diff options
Diffstat (limited to 'src/python/doc/barycenter_user.rst')
-rw-r--r-- | src/python/doc/barycenter_user.rst | 60 |
1 files changed, 60 insertions, 0 deletions
diff --git a/src/python/doc/barycenter_user.rst b/src/python/doc/barycenter_user.rst new file mode 100644 index 00000000..83e9bebb --- /dev/null +++ b/src/python/doc/barycenter_user.rst @@ -0,0 +1,60 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +Barycenter user manual +================================ +Definition +---------- + +.. include:: barycenter_sum.inc + +This implementation is based on ideas from "Frechet means for distribution of +persistence diagrams", Turner et al. 2014. + +Function +-------- +.. autofunction:: gudhi.barycenter.lagrangian_barycenter + + +Basic example +------------- + +This example computes the Frechet mean (aka Wasserstein barycenter) between +four persistence diagrams. +It is initialized on the 4th diagram. +As the algorithm is not convex, its output depends on the initialization and +is only a local minimum of the objective function. +Initialization can be either given as an integer (in which case the i-th +diagram of the list is used as initial estimate) or as a diagram. +If None, it will randomly select one of the diagram of the list +as initial estimate. +Note that persistence diagrams must be submitted as +(n x 2) numpy arrays and must not contain inf values. + +.. testcode:: + + import gudhi.barycenter + import numpy as np + + dg1 = np.array([[0.2, 0.5]]) + dg2 = np.array([[0.2, 0.7]]) + dg3 = np.array([[0.3, 0.6], [0.7, 0.8], [0.2, 0.3]]) + dg4 = np.array([]) + pdiagset = [dg1, dg2, dg3, dg4] + bary = gudhi.barycenter.lagrangian_barycenter(pdiagset=pdiagset,init=3) + + message = "Wasserstein barycenter estimated:" + print(message) + print(bary) + +The output is: + +.. testoutput:: + + Wasserstein barycenter estimated: + [[0.27916667 0.55416667] + [0.7375 0.7625 ] + [0.2375 0.2625 ]] + + |