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 + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. You can apply it to +your programs, too. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +them if you wish), that you receive source code or can get it if you +want it, that you can change the software or use pieces of it in new +free programs, and that you know you can do these things. + + To protect your rights, we need to prevent others from denying you +these rights or asking you to surrender the rights. Therefore, you have +certain responsibilities if you distribute copies of the software, or if +you modify it: responsibilities to respect the freedom of others. + + For example, if you distribute copies of such a program, whether +gratis or for a fee, you must pass on to the recipients the same +freedoms that you received. You must make sure that they, too, receive +or can get the source code. And you must show them these terms so they +know their rights. + + Developers that use the GNU GPL protect your rights with two steps: +(1) assert copyright on the software, and (2) offer you this License +giving you legal permission to copy, distribute and/or modify it. + + For the developers' and authors' protection, the GPL clearly explains +that there is no warranty for this free software. For both users' and +authors' sake, the GPL requires that modified versions be marked as +changed, so that their problems will not be attributed erroneously to +authors of previous versions. + + Some devices are designed to deny users access to install or run +modified versions of the software inside them, although the manufacturer +can do so. This is fundamentally incompatible with the aim of +protecting users' freedom to change the software. The systematic +pattern of such abuse occurs in the area of products for individuals to +use, which is precisely where it is most unacceptable. Therefore, we +have designed this version of the GPL to prohibit the practice for those +products. If such problems arise substantially in other domains, we +stand ready to extend this provision to those domains in future versions +of the GPL, as needed to protect the freedom of users. + + Finally, every program is threatened constantly by software patents. +States should not allow patents to restrict development and use of +software on general-purpose computers, but in those that do, we wish to +avoid the special danger that patents applied to a free program could +make it effectively proprietary. To prevent this, the GPL assures that +patents cannot be used to render the program non-free. + + The precise terms and conditions for copying, distribution and +modification follow. + + TERMS AND CONDITIONS + + 0. Definitions. + + "This License" refers to version 3 of the GNU General Public License. + + "Copyright" also means copyright-like laws that apply to other kinds of +works, such as semiconductor masks. + + "The Program" refers to any copyrightable work licensed under this +License. Each licensee is addressed as "you". "Licensees" and +"recipients" may be individuals or organizations. + + To "modify" a work means to copy from or adapt all or part of the work +in a fashion requiring copyright permission, other than the making of an +exact copy. The resulting work is called a "modified version" of the +earlier work or a work "based on" the earlier work. + + A "covered work" means either the unmodified Program or a work based +on the Program. + + To "propagate" a work means to do anything with it that, without +permission, would make you directly or secondarily liable for +infringement under applicable copyright law, except executing it on a +computer or modifying a private copy. Propagation includes copying, +distribution (with or without modification), making available to the +public, and in some countries other activities as well. + + To "convey" a work means any kind of propagation that enables other +parties to make or receive copies. Mere interaction with a user through +a computer network, with no transfer of a copy, is not conveying. + + An interactive user interface displays "Appropriate Legal Notices" +to the extent that it includes a convenient and prominently visible +feature that (1) displays an appropriate copyright notice, and (2) +tells the user that there is no warranty for the work (except to the +extent that warranties are provided), that licensees may convey the +work under this License, and how to view a copy of this License. If +the interface presents a list of user commands or options, such as a +menu, a prominent item in the list meets this criterion. + + 1. Source Code. + + The "source code" for a work means the preferred form of the work +for making modifications to it. "Object code" means any non-source +form of a work. + + A "Standard Interface" means an interface that either is an official +standard defined by a recognized standards body, or, in the case of +interfaces specified for a particular programming language, one that +is widely used among developers working in that language. + + The "System Libraries" of an executable work include anything, other +than the work as a whole, that (a) is included in the normal form of +packaging a Major Component, but which is not part of that Major +Component, and (b) serves only to enable use of the work with that +Major Component, or to implement a Standard Interface for which an +implementation is available to the public in source code form. A +"Major Component", in this context, means a major essential component +(kernel, window system, and so on) of the specific operating system +(if any) on which the executable work runs, or a compiler used to +produce the work, or an object code interpreter used to run it. + + The "Corresponding Source" for a work in object code form means all +the source code needed to generate, install, and (for an executable +work) run the object code and to modify the work, including scripts to +control those activities. However, it does not include the work's +System Libraries, or general-purpose tools or generally available free +programs which are used unmodified in performing those activities but +which are not part of the work. For example, Corresponding Source +includes interface definition files associated with source files for +the work, and the source code for shared libraries and dynamically +linked subprograms that the work is specifically designed to require, +such as by intimate data communication or control flow between those +subprograms and other parts of the work. + + The Corresponding Source need not include anything that users +can regenerate automatically from other parts of the Corresponding +Source. + + The Corresponding Source for a work in source code form is that +same work. + + 2. Basic Permissions. + + All rights granted under this License are granted for the term of +copyright on the Program, and are irrevocable provided the stated +conditions are met. This License explicitly affirms your unlimited +permission to run the unmodified Program. The output from running a +covered work is covered by this License only if the output, given its +content, constitutes a covered work. This License acknowledges your +rights of fair use or other equivalent, as provided by copyright law. + + You may make, run and propagate covered works that you do not +convey, without conditions so long as your license otherwise remains +in force. You may convey covered works to others for the sole purpose +of having them make modifications exclusively for you, or provide you +with facilities for running those works, provided that you comply with +the terms of this License in conveying all material for which you do +not control copyright. Those thus making or running the covered works +for you must do so exclusively on your behalf, under your direction +and control, on terms that prohibit them from making any copies of +your copyrighted material outside their relationship with you. + + Conveying under any other circumstances is permitted solely under +the conditions stated below. Sublicensing is not allowed; section 10 +makes it unnecessary. + + 3. Protecting Users' Legal Rights From Anti-Circumvention Law. + + No covered work shall be deemed part of an effective technological +measure under any applicable law fulfilling obligations under article +11 of the WIPO copyright treaty adopted on 20 December 1996, or +similar laws prohibiting or restricting circumvention of such +measures. + + When you convey a covered work, you waive any legal power to forbid +circumvention of technological measures to the extent such circumvention +is effected by exercising rights under this License with respect to +the covered work, and you disclaim any intention to limit operation or +modification of the work as a means of enforcing, against the work's +users, your or third parties' legal rights to forbid circumvention of +technological measures. + + 4. Conveying Verbatim Copies. + + You may convey verbatim copies of the Program's source code as you +receive it, in any medium, provided that you conspicuously and +appropriately publish on each copy an appropriate copyright notice; +keep intact all notices stating that this License and any +non-permissive terms added in accord with section 7 apply to the code; +keep intact all notices of the absence of any warranty; and give all +recipients a copy of this License along with the Program. + + You may charge any price or no price for each copy that you convey, +and you may offer support or warranty protection for a fee. + + 5. Conveying Modified Source Versions. + + You may convey a work based on the Program, or the modifications to +produce it from the Program, in the form of source code under the +terms of section 4, provided that you also meet all of these conditions: + + a) The work must carry prominent notices stating that you modified + it, and giving a relevant date. + + b) The work must carry prominent notices stating that it is + released under this License and any conditions added under section + 7. This requirement modifies the requirement in section 4 to + "keep intact all notices". + + c) You must license the entire work, as a whole, under this + License to anyone who comes into possession of a copy. This + License will therefore apply, along with any applicable section 7 + additional terms, to the whole of the work, and all its parts, + regardless of how they are packaged. This License gives no + permission to license the work in any other way, but it does not + invalidate such permission if you have separately received it. + + d) If the work has interactive user interfaces, each must display + Appropriate Legal Notices; however, if the Program has interactive + interfaces that do not display Appropriate Legal Notices, your + work need not make them do so. + + A compilation of a covered work with other separate and independent +works, which are not by their nature extensions of the covered work, +and which are not combined with it such as to form a larger program, +in or on a volume of a storage or distribution medium, is called an +"aggregate" if the compilation and its resulting copyright are not +used to limit the access or legal rights of the compilation's users +beyond what the individual works permit. Inclusion of a covered work +in an aggregate does not cause this License to apply to the other +parts of the aggregate. + + 6. Conveying Non-Source Forms. + + You may convey a covered work in object code form under the terms +of sections 4 and 5, provided that you also convey the +machine-readable Corresponding Source under the terms of this License, +in one of these ways: + + a) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by the + Corresponding Source fixed on a durable physical medium + customarily used for software interchange. + + b) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by a + written offer, valid for at least three years and valid for as + long as you offer spare parts or customer support for that product + model, to give anyone who possesses the object code either (1) a + copy of the Corresponding Source for all the software in the + product that is covered by this License, on a durable physical + medium customarily used for software interchange, for a price no + more than your reasonable cost of physically performing this + conveying of source, or (2) access to copy the + Corresponding Source from a network server at no charge. + + c) Convey individual copies of the object code with a copy of the + written offer to provide the Corresponding Source. This + alternative is allowed only occasionally and noncommercially, and + only if you received the object code with such an offer, in accord + with subsection 6b. + + d) Convey the object code by offering access from a designated + place (gratis or for a charge), and offer equivalent access to the + Corresponding Source in the same way through the same place at no + further charge. You need not require recipients to copy the + Corresponding Source along with the object code. If the place to + copy the object code is a network server, the Corresponding Source + may be on a different server (operated by you or a third party) + that supports equivalent copying facilities, provided you maintain + clear directions next to the object code saying where to find the + Corresponding Source. Regardless of what server hosts the + Corresponding Source, you remain obligated to ensure that it is + available for as long as needed to satisfy these requirements. + + e) Convey the object code using peer-to-peer transmission, provided + you inform other peers where the object code and Corresponding + Source of the work are being offered to the general public at no + charge under subsection 6d. + + A separable portion of the object code, whose source code is excluded +from the Corresponding Source as a System Library, need not be +included in conveying the object code work. + + A "User Product" is either (1) a "consumer product", which means any +tangible personal property which is normally used for personal, family, +or household purposes, or (2) anything designed or sold for incorporation +into a dwelling. In determining whether a product is a consumer product, +doubtful cases shall be resolved in favor of coverage. For a particular +product received by a particular user, "normally used" refers to a +typical or common use of that class of product, regardless of the status +of the particular user or of the way in which the particular user +actually uses, or expects or is expected to use, the product. A product +is a consumer product regardless of whether the product has substantial +commercial, industrial or non-consumer uses, unless such uses represent +the only significant mode of use of the product. + + "Installation Information" for a User Product means any methods, +procedures, authorization keys, or other information required to install +and execute modified versions of a covered work in that User Product from +a modified version of its Corresponding Source. The information must +suffice to ensure that the continued functioning of the modified object +code is in no case prevented or interfered with solely because +modification has been made. + + If you convey an object code work under this section in, or with, or +specifically for use in, a User Product, and the conveying occurs as +part of a transaction in which the right of possession and use of the +User Product is transferred to the recipient in perpetuity or for a +fixed term (regardless of how the transaction is characterized), the +Corresponding Source conveyed under this section must be accompanied +by the Installation Information. But this requirement does not apply +if neither you nor any third party retains the ability to install +modified object code on the User Product (for example, the work has +been installed in ROM). + + The requirement to provide Installation Information does not include a +requirement to continue to provide support service, warranty, or updates +for a work that has been modified or installed by the recipient, or for +the User Product in which it has been modified or installed. Access to a +network may be denied when the modification itself materially and +adversely affects the operation of the network or violates the rules and +protocols for communication across the network. + + Corresponding Source conveyed, and Installation Information provided, +in accord with this section must be in a format that is publicly +documented (and with an implementation available to the public in +source code form), and must require no special password or key for +unpacking, reading or copying. + + 7. Additional Terms. + + "Additional permissions" are terms that supplement the terms of this +License by making exceptions from one or more of its conditions. +Additional permissions that are applicable to the entire Program shall +be treated as though they were included in this License, to the extent +that they are valid under applicable law. If additional permissions +apply only to part of the Program, that part may be used separately +under those permissions, but the entire Program remains governed by +this License without regard to the additional permissions. + + When you convey a copy of a covered work, you may at your option +remove any additional permissions from that copy, or from any part of +it. (Additional permissions may be written to require their own +removal in certain cases when you modify the work.) You may place +additional permissions on material, added by you to a covered work, +for which you have or can give appropriate copyright permission. + + Notwithstanding any other provision of this License, for material you +add to a covered work, you may (if authorized by the copyright holders of +that material) supplement the terms of this License with terms: + + a) Disclaiming warranty or limiting liability differently from the + terms of sections 15 and 16 of this License; or + + b) Requiring preservation of specified reasonable legal notices or + author attributions in that material or in the Appropriate Legal + Notices displayed by works containing it; or + + c) Prohibiting misrepresentation of the origin of that material, or + requiring that modified versions of such material be marked in + reasonable ways as different from the original version; or + + d) Limiting the use for publicity purposes of names of licensors or + authors of the material; or + + e) Declining to grant rights under trademark law for use of some + trade names, trademarks, or service marks; or + + f) Requiring indemnification of licensors and authors of that + material by anyone who conveys the material (or modified versions of + it) with contractual assumptions of liability to the recipient, for + any liability that these contractual assumptions directly impose on + those licensors and authors. + + All other non-permissive additional terms are considered "further +restrictions" within the meaning of section 10. If the Program as you +received it, or any part of it, contains a notice stating that it is +governed by this License along with a term that is a further +restriction, you may remove that term. If a license document contains +a further restriction but permits relicensing or conveying under this +License, you may add to a covered work material governed by the terms +of that license document, provided that the further restriction does +not survive such relicensing or conveying. + + If you add terms to a covered work in accord with this section, you +must place, in the relevant source files, a statement of the +additional terms that apply to those files, or a notice indicating +where to find the applicable terms. + + Additional terms, permissive or non-permissive, may be stated in the +form of a separately written license, or stated as exceptions; +the above requirements apply either way. + + 8. Termination. + + You may not propagate or modify a covered work except as expressly +provided under this License. Any attempt otherwise to propagate or +modify it is void, and will automatically terminate your rights under +this License (including any patent licenses granted under the third +paragraph of section 11). + + However, if you cease all violation of this License, then your +license from a particular copyright holder is reinstated (a) +provisionally, unless and until the copyright holder explicitly and +finally terminates your license, and (b) permanently, if the copyright +holder fails to notify you of the violation by some reasonable means +prior to 60 days after the cessation. + + Moreover, your license from a particular copyright holder is +reinstated permanently if the copyright holder notifies you of the +violation by some reasonable means, this is the first time you have +received notice of violation of this License (for any work) from that +copyright holder, and you cure the violation prior to 30 days after +your receipt of the notice. + + Termination of your rights under this section does not terminate the +licenses of parties who have received copies or rights from you under +this License. If your rights have been terminated and not permanently +reinstated, you do not qualify to receive new licenses for the same +material under section 10. + + 9. Acceptance Not Required for Having Copies. + + You are not required to accept this License in order to receive or +run a copy of the Program. Ancillary propagation of a covered work +occurring solely as a consequence of using peer-to-peer transmission +to receive a copy likewise does not require acceptance. However, +nothing other than this License grants you permission to propagate or +modify any covered work. These actions infringe copyright if you do +not accept this License. Therefore, by modifying or propagating a +covered work, you indicate your acceptance of this License to do so. + + 10. Automatic Licensing of Downstream Recipients. + + Each time you convey a covered work, the recipient automatically +receives a license from the original licensors, to run, modify and +propagate that work, subject to this License. You are not responsible +for enforcing compliance by third parties with this License. + + An "entity transaction" is a transaction transferring control of an +organization, or substantially all assets of one, or subdividing an +organization, or merging organizations. If propagation of a covered +work results from an entity transaction, each party to that +transaction who receives a copy of the work also receives whatever +licenses to the work the party's predecessor in interest had or could +give under the previous paragraph, plus a right to possession of the +Corresponding Source of the work from the predecessor in interest, if +the predecessor has it or can get it with reasonable efforts. + + You may not impose any further restrictions on the exercise of the +rights granted or affirmed under this License. For example, you may +not impose a license fee, royalty, or other charge for exercise of +rights granted under this License, and you may not initiate litigation +(including a cross-claim or counterclaim in a lawsuit) alleging that +any patent claim is infringed by making, using, selling, offering for +sale, or importing the Program or any portion of it. + + 11. Patents. + + A "contributor" is a copyright holder who authorizes use under this +License of the Program or a work on which the Program is based. The +work thus licensed is called the contributor's "contributor version". + + A contributor's "essential patent claims" are all patent claims +owned or controlled by the contributor, whether already acquired or +hereafter acquired, that would be infringed by some manner, permitted +by this License, of making, using, or selling its contributor version, +but do not include claims that would be infringed only as a +consequence of further modification of the contributor version. For +purposes of this definition, "control" includes the right to grant +patent sublicenses in a manner consistent with the requirements of +this License. + + Each contributor grants you a non-exclusive, worldwide, royalty-free +patent license under the contributor's essential patent claims, to +make, use, sell, offer for sale, import and otherwise run, modify and +propagate the contents of its contributor version. + + In the following three paragraphs, a "patent license" is any express +agreement or commitment, however denominated, not to enforce a patent +(such as an express permission to practice a patent or covenant not to +sue for patent infringement). To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + 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()