Commit 374baddd authored by Bedartha Goswami's avatar Bedartha Goswami
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Initial commit: python modules from Nat Comms study, license, and readme files

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UncerTiSe - toolbox to analyse tiem serie swith uncertainties
=============================================================
General Notes
-------------
UncerTiSe is a Python package that contains an array of modules to help analyse
time series with uncertainties. This is part of the DFG Project "Impacts of
uncertainties in climate data analyses (IUCliD): Approaches to working with
measurements as a series of probability distributions" (DFG MA4759/8).
Installation
------------
As of now, there is not setup.py to install this package. To use it, just clone
the contents of this Git repository in your working directory.
Requirements
------------
The Python port needs the following Python packages:
Scipy with Scipy.Weave
Numpy
Matplotlib (optional)
Usage
-----
TBD
Example
-------
TBD
References
----------
B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. F. M.
Breitenbach, J. Kurths
Abrupt transitions in time series with uncertainties,
Nature Communications 9 (2018)
doi:10.1038/s41467-017-02456-6
Author
------
Bedartha Goswami
License
-------
This work is licensed under a Creative Commons
Attribution-NonCommercial-NoDerivatives 4.0 International Public License. For
details please read LICENSE.txt.
Please respect the copyrights! The content is protected by the Creative Commons
License. If you use the provided programmes, text or figures, you have to refer
to the given publications and this web site (tocsy.pik-potsdam.de) as well.
__all__ = [
"distributions",
"networks",
"events",
]
# define the number of surrogates for the random model (configuration model)
NSURR = 1000
# significance levels
ALPHA_TRANSITION = 0.05
"""
A few functions to assist in estimating the cumulative distributions
====================================================================
!! Please import as a module and use it as such -- not as a script !!
"""
# Created: Thu May 26, 2016 11:12PM
# Last modified: Tue Aug 15, 2017 01:28pm
# Copyright: Bedartha Goswami <goswami@pik-potsdam.de>
import numpy as np
from utils import _printmsg
from utils import _progressbar_start
from utils import _progressbar_update
from utils import _progressbar_finish
def cumulative(pdfmat, var_span, verbose, save, pbar):
"""
Estimates the cumulative distributions for the specified dataset.
"""
# get CDF matrix and Inter-Quartile Range
cdfmat = cdf_matrix(pdfmat, var_span, verbose, pbar)
iqr = inter_quartile_range(cdfmat, var_span, verbose)
return cdfmat, iqr
def cdf_matrix(pdfmat, var_span, verbose=False, pbar=False):
"""
Returns Cumulative Distribution Functions from given PDFs.
"""
nt = pdfmat.shape[0]
bj = 0.5 * np.r_[
var_span[1] - var_span[0],
var_span[2:] - var_span[:-2],
var_span[-1] - var_span[-2]
] # Riemann sum width
_printmsg("Estimating CDFs...", verbose)
cdfmat = np.zeros(pdfmat.shape)
prog_bar = _progressbar_start(nt, pbar)
for i in range(nt):
pdf = pdfmat[i]
cdfmat[i] = np.cumsum(pdf * bj)
_progressbar_update(prog_bar, i + 1)
_progressbar_finish(prog_bar)
return cdfmat
def inter_quartile_range(cdfmat, var_span, verbose=False):
"""
Returns the Inter-Quartile Range for the paleo dataset.
"""
nt = cdfmat.shape[0]
_printmsg("Estimating IQR of total proxy probability...", verbose)
cdfhist = np.zeros(len(var_span))
for i in range(nt):
cdfhist += cdfmat[i]
cdfhist /= float(nt)
qHi = np.interp(0.75, cdfhist, var_span)
qLo = np.interp(0.25, cdfhist, var_span)
iqr = qHi - qLo
return iqr
"""
A suite of functions that assist in carrying out the event-detection analysis
=============================================================================
!! Please import as a module and use it as such -- not as a script !!
"""
# Created: Thu May 26, 2016 03:50PM
# Last modified: Tue Aug 15, 2017 01:25pm
# Copyright: Bedartha Goswami <goswami@pik-potsdam.de>
import numpy as np
from scipy.stats import percentileofscore as percentile
from lib import DATPATH
from networks import link_density
from utils import _printmsg, _savedat
from utils import _progressbar_start
from utils import _progressbar_update
from utils import _progressbar_finish
def community_strength(G):
"""
Returns intra-community link fraction for partition in two equal parts.
Traditionally, modularity is estimated as the difference between the
total fraction of links that fall within communities and the expectation
value of the same quantity from a random network with the same degree
sequence. The quantity returned by this fraction is simply the first
term in the traditional definition of modularity. However, this is
estimated only for one specific partition of the considered (recurrence)
network, viz. the partition at the midpoint of time-ordering of the
network which divides the entire graph into two subgraphs of equal size.
Parameters
----------
G : igraph Graph
An igraph Graph object that can be weighted or unweighted, but is
not directed, for which the link density is to be estimated.
Returns
-------
rho : scalar, float
The estimated total fraction of links that fall within the two
communities of the recurrence network G.
See Also
--------
igraph.Graph.density
modularity
"""
n = G.vcount()
tot_possible_edges = 0.5 * float(n * (n - 1))
G1, G2 = __divide_at_midpoint(G)
if G.is_weighted():
edges1, edges2 = np.sum(G1.es["weight"]), np.sum(G2.es["weight"])
else:
edges1, edges2 = G1.ecount(), G2.ecount()
rho = float(edges1 + edges2) / tot_possible_edges
return rho
def __divide_at_midpoint(G):
"""
Returns subgraphs by cutting the recurrence network at the midpoint.
"""
n = G.vcount()
inds1, inds2 = range(0, n / 2), range(n / 2, n)
G1, G2 = G.subgraph(G.vs[inds1]), G.subgraph(G.vs[inds2])
return G1, G2
def community_strength_data(G, time, ld, wsize, wstep,
verbose=False, save=True, pbar=False):
"""
Saves intra-community link fraction for specified data set.
"""
_printmsg("COMMUNITY STRENGTH OF OBSERVED DATA", verbose)
_printmsg("===================================", verbose)
_printmsg("Loading data...", verbose)
n = G.vcount()
nwind = ((n - wsize) / wstep) + 1
tmid = []
Q, LD = [np.zeros(nwind) for i in range(2)]
_printmsg("Estimating intra-community link fraction...", verbose)
prog_bar = _progressbar_start(n, pbar)
for i in range(nwind):
k = i * wstep
start, stop = k, k + wsize
t_ = (time[start:stop]).sum() / wsize
tmid.append(t_)
G_ = G.subgraph(G.vs[start:stop])
Q[i] = community_strength(G_)
LD[i] = link_density(G_)
_progressbar_update(prog_bar, i)
_progressbar_finish(prog_bar)
return Q, LD, tmid
def community_strength_random_model(G, time, ld, wsize, wstep, nsurr,
verbose=False, save=True, pbar=False):
"""
Saves intra-community link fraction for surrogates of specified data set.
"""
_printmsg("COMMUNITY STRENGTH OF RANDOM MODEL", verbose)
_printmsg("==================================", verbose)
_printmsg("Loading data...", verbose)
n = G.vcount()
nwind = ((n - wsize) / wstep) + 1
tmid = []
Qsurr, LDsurr = [np.zeros((nwind, nsurr), "float") for i in range(2)]
_printmsg("Estimating intra-community link fraction...", verbose)
prog_bar = _progressbar_start(nwind*nsurr, pbar)
count = 0
for i in range(nwind):
k = i * wstep
start, stop = k, k + wsize
t_ = (time[start:stop]).sum() / wsize
tmid.append(t_)
G_ = G.subgraph(G.vs[start:stop])
if G.density() > 0.:
wts_ = G_.es["weight"]
str_ = np.array(G_.strength(G_.vs, weights=wts_))
deg = np.round(str_).astype("int").tolist()
for j in range(nsurr):
if sum(deg) % 2 != 0:
deg_nonzero = np.where(np.array(deg) > 0)[0]
idx = np.random.randint(0, len(deg_nonzero))
idx = deg_nonzero[idx]
deg[idx] = deg[idx] - 1
Gsurr_ = G_.Degree_Sequence(out=deg, method="simple")
Qsurr[i, j] = community_strength(Gsurr_)
LDsurr[i, j] = Gsurr_.density()
count += 1
else:
Qsurr[i] = np.nan
LDsurr[i] = np.nan
_progressbar_update(prog_bar, count)
_progressbar_finish(prog_bar)
return Qsurr, LDsurr, tmid
def pvalue(name, dtype, ld, wsize, wstep, nsurr,
verbose=False, save=True, pbar=False):
"""
Returns the p-value of obtaining intra-community link density.
"""
_printmsg("p-VALUE OF AN EVENT FOR %s" % name.upper(), verbose)
_printmsg("=========================================", verbose)
_printmsg("Loading data...", verbose)
prefix = "%s/%s/community_strength" % (DATPATH, dtype)
suffix = "LD%.2f/WSIZE%d/%s_WSTEP%d.npz" % (ld, wsize, name, wstep)
f_data = "%s_data/%s" % (prefix, suffix)
f_cfmd = "%s_random_model/%s" % (prefix, suffix)
d_data = np.load(f_data)
d_cfmd = np.load(f_cfmd)
# check for consistency
tmid1 = d_data["tmid"]
tmid2 = d_cfmd["tmid"]
assert all(tmid1 == tmid2), "Data & random model timescales don't match!"
assert nsurr == d_cfmd["nsurr"], "Incompatible no. of surrogates!"
# initiate relevant variables
time = tmid1
Q = d_data["Q"]
Qsurr = d_cfmd["Qsurr"]
nwind = d_data["nwind"]
_printmsg("Estimating p-value...", verbose)
pvalue = np.zeros(nwind)
prog_bar = _progressbar_start(nwind, pbar)
for i in range(nwind):
Qnull = Qsurr[i]
pvalue[i] = 1. - percentile(Qnull, Q[i], kind="weak") / 100.
_progressbar_update(prog_bar, i)
_progressbar_finish(prog_bar)
p = "%s/%s/pvalues/" % (DATPATH, dtype)
o = "LD%.2f_WSIZE%d_%s_WSTEP%d" % (ld, wsize, name, wstep)
_savedat(p, o, verbose, save,