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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
=============

Index
-----

.. rubric:: Classes

.. autosummary::
:nosignatures:

dreimac.CircularCoords
dreimac.ToroidalCoords
dreimac.ProjectiveCoords
dreimac.ComplexProjectiveCoords
dreimac.LensCoords
dreimac.PartUnity
dreimac.GeometryExamples
dreimac.PlotUtils
dreimac.CircleMapUtils
dreimac.ProjectiveMapUtils
dreimac.LensMapUtils
dreimac.GeometryUtils


.. rubric:: dreimac.CircularCoords methods

.. autosummary::
:nosignatures:

dreimac.CircularCoords.get_coordinates


.. rubric:: dreimac.ToroidalCoords methods

.. autosummary::
:nosignatures:

dreimac.ToroidalCoords.get_coordinates


.. rubric:: dreimac.ProjectiveCoords methods

.. autosummary::
:nosignatures:

dreimac.ProjectiveCoords.get_coordinates


.. rubric:: dreimac.ComplexProjectiveCoords methods

.. autosummary::
:nosignatures:

dreimac.ComplexProjectiveCoords.get_coordinates


.. rubric:: dreimac.LensCoords methods

.. autosummary::
:nosignatures:

dreimac.LensCoords.get_coordinates


.. rubric:: dreimac.PartUnity methods

.. autosummary::
:nosignatures:

dreimac.PartUnity.linear
dreimac.PartUnity.quadratic
dreimac.PartUnity.exp


.. rubric:: dreimac.GeometryExamples methods

.. autosummary::
:nosignatures:

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


.. rubric:: dreimac.PlotUtils methods

.. autosummary::
:nosignatures:

dreimac.PlotUtils.plot_patches
dreimac.PlotUtils.plot_proj_boundary
dreimac.PlotUtils.plot_2sphere_boundary
dreimac.PlotUtils.plot_3sphere_mesh
dreimac.PlotUtils.set_axes_equal


.. rubric:: dreimac.CircleMapUtils methods

.. autosummary::
:nosignatures:

dreimac.CircleMapUtils.offset
dreimac.CircleMapUtils.linear_combination
dreimac.CircleMapUtils.to_sinebow
dreimac.CircleMapUtils.levelset_coloring


.. rubric:: dreimac.ProjectiveMapUtils methods

.. autosummary::
:nosignatures:

dreimac.ProjectiveMapUtils.get_stereo_proj_codim1


.. rubric:: dreimac.LensMapUtils methods

.. autosummary::
:nosignatures:

dreimac.LensMapUtils.lens_3D_to_disk_3D


.. rubric:: dreimac.GeometryUtils methods

.. autosummary::
:nosignatures:

dreimac.GeometryUtils.get_greedy_perm_pc
dreimac.GeometryUtils.landmark_geodesic_distance


Details
-------

.. autoclass:: dreimac.CircularCoords
:members:


.. autoclass:: dreimac.ToroidalCoords
:members:


.. autoclass:: dreimac.ProjectiveCoords
:members:


.. autoclass:: dreimac.ComplexProjectiveCoords
:members:


.. autoclass:: dreimac.LensCoords
:members:


.. autoclass:: dreimac.PartUnity
:members:


.. autoclass:: dreimac.GeometryExamples
:members:


.. autoclass:: dreimac.PlotUtils
:members:


.. autoclass:: dreimac.CircleMapUtils
:members:


.. autoclass:: dreimac.ProjectiveMapUtils
:members:


.. autoclass:: dreimac.LensMapUtils
:members:


.. autoclass:: dreimac.GeometryUtils
:members:
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FAQ
===

.. contents::


Why does my output not look exactly like the output in the examples?
--------------------------------------------------------------------

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.

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.


How can I get further help?
---------------------------

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
====================================================================

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.

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.

Installing
----------

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`.

.. code-block::
pip install dreimac
Contents
========

.. toctree::
:maxdepth: 2
:caption: About

theory
api
faq


.. toctree::
:maxdepth: 2
:caption: Choosing parameters

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

Further examples
----------------


.. toctree::
:maxdepth: 2
:caption: Circular coordinates

notebooks/coil20

.. toctree::
:maxdepth: 2
:caption: Toroidal coordinates

notebooks/bullseye
notebooks/genusTwoSurface

.. toctree::
:maxdepth: 2
:caption: Real projective coordinates

notebooks/ImagePatches

.. toctree::
:maxdepth: 2
:caption: Complex projective coordinates

notebooks/twoSphere
notebooks/movingDot

.. toctree::
:maxdepth: 2
:caption: Lens coordinates

notebooks/circleLensCoordinates
notebooks/MooreSpace

Authors
=======

Jose A. Perea, Luis Scoccola, Chris Tralie

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