diff options
Diffstat (limited to 'src/python/doc')
| -rw-r--r-- | src/python/doc/bottleneck_distance_user.rst | 4 | ||||
| -rwxr-xr-x | src/python/doc/conf.py | 2 | ||||
| -rw-r--r-- | src/python/doc/cubical_complex_user.rst | 22 | ||||
| -rw-r--r-- | src/python/doc/installation.rst | 9 | ||||
| -rw-r--r-- | src/python/doc/representations.rst | 64 | ||||
| -rw-r--r-- | src/python/doc/rips_complex_sum.inc | 22 | ||||
| -rw-r--r-- | src/python/doc/rips_complex_user.rst | 6 | ||||
| -rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 7 |
8 files changed, 83 insertions, 53 deletions
diff --git a/src/python/doc/bottleneck_distance_user.rst b/src/python/doc/bottleneck_distance_user.rst index 6c6e08d9..7baa76cc 100644 --- a/src/python/doc/bottleneck_distance_user.rst +++ b/src/python/doc/bottleneck_distance_user.rst @@ -47,7 +47,7 @@ The following example explains how the distance is computed: :figclass: align-center The point (0, 13) is at distance 6.5 from the diagonal and more - specifically from the point (6.5, 6.5) + specifically from the point (6.5, 6.5). Basic example @@ -72,6 +72,6 @@ The output is: .. testoutput:: - Bottleneck distance approximation = 0.81 + Bottleneck distance approximation = 0.72 Bottleneck distance value = 0.75 diff --git a/src/python/doc/conf.py b/src/python/doc/conf.py index 3cc5d1d6..b06baf9c 100755 --- a/src/python/doc/conf.py +++ b/src/python/doc/conf.py @@ -44,6 +44,8 @@ extensions = [ 'sphinx_paramlinks', ] +bibtex_bibfiles = ['../../biblio/bibliography.bib'] + todo_include_todos = True # plot option : do not show hyperlinks (Source code, png, hires.png, pdf) plot_html_show_source_link = False diff --git a/src/python/doc/cubical_complex_user.rst b/src/python/doc/cubical_complex_user.rst index 3fd4e27a..6a211347 100644 --- a/src/python/doc/cubical_complex_user.rst +++ b/src/python/doc/cubical_complex_user.rst @@ -47,8 +47,8 @@ be a set of two elements). For further details and theory of cubical complexes, please consult :cite:`kaczynski2004computational` as well as the following paper :cite:`peikert2012topological`. -Data structure. ---------------- +Data structure +-------------- The implementation of Cubical complex provides a representation of complexes that occupy a rectangular region in :math:`\mathbb{R}^n`. This extra assumption allows for a memory efficient way of storing cubical complexes in a form @@ -77,8 +77,8 @@ Knowing the sizes of the bitmap, by a series of modulo operation, we can determi present in the product that gives the cube :math:`C`. In a similar way, we can compute boundary and the coboundary of each cube. Further details can be found in the literature. -Input Format. -------------- +Input Format +------------ In the current implantation, filtration is given at the maximal cubes, and it is then extended by the lower star filtration to all cubes. There are a number of constructors that can be used to construct cubical complex by users @@ -108,8 +108,8 @@ the program output is: Cubical complex is of dimension 2 - 49 simplices. -Periodic boundary conditions. ------------------------------ +Periodic boundary conditions +---------------------------- Often one would like to impose periodic boundary conditions to the cubical complex (cf. :doc:`periodic_cubical_complex_ref`). @@ -154,7 +154,13 @@ the program output is: Periodic cubical complex is of dimension 2 - 42 simplices. -Examples. ---------- +Examples +-------- End user programs are available in python/example/ folder. + +Tutorial +-------- + +This `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-cubical-complexes.ipynb>`_ +explains how to represent sublevels sets of functions using cubical complexes.
\ No newline at end of file diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index 78e1af73..66efe45a 100644 --- a/src/python/doc/installation.rst +++ b/src/python/doc/installation.rst @@ -40,7 +40,7 @@ different, and in particular the `python/` subdirectory is actually `src/python/ there. The library uses c++14 and requires `Boost <https://www.boost.org/>`_ :math:`\geq` 1.56.0, -`CMake <https://www.cmake.org/>`_ :math:`\geq` 3.1 to generate makefiles, +`CMake <https://www.cmake.org/>`_ :math:`\geq` 3.5 to generate makefiles, `NumPy <http://numpy.org>`_, `Cython <https://www.cython.org/>`_ and `pybind11 <https://github.com/pybind/pybind11>`_ to compile the GUDHI Python module. @@ -65,7 +65,7 @@ one can build the GUDHI Python module, by running the following commands in a te cd /path-to-gudhi/ mkdir build cd build/ - cmake .. + cmake -DCMAKE_BUILD_TYPE=Release .. cd python make @@ -394,6 +394,11 @@ mathematics, science, and engineering. :class:`~gudhi.point_cloud.knn.KNearestNeighbors` can use the Python package `SciPy <http://scipy.org>`_ as a backend if explicitly requested. +TensorFlow +---------- + +`TensorFlow <https://www.tensorflow.org>`_ is currently only used in some automatic differentiation tests. + Bug reports and contributions ***************************** diff --git a/src/python/doc/representations.rst b/src/python/doc/representations.rst index 041e3247..b0477197 100644 --- a/src/python/doc/representations.rst +++ b/src/python/doc/representations.rst @@ -12,11 +12,45 @@ This module, originally available at https://github.com/MathieuCarriere/sklearn- A diagram is represented as a numpy array of shape (n,2), as can be obtained from :func:`~gudhi.SimplexTree.persistence_intervals_in_dimension` for instance. Points at infinity are represented as a numpy array of shape (n,1), storing only the birth time. The classes in this module can handle several persistence diagrams at once. In that case, the diagrams are provided as a list of numpy arrays. Note that it is not necessary for the diagrams to have the same number of points, i.e., for the corresponding arrays to have the same number of rows: all classes can handle arrays with different shapes. -A small example is provided +Examples +-------- -.. only:: builder_html +Landscapes +^^^^^^^^^^ - * :download:`diagram_vectorizations_distances_kernels.py <../example/diagram_vectorizations_distances_kernels.py>` +This example computes the first two Landscapes associated to a persistence diagram with four points. The landscapes are evaluated on ten samples, leading to two vectors with ten coordinates each, that are eventually concatenated in order to produce a single vector representation. + +.. testcode:: + + import numpy as np + from gudhi.representations import Landscape + # A single diagram with 4 points + D = np.array([[0.,4.],[1.,2.],[3.,8.],[6.,8.]]) + diags = [D] + l=Landscape(num_landscapes=2,resolution=10).fit_transform(diags) + print(l) + +The output is: + +.. testoutput:: + + [[1.02851895 2.05703791 2.57129739 1.54277843 0.89995409 1.92847304 + 2.95699199 3.08555686 2.05703791 1.02851895 0. 0.64282435 + 0. 0. 0.51425948 0. 0. 0. + 0.77138922 1.02851895]] + +Various kernels +^^^^^^^^^^^^^^^ + +This small example is also provided +:download:`diagram_vectorizations_distances_kernels.py <../example/diagram_vectorizations_distances_kernels.py>` + +Machine Learning and Topological Data Analysis +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +This `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-representations.ipynb>`_ explains how to +efficiently combine machine learning and topological data analysis with the +:doc:`representations module<representations>`. Preprocessing @@ -46,27 +80,3 @@ Metrics :members: :special-members: :show-inheritance: - -Basic example -------------- - -This example computes the first two Landscapes associated to a persistence diagram with four points. The landscapes are evaluated on ten samples, leading to two vectors with ten coordinates each, that are eventually concatenated in order to produce a single vector representation. - -.. testcode:: - - import numpy as np - from gudhi.representations import Landscape - # A single diagram with 4 points - D = np.array([[0.,4.],[1.,2.],[3.,8.],[6.,8.]]) - diags = [D] - l=Landscape(num_landscapes=2,resolution=10).fit_transform(diags) - print(l) - -The output is: - -.. testoutput:: - - [[1.02851895 2.05703791 2.57129739 1.54277843 0.89995409 1.92847304 - 2.95699199 3.08555686 2.05703791 1.02851895 0. 0.64282435 - 0. 0. 0.51425948 0. 0. 0. - 0.77138922 1.02851895]] diff --git a/src/python/doc/rips_complex_sum.inc b/src/python/doc/rips_complex_sum.inc index c123ea2a..2cb24990 100644 --- a/src/python/doc/rips_complex_sum.inc +++ b/src/python/doc/rips_complex_sum.inc @@ -1,14 +1,14 @@ .. table:: :widths: 30 40 30 - +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+ - | .. figure:: | The Vietoris-Rips complex is a simplicial complex built as the | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse | - | ../../doc/Rips_complex/rips_complex_representation.png | clique-complex of a proximity graph. | | - | :figclass: align-center | | :Since: GUDHI 2.0.0 | - | | We also provide sparse approximations, to speed-up the computation | | - | | of persistent homology, and weighted versions, which are more robust | :License: MIT | - | | to outliers. | | - | | | | - +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+ - | * :doc:`rips_complex_user` | * :doc:`rips_complex_ref` | - +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+ + | .. figure:: | The Vietoris-Rips complex is a simplicial complex built as the | :Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse, Yuichi Ike | + | ../../doc/Rips_complex/rips_complex_representation.png | clique-complex of a proximity graph. | | + | :figclass: align-center | | :Since: GUDHI 2.0.0 | + | | We also provide sparse approximations, to speed-up the computation | | + | | of persistent homology, and weighted versions, which are more robust | :License: MIT | + | | to outliers. | | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+ + | * :doc:`rips_complex_user` | * :doc:`rips_complex_ref` | + +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/rips_complex_user.rst b/src/python/doc/rips_complex_user.rst index 6048cc4e..27d218d4 100644 --- a/src/python/doc/rips_complex_user.rst +++ b/src/python/doc/rips_complex_user.rst @@ -7,9 +7,9 @@ Rips complex user manual Definition ---------- -==================================================================== ================================ ====================== -:Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse :Since: GUDHI 2.0.0 :License: GPL v3 -==================================================================== ================================ ====================== +================================================================================ ================================ ====================== +:Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau, Marc Glisse, Yuichi Ike :Since: GUDHI 2.0.0 :License: GPL v3 +================================================================================ ================================ ====================== +-------------------------------------------+----------------------------------------------------------------------+ | :doc:`rips_complex_user` | :doc:`rips_complex_ref` | diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 96ec7872..9ffc2759 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -175,3 +175,10 @@ The output is: [[0.27916667 0.55416667] [0.7375 0.7625 ] [0.2375 0.2625 ]] + +Tutorial +******** + +This +`notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-Barycenters-of-persistence-diagrams.ipynb>`_ +presents the concept of barycenter, or Fréchet mean, of a family of persistence diagrams.
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