topopy

topopy

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.. logo

.. image:: docs/_static/topopy.png :align: center :alt: topopy

.. end_logo

.. introduction

A library for computing topological data structures stemming from Morse Theory. Given a set of arbitrarily arranged points in any dimension, this library is able to construct approximate topological structures using a neighborhood graph to simulate manifold structures.

.. end_introduction

.. installation

Installation

Currently, you can use pip_ to install this package
and all of its prerequisite libraries::

    pip install topopy

.. _pip: https://pip.pypa.io/en/stable/

Or to install from source, install all of the prerequiste libraries:

* scipy_
* numpy_
* scikit-learn_
* networkx_
* nglpy_

.. _scipy: https://www.scipy.org/
.. _numpy: http://www.numpy.org/
.. _scikit-learn: http://scikit-learn.org/)
.. _networkx: https://networkx.github.io/
.. _nglpy: https://github.com/maljovec/nglpy


And then clone and build the source repository::

    git clone https://github.com/maljovec/topopy.git
    cd topopy
    make
    python setup.py [develop|install]

.. end_installation

.. usage

Example Usage

::

import nglpy as ngl
import numpy as np
import topopy

def hill(_x):
    _x = np.atleast_2d(_x)
    x = _x[:, 0]
    y = _x[:, 1]
    return np.exp(- ((x - .55)**2 + (y-.75)**2)/.125) + 0.01*(x+y)

X = np.random.rand(100,2)
Y = hill(X)
graph = ngl.EmptyRegionGraph(beta=1.0, relaxed=False, p=2.0)

msc = topopy.MorseSmaleComplex(graph=graph,
                               gradient='steepest',
                               normalization='feature')
msc.build(X, Y)
msc.get_partitions()

.. end_usage