mzprojection

Projection operator method for statistical data analysis (Fortran90 or Python3)

Overview

The Mori-Zwanzig projection operator method splits ensembles of the analyzed time-series data into correlated and uncorrelated parts with regard to the variable of interests .

Contents

fortran/ - Fortran90 source code. See README.txt in detail  
python/ - Python3 source code. See README.txt in detail  
sample_data/ - A sample of time-series data and its projected results  
QUICK_START.txt - Simple explanation on how to run this source code  

Usage (Python3)

mzprojection requires external packages: numpy, scipy.

(i) Input data is ensembles of the analyzed time-series data and the variable of interest , in a prescribed format (nperiod points in time range, and nsample points in ensambles, namely u[0:nperiod,0:nsample], dudt[0:nperiod,0:nsample], f[0:nperiod,0:nsample], and time step size delta_t).

(ii) mzprojection_ensemble_of_time_series calculates the Mori-Zwanzig projection of on as,


The Markov coefficient , the memory function and the uncorrelated term are obtained as outputs. (Some correlations, e.g., , are also obtained to check the result.)

from mzprojection import mzprojection_ensemble_of_time_series

omega, memoryf, s, r, uu, ududt, fdudt, rr, rdudt, ru, fu, ff = \
    mzprojection_ensemble_of_time_series(nsample, nperiod, delta_t, u, dudt, f)

See also python/Demo_Jan2021.ipynb, which clearly shows examples of usage including output figures.

Reference

Shinya Maeyama and Tomo-Hiko Watanabe, "Extracting and Modeling the Effects of Small-Scale Fluctuations on Large-Scale Fluctuations by Mori-Zwanzig Projection operator method", J. Phys. Soc. Jpn. 89, 024401 (2020).