OpenPC is a toolbox for the creation and evaluation of Multi-Element Generalized Polynomial Chaos Expansions When using this toolbox, please cite: Perkó, Zoltán, et al. "Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion." Physics in medicine and biology 61.12 (2016): 4646. and Van Der Voort, Sebastian, et al. "Robustness recipes for minimax robust optimization in intensity modulated proton therapy for oropharyngeal cancer patients." International Journal of Radiation Oncology* Biology* Physics 95.1 (2016): 163-170. QUICK START ---------------- To use OpenPC to make the PCE of a problem two things need to be provided: A settings file and a matlab function to interface with the 'blackbox' Three example settings files are provided in the settings folder. Example_settings.json contains the settings for a simple 4 dimensional problem. As reference for the meaning of the different terms it is suggested to read: Perkó, Zoltán, et al. "Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion." Physics in medicine and biology 61.12 (2016): 4646. Example_settings_arbitrary.json contain the settings for a problem where an arbitrary PDF is defined, which can be found in Multi/PDF/Example_settings_ME.json for the construction of a multi-element Polynomial Chaos Expansion. Each of the settings has an example run in Examples/, first run initOpenPC from the main directory and then run one of the examples. The corresponding blackbox interfaces for the settings and the example runs can be found in Blackbox/Functions NOTATION ---------------- The code has some notation specifications: - functions, variables start with a lower case letter, structures start with a upper case letter. - There are a few shorthands used for easier reading: - N: Number of - u: unique - I: index of - LI: logical index of - i: i-th element of (used in iterations) For example the variable N_dims means: Number of dimensions. These shorthands can also be combined, e.g. N_u_pol_types means the number of unique polynomial types.