pyFTS.common package

Module contents

Submodules

pyFTS.common.Composite module

Composite Fuzzy Sets

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

Bases: pyFTS.common.FuzzySet.FuzzySet

Composite Fuzzy Set

append(mf, parameters)[source]

Adds a new function to composition

Parameters:
  • mf
  • parameters
Returns:

append_set(set)[source]

Adds a new function to composition

Parameters:
  • mf
  • parameters
Returns:

membership(x)[source]

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)[source]

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)[source]

Bases: pyFTS.common.FLR.FLR

Season Indexed Fuzzy Logical Relationship

index = None

seasonal index

pyFTS.common.FLR.generate_high_order_recurrent_flr(fuzzyData)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]
pyFTS.common.FuzzySet.check_bounds_index(data, fuzzy_sets, ordered_sets)[source]
pyFTS.common.FuzzySet.fuzzyfy(data, partitioner, **kwargs)[source]

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)[source]

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)[source]

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)[source]
pyFTS.common.FuzzySet.fuzzyfy_series_old(data, fuzzy_sets, method='maximum')[source]
pyFTS.common.FuzzySet.get_fuzzysets(inst, fuzzy_sets, ordered_sets=None, alpha_cut=0.0)[source]

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)[source]

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)[source]

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)[source]
pyFTS.common.FuzzySet.set_ordered(fuzzy_sets)[source]

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)[source]

Bell shaped membership function

Parameters:
  • x
  • parameters
Returns:

pyFTS.common.Membership.gaussmf(x, parameters)[source]

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)[source]

Sigmoid / Logistic membership function

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

pyFTS.common.Membership.singleton(x, parameters)[source]

Singleton membership function, a single value fuzzy function

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

:returns

pyFTS.common.Membership.trapmf(x, parameters)[source]

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)[source]

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)[source]

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)[source]
between(ge, le)[source]
clear()[source]
copy()[source]
count(item)[source]

Return number of occurrences of item

find(k)[source]

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

find_ge(k)[source]

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

find_gt(k)[source]

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

find_le(k)[source]

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

find_lt(k)[source]

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

index(item)[source]

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

insert(item)[source]

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

insert_right(item)[source]

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

inside(ge, le)[source]
key

key function

remove(item)[source]

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)[source]

Bases: pyFTS.common.Transformations.Transformation

Adaptive Expectation post processing

apply(data, param=None, **kwargs)[source]

Apply the transformation on input data

Parameters:
  • data – input data
  • param
  • kwargs
Returns:

numpy array with transformed data

inverse(data, param, **kwargs)[source]
Parameters:
  • data – transformed data
  • param
  • kwargs
Returns:

numpy array with inverse transformed data

parameters
class pyFTS.common.Transformations.BoxCox(plambda)[source]

Bases: pyFTS.common.Transformations.Transformation

Box-Cox power transformation

apply(data, param=None, **kwargs)[source]

Apply the transformation on input data

Parameters:
  • data – input data
  • param
  • kwargs
Returns:

numpy array with transformed data

inverse(data, param=None, **kwargs)[source]
Parameters:
  • data – transformed data
  • param
  • kwargs
Returns:

numpy array with inverse transformed data

parameters
class pyFTS.common.Transformations.Differential(lag)[source]

Bases: pyFTS.common.Transformations.Transformation

Differentiation data transform

apply(data, param=None, **kwargs)[source]

Apply the transformation on input data

Parameters:
  • data – input data
  • param
  • kwargs
Returns:

numpy array with transformed data

inverse(data, param, **kwargs)[source]
Parameters:
  • data – transformed data
  • param
  • kwargs
Returns:

numpy array with inverse transformed data

parameters
class pyFTS.common.Transformations.Scale(min=0, max=1)[source]

Bases: pyFTS.common.Transformations.Transformation

Scale data inside a interval [min, max]

apply(data, param=None, **kwargs)[source]

Apply the transformation on input data

Parameters:
  • data – input data
  • param
  • kwargs
Returns:

numpy array with transformed data

inverse(data, param, **kwargs)[source]
Parameters:
  • data – transformed data
  • param
  • kwargs
Returns:

numpy array with inverse transformed data

parameters
class pyFTS.common.Transformations.Transformation(**kwargs)[source]

Bases: object

Data transformation used on pre and post processing of the FTS

apply(data, param, **kwargs)[source]

Apply the transformation on input data

Parameters:
  • data – input data
  • param
  • kwargs
Returns:

numpy array with transformed data

inverse(data, param, **kwargs)[source]
Parameters:
  • data – transformed data
  • param
  • kwargs
Returns:

numpy array with inverse transformed data

pyFTS.common.Transformations.Z(original)[source]
pyFTS.common.Transformations.aggregate(original, operation)[source]
pyFTS.common.Transformations.roi(original)[source]
pyFTS.common.Transformations.smoothing(original, lags)[source]

pyFTS.common.Util module

pyFTS.common.flrg module

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

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)[source]
get_key()[source]

Returns a unique identifier for this FLRG

get_lower(sets)[source]

Returns the lower bound value for the RHS fuzzy sets

Parameters:sets – fuzzy sets
Returns:lower bound value
get_membership(data, sets)[source]

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)[source]

Returns the midpoint value for the RHS fuzzy sets

Parameters:sets – fuzzy sets
Returns:the midpoint value
get_midpoints(sets)[source]
get_upper(sets)[source]

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

pyFTS.common.tree module

Tree data structure

class pyFTS.common.tree.FLRGTree[source]

Bases: object

Represents a FLRG set with a tree structure

class pyFTS.common.tree.FLRGTreeNode(value)[source]

Bases: object

Tree node for

appendChild(child)[source]
getChildren()[source]
getStr(k)[source]
paths(acc=[])[source]
pyFTS.common.tree.build_tree_without_order(node, lags, level)[source]
pyFTS.common.tree.flat(dados)[source]