Merge branch 'develop'

Author: devmessias

docs/Makefile

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+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?=
+SPHINXBUILD   ?= sphinx-build
+SOURCEDIR     = source
+BUILDDIR      = build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

docs/make.bat

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+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.http://sphinx-doc.org/
+	exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd

docs/source/conf.py

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+import os
+import sys
+sys.path.insert(0, os.path.abspath('../..'))
+sys.path.insert(0, os.path.abspath('..'))
+sys.setrecursionlimit(1500)
+
+# -- Project information -----------------------------------------------------
+
+project = 'eMaTe'
+copyright = '2019, Bruno Messias; Thomas Peron'
+author = 'Bruno Messias; Thomas Peron'
+
+# The short X.Y version
+version = ''
+# The full version, including alpha/beta/rc tags
+release = '1.0.3'
+
+
+# -- General configuration ---------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+#
+# needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = [
+    'sphinx.ext.autodoc',
+   # 'sphinx.ext.intersphinx',
+    'sphinx.ext.todo',
+    'sphinx.ext.mathjax',
+    'sphinx.ext.ifconfig',
+    'sphinx.ext.viewcode',
+    'sphinx.ext.githubpages',
+    'sphinxcontrib.napoleon',
+   # 'sphinx.ext.napoleon',
+]
+napoleon_google_docstring = False
+
+napoleon_numpy_docstring = True
+napoleon_include_init_with_doc = True
+napoleon_include_private_with_doc = False
+napoleon_include_special_with_doc = True
+napoleon_use_admonition_for_examples = True
+napoleon_use_admonition_for_notes = True
+napoleon_use_admonition_for_references = True
+napoleon_use_ivar = True
+napoleon_use_param = True
+napoleon_use_rtype = True
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix(es) of source filenames.
+# You can specify multiple suffix as a list of string:
+#
+# source_suffix = ['.rst', '.md']
+source_suffix = '.rst'
+
+# The master toctree document.
+master_doc = 'index'
+html_logo = "imgs/logo_100.png"
+html_favicon = "imgs/logo_36.ico"
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#
+# This is also used if you do content translation via gettext catalogs.
+# Usually you set "language" from the command line for these cases.
+language = None
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This pattern also affects html_static_path and html_extra_path.
+exclude_patterns = []
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = None
+
+
+# -- Options for HTML output -------------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+
+html_theme = 'sphinx_rtd_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 = {}
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# Custom sidebar templates, must be a dictionary that maps document names
+# to template names.
+#
+# The default sidebars (for documents that don't match any pattern) are
+# defined by theme itself.  Builtin themes are using these templates by
+# default: ``['localtoc.html', 'relations.html', 'sourcelink.html',
+# 'searchbox.html']``.
+#
+# html_sidebars = {}
+
+
+# -- Options for HTMLHelp output ---------------------------------------------
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'eMaTedoc'
+
+
+# -- Options for LaTeX output ------------------------------------------------
+
+latex_elements = {
+    # The paper size ('letterpaper' or 'a4paper').
+    #
+    # 'papersize': 'letterpaper',
+
+    # The font size ('10pt', '11pt' or '12pt').
+    #
+    # 'pointsize': '10pt',
+
+    # Additional stuff for the LaTeX preamble.
+    #
+    # 'preamble': '',
+
+    # Latex figure (float) alignment
+    #
+    # 'figure_align': 'htbp',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+#  author, documentclass [howto, manual, or own class]).
+latex_documents = [
+    (master_doc, 'eMaTe.tex', 'eMaTe Documentation',
+     'Bruno Messias; Thomas Peron', 'manual'),
+]
+
+
+# -- Options for manual page output ------------------------------------------
+
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+man_pages = [
+    (master_doc, 'emate', 'eMaTe Documentation',
+     [author], 1)
+]
+
+
+# -- Options for Texinfo output ----------------------------------------------
+
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+#  dir menu entry, description, category)
+texinfo_documents = [
+    (master_doc, 'eMaTe', 'eMaTe Documentation',
+     author, 'eMaTe', 'One line description of project.',
+     'Miscellaneous'),
+]
+
+
+# -- Options for Epub output -------------------------------------------------
+
+# Bibliographic Dublin Core info.
+epub_title = project
+
+# The unique identifier of the text. This can be a ISBN number
+# or the project homepage.
+#
+# epub_identifier = ''
+
+# A unique identification for the text.
+#
+# epub_uid = ''
+
+# A list of files that should not be packed into the epub file.
+epub_exclude_files = ['search.html']
+
+
+# -- Extension configuration -------------------------------------------------
+
+# -- Options for intersphinx extension ---------------------------------------
+
+# Example configuration for intersphinx: refer to the Python standard library.
+#intersphinx_mapping = {'https://docs.python.org/': None}
+
+# -- Options for todo extension ----------------------------------------------
+
+# If true, `todo` and `todoList` produce output, else they produce nothing.
+todo_include_todos = True

docs/source/examples.rst

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+========
+Examples
+========
+
+Kernel Polynomial Method (Chebyshev Polynomial expansion) 
+=========================================================
+
+
+The Kernel Polynomial Method can estimate the spectral density of large
+sparse Hermitan matrices with a low computational cost. This method
+combines three key ingredients: the Chebyshev expansion + the stochastic
+trace estimator + kernel smoothing.
+
+
+.. code-block:: python
+
+    import igraph as ig
+    import numpy as np
+
+    N = 3000
+    G = ig.Graph.Erdos_Renyi(N, 3/N)
+
+    W = np.array(G.get_adjacency().data, dtype=np.float64)
+    vals = np.linalg.eigvalsh(W).real
+
+.. code-block:: python
+
+    from emate.hermitian import pykpm
+    from stdog.utils.misc import ig2sparse 
+
+    W = ig2sparse(G)
+
+    num_moments = 300
+    num_vecs = 200
+    extra_points = 10
+    ek, rho = pykpm(W, num_moments, num_vecs, extra_points)
+
+.. code-block:: python
+
+    import matplotlib.pyplot as plt
+    plt.hist(vals, density=True, bins=100, alpha=.9, color="steelblue")
+    plt.scatter(ek, rho, c="tomato", zorder=999, alpha=0.9, marker="d")
+    plt.ylim(0, 1)
+    plt.show()
+
+
+.. image:: imgs/kpm.png
+
+References
+----------
+
+    [1] Wang, L.W., 1994. Calculating the density of states and
+    optical-absorption spectra of large quantum systems by the plane-wave moments
+    method. Physical Review B, 49(15), p.10154.
+
+    [2] Hutchinson, M.F., 1990. A stochastic estimator of the trace of the
+    influence matrix for laplacian smoothing splines. Communications in
+    Statistics-Simulation and Computation, 19(2), pp.433-450.
+
+
+
+Sthocastic Lanczos Quadrature
+=============================
+
+Given a semi-positive definite matrix :math:`A \in \mathbb R^{|V|\times|V|}`,
+which has the set of eigenvalues given by :math:`\{\lambda_i\}` a trace of
+a matrix function is given by
+
+.. math:: 
+
+    \mathrm{tr}(f(A)) = \sum\limits_{i=0}^{|V|} f(\lambda_i)
+
+The methods for calculating such traces functions have a
+cubic computational complexity lower bound,  :math:`O(|V|^3)`.
+Therefore, it is not feasible for  large networks. One way
+to overcome such computational complexity it is use stochastic approximations
+combined with a mryiad of another methods
+to get the results with enough accuracy and with a small computational cost. 
+The methods available in this module uses the Sthocastic Lanczos Quadrature, 
+a procedure proposed in the work made by Ubaru, S. et.al. [1] (you need to cite them).
+
+
+Estrada Index
+^^^^^^^^^^^^^^^^
+
+.. code-block:: python
+
+    import scipy
+    import scipy.sparse
+    import igraph as ig
+    import numpy as np
+
+    N = 3000
+    G = ig.Graph.Erdos_Renyi(N, 3/N) 
+
+.. code-block:: python
+
+    from emate.symmetric.slq import pyslq
+    import tensorflow as tf
+
+    def trace_function(eig_vals):
+        return tf.exp(eig_vals)
+
+    num_vecs = 100
+    num_steps = 50
+    approximated_estrada_index, _ = pyslq(L_sparse, num_vecs, num_steps,  trace_function)
+    exact_estrada_index =  np.sum(np.exp(vals_laplacian))
+    approximated_estrada_index, exact_estrada_index
+
+
+The above code returns
+
+.. code-block:: bash
+
+    (3058.012, 3063.16457163222)
+
+References
+----------
+
+    1 - Ubaru, S., Chen, J., & Saad, Y. (2017). Fast Estimation of tr(f(A)) via Stochastic Lanczos Quadrature. 
+    SIAM Journal on Matrix Analysis and Applications, 38(4), 1075-1099.
+
+    2 - Hutchinson, M. F. (1990). A stochastic estimator of the trace of the
+    influence matrix for laplacian smoothing splines. Communications in
+    Statistics-Simulation and Computation, 19(2), 433-450.

docs/source/hermitian.rst

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+==========
+Hermitian
+==========
+
+.. automodule:: emate.hermitian.kpm
+	:members:
+
+
+