HaskellNN (empty) → 0.1
raw patch · 19 files changed
+3343/−0 lines, 19 filesdep +basedep +hmatrixdep +randomsetup-changed
Dependencies added: base, hmatrix, random
Files
- HaskellNN.cabal +62/−0
- LICENSE +674/−0
- Setup.hs +2/−0
- cbits/lbfgs.c +1371/−0
- src/AI/Calculation.hs +25/−0
- src/AI/Calculation/Activation.hs +66/−0
- src/AI/Calculation/Cost.hs +155/−0
- src/AI/Calculation/Gradients.hs +205/−0
- src/AI/Calculation/NetworkOutput.hs +35/−0
- src/AI/Model.hs +24/−0
- src/AI/Model/Classification.hs +41/−0
- src/AI/Model/General.hs +42/−0
- src/AI/Model/GenericModel.hs +88/−0
- src/AI/Network.hs +101/−0
- src/AI/Signatures.hs +93/−0
- src/AI/Training.hs +122/−0
- src/AI/Training/Internal.hs +29/−0
- src/AI/Training/Internal/LBFGSAux.hs +123/−0
- src/AI/Training/Internal/lbfgs_aux.c +85/−0
+ HaskellNN.cabal view
@@ -0,0 +1,62 @@+Name: HaskellNN+Version: 0.1+License: GPL+License-file: LICENSE+Author: Kiet Lam+Maintainer: Kiet Lam <ktklam9@gmail.com>+Synopsis: High Performance Neural Network in Haskell+Description: High Performance Neural Network in Haskell+ .+ Provides fast training algorithms using+ hmatrix's bindings to GSL and custom bindings+ to the liblbfgs C-library+ .+ Supported training algorithms: Gradient Descent, Conjugate Gradient, BFGS, LBFGS+ .+ - Users should focus on "AI.Model" for most usages (classification / regression)+ .+ - Other modules are provided for user expansion if needed+ .+ Go to <https://github.com/ktklam9/HaskellNN> for examples and tests for usage++Category: AI++Build-type: Simple+Cabal-version: >= 1.6++Library++ Build-depends: base >= 4 && < 5,+ hmatrix >= 0.13.0.0,+ random++ Extensions: ForeignFunctionInterface++ hs-source-dirs: src+ Exposed-modules: AI.Calculation,+ AI.Calculation.Activation,+ AI.Calculation.Cost,+ AI.Calculation.Gradients,+ AI.Calculation.NetworkOutput,+ AI.Signatures,+ AI.Model,+ AI.Model.Classification,+ AI.Model.General,+ AI.Model.GenericModel,+ AI.Training,+ AI.Network++ Other-modules: AI.Training.Internal,+ AI.Training.Internal.LBFGSAux+++ ghc-prof-options: -prof -auto-all+ Include-Dirs: cbits+ C-sources: src/AI/Training/Internal/lbfgs_aux.c,+ cbits/lbfgs.c+ Includes: lbfgs.h+++source-repository head+ type: git+ location: https://github.com/ktklam9/HaskellNN
+ LICENSE view
@@ -0,0 +1,674 @@+ GNU GENERAL PUBLIC LICENSE+ Version 3, 29 June 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://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++ How to Apply These Terms to Your New Programs++ If you develop a new program, and you want it to be of the greatest+possible use to the public, the best way to achieve this is to make it+free software which everyone can redistribute and change under these terms.++ To do so, attach the following notices to the program. It is safest+to attach them to the start of each source file to most effectively+state the exclusion of warranty; and each file should have at least+the "copyright" line and a pointer to where the full notice is found.++ <one line to give the program's name and a brief idea of what it does.>+ Copyright (C) <year> <name of author>++ 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/>.++Also add information on how to contact you by electronic and paper mail.++ If the program does terminal interaction, make it output a short+notice like this when it starts in an interactive mode:++ <program> Copyright (C) <year> <name of author>+ This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.+ This is free software, and you are welcome to redistribute it+ under certain conditions; type `show c' for details.++The hypothetical commands `show w' and `show c' should show the appropriate+parts of the General Public License. Of course, your program's commands+might be different; for a GUI interface, you would use an "about box".++ You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU GPL, see+<http://www.gnu.org/licenses/>.++ The GNU General Public License does not permit incorporating your program+into proprietary programs. If your program is a subroutine library, you+may consider it more useful to permit linking proprietary applications with+the library. If this is what you want to do, use the GNU Lesser General+Public License instead of this License. But first, please read+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ cbits/lbfgs.c view
@@ -0,0 +1,1371 @@+/*+ * Limited memory BFGS (L-BFGS).+ *+ * Copyright (c) 1990, Jorge Nocedal+ * Copyright (c) 2007-2010 Naoaki Okazaki+ * All rights reserved.+ *+ * Permission is hereby granted, free of charge, to any person obtaining a copy+ * of this software and associated documentation files (the "Software"), to deal+ * in the Software without restriction, including without limitation the rights+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell+ * copies of the Software, and to permit persons to whom the Software is+ * furnished to do so, subject to the following conditions:+ *+ * The above copyright notice and this permission notice shall be included in+ * all copies or substantial portions of the Software.+ *+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN+ * THE SOFTWARE.+ */++/* $Id$ */++/*+This library is a C port of the FORTRAN implementation of Limited-memory+Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method written by Jorge Nocedal.+The original FORTRAN source code is available at:+http://www.ece.northwestern.edu/~nocedal/lbfgs.html++The L-BFGS algorithm is described in:+ - Jorge Nocedal.+ Updating Quasi-Newton Matrices with Limited Storage.+ <i>Mathematics of Computation</i>, Vol. 35, No. 151, pp. 773--782, 1980.+ - Dong C. Liu and Jorge Nocedal.+ On the limited memory BFGS method for large scale optimization.+ <i>Mathematical Programming</i> B, Vol. 45, No. 3, pp. 503-528, 1989.++The line search algorithms used in this implementation are described in:+ - John E. Dennis and Robert B. Schnabel.+ <i>Numerical Methods for Unconstrained Optimization and Nonlinear+ Equations</i>, Englewood Cliffs, 1983.+ - Jorge J. More and David J. Thuente.+ Line search algorithm with guaranteed sufficient decrease.+ <i>ACM Transactions on Mathematical Software (TOMS)</i>, Vol. 20, No. 3,+ pp. 286-307, 1994.++This library also implements Orthant-Wise Limited-memory Quasi-Newton (OWL-QN)+method presented in:+ - Galen Andrew and Jianfeng Gao.+ Scalable training of L1-regularized log-linear models.+ In <i>Proceedings of the 24th International Conference on Machine+ Learning (ICML 2007)</i>, pp. 33-40, 2007.++I would like to thank the original author, Jorge Nocedal, who has been+distributing the effieicnt and explanatory implementation in an open source+licence.+*/++#ifdef HAVE_CONFIG_H+#include <config.h>+#endif/*HAVE_CONFIG_H*/++#include <stdint.h>+#include <stdio.h>+#include <stdlib.h>+#include <math.h>++#include <lbfgs.h>++#ifdef _MSC_VER+#define inline __inline+#endif/*_MSC_VER*/++#if defined(USE_SSE) && defined(__SSE2__) && LBFGS_FLOAT == 64+/* Use SSE2 optimization for 64bit double precision. */+#include "arithmetic_sse_double.h"++#elif defined(USE_SSE) && defined(__SSE__) && LBFGS_FLOAT == 32+/* Use SSE optimization for 32bit float precision. */+#include "arithmetic_sse_float.h"++#else+/* No CPU specific optimization. */+#include "arithmetic_ansi.h"++#endif++#define min2(a, b) ((a) <= (b) ? (a) : (b))+#define max2(a, b) ((a) >= (b) ? (a) : (b))+#define max3(a, b, c) max2(max2((a), (b)), (c));++struct tag_callback_data {+ int n;+ void *instance;+ lbfgs_evaluate_t proc_evaluate;+ lbfgs_progress_t proc_progress;+};+typedef struct tag_callback_data callback_data_t;++struct tag_iteration_data {+ lbfgsfloatval_t alpha;+ lbfgsfloatval_t *s; /* [n] */+ lbfgsfloatval_t *y; /* [n] */+ lbfgsfloatval_t ys; /* vecdot(y, s) */+};+typedef struct tag_iteration_data iteration_data_t;++static const lbfgs_parameter_t _defparam = {+ 6, 1e-5, 0, 1e-5,+ 0, LBFGS_LINESEARCH_DEFAULT, 40,+ 1e-20, 1e20, 1e-4, 0.9, 0.9, 1.0e-16,+ 0.0, 0, -1,+};++/* Forward function declarations. */++typedef int (*line_search_proc)(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wa,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ );+ +static int line_search_backtracking(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wa,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ );++static int line_search_backtracking_owlqn(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wp,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ );++static int line_search_morethuente(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wa,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ );++static int update_trial_interval(+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *fx,+ lbfgsfloatval_t *dx,+ lbfgsfloatval_t *y,+ lbfgsfloatval_t *fy,+ lbfgsfloatval_t *dy,+ lbfgsfloatval_t *t,+ lbfgsfloatval_t *ft,+ lbfgsfloatval_t *dt,+ const lbfgsfloatval_t tmin,+ const lbfgsfloatval_t tmax,+ int *brackt+ );++static lbfgsfloatval_t owlqn_x1norm(+ const lbfgsfloatval_t* x,+ const int start,+ const int n+ );++static void owlqn_pseudo_gradient(+ lbfgsfloatval_t* pg,+ const lbfgsfloatval_t* x,+ const lbfgsfloatval_t* g,+ const int n,+ const lbfgsfloatval_t c,+ const int start,+ const int end+ );++static void owlqn_project(+ lbfgsfloatval_t* d,+ const lbfgsfloatval_t* sign,+ const int start,+ const int end+ );+++#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))+static int round_out_variables(int n)+{+ n += 7;+ n /= 8;+ n *= 8;+ return n;+}+#endif/*defined(USE_SSE)*/++lbfgsfloatval_t* lbfgs_malloc(int n)+{+#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))+ n = round_out_variables(n);+#endif/*defined(USE_SSE)*/+ return (lbfgsfloatval_t*)vecalloc(sizeof(lbfgsfloatval_t) * n);+}++void lbfgs_free(lbfgsfloatval_t *x)+{+ vecfree(x);+}++void lbfgs_parameter_init(lbfgs_parameter_t *param)+{+ memcpy(param, &_defparam, sizeof(*param));+}++int lbfgs(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *ptr_fx,+ lbfgs_evaluate_t proc_evaluate,+ lbfgs_progress_t proc_progress,+ void *instance,+ lbfgs_parameter_t *_param+ )+{+ int ret;+ int i, j, k, ls, end, bound;+ lbfgsfloatval_t step;++ /* Constant parameters and their default values. */+ lbfgs_parameter_t param = (_param != NULL) ? (*_param) : _defparam;+ const int m = param.m;++ lbfgsfloatval_t *xp = NULL;+ lbfgsfloatval_t *g = NULL, *gp = NULL, *pg = NULL;+ lbfgsfloatval_t *d = NULL, *w = NULL, *pf = NULL;+ iteration_data_t *lm = NULL, *it = NULL;+ lbfgsfloatval_t ys, yy;+ lbfgsfloatval_t xnorm, gnorm, beta;+ lbfgsfloatval_t fx = 0.;+ lbfgsfloatval_t rate = 0.;+ line_search_proc linesearch = line_search_morethuente;++ /* Construct a callback data. */+ callback_data_t cd;+ cd.n = n;+ cd.instance = instance;+ cd.proc_evaluate = proc_evaluate;+ cd.proc_progress = proc_progress;++#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))+ /* Round out the number of variables. */+ n = round_out_variables(n);+#endif/*defined(USE_SSE)*/++ /* Check the input parameters for errors. */+ if (n <= 0) {+ return LBFGSERR_INVALID_N;+ }+#if defined(USE_SSE) && (defined(__SSE__) || defined(__SSE2__))+ if (n % 8 != 0) {+ return LBFGSERR_INVALID_N_SSE;+ }+ if ((uintptr_t)(const void*)x % 16 != 0) {+ return LBFGSERR_INVALID_X_SSE;+ }+#endif/*defined(USE_SSE)*/+ if (param.epsilon < 0.) {+ return LBFGSERR_INVALID_EPSILON;+ }+ if (param.past < 0) {+ return LBFGSERR_INVALID_TESTPERIOD;+ }+ if (param.delta < 0.) {+ return LBFGSERR_INVALID_DELTA;+ }+ if (param.min_step < 0.) {+ return LBFGSERR_INVALID_MINSTEP;+ }+ if (param.max_step < param.min_step) {+ return LBFGSERR_INVALID_MAXSTEP;+ }+ if (param.ftol < 0.) {+ return LBFGSERR_INVALID_FTOL;+ }+ if (param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE ||+ param.linesearch == LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {+ if (param.wolfe <= param.ftol || 1. <= param.wolfe) {+ return LBFGSERR_INVALID_WOLFE;+ }+ }+ if (param.gtol < 0.) {+ return LBFGSERR_INVALID_GTOL;+ }+ if (param.xtol < 0.) {+ return LBFGSERR_INVALID_XTOL;+ }+ if (param.max_linesearch <= 0) {+ return LBFGSERR_INVALID_MAXLINESEARCH;+ }+ if (param.orthantwise_c < 0.) {+ return LBFGSERR_INVALID_ORTHANTWISE;+ }+ if (param.orthantwise_start < 0 || n < param.orthantwise_start) {+ return LBFGSERR_INVALID_ORTHANTWISE_START;+ }+ if (param.orthantwise_end < 0) {+ param.orthantwise_end = n;+ }+ if (n < param.orthantwise_end) {+ return LBFGSERR_INVALID_ORTHANTWISE_END;+ }+ if (param.orthantwise_c != 0.) {+ switch (param.linesearch) {+ case LBFGS_LINESEARCH_BACKTRACKING:+ linesearch = line_search_backtracking_owlqn;+ break;+ default:+ /* Only the backtracking method is available. */+ return LBFGSERR_INVALID_LINESEARCH;+ }+ } else {+ switch (param.linesearch) {+ case LBFGS_LINESEARCH_MORETHUENTE:+ linesearch = line_search_morethuente;+ break;+ case LBFGS_LINESEARCH_BACKTRACKING_ARMIJO:+ case LBFGS_LINESEARCH_BACKTRACKING_WOLFE:+ case LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE:+ linesearch = line_search_backtracking;+ break;+ default:+ return LBFGSERR_INVALID_LINESEARCH;+ }+ }++ /* Allocate working space. */+ xp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ g = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ gp = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ d = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ w = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ if (xp == NULL || g == NULL || gp == NULL || d == NULL || w == NULL) {+ ret = LBFGSERR_OUTOFMEMORY;+ goto lbfgs_exit;+ }++ if (param.orthantwise_c != 0.) {+ /* Allocate working space for OW-LQN. */+ pg = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ if (pg == NULL) {+ ret = LBFGSERR_OUTOFMEMORY;+ goto lbfgs_exit;+ }+ }++ /* Allocate limited memory storage. */+ lm = (iteration_data_t*)vecalloc(m * sizeof(iteration_data_t));+ if (lm == NULL) {+ ret = LBFGSERR_OUTOFMEMORY;+ goto lbfgs_exit;+ }++ /* Initialize the limited memory. */+ for (i = 0;i < m;++i) {+ it = &lm[i];+ it->alpha = 0;+ it->ys = 0;+ it->s = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ it->y = (lbfgsfloatval_t*)vecalloc(n * sizeof(lbfgsfloatval_t));+ if (it->s == NULL || it->y == NULL) {+ ret = LBFGSERR_OUTOFMEMORY;+ goto lbfgs_exit;+ }+ }++ /* Allocate an array for storing previous values of the objective function. */+ if (0 < param.past) {+ pf = (lbfgsfloatval_t*)vecalloc(param.past * sizeof(lbfgsfloatval_t));+ }++ /* Evaluate the function value and its gradient. */+ fx = cd.proc_evaluate(cd.instance, x, g, cd.n, 0);+ if (0. != param.orthantwise_c) {+ /* Compute the L1 norm of the variable and add it to the object value. */+ xnorm = owlqn_x1norm(x, param.orthantwise_start, param.orthantwise_end);+ fx += xnorm * param.orthantwise_c;+ owlqn_pseudo_gradient(+ pg, x, g, n,+ param.orthantwise_c, param.orthantwise_start, param.orthantwise_end+ );+ }++ /* Store the initial value of the objective function. */+ if (pf != NULL) {+ pf[0] = fx;+ }++ /*+ Compute the direction;+ we assume the initial hessian matrix H_0 as the identity matrix.+ */+ if (param.orthantwise_c == 0.) {+ vecncpy(d, g, n);+ } else {+ vecncpy(d, pg, n);+ }++ /*+ Make sure that the initial variables are not a minimizer.+ */+ vec2norm(&xnorm, x, n);+ if (param.orthantwise_c == 0.) {+ vec2norm(&gnorm, g, n);+ } else {+ vec2norm(&gnorm, pg, n);+ }+ if (xnorm < 1.0) xnorm = 1.0;+ if (gnorm / xnorm <= param.epsilon) {+ ret = LBFGS_ALREADY_MINIMIZED;+ goto lbfgs_exit;+ }++ /* Compute the initial step:+ step = 1.0 / sqrt(vecdot(d, d, n))+ */+ vec2norminv(&step, d, n);++ k = 1;+ end = 0;+ for (;;) {+ /* Store the current position and gradient vectors. */+ veccpy(xp, x, n);+ veccpy(gp, g, n);++ /* Search for an optimal step. */+ if (param.orthantwise_c == 0.) {+ ls = linesearch(n, x, &fx, g, d, &step, xp, gp, w, &cd, ¶m);+ } else {+ ls = linesearch(n, x, &fx, g, d, &step, xp, pg, w, &cd, ¶m);+ owlqn_pseudo_gradient(+ pg, x, g, n,+ param.orthantwise_c, param.orthantwise_start, param.orthantwise_end+ );+ }+ if (ls < 0) {+ /* Revert to the previous point. */+ veccpy(x, xp, n);+ veccpy(g, gp, n);+ ret = ls;+ goto lbfgs_exit;+ }++ /* Compute x and g norms. */+ vec2norm(&xnorm, x, n);+ if (param.orthantwise_c == 0.) {+ vec2norm(&gnorm, g, n);+ } else {+ vec2norm(&gnorm, pg, n);+ }++ /* Report the progress. */+ if (cd.proc_progress) {+ if ((ret = cd.proc_progress(cd.instance, x, g, fx, xnorm, gnorm, step, cd.n, k, ls))) {+ goto lbfgs_exit;+ }+ }++ /*+ Convergence test.+ The criterion is given by the following formula:+ |g(x)| / \max(1, |x|) < \epsilon+ */+ if (xnorm < 1.0) xnorm = 1.0;+ if (gnorm / xnorm <= param.epsilon) {+ /* Convergence. */+ ret = LBFGS_SUCCESS;+ break;+ }++ /*+ Test for stopping criterion.+ The criterion is given by the following formula:+ (f(past_x) - f(x)) / f(x) < \delta+ */+ if (pf != NULL) {+ /* We don't test the stopping criterion while k < past. */+ if (param.past <= k) {+ /* Compute the relative improvement from the past. */+ rate = (pf[k % param.past] - fx) / fx;++ /* The stopping criterion. */+ if (rate < param.delta) {+ ret = LBFGS_STOP;+ break;+ }+ }++ /* Store the current value of the objective function. */+ pf[k % param.past] = fx;+ }++ if (param.max_iterations != 0 && param.max_iterations < k+1) {+ /* Maximum number of iterations. */+ ret = LBFGSERR_MAXIMUMITERATION;+ break;+ }++ /*+ Update vectors s and y:+ s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.+ y_{k+1} = g_{k+1} - g_{k}.+ */+ it = &lm[end];+ vecdiff(it->s, x, xp, n);+ vecdiff(it->y, g, gp, n);++ /*+ Compute scalars ys and yy:+ ys = y^t \cdot s = 1 / \rho.+ yy = y^t \cdot y.+ Notice that yy is used for scaling the hessian matrix H_0 (Cholesky factor).+ */+ vecdot(&ys, it->y, it->s, n);+ vecdot(&yy, it->y, it->y, n);+ it->ys = ys;++ /*+ Recursive formula to compute dir = -(H \cdot g).+ This is described in page 779 of:+ Jorge Nocedal.+ Updating Quasi-Newton Matrices with Limited Storage.+ Mathematics of Computation, Vol. 35, No. 151,+ pp. 773--782, 1980.+ */+ bound = (m <= k) ? m : k;+ ++k;+ end = (end + 1) % m;++ /* Compute the steepest direction. */+ if (param.orthantwise_c == 0.) {+ /* Compute the negative of gradients. */+ vecncpy(d, g, n);+ } else {+ vecncpy(d, pg, n);+ }++ j = end;+ for (i = 0;i < bound;++i) {+ j = (j + m - 1) % m; /* if (--j == -1) j = m-1; */+ it = &lm[j];+ /* \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}. */+ vecdot(&it->alpha, it->s, d, n);+ it->alpha /= it->ys;+ /* q_{i} = q_{i+1} - \alpha_{i} y_{i}. */+ vecadd(d, it->y, -it->alpha, n);+ }++ vecscale(d, ys / yy, n);++ for (i = 0;i < bound;++i) {+ it = &lm[j];+ /* \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}. */+ vecdot(&beta, it->y, d, n);+ beta /= it->ys;+ /* \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}. */+ vecadd(d, it->s, it->alpha - beta, n);+ j = (j + 1) % m; /* if (++j == m) j = 0; */+ }++ /*+ Constrain the search direction for orthant-wise updates.+ */+ if (param.orthantwise_c != 0.) {+ for (i = param.orthantwise_start;i < param.orthantwise_end;++i) {+ if (d[i] * pg[i] >= 0) {+ d[i] = 0;+ }+ }+ }++ /*+ Now the search direction d is ready. We try step = 1 first.+ */+ step = 1.0;+ }++lbfgs_exit:+ /* Return the final value of the objective function. */+ if (ptr_fx != NULL) {+ *ptr_fx = fx;+ }++ vecfree(pf);++ /* Free memory blocks used by this function. */+ if (lm != NULL) {+ for (i = 0;i < m;++i) {+ vecfree(lm[i].s);+ vecfree(lm[i].y);+ }+ vecfree(lm);+ }+ vecfree(pg);+ vecfree(w);+ vecfree(d);+ vecfree(gp);+ vecfree(g);+ vecfree(xp);++ return ret;+}++++static int line_search_backtracking(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wp,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ )+{+ int count = 0;+ lbfgsfloatval_t width, dg;+ lbfgsfloatval_t finit, dginit = 0., dgtest;+ const lbfgsfloatval_t dec = 0.5, inc = 2.1;++ /* Check the input parameters for errors. */+ if (*stp <= 0.) {+ return LBFGSERR_INVALIDPARAMETERS;+ }++ /* Compute the initial gradient in the search direction. */+ vecdot(&dginit, g, s, n);++ /* Make sure that s points to a descent direction. */+ if (0 < dginit) {+ return LBFGSERR_INCREASEGRADIENT;+ }++ /* The initial value of the objective function. */+ finit = *f;+ dgtest = param->ftol * dginit;++ for (;;) {+ veccpy(x, xp, n);+ vecadd(x, s, *stp, n);++ /* Evaluate the function and gradient values. */+ *f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);++ ++count;++ if (*f > finit + *stp * dgtest) {+ width = dec;+ } else {+ /* The sufficient decrease condition (Armijo condition). */+ if (param->linesearch == LBFGS_LINESEARCH_BACKTRACKING_ARMIJO) {+ /* Exit with the Armijo condition. */+ return count;+ }++ /* Check the Wolfe condition. */+ vecdot(&dg, g, s, n);+ if (dg < param->wolfe * dginit) {+ width = inc;+ } else {+ if(param->linesearch == LBFGS_LINESEARCH_BACKTRACKING_WOLFE) {+ /* Exit with the regular Wolfe condition. */+ return count;+ }++ /* Check the strong Wolfe condition. */+ if(dg > -param->wolfe * dginit) {+ width = dec;+ } else {+ /* Exit with the strong Wolfe condition. */+ return count;+ }+ }+ }++ if (*stp < param->min_step) {+ /* The step is the minimum value. */+ return LBFGSERR_MINIMUMSTEP;+ }+ if (*stp > param->max_step) {+ /* The step is the maximum value. */+ return LBFGSERR_MAXIMUMSTEP;+ }+ if (param->max_linesearch <= count) {+ /* Maximum number of iteration. */+ return LBFGSERR_MAXIMUMLINESEARCH;+ }++ (*stp) *= width;+ }+}++++static int line_search_backtracking_owlqn(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wp,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ )+{+ int i, count = 0;+ lbfgsfloatval_t width = 0.5, norm = 0.;+ lbfgsfloatval_t finit = *f, dgtest;++ /* Check the input parameters for errors. */+ if (*stp <= 0.) {+ return LBFGSERR_INVALIDPARAMETERS;+ }++ /* Choose the orthant for the new point. */+ for (i = 0;i < n;++i) {+ wp[i] = (xp[i] == 0.) ? -gp[i] : xp[i];+ }++ for (;;) {+ /* Update the current point. */+ veccpy(x, xp, n);+ vecadd(x, s, *stp, n);++ /* The current point is projected onto the orthant. */+ owlqn_project(x, wp, param->orthantwise_start, param->orthantwise_end);++ /* Evaluate the function and gradient values. */+ *f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);++ /* Compute the L1 norm of the variables and add it to the object value. */+ norm = owlqn_x1norm(x, param->orthantwise_start, param->orthantwise_end);+ *f += norm * param->orthantwise_c;++ ++count;++ dgtest = 0.;+ for (i = 0;i < n;++i) {+ dgtest += (x[i] - xp[i]) * gp[i];+ }++ if (*f <= finit + param->ftol * dgtest) {+ /* The sufficient decrease condition. */+ return count;+ }++ if (*stp < param->min_step) {+ /* The step is the minimum value. */+ return LBFGSERR_MINIMUMSTEP;+ }+ if (*stp > param->max_step) {+ /* The step is the maximum value. */+ return LBFGSERR_MAXIMUMSTEP;+ }+ if (param->max_linesearch <= count) {+ /* Maximum number of iteration. */+ return LBFGSERR_MAXIMUMLINESEARCH;+ }++ (*stp) *= width;+ }+}++++static int line_search_morethuente(+ int n,+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *f,+ lbfgsfloatval_t *g,+ lbfgsfloatval_t *s,+ lbfgsfloatval_t *stp,+ const lbfgsfloatval_t* xp,+ const lbfgsfloatval_t* gp,+ lbfgsfloatval_t *wa,+ callback_data_t *cd,+ const lbfgs_parameter_t *param+ )+{+ int count = 0;+ int brackt, stage1, uinfo = 0;+ lbfgsfloatval_t dg;+ lbfgsfloatval_t stx, fx, dgx;+ lbfgsfloatval_t sty, fy, dgy;+ lbfgsfloatval_t fxm, dgxm, fym, dgym, fm, dgm;+ lbfgsfloatval_t finit, ftest1, dginit, dgtest;+ lbfgsfloatval_t width, prev_width;+ lbfgsfloatval_t stmin, stmax;++ /* Check the input parameters for errors. */+ if (*stp <= 0.) {+ return LBFGSERR_INVALIDPARAMETERS;+ }++ /* Compute the initial gradient in the search direction. */+ vecdot(&dginit, g, s, n);++ /* Make sure that s points to a descent direction. */+ if (0 < dginit) {+ return LBFGSERR_INCREASEGRADIENT;+ }++ /* Initialize local variables. */+ brackt = 0;+ stage1 = 1;+ finit = *f;+ dgtest = param->ftol * dginit;+ width = param->max_step - param->min_step;+ prev_width = 2.0 * width;++ /*+ The variables stx, fx, dgx contain the values of the step,+ function, and directional derivative at the best step.+ The variables sty, fy, dgy contain the value of the step,+ function, and derivative at the other endpoint of+ the interval of uncertainty.+ The variables stp, f, dg contain the values of the step,+ function, and derivative at the current step.+ */+ stx = sty = 0.;+ fx = fy = finit;+ dgx = dgy = dginit;++ for (;;) {+ /*+ Set the minimum and maximum steps to correspond to the+ present interval of uncertainty.+ */+ if (brackt) {+ stmin = min2(stx, sty);+ stmax = max2(stx, sty);+ } else {+ stmin = stx;+ stmax = *stp + 4.0 * (*stp - stx);+ }++ /* Clip the step in the range of [stpmin, stpmax]. */+ if (*stp < param->min_step) *stp = param->min_step;+ if (param->max_step < *stp) *stp = param->max_step;++ /*+ If an unusual termination is to occur then let+ stp be the lowest point obtained so far.+ */+ if ((brackt && ((*stp <= stmin || stmax <= *stp) || param->max_linesearch <= count + 1 || uinfo != 0)) || (brackt && (stmax - stmin <= param->xtol * stmax))) {+ *stp = stx;+ }++ /*+ Compute the current value of x:+ x <- x + (*stp) * s.+ */+ veccpy(x, xp, n);+ vecadd(x, s, *stp, n);++ /* Evaluate the function and gradient values. */+ *f = cd->proc_evaluate(cd->instance, x, g, cd->n, *stp);+ vecdot(&dg, g, s, n);++ ftest1 = finit + *stp * dgtest;+ ++count;++ /* Test for errors and convergence. */+ if (brackt && ((*stp <= stmin || stmax <= *stp) || uinfo != 0)) {+ /* Rounding errors prevent further progress. */+ return LBFGSERR_ROUNDING_ERROR;+ }+ if (*stp == param->max_step && *f <= ftest1 && dg <= dgtest) {+ /* The step is the maximum value. */+ return LBFGSERR_MAXIMUMSTEP;+ }+ if (*stp == param->min_step && (ftest1 < *f || dgtest <= dg)) {+ /* The step is the minimum value. */+ return LBFGSERR_MINIMUMSTEP;+ }+ if (brackt && (stmax - stmin) <= param->xtol * stmax) {+ /* Relative width of the interval of uncertainty is at most xtol. */+ return LBFGSERR_WIDTHTOOSMALL;+ }+ if (param->max_linesearch <= count) {+ /* Maximum number of iteration. */+ return LBFGSERR_MAXIMUMLINESEARCH;+ }+ if (*f <= ftest1 && fabs(dg) <= param->gtol * (-dginit)) {+ /* The sufficient decrease condition and the directional derivative condition hold. */+ return count;+ }++ /*+ In the first stage we seek a step for which the modified+ function has a nonpositive value and nonnegative derivative.+ */+ if (stage1 && *f <= ftest1 && min2(param->ftol, param->gtol) * dginit <= dg) {+ stage1 = 0;+ }++ /*+ A modified function is used to predict the step only if+ we have not obtained a step for which the modified+ function has a nonpositive function value and nonnegative+ derivative, and if a lower function value has been+ obtained but the decrease is not sufficient.+ */+ if (stage1 && ftest1 < *f && *f <= fx) {+ /* Define the modified function and derivative values. */+ fm = *f - *stp * dgtest;+ fxm = fx - stx * dgtest;+ fym = fy - sty * dgtest;+ dgm = dg - dgtest;+ dgxm = dgx - dgtest;+ dgym = dgy - dgtest;++ /*+ Call update_trial_interval() to update the interval of+ uncertainty and to compute the new step.+ */+ uinfo = update_trial_interval(+ &stx, &fxm, &dgxm,+ &sty, &fym, &dgym,+ stp, &fm, &dgm,+ stmin, stmax, &brackt+ );++ /* Reset the function and gradient values for f. */+ fx = fxm + stx * dgtest;+ fy = fym + sty * dgtest;+ dgx = dgxm + dgtest;+ dgy = dgym + dgtest;+ } else {+ /*+ Call update_trial_interval() to update the interval of+ uncertainty and to compute the new step.+ */+ uinfo = update_trial_interval(+ &stx, &fx, &dgx,+ &sty, &fy, &dgy,+ stp, f, &dg,+ stmin, stmax, &brackt+ );+ }++ /*+ Force a sufficient decrease in the interval of uncertainty.+ */+ if (brackt) {+ if (0.66 * prev_width <= fabs(sty - stx)) {+ *stp = stx + 0.5 * (sty - stx);+ }+ prev_width = width;+ width = fabs(sty - stx);+ }+ }++ return LBFGSERR_LOGICERROR;+}++++/**+ * Define the local variables for computing minimizers.+ */+#define USES_MINIMIZER \+ lbfgsfloatval_t a, d, gamma, theta, p, q, r, s;++/**+ * Find a minimizer of an interpolated cubic function.+ * @param cm The minimizer of the interpolated cubic.+ * @param u The value of one point, u.+ * @param fu The value of f(u).+ * @param du The value of f'(u).+ * @param v The value of another point, v.+ * @param fv The value of f(v).+ * @param du The value of f'(v).+ */+#define CUBIC_MINIMIZER(cm, u, fu, du, v, fv, dv) \+ d = (v) - (u); \+ theta = ((fu) - (fv)) * 3 / d + (du) + (dv); \+ p = fabs(theta); \+ q = fabs(du); \+ r = fabs(dv); \+ s = max3(p, q, r); \+ /* gamma = s*sqrt((theta/s)**2 - (du/s) * (dv/s)) */ \+ a = theta / s; \+ gamma = s * sqrt(a * a - ((du) / s) * ((dv) / s)); \+ if ((v) < (u)) gamma = -gamma; \+ p = gamma - (du) + theta; \+ q = gamma - (du) + gamma + (dv); \+ r = p / q; \+ (cm) = (u) + r * d;++/**+ * Find a minimizer of an interpolated cubic function.+ * @param cm The minimizer of the interpolated cubic.+ * @param u The value of one point, u.+ * @param fu The value of f(u).+ * @param du The value of f'(u).+ * @param v The value of another point, v.+ * @param fv The value of f(v).+ * @param du The value of f'(v).+ * @param xmin The maximum value.+ * @param xmin The minimum value.+ */+#define CUBIC_MINIMIZER2(cm, u, fu, du, v, fv, dv, xmin, xmax) \+ d = (v) - (u); \+ theta = ((fu) - (fv)) * 3 / d + (du) + (dv); \+ p = fabs(theta); \+ q = fabs(du); \+ r = fabs(dv); \+ s = max3(p, q, r); \+ /* gamma = s*sqrt((theta/s)**2 - (du/s) * (dv/s)) */ \+ a = theta / s; \+ gamma = s * sqrt(max2(0, a * a - ((du) / s) * ((dv) / s))); \+ if ((u) < (v)) gamma = -gamma; \+ p = gamma - (dv) + theta; \+ q = gamma - (dv) + gamma + (du); \+ r = p / q; \+ if (r < 0. && gamma != 0.) { \+ (cm) = (v) - r * d; \+ } else if (a < 0) { \+ (cm) = (xmax); \+ } else { \+ (cm) = (xmin); \+ }++/**+ * Find a minimizer of an interpolated quadratic function.+ * @param qm The minimizer of the interpolated quadratic.+ * @param u The value of one point, u.+ * @param fu The value of f(u).+ * @param du The value of f'(u).+ * @param v The value of another point, v.+ * @param fv The value of f(v).+ */+#define QUARD_MINIMIZER(qm, u, fu, du, v, fv) \+ a = (v) - (u); \+ (qm) = (u) + (du) / (((fu) - (fv)) / a + (du)) / 2 * a;++/**+ * Find a minimizer of an interpolated quadratic function.+ * @param qm The minimizer of the interpolated quadratic.+ * @param u The value of one point, u.+ * @param du The value of f'(u).+ * @param v The value of another point, v.+ * @param dv The value of f'(v).+ */+#define QUARD_MINIMIZER2(qm, u, du, v, dv) \+ a = (u) - (v); \+ (qm) = (v) + (dv) / ((dv) - (du)) * a;++/**+ * Update a safeguarded trial value and interval for line search.+ *+ * The parameter x represents the step with the least function value.+ * The parameter t represents the current step. This function assumes+ * that the derivative at the point of x in the direction of the step.+ * If the bracket is set to true, the minimizer has been bracketed in+ * an interval of uncertainty with endpoints between x and y.+ *+ * @param x The pointer to the value of one endpoint.+ * @param fx The pointer to the value of f(x).+ * @param dx The pointer to the value of f'(x).+ * @param y The pointer to the value of another endpoint.+ * @param fy The pointer to the value of f(y).+ * @param dy The pointer to the value of f'(y).+ * @param t The pointer to the value of the trial value, t.+ * @param ft The pointer to the value of f(t).+ * @param dt The pointer to the value of f'(t).+ * @param tmin The minimum value for the trial value, t.+ * @param tmax The maximum value for the trial value, t.+ * @param brackt The pointer to the predicate if the trial value is+ * bracketed.+ * @retval int Status value. Zero indicates a normal termination.+ * + * @see+ * Jorge J. More and David J. Thuente. Line search algorithm with+ * guaranteed sufficient decrease. ACM Transactions on Mathematical+ * Software (TOMS), Vol 20, No 3, pp. 286-307, 1994.+ */+static int update_trial_interval(+ lbfgsfloatval_t *x,+ lbfgsfloatval_t *fx,+ lbfgsfloatval_t *dx,+ lbfgsfloatval_t *y,+ lbfgsfloatval_t *fy,+ lbfgsfloatval_t *dy,+ lbfgsfloatval_t *t,+ lbfgsfloatval_t *ft,+ lbfgsfloatval_t *dt,+ const lbfgsfloatval_t tmin,+ const lbfgsfloatval_t tmax,+ int *brackt+ )+{+ int bound;+ int dsign = fsigndiff(dt, dx);+ lbfgsfloatval_t mc; /* minimizer of an interpolated cubic. */+ lbfgsfloatval_t mq; /* minimizer of an interpolated quadratic. */+ lbfgsfloatval_t newt; /* new trial value. */+ USES_MINIMIZER; /* for CUBIC_MINIMIZER and QUARD_MINIMIZER. */++ /* Check the input parameters for errors. */+ if (*brackt) {+ if (*t <= min2(*x, *y) || max2(*x, *y) <= *t) {+ /* The trival value t is out of the interval. */+ return LBFGSERR_OUTOFINTERVAL;+ }+ if (0. <= *dx * (*t - *x)) {+ /* The function must decrease from x. */+ return LBFGSERR_INCREASEGRADIENT;+ }+ if (tmax < tmin) {+ /* Incorrect tmin and tmax specified. */+ return LBFGSERR_INCORRECT_TMINMAX;+ }+ }++ /*+ Trial value selection.+ */+ if (*fx < *ft) {+ /*+ Case 1: a higher function value.+ The minimum is brackt. If the cubic minimizer is closer+ to x than the quadratic one, the cubic one is taken, else+ the average of the minimizers is taken.+ */+ *brackt = 1;+ bound = 1;+ CUBIC_MINIMIZER(mc, *x, *fx, *dx, *t, *ft, *dt);+ QUARD_MINIMIZER(mq, *x, *fx, *dx, *t, *ft);+ if (fabs(mc - *x) < fabs(mq - *x)) {+ newt = mc;+ } else {+ newt = mc + 0.5 * (mq - mc);+ }+ } else if (dsign) {+ /*+ Case 2: a lower function value and derivatives of+ opposite sign. The minimum is brackt. If the cubic+ minimizer is closer to x than the quadratic (secant) one,+ the cubic one is taken, else the quadratic one is taken.+ */+ *brackt = 1;+ bound = 0;+ CUBIC_MINIMIZER(mc, *x, *fx, *dx, *t, *ft, *dt);+ QUARD_MINIMIZER2(mq, *x, *dx, *t, *dt);+ if (fabs(mc - *t) > fabs(mq - *t)) {+ newt = mc;+ } else {+ newt = mq;+ }+ } else if (fabs(*dt) < fabs(*dx)) {+ /*+ Case 3: a lower function value, derivatives of the+ same sign, and the magnitude of the derivative decreases.+ The cubic minimizer is only used if the cubic tends to+ infinity in the direction of the minimizer or if the minimum+ of the cubic is beyond t. Otherwise the cubic minimizer is+ defined to be either tmin or tmax. The quadratic (secant)+ minimizer is also computed and if the minimum is brackt+ then the the minimizer closest to x is taken, else the one+ farthest away is taken.+ */+ bound = 1;+ CUBIC_MINIMIZER2(mc, *x, *fx, *dx, *t, *ft, *dt, tmin, tmax);+ QUARD_MINIMIZER2(mq, *x, *dx, *t, *dt);+ if (*brackt) {+ if (fabs(*t - mc) < fabs(*t - mq)) {+ newt = mc;+ } else {+ newt = mq;+ }+ } else {+ if (fabs(*t - mc) > fabs(*t - mq)) {+ newt = mc;+ } else {+ newt = mq;+ }+ }+ } else {+ /*+ Case 4: a lower function value, derivatives of the+ same sign, and the magnitude of the derivative does+ not decrease. If the minimum is not brackt, the step+ is either tmin or tmax, else the cubic minimizer is taken.+ */+ bound = 0;+ if (*brackt) {+ CUBIC_MINIMIZER(newt, *t, *ft, *dt, *y, *fy, *dy);+ } else if (*x < *t) {+ newt = tmax;+ } else {+ newt = tmin;+ }+ }++ /*+ Update the interval of uncertainty. This update does not+ depend on the new step or the case analysis above.++ - Case a: if f(x) < f(t),+ x <- x, y <- t.+ - Case b: if f(t) <= f(x) && f'(t)*f'(x) > 0,+ x <- t, y <- y.+ - Case c: if f(t) <= f(x) && f'(t)*f'(x) < 0, + x <- t, y <- x.+ */+ if (*fx < *ft) {+ /* Case a */+ *y = *t;+ *fy = *ft;+ *dy = *dt;+ } else {+ /* Case c */+ if (dsign) {+ *y = *x;+ *fy = *fx;+ *dy = *dx;+ }+ /* Cases b and c */+ *x = *t;+ *fx = *ft;+ *dx = *dt;+ }++ /* Clip the new trial value in [tmin, tmax]. */+ if (tmax < newt) newt = tmax;+ if (newt < tmin) newt = tmin;++ /*+ Redefine the new trial value if it is close to the upper bound+ of the interval.+ */+ if (*brackt && bound) {+ mq = *x + 0.66 * (*y - *x);+ if (*x < *y) {+ if (mq < newt) newt = mq;+ } else {+ if (newt < mq) newt = mq;+ }+ }++ /* Return the new trial value. */+ *t = newt;+ return 0;+}++++++static lbfgsfloatval_t owlqn_x1norm(+ const lbfgsfloatval_t* x,+ const int start,+ const int n+ )+{+ int i;+ lbfgsfloatval_t norm = 0.;++ for (i = start;i < n;++i) {+ norm += fabs(x[i]);+ }++ return norm;+}++static void owlqn_pseudo_gradient(+ lbfgsfloatval_t* pg,+ const lbfgsfloatval_t* x,+ const lbfgsfloatval_t* g,+ const int n,+ const lbfgsfloatval_t c,+ const int start,+ const int end+ )+{+ int i;++ /* Compute the negative of gradients. */+ for (i = 0;i < start;++i) {+ pg[i] = g[i];+ }++ /* Compute the psuedo-gradients. */+ for (i = start;i < end;++i) {+ if (x[i] < 0.) {+ /* Differentiable. */+ pg[i] = g[i] - c;+ } else if (0. < x[i]) {+ /* Differentiable. */+ pg[i] = g[i] + c;+ } else {+ if (g[i] < -c) {+ /* Take the right partial derivative. */+ pg[i] = g[i] + c;+ } else if (c < g[i]) {+ /* Take the left partial derivative. */+ pg[i] = g[i] - c;+ } else {+ pg[i] = 0.;+ }+ }+ }++ for (i = end;i < n;++i) {+ pg[i] = g[i];+ }+}++static void owlqn_project(+ lbfgsfloatval_t* d,+ const lbfgsfloatval_t* sign,+ const int start,+ const int end+ )+{+ int i;++ for (i = start;i < end;++i) {+ if (d[i] * sign[i] <= 0) {+ d[i] = 0;+ }+ }+}
+ src/AI/Calculation.hs view
@@ -0,0 +1,25 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides common calculation functions+--+--+----------------------------------------------------+++module AI.Calculation (+ module AI.Calculation.Activation,+ module AI.Calculation.Cost,+ module AI.Calculation.Gradients,+ module AI.Calculation.NetworkOutput+ ) where++import AI.Calculation.Activation+import AI.Calculation.Cost+import AI.Calculation.Gradients+import AI.Calculation.NetworkOutput
+ src/AI/Calculation/Activation.hs view
@@ -0,0 +1,66 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides common activation functions+-- and their derivative+--+--+----------------------------------------------------+++module AI.Calculation.Activation (+ Activation(..),+ getActivation,+ getDerivative+ ) where++import AI.Signatures+++-- | Represents the activation of+-- each neuron in the neural network+data Activation = Sigmoid -- ^ The sigmoid activation function+ | HyperbolicTangent -- ^ The hyperbolic tangent activation function+++-- | Get the activation function associated with an activation+getActivation :: Activation -> ActivationFunction+getActivation Sigmoid = sigmoid+getActivation HyperbolicTangent = hTangent+++-- | Get the derivative function associated with an activation+getDerivative :: Activation -> DerivativeFunction+getDerivative Sigmoid = sigmoidDeriv+getDerivative HyperbolicTangent = hTangentDeriv+++-- The sigmoid function+sigmoid :: ActivationFunction+sigmoid x = (1 / (1 + exp(-x)))+++-- The derivative of the sigmoid function+--+-- NOTE: The derivative is (sigmoid x) * (1 - sigmoid x)+-- NOT (x * (1 - x))+sigmoidDeriv :: DerivativeFunction+sigmoidDeriv x = (sigmoid x) * (1 - (sigmoid x))+++-- The hyperbolic tangent function+hTangent :: ActivationFunction+hTangent x = tanh x+++-- The derivative of the hyperbolic tangent+--+-- NOTE: The derivative is 1 - (tanh x)^2+-- NOT 1 - x^2+hTangentDeriv :: DerivativeFunction+hTangentDeriv x = 1 - ((tanh x) ** 2)
+ src/AI/Calculation/Cost.hs view
@@ -0,0 +1,155 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides common cost functions+-- and their derivatives+--+--+----------------------------------------------------+++module AI.Calculation.Cost (+ Cost(..),+ getCostFunction,+ getCostDerivative,+) where++import Data.Packed.Matrix+import Data.Packed.Vector+import Numeric.Container++import AI.Signatures+import AI.Network+++-- | Represents the cost model+-- of the Neural Network+data Cost = MeanSquared -- ^ The mean-squared cost+ | Logistic -- ^ The logistic cost+++-- | Gets the cost function associated+-- with the cost model+getCostFunction :: Cost -> CostFunction+getCostFunction = generalCost . getErrorFunction+++-- | Gets the cost derivative associated+-- with the cost model+getCostDerivative :: Cost -> CostDerivative+getCostDerivative MeanSquared = meanSquaredDerivative+getCostDerivative Logistic = logisticDerivative+++-- The general cost function that can be extended by+-- partial function application+generalCost :: ErrorFunction -- The error function to be used+ -> Network -- The neural network of interest+ -> Matrix Double -- The matrix of the inputs, where the ith row+ -- is the input vector of a training set+ -> Matrix Double -- The matrix of the expected output, where the ith+ -- row is the expected output vector of a+ -- training set+ -> Double -- Returns the cost by comparing the network's+ -- output neurons and the expected output matrix+generalCost errorF nn inMatrix exMatrix =+ let activF = toActivation nn -- The activation function+ ws = toWeightMatrices nn -- The list of weight matrices+ la = toLambda nn -- The regularization constant+ n = rows exMatrix -- Get us the number of training sets++ -- Set up the bias neurons for each forward propagation+ fBias = \m -> (fromColumns . ((fromList (replicate n 1)):) . toColumns) m++ -- This is forward propagation right here+ -- We propagate forward by using the functional+ -- foldl accumulating over the weight matrices+ f = \a w -> fBias (mapMatrix activF (a `multiply` w))++ -- Prepare the inMatrix to be used+ inMatrix' = fBias inMatrix++ -- We fold f over the weight matrices accumulating+ -- the activation matrix. The resulting activation matrix+ -- is our output.+ -- We take out the bias neurons in our output layer+ outMatrix = (fromColumns . tail . toColumns) $ foldl f inMatrix' ws++ -- We first convert the outMatrix and the exMatrix into+ -- list of rows. Then we zip them into oVec and eVec+ -- Then get the error between the oVec and the eVec using our+ -- errorF (error function) and the result+ -- is a list of errors. Then we create a vector+ -- from the list, thus resulting in an errorVec+ errorVec = fromList [errorF oVec eVec |+ (oVec, eVec) <- zip (toRows outMatrix) (toRows exMatrix)]++ -- Now we get the un-regularized cost by+ -- summing the elements and taking the average+ -- by dividing by the number of the training sets+ j = (1 / fromIntegral n) * sumElements errorVec++ -- Now we get the vector representation of the+ -- weights to prepare for regularization+ wsFlattened = toWeights nn+ in+ -- Finally, we regularize our cost by using the lambda constant+ j + (la / (2.0 * fromIntegral n)) * (sumElements $ mapVector (**2) wsFlattened)+++-- This is the general error function+-- It requires a function that will calculate an+-- error when given a calculated value and an+-- expected value+generalErrorFunction :: (Double -> Double -> Double) -- The function to calculate an "error"+ -- Given a calculated value and an+ -- expected value+ -> ErrorFunction -- Returns the error function+generalErrorFunction errF calVec exVec =+ let n = dim calVec -- Get us the size of the vectors++ -- Get us the error vector between the calculated+ -- vector and the expected vector by zipping+ -- the error function+ errorVec = zipVectorWith errF calVec exVec+ in+ -- Now we take the average of the sum of the errors+ (1 / fromIntegral n) * (sumElements errorVec)+++-- Returns the error function given a cost detail+getErrorFunction :: Cost -> ErrorFunction+getErrorFunction MeanSquared = generalErrorFunction meanSquaredError+getErrorFunction Logistic = generalErrorFunction logisticError+++-- The mean squared error function+meanSquaredError :: Double -> Double -> Double+meanSquaredError cal ex =+ (cal - ex) ** 2+++-- The derivative of the mean squared error function+-- with respect to each parameter+meanSquaredDerivative :: CostDerivative+meanSquaredDerivative (Network {derivative = df}) inMat actMat exMat =+ mapMatrix (*2) ((mapMatrix df inMat) `mul` (actMat `sub` exMat))+++-- The logistic error function+-- Also known as the cross-entropy+-- error function+logisticError :: Double -> Double -> Double+logisticError cal ex=+ (-1) * ((ex) * (log cal) + (1 - ex) * (log (1 - cal)))+++-- The derivative of the logistic error function+-- with respect to each parameter+logisticDerivative :: CostDerivative+logisticDerivative _ _ actMat exMat = actMat `sub` exMat
+ src/AI/Calculation/Gradients.hs view
@@ -0,0 +1,205 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module represents ways to calculate the gradient+-- vector of the weights of the neural network+--+-- Backpropagation should always be preferred over+-- the Numerical Gradient method+--+--+----------------------------------------------------+++module AI.Calculation.Gradients (+ backpropagation,+ numericalGradients+ ) where++import Numeric.Container++import AI.Signatures+import AI.Network+++-- | Calculate the analytical gradient of the weights of the network+-- by using backpropagation+backpropagation :: GradientFunction+backpropagation _ outputDeltasF nn inMatrix exMatrix =+ let n = rows exMatrix -- Get us the number of training sets++ -- Get important informations from the neural network+ activF = toActivation nn+ df = toDerivative nn+ ws = toWeightMatrices nn+ la = toLambda nn++ -- Function to set up the bias neurons for each forward propagation+ fBias = fromColumns . ((fromList (replicate n 1)):) . toColumns++ -- This is forward propagation right here+ -- We propagate forward by using the functional+ -- foldl accumulating over the weight matrices+ -- NOTE: Also, for the ability to use more complex activation+ -- function with non-trivial derivatives, we also accumulate+ -- the weighted inputs to each layer, so the accumulation+ -- for each forward propagation is a tuple of the activation+ -- of each neuron in the layer and the weighted inputs into the+ -- layer.+ f = \p w -> ((fBias . mapMatrix activF) (p `multiply` w), fBias $ p `multiply` w)++ -- Prepare the inMatrix to be used+ inMatrix' = fBias inMatrix++ -- Forward propagate each row of the inputs matrix and matrix-multiply it with the+ -- weight matrices calculated before.+ -- NOTE: Forward propagation can be calculated efficiently by using+ -- foldl where the initial value is the input matrix and we calculate+ -- and simultaneously accumulate the activation values of each layer+ activations = foldl (\(a@(p,_):as) w -> ((f p w):a:as)) [(inMatrix',inMatrix')] ws++ -- Helper function to remove bias neurons+ fRemoveBias = fromColumns . tail . toColumns++ -- Because we cannot possibly calculate the outputs node deltas,+ -- the user must supply a function that will do that+ -- We pass in the weighted inputs to the output neurons,+ -- the activation values of the output neurons,+ -- the expected matrix of the training set,+ -- the derivative of the activation function of the networks+ -- And we expect it to return for us the output nodes+ -- deltas for us to propagate backwards to each layer+ initialDeltas = outputDeltasF nn ((fRemoveBias . snd . head) activations)+ ((fRemoveBias . fst . head) activations) exMatrix++ -- This one line is basically the entire backpropagation+ --+ -- NOTE: Backpropagation can be computed efficiently+ -- using foldl. Because the activations we calculated above+ -- are in reverse order, we can efficiently backpropagate+ -- the initial output nodes deltas by simply folding+ -- backwards on the reverse of the weights+ -- The initial value for foldl is our initialDeltas+ -- and we accumulate the node deltas of each+ -- previous layer.+ --+ -- NOTE: Because we also accumulated the weighted inputs+ -- to each layer, we can use more exotic activation+ -- function instead of the ones with trivial derivatives.+ --+ -- Example: Instead of using the derivative of the+ -- sigmoid function as x * (1 - x), where x is the+ -- "sigmoided value", we can actually use the real+ -- derivative, which is (sigmoid x) * (1 - sigmoid x)+ -- where x is the weighted input+ --+ -- This allows us to use more exotic activation+ -- function whose derivatives is non-trivial+ allDeltas = foldl (\(d:ds) (as,w) -> (fRemoveBias $ (d `multiply` (trans w)) `mul` (mapMatrix df as)):d:ds)+ [initialDeltas] (zip ((tail . map snd) activations) (reverse ws))++ -- Now this is where we finally calculate the gradients+ -- by multiplying activations of each layer to the+ -- node deltas of the next layer+ grads = [[a `outer` d | (a, d) <- zip (toRows as) (toRows deltas)]+ | (as, deltas) <- zip ((tail . map fst) activations) (reverse allDeltas)]++ -- zeroF gets us a zero matrix given a row and a column+ -- I believe the HMatrix package must have a function to+ -- create zero matrices, but I haven't fond it yet... >_<+ zeroF = \m -> buildMatrix (rows m) (cols m) (\_ -> 0.0)++ -- Now we add all of the gradients together+ -- and the average of the gradients by dividing by+ -- the number of the training sets+ gradsSums = map (mapMatrix (/(fromIntegral n))) [foldl add ((zeroF . head) g) g | g <- grads]+ in+ -- And after all that exhaustive work, we flatten the matrices into+ -- one big vector and add regularization to it+ zipVectorWith (\x y -> x + (la / fromIntegral n) * y) ((join . map flatten) (reverse gradsSums)) (toWeights nn)+++-- | NOTE: This should only be used as a last resort+-- if for some reason (bugs?) the backpropagation+-- algorithm does not give you good gradients+--+-- The numerical algorithm requires two forward+-- propagations, while the backpropagation algorithm+-- only requires one, so this is more costly+--+-- Also, analytical gradients almost always perform+-- better than numerical gradients+--+-- User must provide an epsilon value.+-- Make sure to use a very small value for the epsilon+-- for more accurate gradients+numericalGradients :: Double -- ^ The epsilon+ -> GradientFunction -- ^ Returns a gradient function+ -- that calculates the numerical+ -- gradients of the weights+numericalGradients epsilon costF _ nn inMat exMat =+ let plusE = \x -> x + epsilon -- Add epsilon to the argument+ minusE = \x -> x - epsilon -- Subtract epsilon from the argument++ -- Get the vector representation of the weights+ params = toWeights nn++ -- Calculate a matrix of parameters that have been+ -- modified by adding and subtracting the epsilon value+ -- The result is two lists whose element is a vector+ -- of the parameters that have been modified+ dx1s = (toRows . mapElementToVector (modifyElementAt plusE)) params+ dx2s = (toRows . mapElementToVector (modifyElementAt minusE)) params++ f = \ws -> costF (setWeights nn ws) inMat exMat+ -- Now we calculate the costs of each modified parameters+ cost1 = (fromList . map f) dx1s+ cost2 = (fromList . map f) dx2s+ in+ -- Use the (f(x+e) - (f(x-e)))/(2*e) to get the gradients+ mapVector (/ (2 * epsilon)) $ cost1 `sub` cost2+++-- Map over every single element of a vector+-- and apply the function on each vector+-- This returns a matrix where the ith row is+-- a vector whose ith element is applied+-- to the function f+mapElementToVector :: (Vector Double -> Int -> Vector Double)+ -> Vector Double+ -> Matrix Double+mapElementToVector f vec =+ let n = dim vec+ -- Get the size of the vector++ -- Apply f over each element indexed by i+ -- and we join the list of vectors into a giant+ -- vector+ flattened = join [f vec i | i <- [0..n - 1]]+ in+ -- Reshape the flattened vector into a matrix+ -- by using the size of the vector calculated before+ reshape n flattened+++-- Modify one single element of the vector+-- by applying f to it+modifyElementAt :: (Double -> Double) -- The function to be applied+ -> Vector Double -- The vector of interest+ -> Int -- The index of the element ot be modified+ -> Vector Double -- The resulting modified vector+modifyElementAt f vec index =+ -- If the index passed into us is the index, we apply the+ -- function to the element, otherwise we leave it alone+ let g = \i v -> if' (i == index) (f v) (v) in+ mapVectorWithIndex g vec+++if' :: Bool -> a -> a -> a+if' True x _ = x+if' False _ y = y
+ src/AI/Calculation/NetworkOutput.hs view
@@ -0,0 +1,35 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides forward propagation+-- to let the user get the output of the neural+-- network given an input vector+--+--+----------------------------------------------------+++module AI.Calculation.NetworkOutput (+ networkOutput+ ) where++import Numeric.Container++import AI.Network+++-- | Forward propagate to get the network's output+networkOutput :: Network -- ^ The neural network of interest+ -> Vector Double -- ^ The input vector+ -> Vector Double -- ^ The output vector of the output neurons+networkOutput nn inVec =+ let activF = toActivation nn+ ws = toWeightMatrices nn+ fBias = \v -> fromList $ 1.0:(toList v :: [Double])+ in+ foldl (\as w -> mapVector activF ((fBias as) `vXm` w)) inVec ws
+ src/AI/Model.hs view
@@ -0,0 +1,24 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- Provides models interface for easy initialization and+-- training of neural networks+--+--+----------------------------------------------------+++module AI.Model (+ module AI.Model.GenericModel,+ module AI.Model.General,+ module AI.Model.Classification+ ) where++import AI.Model.GenericModel+import AI.Model.General+import AI.Model.Classification
+ src/AI/Model/Classification.hs view
@@ -0,0 +1,41 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides an initialization for+-- a classification neural network model+--+-- NOTE: This theoretically should be faster than+-- the General model if used for classification+--+--+----------------------------------------------------+++module AI.Model.Classification (+ initializeClassification+ ) where++import Data.Packed.Vector+import System.Random++import AI.Calculation+import AI.Network+import AI.Model.GenericModel+++-- | Make a neural network model+-- that should be used for classification+-- using the Sigmoid as the activation model+-- and Logistic as the cost model+initializeClassification :: [Int] -- ^ The architecture of the neural network+ -> Double -- ^ The regularization constant+ -> StdGen -- ^ The random generator+ -> GenericModel -- ^ Returns the initialized classification+ -- model+initializeClassification arch la gen =+ initializeModel Sigmoid Logistic arch la gen
+ src/AI/Model/General.hs view
@@ -0,0 +1,42 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides an initialization for+-- a general neural network model that can do+-- either regression or classification+--+-- If for regression, the training+-- data must be normalized by user to have+-- range of [-1,1]+--+----------------------------------------------------+++module AI.Model.General (+ initializeGeneral+ ) where++import Data.Packed.Vector+import System.Random++import AI.Calculation+import AI.Network+import AI.Model.GenericModel+++-- | This is a general neural network+-- model that can be used for classification+-- or regression using HyperbolicTangent+-- as the activation model and MeanSquared as+-- the cost model+initializeGeneral :: [Int] -- ^ The architecture of the neural network+ -> Double -- ^ The regularization constant+ -> StdGen -- ^ The random generator+ -> GenericModel -- ^ Returns the initialized general model+initializeGeneral arch la gen =+ initializeModel HyperbolicTangent MeanSquared arch la gen
+ src/AI/Model/GenericModel.hs view
@@ -0,0 +1,88 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides a generic module for+-- initiialization and training of neural networks+--+-- User must provide the needed functions+--+--+----------------------------------------------------+++module AI.Model.GenericModel (+ GenericModel(..),+ initializeModel,+ getOutput,+ trainModel+ ) where++import System.Random+import Data.Packed.Vector+import Data.Packed.Matrix++import AI.Signatures+import AI.Calculation+import AI.Network+import AI.Training+++-- | Generic neural network model for expansion+data GenericModel = GenericModel+ {+ cost :: Cost, -- ^ The cost model of the model+ net :: Network -- ^ The neural network to be used for modeling+ }+++-- | Initialize neural network model with the weights+-- randomized within [-1.0,1.0]+initializeModel :: Activation -- ^ The activation model of each neuron+ -> Cost -- ^ The cost model of the output neurons+ -- compared to the expected output+ -> [Int] -- ^ The architecture of the network+ -- e.g., a 2-3-1 architecture would be [2,3,1]+ -> Double -- ^ The regularization constant+ -- should be 0 if you do not want regularization+ -> StdGen -- ^ The random generator+ -> GenericModel -- ^ Returns the initialized model+initializeModel ac co arch la gen =+ let n = foldl (+) 0 [((x + 1) * y) | (x,y) <- zip arch (tail arch)]+ ws = (fromList . take n) (randomRs (-1.0, 1.0) gen :: [Double])+ in+ GenericModel { cost = co,+ net = Network { activation = getActivation ac,+ derivative = getDerivative ac,+ lambda = la,+ weights = ws,+ architecture = arch+ }+ }+++-- | Get the output of the model+getOutput :: GenericModel -- ^ The model of interest+ -> Vector Double -- ^ The input vector to the input layer+ -> Vector Double -- ^ The output of the network model+getOutput (GenericModel {net = nn}) input = networkOutput nn input+++-- | Train the model given the parameters and the training algorithm+trainModel :: GenericModel -- ^ The model to be trained+ -> TrainingAlgorithm -- ^ The training algorithm to be used+ -> Double -- ^ The precision to train with regards to+ -- the cost function+ -> Int -- ^ The maximum amount of epochs to train+ -> Matrix Double -- ^ The input matrix+ -> Matrix Double -- ^ The expected output matrix+ -> GenericModel -- ^ Returns the trained model+trainModel (GenericModel {cost = co, net = nn}) algo prec epochs inMat exMat =+ let trainedNet = trainNetwork algo co backpropagation nn prec epochs inMat exMat in+ GenericModel { net = trainedNet,+ cost = co+ }
+ src/AI/Network.hs view
@@ -0,0 +1,101 @@+----------------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- Efficient representation of an Artificial Neural Network+-- using vector to represent the weights between each layer+--+-- This module provides the neural network data representation+-- that will be used extensively+--+--+---------------------------------------------------------+++module AI.Network (+ Network(..),+ toActivation, toDerivative,+ toLambda, toWeights,+ toWeightMatrices, toArchitecture,+ setActivation, setDerivative,+ setLambda, setWeights,+ setArchitecture+ ) where++import Data.Packed.Vector+import Data.Packed.Matrix+++-- | The representation of an Artificial Neural Network+data Network = Network+ {+ activation :: (Double -> Double), -- ^ The activation function for each+ -- neuron+ derivative :: (Double -> Double), -- ^ The derivative of the activation+ -- function+ lambda :: Double, -- ^ The regularization constant+ weights :: Vector Double, -- ^ The vector of the weights between each+ -- layer of the neural network+ architecture :: [Int] -- ^ The architecture of the neural+ -- networks.+ --+ -- e.g., a network of an architecture+ -- of 2-3-1 would have an architecture+ -- representation of [2,3,1]+ --+ -- NOTE: The library will automatically create+ -- a bias neuron in each layer, so you do not need+ -- to state them explicitly+ }+++-- Self-explanatory+toActivation :: Network -> (Double -> Double)+toActivation (Network {activation = f}) = f++toDerivative :: Network -> (Double -> Double)+toDerivative (Network {derivative = df}) = df++toLambda :: Network -> Double+toLambda (Network {lambda = la}) = la++toWeights :: Network -> Vector Double+toWeights (Network {weights = w}) = w++-- | Get the list of matrices of weights between+-- each layer. This can be more useful+-- than the barebone vector representation+-- of the weights+toWeightMatrices :: Network -> [Matrix Double]+toWeightMatrices (Network {weights = ws, architecture = arch}) =+ let elems = 0:[((x + 1) * y) | (x,y) <- zip arch (tail arch)] in+ [reshape i v | (i, v) <- zip (tail arch) (takesV (tail elems) ws)]++toArchitecture :: Network -> [Int]+toArchitecture (Network {architecture = a}) = a+++-- Self-explanatory+setActivation :: Network -> (Double -> Double) -> Network+setActivation (Network {derivative = df, lambda = la, weights = w, architecture = a}) f =+ (Network {activation = f, derivative = df, lambda = la, weights = w, architecture = a})++setDerivative :: Network -> (Double -> Double) -> Network+setDerivative (Network {activation = f, lambda = la, weights = w, architecture = a}) df =+ (Network {activation = f, derivative = df, lambda = la, weights = w, architecture = a})++setLambda :: Network -> Double -> Network+setLambda (Network {activation = f, derivative = df, weights = w, architecture = a}) la =+ Network {activation = f, derivative = df, lambda = la, weights = w, architecture = a}++setWeights :: Network -> Vector Double -> Network+setWeights (Network {activation = f, derivative = df, lambda = la, architecture = a}) w =+ (Network {activation = f, derivative = df, lambda = la, weights = w, architecture = a})++setArchitecture :: Network -> [Int] -> Network+setArchitecture (Network {activation = f, derivative = df, lambda = la, weights = w}) a =+ (Network {activation = f, derivative = df, lambda = la, weights = w, architecture = a})
+ src/AI/Signatures.hs view
@@ -0,0 +1,93 @@+---------------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides the signatures for needed+-- functions in a neural network+--+--+---------------------------------------------------------+++module AI.Signatures (+ ActivationFunction,+ DerivativeFunction,+ ErrorFunction,+ CostFunction,+ CostDerivative,+ GradientFunction+ ) where++import Data.Packed.Matrix+import Data.Packed.Vector++import AI.Network+++-- | Type that represents the activation function+type ActivationFunction = Double -> Double+++-- | Type that represents the derivative of the activation function+--+-- NOTE: The derivative can be non-trivial and must be continuous+type DerivativeFunction = Double -> Double+++-- | Type that represents the error function+-- between the calculated output vector+-- and the expected output vector+type ErrorFunction = Vector Double -- ^ The calculated output vector+ -> Vector Double -- ^ The expected output vector+ -> Double -- ^ Returns the error of how far off+ -- the calculated vector is from the+ -- expected vector+++-- | Type that represents the function+-- that can calculate the total cost of the neural networks+-- given the neural networks, the input matrix and an expected output matrix+type CostFunction = Network -- ^ The neural networks of interest+ -> Matrix Double -- ^ The input matrix, where the ith row+ -- is the input vector of a training set+ -> Matrix Double -- ^ The expected output matrix, where the+ -- ith row is the expected output vector+ -- of a training set+ -> Double -- ^ Returns the cost of the calculated output vector+ -- from the neural network and the given+ -- expected output vector+++-- | Type that represents the cost function derivative.+-- on the output nodes+type CostDerivative = Network -- ^ The neural networks of interest+ -> Matrix Double -- ^ The matrix of inputs where the ith row+ -- is the ith training set+ -> Matrix Double -- ^ The matrix of calculated outputs where the+ -- ith row is the ith training set+ -> Matrix Double -- ^ The matrix of expected outputs where the+ -- ith row is the ith expected output of+ -- of the training set+ -> Matrix Double -- ^ Returns the matrix of the derivatives+ -- of the cost of the output nodes+ -- compared to the expected matrix+++-- | The type to represent a function that+-- can calculate the gradient vector+-- of the weights of the neural network+--+-- NOTE: Must be supplied a function to calculate the cost, the+-- cost derivative of the output neurons, the neural network+-- the input matrix, and the expected output matrix+type GradientFunction = CostFunction -- ^ The cost function+ -> CostDerivative -- ^ The cost derivative+ -> Network -- ^ The neural network+ -> Matrix Double -- ^ The input matrix+ -> Matrix Double -- ^ The expected output matrix+ -> Vector Double -- ^ Returns the gradient vector+ -- of the weights
+ src/AI/Training.hs view
@@ -0,0 +1,122 @@+----------------------------------------------------+-- |+-- Module : AI.Network+-- License : GPL+--+-- Maintainer : Kiet Lam <ktklam9@gmail.com>+--+--+-- This module provides training algorithms to train+-- a neural network given training data.+--+-- User should only use LBFGS though because+-- it uses custom bindings to the C-library liblbfgs+--+-- GSL's multivariate minimization algorithms are known to be inefficient+-- <http://www.alglib.net/optimization/lbfgsandcg.php#header6>+-- and LBFGS outperforms them on many (of my) tests+--+--+----------------------------------------------------+++module AI.Training (+ TrainingAlgorithm(..),+ trainNetwork+ ) where++import Numeric.GSL.Minimization+import Data.Packed.Vector+import Data.Packed.Matrix++import AI.Training.Internal+import AI.Signatures+import AI.Calculation+import AI.Network+++-- | The types of training algorithm to use+--+-- NOTE: These are all batch training algorithms+data TrainingAlgorithm = GradientDescent -- ^ hmatrix's binding to GSL+ | ConjugateGradient -- ^ hmatrix's binding to GSL+ | BFGS -- ^ hmatrix's binding to GSL+ | LBFGS -- ^ home-made binding to liblbfgs+ deriving (Show, Read, Enum)+++-- This function is needed to work with HMatrix's+-- multivariate minimization algorithms+vectorWeightToCost :: CostFunction -- The cost function+ -> Network -- The neural network+ -> Matrix Double -- The input matrix+ -> Matrix Double -- The output matrix+ -> Vector Double -- The vector weights+ -> Double -- Returns the calculated cost+vectorWeightToCost costF nn inMat exMat ws = costF (setWeights nn ws) inMat exMat+++-- This function is needed to work with HMatrix's+-- multivariate minimization algorithms+vectorWeightToGradients :: GradientFunction -- The function can can calculate the+ -- gradient vector given a cost model+ -> Cost -- the cost model+ -> Network -- The neural network+ -> Matrix Double -- The input matrix+ -> Matrix Double -- The output matrix+ -> Vector Double -- The vector weights+ -> Vector Double -- Returns the vector gradients+vectorWeightToGradients gradF cost nn inMat exMat ws =+ gradF (getCostFunction cost) (getCostDerivative cost) (setWeights nn ws) inMat exMat+++-- | Train the neural network given a training algorithm,+-- the training parameters and the training data+trainNetwork :: TrainingAlgorithm -- ^ The training algorithm to use+ -> Cost -- ^ The cost model of the neural network+ -> GradientFunction -- ^ The function that can calculate the+ -- gradients vector+ -> Network -- ^ The network to be trained+ -> Double -- ^ The precision of the training with regards+ -- to the cost function+ -> Int -- ^ The maximum number of iterations+ -> Matrix Double -- ^ The input matrix+ -> Matrix Double -- ^ The expected output matrix+ -> Network -- ^ Returns the trained network+trainNetwork algo cost gradF nn prec iterations inMat exMat =+ let ws = toWeights nn -- Get the initial weights of the network++ -- f represents the cost function to minimize+ f = vectorWeightToCost (getCostFunction cost) nn inMat exMat++ -- g represents the function that can calculate the gradient+ -- vector of the parameters (the weights)+ g = vectorWeightToGradients gradF cost nn inMat exMat++ -- Get the training algorithm+ trainAlgo = getTrainAlgo algo++ -- Set the tol and initial step size+ initStepSize = 0.1+ tol = 0.1++ -- Use the training algorithm to train the weights+ trainedWeights = trainAlgo prec iterations initStepSize tol f g ws+ in+ setWeights nn trainedWeights+++-- Auxilary function for trainNetwork+getTrainAlgo :: TrainingAlgorithm+ -> Double+ -> Int+ -> Double+ -> Double+ -> (Vector Double -> Double)+ -> (Vector Double -> Vector Double)+ -> Vector Double+ -> Vector Double+getTrainAlgo GradientDescent prec iter step tol f df initVec = fst $ minimizeVD SteepestDescent prec iter step tol f df initVec+getTrainAlgo ConjugateGradient prec iter step tol f df initVec = fst $ minimizeVD ConjugatePR prec iter step tol f df initVec+getTrainAlgo BFGS prec iter step tol f df initVec = fst $ minimizeVD VectorBFGS2 prec iter step tol f df initVec+getTrainAlgo LBFGS prec iter step tol f df initVec = minimizeLBFGS prec iter step tol f df initVec
+ src/AI/Training/Internal.hs view
@@ -0,0 +1,29 @@+-- -------------------------------------------------+--+-- Author: Kiet Lam+-- File INTERNAL_HS+--+-- -------------------------------------------------+-- Last Updated: Time-stamp: <2012-01-18 18:37:35 (lam)>+--+--+--+-- 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/>.+++module AI.Training.Internal (+ module AI.Training.Internal.LBFGSAux+ ) where++import AI.Training.Internal.LBFGSAux
+ src/AI/Training/Internal/LBFGSAux.hs view
@@ -0,0 +1,123 @@+-- -------------------------------------------------+--+-- Author: Kiet Lam+-- File LBFGSAUX_HS+--+-- -------------------------------------------------+-- Last Updated: Time-stamp: <2012-01-19 00:25:43 (lam)>+--+--+--+-- 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/>.+++module AI.Training.Internal.LBFGSAux (+ minimizeLBFGS+ ) where+++import Data.Packed.Vector+import Foreign.C.Types+import Foreign.Ptr(Ptr, FunPtr)+import Foreign.Marshal.Array+import System.IO.Unsafe(unsafePerformIO)++++-- Don't make too much changes here++type TV = CInt -> Ptr Double -> IO CInt+type TVV = CInt -> Ptr Double -> TV+++aux_LToL :: ([Double] -> [Double]) -> TVV+aux_LToL f n1 p1 _ p2 =+ do+ v <- peekArray (fromIntegral n1) p1+ let vr = f v in+ do+ pokeArray p2 vr+ return 0+++aux_LToD :: ([Double] -> Double)+ -> CInt -> Ptr Double -> Double+aux_LToD f n p =+ unsafePerformIO $+ do+ v <- peekArray (fromIntegral n) p+ return $ f v+++foreign import ccall "wrapper"+ mkListFun :: (CInt -> Ptr Double -> Double)+ -> IO (FunPtr (CInt -> Ptr Double -> Double))+++foreign import ccall "wrapper"+ mkListListFun :: (TVV) -> IO (FunPtr TVV)+++foreign import ccall "lbfgs_aux.c minimizeLBFGS"+ c_minimizeLBFGS :: Double+ -> CInt+ -> Double+ -> Double+ -> FunPtr (CInt -> Ptr Double -> Double)+ -> FunPtr (CInt -> Ptr Double -> CInt -> Ptr Double -> IO CInt)+ -> CInt -> Ptr Double+ -> CInt -> Ptr Double+ -> IO CInt+++vecFuncToLFunc :: (Vector Double -> Vector Double) -> [Double] -> [Double]+vecFuncToLFunc f vec = (toList . f . fromList) vec+++vecFuncToFunc :: (Vector Double -> Double) -> [Double] -> Double+vecFuncToFunc f vec = (f . fromList) vec+++minimizeLBFGS_aux :: Double+ -> Int+ -> Double+ -> Double+ -> (Vector Double -> Double)+ -> (Vector Double -> Vector Double)+ -> Vector Double+ -> [Double]+minimizeLBFGS_aux prec maxIter initStep tol f df initVec =+ let f' = vecFuncToFunc f+ df' = vecFuncToLFunc df+ initVec' = toList initVec+ n = length initVec'+ in+ unsafePerformIO $ withArray initVec' $ \ar -> allocaArray n $ \res ->+ do+ fp <- mkListFun (aux_LToD f')+ dfp <- mkListListFun (aux_LToL df')+ _ <- c_minimizeLBFGS prec (fromIntegral maxIter) initStep tol fp dfp (fromIntegral n) ar (fromIntegral n) res+ peekArray n res+++minimizeLBFGS :: Double+ -> Int+ -> Double+ -> Double+ -> (Vector Double -> Double)+ -> (Vector Double -> Vector Double)+ -> Vector Double+ -> Vector Double+minimizeLBFGS prec maxIter initStep tol f df initVec =+ fromList $ minimizeLBFGS_aux prec maxIter initStep tol f df initVec
+ src/AI/Training/Internal/lbfgs_aux.c view
@@ -0,0 +1,85 @@+//_______________________________________________________________________________+//+// Author: Kiet Lam+// File lbfgs_aux.c+//_______________________________________________________________________________+// Last Updated: Time-stamp: <2012-01-18 23:41:52 (lam)>+//+//+// 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/>.+++#include <lbfgs.h>+#include <stdio.h>+++#define HASKELLARRAY(A) int A##n, double* A##p+++typedef double (*fFunc) (int, const lbfgsfloatval_t*);+typedef int (*dfFunc) (int, const lbfgsfloatval_t*, int, lbfgsfloatval_t*);+++typedef struct+{+ double (*f) (int, const lbfgsfloatval_t*);+ int (*df) (int, const lbfgsfloatval_t*, int, double*);+} FdfData;+++lbfgsfloatval_t lbfgs_evaluate_aux (void* data,+ const lbfgsfloatval_t* x,+ lbfgsfloatval_t* g,+ const int n,+ const lbfgsfloatval_t step)+{+ FdfData* fdf = (FdfData*) data;+ fdf->df(n, x, n, g);+ return fdf->f(n, x);+}++++int minimizeLBFGS (double precision, int max_iter, double init_step, double tol,+ fFunc fun, dfFunc dfun, HASKELLARRAY(x), HASKELLARRAY(r))+{+ FdfData fdfDat;+ fdfDat.f = fun;+ fdfDat.df = dfun;++ lbfgs_parameter_t param;++ lbfgs_parameter_init(¶m);++ param.epsilon = precision;+ param.max_iterations = max_iter;++ lbfgsfloatval_t* v = lbfgs_malloc(xn);++ int i;+ for (i = 0; i < xn; ++i)+ {+ v[i] = xp[i];+ }++ lbfgs(xn, v, NULL, lbfgs_evaluate_aux, NULL, &fdfDat, ¶m);++ int j;+ for (j = 0; j < xn; ++j)+ {+ rp[j] = v[j];+ }++ lbfgs_free(v);+}