mbaudin47

"""
Let d be the dimension of the input vector.
Let n be the sample size.
Let alpha in [0, 1] a proportion of the sample size.
Compute the largest polynomial degree p such that the 
number of coefficients of the polynomial chaos expansion is lower or 
equal to alpha * n.

For example, the next table presents the number of coefficients 
of the PCE of the Ishigami function, which has dimension 3.

mbaudin47

"""
Estimate the expected value of the test functions using quasi-Monte Carlo.

See the effect of:
- scrambling the Sobol' sequence,
- including or excluding the first Sobol' point (zero).

See:

- The first zero point should be moved back into the low discrepancy sequences

mbaudin47

"""
Michaël Baudin, 2025
Benchmark the elapsed time of the cross-validation of a PCE.

Compare two methods for cross-validation:
- leave-one-out,
- K-fold.

Compare two methods for performing the CV:
- classical cross-validation, using MetaModelValidation,

mbaudin47

"""
Michaël Baudin, 2025
Benchmark the elapsed time of solving a linear least squares problem using OpenTURNS.
Uses the Ishigami function.
Compute its polynomial chaos expansion.
"""

# %%
import openturns as ot
import time

mbaudin47

"""
Get the (output) marginal of a PCE.

There is no FunctionalChaosResult.getMarginal()
https://github.com/openturns/openturns/issues/2985

Limitation
----------

This script involves more PCE indices than necessary i.e. the number 

mbaudin47

"""
Smallest possible script to create a FunctionalChaosResult.
Uses the Ishigami function.
"""

# %%
from openturns.usecases import ishigami_function
import openturns as ot

# %%

mbaudin47

"""Implements the selection method of a polynomial chaos expansion algorithm in Python.

This implements 2 algorithms:
- Algorithm B.1 page 628 of (Lüthen, et al., 2021),
- Algorithm B.1 with with CV using Corrected Leave-One-Out or K-Fold.

TODO-List
---------
- Extend the code to multiple output dimensions.
- Early stopping of the algorithm using the K-Fold or Corrected LOO score.

mbaudin47

"""
This script uses SALib to estimate Sobol' indices from the Beam model.
The beam model is implemented as a Python function.
Moreover, we measure the time necessary to evaluate the model and estimate 
the Sobol' indices.

Output
------
N = 100000
Elapsed = 218.30088353157043 (s)

mbaudin47

"""
This script uses OpenTURNS to estimate Sobol' indices from the Beam model implemented as an OpenTURNS's function.
Moreover, we measure the time necessary to evaluate the model and estimate the Sobol' indices.

Output
------
Elapsed = 1.0558149814605713 (s)

References
----------

mbaudin47

"""
Create a polynomial chaos for the Ishigami function and export
it as a standalone Python code.

See https://github.com/openturns/openturns/blob/master/lib/src/Uncertainty/Algorithm/MetaModel/FunctionalChaos/FunctionalChaosResult.cxx

This code produces a file which content is:

from openturns import *
def pceModel(X):