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

Project description

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.


The code of the PyRQA package is hosted under


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


PyRQA can be installed via the following command.

pip install PyRQA


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],
settings = Settings(time_series,
computation = RQAComputation.create(settings,
result =
result.min_diagonal_line_length = 1
result.min_vertical_line_length = 2
result.min_white_vertical_line_length = 1

Recurrence plot computations can be conducted likewise.

from pyrqa.computation import RecurrencePlotComputation
from pyrqa.image_generator import ImageGenerator
computation = RecurrencePlotComputation.create(settings)
result =
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',

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,
computation = RQAComputation.create(settings,
result =

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 =

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,
                                    variants_kwargs={'optimisations_enabled': True})
result =


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.


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


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 for further information on recurrence analysis.


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

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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