This repository contains code for calculating the c-u-curve and some example applications.

The c-u-curve method can be used to analyse, classify and compare dynamical systems of arbitrary dimension by the two key features uncertainty and complexity. The method is applicable to uni- and multivariate data sets, and accepts both deterministic and probabilistic value representations.

For detail information see the related publication by Ehret and Dey (2022): Ehret, U., and P. Dey (2022), Technical note: c-u-curve: A method to analyse, classify and compare dynamical systems by uncertainty and complexity, Hydrol. Earth Syst. Sci. Discuss., 2022, 1-12.

MATLAB 9.9

See test_c_u_curve.m for simple test cases See test_c_u_curve_EhretDeyHESS2022.m for an application with real data

• test_c_u_curve.m contains example applications for single- and multivariate data sets, and for deterministic and probabilisitc value representations
• test_c_u_curve_EhretDeyHESS2022.m contains all code to reproduce the results from Ehret and Dej (2022)
• f_c_u_curve.m function returning all values to plot the c_u_curve (uncertainty and complexity values for user-selected time slicing schemes)
• f_entropy.m function returning the (joint) entropy of an 1-to-any-dimensional discrete (binned) frequency distribution
• f_binme.m returns values classified in bins
• f_maxEnt_known_mean.m returns the maximum possible entropy of a discrete distribution for which the mean is known.
• test_f_maxEnt_known_mean.m constains example applications for f_maxEnt_known_mean.m

Uwe Ehret | [email protected]