import files

.gitignore

+*.py[co]
+
+# Packages
+*.egg
+*.egg-info
+dist
+build
+eggs
+parts
+bin
+var
+sdist
+develop-eggs
+.installed.cfg
+
+# Installer logs
+pip-log.txt
+
+# Mac OS X files
+.DS_Store
+.DS_Store?
+._*
+.Spotlight-V100
+.Trashes
+ehthumbs.db
+Thumbs.db
+
+# Sphinx stuff
+docs/generated/
+docs/build/
+
+# jupyter notebook
+.ipynb_checkpoints
+
+# coverage
+htmlcov
+.coverage
+
+# ide 
+.idea
+.spyderproject
+
+# Misc
+.cache
+.pytest_cache
+

.gitlab-ci.yml

+# run the test suite
+tests:
+    image: registry.gitlab.lis-lab.fr:5005/skmad-suite/madarrays/ubuntu:18.04
+    tags:
+        - docker
+    script:
+        - pip3 install --no-deps .
+        - pytest-3
+
+# generate the documentation
+pages:
+    image: registry.gitlab.lis-lab.fr:5005/skmad-suite/madarrays/ubuntu:18.04
+    tags:
+        - docker
+    only:
+        - master
+    script:
+        - pip3 install --no-deps .
+        - python3 setup.py build_sphinx
+        - cp -r build/sphinx/html public
+    artifacts:
+        paths:
+            - public
+

MANIFEST.in

+include *.txt
+include *.rst
+include VERSION
+recursive-include doc *.rst *.py *.ipynb
+
+include pomad/tests/*.py
+
+prune doc/build

README.rst

+pomad
+=====
+
+pomad: PrObabilistic MAtrix Decompositions from Halko et al., 2011
+
+Python implementation of algorithms from paper *Finding Structure
+with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix
+Decompositions*, by N. Halko, P. G. Martinsson and J. A. Tropp, SIAM review,
+53 (2), 2011.
+
+
+Install
+-------
+
+Install the current release with ``pip``::
+
+    pip install pomad
+
+For additional details, see doc/install.rst.
+
+Usage
+-----
+
+See the `documentation <http://templates.pages.lis-lab.fr/pomad/>`_.
+
+Bugs
+----
+
+Please report any bugs that you find through the `pomad GitLab project
+<https://gitlab.lis-lab.fr/valentin.emiya/pomad/issues>`_.
+
+You can also fork the repository and create a merge request.
+
+Source code
+-----------
+
+The source code of pomad is available via its `GitLab project
+<https://gitlab.lis-lab.fr/valentin.emiya/pomad>`_.
+
+You can clone the git repository of the project using the command::
+
+    git clone git@gitlab.lis-lab.fr:valentin.emiya/pomad.git
+
+Copyright © 2019-2020
+---------------------
+
+* `Laboratoire d'Informatique et Systèmes <http://www.lis-lab.fr/>`_
+* `Université d'Aix-Marseille <http://www.univ-amu.fr/>`_
+* `Centre National de la Recherche Scientifique <http://www.cnrs.fr/>`_
+* `Université de Toulon <http://www.univ-tln.fr/>`_
+
+Contributors
+------------
+
+* `Valentin Emiya <mailto:valentin.emiya@lis-lab.fr>`_
+
+License
+-------
+
+Released under the GNU General Public License version 3 or later
+(see `LICENSE.txt`).

VERSION

+pomad:0.1

doc/Makefile

+# Makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS    =
+SPHINXBUILD   = python -m sphinx 
+PAPER         =
+
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d build/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+
+.PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest epub
+
+help:
+	@echo "Please use \`make <target>' where <target> is one of"
+	@echo "  html      to make standalone HTML files"
+	@echo "  dirhtml   to make HTML files named index.html in directories"
+	@echo "  pickle    to make pickle files"
+	@echo "  epub       to make an epub"
+	@echo "  json      to make JSON files"
+	@echo "  htmlhelp  to make HTML files and a HTML help project"
+	@echo "  qthelp    to make HTML files and a qthelp project"
+	@echo "  latex     to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+	@echo "  changes   to make an overview of all changed/added/deprecated items"
+	@echo "  linkcheck to check all external links for integrity"
+	@echo "  doctest   to run all doctests embedded in the documentation (if enabled)"
+	@echo "  gitwash   to update the gitwash documentation"
+
+
+clean:
+	-rm -rf build/*
+	-rm -rf ghpages_build
+	-rm -rf auto_examples modules
+	-rm -rf reference/generated reference/algorithms/generated reference/classes/generated reference/readwrite/generated
+
+dist: html
+	test -d build/latex || make latex
+	make -C build/latex all-pdf
+	-rm -rf build/dist
+	(cd build/html; cp -r . ../../build/dist)
+	(cd build/dist && tar czf ../dist.tar.gz .)
+
+html:
+	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) build/html
+	@echo
+	@echo "Build finished. The HTML pages are in build/html."
+
+dirhtml:
+	$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) build/dirhtml
+	@echo
+	@echo "Build finished. The HTML pages are in build/dirhtml."
+
+pickle:
+	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) build/pickle
+	@echo
+	@echo "Build finished; now you can process the pickle files."
+
+json:
+	$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) build/json
+	@echo
+	@echo "Build finished; now you can process the JSON files."
+
+htmlhelp:
+	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) build/htmlhelp
+	@echo
+	@echo "Build finished; now you can run HTML Help Workshop with the" \
+	      ".hhp project file in build/htmlhelp."
+
+qthelp:
+	$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) build/qthelp
+	@echo
+	@echo "Build finished; now you can run "qcollectiongenerator" with the" \
+	      ".qhcp project file in build/qthelp, like this:"
+	@echo "# qcollectiongenerator build/qthelp/test.qhcp"
+	@echo "To view the help file:"
+	@echo "# assistant -collectionFile build/qthelp/test.qhc"
+
+epub:
+	$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) build/epub
+	@echo
+	@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
+
+
+latex:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) build/latex
+	@echo
+	@echo "Build finished; the LaTeX files are in build/latex."
+	@echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \
+	      "run these through (pdf)latex."
+
+changes:
+	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) build/changes
+	@echo
+	@echo "The overview file is in build/changes."
+
+linkcheck:
+	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) build/linkcheck
+	@echo
+	@echo "Link check complete; look for any errors in the above output " \
+	      "or in build/linkcheck/output.txt."
+
+doctest:
+	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) build/doctest
+	@echo "Testing of doctests in the sources finished, look at the " \
+	      "results in build/doctest/output.txt."
+
+latexpdf: latex
+	@echo "Running LaTeX files through latexmk..."
+	$(MAKE) -C build/latex all-pdf
+	@echo "latexmk finished; the PDF files are in build/latex."
+
+docs: clean html latexpdf
+	cp build/latex/networkx_reference.pdf build/html/_downloads/.
+	
+gitwash-update:
+	python ../tools/gitwash_dumper.py developer networkx \
+	--project-url=http://networkx.github.io \
+	--project-ml-url=http://groups.google.com/group/networkx-discuss/ \
+	--gitwash-url git@github.com:matthew-brett/gitwash.git

doc/README.md

+If you only want to get the documentation, note that a pre-built
+version for the latest release is available
+[online](http://templates.pages.lis-lab.fr/pomad/).
+
+Sphinx is used to generate the API and reference documentation.
+
+## Instructions to build the documentation
+
+In addition to installing ``pomad`` and its dependencies, install the
+Python packages needed to build the documentation by entering
+
+```
+pip install -r ../requirements/doc.txt
+```
+in the ``doc/`` directory.
+
+To build the HTML documentation, run:
+```
+make html
+```
+in the ``doc/`` directory. This will generate a ``build/html`` subdirectory
+containing the built documentation.
+
+To build the PDF documentation, run:
+```
+make latexpdf
+```
+You will need to have Latex installed for this.

doc/_notebooks/pomad.ipynb

+%% Cell type:markdown id: tags:
+
+# Tutorial for `pomad`:  PrObabilistic MAtrix Decompositions
+
+%% Cell type:code id: tags:
+
+``` python
+%load_ext autoreload
+%autoreload 2
+```
+
+%% Cell type:code id: tags:
+
+``` python
+%matplotlib inline
+```
+
+%% Cell type:code id: tags:
+
+``` python
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy as sp
+from scipy.sparse.linalg import aslinearoperator
+```
+
+%% Cell type:code id: tags:
+
+``` python
+from pomad.utils import build_test_matrix
+from pomad.range_approximation import randomized_range_finder, adaptive_randomized_range_finder
+```
+
+%% Cell type:code id: tags:
+
+``` python
+# Test behavior of build_test_matrix
+m = 29
+n = 17
+seed = 0
+p_max = 5
+rand_state = np.random.RandomState(seed)
+A = rand_state.randn(m, n)
+A = A / np.linalg.norm(A, ord=2)
+M = A.copy()
+for p in range(p_max):
+    U, s, Vh = np.linalg.svd(M)
+    plt.semilogy(s, label=r'$(A A^T)^{} \times A$'.format(p))
+    M = A @ A.T @ M
+plt.title(r'Singular values of $(A A^T)^p \times A$')
+plt.legend()
+plt.grid()
+
+plt.figure()
+for p in range(p_max):
+    M = build_test_matrix(m, n, p=p, rand_state=seed)
+    U, s, Vh = np.linalg.svd(M)
+    plt.semilogy(s, label='p={}'.format(p))
+plt.title('Similar result using build_test_matrix(m, n, p)')
+plt.legend()
+plt.grid()
+
+```
+
+%% Cell type:code id: tags:
+
+``` python
+# Approximation quality of randomized_range_finder(A, n_l=l)
+m = 29
+n = 23
+p = 3
+A = build_test_matrix(m, n, p=10, rand_state=0)
+_, s, _ = np.linalg.svd(A)
+for k in range(1, 18):
+    Q = randomized_range_finder(A, n_l=k+p)
+    print("k =", k, "p =", p, 
+          "||A - Q @ Q.T @ A|| < s[k]?", np.linalg.norm(A - Q @ Q.T @ A, ord=2) < s[k], 
+          "({} < {})".format(np.linalg.norm(A - Q @ Q.T @ A, ord=2), s[k]))
+```
+
+%% Cell type:code id: tags:
+
+``` python
+m = 290
+n = 170
+A = build_test_matrix(m, n, p=10, rand_state=0)
+_, s, _ = np.linalg.svd(A)
+plt.figure(figsize=(15,5))
+plt.semilogy(s)
+plt.grid()
+for l in range(10):
+    tolerance = 10**-l
+    Q = adaptive_randomized_range_finder(A, tolerance=tolerance, r=5)
+    print(tolerance, np.linalg.norm(A-Q@Q.T@A, ord=2), Q.shape[1])
+```
+
+%% Cell type:code id: tags:
+
+``` python
+m = n = 345
+A = build_test_matrix(m, n, p=10, rand_state=0)
+Aop = aslinearoperator(A)
+tolerance = 10**-5
+%timeit -r2 -p2 Q = adaptive_randomized_range_finder(Aop, tolerance=tolerance, r=5)
+A_rank = Q.shape[1]
+print(A_rank)
+%timeit -r2 -p2 QQ = randomized_range_finder(Aop, n_l=A_rank)
+QQ = randomized_range_finder(Aop, n_l=A_rank)
+%timeit -r2 -p2 np.linalg.svd(np.conjugate(QQ).T @ A)
+%timeit -r2 -p2 ss=sp.sparse.linalg.svds(Aop, k=A_rank)
+%timeit -r2 -p2 sss=np.linalg.svd(A)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+
+```

doc/conf.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+import sys
+import os
+
+from datetime import date
+
+import pomad
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+sys.path.insert(0, os.path.abspath('../pomad/'))
+
+# -- General configuration ------------------------------------------------
+
+# 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.autosummary',
+              'sphinx.ext.doctest',
+              'sphinx.ext.intersphinx',
+              'sphinx.ext.todo',
+              'sphinx.ext.coverage',
+              'sphinx.ext.mathjax',
+              'sphinx.ext.viewcode',
+              'numpydoc',
+              'nbsphinx',
+              'IPython.sphinxext.ipython_console_highlighting',
+              ]
+
+
+# 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 encoding of source files.
+source_encoding = 'utf-8-sig'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = 'pomad'
+author = 'V. Emiya'
+copyright = '2019-{}, {}'.format(date.today().year, author)
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = pomad.__version__
+# The full version, including alpha/beta/rc tags.
+release = pomad.__version__.replace('_', '')
+
+# 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
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+# Else, today_fmt is used as the format for a strftime call.
+today_fmt = '%B %d, %Y'
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+exclude_patterns = ['_build', '**/test_*.rst', '**.ipynb_checkpoints']
+# The reST default role (used for this markup: `text`) to use for all
+# documents.
+default_role = None
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+add_function_parentheses = True
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+add_module_names = True
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# A list of ignored prefixes for module index sorting.
+modindex_common_prefix = []
+
+# If true, keep warnings as "system message" paragraphs in the built documents.
+keep_warnings = False
+
+# If true, `todo` and `todoList` produce output, else they produce nothing.
+todo_include_todos = True
+
+# -- 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 = 'bizstyle'
+
+# 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 themes here, relative to this directory.
+html_theme_path = []
+
+# The name for this set of Sphinx documents.  If None, it defaults to
+# "<project> v<release> documentation".
+# html_title = None
+
+# A shorter title for the navigation bar.  Default is the same as html_title.
+# html_short_title = None
+
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+# html_logo = None
+
+# The name of an image file (within the static path) to use as favicon of the
+# docs.  This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+html_favicon = None
+
+# 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 = []
+
+# Add any extra paths that contain custom files (such as robots.txt or
+# .htaccess) here, relative to this directory. These files are copied
+# directly to the root of the documentation.
+html_extra_path = []
+
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+html_last_updated_fmt = '%b %d, %Y'
+
+# Custom sidebar templates, maps document names to template names.
+html_sidebars = {}
+
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+html_additional_pages = {}
+
+# If false, no module index is generated.
+html_domain_indices = True
+
+# If false, no index is generated.
+html_use_index = True
+
+# If true, the index is split into individual pages for each letter.
+html_split_index = False
+
+# If true, links to the reST sources are added to the pages.
+html_show_sourcelink = True
+
+# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
+html_show_sphinx = True
+
+# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
+html_show_copyright = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it.  The value of this option must be the
+# base URL from which the finished HTML is served.
+html_use_opensearch = ''
+
+# This is the file name suffix for HTML files (e.g. ".xhtml").
+html_file_suffix = None
+
+# Language to be used for generating the HTML full-text search index.
+# Sphinx supports the following languages:
+#   'da', 'de', 'en', 'es', 'fi', 'fr', 'h', 'it', 'ja'
+#   'nl', 'no', 'pt', 'ro', 'r', 'sv', 'tr'
+html_search_language = 'en'
+
+# A dictionary with options for the search language support, empty by default.
+# Now only 'ja' uses this config value
+html_search_options = {'type': 'default'}
+
+# The name of a javascript file (relative to the configuration directory) that
+# implements a search results scorer. If empty, the default will be used.
+html_search_scorer = ''
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'pomaddoc'
+
+# -- Options for LaTeX output ---------------------------------------------
+
+latex_elements = {
+    # The paper size ('letterpaper' or 'a4paper').
+    'papersize': 'a4paper',
+
+    # 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, 'pomad.tex', 'pomad Documentation', author, 'manual'),