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:orphan:
.. To get rid of WARNING: document isn't included in any toctree
=============================
Rips complex reference manual
=============================
.. autoclass:: gudhi.RipsComplex
:members:
:undoc-members:
:show-inheritance:
.. automethod:: gudhi.RipsComplex.__init__
======================================
Weighted Rips complex reference manual
======================================
.. autoclass:: gudhi.WeightedRipsComplex
:members:
:undoc-members:
:show-inheritance:
.. automethod:: gudhi.WeightedRipsComplex.__init__
Basic examples
-------------
The following example computes the weighted Rips filtration associated with a distance matrix and weights on vertices.
.. testcode::
from gudhi.weighted_rips_complex import WeightedRipsComplex
dist = [[], [1]]
weights = [1, 100]
w_rips = WeightedRipsComplex(distance_matrix=dist, weights=weights)
st = w_rips.create_simplex_tree(max_dimension=2)
print(st.get_filtration())
The output is:
.. testoutput::
[([0], 2.0), ([1], 200.0), ([0, 1], 200.0)]
Combining with DistanceToMeasure, one can compute the DTM-filtration of a point set, as in `this notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-DTM-filtrations.ipynb>`_.
.. testcode::
import numpy as np
from scipy.spatial.distance import cdist
from gudhi.point_cloud.dtm import DistanceToMeasure
from gudhi.weighted_rips_complex import WeightedRipsComplex
pts = np.array([[2.0, 2.0], [0.0, 1.0], [3.0, 4.0]])
dist = cdist(pts,pts)
dtm = DistanceToMeasure(2, q=2, metric="precomputed")
r = dtm.fit_transform(dist)
w_rips = WeightedRipsComplex(distance_matrix=dist, weights=r)
st = w_rips.create_simplex_tree(max_dimension=2)
print(st.persistence())
.. testoutput::
[(0, (3.1622776601683795, inf)), (0, (3.1622776601683795, 5.39834563766817)), (0, (3.1622776601683795, 5.39834563766817))]
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