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Diffstat (limited to 'src/python/doc')
| -rw-r--r-- | src/python/doc/_templates/layout.html | 1 | ||||
| -rw-r--r-- | src/python/doc/alpha_complex_ref.rst | 1 | ||||
| -rw-r--r-- | src/python/doc/alpha_complex_sum.inc | 24 | ||||
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 109 | ||||
| -rwxr-xr-x | src/python/doc/conf.py | 5 | ||||
| -rw-r--r-- | src/python/doc/datasets_generators.inc | 14 | ||||
| -rw-r--r-- | src/python/doc/datasets_generators.rst | 105 | ||||
| -rw-r--r-- | src/python/doc/examples.rst | 1 | ||||
| -rw-r--r-- | src/python/doc/img/sphere_3d.png | bin | 0 -> 529148 bytes | |||
| -rw-r--r-- | src/python/doc/index.rst | 5 | ||||
| -rw-r--r-- | src/python/doc/installation.rst | 17 | ||||
| -rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 29 |
12 files changed, 256 insertions, 55 deletions
diff --git a/src/python/doc/_templates/layout.html b/src/python/doc/_templates/layout.html index cd40a51b..e074b6c7 100644 --- a/src/python/doc/_templates/layout.html +++ b/src/python/doc/_templates/layout.html @@ -194,6 +194,7 @@ <li><a href="/relatedprojects/">Related projects</a></li> <li><a href="/theyaretalkingaboutus/">They are talking about us</a></li> <li><a href="/inaction/">GUDHI in action</a></li> + <li><a href="/etymology/">Etymology</a></li> </ul> </li> <li class="divider"></li> diff --git a/src/python/doc/alpha_complex_ref.rst b/src/python/doc/alpha_complex_ref.rst index 7da79543..eaa72551 100644 --- a/src/python/doc/alpha_complex_ref.rst +++ b/src/python/doc/alpha_complex_ref.rst @@ -9,6 +9,5 @@ Alpha complex reference manual .. autoclass:: gudhi.AlphaComplex :members: :undoc-members: - :show-inheritance: .. automethod:: gudhi.AlphaComplex.__init__ diff --git a/src/python/doc/alpha_complex_sum.inc b/src/python/doc/alpha_complex_sum.inc index aeab493f..5c76fd54 100644 --- a/src/python/doc/alpha_complex_sum.inc +++ b/src/python/doc/alpha_complex_sum.inc @@ -1,15 +1,15 @@ .. table:: :widths: 30 40 30 - +----------------------------------------------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------+ - | .. figure:: | Alpha complex is a simplicial complex constructed from the finite | :Author: Vincent Rouvreau | - | ../../doc/Alpha_complex/alpha_complex_representation.png | cells of a Delaunay Triangulation. It has the same persistent homology | | - | :alt: Alpha complex representation | as the Čech complex and is significantly smaller. | :Since: GUDHI 2.0.0 | - | :figclass: align-center | | | - | | | :License: MIT (`GPL v3 </licensing/>`_) | - | | | | - | | | :Requires: `Eigen <installation.html#eigen>`_ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`_ :math:`\geq` 4.11.0 | - | | | | - +----------------------------------------------------------------+-------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------+ - | * :doc:`alpha_complex_user` | * :doc:`alpha_complex_ref` | - +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ + +----------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+ + | .. figure:: | Alpha complex is a simplicial complex constructed from the finite | :Author: Vincent Rouvreau | + | ../../doc/Alpha_complex/alpha_complex_representation.png | cells of a Delaunay Triangulation. It has the same persistent homology | | + | :alt: Alpha complex representation | as the Čech complex and is significantly smaller. | :Since: GUDHI 2.0.0 | + | :figclass: align-center | | | + | | | :License: MIT (`GPL v3 </licensing/>`_) | + | | | | + | | | :Requires: `Eigen <installation.html#eigen>`_ :math:`\geq` 3.1.0 and `CGAL <installation.html#cgal>`_ :math:`\geq` 5.1 | + | | | | + +----------------------------------------------------------------+-------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------+ + | * :doc:`alpha_complex_user` | * :doc:`alpha_complex_ref` | + +----------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index fffcb3db..cfd22742 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -9,7 +9,7 @@ Definition .. include:: alpha_complex_sum.inc -:doc:`AlphaComplex <alpha_complex_ref>` is constructing a :doc:`SimplexTree <simplex_tree_ref>` using +:class:`~gudhi.AlphaComplex` is constructing a :doc:`SimplexTree <simplex_tree_ref>` using `Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ :cite:`cgal:hdj-t-19b` from the `Computational Geometry Algorithms Library <http://www.cgal.org/>`_ :cite:`cgal:eb-19b`. @@ -33,9 +33,6 @@ Remarks Using :code:`precision = 'fast'` makes the computations slightly faster, and the combinatorics are still exact, but the computation of filtration values can exceptionally be arbitrarily bad. In all cases, we still guarantee that the output is a valid filtration (faces have a filtration value no larger than their cofaces). -* For performances reasons, it is advised to use Alpha_complex with `CGAL <installation.html#cgal>`_ :math:`\geq` 5.0.0. -* The vertices in the output simplex tree are not guaranteed to match the order of the input points. One can use - :func:`~gudhi.AlphaComplex.get_point` to get the initial point back. Example from points ------------------- @@ -44,23 +41,22 @@ This example builds the alpha-complex from the given points: .. testcode:: - import gudhi - alpha_complex = gudhi.AlphaComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]]) + from gudhi import AlphaComplex + ac = AlphaComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]]) + + stree = ac.create_simplex_tree() + print('Alpha complex is of dimension ', stree.dimension(), ' - ', + stree.num_simplices(), ' simplices - ', stree.num_vertices(), ' vertices.') - simplex_tree = alpha_complex.create_simplex_tree() - result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ - repr(simplex_tree.num_simplices()) + ' simplices - ' + \ - repr(simplex_tree.num_vertices()) + ' vertices.' - print(result_str) fmt = '%s -> %.2f' - for filtered_value in simplex_tree.get_filtration(): + for filtered_value in stree.get_filtration(): print(fmt % tuple(filtered_value)) The output is: .. testoutput:: - Alpha complex is of dimension 2 - 25 simplices - 7 vertices. + Alpha complex is of dimension 2 - 25 simplices - 7 vertices. [0] -> 0.00 [1] -> 0.00 [2] -> 0.00 @@ -163,7 +159,10 @@ As the squared radii computed by CGAL are an approximation, it might happen that :math:`\alpha^2` values do not quite define a proper filtration (i.e. non-decreasing with respect to inclusion). We fix that up by calling :func:`~gudhi.SimplexTree.make_filtration_non_decreasing` (cf. -`C++ version <http://gudhi.gforge.inria.fr/doc/latest/index.html>`_). +`C++ version <https://gudhi.inria.fr/doc/latest/class_gudhi_1_1_simplex__tree.html>`_). + +.. note:: + This is not the case in `exact` version, this is the reason why it is not called in this case. Prune above given filtration value ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -174,11 +173,75 @@ of speed-up, since we always first build the full filtered complex, so it is rec :paramref:`~gudhi.AlphaComplex.create_simplex_tree.max_alpha_square`. In the following example, a threshold of :math:`\alpha^2 = 32.0` is used. +Weighted version +^^^^^^^^^^^^^^^^ + +A weighted version for Alpha complex is available. It is like a usual Alpha complex, but based on a +`CGAL regular triangulation <https://doc.cgal.org/latest/Triangulation/index.html#title20>`_. + +This example builds the weighted alpha-complex of a small molecule, where atoms have different sizes. +It is taken from +`CGAL 3d weighted alpha shapes <https://doc.cgal.org/latest/Alpha_shapes_3/index.html#title13>`_. + +Then, it is asked to display information about the alpha complex. + +.. testcode:: + + from gudhi import AlphaComplex + wgt_ac = AlphaComplex(points=[[ 1., -1., -1.], + [-1., 1., -1.], + [-1., -1., 1.], + [ 1., 1., 1.], + [ 2., 2., 2.]], + weights = [4., 4., 4., 4., 1.]) + + stree = wgt_ac.create_simplex_tree() + print('Weighted alpha complex is of dimension ', stree.dimension(), ' - ', + stree.num_simplices(), ' simplices - ', stree.num_vertices(), ' vertices.') + fmt = '%s -> %.2f' + for simplex in stree.get_simplices(): + print(fmt % tuple(simplex)) + +The output is: + +.. testoutput:: + + Weighted alpha complex is of dimension 3 - 29 simplices - 5 vertices. + [0, 1, 2, 3] -> -1.00 + [0, 1, 2] -> -1.33 + [0, 1, 3, 4] -> 95.00 + [0, 1, 3] -> -1.33 + [0, 1, 4] -> 95.00 + [0, 1] -> -2.00 + [0, 2, 3, 4] -> 95.00 + [0, 2, 3] -> -1.33 + [0, 2, 4] -> 95.00 + [0, 2] -> -2.00 + [0, 3, 4] -> 23.00 + [0, 3] -> -2.00 + [0, 4] -> 23.00 + [0] -> -4.00 + [1, 2, 3, 4] -> 95.00 + [1, 2, 3] -> -1.33 + [1, 2, 4] -> 95.00 + [1, 2] -> -2.00 + [1, 3, 4] -> 23.00 + [1, 3] -> -2.00 + [1, 4] -> 23.00 + [1] -> -4.00 + [2, 3, 4] -> 23.00 + [2, 3] -> -2.00 + [2, 4] -> 23.00 + [2] -> -4.00 + [3, 4] -> -1.00 + [3] -> -4.00 + [4] -> -1.00 Example from OFF file ^^^^^^^^^^^^^^^^^^^^^ -This example builds the alpha complex from 300 random points on a 2-torus. +This example builds the alpha complex from 300 random points on a 2-torus, given by an +`OFF file <fileformats.html#off-file-format>`_. Then, it computes the persistence diagram and displays it: @@ -186,14 +249,10 @@ Then, it computes the persistence diagram and displays it: :include-source: import matplotlib.pyplot as plt - import gudhi - alpha_complex = gudhi.AlphaComplex(off_file=gudhi.__root_source_dir__ + \ - '/data/points/tore3D_300.off') - simplex_tree = alpha_complex.create_simplex_tree() - result_str = 'Alpha complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \ - repr(simplex_tree.num_simplices()) + ' simplices - ' + \ - repr(simplex_tree.num_vertices()) + ' vertices.' - print(result_str) - diag = simplex_tree.persistence() - gudhi.plot_persistence_diagram(diag) + import gudhi as gd + off_file = gd.__root_source_dir__ + '/data/points/tore3D_300.off' + points = gd.read_points_from_off_file(off_file = off_file) + stree = gd.AlphaComplex(points = points).create_simplex_tree() + dgm = stree.persistence() + gd.plot_persistence_diagram(dgm, legend = True) plt.show() diff --git a/src/python/doc/conf.py b/src/python/doc/conf.py index b06baf9c..e69e2751 100755 --- a/src/python/doc/conf.py +++ b/src/python/doc/conf.py @@ -120,15 +120,12 @@ pygments_style = 'sphinx' # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. -html_theme = 'classic' +html_theme = 'python_docs_theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. html_theme_options = { - "sidebarbgcolor": "#A1ADCD", - "sidebartextcolor": "black", - "sidebarlinkcolor": "#334D5C", "body_max_width": "100%", } diff --git a/src/python/doc/datasets_generators.inc b/src/python/doc/datasets_generators.inc new file mode 100644 index 00000000..8d169275 --- /dev/null +++ b/src/python/doc/datasets_generators.inc @@ -0,0 +1,14 @@ +.. table:: + :widths: 30 40 30 + + +-----------------------------------+--------------------------------------------+--------------------------------------------------------------------------------------+ + | .. figure:: | Datasets generators (points). | :Authors: Hind Montassif | + | img/sphere_3d.png | | | + | | | :Since: GUDHI 3.5.0 | + | | | | + | | | :License: MIT (`LGPL v3 </licensing/>`_) | + | | | | + | | | :Requires: `CGAL <installation.html#cgal>`_ | + +-----------------------------------+--------------------------------------------+--------------------------------------------------------------------------------------+ + | * :doc:`datasets_generators` | + +-----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+ diff --git a/src/python/doc/datasets_generators.rst b/src/python/doc/datasets_generators.rst new file mode 100644 index 00000000..260c3882 --- /dev/null +++ b/src/python/doc/datasets_generators.rst @@ -0,0 +1,105 @@ + +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +=========================== +Datasets generators manual +=========================== + +We provide the generation of different customizable datasets to use as inputs for Gudhi complexes and data structures. + + +Points generators +------------------ + +The module **points** enables the generation of random points on a sphere, random points on a torus and as a grid. + +Points on sphere +^^^^^^^^^^^^^^^^ + +The function **sphere** enables the generation of random i.i.d. points uniformly on a (d-1)-sphere in :math:`R^d`. +The user should provide the number of points to be generated on the sphere :code:`n_samples` and the ambient dimension :code:`ambient_dim`. +The :code:`radius` of sphere is optional and is equal to **1** by default. +Only random points generation is currently available. + +The generated points are given as an array of shape :math:`(n\_samples, ambient\_dim)`. + +Example +""""""" + +.. code-block:: python + + from gudhi.datasets.generators import points + from gudhi import AlphaComplex + + # Generate 50 points on a sphere in R^2 + gen_points = points.sphere(n_samples = 50, ambient_dim = 2, radius = 1, sample = "random") + + # Create an alpha complex from the generated points + alpha_complex = AlphaComplex(points = gen_points) + +.. autofunction:: gudhi.datasets.generators.points.sphere + +Points on a flat torus +^^^^^^^^^^^^^^^^^^^^^^ + +You can also generate points on a torus. + +Two functions are available and give the same output: the first one depends on **CGAL** and the second does not and consists of full python code. + +On another hand, two sample types are provided: you can either generate i.i.d. points on a d-torus in :math:`R^{2d}` *randomly* or on a *grid*. + +First function: **ctorus** +""""""""""""""""""""""""""" + +The user should provide the number of points to be generated on the torus :code:`n_samples`, and the dimension :code:`dim` of the torus on which points would be generated in :math:`R^{2dim}`. +The :code:`sample` argument is optional and is set to **'random'** by default. +In this case, the returned generated points would be an array of shape :math:`(n\_samples, 2*dim)`. +Otherwise, if set to **'grid'**, the points are generated on a grid and would be given as an array of shape: + +.. math:: + + ( ⌊n\_samples^{1 \over {dim}}⌋^{dim}, 2*dim ) + +**Note 1:** The output array first shape is rounded down to the closest perfect :math:`dim^{th}` power. + +**Note 2:** This version is recommended when the user wishes to use **'grid'** as sample type, or **'random'** with a relatively small number of samples (~ less than 150). + +Example +""""""" +.. code-block:: python + + from gudhi.datasets.generators import points + + # Generate 50 points randomly on a torus in R^6 + gen_points = points.ctorus(n_samples = 50, dim = 3) + + # Generate 27 points on a torus as a grid in R^6 + gen_points = points.ctorus(n_samples = 50, dim = 3, sample = 'grid') + +.. autofunction:: gudhi.datasets.generators.points.ctorus + +Second function: **torus** +""""""""""""""""""""""""""" + +The user should provide the number of points to be generated on the torus :code:`n_samples` and the dimension :code:`dim` of the torus on which points would be generated in :math:`R^{2dim}`. +The :code:`sample` argument is optional and is set to **'random'** by default. +The other allowed value of sample type is **'grid'**. + +**Note:** This version is recommended when the user wishes to use **'random'** as sample type with a great number of samples and a low dimension. + +Example +""""""" +.. code-block:: python + + from gudhi.datasets.generators import points + + # Generate 50 points randomly on a torus in R^6 + gen_points = points.torus(n_samples = 50, dim = 3) + + # Generate 27 points on a torus as a grid in R^6 + gen_points = points.torus(n_samples = 50, dim = 3, sample = 'grid') + + +.. autofunction:: gudhi.datasets.generators.points.torus diff --git a/src/python/doc/examples.rst b/src/python/doc/examples.rst index 76e5d4c7..1442f185 100644 --- a/src/python/doc/examples.rst +++ b/src/python/doc/examples.rst @@ -8,6 +8,7 @@ Examples .. only:: builder_html * :download:`alpha_complex_diagram_persistence_from_off_file_example.py <../example/alpha_complex_diagram_persistence_from_off_file_example.py>` + * :download:`alpha_complex_from_generated_points_on_sphere_example.py <../example/alpha_complex_from_generated_points_on_sphere_example.py>` * :download:`alpha_complex_from_points_example.py <../example/alpha_complex_from_points_example.py>` * :download:`alpha_rips_persistence_bottleneck_distance.py <../example/alpha_rips_persistence_bottleneck_distance.py>` * :download:`bottleneck_basic_example.py <../example/bottleneck_basic_example.py>` diff --git a/src/python/doc/img/sphere_3d.png b/src/python/doc/img/sphere_3d.png Binary files differnew file mode 100644 index 00000000..70f3184f --- /dev/null +++ b/src/python/doc/img/sphere_3d.png diff --git a/src/python/doc/index.rst b/src/python/doc/index.rst index 040e57a4..2d7921ae 100644 --- a/src/python/doc/index.rst +++ b/src/python/doc/index.rst @@ -91,3 +91,8 @@ Clustering ********** .. include:: clustering.inc + +Datasets generators +******************* + +.. include:: datasets_generators.inc diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index 9c16b04e..35c344e3 100644 --- a/src/python/doc/installation.rst +++ b/src/python/doc/installation.rst @@ -194,8 +194,10 @@ A complete configuration would be : Documentation ============= -To build the documentation, `sphinx-doc <http://www.sphinx-doc.org>`_ and -`sphinxcontrib-bibtex <https://sphinxcontrib-bibtex.readthedocs.io>`_ are +To build the documentation, `sphinx-doc <http://www.sphinx-doc.org>`_, +`sphinxcontrib-bibtex <https://sphinxcontrib-bibtex.readthedocs.io>`_, +`sphinxcontrib-paramlinks <https://github.com/sqlalchemyorg/sphinx-paramlinks>`_ and +`python-docs-theme <https://github.com/python/python-docs-theme>`_ are required. As the documentation is auto-tested, `CGAL`_, `Eigen`_, `Matplotlib`_, `NumPy`_, `POT`_, `Scikit-learn`_ and `SciPy`_ are also mandatory to build the documentation. @@ -357,7 +359,7 @@ Python Optimal Transport ------------------------ The :doc:`Wasserstein distance </wasserstein_distance_user>` -module requires `POT <https://pot.readthedocs.io/>`_, a library that provides +module requires `POT <https://pythonot.github.io/>`_, a library that provides several solvers for optimization problems related to Optimal Transport. PyTorch @@ -396,8 +398,9 @@ TensorFlow Bug reports and contributions ***************************** -Please help us improving the quality of the GUDHI library. You may report bugs or suggestions to: +Please help us improving the quality of the GUDHI library. +You may `report bugs <https://github.com/GUDHI/gudhi-devel/issues>`_ or +`contact us <https://gudhi.inria.fr/contact/>`_ for any suggestions. - Contact: gudhi-users@lists.gforge.inria.fr - -GUDHI is open to external contributions. If you want to join our development team, please contact us. +GUDHI is open to external contributions. If you want to join our development team, please take some time to read our +`contributing guide <https://github.com/GUDHI/gudhi-devel/blob/master/.github/CONTRIBUTING.md>`_. diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index 9ffc2759..76eb1469 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -44,7 +44,7 @@ Basic example ************* This example computes the 1-Wasserstein distance from 2 persistence diagrams with Euclidean ground metric. -Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values. +Note that persistence diagrams must be submitted as (n x 2) numpy arrays. .. testcode:: @@ -67,14 +67,16 @@ We can also have access to the optimal matching by letting `matching=True`. It is encoded as a list of indices (i,j), meaning that the i-th point in X is mapped to the j-th point in Y. An index of -1 represents the diagonal. +It handles essential parts (points with infinite coordinates). However if the cardinalities of the essential parts differ, +any matching has a cost +inf and thus can be considered to be optimal. In such a case, the function returns `(np.inf, None)`. .. testcode:: import gudhi.wasserstein import numpy as np - dgm1 = np.array([[2.7, 3.7],[9.6, 14.],[34.2, 34.974]]) - dgm2 = np.array([[2.8, 4.45], [5, 6], [9.5, 14.1]]) + dgm1 = np.array([[2.7, 3.7],[9.6, 14.],[34.2, 34.974], [3, np.inf]]) + dgm2 = np.array([[2.8, 4.45], [5, 6], [9.5, 14.1], [4, np.inf]]) cost, matchings = gudhi.wasserstein.wasserstein_distance(dgm1, dgm2, matching=True, order=1, internal_p=2) message_cost = "Wasserstein distance value = %.2f" %cost @@ -90,16 +92,31 @@ An index of -1 represents the diagonal. for j in dgm2_to_diagonal: print("point %s in dgm2 is matched to the diagonal" %j) -The output is: + # An example where essential part cardinalities differ + dgm3 = np.array([[1, 2], [0, np.inf]]) + dgm4 = np.array([[1, 2], [0, np.inf], [1, np.inf]]) + cost, matchings = gudhi.wasserstein.wasserstein_distance(dgm3, dgm4, matching=True, order=1, internal_p=2) + print("\nSecond example:") + print("cost:", cost) + print("matchings:", matchings) + + +The output is: .. testoutput:: - Wasserstein distance value = 2.15 + Wasserstein distance value = 3.15 point 0 in dgm1 is matched to point 0 in dgm2 point 1 in dgm1 is matched to point 2 in dgm2 + point 3 in dgm1 is matched to point 3 in dgm2 point 2 in dgm1 is matched to the diagonal point 1 in dgm2 is matched to the diagonal + Second example: + cost: inf + matchings: None + + Barycenters ----------- @@ -181,4 +198,4 @@ 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.
\ No newline at end of file +presents the concept of barycenter, or Fréchet mean, of a family of persistence diagrams. |
