diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000000000000000000000000000000000000..56eb9ea9bf7e2e450bb982763d4a88b1fce77fc7
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,46 @@
+*.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
+
diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
new file mode 100644
index 0000000000000000000000000000000000000000..08e3844621f16b025513b84caa241df839a7f695
--- /dev/null
+++ b/.gitlab-ci.yml
@@ -0,0 +1,24 @@
+# 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
+
diff --git a/LICENSE.txt b/LICENSE.txt
new file mode 100755
index 0000000000000000000000000000000000000000..810fce6e9bf2aa10265b85614db5ac65941ecf81
--- /dev/null
+++ b/LICENSE.txt
@@ -0,0 +1,621 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
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+ Each version is given a distinguishing version number. If the
+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation. If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+ If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+ Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+ 15. Disclaimer of Warranty.
+
+ THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+ 16. Limitation of Liability.
+
+ IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+ 17. Interpretation of Sections 15 and 16.
+
+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
diff --git a/MANIFEST.in b/MANIFEST.in
new file mode 100755
index 0000000000000000000000000000000000000000..eeb4dd5c0f6f9b91c8ceaa68179c33f9a8b31ec7
--- /dev/null
+++ b/MANIFEST.in
@@ -0,0 +1,8 @@
+include *.txt
+include *.rst
+include VERSION
+recursive-include doc *.rst *.py *.ipynb
+
+include pomad/tests/*.py
+
+prune doc/build
diff --git a/README.md b/README.md
deleted file mode 100644
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..0000000000000000000000000000000000000000
diff --git a/README.rst b/README.rst
new file mode 100755
index 0000000000000000000000000000000000000000..6e0a0308169022e93448395886450ed72767198b
--- /dev/null
+++ b/README.rst
@@ -0,0 +1,61 @@
+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`).
diff --git a/VERSION b/VERSION
new file mode 100755
index 0000000000000000000000000000000000000000..6eec302096c96f3b65121bf64283ea6f63f11f22
--- /dev/null
+++ b/VERSION
@@ -0,0 +1 @@
+pomad:0.1
diff --git a/doc/Makefile b/doc/Makefile
new file mode 100755
index 0000000000000000000000000000000000000000..64227f569466b8601987972e617aabe461d39d71
--- /dev/null
+++ b/doc/Makefile
@@ -0,0 +1,121 @@
+# 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
diff --git a/doc/README.md b/doc/README.md
new file mode 100755
index 0000000000000000000000000000000000000000..5d2c9e95f0f138053f2d966c3d07e7de1029cab4
--- /dev/null
+++ b/doc/README.md
@@ -0,0 +1,28 @@
+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.
diff --git a/doc/_notebooks/pomad.ipynb b/doc/_notebooks/pomad.ipynb
new file mode 100755
index 0000000000000000000000000000000000000000..950b15439c8572bc2cc5a4358eeea204392c8d45
--- /dev/null
+++ b/doc/_notebooks/pomad.ipynb
@@ -0,0 +1,189 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Tutorial for `pomad`: PrObabilistic MAtrix Decompositions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "%load_ext autoreload\n",
+ "%autoreload 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "import scipy as sp\n",
+ "from scipy.sparse.linalg import aslinearoperator"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from pomad.utils import build_test_matrix\n",
+ "from pomad.range_approximation import randomized_range_finder, adaptive_randomized_range_finder"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Test behavior of build_test_matrix\n",
+ "m = 29\n",
+ "n = 17\n",
+ "seed = 0\n",
+ "p_max = 5\n",
+ "rand_state = np.random.RandomState(seed)\n",
+ "A = rand_state.randn(m, n)\n",
+ "A = A / np.linalg.norm(A, ord=2)\n",
+ "M = A.copy()\n",
+ "for p in range(p_max):\n",
+ " U, s, Vh = np.linalg.svd(M)\n",
+ " plt.semilogy(s, label=r'$(A A^T)^{} \\times A$'.format(p))\n",
+ " M = A @ A.T @ M\n",
+ "plt.title(r'Singular values of $(A A^T)^p \\times A$')\n",
+ "plt.legend()\n",
+ "plt.grid()\n",
+ "\n",
+ "plt.figure()\n",
+ "for p in range(p_max):\n",
+ " M = build_test_matrix(m, n, p=p, rand_state=seed)\n",
+ " U, s, Vh = np.linalg.svd(M)\n",
+ " plt.semilogy(s, label='p={}'.format(p))\n",
+ "plt.title('Similar result using build_test_matrix(m, n, p)')\n",
+ "plt.legend()\n",
+ "plt.grid()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Approximation quality of randomized_range_finder(A, n_l=l)\n",
+ "m = 29\n",
+ "n = 23\n",
+ "p = 3\n",
+ "A = build_test_matrix(m, n, p=10, rand_state=0)\n",
+ "_, s, _ = np.linalg.svd(A)\n",
+ "for k in range(1, 18):\n",
+ " Q = randomized_range_finder(A, n_l=k+p)\n",
+ " print(\"k =\", k, \"p =\", p, \n",
+ " \"||A - Q @ Q.T @ A|| < s[k]?\", np.linalg.norm(A - Q @ Q.T @ A, ord=2) < s[k], \n",
+ " \"({} < {})\".format(np.linalg.norm(A - Q @ Q.T @ A, ord=2), s[k]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "m = 290\n",
+ "n = 170\n",
+ "A = build_test_matrix(m, n, p=10, rand_state=0)\n",
+ "_, s, _ = np.linalg.svd(A)\n",
+ "plt.figure(figsize=(15,5))\n",
+ "plt.semilogy(s)\n",
+ "plt.grid()\n",
+ "for l in range(10):\n",
+ " tolerance = 10**-l\n",
+ " Q = adaptive_randomized_range_finder(A, tolerance=tolerance, r=5)\n",
+ " print(tolerance, np.linalg.norm(A-Q@Q.T@A, ord=2), Q.shape[1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "m = n = 345\n",
+ "A = build_test_matrix(m, n, p=10, rand_state=0)\n",
+ "Aop = aslinearoperator(A)\n",
+ "tolerance = 10**-5\n",
+ "%timeit -r2 -p2 Q = adaptive_randomized_range_finder(Aop, tolerance=tolerance, r=5)\n",
+ "A_rank = Q.shape[1]\n",
+ "print(A_rank)\n",
+ "%timeit -r2 -p2 QQ = randomized_range_finder(Aop, n_l=A_rank)\n",
+ "QQ = randomized_range_finder(Aop, n_l=A_rank)\n",
+ "%timeit -r2 -p2 np.linalg.svd(np.conjugate(QQ).T @ A)\n",
+ "%timeit -r2 -p2 ss=sp.sparse.linalg.svds(Aop, k=A_rank)\n",
+ "%timeit -r2 -p2 sss=np.linalg.svd(A)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/doc/conf.py b/doc/conf.py
new file mode 100755
index 0000000000000000000000000000000000000000..addf02bcb697a696b567ecc3206e9c24b78a5a7c
--- /dev/null
+++ b/doc/conf.py
@@ -0,0 +1,286 @@
+#!/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'),
+]
+
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+latex_logo = None
+
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+latex_use_parts = False
+
+# If true, show page references after internal links.
+latex_show_pagerefs = False
+
+# If true, show URL addresses after external links.
+# latex_show_urls = False
+
+# Documents to append as an appendix to all manuals.
+latex_appendices = []
+
+# If false, no module index is generated.
+latex_domain_indices = True
+
+# -- 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, 'pomad', 'pomad Documentation', [author], 1)]
+
+# If true, show URL addresses after external links.
+man_show_urls = False
+
+# -- 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, 'pomad.tex', 'pomad Documentation', author, 'manual'),
+]
+
+# Documents to append as an appendix to all manuals.
+texinfo_appendices = []
+
+# If false, no module index is generated.
+texinfo_domain_indices = True
+
+# How to display URL addresses: 'footnote', 'no', or 'inline'.
+texinfo_show_urls = 'footnote'
+
+# If true, do not generate a @detailmenu in the "Top" node's menu.
+texinfo_no_detailmenu = False
+
+# Example configuration for intersphinx: refer to the Python standard library.
+intersphinx_mapping = {
+ 'numpy': ('https://docs.scipy.org/doc/numpy/', None),
+}
+
+# Allow errors in notebook
+nbsphinx_allow_errors = True
+
+# Do not show class members
+numpydoc_show_class_members = False
+
+# Include todos
+todo_include_todos = True
+
+# Order members by member type
+autodoc_member_order = 'groupwise'
diff --git a/doc/copyright.rst b/doc/copyright.rst
new file mode 100755
index 0000000000000000000000000000000000000000..180e86a44689775ac74ed164e0bcb663615ca5b7
--- /dev/null
+++ b/doc/copyright.rst
@@ -0,0 +1,49 @@
+Credits
+#######
+
+Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+
+This package has been created thanks to the joint work with Florent Jaillet
+and Ronan Hamon on other packages.
+
+Description
+-----------
+
+`pomad` is a 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, https://arxiv.org/abs/0909.4061.
+
+
+Version
+-------
+
+* pomad version = 0.1
+
+Licence
+-------
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+
diff --git a/doc/credits.rst b/doc/credits.rst
new file mode 100755
index 0000000000000000000000000000000000000000..80f497d5223e00a394cd9ba94530666d9770b868
--- /dev/null
+++ b/doc/credits.rst
@@ -0,0 +1,35 @@
+Credits
+=======
+
+Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+
+This package has been created thanks to the joint work with Florent Jaillet
+and Ronan Hamon on other packages.
+
+Licence
+-------
+This file is part of pomad.
+
+pomad is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
diff --git a/doc/index.rst b/doc/index.rst
new file mode 100755
index 0000000000000000000000000000000000000000..9e42c85078a998c4993d055773df6544f5f09446
--- /dev/null
+++ b/doc/index.rst
@@ -0,0 +1,43 @@
+##########################
+:mod:`pomad` documentation
+##########################
+
+Overview
+========
+:mod:`pomad`: stands for PrObabilistic MAtrix Decompositions.
+
+Package :mod:`pomad` offers a 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, https://arxiv.org/abs/0909.4061.
+
+:mod:`pomad`: is mainly composed of two sub-modules:
+
+* :mod:`pomad.range_approximation` contains algorithms for Stage A Randomized Schemes for Approximating the Range
+* :mod:`pomad.factorization_construction` contains algorithms for Stage B Construction of Standard Factorizations
+
+Not all algorithms have been implemented yet.
+
+Documentation
+=============
+
+.. only:: html
+
+ :Release: |version|
+ :Date: |today|
+
+.. toctree::
+ :maxdepth: 1
+
+ installation
+ references
+ tutorials
+ copyright
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`
diff --git a/doc/installation.rst b/doc/installation.rst
new file mode 100755
index 0000000000000000000000000000000000000000..24d8496b2ff78418e5289b720ca992c3c7cb5656
--- /dev/null
+++ b/doc/installation.rst
@@ -0,0 +1,75 @@
+Installation
+############
+
+``pomad`` requires the following packages:
+
+* `python >= 3.5 <https://wiki.python.org/moin/BeginnersGuide/Download>`_
+* `numpy >= 1.13 <http://www.numpy.org>`_
+
+Make sure your Python environment is properly configured. It is recommended to
+install ``pomad`` in a virtual environment.
+
+Release version
+---------------
+
+First, make sure you have the latest version of pip (the Python package
+manager) installed. If you do not, refer to the `Pip documentation
+<https://pip.pypa.io/en/stable/installing/>`_ and install ``pip`` first.
+
+Install the current release with ``pip``::
+
+ pip install pomad
+
+To upgrade to a newer release use the ``--upgrade`` flag::
+
+ pip install --upgrade pomad
+
+If you do not have permission to install software systemwide, you can install
+into your user directory using the ``--user`` flag::
+
+ pip install --user pomad
+
+Alternatively, you can manually download ``pomad`` from its `GitLab project
+<https://gitlab.lis-lab.fr/valentin.emiya/pomad>`_ or `PyPI
+<https://pypi.python.org/pypi/pomad>`_. To install one of these versions,
+unpack it and run the following from the top-level source directory using the
+Terminal::
+
+ pip install .
+
+Development version
+-------------------
+
+If you have `Git <https://git-scm.com/>`_ installed on your system, it is also
+possible to install the development version of ``pomad``.
+
+Before installing the development version, you may need to uninstall the
+standard version of ``pomad`` using ``pip``::
+
+ pip uninstall pomad
+
+Clone the Git repository::
+
+ git clone git@gitlab.lis-lab.fr:valentin.emiya/pomad.git
+ cd pomad
+
+You may also need to install required packages::
+
+ pip install -r requirements/defaults.txt
+
+Then execute ``pip`` with flag ``-e`` to follow the development branch::
+
+ pip install -e .
+
+To update ``pomad`` at any time, in the same directory do::
+
+ git pull
+
+To run unitary tests, first install required packages::
+
+ pip install -r requirements/dev.txt
+
+and execute ``pytest``::
+
+ pytest
+
diff --git a/doc/references.rst b/doc/references.rst
new file mode 100755
index 0000000000000000000000000000000000000000..e3d591d684ed064ef03d4c5ca521ae95e6d74fb0
--- /dev/null
+++ b/doc/references.rst
@@ -0,0 +1,29 @@
+References
+==========
+
+ :Release: |release|
+ :Date: |today|
+
+pomad\.factorization_construction module
+----------------------------------------
+
+.. automodule:: pomad.factorization_construction
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+pomad\.range_approximation module
+---------------------------------
+
+.. automodule:: pomad.range_approximation
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+pomad\.utils module
+-------------------
+
+.. automodule:: pomad.utils
+ :members:
+ :undoc-members:
+ :show-inheritance:
diff --git a/doc/tutorials.rst b/doc/tutorials.rst
new file mode 100755
index 0000000000000000000000000000000000000000..273e21d8106adde60380afb8aa378f5d475cefb5
--- /dev/null
+++ b/doc/tutorials.rst
@@ -0,0 +1,7 @@
+Tutorials
+#########
+
+.. toctree::
+ :maxdepth: 1
+
+ _notebooks/pomad.ipynb
diff --git a/pomad/__init__.py b/pomad/__init__.py
new file mode 100755
index 0000000000000000000000000000000000000000..985033fc17438fadcb5362afbc4073e37ace8b44
--- /dev/null
+++ b/pomad/__init__.py
@@ -0,0 +1,14 @@
+# -*- coding: utf-8 -*-
+"""
+.. moduleauthor:: Valentin Emiya
+"""
+from .factorization_construction import direct_svd, evd_nystrom
+from .range_approximation import \
+ randomized_range_finder, adaptive_randomized_range_finder
+
+# TODO replace RandomState by BitGenerator
+
+__all__ = ['direct_svd', 'evd_nystrom',
+ 'randomized_range_finder', 'adaptive_randomized_range_finder']
+
+__version__ = "0.1"
diff --git a/pomad/_dev_range_approximation.py b/pomad/_dev_range_approximation.py
new file mode 100755
index 0000000000000000000000000000000000000000..ee46029832d589f6e622241cf351c0d5fc60232e
--- /dev/null
+++ b/pomad/_dev_range_approximation.py
@@ -0,0 +1,348 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+"""
+
+.. moduleauthor:: Valentin Emiya
+"""
+import numpy as np
+from scipy.sparse.linalg import aslinearoperator
+
+
+def adaptive_randomized_range_finder_naive(a, tolerance, r=5, rand_state=None):
+ """ Naive implementation for Algo 4.2 """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = [a @ W[:, i] for i in range(r)]
+ j = 0
+ Q = np.empty((m, 0), dtype=a.dtype)
+ y_norms = [np.linalg.norm(Y[i]) for i in range(r)]
+
+ while np.max(y_norms[j:j + r]) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ j += 1
+ Y[j-1] -= Q @ (np.conj(Q).T @ Y[j-1]) # Fixed bug with index j
+ q = Y[j-1] / np.linalg.norm(Y[j-1]) # Fixed bug with index j
+ Q = np.concatenate((Q, q[:, None]), axis=1)
+ w = rand_state.randn(n)
+ Aw = a @ w
+ y = Aw - Q @ (Q.T.conj() @ Aw)
+ Y.append(y)
+ y_norms.append(np.linalg.norm(y))
+ for i in range(j, j + r - 1): # Fixed bug with final index
+ Y[i] -= q * np.dot(q.conj(), Y[i])
+ return Q
+
+
+def adaptive_randomized_range_finder_nolist(a, tolerance, r=5, rand_state=None):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_naive enhanced using nd-array instead
+ of lists """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q = np.empty((m, 0), dtype=a.dtype)
+
+ while np.max(y_norms[j:j + r]) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ Y[:, j] -= Q @ (np.conj(Q).T @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j += 1
+ Q = np.concatenate((Q, q[:, None]), axis=1)
+ w = rand_state.randn(n)
+ Aw = a @ w
+ y = Aw - Q @ (Q.T.conj() @ Aw)
+ Y = np.concatenate((Y, y[:, None]), axis=1)
+ y_norms = np.concatenate((y_norms, [np.linalg.norm(y)]))
+ for i in range(j, j + r - 1):
+ Y[:, i] -= q * np.dot(q.conj(), Y[:, i])
+ return Q
+
+
+def adaptive_randomized_range_finder_circy(a, tolerance, r=5, rand_state=None):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_nolist enhanced using circular array
+ for Y """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ j_incr = 0
+ Q = np.empty((m, 0), dtype=a.dtype)
+
+ while np.max(y_norms[j_incr:j_incr + r]) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ j_incr += 1
+ Y[:, j] -= Q @ (np.conj(Q).T @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q = np.concatenate((Q, q[:, None]), axis=1)
+ w = rand_state.randn(n)
+ A_w = a @ w
+ y = A_w - Q @ (Q.T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms = np.concatenate((y_norms, [np.linalg.norm(y)]))
+ for i in np.arange(j, j + r - 1) % r:
+ Y[:, i] -= q * np.dot(q.conj(), Y[:, i])
+ return Q
+
+
+def adaptive_randomized_range_finder_circynorms(a, tolerance, r=5,
+ rand_state=None):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_circy enhanced using circular array
+ for y_norms """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q = np.empty((m, 0), dtype=a.dtype)
+
+ while np.max(y_norms) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ Y[:, j] -= Q @ (np.conj(Q).T @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q = np.concatenate((Q, q[:, None]), axis=1)
+ w = rand_state.randn(n)
+ A_w = a @ w
+ y = A_w - Q @ (Q.T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms[j - 1] = np.linalg.norm(y)
+ for i in np.arange(j, j + r - 1) % r:
+ Y[:, i] -= q * np.dot(q.conj(), Y[:, i])
+ return Q
+
+
+def adaptive_randomized_range_finder_rmloop(a, tolerance, r=5,
+ rand_state=None):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_circynorms enhanced removing internal
+ loop """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q = np.empty((m, 0), dtype=a.dtype)
+
+ while np.max(y_norms) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ Y[:, j] -= Q @ (Q.T.conj() @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q = np.concatenate((Q, q[:, None]), axis=1)
+ w = rand_state.randn(n)
+ A_w = a @ w
+ Y -= np.outer(q, q.conj() @ Y)
+ y = A_w - Q @ (Q.T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms[j - 1] = np.linalg.norm(y)
+ return Q
+
+
+def adaptive_randomized_range_finder_rmconcQ(a, tolerance, r=5,
+ rand_state=None):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_rmloop enhanced removing concatenation
+ for Q, with maximal size for Q (needs to be reduced) """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q_width = 0
+ Q = np.empty((m, min(m, n)), dtype=a.dtype)
+
+ while np.max(y_norms) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ if Q_width >= n:
+ # TODO to be tested
+ raise RuntimeError('Required tolerance not reached with maximum '
+ 'number of columns ({}). Singular '
+ 'values may decrease too slowly.'.format(n))
+ Y[:, j] -= Q[:, :Q_width] @ (Q[:, :Q_width].T.conj() @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q_width += 1
+ Q[:, Q_width-1] = q
+ w = rand_state.randn(n)
+ A_w = a @ w
+ # Y -= np.outer(q, np.conj(np.conj(q) @ Y))
+ Y -= np.outer(q, q.conj() @ Y)
+ y = A_w - Q[:, :Q_width] @ (Q[:, :Q_width].T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms[j - 1] = np.linalg.norm(y)
+ return Q[:, :Q_width]
+
+
+def adaptive_randomized_range_finder_mem_alloc(a, tolerance, r=5,
+ rand_state=None, n_cols_Q=16):
+ """ Intermediate implementation for Algo 4.2:
+ adaptive_randomized_range_finder_rmconcQ enhanced using memory
+ allocation (subsequently optimized using resize in final version
+ adaptive_randomized_range_finder)
+ """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ if isinstance(a, np.ndarray):
+ a = aslinearoperator(a)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q_width = 0
+ Q = np.empty((m, n_cols_Q), order='F', dtype=a.dtype)
+
+ while np.max(y_norms) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ if Q_width >= n:
+ # TODO to be tested
+ raise RuntimeError('Required tolerance not reached with maximum '
+ 'number of columns ({}). Singular '
+ 'values may decrease too slowly.'.format(n))
+ Y[:, j] -= Q[:, :Q_width] @ (np.conj(Q[:, :Q_width]).T @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q_width += 1
+ if Q_width > Q.shape[1]:
+ Q_new = np.empty((m, Q.shape[1]*2), dtype=a.dtype)
+ Q_new[:, :Q.shape[1]] = Q
+ Q = Q_new
+ Q[:, Q_width-1] = q
+ # This matrix operation is done on the full matrix and column j-1 is
+ # then overwritten with y to comply with the original algorithm,
+ # even if the orthogonalization of Y would not affect y significantly.
+ Y -= np.outer(q, q.conj() @ Y)
+ w = rand_state.randn(n)
+ A_w = a @ w
+ y = A_w - Q[:, :Q_width] @ (Q[:, :Q_width].T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms[j - 1] = np.linalg.norm(y)
+ return Q[:, :Q_width]
+
+# TODO use similar code for measuring running times
+# def main_loop():
+# from time import process_time
+# m = 1000
+# n = m
+# p_a = 10
+# m, n, p_a = 100, 100, 2
+# a_mat = build_test_matrix(m, n, p=p_a, rand_state=0)
+# a_op = aslinearoperator(a_mat)
+# from pomad.utils import FourierMultiplierOp
+# n = 123
+# a_op = FourierMultiplierOp(n=n, p=30)
+# a_mat = a_op @ np.eye(n)
+# tolerance = 10 ** -3
+#
+# def adaptive_randomized_range_finder_q2(**nargs):
+# return adaptive_randomized_range_finder(**nargs, n_cols_Q=2)
+#
+# def adaptive_randomized_range_finder_q16(**nargs):
+# return adaptive_randomized_range_finder(**nargs, n_cols_Q=16)
+#
+# def adaptive_randomized_range_finder_q455(**nargs):
+# return adaptive_randomized_range_finder(**nargs, n_cols_Q=455)
+#
+# f_list = [adaptive_randomized_range_finder_naive,
+# adaptive_randomized_range_finder_nolist,
+# adaptive_randomized_range_finder_circy,
+# adaptive_randomized_range_finder_circynorms,
+# adaptive_randomized_range_finder_rmloop,
+# adaptive_randomized_range_finder_rmconcQ,
+# adaptive_randomized_range_finder_mem_alloc,
+# adaptive_randomized_range_finder_q2,
+# adaptive_randomized_range_finder_q16,
+# adaptive_randomized_range_finder_q455,
+# adaptive_randomized_range_finder,
+# ]
+# dt_list = np.empty(len(f_list))
+# err_list = np.empty(len(f_list))
+# for i_f, f in enumerate(f_list):
+# t0 = process_time()
+# q_mat = f(a=a_op, tolerance=tolerance, r=6, rand_state=0)
+# dt_list[i_f] = process_time() - t0
+# err_list[i_f] = np.linalg.norm(a_mat - q_mat @ q_mat.T.conj() @ a_mat,
+# ord=2)
+# print('t={:.2f}, gain t={:.1%}, err={:.12e}, delta err={:.2e}, '
+# 'Q shape:{} ({})'
+# .format(dt_list[i_f], dt_list[i_f]/dt_list[0], err_list[i_f],
+# abs(err_list[i_f]-err_list[0]), q_mat.shape, f.__name__))
+#
+#
+# if __name__ == '__main__':
+# main_loop()
diff --git a/pomad/factorization_construction.py b/pomad/factorization_construction.py
new file mode 100755
index 0000000000000000000000000000000000000000..924ea7b51ae341b5de49e0e6dcaa96010da03f43
--- /dev/null
+++ b/pomad/factorization_construction.py
@@ -0,0 +1,144 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+""" Algorithms for Stage B: Construction of Standard Factorizations
+
+.. moduleauthor:: Valentin Emiya
+"""
+import numpy as np
+from numpy.linalg import cholesky # TODO check np vs sp implementations
+from scipy.linalg import solve_triangular
+from scipy.sparse.linalg import aslinearoperator, eigs, svds
+
+
+def direct_svd(a_mat, q_mat):
+ """
+ Algo 5.1: direct SVD
+
+ Parameters
+ ----------
+ a_mat : nd-array
+ Positive semidefinite matrix to be decomposed
+ q_mat : nd-array
+ Matrix whose range captures the action of a_mat
+
+ Returns
+ -------
+ u_mat: nd-array
+ Eigenvectors
+ lambda_vec :
+ Eigenvalues
+
+ """
+ b_mat = q_mat.T.conj() @ a_mat
+ u_tilde, lambda_vec, vh_mat = np.linalg.svd(b_mat, full_matrices=False)
+ u_mat = q_mat @ u_tilde
+ return u_mat, lambda_vec, vh_mat
+
+
+def evd_nystrom(a, q_mat):
+ """
+ Algo 5.5: Eigenvalue decomposition via Nyström method
+
+ Parameters
+ ----------
+ a : nd-array or LinearOperator
+ Positive semidefinite matrix or linear operator to be decomposed
+ q_mat : nd-array
+ Matrix whose range captures the action of a_mat
+
+ Returns
+ -------
+ u_mat: nd-array
+ Eigenvectors
+ lambda_vec :
+ Eigenvalues
+ """
+ if isinstance(a, np.ndarray):
+ a = aslinearoperator(a)
+ b1_mat = a(q_mat)
+ b2_mat = q_mat.T.conj() @ b1_mat
+ c = cholesky(b2_mat).T.conj()
+ f_mat = solve_triangular(a=c.T, b=b1_mat.T, lower=True).T
+ u_mat, sigma, _ = np.linalg.svd(f_mat, full_matrices=False)
+ return sigma**2, u_mat
+
+
+# TODO refactor this code into nb
+# if __name__ == '__main__':
+# from pomad.range_approximation import randomized_range_finder
+# import matplotlib.pyplot as plt
+# from pomad.utils import FourierMultiplierOp
+# print('Test evd with operator')
+#
+# n = 53
+# n_l = 41
+# p = 5
+# a_op = FourierMultiplierOp(n, p)
+# q = randomized_range_finder(a_mat=a_op, n_l=n_l)
+# w_sort = np.sort(a_op.w)[::-1]
+# plt.semilogy(w_sort, label='w')
+# print('sing value:', w_sort[n_l])
+# q_op = aslinearoperator(q)
+# qh_op = aslinearoperator(q.T.conj())
+# range_err_op = a_op - q_op @ qh_op @ a_op
+# print('range approx error:', eigs(range_err_op, k=1)[0][0])
+# # u51, s51, vh51 = direct_svd(a_mat=a_op, q_mat=q)
+# # print(eigs(
+# # aslinearoperator(SvdErrOp(a_op=a_op, u=u51, s=s51, vh=vh51), k=1)))
+# s55, u55 = evd_nystrom(a_mat=a_op, q_mat=q)
+# a_est = u55 @ np.diag(s55) @ u55.T.conj()
+# print(eigs(a_op - aslinearoperator(a_est))[0][0])
+#
+# plt.grid()
+# plt.legend()
+# e = a_op - aslinearoperator(u55 @ np.diag(s55) @ u55.T.conj())
diff --git a/pomad/range_approximation.py b/pomad/range_approximation.py
new file mode 100755
index 0000000000000000000000000000000000000000..cddba14794a79e5467c7f7ad63e5b5b12a15961a
--- /dev/null
+++ b/pomad/range_approximation.py
@@ -0,0 +1,162 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+""" Algorithms for Stage A: Randomized Schemes for Approximating the Range
+
+.. moduleauthor:: Valentin Emiya
+"""
+import numpy as np
+
+
+def randomized_range_finder(a, n_l, rand_state=None):
+ """ Algorithm 4.1 : Randomized Range Finder
+
+ Parameters
+ ----------
+ a : nd-array or LinearOperator [m, n]
+ Matrix or linear operator whose range must be computed
+ n_l : int
+ Number of columns in result
+ rand_state : RandomState, int or None
+ If RandomState, random generator.
+ If int or None, random seed used to initialize the pseudo-random
+ number generator.
+
+ Returns
+ -------
+ nd-array [m, n_l]
+ Matrix whose columns are orthonormal and whose range approximates
+ the range of a.
+ """
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ n = a.shape[1]
+ omega = rand_state.randn(n, n_l)
+ y_mat = a @ omega
+ q_mat, _ = np.linalg.qr(y_mat)
+ return q_mat
+
+
+def adaptive_randomized_range_finder(a, tolerance, r=5, proba=None,
+ rand_state=None, n_cols_Q=16):
+ """ Algorithm 4.2 : Adaptive Randomized Range Finder
+
+ Parameters
+ ----------
+ a : nd-array or LinearOperator [m, n]
+ Matrix or linear operator whose range must be computed
+ tolerance : float
+ Required tolerance on the range approximation.
+ r : int
+ Number of Gaussian vectors used for a posteriori error estimation.
+ Either `r` or `proba` should be set, not both.
+ proba : float
+ Probability that the error is lower than the tolerance. Either `r` or
+ `proba` should be set, not both.
+ rand_state : RandomState, int or None
+ If RandomState, random generator.
+ If int or None, random seed used to initialize the pseudo-random
+ number generator.
+ n_cols_Q : int
+ Initial number of columns to be allocated in Q.
+
+ Returns
+ -------
+
+ For computational efficiency, this implementation uses circular arrays
+ for `Y` and `y_norms`, memory allocation for `Q` and no internal loop
+ """
+ if proba is None and r is None:
+ raise ValueError('Either proba or n_r should not be None.')
+ if proba is not None and r is not None:
+ raise ValueError('Either proba or n_r should be None.')
+ if proba is not None:
+ r = int(np.ceil(- np.log10((1 - proba) / np.min(a.shape))))
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ m, n = a.shape
+ W = rand_state.randn(n, r)
+ Y = a @ W
+ y_norms = np.linalg.norm(Y, axis=0)
+ j = 0
+ Q_width = 0
+ # order='F' necessary for Q.resize
+ Q = np.empty((m, n_cols_Q), order='F', dtype=a.dtype)
+
+ while np.max(y_norms) > tolerance / (10 * np.sqrt(2 / np.pi)):
+ if Q_width >= n:
+ # TODO to be tested
+ raise RuntimeError('Required tolerance not reached with maximum '
+ 'number of columns ({}). Singular '
+ 'values may decrease too slowly.'.format(n))
+ Y[:, j] -= Q[:, :Q_width] @ (Q[:, :Q_width].T.conj() @ Y[:, j])
+ q = Y[:, j] / np.linalg.norm(Y[:, j])
+ j = (j + 1) % r
+ Q_width += 1
+ if Q_width > Q.shape[1]:
+ Q.resize(m, Q.shape[1]*2)
+ Q[:, Q_width-1] = q
+ # This matrix operation is done on the full matrix and column j-1 is
+ # then overwritten with y to comply with the original algorithm,
+ # even if the orthogonalization of Y would not affect y significantly.
+ Y -= np.outer(q, q.conj() @ Y)
+ w = rand_state.randn(n)
+ A_w = a @ w
+ y = A_w - Q[:, :Q_width] @ (Q[:, :Q_width].T.conj() @ A_w)
+ Y[:, j - 1] = y
+ y_norms[j - 1] = np.linalg.norm(y)
+ return Q[:, :Q_width]
+
diff --git a/pomad/tests/__init__.py b/pomad/tests/__init__.py
new file mode 100755
index 0000000000000000000000000000000000000000..40a96afc6ff09d58a702b76e3f7dd412fe975e26
--- /dev/null
+++ b/pomad/tests/__init__.py
@@ -0,0 +1 @@
+# -*- coding: utf-8 -*-
diff --git a/pomad/tests/test_dev_range_approximation.py b/pomad/tests/test_dev_range_approximation.py
new file mode 100755
index 0000000000000000000000000000000000000000..7a0fc2e453e73048ededa68fccde09983cc54df0
--- /dev/null
+++ b/pomad/tests/test_dev_range_approximation.py
@@ -0,0 +1,119 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+
+"""Test of the module :module:`pomad._dev_range_approximation`
+
+.. moduleauthor:: Valentin Emiya
+"""
+import unittest
+import numpy as np
+
+from scipy.sparse.linalg import aslinearoperator, svds
+
+from pomad.range_approximation import adaptive_randomized_range_finder
+from pomad.utils import \
+ build_random_psd_matrix, build_test_matrix, FourierMultiplierOp
+from pomad._dev_range_approximation import \
+ adaptive_randomized_range_finder_naive, \
+ adaptive_randomized_range_finder_nolist, \
+ adaptive_randomized_range_finder_circy, \
+ adaptive_randomized_range_finder_circynorms, \
+ adaptive_randomized_range_finder_rmloop, \
+ adaptive_randomized_range_finder_rmconcQ, \
+ adaptive_randomized_range_finder_mem_alloc
+
+
+class TestDevAdaptiveRandomizedRangeFinder(unittest.TestCase):
+ def setUp(self) -> None:
+ m = 79
+ n = 123
+ self.a_dict = {
+ 'random matrix':
+ build_test_matrix(m=m, n=n, p=5, rand_state=None),
+ 'operator from random matrix':
+ aslinearoperator(build_test_matrix(m=m, n=n, p=5,
+ rand_state=None)),
+ 'PSD matrix':
+ build_random_psd_matrix(n=n, rank=m, p=5, rand_state=None),
+ 'Fourier multiplier': FourierMultiplierOp(n=n, p=30)
+ }
+ self.f_list = [
+ adaptive_randomized_range_finder_naive,
+ adaptive_randomized_range_finder_nolist,
+ adaptive_randomized_range_finder_circy,
+ adaptive_randomized_range_finder_circynorms,
+ adaptive_randomized_range_finder_rmloop,
+ adaptive_randomized_range_finder_rmconcQ,
+ adaptive_randomized_range_finder_mem_alloc,
+ adaptive_randomized_range_finder,
+ ]
+
+ def test_approximation_error(self):
+ """ Check equation (4.2).
+ """
+ tolerance = 1e-3
+ r = 6
+ for rand_state in (None, 0):
+ for k_a in self.a_dict:
+ err = []
+ a = self.a_dict[k_a]
+ for f in self.f_list:
+ q = f(a=a, tolerance=tolerance, r=r, rand_state=rand_state)
+
+ a_op = aslinearoperator(a)
+ q_op = aslinearoperator(q)
+ err.append(svds(a_op - q_op @ q_op.H @ a_op, k=1)[1][0])
+ self.assertLessEqual(err[-1], tolerance, msg='Case ' + k_a)
+ if rand_state is not None: # Use same seed to compare results
+ np.testing.assert_array_almost_equal(err[:-1], err[1:],
+ err_msg='Case ' + k_a)
diff --git a/pomad/tests/test_factorization_construction.py b/pomad/tests/test_factorization_construction.py
new file mode 100755
index 0000000000000000000000000000000000000000..075bffa1f6f6f16bc97212a0a8eac6705fe1deb2
--- /dev/null
+++ b/pomad/tests/test_factorization_construction.py
@@ -0,0 +1,193 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+
+"""Test of the module :module:`pomad.factorization_construction`
+
+.. moduleauthor:: Valentin Emiya
+"""
+import unittest
+import numpy as np
+from scipy.sparse.linalg import aslinearoperator, eigs, svds
+
+from pomad.factorization_construction import direct_svd, evd_nystrom
+from pomad.range_approximation import randomized_range_finder
+from pomad.utils import \
+ build_random_psd_matrix, build_test_matrix, FourierMultiplierOp
+
+
+class TestDirectSvd(unittest.TestCase):
+ # TODO add test with complex matrices
+ def test_approximation_error_from_true_range(self):
+ """ Check equation (5.2) using true left singular vectors as matrix Q
+ """
+ m = 47
+ n = 53
+ q_width = 41
+ p = 0
+
+ a = build_test_matrix(m=m, n=n, p=p, rand_state=None)
+ u_true, s_true, vh_true = svds(a, k=q_width)
+
+ # Call to tested code
+ u_est, s_est, vh_est = direct_svd(a_mat=a, q_mat=u_true)
+
+ eps = np.linalg.norm(a - u_true @ np.diag(s_true) @ vh_true)
+ err = np.linalg.norm(a - u_est @ np.diag(s_est) @ vh_est)
+ try:
+ self.assertLessEqual(err, eps)
+ except AssertionError:
+ np.testing.assert_almost_equal(err - eps, 0)
+
+ def test_approximation_error_from_q_est(self):
+ """ Check equation (5.2) using matrix Q estimated with randomized
+ range finder.
+ """
+ m = 47
+ n = 53
+ q_width = 41
+ p = 0
+
+ a = build_test_matrix(m=m, n=n, p=p, rand_state=None)
+ q = randomized_range_finder(a=a, n_l=q_width)
+
+ # Call to tested code
+ u_est, s_est, vh_est = direct_svd(a_mat=a, q_mat=q)
+
+ eps = np.linalg.norm(a - q @ q.T.conj() @ a)
+ err = np.linalg.norm(a - u_est @ np.diag(s_est) @ vh_est)
+ try:
+ self.assertLessEqual(err, eps)
+ except AssertionError:
+ np.testing.assert_almost_equal(err - eps, 0)
+
+
+class TestEvdNystrom(unittest.TestCase):
+ def setUp(self):
+ n = 53
+ p = 0
+ self.a_dict = {False: build_random_psd_matrix(n=n,
+ p=p,
+ rank=None,
+ rand_state=None,
+ is_complex=False),
+ True: build_random_psd_matrix(n=n,
+ p=p,
+ rank=None,
+ rand_state=None,
+ is_complex=True)}
+
+ def test_approximation_error_from_true_range(self):
+ """ Check equation (5.2) using true left singular vectors as matrix Q
+ """
+ k = 41
+ for is_complex in (False, True):
+ a = self.a_dict[is_complex]
+ s_true, u_true = eigs(a, k=k)
+ q = u_true
+
+ # Call to tested code
+ s_est, u_est = evd_nystrom(a=a, q_mat=q)
+
+ eps = np.linalg.norm(a - q @ q.T.conj() @ a)
+ err = np.linalg.norm(a - u_est @ np.diag(s_est) @ u_est.T.conj())
+ try:
+ self.assertLessEqual(
+ err, eps, msg='is_complex={}'.format(is_complex))
+ except AssertionError:
+ np.testing.assert_almost_equal(
+ err - eps, 0, err_msg='is_complex={}'.format(is_complex))
+
+ def test_approximation_error_from_q_est(self):
+ """ Check equation (5.2) using matrix Q estimated with randomized
+ range finder.
+ """
+ k = 41
+ for is_complex in (False, True):
+ a = self.a_dict[is_complex]
+ q = randomized_range_finder(a=a, n_l=k)
+
+ # Call to tested code
+ s_est, u_est = evd_nystrom(a=a, q_mat=q)
+
+ eps = np.linalg.norm(a - q @ q.T.conj() @ a)
+ err = np.linalg.norm(a - u_est @ np.diag(s_est) @ u_est.T.conj())
+ try:
+ self.assertLessEqual(
+ err, eps, msg='is_complex={}'.format(is_complex))
+ except AssertionError:
+ np.testing.assert_almost_equal(
+ err - eps, 0, err_msg='is_complex={}'.format(is_complex))
+
+ def test_approximation_error_operator(self):
+ """ Check equation (5.2) with A as an operator.
+ """
+ n = 53
+ n_l = 41
+ p = 5
+ a_op = FourierMultiplierOp(n, p)
+ q = randomized_range_finder(a=a_op, n_l=n_l)
+
+ # Call to tested code
+ s_est, u_est = evd_nystrom(a=a_op, q_mat=q)
+
+ q_op = aslinearoperator(q)
+ qh_op = aslinearoperator(q.T.conj())
+ eps = eigs(a_op - q_op @ qh_op @ a_op, k=1)[0][0]
+
+ a_op_est = aslinearoperator(u_est @ np.diag(s_est) @ u_est.T.conj())
+ err = eigs(a_op - a_op_est, k=1)[0][0]
+
+ try:
+ self.assertLessEqual(err, eps)
+ except AssertionError:
+ np.testing.assert_almost_equal(err - eps, 0)
diff --git a/pomad/tests/test_range_approximation.py b/pomad/tests/test_range_approximation.py
new file mode 100755
index 0000000000000000000000000000000000000000..70ef880a6924b8b96c2403acbd6dad4045623a07
--- /dev/null
+++ b/pomad/tests/test_range_approximation.py
@@ -0,0 +1,149 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+
+"""Test of the module :module:`pomad.range_approximation`
+
+.. moduleauthor:: Valentin Emiya
+"""
+import unittest
+import numpy as np
+
+from scipy.sparse.linalg import aslinearoperator, svds
+
+from pomad.range_approximation import \
+ randomized_range_finder, adaptive_randomized_range_finder
+from pomad.utils import \
+ build_random_psd_matrix, build_test_matrix, FourierMultiplierOp
+
+
+# TODO to be implemented: approximation, time, complex values
+class TestRandomizedRangeFinder(unittest.TestCase):
+ def setUp(self) -> None:
+ m = 47
+ n = 53
+ self.a_dict = {
+ 'random matrix':
+ build_test_matrix(m=m, n=n, p=0, rand_state=None),
+ 'operator from random matrix':
+ aslinearoperator(build_test_matrix(m=m, n=n, p=2,
+ rand_state=None)),
+ 'PSD matrix':
+ build_random_psd_matrix(n=n, rank=m, p=0, rand_state=None),
+ 'Fourier multiplier': FourierMultiplierOp(n=n)
+ }
+
+ def test_approximation_error(self):
+ """ Check equation (1.9).
+ """
+
+ k = 25
+ p = 5
+ for k_a in self.a_dict:
+ a = self.a_dict[k_a]
+ m, n = a.shape
+
+ # code to be tested
+ q_width = k + p
+ q = randomized_range_finder(a=a, n_l=q_width)
+
+ a_op = aslinearoperator(a)
+ q_op = aslinearoperator(q)
+ _, s_true, _ = svds(a, k=k+1)
+ err = svds(a_op - q_op @ q_op.H @ a_op, k=1)[0][0]
+ err_bound = (1 + 9 * np.sqrt((k + p) * min(m, n))) * s_true[k]
+ self.assertLessEqual(err, err_bound, msg='Case ' + k_a)
+
+
+class TestAdaptiveRandomizedRangeFinder(unittest.TestCase):
+ def setUp(self) -> None:
+ m = 79
+ n = 123
+ self.a_dict = {
+ 'random matrix':
+ build_test_matrix(m=m, n=n, p=5, rand_state=None),
+ 'operator from random matrix':
+ aslinearoperator(build_test_matrix(m=m, n=n, p=5,
+ rand_state=None)),
+ 'PSD matrix':
+ build_random_psd_matrix(n=n, rank=m, p=5, rand_state=None),
+ 'Fourier multiplier': FourierMultiplierOp(n=n, p=20)
+ }
+
+ def test_approximation_error(self):
+ """ Check equation (4.2).
+ """
+ # raise NotImplementedError
+ # TODO debug this test, takes too much time (loop in
+ # adaptive_randomized_range_finder)
+ # k = 11
+ # p = 5
+ tolerance = 1e-4
+ r = 6
+ proba = None
+ rand_state = None
+ n_cols_Q = 4
+ for k_a in self.a_dict:
+ a = self.a_dict[k_a]
+
+ q = adaptive_randomized_range_finder(a=a,
+ tolerance=tolerance,
+ r=r,
+ proba=proba,
+ rand_state=rand_state,
+ n_cols_Q=n_cols_Q
+ )
+
+ a_op = aslinearoperator(a)
+ q_op = aslinearoperator(q)
+ err = svds(a_op - q_op @ q_op.H @ a_op, k=1)[1][0]
+ self.assertLessEqual(err, tolerance, msg='Case ' + k_a)
diff --git a/pomad/tests/test_utils.py b/pomad/tests/test_utils.py
new file mode 100755
index 0000000000000000000000000000000000000000..4c318bde5d81124b942f0fe6f2e86e28f568d189
--- /dev/null
+++ b/pomad/tests/test_utils.py
@@ -0,0 +1,178 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+
+"""Test of the module :module:`pomad.utils`
+
+.. moduleauthor:: Valentin Emiya
+"""
+import unittest
+
+import numpy as np
+
+from pomad.utils import \
+ build_test_matrix, build_random_psd_matrix, FourierMultiplierOp
+
+
+class TestBuildRandomMatrix(unittest.TestCase):
+ def test_real(self):
+ m, n, p = 13, 17, 1
+ for rand_state in (None, 0):
+ a_mat = build_test_matrix(m=m, n=n, p=p, rand_state=rand_state)
+ np.testing.assert_array_equal(a_mat.shape, (m, n))
+ self.assertFalse(np.iscomplexobj(a_mat))
+
+
+class TestBuildRandomPsdMatrix(unittest.TestCase):
+ def test_real(self):
+ n = 29
+ is_complex = False
+ for p in (0, 1):
+ for rand_state in (None, 0):
+ a_mat = build_random_psd_matrix(n=n,
+ p=p,
+ rank=None,
+ rand_state=rand_state,
+ is_complex=is_complex)
+ s_vec, _ = np.linalg.eig(a_mat)
+
+ np.testing.assert_array_equal(a_mat.shape, (n, n))
+ self.assertFalse(np.iscomplexobj(a_mat))
+ np.testing.assert_array_almost_equal(np.imag(s_vec), 0)
+ np.testing.assert_array_equal(np.real(s_vec) > 0, True)
+
+ def test_cpx(self):
+ n = 19
+ is_complex = True
+ for p in (0, 1):
+ a_mat = build_random_psd_matrix(n=n,
+ p=p,
+ rank=None,
+ rand_state=None,
+ is_complex=is_complex)
+ s_vec, _ = np.linalg.eig(a_mat)
+
+ np.testing.assert_array_equal(a_mat.shape, (n, n))
+ self.assertTrue(np.iscomplexobj(a_mat))
+ np.testing.assert_array_almost_equal(np.imag(s_vec), 0)
+ np.testing.assert_array_equal(np.real(s_vec) > 0, True)
+
+ def test_rank(self):
+ n = 17
+ r = 11
+ is_complex = True
+ for p in (0, 1):
+ a_mat = build_random_psd_matrix(n=n,
+ p=p,
+ rank=r,
+ rand_state=None,
+ is_complex=is_complex)
+ s_vec, _ = np.linalg.eig(a_mat)
+ s_vec.sort()
+ s_vec = s_vec[::-1]
+
+ np.testing.assert_array_equal(a_mat.shape, (n, n))
+ self.assertTrue(np.iscomplexobj(a_mat))
+ np.testing.assert_array_almost_equal(np.imag(s_vec), 0)
+ np.testing.assert_array_equal(np.real(s_vec[:r]) > 0, True)
+ np.testing.assert_array_almost_equal(np.real(s_vec[r:]), 0)
+ np.testing.assert_array_equal(np.isclose(np.real(s_vec[:r]), 0),
+ False)
+
+
+class TestFourierMultiplierOp(unittest.TestCase):
+ def test_fourier_mult_op_vec(self):
+ n = 29
+ for p in (0, 1, 5):
+ op = FourierMultiplierOp(n=n, p=p)
+ np.testing.assert_array_equal(op.shape, (n, n))
+
+ w = op.w
+ x = np.random.randn(n)
+ y = np.fft.ifft(w * np.fft.fft(x))
+ np.testing.assert_array_almost_equal(op(x), y)
+ np.testing.assert_array_almost_equal(op @ x, y)
+ # Auto-adjoint
+ np.testing.assert_array_almost_equal(op.H(x), y)
+ np.testing.assert_array_almost_equal(op.H @ x, y)
+
+ def test_fourier_mult_op_mat1(self):
+ n = 17
+ n_samples = 1
+ for p in (0, 1, 7):
+ op = FourierMultiplierOp(n=n, p=p)
+ np.testing.assert_array_equal(op.shape, (n, n))
+
+ w = op.w
+ x_mat = np.random.randn(n, n_samples)
+ y = np.fft.ifft(w[:, None] * np.fft.fft(x_mat, axis=0), axis=0)
+ np.testing.assert_array_almost_equal(op(x_mat), y)
+ np.testing.assert_array_almost_equal(op @ x_mat, y)
+ # Auto-adjoint
+ np.testing.assert_array_almost_equal(op.H(x_mat), y)
+ np.testing.assert_array_almost_equal(op.H @ x_mat, y)
+
+ def test_fourier_mult_op_mat7(self):
+ n = 22
+ n_samples = 7
+ for p in (0, 1, 4):
+ op = FourierMultiplierOp(n=n, p=p)
+ np.testing.assert_array_equal(op.shape, (n, n))
+
+ w = op.w
+ x_mat = np.random.randn(n, n_samples)
+ y = np.fft.ifft(w[:, None] * np.fft.fft(x_mat, axis=0), axis=0)
+ np.testing.assert_array_almost_equal(op(x_mat), y)
+ np.testing.assert_array_almost_equal(op @ x_mat, y)
+ # Auto-adjoint
+ np.testing.assert_array_almost_equal(op.H(x_mat), y)
+ np.testing.assert_array_almost_equal(op.H @ x_mat, y)
diff --git a/pomad/utils.py b/pomad/utils.py
new file mode 100755
index 0000000000000000000000000000000000000000..c7e537d29bcdf4fbc92b5bddb5816476b1852f44
--- /dev/null
+++ b/pomad/utils.py
@@ -0,0 +1,122 @@
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+"""Utils classes and functions for pomad.
+
+.. moduleauthor:: Valentin Emiya
+"""
+import numpy as np
+from scipy.sparse.linalg import LinearOperator
+
+
+def build_test_matrix(m, n, p=10, rand_state=None, is_complex=False):
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+ if is_complex:
+ raise NotImplementedError()
+ A = rand_state.randn(m, n)
+ A = A / np.linalg.norm(A, ord=2)
+ return np.linalg.matrix_power(A @ A.T.conj(), p) @ A
+
+
+def build_random_psd_matrix(n, p=0, rank=None, rand_state=None,
+ is_complex=False):
+ """
+ Generates a random positive semidefinite matrix
+
+ Parameters
+ ----------
+ n
+ p
+ rank
+ rand_state
+ is_complex
+
+ Returns
+ -------
+
+ """
+ if rank is None:
+ rank = n
+ if rand_state is None:
+ rand_state = np.random.RandomState(None)
+ if np.issubdtype(type(rand_state), np.dtype(int).type):
+ rand_state = np.random.RandomState(rand_state)
+
+ if is_complex:
+ B = rand_state.randn(n, rank) + 1j*rand_state.randn(n, rank)
+ else:
+ B = rand_state.randn(n, rank)
+ A = B @ B.T.conj()
+ A = A / np.linalg.norm(A, ord=2)
+ return np.linalg.matrix_power(A @ A.T.conj(), p) @ A
+
+
+class FourierMultiplierOp(LinearOperator):
+ def __init__(self, n, p=1):
+ self.w = np.random.rand(n) ** p
+ LinearOperator.__init__(self,
+ shape=(self.w.size, self.w.size),
+ dtype=np.complex_)
+
+ def _matvec(self, x):
+ if x.ndim == 2:
+ return self._matmat(x)
+ return np.fft.ifft(np.fft.fft(x) * self.w)
+
+ def _matmat(self, x):
+ return np.fft.ifft(np.fft.fft(x, axis=0) * self.w[:, None], axis=0)
+
+ def _adjoint(self):
+ return self
diff --git a/requirements/defaults.txt b/requirements/defaults.txt
new file mode 100755
index 0000000000000000000000000000000000000000..1655484d4aeca0196a4ff03d10c1a61523266bed
--- /dev/null
+++ b/requirements/defaults.txt
@@ -0,0 +1,3 @@
+--index-url https://pypi.python.org/simple/
+
+numpy>=1.13
diff --git a/requirements/dev.txt b/requirements/dev.txt
new file mode 100755
index 0000000000000000000000000000000000000000..b287a430e410a343d9d1e4dbc663b158dbe15fa5
--- /dev/null
+++ b/requirements/dev.txt
@@ -0,0 +1,6 @@
+--index-url https://pypi.python.org/simple/
+
+coverage
+pytest
+pytest-cov
+pytest-randomly
diff --git a/requirements/doc.txt b/requirements/doc.txt
new file mode 100755
index 0000000000000000000000000000000000000000..3f09571e01be27274a79d20a1ca47f9f76be206f
--- /dev/null
+++ b/requirements/doc.txt
@@ -0,0 +1,5 @@
+--index-url https://pypi.python.org/simple/
+
+nbsphinx
+numpydoc
+sphinx
diff --git a/setup.cfg b/setup.cfg
new file mode 100755
index 0000000000000000000000000000000000000000..e793c6e647787d5d3f3d8d375ee260fe38040ac4
--- /dev/null
+++ b/setup.cfg
@@ -0,0 +1,30 @@
+[tool:pytest]
+testpaths = pomad
+addopts = --verbose
+ --cov-report=term-missing
+ --cov-report=html
+ --cov=pomad
+ --doctest-modules
+
+[coverage:run]
+branch = True
+source = pomad
+include = */pomad/*
+omit = */tests/*
+
+[coverage:report]
+exclude_lines =
+ pragma: no cover
+ if self.debug:
+ if settings.DEBUG
+ raise AssertionError
+ raise NotImplementedError
+ if 0:
+ if __name__ == .__main__.:
+ if obj is None: return
+ if verbose > 0:
+ if self.verbose > 0:
+ if verbose > 1:
+ if self.verbose > 1:
+ pass
+ def __str__(self):
diff --git a/setup.py b/setup.py
new file mode 100755
index 0000000000000000000000000000000000000000..cdf66d11d7fd1327626e0f77253fdd0e55017f61
--- /dev/null
+++ b/setup.py
@@ -0,0 +1,144 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# ######### COPYRIGHT #########
+# Credits
+# #######
+#
+# Copyright(c) 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 <firstname.lastname_AT_lis-lab.fr>
+#
+# This package has been created thanks to the joint work with Florent Jaillet
+# and Ronan Hamon on other packages.
+#
+# Description
+# -----------
+#
+# `pomad` is a 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, https://arxiv.org/abs/0909.4061.
+#
+#
+# Version
+# -------
+#
+# * pomad version = 0.1
+#
+# Licence
+# -------
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+# ######### COPYRIGHT #########
+
+import os
+from setuptools import setup, find_packages
+import sys
+
+NAME = 'pomad'
+DESCRIPTION = 'PrObabilistic MAtrix Decompositions from Halko et al., 2011'
+LICENSE = 'GNU General Public License v3 (GPLv3)'
+URL = 'https://gitlab.lis-lab.fr/templates/{}'.format(NAME)
+AUTHOR = 'Valentin Emiya'
+AUTHOR_EMAIL = ('valentin.emiya@lis-lab.fr')
+INSTALL_REQUIRES = ['numpy', 'scipy']
+CLASSIFIERS = [
+ 'Development Status :: 5 - Production/Stable',
+ 'Intended Audience :: Developers',
+ 'Intended Audience :: End Users/Desktop',
+ 'Intended Audience :: Science/Research',
+ 'Topic :: Scientific/Engineering :: Mathematics',
+ 'License :: OSI Approved :: GNU General Public License v3 (GPLv3)',
+ 'Natural Language :: English',
+ 'Operating System :: MacOS :: MacOS X ',
+ 'Operating System :: POSIX :: Linux',
+ 'Programming Language :: Python :: 3.5',
+ 'Programming Language :: Python :: 3.6']
+PYTHON_REQUIRES = '>=3.5'
+EXTRAS_REQUIRE = {
+ 'dev': ['coverage', 'pytest', 'pytest-cov', 'pytest-randomly'],
+ 'doc': ['nbsphinx', 'numpydoc', 'sphinx']}
+PROJECT_URLS = {'Bug Reports': URL + '/issues',
+ 'Source': URL}
+KEYWORDS = 'template, package'
+
+###############################################################################
+if sys.argv[-1] == 'setup.py':
+ print("To install, run 'python setup.py install'\n")
+
+if sys.version_info[:2] < (3, 5):
+ errmsg = '{} requires Python 3.5 or later ({[0]:d}.{[1]:d} detected).'
+ print(errmsg.format(NAME, sys.version_info[:2]))
+ sys.exit(-1)
+
+
+def get_version():
+ v_text = open('VERSION').read().strip()
+ v_text_formted = '{"' + v_text.replace('\n', '","').replace(':', '":"')
+ v_text_formted += '"}'
+ v_dict = eval(v_text_formted)
+ return v_dict[NAME]
+
+
+def set_version(path, VERSION):
+ filename = os.path.join(path, '__init__.py')
+ buf = ""
+ for line in open(filename, "rb"):
+ if not line.decode("utf8").startswith("__version__ ="):
+ buf += line.decode("utf8")
+ f = open(filename, "wb")
+ f.write(buf.encode("utf8"))
+ f.write(('__version__ = "%s"\n' % VERSION).encode("utf8"))
+
+
+def setup_package():
+ """Setup function"""
+ # set version
+ VERSION = get_version()
+
+ here = os.path.abspath(os.path.dirname(__file__))
+ with open(os.path.join(here, 'README.rst'), encoding='utf-8') as f:
+ long_description = f.read()
+
+ mod_dir = NAME
+ set_version(mod_dir, get_version())
+ setup(name=NAME,
+ version=VERSION,
+ description=DESCRIPTION,
+ long_description=long_description,
+ url=URL,
+ author=AUTHOR,
+ author_email=AUTHOR_EMAIL,
+ license=LICENSE,
+ classifiers=CLASSIFIERS,
+ keywords=KEYWORDS,
+ packages=find_packages(exclude=['doc', 'dev']),
+ install_requires=INSTALL_REQUIRES,
+ python_requires=PYTHON_REQUIRES,
+ extras_require=EXTRAS_REQUIRE,
+ project_urls=PROJECT_URLS)
+
+
+if __name__ == "__main__":
+ setup_package()