Sparse Grids Matlab Kit
The Sparse Grids Matlab Kit is a collection of Matlab functions for high-dimensional quadrature and interpolation, based on the combination technique version of sparse grids.
It is lightweight, high-level and (hopefully) easy to use, good for quick prototyping and teaching. It comes with a very extensive documentation and examples (8800 lines of code, 4800 lines of comments).
It is somehow geared towards Uncertainty Quantification (UQ), but it is flexible enough for other purposes.
Lorenzo Tamellini (main developer, maintainer) - CNR-IMATI, Pavia, Italy
Fabio Nobile - École Polytechnique Fédérale de Lausanne, Switzerland
Chiara Piazzola - CNR-IMATI, Pavia, Italy
Björn Sprungk - Technische Universität Bergakademie Freiberg, Germany
Giovanni Porta - Politecnico di Milano, Italy
Diane Guignard - University of Ottawa, Canada
Francesco Tesei - Credit Suisse, Switzerland
The Sparse Grids Matlab Kit is distributed with a BSD2 License
22-2 ("California") - current release. Compatible with Octave 6.2.0
18-10 (“Esperanza”) Compatible with Octave 6.2.0
Sparse-grid-based quadrature and interpolation for several measures/pdf
uniform: Gauss-Legendre, Leja, Clenshaw-Curtis, midpoints, equispaced points
normal: Gauss-Hermite, Leja, Genz-Keister
exponential: Gauss-Laguerre, Leja
gamma: Gauss-Laguerre (generalized), Leja
beta: Gauss-Jacobi, Leja
Dimension-adaptive sparse grid algorithm
Conversion of a sparse-grid interpolant to a Polynomial Chaos Representation (Legendre, Chebyshev, Hermite, Laguerre, Generalized Laguerre, Jacobi polynomials supported)
Sparse-grid-based global and local sensitivity analysis (by computation of Sobol Indices and gradients of a sparse grid interpolant)
Computation of Hessians
Export of sparse grid collocation points and weights to ASCII file
Visualization functions (plot of sparse grid points and sparse grid interpolant)
Please cite our toolbox by mentioning the webpage containing the package and adding the following references to your work:
1) C. Piazzola, L. Tamellini. The Sparse Grids Matlab kit - a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification, ArXiv 2203.09314, 2022.
Paper available at this link
Codes available here
2) J. Bäck, F. Nobile, L. Tamellini, and R. Tempone. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison. In J.S. Hesthaven and E.M. Ronquist, editors, Spectral and High Order Methods for Partial Differential Equations, volume 76 of Lecture Notes in Computational Science and Engineering, pages 43–62. Springer, 2011. Available at this link
selected PUBLICATIONs USING THE SPARSE GRIDS MATLAB KIT - with code
Chiara Piazzola, Lorenzo Tamellini, Raúl Tempone. A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology, Mathematical Biosciences, 2022.
Paper available here.
Matlab code available here
Jesús Martínez-Frutos, Francisco Periago Esparza. Optimal Control of PDEs under Uncertainty - An Introduction with Application to Optimal Shape Design of Structures. Springer International Publishing, 2018.
Book available here.
Matlab code available here
Get in touch
For any questions or to report a bug, send an email to tamellini AT imati DOT cnr DOT it .
Send us your email if you want to be notified when a new version is released online