Polynomial Chaos

Examples demonstrating polynomial chaos (PC) basis construction, random variable operations, multiindex manipulation, quadrature, uncertainty propagation, and model selection.

ex_pcbasis1d.py

1D polynomial chaos basis evaluation and plotting.

Evaluates and plots Hermite polynomial basis functions of various orders to illustrate orthogonal polynomial behavior.

ex_pcrv.py

Polynomial chaos random variable slicing.

Shows how to slice a PC random variable by fixing certain dimensions at nominal values to obtain a reduced-dimension PCRV.

ex_pcrv1.py

PCRV compression and random dimension selection.

Creates a multivariate normal PCRV with specified random dimensions, samples from it, and demonstrates PC compression operations.

ex_pcrv2.py

Basic polynomial chaos random variable operations.

Creates a PCRV with random coefficients and demonstrates computing statistics (mean, variance), basis norms, and sampling.

ex_pcrv_mvn.py

Multivariate normal polynomial chaos random variables.

Creates PCRV_mvn objects with specified means and covariances, and generates samples from the multivariate normal distribution.

ex_mrv.py

Multivariate random variable (MRV) operations.

Shows how to create and manipulate polynomial chaos random variables including independent and multivariate normal PC random variables.

ex_mindex.py

Multiindex generation and encoding.

Shows how to generate polynomial chaos multiindices and encode them for efficient storage and manipulation.

ex_quad.py

Quadrature point generation for PC germ variables.

Generates and visualizes quadrature points for polynomial chaos germ variables using tensor product quadrature rules.

ex_uprop.py

Uncertainty propagation through a model with PC inputs.

Shows how to propagate polynomial chaos input uncertainties through a nonlinear model using projection or regression methods.

ex_uprop2.py

Uncertainty propagation via projection and regression.

Compares projection-based and regression-based methods for propagating PC input uncertainties through nonlinear forward models.