Analyses

An analysis is a function of a source: a system, a trajectory, or measured data. It returns a frozen result. Each analysis reads one kind of data, such as a series, a field, or a network, and may need a capability tag of the system behind the source, such as a deterministic randomness for Lyapunov exponents. The analysis checks the tags of the system, or of the system behind a trajectory, before it does any work, and raises a TagError that names the tag it lacks. Measured data carries no tags, so only its kind is checked. The table lists what every analysis needs, and the kinds of an analysis whose needs differ from its own.

Analysis	Data	Time	Space	Randomness	Kinds that differ
`alignment`	`agents`	any	any	any	none
`applicable_analyses`	any source	any	any	any	none
`autocatalytic_sets`	`network`	any	any	any	none
`automaton`	`system`	any	any	any	none
`cell_complex`	`field`	any	any	any	none
`chain_shape`	`agents`	any	any	any	none
`clusters`	`field`	any	any	any	none
`coarse_grain`	`agents`	any	any	any	none
`complexity`	`series`	any	any	any	none
`correlation`	`field`	any	any	any	`auto`: data `series` `two-time`: data `ensemble`
`data_collapse`	`ensemble`	any	any	any	none
`defects`	`field`	any	any	any	none
`displacement`	`agents`	any	any	any	none
`distribution`	`series`	any	any	any	`records`: data `ensemble`
`domains`	`field`	any	any	any	none
`elementary_modes`	`series`	any	any	any	none
`embedding`	`series`	any	any	any	none
`emergence`	`series`	any	any	any	`causal`: data `path` `effective-information`: data `path`
`entropy`	`series`	any	any	any	`ensemble`: data `ensemble`
`epsilon_machine`	`series`	any	any	any	none
`ergodicity`	`series`	any	any	any	`breaking`: data `ensemble` `distance`: data `ensemble` `metric`: data `ensemble`
`events`	`series`	any	any	any	`counts`: data `path`
`fit_law`	`series`	any	any	any	none
`information`	`series`	any	any	any	none
`invariants`	`system`	any	any	any	none
`irreversibility`	`path`	any	any	any	`fluctuation-dissipation`: data `ensemble` `fluctuation-theorem`: data `ensemble` `langevin-entropy-production`: data `ensemble` `response`: data `ensemble` `uncertainty-relation`: data `ensemble`
`kramers_moyal`	`series`	any	any	any	none
`large_deviations`	`path`	any	any	any	`block`: data `series` `histogram`: data `ensemble` `reweight`: data `ensemble`
`linearization`	`system`	any	any	any	none
`local_information`	`series`	any	any	any	none
`loops`	`system`	any	any	any	none
`lyapunov`	`system`	any	any	`deterministic`	`largest`: data `series`
`markov`	`path`	any	any	any	none
`mode_decomposition`	`series`	any	any	any	none
`motifs`	`network`	any	`network`	any	none
`neighbors`	`agents`	any	any	any	`like-share`: data `field`
`network_measures`	`network`	any	`network`	any	none
`operator_measures`	`system`	any	any	any	none
`partial_information`	`series`	any	any	any	none
`passage`	`path`	any	any	any	`return-times`: data `series`
`recurrence`	`series`	any	any	any	none
`renormalization`	`network`	any	`network`	any	none
`reservoir`	`series`	any	any	any	none
`rolling`	`series`	any	any	any	none
`scaling`	`series`	any	any	any	`box-counting`: data `field` `power`: data `ensemble` `variance-mean`: data `field`
`section`	`system`	`continuous`	any	any	none
`signatures`	`system`	any	any	any	none
`sparse_identification`	`series`	any	any	any	none
`spectrum`	`field`	any	any	any	`power`: data `series`
`stability`	`system`	any	any	any	none
`surrogate_test`	`series`	any	any	any	none
`symbolic`	`system`	any	any	any	none

A compatible analysis

The logistic map at r=4 is deterministic, so lyapunov measures its largest exponent, close to log 2.

from skcomplex.core.analysis import lyapunov
from skcomplex.systems.mathematics.dynamical_systems import LogisticMapSystem

system = LogisticMapSystem(r=4.0)
system.get_tags().randomness
round(float(lyapunov(system, until=20000).exponents[0]), 2)

deterministic
0.69

An incompatible analysis

The stochastic SIR epidemic has random events, so nearby runs do not separate at a rate of their own. lyapunov rejects it and names the randomness it needs.

from skcomplex.core.analysis import lyapunov
from skcomplex.core.errors import TagError
from skcomplex.systems.biology.epidemiology import SIRSystem

system = SIRSystem(stochastic=True)
system.get_tags().randomness
try:
    lyapunov(system)
except TagError as error:
    message = str(error)
message
assert 'randomness deterministic' in message

stochastic
lyapunov of kind 'spectrum' needs the randomness deterministic, but the system has the randomness stochastic.

A network measure needs a system on a network. A trajectory of the SIR epidemic carries the tags of its system, whose space is none.

from skcomplex.core.analysis import network_measures
from skcomplex.core.engine.runtime import simulate
from skcomplex.core.errors import TagError
from skcomplex.systems.biology.epidemiology import SIRSystem

trajectory = simulate(SIRSystem(), until=10)
try:
    network_measures(trajectory)
except TagError as error:
    message = str(error)
message
assert 'space network' in message

network_measures of kind 'summary' needs the space network, but the system has the space none.