Metadata-Version: 1.1
Name: PyRQA
Version: 8.1.0
Summary: Recurrence analysis in a massively parallel manner using the OpenCL framework.
Home-page: UNKNOWN
Author: Tobias Rawald
Author-email: pyrqa@gmx.net
License: Apache License 2.0
Description: PyRQA
        =====
        
        Highlights
        ----------
        
        -  Perform recurrence analysis on long time series in a time efficient
           manner using the OpenCL framework.
        -  Conduct recurrence quantification analysis (*RQA*) and cross
           recurrence quantification analysis (*CRQA*).
        -  Compute recurrence plots (*RP*) and cross recurrence plots (*CRP*).
        -  Compute unthresholded recurrence plots (*URP*) and unthresholded
           cross recurrence plots (*UCRP*).
        -  Conduct joint recurrence quantification analysis (*JRQA*) and compute
           joint recurrence plots (*JRP*).
        -  Employ the euclidean, maximum or taxicab metric for determining state
           similarity.
        -  Choose the fixed radius or radius corridor neighbourhood condition.
        -  Use univariate time series or pre-embedded time series as input data.
        -  Select either the half, single or double floating point precision for
           conducting the analytical computations.
        -  Leverage machine learning techniques that automatically choose the
           fastest from a set of implementations.
        -  Apply the computing capabilities of GPUs, CPUs and other platforms
           that support OpenCL.
        -  Use multiple computing devices of the same or different type in
           parallel.
        
        Table of Contents
        -----------------
        
        1.  `General Information <#general-information>`__
        2.  `Recommended Citation <#recommended-citation>`__
        3.  `Installation <#installation>`__
        4.  `OpenCL Setup <#opencl-setup>`__
        5.  `Usage <#usage>`__
        6.  `Performance Tuning <#performance-tuning>`__
        7.  `Testing <#testing>`__
        8.  `Origin <#origin>`__
        9.  `Acknowledgements <#acknowledgements>`__
        10. `Publications <#publications>`__
        11. `Development Status <#development-status>`__
        12. `Release Notes <#release-notes>`__
        
        General Information
        -------------------
        
        PyRQA is a tool to conduct recurrence analysis in a massively parallel
        manner using the OpenCL framework. It is designed to efficiently process
        time series consisting of hundreds of thousands of data points.
        
        PyRQA supports the computation of the following quantitative measures:
        
        -  Recurrence rate (*RR*)
        -  Determinism (*DET*)
        -  Average diagonal line length (*L*)
        -  Longest diagonal line length (*L_max*)
        -  Divergence (*DIV*)
        -  Entropy diagonal lines (*L_entr*)
        -  Laminarity (*LAM*)
        -  Trapping time (*TT*)
        -  Longest vertical line length (*V_max*)
        -  Entropy vertical lines (*V_entr*)
        -  Average white vertical line length (*W*)
        -  Longest white vertical line length (*W_max*)
        -  Longest white vertical line length divergence (*W_div*)
        -  Entropy white vertical lines (*W_entr*)
        
        PyRQA additionally allows to create the corresponding recurrence plot,
        which can be exported as an image file.
        
        Recommended Citation
        --------------------
        
        Please acknowledge the use of PyRQA by citing the following publication.
        
           Rawald, T., Sips, M., Marwan, N. (2017): PyRQA - Conducting
           Recurrence Quantification Analysis on Very Long Time Series
           Efficiently. - Computers and Geosciences, 104, pp. 101-108.
        
        Installation
        ------------
        
        PyRQA and all of its dependencies can be installed via the following
        command.
        
        .. code:: bash
        
           pip install PyRQA
        
        OpenCL Setup
        ------------
        
        The analytical implementations provided by PyRQA rely on features that
        are part of *OpenCL 1.1*, which is a fairly mature standard and
        supported by a large number of platforms. The OpenCL computing devices
        employed need to support at least this version to being able to use
        PyRQA.
        
        It may be required to install additional software, e.g., runtimes or
        drivers, to execute PyRQA on computing devices such as GPUs and CPUs.
        References to vendor-specific information are presented below.
        
        *AMD*:
        
        -  https://www.amd.com/en/support
        -  https://github.com/RadeonOpenCompute/ROCm
        -  https://community.amd.com/community/devgurus/opencl
        -  https://www.amd.com/en/support/kb/release-notes/amdgpu-installation
        
        *ARM*:
        
        -  https://developer.arm.com/docs/100614/0312
        
        *Intel*:
        
        -  https://software.intel.com/en-us/articles/opencl-drivers
        -  https://software.intel.com/en-us/articles/sdk-for-opencl-gsg
        
        *NVIDIA*:
        
        -  https://developer.nvidia.com/opencl
        -  https://developer.nvidia.com/cuda-downloads
        
        *Vendor-independent*:
        
        -  http://portablecl.org
        
        Usage
        -----
        
        The following subsections depict the usage of PyRQA. Each subsection
        focuses on specific functionality that is provided by the package. The
        presentation of expected output shall ensure the reproducibility of the
        analytical results.
        
        Basic Computations
        ~~~~~~~~~~~~~~~~~~
        
        RQA computations are conducted as follows.
        
        .. code:: python
        
           from pyrqa.time_series import TimeSeries
           from pyrqa.settings import Settings
           from pyrqa.analysis_type import Classic
           from pyrqa.neighbourhood import FixedRadius
           from pyrqa.metric import EuclideanMetric
           from pyrqa.computation import RQAComputation
           data_points = [0.1, 0.5, 1.3, 0.7, 0.8, 1.4, 1.6, 1.2, 0.4, 1.1, 0.8, 0.2, 1.3]
           time_series = TimeSeries(data_points,
                                    embedding_dimension=2,
                                    time_delay=2)
           settings = Settings(time_series,
                               analysis_type=Classic,
                               neighbourhood=FixedRadius(0.65),
                               similarity_measure=EuclideanMetric,
                               theiler_corrector=1)
           computation = RQAComputation.create(settings,
                                               verbose=True)
           result = computation.run()
           result.min_diagonal_line_length = 2
           result.min_vertical_line_length = 2
           result.min_white_vertical_line_length = 2
           print(result)
        
        The following output is expected.
        
        ::
        
           RQA Result:
           ===========
        
           Minimum diagonal line length (L_min): 2
           Minimum vertical line length (V_min): 2
           Minimum white vertical line length (W_min): 2
        
           Recurrence rate (RR): 0.371901
           Determinism (DET): 0.411765
           Average diagonal line length (L): 2.333333
           Longest diagonal line length (L_max): 3
           Divergence (DIV): 0.333333
           Entropy diagonal lines (L_entr): 0.636514
           Laminarity (LAM): 0.400000
           Trapping time (TT): 2.571429
           Longest vertical line length (V_max): 4
           Entropy vertical lines (V_entr): 0.955700
           Average white vertical line length (W): 2.538462
           Longest white vertical line length (W_max): 6
           Longest white vertical line length inverse (W_div): 0.166667
           Entropy white vertical lines (W_entr): 0.839796
        
           Ratio determinism / recurrence rate (DET/RR): 1.107190
           Ratio laminarity / determinism (LAM/DET): 0.971429
        
        The corresponding recurrence plot is created likewise. Note that the
        parameter ``theiler_corrector`` is ignored regarding the creation of the
        plot.
        
        .. code:: python
        
           from pyrqa.computation import RPComputation
           from pyrqa.image_generator import ImageGenerator
           computation = RPComputation.create(settings)
           result = computation.run()
           ImageGenerator.save_recurrence_plot(result.recurrence_matrix_reverse,
                                               'recurrence_plot.png')
        
        Cross Recurrence Analysis
        ~~~~~~~~~~~~~~~~~~~~~~~~~
        
        PyRQA further offers the opportunity to conduct cross recurrence
        analysis (*CRQA* and *CRP*), in addition to the classic recurrence
        analysis (*RQA* and *RP*). For this purpose, two time series of
        potentially different length are provided as input. Note that the
        corresponding computations require to set the same value regarding the
        embedding dimension. Two different time delay values may be used
        regarding the first and the second time series. To enable cross
        recurrence analysis, the parameter ``analysis_type`` has to be changed
        from ``Classic`` to ``Cross``, when creating the ``Settings`` object. A
        *CRQA* example is given below.
        
        .. code:: python
        
           from pyrqa.analysis_type import Cross
           data_points_x = [0.9, 0.1, 0.2, 0.3, 0.5, 1.7, 0.4, 0.8, 1.5]
           time_series_x = TimeSeries(data_points_x,
                                      embedding_dimension=2,
                                      time_delay=1)
           data_points_y = [0.3, 1.3, 0.6, 0.2, 1.1, 1.9, 1.3, 0.4, 0.7, 0.9, 1.6]
           time_series_y = TimeSeries(data_points_y,
                                      embedding_dimension=2,
                                      time_delay=2)
           time_series = (time_series_x,
                          time_series_y)
           settings = Settings(time_series,
                               analysis_type=Cross,
                               neighbourhood=FixedRadius(0.73),
                               similarity_measure=EuclideanMetric,
                               theiler_corrector=0)
           computation = RQAComputation.create(settings,
                                               verbose=True)
           result = computation.run()
           result.min_diagonal_line_length = 2
           result.min_vertical_line_length = 2
           result.min_white_vertical_line_length = 2
           print(result)
        
        The following output is expected.
        
        ::
        
           CRQA Result:
           ============
        
           Minimum diagonal line length (L_min): 2
           Minimum vertical line length (V_min): 2
           Minimum white vertical line length (W_min): 2
        
           Recurrence rate (RR): 0.319444
           Determinism (DET): 0.521739
           Average diagonal line length (L): 2.400000
           Longest diagonal line length (L_max): 3
           Divergence (DIV): 0.333333
           Entropy diagonal lines (L_entr): 0.673012
           Laminarity (LAM): 0.434783
           Trapping time (TT): 2.500000
           Longest vertical line length (V_max): 3
           Entropy vertical lines (V_entr): 0.693147
           Average white vertical line length (W): 3.500000
           Longest white vertical line length (W_max): 8
           Longest white vertical line length inverse (W_div): 0.125000
           Entropy white vertical lines (W_entr): 1.424130
        
           Ratio determinism / recurrence rate (DET/RR): 1.633270
           Ratio laminarity / determinism (LAM/DET): 0.833333
        
        The corresponding cross recurrence plot is created likewise.
        
        .. code:: python
        
           from pyrqa.computation import RPComputation
           from pyrqa.image_generator import ImageGenerator
           computation = RPComputation.create(settings)
           result = computation.run()
           ImageGenerator.save_recurrence_plot(result.recurrence_matrix_reverse,
                                               'cross_recurrence_plot.png')
        
        Neighbourhood Condition Selection
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        
        PyRQA currently supports the fixed radius as well as the radius corridor
        neighbourhood condition. While the first refers to a single radius, the
        latter requires the assignment of an inner and outer radius. The
        specific condition is passed using the parameter ``neighbourhood`` to
        the constructor of a ``Settings`` object. The creation of a fixed radius
        and a radius corridor neighbourhood is presented below.
        
        .. code:: python
        
           from pyrqa.neighbourhood import FixedRadius, RadiusCorridor
           fixed_radius = FixedRadius(radius=0.43)
           radius_corridor = RadiusCorridor(inner_radius=0.32, 
                                            outer_radius=0.86)          
        
        Unthresholded Recurrence Plots
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        
        PyRQA allows to create unthresholded *RP*\ s and *CRP*\ s by selecting
        the ``Unthresholded`` neighbourhood condition. This results in a
        non-binary matrix, containing the mutual distances between the system
        states, based on the similarity measure selected. PyRQA provides
        functionality to normalize these distances to values between ``0`` and
        ``1``. Additionally, the normalized matrix can be represented as a
        grayscale image. Darker shades of grey indicate smaller distances
        whereas lighter shades of grey indicate larger distances. An example on
        how to create an unthresholded cross recurrence plot is given below.
        
        .. code:: python
        
           from pyrqa.neighbourhood import Unthresholded
           settings = Settings(time_series,
                               analysis_type=Cross,
                               neighbourhood=Unthresholded(),
                               similarity_measure=EuclideanMetric)
           computation = RPComputation.create(settings)
           result = computation.run()
           ImageGenerator.save_unthresholded_recurrence_plot(result.recurrence_matrix_reverse_normalized,
                                                             'unthresholded_cross_recurrence_plot.png')
        
        Joint Recurrence Analysis
        ~~~~~~~~~~~~~~~~~~~~~~~~~
        
        In addition to classic and cross recurrence analysis, PyRQA provides
        functionality to conduct joint recurrence analysis. This includes in
        particular joint recurrence quantification analysis (*JRQA*) as well as
        joint recurrence plot (*JRP*). On an abstract level, a joint recurrence
        plot is a combination of two individual plots, both having the same
        extent regarding the *X* and *Y* axis. Regarding PyRQA, each of those
        two plots may either be of the analysis type ``Classic`` or ``Cross``,
        potentially having different characteristics regarding:
        
        -  Time series data,
        -  Embedding dimension,
        -  Time delay,
        -  Neighbourhood condition, and
        -  Similarity measure.
        
        In contrast, the same value for ``theiler_corrector`` is expected
        regarding the quantitative analysis. Note that a joint recurrence plot
        by definition relies on thresholded input plots, eliminating the
        application of the ``Unthresholded`` neighbourhood condition.
        
        The settings of the two individual plots are encapsulated in a
        ``JointSettings`` object. The quantification of joint recurrence plots
        is based on the same measures as for recurrence plots and cross
        recurrence plots. An example on how to conduct *JRQA* is given below.
        
        .. code:: python
        
           from pyrqa.computation import JRQAComputation
           from pyrqa.metric import MaximumMetric, TaxicabMetric
           from pyrqa.settings import JointSettings
           data_points_1 = [1.0, 0.7, 0.5, 0.1, 1.7, 1.5, 1.2, 0.4, 0.6, 1.5, 0.8, 0.3]
           time_series_1 = TimeSeries(data_points,
                                      embedding_dimension=3,
                                      time_delay=1)
           settings_1 = Settings(time_series_1,
                                 analysis_type=Classic,
                                 neighbourhood=RadiusCorridor(inner_radius=0.14,
                                                              outer_radius=0.97),
                                 similarity_measure=MaximumMetric,
                                 theiler_corrector=1)
           data_points_2_x = [0.7, 0.1, 1.1, 1.4, 1.0, 0.5, 1.0, 1.9, 1.7, 0.9, 1.5, 0.6]
           time_series_2_x = TimeSeries(data_points_2_x,
                                        embedding_dimension=2,
                                        time_delay=1)
           data_points_2_y = [0.4, 0.7, 0.9, 0.3, 1.9, 1.3, 1.2, 0.2, 1.1, 0.6, 0.8, 0.1, 0.5]
           time_series_2_y = TimeSeries(data_points_2_y,
                                        embedding_dimension=2,
                                        time_delay=2)
           time_series_2 = (time_series_2_x,
                            time_series_2_y)
           settings_2 = Settings(time_series_2,
                                 analysis_type=Cross,
                                 neighbourhood=FixedRadius(0.83),
                                 similarity_measure=TaxicabMetric,
                                 theiler_corrector=1)
           joint_settings = JointSettings(settings_1,
                                          settings_2)
           computation = JRQAComputation.create(joint_settings,
                                                verbose=True)
           result = computation.run()
           result.min_diagonal_line_length = 2
           result.min_vertical_line_length = 1
           result.min_white_vertical_line_length = 2
           print(result)
        
        The following output is expected.
        
        ::
        
           JRQA Result:
           ============
        
           Minimum diagonal line length (L_min): 2
           Minimum vertical line length (V_min): 1
           Minimum white vertical line length (W_min): 2
        
           Recurrence rate (RR): 0.157025
           Determinism (DET): 0.263158
           Average diagonal line length (L): 2.500000
           Longest diagonal line length (L_max): 3
           Divergence (DIV): 0.333333
           Entropy diagonal lines (L_entr): 0.693147
           Laminarity (LAM): 1.000000
           Trapping time (TT): 1.000000
           Longest vertical line length (V_max): 1
           Entropy vertical lines (V_entr): 0.000000
           Average white vertical line length (W): 3.960000
           Longest white vertical line length (W_max): 11
           Longest white vertical line length inverse (W_div): 0.090909
           Entropy white vertical lines (W_entr): 1.588760
        
           Ratio determinism / recurrence rate (DET/RR): 1.675900
           Ratio laminarity / determinism (LAM/DET): 3.800000
        
        The corresponding joint recurrence plot is created likewise.
        
        .. code:: python
        
           from pyrqa.computation import JRPComputation
           computation = JRPComputation.create(joint_settings)
           result = computation.run()
           ImageGenerator.save_recurrence_plot(result.recurrence_matrix_reverse,
                                               'joint_recurrence_plot.png')
        
        Time Series Embedding
        ~~~~~~~~~~~~~~~~~~~~~
        
        The previous examples refer to one or multiple univariate time series as
        input data. These ``TimeSeries`` are embedded in multi-dimensional space
        using the time delay method. In addition, PyRQA allows to analyze time
        series that are already embedded in multi-dimensional space. These
        ``EmbeddedSeries`` are represented as a list of *m*-dimensional arrays,
        where *m* refers to the embedding dimension. An example of using a
        pre-embedded series considering recurrence quantification analysis is
        given below.
        
        .. code:: python
        
           from pyrqa.time_series import EmbeddedSeries
           data_points = [[0.1, 1.3], [0.5, 0.7], [1.3, 0.8], [0.7, 1.4], [0.8, 1.6], [1.4, 1.2], [1.6, 0.4], [1.2, 1.1], [0.4, 0.8], [1.1, 0.2], [0.8, 1.3]]
           embedded_series = EmbeddedSeries(data_points)
           settings = Settings(embedded_series,
                               analysis_type=Classic,
                               neighbourhood=FixedRadius(0.65),
                               similarity_measure=EuclideanMetric,
                               theiler_corrector=1)
           computation = RQAComputation.create(settings,
                                               verbose=True)
           result = computation.run()
           result.min_diagonal_line_length = 2
           result.min_vertical_line_length = 2
           result.min_white_vertical_line_length = 2
           print(result)
        
        The following output is expected.
        
        ::
        
           RQA Result:
           ===========
        
           Minimum diagonal line length (L_min): 2
           Minimum vertical line length (V_min): 2
           Minimum white vertical line length (W_min): 2
        
           Recurrence rate (RR): 0.371901
           Determinism (DET): 0.411765
           Average diagonal line length (L): 2.333333
           Longest diagonal line length (L_max): 3
           Divergence (DIV): 0.333333
           Entropy diagonal lines (L_entr): 0.636514
           Laminarity (LAM): 0.400000
           Trapping time (TT): 2.571429
           Longest vertical line length (V_max): 4
           Entropy vertical lines (V_entr): 0.955700
           Average white vertical line length (W): 2.538462
           Longest white vertical line length (W_max): 6
           Longest white vertical line length inverse (W_div): 0.166667
           Entropy white vertical lines (W_entr): 0.839796
        
           Ratio determinism / recurrence rate (DET/RR): 1.107190
           Ratio laminarity / determinism (LAM/DET): 0.971429
        
        Note that this example corresponds to the introductory example, which
        demonstrates the basic usage. It differs regarding the representation of
        the multi-dimensional vectors. ``EmbeddedSeries`` objects can be used
        while conducting recurrence analysis, cross recurrence analysis as well
        as joint recurrence analysis. This refers to performing quantitative
        analyses as well as creating recurrence plots. Regarding cross and joint
        recurrence analysis ``TimeSeries`` objects may be combined with
        ``EmbeddedSeries`` objects.
        
        Custom OpenCL Environment
        ~~~~~~~~~~~~~~~~~~~~~~~~~
        
        The previous examples use the default OpenCL environment. A custom
        environment can also be created via command line input. For this
        purpose, the parameter ``command_line`` has to be set to ``True``, when
        creating an ``OpenCL`` object.
        
        .. code:: python
        
           from pyrqa.opencl import OpenCL
           opencl = OpenCL(command_line=True)
        
        The OpenCL platform as well as the computing devices can also be
        selected manually using their identifiers.
        
        .. code:: python
        
           opencl = OpenCL(platform_id=0,
                           device_ids=(0,))
        
        The ``OpenCL`` object generated is passed as a parameter while creating
        a computation object.
        
        .. code:: python
        
           computation = RPComputation.create(settings,
                                              verbose=True,
                                              opencl=opencl)
        
        Floating Point Precision
        ~~~~~~~~~~~~~~~~~~~~~~~~
        
        PyRQA allows to specify the precision of the time series data, which in
        turn determines the precision of the computations conducted by the
        OpenCL devices. Currently, the following precisions are supported:
        
        -  Half precision (16-bit),
        -  Single precision (32-bit), and
        -  Double precision (64-bit).
        
        By default, the single precision is applied. Note that not all
        precisions may be supported by the OpenCL devices employed. Furthermore,
        the selected precision influences the performance of the computations on
        a particular device.
        
        The precision is set by specifying the corresponding data type, short
        ``dtype``, of the time series data. The following example depicts the
        usage of double precision floating point values.
        
        .. code:: python
        
           import numpy as np
           data_points = [0.1, 0.5, 1.3, 0.7, 0.8, 1.4, 1.6, 1.2, 0.4, 1.1, 0.8, 0.2, 1.3]
           time_series = TimeSeries(data_points,
                                    embedding_dimension=2,
                                    time_delay=2,
                                    dtype=np.float64)
        
        Performance Tuning
        ------------------
        
        PyRQA offers the opportunity to reduce the runtime of analytical
        computations using performance tuning. There is a distinction between
        manual as well as automatic performance tuning. Both aspects are
        highlighted in the following subsections. Note that every analytical
        method implemented by PyRQA can be executed without conducting
        performance tuning. Nonetheless, it may enable significant runtime
        reductions regarding the analysis of very long time series.
        
        Adaptive Implementation Selection
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        
        Adaptive implementation selection allows to automatically select well
        performing implementations regarding RQA and recurrence plot
        computations provided by PyRQA. The approach dynamically adapts the
        selection to the current computational scenario as well as the
        properties of the OpenCL devices employed. The selection is performed
        using one of multiple strategies, each referred to as ``selector``. They
        rely on a set of customized implementation ``variants``, which may be
        parameterized using a set of keyword arguments called
        ``variants_kwargs``. Note that the same selection strategies can be used
        for *RQA* and *CRQA*, *RP* and *CRP*, *URP* and *UCRP* as well as *JRQA*
        and *JRP* computations.
        
        .. code:: python
        
           from pyrqa.variants.rqa.radius.column_no_overlap_materialisation_bit_no_recycling import ColumnNoOverlapMaterialisationBitNoRecycling
           from pyrqa.variants.rqa.radius.column_no_overlap_materialisation_bit_recycling import ColumnNoOverlapMaterialisationBitRecycling
           from pyrqa.variants.rqa.radius.column_no_overlap_materialisation_byte_no_recycling import ColumnNoOverlapMaterialisationByteNoRecycling
           from pyrqa.variants.rqa.radius.column_no_overlap_materialisation_byte_recycling import ColumnNoOverlapMaterialisationByteRecycling
           from pyrqa.variants.rqa.radius.column_no_overlap_no_materialisation import ColumnNoOverlapNoMaterialisation
           from pyrqa.variants.rqa.radius.column_overlap_materialisation_bit_no_recycling import ColumnOverlapMaterialisationBitNoRecycling
           from pyrqa.variants.rqa.radius.column_overlap_materialisation_bit_recycling import ColumnOverlapMaterialisationBitRecycling
           from pyrqa.variants.rqa.radius.column_overlap_materialisation_byte_no_recycling import ColumnOverlapMaterialisationByteNoRecycling
           from pyrqa.variants.rqa.radius.column_overlap_materialisation_byte_recycling import ColumnOverlapMaterialisationByteRecycling
           from pyrqa.variants.rqa.radius.column_overlap_no_materialisation import ColumnOverlapNoMaterialisation
           from pyrqa.selector import EpsilonGreedySelector
           data_points = [0.1, 0.5, 1.3, 0.7, 0.8, 1.4, 1.6, 1.2, 0.4, 1.1, 0.8, 0.2, 1.3]
           time_series = TimeSeries(data_points,
                                    embedding_dimension=2,
                                    time_delay=2)
           settings = Settings(time_series,
                               analysis_type=Classic,
                               neighbourhood=FixedRadius(0.65),
                               similarity_measure=EuclideanMetric,
                               theiler_corrector=1)
           computation = RQAComputation.create(settings,
                                               selector=EpsilonGreedySelector(explore=10),
                                               variants=(ColumnNoOverlapMaterialisationBitNoRecycling,
                                                         ColumnNoOverlapMaterialisationBitRecycling,
                                                         ColumnNoOverlapMaterialisationByteNoRecycling,
                                                         ColumnNoOverlapMaterialisationByteRecycling,
                                                         ColumnNoOverlapNoMaterialisation,
                                                         ColumnOverlapMaterialisationBitNoRecycling,
                                                         ColumnOverlapMaterialisationBitRecycling,
                                                         ColumnOverlapMaterialisationByteNoRecycling,
                                                         ColumnOverlapMaterialisationByteRecycling,
                                                         ColumnOverlapNoMaterialisation))
        
        Input Data Overlapping
        ~~~~~~~~~~~~~~~~~~~~~~
        
        PyRQA comprises a set of ``variants`` for each analytical method, which
        differ regarding certain implementation details. The specific
        characteristics of each variant are reflected in its name. The naming
        convention is applied accordingly to all analytical methods.
        
        One criterion is the way how the input data is represented within the
        memory of the computing devices. The multi-dimensional vectors may
        either be stored column-wise or row-wise. Considering ``TimeSeries``
        objects, to which the time delay method is applied, the columns may
        additionally be stored in an overlapped fashion. This allows leveraging
        data compression as well as potential runtime reductions. Using
        ``EmbeddedSeries`` objects as input data, the multi-dimensional vectors
        may only be stored non-overlapping. As an example, variants referring to
        the joint recurrence quantification analysis are mentioned below.
        
        .. code:: python
        
           from pyrqa.variants.jrqa.radius.column_no_overlap_materialisation_byte_no_recycling import ColumnNoOverlapMaterialisationByteNoRecycling
           from pyrqa.variants.jrqa.radius.row_no_overlap_materialisation_byte_no_recycling import RowNoOverlapMaterialisationByteNoRecycling
           from pyrqa.variants.jrqa.radius.column_overlap_materialisation_byte_no_recycling import ColumnOverlapMaterialisationByteNoRecycling
        
        Note that these variants have the same implementation characteristics,
        except from the representation of the input data. Only those variants
        that store the input data non-overlapping may be applied to
        ``EmbeddedSeries`` objects. By default, non-overlapping variants are
        selected.
        
        OpenCL Compiler Optimisations
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        
        OpenCL compiler optimisations aim at improving the performance of the
        operations conducted by the computing devices. Regarding PyRQA, they are
        disabled by default to ensure the comparability of the analytical
        results. They can be enabled by assigning the value ``True`` to the
        corresponding keyword argument ``optimisations_enabled``.
        
        .. code:: python
        
           computation = RQAComputation.create(settings,
                                               selector=EpsilonGreedySelector(explore=10),
                                               variants=(ColumnNoOverlapMaterialisationBitNoRecycling,
                                                         ColumnNoOverlapMaterialisationBitRecycling,
                                                         ColumnNoOverlapMaterialisationByteNoRecycling,
                                                         ColumnNoOverlapMaterialisationByteRecycling,
                                                         ColumnNoOverlapNoMaterialisation,
                                                         ColumnOverlapMaterialisationBitNoRecycling,
                                                         ColumnOverlapMaterialisationBitRecycling,
                                                         ColumnOverlapMaterialisationByteNoRecycling,
                                                         ColumnOverlapMaterialisationByteRecycling,
                                                         ColumnOverlapNoMaterialisation),
                                               variants_kwargs={'optimisations_enabled': True})
        
        Loop Unrolling
        ~~~~~~~~~~~~~~
        
        Besides gaining drastic performance improvements using parallel
        computing techniques, parts of the PyRQA kernel processing rely on
        loops. OpenCL offers the opportunity to leverage additional performance
        improvements by unrolling these loops. This is conducted by the OpenCL
        compiler that is applied to the kernel functions. Note that loop
        unrolling may not be supported by all OpenCL platforms.
        
        PyRQA offers the opportunity to manually specify loop unrolling factors
        that can be passed as a tuple when creating a selector. While creating a
        computation object, each factor is combined with each implementation
        variant. The resulting combinations are further used regarding adaptive
        implementation selection. An example on how to specify loop unrolling
        factors is given below.
        
        .. code:: python
        
           from pyrqa.selector import EpsilonFirstSelector
           selector = EpsilonFirstSelector(explore=15,
                                           loop_unroll_factors=(1,2,4,8,16,32))
        
        Submatrix Edge Length
        ~~~~~~~~~~~~~~~~~~~~~
        
        During the analytical processing, PyRQA subdivides the recurrence matrix
        into a number of submatrices. To get more information on the recurrence
        matrix partitioning, please refer to the publications mentioned below.
        The corresponding parameter ``edge_length`` can be set while creating a
        computation object.
        
        .. code:: python
        
           computation = RQAComputation.create(settings,
                                               edge_length=12800)
        
        Note that the edge length has to be chosen such that a submatrix fits in
        the memory of the OpenCL computing devices. Experiments have shown that
        values between ``10000`` and ``20000`` are a reasonable choice.
        Nonetheless, values outside of these boundaries may lead to lower
        runtimes for specific computational scenarios. Furthermore, recurrence
        matrices with a smaller extent than the value of ``edge_length`` are
        processed without being partitioned.
        
        Testing
        -------
        
        PyRQA provides a single-threaded baseline implementation for each
        analytical method. These implementations do not use OpenCL
        functionality. They serve as a ground truth regarding the analytical
        computations. The basic tests for all supported analytical methods can
        be executed cumulatively.
        
        .. code:: bash
        
           python -m pyrqa.test
        
        The complete set of tests can be executed by adding the option
        ``--all``.
        
        .. code:: bash
        
           python -m pyrqa.test --all
        
        Note that there might occur minor deviations regarding the analytical
        results. These deviations may stem from varying precisions regarding the
        computing devices employed.
        
        Origin
        ------
        
        The PyRQA package was initiated by computer scientists from the
        Humboldt-Universität zu Berlin (https://www.hu-berlin.de) and the GFZ
        German Research Centre for Geosciences (https://www.gfz-potsdam.de).
        
        Acknowledgements
        ----------------
        
        We would like to thank Norbert Marwan from the Potsdam Institute for
        Climate Impact Research (https://www.pik-potsdam.de) for his continuous
        support of the project. Please visit his website
        http://recurrence-plot.tk/ for further information on recurrence
        analysis. Initial research and development of PyRQA was funded by the
        Deutsche Forschungsgemeinschaft (https://www.dfg.de/).
        
        Publications
        ------------
        
        The underlying computational approach of PyRQA is described in detail
        within the following thesis, which is openly accessible at
        https://edoc.hu-berlin.de/handle/18452/19518.
        
           Rawald, T. (2018): Scalable and Efficient Analysis of Large
           High-Dimensional Data Sets in the Context of Recurrence Analysis, PhD
           Thesis, Berlin : Humboldt-Universität zu Berlin, 299 p.
        
        Selected aspects of the computational approach are presented within the
        following publications.
        
           Rawald, T., Sips, M., Marwan, N., Dransch, D. (2014): Fast
           Computation of Recurrences in Long Time Series. - In: Marwan, N.,
           Riley, M., Guiliani, A., Webber, C. (Eds.), Translational
           Recurrences. From Mathematical Theory to Real-World Applications,
           (Springer Proceedings in Mathematics and Statistics ; 103), p. 17-29.
        
        ..
        
           Rawald, T., Sips, M., Marwan, N., Leser, U. (2015): Massively
           Parallel Analysis of Similarity Matrices on Heterogeneous Hardware. -
           In: Fischer, P. M., Alonso, G., Arenas, M., Geerts, F. (Eds.),
           Proceedings of the Workshops of the EDBT/ICDT 2015 Joint Conference
           (EDBT/ICDT), (CEUR Workshop Proceedings ; 1330), p. 56-62.
        
        Development Status
        ------------------
        
        The development status of the PyRQA package is considered as *Beta*.
        Please send feature requests and bug reports to the email address that
        is listed in the project metadata.
        
        Release Notes
        -------------
        
        8.1.0
        ~~~~~
        
        -  Addition of a JRQA variant referring to non-overlapping column-wise
           storage of input data.
        -  Replaced all occurrences of ``numpy.float`` with ``numpy.float32``.
        
        .. _section-1:
        
        8.0.0
        ~~~~~
        
        -  Usage of pre-embedded time series as input data.
        -  Addition of variants referring to non-overlapping column-wise storage
           of input data.
        -  Refactoring of the public API.
        -  Updated documentation.
        
        .. _section-2:
        
        7.0.1
        ~~~~~
        
        -  Modification of the build configuration.
        -  Updated documentation.
        
        .. _section-3:
        
        7.0.0
        ~~~~~
        
        -  Addition of two variants regarding joint recurrence quantification
           analysis computations.
        -  Removal of obsolete source code.
        -  Refactoring of the public API.
        -  Updated documentation.
        
        .. _section-4:
        
        6.0.0
        ~~~~~
        
        -  Addition of the joint recurrence quantification analysis (*JRQA*) and
           joint recurrence plot (*JRP*) computations.
        -  Refactoring of the test implementation.
        -  Refactoring of the public API.
        -  Updated documentation.
        
        .. _section-5:
        
        5.1.0
        ~~~~~
        
        -  Addition of the unthresholded recurrence plot (*URP*) and
           unthresholded cross recurrence plot (*UCRP*) computations.
        -  Updated documentation.
        
        .. _section-6:
        
        5.0.0
        ~~~~~
        
        -  Refactoring of the public API.
        -  Updated documentation.
        
        .. _section-7:
        
        4.1.0
        ~~~~~
        
        -  Usage of two different time delay values regarding the cross
           recurrence plot (*CRP*) and cross recurrence quantification analysis
           (*CRQA*).
        -  Updated documentation.
        
        .. _section-8:
        
        4.0.0
        ~~~~~
        
        -  Addition of the cross recurrence plot (*CRP*) and cross recurrence
           quantification analysis (*CRQA*) computations.
        -  Addition of the radius corridor neighbourhood condition for
           determining state similarity.
        -  Addition of an additional variant regarding recurrence plot
           computations.
        -  Renaming of directories and classes referring to recurrence plot
           computations.
        -  Removal of obsolete source code.
        -  Updated documentation.
        
        .. _section-9:
        
        3.0.0
        ~~~~~
        
        -  Source code cleanup.
        -  Renaming of the implementation variants regarding RQA and recurrence
           plot processing.
        -  Removal of the module ``file_reader.py``. Please refer for example to
           ``numpy.genfromtxt`` to read data from files (see
           https://docs.scipy.org/doc/numpy/reference/generated/numpy.genfromtxt.html).
        -  Updated documentation.
        
        .. _section-10:
        
        2.0.1
        ~~~~~
        
        -  Updated documentation.
        
        .. _section-11:
        
        2.0.0
        ~~~~~
        
        -  Major refactoring.
        -  Removal of operator and variant implementations that do not refer to
           OpenCL brute force computing.
        -  Time series data may be represented using half, single and double
           precision floating point values, which is reflected in the
           computations on the OpenCL devices.
        -  Several changes to the public API.
        
        .. _section-12:
        
        1.0.6
        ~~~~~
        
        -  Changes to the public API have been made, e.g., to the definition of
           the settings. This leads to an increase in the major version number
           (see https://semver.org/).
        -  Time series objects either consist of one or multiple series. The
           former requires to specify a value for the embedding delay as well as
           the time delay parameter.
        -  Regarding the RQA computations, minimum line lengths are now
           specified on the result object. This allows to compute quantitative
           results using different lengths without having to inspect the matrix
           using the same parametrisation multiple times.
        -  Modules for selecting well-performing implementations based on greedy
           selection strategies have been added. By default, the selection pool
           consists of a single pre-defined implementation.
        -  Operators and implementation variants based on multidimensional
           search trees and grid data structures have been added.
        -  The diagonal line based quantitative measures are modified regarding
           the semantics of the Theiler corrector.
        -  The creation of the OpenCL environment now supports device fission.
        
        .. _section-13:
        
        0.1.0
        ~~~~~
        
        -  Initial release.
        
Keywords: nonlinear,time series analysis,dynamical system,recurrence quantification analysis,RQA,cross recurrence quantification analysis,CRQA,joint recurrence quantification analysis,JRQA,recurrence plot,RP,cross recurrence plot,CRP,joint recurrence plot,JRP
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Financial and Insurance Industry
Classifier: Intended Audience :: Healthcare Industry
Classifier: Intended Audience :: Manufacturing
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: Apache Software License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 3
Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Physics
