Functions & Optimization

Examples demonstrating function construction, gradient checking, benchmark functions, optimization algorithms, and numerical integration.

ex_func.py

Function composition and operations.

Shows how to combine, transform, and manipulate various function objects including toy functions, Genz functions, chemistry functions, and benchmark functions.

ex_funcall.py

Automatic testing of all function classes.

Automatically creates instances of all available function classes from PyTUQ’s function modules and validates their gradient implementations.

ex_funcgrad.py

Gradient checking and evaluation.

Tests analytical gradients of benchmark functions against numerical gradients, and visualizes function values and derivatives.

ex_genz1d.py

1D Genz test functions.

Evaluates and plots various 1D Genz functions including oscillatory, corner peak, and sum functions across their domains.

ex_optim.py

Optimization algorithms on the Rosenbrock function.

Compares different optimization methods (Gradient Descent, Adam, PSO, Scipy) for minimizing the Rosenbrock function.

ex_integrate.py

Numerical integration of Gaussian functions.

Tests various integration methods (MCMC, GMM, MC) on single and double Gaussian functions, comparing numerical results with analytical solutions.

ex_orf.py

Orthonormalization of functions.

Tests orthonormalization of functions using Gram-Schmidt or QR decomposition. Written by Habib N. Najm (2025).