pyFTS.common package

Module contents

Submodules

pyFTS.common.Composite module

Composite Fuzzy Sets

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

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
transform(x)

Preprocess the data point for non native types

Parameters:x –
Returns:return a native type value for the structured type

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.

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

Bases: pyFTS.common.FLR.FLR

Season Indexed Fuzzy Logical Relationship

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

membership(x)

Calculate the membership value of a given input

Parameters:x – input value
Returns:membership value of x at this fuzzy set
partition_function(uod=None, nbins=100)

Calculate the partition function over the membership function.

Parameters:
  • uod –
  • nbins –
Returns:
transform(x)

Preprocess the data point for non native types

Parameters:x –
Returns:return a native type value for the structured type
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, both: return a list with tuples (fuzzy set, membership value) ) :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)

:return

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.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_compared_intervals_ahead(original, models, colors, distributions, time_from, time_to, intervals=True, save=False, file=None, tam=[20, 5], resolution=None, cmap='Blues', linewidth=1.5)

Plot the forecasts of several one step ahead models, by point or by interval

Parameters:
  • original – Original time series data (list)
  • models – List of models to compare
  • colors – List of models colors
  • distributions – True to plot a distribution
  • time_from – index of data poit to start the ahead forecasting
  • time_to – number of steps ahead to forecast
  • interpol – Fill space between distribution plots
  • save – Save the picture on file
  • file – Filename to save the picture
  • tam – Size of the picture
  • resolution –
  • cmap – Color map to be used on distribution plot
  • option – Distribution type to be passed for models
Returns:
pyFTS.common.Util.plot_density_rectange(ax, cmap, density, fig, resolution, time_from, time_to)

Auxiliar function to plot_compared_intervals_ahead

pyFTS.common.Util.plot_distribution(ax, cmap, probabilitydist, fig, time_from, reference_data=None)

Plot forecasted ProbabilityDistribution objects on a matplotlib axis

Parameters:
  • ax – matplotlib axis
  • cmap – matplotlib colormap name
  • probabilitydist – list of ProbabilityDistribution objects
  • fig – matplotlib figure
  • time_from – starting time (on x axis) to begin the plots
  • reference_data –
Returns:
pyFTS.common.Util.plot_distribution2(probabilitydist, data, **kwargs)

Plot distributions over the time (x-axis)

Parameters:
  • probabilitydist – the forecasted probability distributions to plot
  • data – the original test sample
  • start_at – the time index (inside of data) to start to plot the probability distributions
  • ax – a matplotlib axis. If no value was provided a new axis is created.
  • cmap – a matplotlib colormap name, the default value is ‘Blues’
  • quantiles – the list of quantiles intervals to plot, e. g. [.05, .25, .75, .95]
  • median – a boolean value indicating if the median value will be plot.
pyFTS.common.Util.plot_interval(axis, intervals, order, label, color='red', typeonlegend=False, ls='-', linewidth=1)

Plot forecasted intervals on matplotlib

Parameters:
  • axis – matplotlib axis
  • intervals – list of forecasted intervals
  • order – order of the model that create the forecasts
  • label – figure label
  • color – matplotlib color name
  • typeonlegend –
  • ls – matplotlib line style
  • linewidth – matplotlib width
Returns:
pyFTS.common.Util.plot_interval2(intervals, data, **kwargs)

Plot forecasted intervals on matplotlib

Parameters:
  • intervals – list of forecasted intervals
  • data – the original test sample
  • start_at – the time index (inside of data) to start to plot the intervals
  • label – figure label
  • color – matplotlib color name
  • typeonlegend –
  • ls – matplotlib line style
  • linewidth – matplotlib width
pyFTS.common.Util.plot_probability_distributions(pmfs, lcolors, tam=[15, 7])
pyFTS.common.Util.plot_rules(model, size=[5, 5], axis=None, rules_by_axis=None, columns=1)

Plot the FLRG rules of a FTS model on a matplotlib axis

Parameters:
  • model – FTS model
  • size – figure size
  • axis – matplotlib axis
  • rules_by_axis – number of rules plotted by column
  • columns – number of columns
Returns:
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.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.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.

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
reset_calculated_values()

pyFTS.common.fts module

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

Bases: object

Fuzzy Time Series object model

append_log(operation, value)
append_rule(flrg)

Append FLRG rule to the model

Parameters:flrg – rule
Returns:
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
clip_uod(ndata)
clone_parameters(model)

Import the parameters values from other model

Parameters:model –
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
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 (default: 1)
  • start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)
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
  • start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)
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
  • start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)
Returns:

a list with the forecasted intervals
forecast_ahead_multivariate(data, steps, **kwargs)

Multivariate forecast n step ahead

Parameters:
  • data – Pandas dataframe with one column for each variable and with the minimal length equal to the max_lag of the model
  • steps – the number of steps ahead to forecast
  • start_at – in the multi step forecasting, the index of the data where to start forecasting (default: 0)
Returns:

a Pandas Dataframe object representing the forecasted values for each variable
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
forecast_multivariate(data, **kwargs)

Multivariate forecast one step ahead

Parameters:
  • data – Pandas dataframe with one column for each variable and with the minimal length equal to the max_lag of the model
  • kwargs – model specific parameters
Returns:

a Pandas Dataframe object representing the forecasted values for each variable
fuzzy(data)

Fuzzify a data point

Parameters:data – data point
Returns:maximum membership fuzzy set
get_UoD()
len_total()

Total length of the model, adding the number of terms in all rules

Returns:
merge(model)

Merge the FLRG rules from other model

Parameters:model – source model
Returns:
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, distribution or multivariate.
  • steps_ahead – The forecasting horizon, i. e., the number of steps ahead to forecast (default value: 1)
  • start_at – in the multi step forecasting, the index of the data where to start forecasting (default value: 0)
  • distributed – boolean, indicate if the forecasting procedure will be distributed in a dispy cluster (default value: False)
  • 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. (default value: False)
  • generators – for multivariate methods on multi step ahead forecasting, generators is a dict where the keys are the dataframe columun names (except the target_variable) and the values are lambda functions that accept one value (the actual value of the variable) and return the next value or trained FTS models that accept the actual values and forecast new ones.
Returns:

a numpy array with the forecasted data
reset_calculated_values()

Reset all pre-calculated values on the FLRG’s

Returns:
train(data, **kwargs)

Method specific parameter fitting

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

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)