Tissot, Clémentine Prieur (2012) “Bias correction for the estimation of sensitivity indices based on random balance designs.”, Reliability Engineering and System Safety, Elsevier, 107, 205-213. doi:10.1016/j.ress.2012.06.010

4

Jeanne Goffart, Mickael Rabouille & Nathan Mendes (2015) “Uncertainty and sensitivity analysis applied to hygrothermal simulation of a brick building in a hot and humid climate”, Journal of Building Performance Simulation. doi:10.1080/19401493.2015.1112430

SALib.analyze.rbd_fast.bootstrap(X_d, Y, M, resamples, conf_level)[source]#
SALib.analyze.rbd_fast.cli_action(args)[source]#
SALib.analyze.rbd_fast.cli_parse(parser)[source]#
SALib.analyze.rbd_fast.compute_first_order(permuted_outputs, M)[source]#
SALib.analyze.rbd_fast.permute_outputs(X, Y)[source]#

Permute the output according to one of the inputs as in [_2]

References

2

Elmar Plischke (2010) “An effective algorithm for computing global sensitivity indices (EASI) Reliability Engineering & System Safety”, 95:4, 354-360. doi:10.1016/j.ress.2009.11.005

SALib.analyze.rbd_fast.unskew_S1(S1, M, N)[source]#

Unskew the sensivity indice (Jean-Yves Tissot, Clémentine Prieur (2012) “Bias correction for the estimation of sensitivity indices based on random balance designs.”, Reliability Engineering and System Safety, Elsevier, 107, 205-213. doi:10.1016/j.ress.2012.06.010)

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’.

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. (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.

3

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.

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

Example

>>> 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

Module contents#