This module allows to perform sensitivity analysis.
This is the analysis of the uncertainty in the
output of a given model, depending on the uncertainty in its
inputs.
The analysis is based on chaos polynomials, which are orthogonal polynomials
which are used as an approximation of the original model. Once the coefficients
of the chaos polynomial are computed, the associated sensitivity indices are
straightforward to get.
This toolbox has been created in the context of the
OPUS project :
http://opus-project.fr/
within the workpackage 2.1.1 "Construction de méta-modèles".
This project has received funding by Agence Nationale de la recherche :
http://www.agence-nationale-recherche.fr/
See in the help provided in the help/en_US directory of the
toolbox for more information about its use.
Use cases are presented in the demos directory.
Features
--------
Main Features:
* randvar:
* Manage various types of random variables
* uniform, normal, exponential, log-normal
* setrandvar:
* Manage various sampling methods for sets of random variables
* Monte-Carlo, Sobol Quasi-Random, Latin Hypercube Sampling,
LHS Max Min sampling, and various samplings based
on Smolyak Cubature points.
* polychaos:
* Manage polynomial chaos expansion and get specific outputs
* mean, variance, sensitivity indices, quantiles, Wilks quantiles,
correlation, etc...
* Generate a stand-alone C source code which computes the output of
the polynomial chaos expansion.
Configuration Functions:
* nisp_destroyall : Destroy all current objects.
* nisp_getpath : Returns the path to the current module.
* nisp_initseed : Sets the seed of the uniform random number generator.
* nisp_printall : Prints all current objects.
* nisp_shutdown : Shuts down the NISP toolbox.
* nisp_startup : Starts up the NISP toolbox.
* nisp_verboselevelget : Returns the current verbose level.
* nisp_verboselevelset : Sets the current verbose level.
Sensitivity Analysis Functions:
* nisp_bruteforcesa : Compute sensitivity indices by brute force.
* nisp_sobolsa : Compute sensitivity indices by Sobol, Ishigami, Homma.
Support functions:
* nisp_buildlhs : Creates a LHS design
* nisp_corrcoef : Returns the linear correlation coefficient of x and y.
* nisp_cov : Returns the empirical covariance matrix of x and y.
* nisp_erfcinv : Computes the inverse erfc function.
* nisp_expcdf : Computes the Exponential CDF.
* nisp_expinv : Computes the Exponential quantile.
* nisp_exppdf : Computes the Exponential PDF.
* nisp_lognormalcdf : Computes the Lognormal CDF.
* nisp_lognormalinv : Computes the Lognormal quantile.
* nisp_lognormalpdf : Computes the Lognormal PDF.
Test functions:
* nisp_ishigami : Returns the Ishigami function.
* nisp_ishigamisa : Exact sensitivity analysis for the Ishigami function
* nisp_product : Returns the value of the Product function
* nisp_productsa : Exact sensitivity analysis for the Product function
* nisp_sum : Returns the value of the Product function
* nisp_sumsa : Returns the sensitivity indices of the Sum function
Acknowledgements
----------------
* Paul Beaucaire
* Allan Cornet