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# Sphinx build info version 1 | ||
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. | ||
config: 4cfbc83e63b16564b19272d94b7868c5 | ||
tags: 645f666f9bcd5a90fca523b33c5a78b7 |
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API Reference | ||
============= | ||
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Index | ||
----- | ||
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.. rubric:: Classes | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.CircularCoords | ||
dreimac.ToroidalCoords | ||
dreimac.ProjectiveCoords | ||
dreimac.ComplexProjectiveCoords | ||
dreimac.LensCoords | ||
dreimac.PartUnity | ||
dreimac.GeometryExamples | ||
dreimac.PlotUtils | ||
dreimac.CircleMapUtils | ||
dreimac.ProjectiveMapUtils | ||
dreimac.LensMapUtils | ||
dreimac.GeometryUtils | ||
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.. rubric:: dreimac.CircularCoords methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.CircularCoords.get_coordinates | ||
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.. rubric:: dreimac.ToroidalCoords methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.ToroidalCoords.get_coordinates | ||
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.. rubric:: dreimac.ProjectiveCoords methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.ProjectiveCoords.get_coordinates | ||
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.. rubric:: dreimac.ComplexProjectiveCoords methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.ComplexProjectiveCoords.get_coordinates | ||
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.. rubric:: dreimac.LensCoords methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.LensCoords.get_coordinates | ||
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.. rubric:: dreimac.PartUnity methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.PartUnity.linear | ||
dreimac.PartUnity.quadratic | ||
dreimac.PartUnity.exp | ||
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.. rubric:: dreimac.GeometryExamples methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.GeometryExamples.line_patches | ||
dreimac.GeometryExamples.moving_dot | ||
dreimac.GeometryExamples.torus_3d | ||
dreimac.GeometryExamples.klein_bottle_4d | ||
dreimac.GeometryExamples.genus_two_surface | ||
dreimac.GeometryExamples.trefoil | ||
dreimac.GeometryExamples.bullseye | ||
dreimac.GeometryExamples.sphere | ||
dreimac.GeometryExamples.noisy_circle | ||
dreimac.GeometryExamples.moore_space_distance_matrix | ||
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.. rubric:: dreimac.PlotUtils methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.PlotUtils.plot_patches | ||
dreimac.PlotUtils.plot_proj_boundary | ||
dreimac.PlotUtils.plot_2sphere_boundary | ||
dreimac.PlotUtils.plot_3sphere_mesh | ||
dreimac.PlotUtils.set_axes_equal | ||
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.. rubric:: dreimac.CircleMapUtils methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.CircleMapUtils.offset | ||
dreimac.CircleMapUtils.linear_combination | ||
dreimac.CircleMapUtils.to_sinebow | ||
dreimac.CircleMapUtils.levelset_coloring | ||
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.. rubric:: dreimac.ProjectiveMapUtils methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.ProjectiveMapUtils.get_stereo_proj_codim1 | ||
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.. rubric:: dreimac.LensMapUtils methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.LensMapUtils.lens_3D_to_disk_3D | ||
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.. rubric:: dreimac.GeometryUtils methods | ||
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.. autosummary:: | ||
:nosignatures: | ||
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dreimac.GeometryUtils.get_greedy_perm_pc | ||
dreimac.GeometryUtils.landmark_geodesic_distance | ||
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Details | ||
------- | ||
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.. autoclass:: dreimac.CircularCoords | ||
:members: | ||
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.. autoclass:: dreimac.ToroidalCoords | ||
:members: | ||
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.. autoclass:: dreimac.ProjectiveCoords | ||
:members: | ||
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.. autoclass:: dreimac.ComplexProjectiveCoords | ||
:members: | ||
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.. autoclass:: dreimac.LensCoords | ||
:members: | ||
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.. autoclass:: dreimac.PartUnity | ||
:members: | ||
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.. autoclass:: dreimac.GeometryExamples | ||
:members: | ||
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.. autoclass:: dreimac.PlotUtils | ||
:members: | ||
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.. autoclass:: dreimac.CircleMapUtils | ||
:members: | ||
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.. autoclass:: dreimac.ProjectiveMapUtils | ||
:members: | ||
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.. autoclass:: dreimac.LensMapUtils | ||
:members: | ||
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.. autoclass:: dreimac.GeometryUtils | ||
:members: |
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FAQ | ||
=== | ||
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.. contents:: | ||
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Why does my output not look exactly like the output in the examples? | ||
-------------------------------------------------------------------- | ||
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There is more than one source of indeterminacy. | ||
First, cohomological coordinates take values in spaces with many symmetries; for example, any rotation induces an isometry from the circle to the circle. | ||
As such, cohomological coordinates are only well-defined up to rigid symmetries of the target space. | ||
Secondly, since several of DREiMac's subroutines are numerical, the exact output can depend on your machine's specific architecture. | ||
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Having said this, if you are getting outputs that are qualitatively different from those in the examples, please let us know by filing an issue on DREiMac's repository. | ||
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How can I get further help? | ||
--------------------------- | ||
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If you have further questions, please | ||
`open an issue <https://github.com/scikit-tda/DREiMac/issues/new>`_ and we will do our best to help you. | ||
Please include as much information as possible, including your system's information, warnings, logs, screenshots, and anything else you think may be of use. |
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DREiMac: Dimensionality Reduction with Eilenberg-MacLane Coordinates | ||
==================================================================== | ||
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DREiMac is a library for topological data coordinatization, visualization, and dimensionality reduction. | ||
Currently, DREiMac is able to find topology-preserving representations of point clouds taking values in the circle, in higher dimensional tori, in the real and complex projective space, and in lens spaces. | ||
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In a few words, DREiMac takes as input a point cloud together with a topological feature of the point cloud (in the form of a persistent cohomology class), and returns a map from the point cloud to a well-understood topological space (a circle, a product of circles, a projective space, or a lens space), which preserves the given topological feature in a precise sense. | ||
You can check the :ref:`theory section <theory>` for details and or the examples below to see how DREiMac works in practice. | ||
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Installing | ||
---------- | ||
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Make sure your Python version is >=3.8 and <3.12. | ||
DREiMac depends on the following python packages, which will be installed automatically when you install with pip: | ||
`matplotlib`, | ||
`numba`, | ||
`numpy`, | ||
`persim`, | ||
`ripser`, and | ||
`scipy`. | ||
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.. code-block:: | ||
pip install dreimac | ||
Contents | ||
======== | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: About | ||
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theory | ||
api | ||
faq | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Choosing parameters | ||
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notebooks/parameters_n_landmarks_and_cocycle_idx | ||
notebooks/parameter_perc | ||
notebooks/parameter_standard_range | ||
notebooks/parameter_n_samples | ||
notebooks/parameters_prime_and_check_cocycle_condition | ||
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Further examples | ||
---------------- | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Circular coordinates | ||
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notebooks/coil20 | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Toroidal coordinates | ||
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notebooks/bullseye | ||
notebooks/genusTwoSurface | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Real projective coordinates | ||
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notebooks/ImagePatches | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Complex projective coordinates | ||
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notebooks/twoSphere | ||
notebooks/movingDot | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
:caption: Lens coordinates | ||
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notebooks/circleLensCoordinates | ||
notebooks/MooreSpace | ||
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Authors | ||
======= | ||
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Jose A. Perea, Luis Scoccola, Chris Tralie | ||
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