A tool to conduct recurrence quantification analysis and to create recurrence plots in a massively parallel manner using the OpenCL framework.

## Project description

## Table of Contents

## General Information

PyRQA is a tool to conduct recurrence quantification analysis (RQA) and to create recurrence plots 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 RQA 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)

In addition, PyRQA allows to compute the corresponding recurrence plot and to export it as an image file.

## Contribution

The code of the PyRQA package is hosted under https://gitlab.com/tobiasr/PyRQA.

## Contact

Please write an email to pyrqa@gmx.net, if you have any questions related to the PyRQA package.

## Installation

PyRQA can be installed via the following command.

pip install PyRQA

## OpenCL Setup

It may be required to install hardware vendor specific software, e.g., device drivers, to run PyRQA on OpenCL devices (such as GPUs and CPUs). Vendor-specific information is presented below.

- AMD:
- Intel:
- NVIDIA:
- ARM:

## Usage

RQA computations are conducted as follows.

from pyrqa.time_series import SingleTimeSeries from pyrqa.settings import Settings from pyrqa.neighbourhood import FixedRadius from pyrqa.metric import EuclideanMetric from pyrqa.computation import RQAComputation time_series = SingleTimeSeries([0.1, 0.5, 0.3, 1.7, 0.8, 2.4, 0.6, 1.2, 1.4, 2.1, 0.8], embedding_dimension=3, time_delay=2) settings = Settings(time_series, neighbourhood=FixedRadius(1.0), similarity_measure=EuclideanMetric, theiler_corrector=1) computation = RQAComputation.create(settings, verbose=True) result = computation.run() result.min_diagonal_line_length = 1 result.min_vertical_line_length = 2 result.min_white_vertical_line_length = 1 print(result)

Recurrence plot computations can be conducted likewise.

from pyrqa.computation import RecurrencePlotComputation from pyrqa.image_generator import ImageGenerator computation = RecurrencePlotComputation.create(settings) result = computation.run() ImageGenerator.save_recurrence_plot(result.recurrence_matrix_reverse, 'recurrence_plot.png')

Moreover, it is possible to read time series data that is stored column-wise from a file.

from pyrqa.file_reader import FileReader time_series = SingleTimeSeries(FileReader.file_as_float_array('data.csv', delimiter=';', column=0))

The previous examples use the default OpenCL environment. A custom environment using command line input can also be created

from pyrqa.opencl import OpenCL opencl = OpenCL(command_line=True)

The OpenCL platform as well as the computing devices can also be selected using their IDs.

opencl = OpenCL(platform_id=0, device_ids=(0,)) computation = RQAComputation.create(settings, verbose=True, opencl=opencl) result = computation.run()

Default OpenCL compiler optimisation are deactivated by default to ensure the comparability of computing results. They can be activated to leverage additional performance improvements.

computation = RQAComputation.create(settings, variants_kwargs={'optimisation_enabled': True}) result = computation.run()

Adaptive implementation selection is performed using one of multiple greedy selection strategies supported. It is conducted based on a customized pool of implementation variants. These variants may be enriched with a set of keyword arguments.

from pyrqa.variants.rqa.fixed_radius.brute_force.column_materialisation_uncompressed_bit_no_recycling import ColumnMaterialisationUncompressedBitNoRecycling from pyrqa.variants.rqa.fixed_radius.brute_force.column_materialisation_uncompressed_bit_recycling import ColumnMaterialisationUncompressedBitRecycling from pyrqa.variants.rqa.fixed_radius.brute_force.column_materialisation_uncompressed_byte_no_recycling import ColumnMaterialisationUncompressedByteNoRecycling from pyrqa.variants.rqa.fixed_radius.brute_force.column_materialisation_uncompressed_byte_recycling import ColumnMaterialisationUncompressedByteRecycling from pyrqa.variants.rqa.fixed_radius.brute_force.column_no_materialisation import ColumnNoMaterialisation from pyrqa.selector import EpsilonGreedySelector computation = RQAComputation.create(settings, selector=EpsilonGreedySelector(explore=10), variants=(ColumnMaterialisationUncompressedBitNoRecycling, ColumnMaterialisationUncompressedBitRecycling, ColumnMaterialisationUncompressedByteNoRecycling, ColumnMaterialisationUncompressedByteRecycling, ColumnNoMaterialisation), variants_kwargs={'optimisations_enabled': True}) result = computation.run()

## Testing

All tests available within the PyRQA package can be executed cumulatively.

python -m pyrqa.test

Note that it might be required to execute the command as super user.

## Origin

The PyRQA package was initiated by computer scientists from the Humboldt-Universität zu Berlin and the GFZ German Research Centre for Geosciences.

## Acknowledgements

We would like to thank Norbert Marwan from the Potsdam Institute for Climate Impact Research for his continuous support of the project. Please visit his website http://recurrence-plot.tk/ for further information on recurrence analysis.

## Publications

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.

The underlying computational approach of PyRQA is described in detail within the following thesis, which is openly accessible under 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.

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