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mzprojection package

Project description

mzprojection

Projection operator method for statistical data analysis (Fortran90 or Python3)
Language grade: Python

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 f(t)^i and the variable of interest u(t)^i, du(t)^i/dt 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 f(t)^i on u(t)^i as,
f(t)=\Omega u(t)+s(t)+r(t),
s(t)=-\int_0^t \Gamma(t) u(t-v)dv.
The Markov coefficient \Omega, the memory function \Gamma(t) and the uncorrelated term r(t) are obtained as outputs. (Some correlations, e.g., <r(t)u>, 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).
doi

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