mzprojection package
Project description
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).
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