pyFTS.common package

Module contents

Submodules

pyFTS.common.Composite module

Composite Fuzzy Sets

class pyFTS.common.Composite.FuzzySet(name, superset=False)

Bases: pyFTS.common.FuzzySet.FuzzySet

Composite Fuzzy Set

append(mf, parameters)

Adds a new function to composition

Parameters:

• mf –
• parameters –

Returns:

append_set(set)

Adds a new function to composition

Parameters:

• mf –
• parameters –

Returns:

membership(x)

Calculate the membership value of a given input

Parameters:x – input value Returns:membership value of x at this fuzzy set

pyFTS.common.FLR module

This module implements functions for Fuzzy Logical Relationship generation

class pyFTS.common.FLR.FLR(LHS, RHS)

Bases: object

Fuzzy Logical Relationship

Represents a temporal transition of the fuzzy set LHS on time t for the fuzzy set RHS on time t+1.

LHS = None

Left Hand Side fuzzy set

RHS = None

Right Hand Side fuzzy set

class pyFTS.common.FLR.IndexedFLR(index, LHS, RHS)

Bases: pyFTS.common.FLR.FLR

Season Indexed Fuzzy Logical Relationship

index = None

seasonal index

pyFTS.common.FLR.generate_high_order_recurrent_flr(fuzzyData)

Create a ordered FLR set from a list of fuzzy sets with recurrence

Parameters:fuzzyData – ordered list of fuzzy sets Returns:ordered list of FLR

pyFTS.common.FLR.generate_indexed_flrs(sets, indexer, data, transformation=None, alpha_cut=0.0)

Create a season-indexed ordered FLR set from a list of fuzzy sets with recurrence

Parameters:

• sets – fuzzy sets
• indexer – seasonality indexer
• data – original data

Returns:

ordered list of FLR

pyFTS.common.FLR.generate_non_recurrent_flrs(fuzzyData)

Create a ordered FLR set from a list of fuzzy sets without recurrence

Parameters:fuzzyData – ordered list of fuzzy sets Returns:ordered list of FLR

pyFTS.common.FLR.generate_recurrent_flrs(fuzzyData)

Create a ordered FLR set from a list of fuzzy sets with recurrence

Parameters:fuzzyData – ordered list of fuzzy sets Returns:ordered list of FLR

pyFTS.common.FuzzySet module

class pyFTS.common.FuzzySet.FuzzySet(name, mf, parameters, centroid, alpha=1.0, **kwargs)

Bases: object

Fuzzy Set

Z = None

Partition function in respect to the membership function

alpha = None

The alpha cut value

centroid = None

The fuzzy set center of mass (or midpoint)

membership(x)

Calculate the membership value of a given input

Parameters:x – input value Returns:membership value of x at this fuzzy set

mf = None

The membership function

name = None

The fuzzy set name

parameters = None

The parameters of the membership function

partition_function(uod=None, nbins=100)

Calculate the partition function over the membership function.

Parameters:

• uod –
• nbins –

Returns:

type = None

The fuzzy set type (common, composite, nonstationary, etc)

variable = None

In multivariate time series, indicate for which variable this fuzzy set belogs

pyFTS.common.FuzzySet.check_bounds(data, fuzzy_sets, ordered_sets)

pyFTS.common.FuzzySet.check_bounds_index(data, fuzzy_sets, ordered_sets)

pyFTS.common.FuzzySet.fuzzyfy(data, partitioner, **kwargs)

A general method for fuzzyfication.

Parameters:

• data – input value to be fuzzyfied
• partitioner – a trained pyFTS.partitioners.Partitioner object
• kwargs – dict, optional arguments
• alpha_cut – the minimal membership value to be considered on fuzzyfication (only for mode=’sets’)
• method – the fuzzyfication method (fuzzy: all fuzzy memberships, maximum: only the maximum membership)
• mode – the fuzzyfication mode (sets: return the fuzzy sets names, vector: return a vector with the membership values for all fuzzy sets)

:returns a list with the fuzzyfied values, depending on the mode

pyFTS.common.FuzzySet.fuzzyfy_instance(inst, fuzzy_sets, ordered_sets=None)

Calculate the membership values for a data point given fuzzy sets

Parameters:

• inst – data point
• fuzzy_sets – a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
• ordered_sets – a list with the fuzzy sets names ordered by their centroids.

Returns:

array of membership values

pyFTS.common.FuzzySet.fuzzyfy_instances(data, fuzzy_sets, ordered_sets=None)

Calculate the membership values for a data point given fuzzy sets

Parameters:

• inst – data point
• fuzzy_sets – a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
• ordered_sets – a list with the fuzzy sets names ordered by their centroids.

Returns:

array of membership values

pyFTS.common.FuzzySet.fuzzyfy_series(data, fuzzy_sets, method='maximum', alpha_cut=0.0, ordered_sets=None)

pyFTS.common.FuzzySet.fuzzyfy_series_old(data, fuzzy_sets, method='maximum')

pyFTS.common.FuzzySet.get_fuzzysets(inst, fuzzy_sets, ordered_sets=None, alpha_cut=0.0)

Return the fuzzy sets which membership value for a inst is greater than the alpha_cut

Parameters:

• inst – data point
• fuzzy_sets – a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
• ordered_sets – a list with the fuzzy sets names ordered by their centroids.
• alpha_cut – Minimal membership to be considered on fuzzyfication process

Returns:

array of membership values

pyFTS.common.FuzzySet.get_maximum_membership_fuzzyset(inst, fuzzy_sets, ordered_sets=None)

Fuzzify a data point, returning the fuzzy set with maximum membership value

Parameters:

• inst – data point
• fuzzy_sets – a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
• ordered_sets – a list with the fuzzy sets names ordered by their centroids.

Returns:

fuzzy set with maximum membership

pyFTS.common.FuzzySet.get_maximum_membership_fuzzyset_index(inst, fuzzy_sets)

Fuzzify a data point, returning the fuzzy set with maximum membership value

Parameters:

• inst – data point
• fuzzy_sets – dict of fuzzy sets

Returns:

fuzzy set with maximum membership

pyFTS.common.FuzzySet.grant_bounds(data, fuzzy_sets, ordered_sets)

pyFTS.common.FuzzySet.set_ordered(fuzzy_sets)

Order a fuzzy set list by their centroids

Parameters:fuzzy_sets – a dictionary where the key is the fuzzy set name and the value is the fuzzy set object. Returns:a list with the fuzzy sets names ordered by their centroids.

pyFTS.common.Membership module

Membership functions for Fuzzy Sets

pyFTS.common.Membership.bellmf(x, parameters)

Bell shaped membership function

Parameters:

• x –
• parameters –

Returns:

pyFTS.common.Membership.gaussmf(x, parameters)

Gaussian fuzzy membership function

Parameters:

• x – data point
• parameters – a list with 2 real values (mean and variance)

Returns:

the membership value of x given the parameters

pyFTS.common.Membership.sigmf(x, parameters)

Sigmoid / Logistic membership function

Parameters:

• x –
• parameters – an list with 2 real values (smoothness and midpoint)

Returns:

pyFTS.common.Membership.singleton(x, parameters)

Singleton membership function, a single value fuzzy function

Parameters:

• x –
• parameters – a list with one real value

:returns

pyFTS.common.Membership.trapmf(x, parameters)

Trapezoidal fuzzy membership function

Parameters:

• x – data point
• parameters – a list with 4 real values

Returns:

the membership value of x given the parameters

pyFTS.common.Membership.trimf(x, parameters)

Triangular fuzzy membership function

Parameters:

• x – data point
• parameters – a list with 3 real values

Returns:

the membership value of x given the parameters

pyFTS.common.SortedCollection module

class pyFTS.common.SortedCollection.SortedCollection(iterable=(), key=None)

Bases: object

Sequence sorted by a key function.

SortedCollection() is much easier to work with than using bisect() directly. It supports key functions like those use in sorted(), min(), and max(). The result of the key function call is saved so that keys can be searched efficiently.

Instead of returning an insertion-point which can be hard to interpret, the five find-methods return a specific item in the sequence. They can scan for exact matches, the last item less-than-or-equal to a key, or the first item greater-than-or-equal to a key.

Once found, an item’s ordinal position can be located with the index() method. New items can be added with the insert() and insert_right() methods. Old items can be deleted with the remove() method.

The usual sequence methods are provided to support indexing, slicing, length lookup, clearing, copying, forward and reverse iteration, contains checking, item counts, item removal, and a nice looking repr.

Finding and indexing are O(log n) operations while iteration and insertion are O(n). The initial sort is O(n log n).

The key function is stored in the ‘key’ attibute for easy introspection or so that you can assign a new key function (triggering an automatic re-sort).

In short, the class was designed to handle all of the common use cases for bisect but with a simpler API and support for key functions.

>>> from pprint import pprint
>>> from operator import itemgetter

>>> s = SortedCollection(key=itemgetter(2))
>>> for record in [
...         ('roger', 'young', 30),
...         ('angela', 'jones', 28),
...         ('bill', 'smith', 22),
...         ('david', 'thomas', 32)]:
...     s.insert(record)

>>> pprint(list(s))         # show records sorted by age
[('bill', 'smith', 22),
 ('angela', 'jones', 28),
 ('roger', 'young', 30),
 ('david', 'thomas', 32)]

>>> s.find_le(29)           # find oldest person aged 29 or younger
('angela', 'jones', 28)
>>> s.find_lt(28)           # find oldest person under 28
('bill', 'smith', 22)
>>> s.find_gt(28)           # find youngest person over 28
('roger', 'young', 30)

>>> r = s.find_ge(32)       # find youngest person aged 32 or older
>>> s.index(r)              # get the index of their record
3
>>> s[3]                    # fetch the record at that index
('david', 'thomas', 32)

>>> s.key = itemgetter(0)   # now sort by first name
>>> pprint(list(s))
[('angela', 'jones', 28),
 ('bill', 'smith', 22),
 ('david', 'thomas', 32),
 ('roger', 'young', 30)]

around(k)

between(ge, le)

clear()

copy()

count(item)

Return number of occurrences of item

find(k)

Return first item with a key == k. Raise ValueError if not found.

find_ge(k)

Return first item with a key >= equal to k. Raise ValueError if not found

find_gt(k)

Return first item with a key > k. Raise ValueError if not found

find_le(k)

Return last item with a key <= k. Raise ValueError if not found.

find_lt(k)

Return last item with a key < k. Raise ValueError if not found.

index(item)

Find the position of an item. Raise ValueError if not found.

insert(item)

Insert a new item. If equal keys are found, add to the left

insert_right(item)

Insert a new item. If equal keys are found, add to the right

inside(ge, le)

key

key function

remove(item)

Remove first occurence of item. Raise ValueError if not found

pyFTS.common.Transformations module

Common data transformation used on pre and post processing of the FTS

class pyFTS.common.Transformations.AdaptiveExpectation(parameters)

Bases: pyFTS.common.Transformations.Transformation

Adaptive Expectation post processing

apply(data, param=None, **kwargs)

Apply the transformation on input data

Parameters:

• data – input data
• param –
• kwargs –

Returns:

numpy array with transformed data

inverse(data, param, **kwargs)

Parameters:

• data – transformed data
• param –
• kwargs –

Returns:

numpy array with inverse transformed data

parameters

class pyFTS.common.Transformations.BoxCox(plambda)

Bases: pyFTS.common.Transformations.Transformation

Box-Cox power transformation

apply(data, param=None, **kwargs)

Apply the transformation on input data

Parameters:

• data – input data
• param –
• kwargs –

Returns:

numpy array with transformed data

inverse(data, param=None, **kwargs)

Parameters:

• data – transformed data
• param –
• kwargs –

Returns:

numpy array with inverse transformed data

parameters

class pyFTS.common.Transformations.Differential(lag)

Bases: pyFTS.common.Transformations.Transformation

Differentiation data transform

apply(data, param=None, **kwargs)

Apply the transformation on input data

Parameters:

• data – input data
• param –
• kwargs –

Returns:

numpy array with transformed data

inverse(data, param, **kwargs)

Parameters:

• data – transformed data
• param –
• kwargs –

Returns:

numpy array with inverse transformed data

parameters

class pyFTS.common.Transformations.Scale(min=0, max=1)

Bases: pyFTS.common.Transformations.Transformation

Scale data inside a interval [min, max]

apply(data, param=None, **kwargs)

Apply the transformation on input data

Parameters:

• data – input data
• param –
• kwargs –

Returns:

numpy array with transformed data

inverse(data, param, **kwargs)

Parameters:

• data – transformed data
• param –
• kwargs –

Returns:

numpy array with inverse transformed data

parameters

class pyFTS.common.Transformations.Transformation(**kwargs)

Bases: object

Data transformation used on pre and post processing of the FTS

apply(data, param, **kwargs)

Apply the transformation on input data

Parameters:

• data – input data
• param –
• kwargs –

Returns:

numpy array with transformed data

inverse(data, param, **kwargs)

Parameters:

• data – transformed data
• param –
• kwargs –

Returns:

numpy array with inverse transformed data

pyFTS.common.Transformations.Z(original)

pyFTS.common.Transformations.aggregate(original, operation)

pyFTS.common.Transformations.roi(original)

pyFTS.common.Transformations.smoothing(original, lags)

pyFTS.common.Util module

Common facilities for pyFTS

pyFTS.common.Util.current_milli_time()

pyFTS.common.Util.distributed_predict(model, parameters, nodes, data, num_batches)

pyFTS.common.Util.distributed_train(model, train_method, nodes, fts_method, data, num_batches=10, train_parameters={}, **kwargs)

pyFTS.common.Util.draw_sets_on_axis(axis, model, size)

pyFTS.common.Util.enumerate2(xs, start=0, step=1)

pyFTS.common.Util.load_env(file)

pyFTS.common.Util.load_obj(file)

Load to memory an object stored filesystem. This function depends on Dill package

Parameters:file – file name where the object is stored Returns:object

pyFTS.common.Util.persist_env(file)

Persist an entire environment on file. This function depends on Dill package

Parameters:file – file name to store the environment

pyFTS.common.Util.persist_obj(obj, file)

Persist an object on filesystem. This function depends on Dill package

Parameters:

• obj – object on memory
• file – file name to store the object

pyFTS.common.Util.plot_rules(model, size=[5, 5], axis=None, rules_by_axis=None, columns=1)

pyFTS.common.Util.show_and_save_image(fig, file, flag, lgd=None)

Show and image and save on file

Parameters:

• fig – Matplotlib Figure object
• file – filename to save the picture
• flag – if True the image will be saved
• lgd – legend

pyFTS.common.Util.simple_model_predict(model, data, parameters)

pyFTS.common.Util.simple_model_train(model, data, parameters)

pyFTS.common.Util.sliding_window(data, windowsize, train=0.8, inc=0.1, **kwargs)

Sliding window method of cross validation for time series

Parameters:

• data – the entire dataset
• windowsize – window size
• train – percentual of the window size will be used for training the models
• inc – percentual of data used for slide the window

Returns:

window count, training set, test set

pyFTS.common.Util.start_dispy_cluster(method, nodes)

pyFTS.common.Util.stop_dispy_cluster(cluster, http_server)

pyFTS.common.Util.uniquefilename(name)

pyFTS.common.flrg module

class pyFTS.common.flrg.FLRG(order, **kwargs)

Bases: object

Fuzzy Logical Relationship Group

Group a set of FLR’s with the same LHS. Represents the temporal patterns for time t+1 (the RHS fuzzy sets) when the LHS pattern is identified on time t.

LHS = None

Left Hand Side of the rule

RHS = None

Right Hand Side of the rule

append_rhs(set, **kwargs)

get_key()

Returns a unique identifier for this FLRG

get_lower(sets)

Returns the lower bound value for the RHS fuzzy sets

Parameters:sets – fuzzy sets Returns:lower bound value

get_membership(data, sets)

Returns the membership value of the FLRG for the input data

Parameters:

• data – input data
• sets – fuzzy sets

Returns:

the membership value

get_midpoint(sets)

Returns the midpoint value for the RHS fuzzy sets

Parameters:sets – fuzzy sets Returns:the midpoint value

get_midpoints(sets)

get_upper(sets)

Returns the upper bound value for the RHS fuzzy sets

Parameters:sets – fuzzy sets Returns:upper bound value

order = None

Number of lags on LHS

pyFTS.common.fts module

class pyFTS.common.fts.FTS(**kwargs)

Bases: object

Fuzzy Time Series object model

alpha_cut = None

A float with the minimal membership to be considered on fuzzyfication process

append_transformation(transformation)

apply_inverse_transformations(data, params=None, **kwargs)

Apply the data transformations for data postprocessing

Parameters:

• data – input data
• params – transformation parameters
• updateUoD –
• kwargs –

Returns:

postprocessed data

apply_transformations(data, params=None, updateUoD=False, **kwargs)

Apply the data transformations for data preprocessing

Parameters:

• data – input data
• params – transformation parameters
• updateUoD –
• kwargs –

Returns:

preprocessed data

auto_update = None

A boolean value indicating that model is incremental

benchmark_only = None

A boolean value indicating a façade for external (non-FTS) model used on benchmarks or ensembles.

clone_parameters(model)

Import the parameters values from other model

Parameters:model –

detail = None

A string with the model detailed information

fit(ndata, **kwargs)

Fit the model’s parameters based on the training data.

Parameters:

• ndata – training time series data
• kwargs –
• num_batches – split the training data in num_batches to save memory during the training process
• save_model – save final model on disk
• batch_save – save the model between each batch
• file_path – path to save the model
• distributed – boolean, indicate if the training procedure will be distributed in a dispy cluster
• nodes – a list with the dispy cluster nodes addresses

flrgs = None

The list of Fuzzy Logical Relationship Groups - FLRG

forecast(data, **kwargs)

Point forecast one step ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• kwargs – model specific parameters

Returns:

a list with the forecasted values

forecast_ahead(data, steps, **kwargs)

Point forecast n steps ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• steps – the number of steps ahead to forecast
• kwargs – model specific parameters

Returns:

a list with the forecasted values

forecast_ahead_distribution(data, steps, **kwargs)

Probabilistic forecast n steps ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• steps – the number of steps ahead to forecast
• kwargs – model specific parameters

Returns:

a list with the forecasted Probability Distributions

forecast_ahead_interval(data, steps, **kwargs)

Interval forecast n steps ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• steps – the number of steps ahead to forecast
• kwargs – model specific parameters

Returns:

a list with the forecasted intervals

forecast_distribution(data, **kwargs)

Probabilistic forecast one step ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• kwargs – model specific parameters

Returns:

a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions

forecast_interval(data, **kwargs)

Interval forecast one step ahead

Parameters:

• data – time series data with the minimal length equal to the max_lag of the model
• kwargs – model specific parameters

Returns:

a list with the prediction intervals

fuzzy(data)

Fuzzify a data point

Parameters:data – data point Returns:maximum membership fuzzy set

get_UoD()

has_interval_forecasting = None

A boolean value indicating if the model supports interval forecasting, default: False

has_point_forecasting = None

A boolean value indicating if the model supports point forecasting, default: True

has_probability_forecasting = None

A boolean value indicating if the model support probabilistic forecasting, default: False

has_seasonality = None

A boolean value indicating if the model supports seasonal indexers, default: False

indexer = None

An pyFTS.models.seasonal.Indexer object for indexing the time series data

is_high_order = None

A boolean value indicating if the model support orders greater than 1, default: False

is_multivariate = None

A boolean value indicating if the model support multivariate time series (Pandas DataFrame), default: False

len_total()

max_lag = None

A integer indicating the largest lag used by the model. This value also indicates the minimum number of past lags needed to forecast a single step ahead

merge(model)

Merge the FLRG rules from other model

Parameters:model – source model Returns:

min_order = None

In high order models, this integer value indicates the minimal order supported for the model, default: 1

name = None

A string with the model name

order = None

A integer with the model order (number of past lags are used on forecasting)

original_max = None

A float with the upper limit of the Universe of Discourse, the maximal value found on training data

original_min = None

A float with the lower limit of the Universe of Discourse, the minimal value found on training data

partitioner = None

A pyFTS.partitioners.Partitioner object with the Universe of Discourse partitioner used on the model. This is a mandatory dependecy.

predict(data, **kwargs)

Forecast using trained model

Parameters:

• data – time series with minimal length to the order of the model
• type – the forecasting type, one of these values: point(default), interval or distribution.
• steps_ahead – The forecasting horizon, i. e., the number of steps ahead to forecast
• start – in the multi step forecasting, the index of the data where to start forecasting
• distributed – boolean, indicate if the forecasting procedure will be distributed in a dispy cluster
• nodes – a list with the dispy cluster nodes addresses
• explain – try to explain, step by step, the one-step-ahead point forecasting result given the input data.

Returns:

a numpy array with the forecasted data

sets = None

The list of fuzzy sets used on this model

shortname = None

A string with a short name or alias for the model

train(data, **kwargs)

Method specific parameter fitting

Parameters:

• data – training time series data
• kwargs – Method specific parameters

transformations = None

A list with the data transformations (common.Transformations) applied on model pre and post processing, default: []

transformations_param = None

A list with the specific parameters for each data transformation

uod_clip = None

Flag indicating if the test data will be clipped inside the training Universe of Discourse

pyFTS.common.tree module

Tree data structure

class pyFTS.common.tree.FLRGTree

Bases: object

Represents a FLRG set with a tree structure

class pyFTS.common.tree.FLRGTreeNode(value)

Bases: object

Tree node for

appendChild(child)

getChildren()

getStr(k)

paths(acc=[])

pyFTS.common.tree.build_tree_without_order(node, lags, level)

pyFTS.common.tree.flat(dados)