1: [((1, -1), a), ((0, -1), c1)],

2: [((2, -1), a), ((1, -2), c2)],

3: [((3, -1), a), ((0, -3), c3)],

# Data

'fulldata': fulldata_list,

'N': fulldata_list[0].shape[1],

'T': [data.shape[0] for data in fulldata_list],

'datatime': datatime_list,

# Analyze only masked samples

# selector_type needs to be a list containing 'x' or 'y'or 'z' or any

# combination. This will ignore masked values if they are in the

# lagged variable X, the 'driven' variable Y and/or the condition Z in

# the association measure I(X;Y | Z), which enables to, e.g., only

# consider the impacton summer months. More use cases will bediscussed

# in future papers...

'selector': False,

'sample_selector': sample_selector_list,

'selector_type': ['y'],

# Measure of association and params

# - 'par_corr': linear partial correlation,

# - 'reg': linear standardized partial regression

# - 'cmi_knn': conditional mutual information (CMI)

# estimated using nearest neighbors

# - 'cmi_symb': CMI using symbolic time series

# (from binning or ordinal patterns, the data

# can be converted using the functions in

# the module "pp")

'measure': 'par_corr',

# Quantities to estimate using estimated parents

# 'none' for MI/cross correlation

# 'parents_xy' for MIT

# 'parents_y' for ITY

# 'parents_x' for ITX

# These measures are described in Runge et al. PRE (2012).

'cond_types': ['none', 'parents_xy'],

# for measure='cmi_knn': nearest neighbor parameter

# used in causal algorithm (higher k reduce the

# variance of the estimator, better for

# independence tests).

# Recommended: 5% - 50% of time series length

'measure_params_algo': {'knn': 100},

# nearest neighbor parameter used in the

# subsequent estimation of MI, MIT, ITY, ...

# (smaller k has smaller bias)

# Recommended: 5..10, independent of T

'measure_params_lagfuncs': {'knn': 10},

# Causal Algorithm for estimation of parents/neighbors

# Maximum time lag up to which links are tested

'tau_max': 1,

# Initial number of conditions to use, corresponds

# to n_0 in Runge et al. PRL (2012).

# Larger initial_conds speeds up the algorithm,

# but leads to slightly more false positives.

'initial_conds': 2,

# Maximum number of conditions to use

# (parameter n_max in my phd thesis)

# Recommended: 4..6 for CMI estimation,

# for 'par_corr' or 'reg' more can be used.

'max_conds': 4,

# Maximum number of combinations of conditions

# to check in algorithm (corresponds to number i

# of iterations in n-loop in Runge PRL (2012))

# Recommended: 3..6

'max_trials': 5,

# True for solid links as defined in Runge PRL + PRE (2012)

# Recommended is "True".

'solid_contemp_links': True,

# Significance testing in algorithm and lag functions estimation

# - 'fixed': fixed threshold (specified below)

# - 'analytic': sig_lev for analytical sample

# distribution of partial correlation or

# regression (Student's t)

# - 'full_shuffle': shuffle test as described in

# Runge et al. PRL (2012)

# - 'block_shuffle': block shuffle test works better for serially

# dependent data. Block length determined using approach in Mader (2013)

# [Eq. (6)]

# Recommended for CMI: 'full_shuffle' or 'fixed'

# Recommended for par_corr and reg: 'analytic'

'significance': 'analytic',

# significance level (1-alpha). Note that for

# 'par_corr' or 'reg' the test is two-sided,

# such that 0.95 actually corresponds to a 90%

# significance level

# Here the divisor "/ 2." accounts for a two-sided level

'sig_lev': (1. - .01 / 2.),

# Higher significance levels require a larger

# number of shuffle test samples, i.e. 0.9 needs

# about 50 samples, 0.95 about 100, .98 about 500.

'sig_samples': 100,

# fixed threshold for CMI. I recommend to use a

# shuffle test for CMI to get an idea of typical

# values (see output in command line). Note that

# shuffle significance thresholds depend on the

# estimation dimension.

'fixed_thres': 0.05,

# Confidence bounds to be displayed

# in lag functions (not used in the algorithm)

# - False: no bounds

# - 'analytic': conf_lev for analytical sample

# distribution (Student's t)

# - 'bootstrap': bootstrap confidence bounds

# Recommended for CMI: 'bootstrap'

# Recommended for par_corr and reg: 'analytic'

'confidence': 'analytic',

# 0.9 corresponds to 90% confidence interval.

'conf_lev': .9,

'conf_samples': 100,

# Variable names and node positions for graph plots (in figure coords)

# These can be adapted to basemap plots in plot section below

'var_names': ['0', '1', '2', '3'],

'node_pos': None,

# {'y': numpy.array([0.5, 1., 0., 0.5]),

# 'x': numpy.array([0., 0.5, 0.5, 1.])},

###

# Estimate parents and neighbors

###

ensemble_members = range(len(fulldata_list))

d['ensemble_members'] = ensemble_members

for ens in ensemble_members:

tigramite_estimation._sanity_checks(

which='pc_algo',

data=d['fulldata'][ens],

selector=d['selector'],

selector_type=d['selector_type'],

sample_selector=d['sample_selector'][ens],

measure=d['measure'],

measure_params=d['measure_params_algo'],

estimate_parents_neighbors='both',

tau_max=d['tau_max'],

initial_conds=d['initial_conds'],

max_conds=d['max_conds'],

max_trials=d['max_trials'],

significance=d['significance'],

sig_lev=d['sig_lev'],

fixed_thres=d['fixed_thres'],

verbosity=verbosity)

d['results'] = {}

if verbosity > 0:

print("\n" + "-" * 60 +

"\nEstimating parents for all variables:"

"\n" + "-" * 60)

job_index = 0

for ens in ensemble_members:

for j in range(d['N']):

mpi.submit_call(

"tigramite_estimation._pc_algo",

kwargs={

'data': d['fulldata'][ens],

'j': j,

'parents_or_neighbors': 'parents',

'all_parents': None,

'tau_max': d['tau_max'],

'initial_conds': d['initial_conds'],

'max_conds': d['max_conds'],

'max_trials': d['max_trials'],

'measure': d['measure'],

'measure_params': d['measure_params_algo'],

'significance': d['significance'],

'sig_lev': d['sig_lev'],

'fixed_thres': d['fixed_thres'],

'sig_samples': d['sig_samples'],

'selector': d['selector'],

'selector_type': d['selector_type'],

'sample_selector': d['sample_selector'][ens],

'verbosity': verbosity

},

id=job_index)

job_index += 1

job_index = 0

for ens in ensemble_members:

d['results'][ens] = {'parents_neighbors': {}}

for j in range(d['N']):

d['results'][ens]['parents_neighbors'][j] = \

mpi.get_result(id=job_index)

job_index += 1

if d['solid_contemp_links']:

if verbosity > 0:

print("\n" + "-" * 60 +

"\nEstimating neighbors for all variables:"

"\n" + "-" * 60)

job_index = 0

for ens in ensemble_members:

for j in range(d['N']):

mpi.submit_call(

"tigramite_estimation._pc_algo",

kwargs={

'data': d['fulldata'][ens],

'j': j,

'parents_or_neighbors': 'neighbors',

'all_parents': d['results'][ens]['parents_neighbors'],

'tau_max': d['tau_max'],

'initial_conds': d['initial_conds'],

'max_conds': d['max_conds'],

'max_trials': d['max_trials'],

'measure': d['measure'],

'measure_params': d['measure_params_algo'],

'significance': d['significance'],

'sig_lev': d['sig_lev'],

'fixed_thres': d['fixed_thres'],

'sig_samples': d['sig_samples'],

'selector': d['selector'],

'selector_type': d['selector_type'],

'sample_selector': d['sample_selector'][ens],

'verbosity': verbosity

},

id=job_index)

job_index += 1

job_index = 0

for ens in ensemble_members:

for j in range(d['N']):

d['results'][ens]['parents_neighbors'][j] += \

mpi.get_result(id=job_index)

job_index += 1

###

# Estimate lag functions for MIT, ITY, ...

###

# 'none' for MI/cross correlation

# 'parents_xy' for MIT

# 'parents_y' for ITY

# 'parents_x' for ITX

# These measures are described in Runge et al. PRE (2012).

# cond_types = ['none', 'parents_xy']

# d['cond_types'] = cond_types

if verbosity > 0:

print("\n" + "-" * 60 +

"\nEstimating lag functions for all variables:"

"\n" + "-" * 60)

job_index = 0

for ens in ensemble_members:

for which in d['cond_types']:

# if verbosity > 0:

# print("Estimating lag functions for ensemble "

# "member %d and condition type %s" % (ens, which))

for j in range(d['N']):

mpi.submit_call(

"tigramite_estimation.get_lagfunctions",

kwargs={

'selected_variables': [j],

'data': d['fulldata'][ens],

'selector': d['selector'],

'selector_type': d['selector_type'],

'sample_selector': d['sample_selector'][ens],

'parents_neighbors': d['results'][ens][

'parents_neighbors'],

'cond_mode': which,

'solid_contemp_links': d['solid_contemp_links'],

'tau_max': d['tau_max'],

'max_conds': d['max_conds'],

'measure': d['measure'],

'measure_params': d['measure_params_lagfuncs'],

'significance': d['significance'],

'sig_lev': d['sig_lev'],

'sig_samples': d['sig_samples'],

'fixed_thres': d['fixed_thres'],

'confidence': d['confidence'],

'conf_lev': d['conf_lev'],

'conf_samples': d['conf_samples'],

'verbosity': verbosity

},

id=job_index)

job_index += 1

job_index = 0

for ens in ensemble_members:

for which in d['cond_types']:

d['results'][ens][which] = numpy.zeros(

(d['N'], d['N'], d['tau_max'] + 1))

d['results'][ens]['sig_thres_' + which] = numpy.zeros(

(d['N'], d['N'], d['tau_max'] + 1))

d['results'][ens]['conf_' + which] = numpy.zeros(

(d['N'], d['N'], d['tau_max'] + 1, 2))

for j in range(d['N']):

res = mpi.get_result(id=job_index)

(d['results'][ens][which][:, j, :],

d['results'][ens]['sig_thres_' + which][:, j, :],

d['results'][ens]['conf_' + which][:, j, :]

) = res[0][:, j, :], res[1][:, j, :], res[2][:, j, :]

job_index += 1

if verbosity > 0:

print("Saving results as %s" % (os.path.expanduser(save_folder) +

project_name +

'_results.pkl'))

pickle.dump(d, open(os.path.expanduser(save_folder) + project_name +