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.gitignore
vendored
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.gitignore
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/target
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1199
Cargo.lock
generated
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Cargo.toml
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[package]
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||||||
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name = "rustmodel"
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||||||
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version = "0.1.0"
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||||||
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edition = "2021"
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||||||
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description = "simple ODE solving framework"
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||||||
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authors = ["tuxmain <tuxmain@zettascript.org>"]
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||||||
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repository = "https://git.txmn.tk/tuxmain/rustmodel"
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||||||
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license = "AGPL-3.0-only"
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||||||
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||||||
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[dependencies]
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||||||
|
derive_builder = { version = "0.12.0", optional = true }
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nalgebra = "0.32.3"
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num-traits = "0.2.17"
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palette = { version = "0.7.3", optional = true }
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plotters = { version = "0.3.5", optional = true }
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#plotters = { git = "https://github.com/plotters-rs/plotters" }
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#rand = {version = "0.8.5", optional = true }
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#rayon = "1.8.0"
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#sdl2 = "0.35.2"
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[features]
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default = ["plot"]
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# opti is about numerical optimization methods, not computing speed!
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#opti = ["nalgebra/rand", "rand"]
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plot = ["derive_builder", "palette", "plotters"]
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||||||
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[workspace]
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members = ["examples/epidemics"]
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||||||
661
LICENSE
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661
LICENSE
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||||||
|
GNU AFFERO GENERAL PUBLIC LICENSE
|
||||||
|
Version 3, 19 November 2007
|
||||||
|
|
||||||
|
Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
|
||||||
|
Everyone is permitted to copy and distribute verbatim copies
|
||||||
|
of this license document, but changing it is not allowed.
|
||||||
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|
||||||
|
Preamble
|
||||||
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|
||||||
|
The GNU Affero General Public License is a free, copyleft license for
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|
software and other kinds of works, specifically designed to ensure
|
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cooperation with the community in the case of network server software.
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The licenses for most software and other practical works are designed
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our General Public Licenses are intended to guarantee your freedom to
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share and change all versions of a program--to make sure it remains free
|
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software for all its users.
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When we speak of free software, we are referring to freedom, not
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The precise terms and conditions for copying, distribution and
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TERMS AND CONDITIONS
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0. Definitions.
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"This License" refers to version 3 of the GNU Affero General Public License.
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If you convey an object code work under this section in, or with, or
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||||||
|
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. Remote Network Interaction; Use with the GNU General Public License.
|
||||||
|
|
||||||
|
Notwithstanding any other provision of this License, if you modify the
|
||||||
|
Program, your modified version must prominently offer all users
|
||||||
|
interacting with it remotely through a computer network (if your version
|
||||||
|
supports such interaction) an opportunity to receive the Corresponding
|
||||||
|
Source of your version by providing access to the Corresponding Source
|
||||||
|
from a network server at no charge, through some standard or customary
|
||||||
|
means of facilitating copying of software. This Corresponding Source
|
||||||
|
shall include the Corresponding Source for any work covered by version 3
|
||||||
|
of the GNU General Public License that is incorporated pursuant to the
|
||||||
|
following paragraph.
|
||||||
|
|
||||||
|
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 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 work with which it is combined will remain governed by version
|
||||||
|
3 of the GNU General Public License.
|
||||||
|
|
||||||
|
14. Revised Versions of this License.
|
||||||
|
|
||||||
|
The Free Software Foundation may publish revised and/or new versions of
|
||||||
|
the GNU Affero 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 Affero 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 Affero 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 Affero 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 Affero 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 Affero General Public License for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU Affero General Public License
|
||||||
|
along with this program. If not, see <https://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
Also add information on how to contact you by electronic and paper mail.
|
||||||
|
|
||||||
|
If your software can interact with users remotely through a computer
|
||||||
|
network, you should also make sure that it provides a way for users to
|
||||||
|
get its source. For example, if your program is a web application, its
|
||||||
|
interface could display a "Source" link that leads users to an archive
|
||||||
|
of the code. There are many ways you could offer source, and different
|
||||||
|
solutions will be better for different programs; see section 13 for the
|
||||||
|
specific requirements.
|
||||||
|
|
||||||
|
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 AGPL, see
|
||||||
|
<https://www.gnu.org/licenses/>.
|
||||||
17
README.md
Normal file
17
README.md
Normal file
|
|
@ -0,0 +1,17 @@
|
||||||
|
Simple framework for solving first-order ODEs
|
||||||
|
|
||||||
|
## Example
|
||||||
|
|
||||||
|
Simulate an epidemics using the compartmental model SIR (Susceptible-Infected-Removed). This command prints tab-separated columns Susceptible and Infected, then writes a plot at `target/sir.png`.
|
||||||
|
|
||||||
|
```bash
|
||||||
|
cargo run -p epidemics
|
||||||
|
```
|
||||||
|
|
||||||
|
## License
|
||||||
|
|
||||||
|
GNU AGPL v3, CopyLeft 2021-2023 Pascal Engélibert [(why copyleft?)](https://txmn.tk/blog/why-copyleft/)
|
||||||
|
|
||||||
|
This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, version 3 of the License.
|
||||||
|
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 Affero General Public License for more details.
|
||||||
|
You should have received a copy of the GNU Affero General Public License along with this program. If not, see https://www.gnu.org/licenses/.
|
||||||
9
examples/epidemics/Cargo.toml
Normal file
9
examples/epidemics/Cargo.toml
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
[package]
|
||||||
|
name = "epidemics"
|
||||||
|
version = "0.1.0"
|
||||||
|
edition = "2021"
|
||||||
|
|
||||||
|
[dependencies]
|
||||||
|
nalgebra = "0.32.3"
|
||||||
|
rand = "0.8.5"
|
||||||
|
rustmodel = { path = "../..", features = ["plot"] }
|
||||||
107
examples/epidemics/src/main.rs
Normal file
107
examples/epidemics/src/main.rs
Normal file
|
|
@ -0,0 +1,107 @@
|
||||||
|
use nalgebra::vector;
|
||||||
|
use rustmodel::prelude::*;
|
||||||
|
|
||||||
|
fn main() {
|
||||||
|
// Start with 1% infected
|
||||||
|
let x0 = vector![0.99, 0.01];
|
||||||
|
let dt = 0.1;
|
||||||
|
let nsamples: usize = 400;
|
||||||
|
|
||||||
|
let settings = sir::SirSettings {
|
||||||
|
beta: 0.6,
|
||||||
|
gamma: 0.1,
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
|
||||||
|
let model = sir::Sir {
|
||||||
|
s: settings.clone(),
|
||||||
|
};
|
||||||
|
let solver = ImplicitEuler {
|
||||||
|
dt,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 1..nsamples {
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
xlist.iter().for_each(|x| println!("{}\t{}", x[0], x[1]));
|
||||||
|
|
||||||
|
PlotBuilder::default()
|
||||||
|
.dt(dt)
|
||||||
|
.title(Some(String::from("Epidemics Compartmental Model")))
|
||||||
|
.y_min(Some(0.0))
|
||||||
|
.y_max(Some(1.0))
|
||||||
|
.x_label(Some(String::from("Time")))
|
||||||
|
.build()
|
||||||
|
.unwrap()
|
||||||
|
.plot(
|
||||||
|
"target/sir.png",
|
||||||
|
&xlist,
|
||||||
|
&[("Susceptible", colors::BLUE), ("Infected", colors::RED)],
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
/// SIR model without vital dynamics
|
||||||
|
pub mod sir {
|
||||||
|
use nalgebra::{base::*, matrix, vector};
|
||||||
|
use rustmodel::prelude::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct SirSettings<T> {
|
||||||
|
/// Transmission probability
|
||||||
|
pub beta: T,
|
||||||
|
/// Removal probability
|
||||||
|
pub gamma: T,
|
||||||
|
/// Total population
|
||||||
|
pub pop: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for SirSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Sir<T> {
|
||||||
|
pub s: SirSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, SirSettings<f64>, 2> for Sir<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
-self.s.beta * x[0] * x[1] / self.s.pop,
|
||||||
|
self.s.beta * x[0] * x[1] / self.s.pop - self.s.gamma * x[1]
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
matrix![
|
||||||
|
-self.s.beta*x[1]/self.s.pop, -self.s.beta*x[0]/self.s.pop;
|
||||||
|
self.s.beta*x[1]/self.s.pop, self.s.beta*x[0]/self.s.pop-self.s.gamma
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &SirSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut SirSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<SirSettings<T>> for Vect<T, 3> {
|
||||||
|
fn from(s: SirSettings<T>) -> Self {
|
||||||
|
vector![s.beta, s.gamma, s.pop]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 3>> for SirSettings<T> {
|
||||||
|
fn from(v: Vect<T, 3>) -> Self {
|
||||||
|
Self {
|
||||||
|
beta: v[0],
|
||||||
|
gamma: v[1],
|
||||||
|
pop: v[2],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
608
examples/old/charts.rs
Normal file
608
examples/old/charts.rs
Normal file
|
|
@ -0,0 +1,608 @@
|
||||||
|
use crate::{
|
||||||
|
model::{self, Model},
|
||||||
|
opti::GradientDescentOptimizer,
|
||||||
|
solver::Solver,
|
||||||
|
utils::*,
|
||||||
|
};
|
||||||
|
|
||||||
|
use plotters::prelude::*;
|
||||||
|
use rayon::prelude::*;
|
||||||
|
|
||||||
|
const CHART_SIZE: (u32, u32) = (1000, 800); //(500, 400);
|
||||||
|
const CHART_SIZE_OBJ: (u32, u32) = (960, 960); //(480, 480);
|
||||||
|
|
||||||
|
pub fn draw_chart(filename: &str, title: Option<&str>, pop: f64, xlist: &[Vect<f64, 2>], dt: f64) {
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, CHART_SIZE).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.y_label_area_size(30)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(0.0f64..xlist.len() as f64 * dt, 0.0f64..1.)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart.configure_mesh().x_desc("Time").draw().unwrap();
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist.iter().enumerate().map(|(i, x)| (i as f64 * dt, x[0])),
|
||||||
|
BLUE,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Susceptible")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], BLUE));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist.iter().enumerate().map(|(i, x)| (i as f64 * dt, x[1])),
|
||||||
|
RED,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Infected")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RED));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt, pop - x[0] - x[1])),
|
||||||
|
GREEN,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Removed")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], GREEN));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.border_style(BLACK)
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn draw_error_chart(filename: &str, title: Option<&str>, xlist: &[f64]) {
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, CHART_SIZE).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.y_label_area_size(50)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(0..xlist.len(), (0.0f64..max(xlist)).log_scale())
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
let printer = plotters::data::float::FloatPrettyPrinter {
|
||||||
|
allow_scientific: true,
|
||||||
|
min_decimal: 0,
|
||||||
|
max_decimal: 2,
|
||||||
|
};
|
||||||
|
chart
|
||||||
|
.configure_mesh()
|
||||||
|
.x_desc("Iterations")
|
||||||
|
.y_desc("Mean error")
|
||||||
|
.y_label_formatter(&|y| printer.print(*y))
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(xlist.iter().copied().enumerate(), BLACK))
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn draw_error_chart2(
|
||||||
|
filename: &str,
|
||||||
|
title: Option<&str>,
|
||||||
|
xlist_batch: &[f64],
|
||||||
|
xlist_sto: &[f64],
|
||||||
|
) {
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, CHART_SIZE).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.y_label_area_size(50)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(
|
||||||
|
0..xlist_batch.len().max(xlist_sto.len()),
|
||||||
|
(0.0f64..max(xlist_batch).max(max(xlist_sto))).log_scale(),
|
||||||
|
)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
let printer = plotters::data::float::FloatPrettyPrinter {
|
||||||
|
allow_scientific: true,
|
||||||
|
min_decimal: 0,
|
||||||
|
max_decimal: 2,
|
||||||
|
};
|
||||||
|
chart
|
||||||
|
.configure_mesh()
|
||||||
|
.x_desc("Iterations")
|
||||||
|
.y_desc("Mean error")
|
||||||
|
.y_label_formatter(&|y| printer.print(*y))
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_batch.iter().copied().enumerate(),
|
||||||
|
BLACK,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Batch")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], BLACK));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(xlist_sto.iter().copied().enumerate(), RED))
|
||||||
|
.unwrap()
|
||||||
|
.label("Stochastic")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RED));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.border_style(BLACK)
|
||||||
|
.position(SeriesLabelPosition::MiddleLeft)
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn plot_objective<
|
||||||
|
R: Solver<f64, model::sir::SirSettings<f64>, model::sir::Sir<f64>, 2> + Clone + Sync,
|
||||||
|
>(
|
||||||
|
filename: &str,
|
||||||
|
title: Option<&str>,
|
||||||
|
optimizer: GradientDescentOptimizer<
|
||||||
|
f64,
|
||||||
|
model::sir::SirSettings<f64>,
|
||||||
|
model::sir::Sir<f64>,
|
||||||
|
R,
|
||||||
|
2,
|
||||||
|
3,
|
||||||
|
>,
|
||||||
|
ylist_true: &[Vect<f64, 2>],
|
||||||
|
path_batch: Option<&[(f64, f64)]>,
|
||||||
|
path_sto: Option<&[(f64, f64)]>,
|
||||||
|
) {
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, CHART_SIZE_OBJ).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.y_label_area_size(40)
|
||||||
|
.build_cartesian_2d(0.0f64..1., 0.0f64..1.)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_mesh()
|
||||||
|
.x_desc("beta")
|
||||||
|
.y_desc("gamma")
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
let area = chart.plotting_area();
|
||||||
|
|
||||||
|
let range = area.get_pixel_range();
|
||||||
|
let (pw, ph) = (range.0.end - range.0.start, range.1.end - range.1.start);
|
||||||
|
let (xr, yr) = (chart.x_range(), chart.y_range());
|
||||||
|
let step = (
|
||||||
|
(xr.end - xr.start) / pw as f64,
|
||||||
|
(yr.end - yr.start) / ph as f64,
|
||||||
|
);
|
||||||
|
|
||||||
|
let mut min = f64::MAX;
|
||||||
|
let mut max = f64::MIN;
|
||||||
|
let vals: Vec<(f64, f64, f64)> = (0..pw * ph)
|
||||||
|
.into_par_iter()
|
||||||
|
.map(|i| {
|
||||||
|
let (x, y) = (
|
||||||
|
xr.start + step.0 * (i % pw) as f64,
|
||||||
|
yr.start + step.1 * (i / pw) as f64,
|
||||||
|
);
|
||||||
|
let mut optimizer = optimizer.clone();
|
||||||
|
let s = optimizer.model.get_settings_mut();
|
||||||
|
s.beta = x;
|
||||||
|
s.gamma = y;
|
||||||
|
let val = optimizer.objective_batch(&optimizer.model, ylist_true);
|
||||||
|
(x, y, val)
|
||||||
|
})
|
||||||
|
.collect();
|
||||||
|
vals.iter().for_each(|(_, _, val)| {
|
||||||
|
if *val > max {
|
||||||
|
max = *val;
|
||||||
|
}
|
||||||
|
if *val < min {
|
||||||
|
min = *val;
|
||||||
|
}
|
||||||
|
});
|
||||||
|
let ampl = 0.825 / (max - min);
|
||||||
|
|
||||||
|
for (x, y, c) in vals {
|
||||||
|
area.draw_pixel((x, y), &HSLColor((c - min) * ampl, 1.0, 0.5))
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
if let Some(path_sto) = path_sto {
|
||||||
|
chart
|
||||||
|
.draw_series(std::iter::once(PathElement::new(
|
||||||
|
path_sto,
|
||||||
|
RGBColor(128, 128, 128),
|
||||||
|
)))
|
||||||
|
.unwrap()
|
||||||
|
.label("Stochastic")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RGBColor(128, 128, 128)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if let Some(path_batch) = path_batch {
|
||||||
|
chart
|
||||||
|
.draw_series(std::iter::once(PathElement::new(path_batch, BLACK)))
|
||||||
|
.unwrap()
|
||||||
|
.label("Batch")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], BLACK));
|
||||||
|
}
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.border_style(BLACK)
|
||||||
|
.position(SeriesLabelPosition::UpperRight)
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn draw_comparison_chart(
|
||||||
|
filename: &str,
|
||||||
|
title: Option<&str>,
|
||||||
|
s: &model::sir::SirSettings<f64>,
|
||||||
|
xlist_explicit: &[Vect<f64, 2>],
|
||||||
|
xlist_implicit: &[Vect<f64, 2>],
|
||||||
|
xlist_true: &[Vect<f64, 2>],
|
||||||
|
dt_explicit: f64,
|
||||||
|
dt_implicit: f64,
|
||||||
|
dt_true: f64,
|
||||||
|
) {
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, CHART_SIZE).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.y_label_area_size(30)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(0.0f64..xlist_true.len() as f64 * dt_true, 0.0f64..1.)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart.configure_mesh().x_desc("Time").draw().unwrap();
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_explicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_explicit, x[0])),
|
||||||
|
ShapeStyle::from(BLUE).stroke_width(3),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Susceptible (explicit)")
|
||||||
|
.legend(|(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
ShapeStyle::from(BLUE).stroke_width(3),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_explicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_explicit, x[1])),
|
||||||
|
ShapeStyle::from(RED).stroke_width(3),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Infected (explicit)")
|
||||||
|
.legend(|(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
ShapeStyle::from(RED).stroke_width(3),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_explicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_explicit, s.pop - x[0] - x[1])),
|
||||||
|
ShapeStyle::from(GREEN).stroke_width(3),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Removed (explicit)")
|
||||||
|
.legend(|(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
ShapeStyle::from(GREEN).stroke_width(3),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_implicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_implicit, x[0])),
|
||||||
|
BLUE,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Susceptible (implicit)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], BLUE));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_implicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_implicit, x[1])),
|
||||||
|
RED,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Infected (implicit)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RED));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_implicit
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_implicit, s.pop - x[0] - x[1])),
|
||||||
|
GREEN,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Removed (implicit)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], GREEN));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_true
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_true, x[0])),
|
||||||
|
RGBColor(0, 0, 128),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Susceptible (true)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RGBColor(0, 0, 128)));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_true
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_true, x[1])),
|
||||||
|
RGBColor(128, 0, 0),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Infected (true)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RGBColor(128, 0, 0)));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist_true
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(i, x)| (i as f64 * dt_true, s.pop - x[0] - x[1])),
|
||||||
|
RGBColor(0, 128, 0),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label("Removed (true)")
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], RGBColor(0, 128, 0)));
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.border_style(BLACK)
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn draw_bike_chart(filename: &str, title: Option<&str>, xlists: &[(&str, &[f64])], dt: f64) {
|
||||||
|
let max_x = xlists
|
||||||
|
.iter()
|
||||||
|
.map(|(_, xlist)| xlist.len())
|
||||||
|
.max()
|
||||||
|
.expect("at least one series expected");
|
||||||
|
let max_y = *xlists
|
||||||
|
.iter()
|
||||||
|
.map(|(_, xlist)| {
|
||||||
|
xlist
|
||||||
|
.iter()
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.expect("at least one sample per series expected")
|
||||||
|
})
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.unwrap();
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, (640, 480)).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.margin_top(12)
|
||||||
|
.y_label_area_size(30)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(0.0f64..max_x as f64 * dt, 0.0f64..max_y)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
chart.configure_mesh().x_desc("Temps (s)").draw().unwrap();
|
||||||
|
|
||||||
|
for (list_i, (label, xlist)) in xlists.into_iter().enumerate() {
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist.iter().enumerate().map(|(i, x)| (i as f64 * dt, *x)),
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label(*label)
|
||||||
|
.legend(move |(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.border_style(BLACK)
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.label_font(("Libertinus Serif", 20))
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn draw_bike_chart2(
|
||||||
|
filename: &str,
|
||||||
|
title: Option<&str>,
|
||||||
|
xlists1: &[(&str, &[f64])],
|
||||||
|
xlists2: &[(&str, &[f64])],
|
||||||
|
dt: f64,
|
||||||
|
) {
|
||||||
|
let max_x = xlists1
|
||||||
|
.iter()
|
||||||
|
.chain(xlists2.iter())
|
||||||
|
.map(|(_, xlist)| xlist.len())
|
||||||
|
.max()
|
||||||
|
.expect("at least one series expected");
|
||||||
|
let max_y1 = *xlists1
|
||||||
|
.iter()
|
||||||
|
.map(|(_, xlist)| {
|
||||||
|
xlist
|
||||||
|
.iter()
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.expect("at least one sample per series expected")
|
||||||
|
})
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.unwrap();
|
||||||
|
let max_y2 = *xlists2
|
||||||
|
.iter()
|
||||||
|
.map(|(_, xlist)| {
|
||||||
|
xlist
|
||||||
|
.iter()
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.expect("at least one sample per series expected")
|
||||||
|
})
|
||||||
|
.max_by(|a, b| a.total_cmp(b))
|
||||||
|
.unwrap();
|
||||||
|
let filepath = format!("target/{}.png", filename);
|
||||||
|
let root = BitMapBackend::new(&filepath, (640, 480)).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::Name("cantarell"), 28.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.margin_top(12)
|
||||||
|
.y_label_area_size(50)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.right_y_label_area_size(50)
|
||||||
|
.build_cartesian_2d(0.0f64..max_x as f64 * dt, 0.0f64..max_y1)
|
||||||
|
.unwrap()
|
||||||
|
.set_secondary_coord(0.0f64..max_x as f64 * dt, 0.0f64..max_y2);
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_mesh()
|
||||||
|
.x_desc("Temps (s)")
|
||||||
|
.y_desc("Vitesse (m/s)")
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
chart
|
||||||
|
.configure_secondary_axes()
|
||||||
|
.y_desc("Freinage")
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
for (list_i, (label, xlist)) in xlists1.into_iter().enumerate() {
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
xlist.iter().enumerate().map(|(i, x)| (i as f64 * dt, *x)),
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label(*label)
|
||||||
|
.legend(move |(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
||||||
|
for (list_i, (label, xlist)) in (xlists1.len()..).zip(xlists2.into_iter()) {
|
||||||
|
chart
|
||||||
|
.draw_secondary_series(LineSeries::new(
|
||||||
|
xlist.iter().enumerate().map(|(i, x)| (i as f64 * dt, *x)),
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label(*label)
|
||||||
|
.legend(move |(x, y)| {
|
||||||
|
PathElement::new(
|
||||||
|
vec![(x, y), (x + 20, y)],
|
||||||
|
Palette100::pick(list_i + 1).stroke_width(2),
|
||||||
|
)
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.border_style(BLACK)
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.label_font(("Libertinus Serif", 20))
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
91
examples/old/live.rs
Normal file
91
examples/old/live.rs
Normal file
|
|
@ -0,0 +1,91 @@
|
||||||
|
use crate::{
|
||||||
|
model::{Coloring, Model, Settings},
|
||||||
|
solver::Solver,
|
||||||
|
space::Space,
|
||||||
|
};
|
||||||
|
|
||||||
|
use sdl2::{event::Event, keyboard::Keycode, pixels::PixelFormatEnum};
|
||||||
|
use std::{
|
||||||
|
sync::{Arc, RwLock, RwLockReadGuard},
|
||||||
|
time::Duration,
|
||||||
|
};
|
||||||
|
|
||||||
|
const FRAMEDUR: u64 = 30;
|
||||||
|
|
||||||
|
pub fn run<
|
||||||
|
T: Copy,
|
||||||
|
P,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D> + Coloring<T, P, [u8; 3], D>,
|
||||||
|
V: Solver<T, S, M, D>,
|
||||||
|
const D: usize,
|
||||||
|
>(
|
||||||
|
space: Arc<RwLock<Space<T, S, M, V, D>>>,
|
||||||
|
) {
|
||||||
|
let sdl_context = sdl2::init().unwrap();
|
||||||
|
let video_subsystem = sdl_context.video().unwrap();
|
||||||
|
|
||||||
|
let size = space.read().unwrap().size;
|
||||||
|
|
||||||
|
let window = video_subsystem
|
||||||
|
.window("Model", size.0 as u32, size.1 as u32)
|
||||||
|
.resizable()
|
||||||
|
.position_centered()
|
||||||
|
.opengl()
|
||||||
|
.build()
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
let mut canvas = window.into_canvas().build().unwrap();
|
||||||
|
let texture_creator = canvas.texture_creator();
|
||||||
|
|
||||||
|
let mut event_pump = sdl_context.event_pump().unwrap();
|
||||||
|
let interval = Duration::from_millis(FRAMEDUR);
|
||||||
|
|
||||||
|
let mut image = vec![0u8; size.0 * size.1 * 3];
|
||||||
|
|
||||||
|
'running: loop {
|
||||||
|
for event in event_pump.poll_iter() {
|
||||||
|
match event {
|
||||||
|
Event::Quit { .. }
|
||||||
|
| Event::KeyDown {
|
||||||
|
keycode: Some(Keycode::Escape),
|
||||||
|
..
|
||||||
|
} => {
|
||||||
|
break 'running;
|
||||||
|
}
|
||||||
|
_ => {}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
render(space.read().unwrap(), &mut image);
|
||||||
|
|
||||||
|
let mut texture = texture_creator
|
||||||
|
.create_texture_streaming(PixelFormatEnum::RGB24, size.0 as u32, size.1 as u32)
|
||||||
|
.unwrap();
|
||||||
|
texture.update(None, &image, size.0 * 3).unwrap();
|
||||||
|
canvas.copy(&texture, None, None).unwrap();
|
||||||
|
|
||||||
|
canvas.present();
|
||||||
|
|
||||||
|
std::thread::sleep(interval);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn render<
|
||||||
|
T: Copy,
|
||||||
|
P,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D> + Coloring<T, P, [u8; 3], D>,
|
||||||
|
V: Solver<T, S, M, D>,
|
||||||
|
const D: usize,
|
||||||
|
>(
|
||||||
|
space: RwLockReadGuard<Space<T, S, M, V, D>>,
|
||||||
|
image: &mut Vec<u8>,
|
||||||
|
) {
|
||||||
|
image.resize(space.points.len() * 3, 0);
|
||||||
|
if let Some(pre) = M::prepare(space.points.iter().map(|point| point.pos)) {
|
||||||
|
for (i, point) in space.points.iter().enumerate() {
|
||||||
|
image[i * 3..i * 3 + 3].copy_from_slice(&M::color(&pre, point.pos));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
676
examples/old/main.rs
Normal file
676
examples/old/main.rs
Normal file
|
|
@ -0,0 +1,676 @@
|
||||||
|
mod charts;
|
||||||
|
mod live;
|
||||||
|
mod model;
|
||||||
|
mod opti;
|
||||||
|
mod solver;
|
||||||
|
mod space;
|
||||||
|
mod utils;
|
||||||
|
|
||||||
|
use model::Model;
|
||||||
|
use opti::GradientDescentOptimizer;
|
||||||
|
use solver::*;
|
||||||
|
|
||||||
|
use nalgebra::vector;
|
||||||
|
use rand::Rng;
|
||||||
|
use std::{
|
||||||
|
collections::HashMap,
|
||||||
|
sync::{Arc, RwLock},
|
||||||
|
thread,
|
||||||
|
time::Duration,
|
||||||
|
};
|
||||||
|
|
||||||
|
fn main() {
|
||||||
|
bike();
|
||||||
|
//lyfe();
|
||||||
|
//stage();
|
||||||
|
}
|
||||||
|
|
||||||
|
#[allow(dead_code)]
|
||||||
|
fn lyfe() {
|
||||||
|
let size = (800, 800);
|
||||||
|
let diffusion = vector![0.2, 0.2];
|
||||||
|
|
||||||
|
let model = model::constrained::Constrained {
|
||||||
|
s: model::constrained::ConstrainedSettings {
|
||||||
|
model: model::lyfe::Lyfe {
|
||||||
|
s: model::lyfe::LyfeSettings {
|
||||||
|
da: 0.2,
|
||||||
|
db: 0.3,
|
||||||
|
f: 0.03,
|
||||||
|
r: 0.061,
|
||||||
|
},
|
||||||
|
},
|
||||||
|
constraint: model::MinMaxConstraint {
|
||||||
|
min: [0.0, 0.0],
|
||||||
|
max: [1.0, 1.0],
|
||||||
|
},
|
||||||
|
_p: Default::default(),
|
||||||
|
},
|
||||||
|
};
|
||||||
|
/*let solver = ImplicitEulerSolver {
|
||||||
|
dt: 0.1,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};*/
|
||||||
|
let solver = ExplicitEulerSolver { dt: 0.01 };
|
||||||
|
|
||||||
|
let mut space = space::Space {
|
||||||
|
model,
|
||||||
|
solver,
|
||||||
|
old_points: vec![
|
||||||
|
space::Point {
|
||||||
|
pos: vector![0.0, 0.0],
|
||||||
|
diffusion,
|
||||||
|
};
|
||||||
|
size.0 * size.1
|
||||||
|
],
|
||||||
|
points: vec![
|
||||||
|
space::Point {
|
||||||
|
pos: vector![0.0, 0.0],
|
||||||
|
diffusion,
|
||||||
|
};
|
||||||
|
size.0 * size.1
|
||||||
|
],
|
||||||
|
size,
|
||||||
|
sources: HashMap::new(),
|
||||||
|
time: 0.0,
|
||||||
|
_p: Default::default(),
|
||||||
|
};
|
||||||
|
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
for _ in 0..100 {
|
||||||
|
space.points[rng.gen_range(0..space.old_points.len())].pos[0] = 0.8;
|
||||||
|
}
|
||||||
|
//space.points[size.0 * size.1 / 2 + size.0 / 2].pos[0] = 0.1;
|
||||||
|
//space.points[size.0 * size.1 / 2 + size.0 / 2 + 100].pos[0] = 0.05;
|
||||||
|
|
||||||
|
let space = Arc::new(RwLock::new(space));
|
||||||
|
|
||||||
|
thread::spawn({
|
||||||
|
let space = space.clone();
|
||||||
|
let interval = Duration::from_millis(1);
|
||||||
|
move || loop {
|
||||||
|
space.write().unwrap().simulate(0.1);
|
||||||
|
std::thread::sleep(interval);
|
||||||
|
}
|
||||||
|
});
|
||||||
|
|
||||||
|
thread::spawn(move || live::run(space)).join().unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
#[allow(dead_code)]
|
||||||
|
fn giraffe() {
|
||||||
|
let size = (800, 800);
|
||||||
|
let diffusion = vector![0.1, 0.1];
|
||||||
|
|
||||||
|
let model = model::constrained::Constrained {
|
||||||
|
s: model::constrained::ConstrainedSettings {
|
||||||
|
model: model::giraffe::Giraffe {
|
||||||
|
s: model::giraffe::GiraffeSettings {
|
||||||
|
a_a: 0.7,
|
||||||
|
a_b: 0.2,
|
||||||
|
b_a: -0.5,
|
||||||
|
b_b: 0.1,
|
||||||
|
},
|
||||||
|
},
|
||||||
|
constraint: model::MinMaxConstraint {
|
||||||
|
min: [0.0, 0.0],
|
||||||
|
max: [1.0, 1.0],
|
||||||
|
},
|
||||||
|
_p: Default::default(),
|
||||||
|
},
|
||||||
|
};
|
||||||
|
/*let solver = ImplicitEulerSolver {
|
||||||
|
dt: 0.1,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};*/
|
||||||
|
let solver = ExplicitEulerSolver { dt: 0.1 };
|
||||||
|
|
||||||
|
let mut space = space::Space {
|
||||||
|
model,
|
||||||
|
solver,
|
||||||
|
old_points: vec![
|
||||||
|
space::Point {
|
||||||
|
pos: vector![0.0, 0.0],
|
||||||
|
diffusion,
|
||||||
|
};
|
||||||
|
size.0 * size.1
|
||||||
|
],
|
||||||
|
points: vec![
|
||||||
|
space::Point {
|
||||||
|
pos: vector![0.0, 0.0],
|
||||||
|
diffusion,
|
||||||
|
};
|
||||||
|
size.0 * size.1
|
||||||
|
],
|
||||||
|
size,
|
||||||
|
sources: HashMap::new(),
|
||||||
|
time: 0.0,
|
||||||
|
_p: Default::default(),
|
||||||
|
};
|
||||||
|
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
for _ in 0..100 {
|
||||||
|
space.points[rng.gen_range(0..space.old_points.len())].pos[0] = 0.5;
|
||||||
|
}
|
||||||
|
//space.points[size.0 * size.1 / 2 + size.0 / 2].pos[0] = 0.1;
|
||||||
|
//space.points[size.0 * size.1 / 2 + size.0 / 2 + 100].pos[0] = 0.05;
|
||||||
|
|
||||||
|
let space = Arc::new(RwLock::new(space));
|
||||||
|
|
||||||
|
thread::spawn({
|
||||||
|
let space = space.clone();
|
||||||
|
let interval = Duration::from_millis(1);
|
||||||
|
move || loop {
|
||||||
|
space.write().unwrap().simulate(0.1);
|
||||||
|
std::thread::sleep(interval);
|
||||||
|
}
|
||||||
|
});
|
||||||
|
|
||||||
|
thread::spawn(move || live::run(space)).join().unwrap();
|
||||||
|
}
|
||||||
|
|
||||||
|
#[allow(dead_code)]
|
||||||
|
fn stage() {
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
|
||||||
|
// ---- Initialization
|
||||||
|
|
||||||
|
let x0 = vector![0.99, 0.01];
|
||||||
|
let dt = 0.1;
|
||||||
|
let nsamples: usize = 400;
|
||||||
|
let nsamples_partial: usize = 40;
|
||||||
|
|
||||||
|
// ---- True data generation
|
||||||
|
|
||||||
|
let settings_true = model::sir::SirSettings {
|
||||||
|
beta: 0.6,
|
||||||
|
gamma: 0.1,
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
|
||||||
|
let model = model::sir::Sir {
|
||||||
|
s: settings_true.clone(),
|
||||||
|
};
|
||||||
|
let solver = ImplicitEulerSolver {
|
||||||
|
dt: 0.1,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let mut xlist_true = Vec::with_capacity(nsamples);
|
||||||
|
xlist_true.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
xlist_true.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// ---- Calibration
|
||||||
|
|
||||||
|
let mut optimizer = GradientDescentOptimizer::new(model, solver);
|
||||||
|
let settings_random = model::sir::SirSettings {
|
||||||
|
beta: rng.gen(),
|
||||||
|
gamma: rng.gen(),
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
*optimizer.model.get_settings_mut() = model::sir::SirSettings {
|
||||||
|
beta: 0.38960491052564317,
|
||||||
|
gamma: 0.6549130899826807,
|
||||||
|
pop: 1.0,
|
||||||
|
}; //settings_random.clone();
|
||||||
|
let mut optimizer_sto = optimizer.clone();
|
||||||
|
|
||||||
|
let mut xlist_random = Vec::with_capacity(nsamples);
|
||||||
|
xlist_random.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = optimizer.solver.f(&optimizer.model, x);
|
||||||
|
xlist_random.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Batch
|
||||||
|
|
||||||
|
let mut path = Vec::new();
|
||||||
|
let mut error = Vec::new();
|
||||||
|
for rate in [1.0, 0.1, 0.01, 0.001] {
|
||||||
|
let (path_, error_) = &mut optimizer.calibrate_batch_record(
|
||||||
|
&xlist_true[..nsamples_partial],
|
||||||
|
0.00001,
|
||||||
|
rate,
|
||||||
|
1000,
|
||||||
|
0..2,
|
||||||
|
);
|
||||||
|
path.append(path_);
|
||||||
|
error.append(error_);
|
||||||
|
}
|
||||||
|
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = optimizer.solver.f(&optimizer.model, x);
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Stochastic
|
||||||
|
|
||||||
|
let mut path_sto = Vec::new();
|
||||||
|
let mut error_sto = Vec::new();
|
||||||
|
for rate in [1.0, 0.1, 0.01, 0.001] {
|
||||||
|
let (path_, error_) = &mut optimizer_sto.calibrate_stochastic_record(
|
||||||
|
&xlist_true[..nsamples_partial],
|
||||||
|
0.00001,
|
||||||
|
rate,
|
||||||
|
10,
|
||||||
|
0..2,
|
||||||
|
);
|
||||||
|
path_sto.append(path_);
|
||||||
|
error_sto.append(error_);
|
||||||
|
}
|
||||||
|
|
||||||
|
let mut xlist_sto = Vec::with_capacity(nsamples);
|
||||||
|
xlist_sto.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = optimizer_sto.solver.f(&optimizer_sto.model, x);
|
||||||
|
xlist_sto.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// ---- Printing
|
||||||
|
|
||||||
|
println!("Random settings:\n{:?}", settings_random);
|
||||||
|
println!("Calibrated settings:\n{:?}", optimizer.model.get_settings());
|
||||||
|
println!("True settings:\n{:?}", settings_true);
|
||||||
|
|
||||||
|
// ---- Drawing
|
||||||
|
|
||||||
|
// Main plots
|
||||||
|
|
||||||
|
charts::draw_chart("sir_true", None, settings_true.pop, &xlist_true, dt);
|
||||||
|
charts::draw_chart("sir_random", None, settings_random.pop, &xlist_random, dt);
|
||||||
|
charts::draw_chart(
|
||||||
|
"sir_calibrated",
|
||||||
|
None,
|
||||||
|
optimizer.model.get_settings().pop,
|
||||||
|
&xlist,
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_error_chart2("error", None, &error, &error_sto);
|
||||||
|
|
||||||
|
charts::plot_objective(
|
||||||
|
"obj_partial",
|
||||||
|
None,
|
||||||
|
optimizer.clone(),
|
||||||
|
&xlist_true[..nsamples_partial],
|
||||||
|
Some(&path.iter().map(|v| (v[0], v[1])).collect::<Vec<_>>()),
|
||||||
|
Some(&path_sto.iter().map(|v| (v[0], v[1])).collect::<Vec<_>>()),
|
||||||
|
);
|
||||||
|
charts::plot_objective(
|
||||||
|
"obj",
|
||||||
|
None,
|
||||||
|
optimizer.clone(),
|
||||||
|
&xlist_true,
|
||||||
|
Some(&path.iter().map(|v| (v[0], v[1])).collect::<Vec<_>>()),
|
||||||
|
Some(&path_sto.iter().map(|v| (v[0], v[1])).collect::<Vec<_>>()),
|
||||||
|
);
|
||||||
|
|
||||||
|
// Implicit/explicit Euler comparison
|
||||||
|
|
||||||
|
{
|
||||||
|
let dur = 40f64;
|
||||||
|
let settings = model::sir::SirSettings {
|
||||||
|
beta: 0.999,
|
||||||
|
gamma: 0.5,
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
let model = model::sir::Sir {
|
||||||
|
s: settings.clone(),
|
||||||
|
};
|
||||||
|
let solver_explicit = ExplicitEulerSolver { dt: 1.0 };
|
||||||
|
let solver_implicit = ImplicitEulerSolver {
|
||||||
|
dt: 1.0,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let solver_true = ImplicitEulerSolver {
|
||||||
|
dt: 0.001,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let nsamples_explicit = (dur / solver_explicit.dt) as usize;
|
||||||
|
let nsamples_implicit = (dur / solver_implicit.dt) as usize;
|
||||||
|
let nsamples_true = (dur / solver_true.dt) as usize;
|
||||||
|
let mut xlist_explicit = Vec::with_capacity(nsamples_explicit);
|
||||||
|
xlist_explicit.push(x0);
|
||||||
|
let mut xlist_implicit = Vec::with_capacity(nsamples_implicit);
|
||||||
|
xlist_implicit.push(x0);
|
||||||
|
let mut xlist_true = Vec::with_capacity(nsamples_true);
|
||||||
|
xlist_true.push(x0);
|
||||||
|
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 1..nsamples_explicit {
|
||||||
|
x = solver_explicit.f(&model, x);
|
||||||
|
xlist_explicit.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
x = x0;
|
||||||
|
for _ in 1..nsamples_implicit {
|
||||||
|
x = solver_implicit.f(&model, x);
|
||||||
|
xlist_implicit.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
x = x0;
|
||||||
|
for _ in 1..nsamples_true {
|
||||||
|
x = solver_true.f(&model, x);
|
||||||
|
xlist_true.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
charts::draw_comparison_chart(
|
||||||
|
"comp_euler",
|
||||||
|
None,
|
||||||
|
&settings,
|
||||||
|
&xlist_explicit,
|
||||||
|
&xlist_implicit,
|
||||||
|
&xlist_true,
|
||||||
|
solver_explicit.dt,
|
||||||
|
solver_implicit.dt,
|
||||||
|
solver_true.dt,
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
// SIRV charts
|
||||||
|
|
||||||
|
{
|
||||||
|
let nsamples = 1000;
|
||||||
|
let settings = model::sirv::SirvSettings {
|
||||||
|
beta: 0.8,
|
||||||
|
gamma: 0.2,
|
||||||
|
lambda: 0.025,
|
||||||
|
mu: 0.02,
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
let model = model::sirv::Sirv { s: settings };
|
||||||
|
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 1..nsamples {
|
||||||
|
x = optimizer.solver.f(&model, x);
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
charts::draw_chart("sirv", None, model.get_settings().pop, &xlist, dt);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[allow(dead_code)]
|
||||||
|
fn bike() {
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
|
||||||
|
// ---- Initialization
|
||||||
|
|
||||||
|
let x0 = vector![0.0, 60. / 3.6];
|
||||||
|
let dt = 0.1;
|
||||||
|
let nsamples: usize = 2000;
|
||||||
|
|
||||||
|
// ---- Data generation
|
||||||
|
|
||||||
|
let settings_true = model::bike::BikeSettings::<f64> {
|
||||||
|
cx: 0.25,
|
||||||
|
g: 9.81,
|
||||||
|
m: 70.0,
|
||||||
|
th: 0.11,
|
||||||
|
};
|
||||||
|
println!(
|
||||||
|
"true: A={} ; B={}",
|
||||||
|
-settings_true.cx / settings_true.m,
|
||||||
|
settings_true.g * settings_true.th.sin() - 80. / settings_true.m
|
||||||
|
);
|
||||||
|
|
||||||
|
let model = model::bike::Bike {
|
||||||
|
s: settings_true.clone(),
|
||||||
|
};
|
||||||
|
/*let solver = ImplicitEulerSolver {
|
||||||
|
dt,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};*/
|
||||||
|
let solver = ExplicitEulerSolver { dt };
|
||||||
|
let mut xlist_true = Vec::with_capacity(nsamples);
|
||||||
|
xlist_true.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
if x[1] < 0. {
|
||||||
|
x[1] = 0.;
|
||||||
|
}
|
||||||
|
xlist_true.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Alternative settings
|
||||||
|
|
||||||
|
// Greater theta
|
||||||
|
|
||||||
|
let mut settings_greater_th = settings_true.clone();
|
||||||
|
settings_greater_th.th = 0.12;
|
||||||
|
println!(
|
||||||
|
"gtth: A={} ; B={}",
|
||||||
|
-settings_greater_th.cx / settings_greater_th.m,
|
||||||
|
settings_greater_th.g * settings_greater_th.th.sin() - 80. / settings_greater_th.m
|
||||||
|
);
|
||||||
|
|
||||||
|
let xlist_greater_th = {
|
||||||
|
let model = model::bike::Bike {
|
||||||
|
s: settings_greater_th.clone(),
|
||||||
|
};
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
if x[1] < 0. {
|
||||||
|
x[1] = 0.;
|
||||||
|
}
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
xlist
|
||||||
|
};
|
||||||
|
|
||||||
|
// Optimal braking
|
||||||
|
|
||||||
|
let mut settings_opti1 = model::bike2::BikeSettings {
|
||||||
|
cx: settings_true.cx,
|
||||||
|
g: settings_true.g,
|
||||||
|
m: settings_true.m,
|
||||||
|
th: std::f64::consts::PI / 180. * 15.,
|
||||||
|
b: |x, v, s| {
|
||||||
|
let mu = 0.1;
|
||||||
|
let gx = 0.65;
|
||||||
|
let gy = 1.05;
|
||||||
|
let magic = 1.0;
|
||||||
|
(
|
||||||
|
(
|
||||||
|
s.m * s.g * (mu * s.th.cos() + s.th.sin()) - s.cx * v * v,
|
||||||
|
0.,
|
||||||
|
),
|
||||||
|
(-2. * s.cx * v, 0.),
|
||||||
|
)
|
||||||
|
},
|
||||||
|
};
|
||||||
|
|
||||||
|
let (xlist_opti1, blist_opti1) = {
|
||||||
|
let model = model::bike2::Bike {
|
||||||
|
s: settings_opti1.clone(),
|
||||||
|
};
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut blist = Vec::with_capacity(nsamples);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
blist.push((settings_opti1.b)(x[0], x[1], &settings_opti1).0 .0);
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
if x[1] < 0. {
|
||||||
|
x[1] = 0.;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
(xlist, blist)
|
||||||
|
};
|
||||||
|
|
||||||
|
let mut settings_opti2 = model::bike2::BikeSettings {
|
||||||
|
cx: settings_true.cx,
|
||||||
|
g: settings_true.g,
|
||||||
|
m: settings_true.m,
|
||||||
|
th: std::f64::consts::PI / 180. * 15.,
|
||||||
|
b: |x, v, s| {
|
||||||
|
let mu = 0.1;
|
||||||
|
let gx = 0.65;
|
||||||
|
let gy = 1.05;
|
||||||
|
let magic = 1.0;
|
||||||
|
(
|
||||||
|
(
|
||||||
|
s.m * s.g * (mu * s.th.cos() + s.th.sin()) - s.cx * v * v,
|
||||||
|
s.m * s.g * s.th.cos() * (mu + gx / gy),
|
||||||
|
),
|
||||||
|
(-2. * s.cx * v, 0.),
|
||||||
|
)
|
||||||
|
},
|
||||||
|
};
|
||||||
|
|
||||||
|
let xlist_opti2 = {
|
||||||
|
let model = model::bike2::Bike {
|
||||||
|
s: settings_opti2.clone(),
|
||||||
|
};
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..nsamples - 1 {
|
||||||
|
x = solver.f(&model, x);
|
||||||
|
if x[1] < 0. {
|
||||||
|
x[1] = 0.;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
xlist.push(x);
|
||||||
|
}
|
||||||
|
xlist
|
||||||
|
};
|
||||||
|
|
||||||
|
// -- ODE solution
|
||||||
|
|
||||||
|
let xlist_ode = {
|
||||||
|
let settings = settings_true.clone();
|
||||||
|
let a = -settings.cx / settings.m;
|
||||||
|
let b = settings.g * settings.th.sin() - 80. / settings.m;
|
||||||
|
/*let r = (-a*b).sqrt();
|
||||||
|
assert!(!r.is_nan());
|
||||||
|
let alpha = (1.+x0[1]*a/r)/(1.-x0[1]*a/r);*/
|
||||||
|
let r = (a * b).sqrt();
|
||||||
|
assert!(!r.is_nan());
|
||||||
|
let alpha = -r / (a * x0[1]);
|
||||||
|
println!("alpha: {alpha}");
|
||||||
|
let stop = (1. / alpha).atan() / r;
|
||||||
|
println!("Stop: {stop}");
|
||||||
|
|
||||||
|
let bmax =
|
||||||
|
settings.m * settings.g * (settings.th.cos() + settings.th.sin()) - settings.cx * 27.;
|
||||||
|
println!("bmax: {bmax}");
|
||||||
|
|
||||||
|
let mut xlist = Vec::with_capacity(nsamples);
|
||||||
|
xlist.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for t in 0..nsamples - 1 {
|
||||||
|
let t = t as f64 * dt;
|
||||||
|
//dbg!((beta*c*(-t*c).exp()-alpha*c*(t*c).exp()));
|
||||||
|
//dbg!((alpha*(t*c).exp()+beta*(-t*c).exp()));
|
||||||
|
//let v = (beta*c*(-t*c).exp()-alpha*c*(t*c).exp())/a/(alpha*(t*c).exp()+beta*(-t*c).exp());
|
||||||
|
//let v = r/a*(alpha*(-t*r).exp()-(t*r).exp())/(alpha*(-t*r).exp()+(t*r).exp());
|
||||||
|
let mut v = r / a * (alpha * (t * r).sin() - (t * r).cos())
|
||||||
|
/ (alpha * (t * r).cos() + (t * r).sin());
|
||||||
|
if v.is_nan() {
|
||||||
|
panic!("NaN");
|
||||||
|
}
|
||||||
|
v = v.max(0.).min(100.);
|
||||||
|
x = vector![0., v];
|
||||||
|
xlist.push(x);
|
||||||
|
if t > stop {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
xlist
|
||||||
|
};
|
||||||
|
|
||||||
|
// ---- Drawing
|
||||||
|
|
||||||
|
// Main plots
|
||||||
|
|
||||||
|
charts::draw_bike_chart(
|
||||||
|
"bike_x",
|
||||||
|
None,
|
||||||
|
&[(
|
||||||
|
"x (m)",
|
||||||
|
&xlist_true.iter().map(|x| x[0]).collect::<Vec<_>>(),
|
||||||
|
)],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_bike_chart(
|
||||||
|
"bike_v",
|
||||||
|
None,
|
||||||
|
&[(
|
||||||
|
"v (m/s)",
|
||||||
|
&xlist_true.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
)],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_bike_chart2(
|
||||||
|
"bike_opti1",
|
||||||
|
None,
|
||||||
|
&[(
|
||||||
|
"v (m/s)",
|
||||||
|
&xlist_opti1.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
)],
|
||||||
|
&[("b", &blist_opti1)],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_bike_chart(
|
||||||
|
"bike_opti2",
|
||||||
|
None,
|
||||||
|
&[
|
||||||
|
(
|
||||||
|
"v (m/s) (arrière)",
|
||||||
|
&xlist_opti1.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
),
|
||||||
|
(
|
||||||
|
"v (m/s) (arrière+avant)",
|
||||||
|
&xlist_opti2.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
),
|
||||||
|
],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_bike_chart(
|
||||||
|
"bike_var_theta",
|
||||||
|
None,
|
||||||
|
&[
|
||||||
|
(
|
||||||
|
&format!("v (θ={}, B<0)", settings_true.th),
|
||||||
|
&xlist_true.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
),
|
||||||
|
(
|
||||||
|
&format!("v (θ={}, B>0)", settings_greater_th.th),
|
||||||
|
&xlist_greater_th.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
),
|
||||||
|
],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
charts::draw_bike_chart(
|
||||||
|
"bike_ode_v",
|
||||||
|
None,
|
||||||
|
&[(
|
||||||
|
"v (m/s)",
|
||||||
|
&xlist_ode.iter().map(|x| x[1]).collect::<Vec<_>>(),
|
||||||
|
)],
|
||||||
|
dt,
|
||||||
|
);
|
||||||
|
}
|
||||||
595
examples/old/model.rs
Normal file
595
examples/old/model.rs
Normal file
|
|
@ -0,0 +1,595 @@
|
||||||
|
use crate::utils::*;
|
||||||
|
|
||||||
|
use nalgebra::{base::*, matrix, vector};
|
||||||
|
use std::marker::PhantomData;
|
||||||
|
|
||||||
|
pub trait Settings {}
|
||||||
|
|
||||||
|
pub trait Model<T, S: Settings, const D: usize> {
|
||||||
|
/// Returns f(x)
|
||||||
|
fn f(&self, x: Vect<T, D>) -> Vect<T, D>;
|
||||||
|
/// Returns df(x)/dx
|
||||||
|
fn df(&self, x: Vect<T, D>) -> Mat<T, D, D>;
|
||||||
|
fn get_settings(&self) -> &S;
|
||||||
|
fn get_settings_mut(&mut self) -> &mut S;
|
||||||
|
}
|
||||||
|
|
||||||
|
pub trait Coloring<T, P, C, const D: usize> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<T, D>>>(iter: I) -> Option<P>;
|
||||||
|
fn color(pre: &P, val: Vect<T, D>) -> C;
|
||||||
|
}
|
||||||
|
|
||||||
|
pub struct MinMaxColoringInfo<T, const D: usize> {
|
||||||
|
pub min: [T; D],
|
||||||
|
pub max: [T; D],
|
||||||
|
}
|
||||||
|
|
||||||
|
pub trait Constraint<T, const D: usize> {
|
||||||
|
fn constrain_mut(&self, val: &mut Vect<T, D>);
|
||||||
|
fn constrain(&self, mut val: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
self.constrain_mut(&mut val);
|
||||||
|
val
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
pub struct MinMaxConstraint<T, const D: usize> {
|
||||||
|
pub min: [T; D],
|
||||||
|
pub max: [T; D],
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Copy + PartialOrd, const D: usize> Constraint<T, D> for MinMaxConstraint<T, D> {
|
||||||
|
fn constrain_mut(&self, val: &mut Vect<T, D>) {
|
||||||
|
for ((comp, min), max) in val.iter_mut().zip(self.min.iter()).zip(self.max.iter()) {
|
||||||
|
*comp = num_traits::clamp(*comp, *min, *max)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// Models
|
||||||
|
|
||||||
|
pub mod constrained {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct ConstrainedSettings<T, O, M, S> {
|
||||||
|
pub constraint: O,
|
||||||
|
pub model: M,
|
||||||
|
pub _p: PhantomData<(T, S)>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T, O, M, S> Settings for ConstrainedSettings<T, O, M, S> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Constrained<T, O, M, S> {
|
||||||
|
pub s: ConstrainedSettings<T, O, M, S>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T, O: Constraint<T, D>, M: Model<T, S, D>, S: Settings, const D: usize>
|
||||||
|
Model<T, ConstrainedSettings<T, O, M, S>, D> for Constrained<T, O, M, S>
|
||||||
|
{
|
||||||
|
fn f(&self, x: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
self.s.constraint.constrain(self.s.model.f(x))
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vect<T, D>) -> Mat<T, D, D> {
|
||||||
|
self.s.model.df(x)
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &ConstrainedSettings<T, O, M, S> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut ConstrainedSettings<T, O, M, S> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T, O, M: Coloring<T, P, C, D>, S, P, C, const D: usize> Coloring<T, P, C, D>
|
||||||
|
for Constrained<T, O, M, S>
|
||||||
|
{
|
||||||
|
fn prepare<I: Iterator<Item = Vect<T, D>>>(iter: I) -> Option<P> {
|
||||||
|
M::prepare(iter)
|
||||||
|
}
|
||||||
|
fn color(pre: &P, val: Vect<T, D>) -> C {
|
||||||
|
M::color(pre, val)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// SIR model without vital dynamics
|
||||||
|
pub mod sir {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct SirSettings<T> {
|
||||||
|
/// Transmission probability
|
||||||
|
pub beta: T,
|
||||||
|
/// Removal probability
|
||||||
|
pub gamma: T,
|
||||||
|
pub pop: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for SirSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Sir<T> {
|
||||||
|
pub s: SirSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, SirSettings<f64>, 2> for Sir<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
-self.s.beta * x[0] * x[1] / self.s.pop,
|
||||||
|
self.s.beta * x[0] * x[1] / self.s.pop - self.s.gamma * x[1]
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
matrix![
|
||||||
|
-self.s.beta*x[1]/self.s.pop, -self.s.beta*x[0]/self.s.pop;
|
||||||
|
self.s.beta*x[1]/self.s.pop, self.s.beta*x[0]/self.s.pop-self.s.gamma
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &SirSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut SirSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<SirSettings<T>> for Vect<T, 3> {
|
||||||
|
fn from(s: SirSettings<T>) -> Self {
|
||||||
|
vector![s.beta, s.gamma, s.pop]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 3>> for SirSettings<T> {
|
||||||
|
fn from(v: Vect<T, 3>) -> Self {
|
||||||
|
Self {
|
||||||
|
beta: v[0],
|
||||||
|
gamma: v[1],
|
||||||
|
pop: v[2],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// SIR model with vital dynamics, constant population
|
||||||
|
pub mod sirv {
|
||||||
|
use super::*;
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct SirvSettings<T> {
|
||||||
|
/// Transmission probability
|
||||||
|
pub beta: T,
|
||||||
|
/// Removal probability
|
||||||
|
pub gamma: T,
|
||||||
|
/// Birth rate
|
||||||
|
pub lambda: T,
|
||||||
|
/// Death rate
|
||||||
|
pub mu: T,
|
||||||
|
pub pop: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for SirvSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Sirv<T> {
|
||||||
|
pub s: SirvSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, SirvSettings<f64>, 2> for Sirv<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
self.s.lambda - self.s.beta * x[0] * x[1] / self.s.pop - self.s.mu * x[0],
|
||||||
|
self.s.beta * x[0] * x[1] / self.s.pop - self.s.gamma * x[1] - self.s.mu * x[1]
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
matrix![
|
||||||
|
-self.s.beta*x[1]/self.s.pop - self.s.mu, -self.s.beta*x[0]/self.s.pop;
|
||||||
|
self.s.beta*x[1]/self.s.pop, self.s.beta*x[0]/self.s.pop-self.s.gamma - self.s.mu
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &SirvSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut SirvSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<SirvSettings<T>> for Vect<T, 5> {
|
||||||
|
fn from(s: SirvSettings<T>) -> Self {
|
||||||
|
vector![s.beta, s.gamma, s.lambda, s.mu, s.pop]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 5>> for SirvSettings<T> {
|
||||||
|
fn from(v: Vect<T, 5>) -> Self {
|
||||||
|
Self {
|
||||||
|
beta: v[0],
|
||||||
|
gamma: v[1],
|
||||||
|
lambda: v[2],
|
||||||
|
mu: v[3],
|
||||||
|
pop: v[4],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Giraffe
|
||||||
|
pub mod giraffe {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct GiraffeSettings<T> {
|
||||||
|
pub a_a: T,
|
||||||
|
pub a_b: T,
|
||||||
|
pub b_a: T,
|
||||||
|
pub b_b: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for GiraffeSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Giraffe<T> {
|
||||||
|
pub s: GiraffeSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, GiraffeSettings<f64>, 2> for Giraffe<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
self.s.a_a * x[0] + self.s.b_a * x[1],
|
||||||
|
self.s.a_b * x[0] + self.s.b_b * x[1]
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, _x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
matrix![
|
||||||
|
self.s.a_a, self.s.b_a;
|
||||||
|
self.s.a_b, self.s.b_b
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &GiraffeSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut GiraffeSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<GiraffeSettings<T>> for Vect<T, 4> {
|
||||||
|
fn from(s: GiraffeSettings<T>) -> Self {
|
||||||
|
vector![s.a_a, s.a_b, s.b_a, s.b_b]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 4>> for GiraffeSettings<T> {
|
||||||
|
fn from(v: Vect<T, 4>) -> Self {
|
||||||
|
Self {
|
||||||
|
a_a: v[0],
|
||||||
|
a_b: v[1],
|
||||||
|
b_a: v[2],
|
||||||
|
b_b: v[3],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*impl Coloring<f64, MinMaxColoringInfo<f64, 2>, [u8; 3], 2> for Giraffe<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(
|
||||||
|
iter: I,
|
||||||
|
) -> Option<MinMaxColoringInfo<f64, 2>> {
|
||||||
|
let mut r = MinMaxColoringInfo {
|
||||||
|
min: [1.0, 1.0],
|
||||||
|
max: [0.0, 0.0],
|
||||||
|
};
|
||||||
|
for val in iter {
|
||||||
|
if val[0] < r.min[0] {
|
||||||
|
r.min[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[0] > r.max[0] {
|
||||||
|
r.max[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[1] < r.min[1] {
|
||||||
|
r.min[1] = val[1];
|
||||||
|
}
|
||||||
|
if val[1] > r.max[1] {
|
||||||
|
r.max[1] = val[1];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if r.min[0] == r.max[0] || r.min[1] == r.max[1] {
|
||||||
|
None
|
||||||
|
} else {
|
||||||
|
Some(r)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
fn color(pre: &MinMaxColoringInfo<f64, 2>, val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
((val[1] - pre.min[1]).abs() / (pre.max[1] - pre.min[1]).abs() * 255.0) as u8,
|
||||||
|
0,
|
||||||
|
((val[0] - pre.min[0]).abs() / (pre.max[0] - pre.min[0]).abs() * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}*/
|
||||||
|
|
||||||
|
impl Coloring<f64, (), [u8; 3], 2> for Giraffe<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(_iter: I) -> Option<()> {
|
||||||
|
Some(())
|
||||||
|
}
|
||||||
|
fn color(_pre: &(), val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
(val[0] * 255.0) as u8,
|
||||||
|
((val[0] + val[1]) * 127.5) as u8,
|
||||||
|
255 - (val[1] * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// https://arxiv.org/abs/2210.05227
|
||||||
|
pub mod lyfe {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct LyfeSettings<T> {
|
||||||
|
pub da: T,
|
||||||
|
pub db: T,
|
||||||
|
pub f: T,
|
||||||
|
pub r: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for LyfeSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Lyfe<T> {
|
||||||
|
pub s: LyfeSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, LyfeSettings<f64>, 2> for Lyfe<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
x[0] * x[1].powi(2) + self.s.f * (1.0 - x[0]),
|
||||||
|
x[0] * x[1].powi(2) - (self.s.f + self.s.r) * x[1]
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
matrix![
|
||||||
|
x[1].powi(2)-self.s.f, 2.0*x[0]*x[1];
|
||||||
|
x[1].powi(2), 2.0*x[0]*x[1] - (self.s.f+self.s.r)
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &LyfeSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut LyfeSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<LyfeSettings<T>> for Vect<T, 4> {
|
||||||
|
fn from(s: LyfeSettings<T>) -> Self {
|
||||||
|
vector![s.da, s.db, s.f, s.r]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 4>> for LyfeSettings<T> {
|
||||||
|
fn from(v: Vect<T, 4>) -> Self {
|
||||||
|
Self {
|
||||||
|
da: v[0],
|
||||||
|
db: v[1],
|
||||||
|
f: v[2],
|
||||||
|
r: v[3],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*impl Coloring<f64, MinMaxColoringInfo<f64, 2>, [u8; 3], 2> for Lyfe<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(
|
||||||
|
iter: I,
|
||||||
|
) -> Option<MinMaxColoringInfo<f64, 2>> {
|
||||||
|
let mut r = MinMaxColoringInfo {
|
||||||
|
min: [1.0, 1.0],
|
||||||
|
max: [0.0, 0.0],
|
||||||
|
};
|
||||||
|
for val in iter {
|
||||||
|
if val[0] < r.min[0] {
|
||||||
|
r.min[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[0] > r.max[0] {
|
||||||
|
r.max[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[1] < r.min[1] {
|
||||||
|
r.min[1] = val[1];
|
||||||
|
}
|
||||||
|
if val[1] > r.max[1] {
|
||||||
|
r.max[1] = val[1];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if r.min[0] == r.max[0] || r.min[1] == r.max[1] {
|
||||||
|
None
|
||||||
|
} else {
|
||||||
|
Some(r)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
fn color(pre: &MinMaxColoringInfo<f64, 2>, val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
((val[1] - pre.min[1]).abs() / (pre.max[1] - pre.min[1]).abs() * 255.0) as u8,
|
||||||
|
0,
|
||||||
|
((val[0] - pre.min[0]).abs() / (pre.max[0] - pre.min[0]).abs() * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}*/
|
||||||
|
|
||||||
|
impl Coloring<f64, (), [u8; 3], 2> for Lyfe<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(_iter: I) -> Option<()> {
|
||||||
|
Some(())
|
||||||
|
}
|
||||||
|
fn color(_pre: &(), val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
(val[0] * 255.0) as u8,
|
||||||
|
((val[0] + val[1]) * 127.5) as u8,
|
||||||
|
255 - (val[1] * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
pub mod bike {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct BikeSettings<T> {
|
||||||
|
/// Pénétration dans l'air
|
||||||
|
pub cx: T,
|
||||||
|
/// Gravité
|
||||||
|
pub g: T,
|
||||||
|
/// Masse
|
||||||
|
pub m: T,
|
||||||
|
/// Pente
|
||||||
|
pub th: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> Settings for BikeSettings<T> {}
|
||||||
|
|
||||||
|
fn b(x: f64, v: f64) -> f64 {
|
||||||
|
80.
|
||||||
|
}
|
||||||
|
|
||||||
|
fn db(x: f64, v: f64) -> Vector2<f64> {
|
||||||
|
vector![0., 0.]
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Bike<T> {
|
||||||
|
pub s: BikeSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, BikeSettings<f64>, 2> for Bike<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
vector![
|
||||||
|
x[1],
|
||||||
|
self.s.g * self.s.th.sin() - (self.s.cx * x[1].powi(2) + b(x[0], x[1])) / self.s.m
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
let dbx = db(x[0], x[1]);
|
||||||
|
matrix![
|
||||||
|
0., 1.;
|
||||||
|
-dbx[0]/self.s.m, -(2.*self.s.cx*x[1]+dbx[1])/self.s.m
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &BikeSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut BikeSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T> From<BikeSettings<T>> for Vect<T, 4> {
|
||||||
|
fn from(s: BikeSettings<T>) -> Self {
|
||||||
|
vector![s.cx, s.g, s.m, s.th]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Scalar + Copy> From<Vect<T, 4>> for BikeSettings<T> {
|
||||||
|
fn from(v: Vect<T, 4>) -> Self {
|
||||||
|
Self {
|
||||||
|
cx: v[0],
|
||||||
|
g: v[1],
|
||||||
|
m: v[2],
|
||||||
|
th: v[3],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*impl Coloring<f64, MinMaxColoringInfo<f64, 2>, [u8; 3], 2> for Lyfe<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(
|
||||||
|
iter: I,
|
||||||
|
) -> Option<MinMaxColoringInfo<f64, 2>> {
|
||||||
|
let mut r = MinMaxColoringInfo {
|
||||||
|
min: [1.0, 1.0],
|
||||||
|
max: [0.0, 0.0],
|
||||||
|
};
|
||||||
|
for val in iter {
|
||||||
|
if val[0] < r.min[0] {
|
||||||
|
r.min[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[0] > r.max[0] {
|
||||||
|
r.max[0] = val[0];
|
||||||
|
}
|
||||||
|
if val[1] < r.min[1] {
|
||||||
|
r.min[1] = val[1];
|
||||||
|
}
|
||||||
|
if val[1] > r.max[1] {
|
||||||
|
r.max[1] = val[1];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if r.min[0] == r.max[0] || r.min[1] == r.max[1] {
|
||||||
|
None
|
||||||
|
} else {
|
||||||
|
Some(r)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
fn color(pre: &MinMaxColoringInfo<f64, 2>, val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
((val[1] - pre.min[1]).abs() / (pre.max[1] - pre.min[1]).abs() * 255.0) as u8,
|
||||||
|
0,
|
||||||
|
((val[0] - pre.min[0]).abs() / (pre.max[0] - pre.min[0]).abs() * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}*/
|
||||||
|
|
||||||
|
impl Coloring<f64, (), [u8; 3], 2> for Bike<f64> {
|
||||||
|
fn prepare<I: Iterator<Item = Vect<f64, 2>>>(_iter: I) -> Option<()> {
|
||||||
|
Some(())
|
||||||
|
}
|
||||||
|
fn color(_pre: &(), val: Vect<f64, 2>) -> [u8; 3] {
|
||||||
|
[
|
||||||
|
(val[0] * 255.0) as u8,
|
||||||
|
((val[0] + val[1]) * 127.5) as u8,
|
||||||
|
255 - (val[1] * 255.0) as u8,
|
||||||
|
]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
pub mod bike2 {
|
||||||
|
use super::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug)]
|
||||||
|
pub struct BikeSettings<T> {
|
||||||
|
/// Pénétration dans l'air
|
||||||
|
pub cx: T,
|
||||||
|
/// Gravité
|
||||||
|
pub g: T,
|
||||||
|
/// Masse
|
||||||
|
pub m: T,
|
||||||
|
/// Pente
|
||||||
|
pub th: T,
|
||||||
|
/// (x, v, settings) -> ((b1, b2), (b1', b2'))
|
||||||
|
pub b: fn(T, T, &BikeSettings<T>) -> ((T, T), (T, T)),
|
||||||
|
}
|
||||||
|
impl<T> Settings for BikeSettings<T> {}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Bike<T> {
|
||||||
|
pub s: BikeSettings<T>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Model<f64, BikeSettings<f64>, 2> for Bike<f64> {
|
||||||
|
fn f(&self, x: Vector2<f64>) -> Vector2<f64> {
|
||||||
|
let ((b1, b2), (_db1, _db2)) = (self.s.b)(x[0], x[1], &self.s);
|
||||||
|
vector![
|
||||||
|
x[1],
|
||||||
|
self.s.g * self.s.th.sin() - (self.s.cx * x[1].powi(2) + b1 + b2) / self.s.m
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn df(&self, x: Vector2<f64>) -> Matrix2<f64> {
|
||||||
|
let ((_b1, _b2), (db1, db2)) = (self.s.b)(x[0], x[1], &self.s);
|
||||||
|
matrix![
|
||||||
|
0., 1.;
|
||||||
|
0., -(2.*self.s.cx*x[1]+db1+db2)/self.s.m
|
||||||
|
]
|
||||||
|
}
|
||||||
|
fn get_settings(&self) -> &BikeSettings<f64> {
|
||||||
|
&self.s
|
||||||
|
}
|
||||||
|
fn get_settings_mut(&mut self) -> &mut BikeSettings<f64> {
|
||||||
|
&mut self.s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
399
examples/old/opti.rs
Normal file
399
examples/old/opti.rs
Normal file
|
|
@ -0,0 +1,399 @@
|
||||||
|
use crate::{model::*, solver::*, utils::*};
|
||||||
|
|
||||||
|
use nalgebra::{base::*, ComplexField};
|
||||||
|
use num_traits::{FromPrimitive, Zero};
|
||||||
|
use std::marker::PhantomData;
|
||||||
|
|
||||||
|
pub fn newton<
|
||||||
|
T: Copy + Scalar + ComplexField<RealField = T> + PartialOrd,
|
||||||
|
S: Settings,
|
||||||
|
const D: usize,
|
||||||
|
>(
|
||||||
|
model: &impl Model<T, S, D>,
|
||||||
|
x0: Vect<T, D>,
|
||||||
|
dt: T,
|
||||||
|
tol: T,
|
||||||
|
niters: usize,
|
||||||
|
) -> Vect<T, D>
|
||||||
|
where
|
||||||
|
Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
|
||||||
|
{
|
||||||
|
let mut x = x0;
|
||||||
|
|
||||||
|
for _ in 0..niters {
|
||||||
|
if let Some(m) = (Mat::<T, D, D>::identity() - model.df(x) * dt).try_inverse() {
|
||||||
|
let dx = m * (x - x0 - model.f(x) * dt);
|
||||||
|
if dx.norm() < tol {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
x -= dx;
|
||||||
|
} else {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
x
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Slower version using a linear system.
|
||||||
|
pub fn _newton_slow<
|
||||||
|
T: Copy + Scalar + ComplexField<RealField = T> + PartialOrd,
|
||||||
|
S: Settings,
|
||||||
|
const D: usize,
|
||||||
|
>(
|
||||||
|
model: &impl Model<T, S, D>,
|
||||||
|
x0: Vect<T, D>,
|
||||||
|
dt: T,
|
||||||
|
tol: T,
|
||||||
|
niters: usize,
|
||||||
|
) -> Vect<T, D>
|
||||||
|
where
|
||||||
|
Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
|
||||||
|
{
|
||||||
|
let mut x = x0;
|
||||||
|
|
||||||
|
for _ in 0..niters {
|
||||||
|
let fi = model.f(x);
|
||||||
|
let dfi = model.df(x);
|
||||||
|
let g = x0 + fi * dt - x;
|
||||||
|
let dgdx = dfi * dt - Mat::<T, D, D>::identity();
|
||||||
|
if let Some(dx) = dgdx.lu().solve(&g) {
|
||||||
|
if dx.norm() < tol {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
x -= dx;
|
||||||
|
} else {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
x
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct GradientDescentOptimizer<
|
||||||
|
T,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D> + Clone,
|
||||||
|
R: Solver<T, S, M, D>,
|
||||||
|
const D: usize,
|
||||||
|
const DS: usize,
|
||||||
|
> {
|
||||||
|
pub model: M,
|
||||||
|
pub solver: R,
|
||||||
|
_ph: PhantomData<(T, S)>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<
|
||||||
|
T: Copy + ComplexField<RealField = T> + FromPrimitive,
|
||||||
|
S: Settings + Clone + Into<Vect<T, DS>> + From<Vect<T, DS>>,
|
||||||
|
M: Model<T, S, D> + Clone,
|
||||||
|
R: Solver<T, S, M, D>,
|
||||||
|
const D: usize,
|
||||||
|
const DS: usize,
|
||||||
|
> GradientDescentOptimizer<T, S, M, R, D, DS>
|
||||||
|
where
|
||||||
|
Vect<T, DS>: std::ops::DivAssign<T> + std::ops::Mul<T, Output = Vect<T, DS>>,
|
||||||
|
{
|
||||||
|
pub fn new(model: M, solver: R) -> Self {
|
||||||
|
Self {
|
||||||
|
model,
|
||||||
|
solver,
|
||||||
|
_ph: PhantomData {},
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Distance between f(x) and y_true, that we want to minimize
|
||||||
|
pub fn objective(&self, model: &M, x: Vect<T, D>, y_true: Vect<T, D>) -> T {
|
||||||
|
(self.solver.f(model, x) - y_true).norm()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Return gradient of the objective function
|
||||||
|
/// (opposite direction for Settings in order to make f(x) closer to y_true)
|
||||||
|
///
|
||||||
|
/// `free_settings` gives the indices of the settings we can change.
|
||||||
|
/// For example, if all the settings can change, set it to `0..DS`.
|
||||||
|
pub fn objective_gradient(
|
||||||
|
&self,
|
||||||
|
x: Vect<T, D>,
|
||||||
|
y_true: Vect<T, D>,
|
||||||
|
ep: T,
|
||||||
|
free_settings: impl Iterator<Item = usize>,
|
||||||
|
) -> Vect<T, DS> {
|
||||||
|
let diff = self.objective(&self.model, x, y_true);
|
||||||
|
let mut model = self.model.clone();
|
||||||
|
let s: Vect<T, DS> = model.get_settings().clone().into();
|
||||||
|
let mut si = s;
|
||||||
|
let mut ds = Vect::<T, DS>::zero();
|
||||||
|
for i in free_settings {
|
||||||
|
si[i] += ep;
|
||||||
|
*model.get_settings_mut() = si.into();
|
||||||
|
ds[i] = (self.objective(&model, x, y_true) - diff) / ep;
|
||||||
|
si[i] = s[i];
|
||||||
|
}
|
||||||
|
ds
|
||||||
|
}
|
||||||
|
|
||||||
|
pub fn objective_gradient_batch(
|
||||||
|
&self,
|
||||||
|
ylist_true: &[Vect<T, D>],
|
||||||
|
ep: T,
|
||||||
|
free_settings: impl Iterator<Item = usize> + Clone,
|
||||||
|
) -> Vect<T, DS> {
|
||||||
|
let nsamples = T::from_usize(ylist_true.len() - 1).unwrap();
|
||||||
|
|
||||||
|
let mut ds_batch = Vect::<T, DS>::zero();
|
||||||
|
for (x, y_true) in ylist_true.iter().zip(ylist_true.iter().skip(1)) {
|
||||||
|
let ds = self.objective_gradient(*x, *y_true, ep, free_settings.clone());
|
||||||
|
ds_batch += ds;
|
||||||
|
}
|
||||||
|
ds_batch / nsamples
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Calibrate settings using batch GD
|
||||||
|
pub fn calibrate_batch(
|
||||||
|
&mut self,
|
||||||
|
ylist_true: &[Vect<T, D>],
|
||||||
|
ep: T,
|
||||||
|
rate: T,
|
||||||
|
niters: usize,
|
||||||
|
free_settings: impl Iterator<Item = usize> + Clone,
|
||||||
|
) {
|
||||||
|
for _ in 0..niters {
|
||||||
|
let ds_batch = self.objective_gradient_batch(ylist_true, ep, free_settings.clone());
|
||||||
|
|
||||||
|
// ds_batch is the mean of the gradient of the objective function for each sample
|
||||||
|
let mut s: Vect<T, DS> = self.model.get_settings().clone().into();
|
||||||
|
s -= ds_batch * rate;
|
||||||
|
*self.model.get_settings_mut() = s.into();
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Calibrate settings using stochastic GD
|
||||||
|
pub fn calibrate_stochastic(
|
||||||
|
&mut self,
|
||||||
|
ylist_true: &[Vect<T, D>],
|
||||||
|
ep: T,
|
||||||
|
rate: T,
|
||||||
|
niters: usize,
|
||||||
|
free_settings: impl Iterator<Item = usize> + Clone,
|
||||||
|
) {
|
||||||
|
for _ in 0..niters {
|
||||||
|
for (x, y_true) in ylist_true.iter().zip(ylist_true.iter().skip(1)) {
|
||||||
|
let ds = self.objective_gradient(*x, *y_true, ep, free_settings.clone());
|
||||||
|
|
||||||
|
let mut s: Vect<T, DS> = self.model.get_settings().clone().into();
|
||||||
|
s -= ds * rate;
|
||||||
|
*self.model.get_settings_mut() = s.into();
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Calibrate settings using batch GD and record path and error
|
||||||
|
///
|
||||||
|
/// Returns (path, error)
|
||||||
|
pub fn calibrate_batch_record(
|
||||||
|
&mut self,
|
||||||
|
ylist_true: &[Vect<T, D>],
|
||||||
|
ep: T,
|
||||||
|
rate: T,
|
||||||
|
niters: usize,
|
||||||
|
free_settings: impl Iterator<Item = usize> + Clone,
|
||||||
|
) -> (Vec<Vect<T, DS>>, Vec<T>)
|
||||||
|
where
|
||||||
|
T: PartialOrd,
|
||||||
|
{
|
||||||
|
let mut path = Vec::with_capacity(niters + 1);
|
||||||
|
path.push(self.model.get_settings().clone().into());
|
||||||
|
let mut errorlist = Vec::with_capacity(niters + 1);
|
||||||
|
errorlist.push(self.objective_batch(&self.model, ylist_true));
|
||||||
|
|
||||||
|
for _ in 0..niters {
|
||||||
|
let ds_batch = self.objective_gradient_batch(ylist_true, ep, free_settings.clone());
|
||||||
|
|
||||||
|
// ds_batch is the mean of the gradient of the objective function for each sample
|
||||||
|
let mut s: Vect<T, DS> = self.model.get_settings().clone().into();
|
||||||
|
s -= ds_batch * rate;
|
||||||
|
path.push(s);
|
||||||
|
*self.model.get_settings_mut() = s.into();
|
||||||
|
|
||||||
|
let error = self.objective_batch(&self.model, ylist_true);
|
||||||
|
if error > *errorlist.last().unwrap() {
|
||||||
|
path.pop();
|
||||||
|
*self.model.get_settings_mut() = (*path.last().unwrap()).into();
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
errorlist.push(error);
|
||||||
|
}
|
||||||
|
(path, errorlist)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Calibrate settings using stochastic GD and record path and error
|
||||||
|
///
|
||||||
|
/// Returns (path, error)
|
||||||
|
pub fn calibrate_stochastic_record(
|
||||||
|
&mut self,
|
||||||
|
ylist_true: &[Vect<T, D>],
|
||||||
|
ep: T,
|
||||||
|
rate: T,
|
||||||
|
niters: usize,
|
||||||
|
free_settings: impl Iterator<Item = usize> + Clone,
|
||||||
|
) -> (Vec<Vect<T, DS>>, Vec<T>)
|
||||||
|
where
|
||||||
|
T: PartialOrd,
|
||||||
|
{
|
||||||
|
let mut path = Vec::with_capacity(niters * (niters - 1) + 1);
|
||||||
|
path.push(self.model.get_settings().clone().into());
|
||||||
|
let mut errorlist = Vec::with_capacity(niters * (niters - 1) + 1);
|
||||||
|
errorlist.push(self.objective_batch(&self.model, ylist_true));
|
||||||
|
|
||||||
|
for _ in 0..niters {
|
||||||
|
for (x, y_true) in ylist_true.iter().zip(ylist_true.iter().skip(1)) {
|
||||||
|
let ds = self.objective_gradient(*x, *y_true, ep, free_settings.clone());
|
||||||
|
|
||||||
|
let mut s: Vect<T, DS> = self.model.get_settings().clone().into();
|
||||||
|
s -= ds * rate;
|
||||||
|
path.push(s);
|
||||||
|
*self.model.get_settings_mut() = s.into();
|
||||||
|
|
||||||
|
let error = self.objective_batch(&self.model, ylist_true);
|
||||||
|
if error > *errorlist.last().unwrap() {
|
||||||
|
path.pop();
|
||||||
|
*self.model.get_settings_mut() = (*path.last().unwrap()).into();
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
errorlist.push(error);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
(path, errorlist)
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Mean of the objective function on all the samples
|
||||||
|
pub fn objective_batch(&self, model: &M, ylist_true: &[Vect<T, D>]) -> T {
|
||||||
|
let nsamples = T::from_usize(ylist_true.len() - 1).unwrap();
|
||||||
|
|
||||||
|
let mut obj_batch = T::zero();
|
||||||
|
for (x, y_true) in ylist_true.iter().zip(ylist_true.iter().skip(1)) {
|
||||||
|
obj_batch += self.objective(model, *x, *y_true);
|
||||||
|
}
|
||||||
|
obj_batch / nsamples
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
mod test {
|
||||||
|
use super::*;
|
||||||
|
use nalgebra::vector;
|
||||||
|
use rand::Rng;
|
||||||
|
|
||||||
|
/// This test can fail, but should succeed most of the time
|
||||||
|
#[test]
|
||||||
|
fn test_objective_gradient_convergence() {
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
|
||||||
|
let ep0 = 0.01;
|
||||||
|
let nep = 20;
|
||||||
|
let ntests = 1000;
|
||||||
|
|
||||||
|
let mut fail_spikes = 0;
|
||||||
|
let mut fail_d = 0;
|
||||||
|
|
||||||
|
for _ in 0..ntests {
|
||||||
|
let model = sir::Sir {
|
||||||
|
s: sir::SirSettings {
|
||||||
|
beta: rng.gen(),
|
||||||
|
gamma: rng.gen(),
|
||||||
|
pop: 1.0,
|
||||||
|
},
|
||||||
|
};
|
||||||
|
let solver = ImplicitEulerSolver {
|
||||||
|
dt: 0.1,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let optimizer = GradientDescentOptimizer::new(model, solver);
|
||||||
|
let x = rng.gen();
|
||||||
|
let y_true = rng.gen();
|
||||||
|
|
||||||
|
let mut g = optimizer.objective_gradient(x, y_true, ep0, 0..2);
|
||||||
|
let mut d = f64::MAX;
|
||||||
|
let mut spikes = 5;
|
||||||
|
for ep in (1..nep).map(|i| ep0 / 2.0.powi(i)) {
|
||||||
|
let ng = optimizer.objective_gradient(x, y_true, dbg!(ep), 0..2);
|
||||||
|
let nd = (dbg!(ng) - g).norm();
|
||||||
|
if nd.is_zero() {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
// Allow obj' having a local minimum between s and s+ep
|
||||||
|
if dbg!(nd) >= dbg!(d) {
|
||||||
|
if spikes == 0 {
|
||||||
|
fail_spikes += 1;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
spikes -= 1;
|
||||||
|
}
|
||||||
|
g = ng;
|
||||||
|
d = nd;
|
||||||
|
}
|
||||||
|
// d should be very small
|
||||||
|
if d > 10.0 * ep0 / 2.0.powi(nep - 1) {
|
||||||
|
fail_d += 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
let prop_fail_spikes = fail_spikes as f64 / ntests as f64;
|
||||||
|
let prop_fail_d = fail_d as f64 / ntests as f64;
|
||||||
|
println!("Fail spikes: {} %", prop_fail_spikes * 100.0);
|
||||||
|
println!("Fail d: {} %", prop_fail_d * 100.0);
|
||||||
|
assert!(prop_fail_spikes < 0.015);
|
||||||
|
assert!(prop_fail_d < 0.0015);
|
||||||
|
}
|
||||||
|
|
||||||
|
// TODO fix
|
||||||
|
//#[test]
|
||||||
|
fn _test_objective_gradient_direction() {
|
||||||
|
let mut rng = rand::thread_rng();
|
||||||
|
|
||||||
|
let niters: usize = 1000;
|
||||||
|
let x0 = vector![0.99, 0.01];
|
||||||
|
let dt = 0.1;
|
||||||
|
|
||||||
|
// Generate "true" data
|
||||||
|
let settings_true = sir::SirSettings {
|
||||||
|
beta: rng.gen(),
|
||||||
|
gamma: rng.gen(),
|
||||||
|
pop: 1.0,
|
||||||
|
};
|
||||||
|
let model = sir::Sir {
|
||||||
|
s: dbg!(settings_true),
|
||||||
|
};
|
||||||
|
let solver = ImplicitEulerSolver {
|
||||||
|
dt,
|
||||||
|
tol: 0.000001,
|
||||||
|
niters: 100,
|
||||||
|
};
|
||||||
|
let mut optimizer = GradientDescentOptimizer::new(model, solver);
|
||||||
|
let mut xlist_true = Vec::with_capacity(niters + 1);
|
||||||
|
xlist_true.push(x0);
|
||||||
|
let mut x = x0;
|
||||||
|
for _ in 0..niters {
|
||||||
|
x = optimizer.solver.f(&optimizer.model, x);
|
||||||
|
xlist_true.push(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
// Start with random settings
|
||||||
|
*optimizer.model.get_settings_mut() = dbg!(sir::SirSettings {
|
||||||
|
beta: rng.gen(),
|
||||||
|
gamma: rng.gen(),
|
||||||
|
pop: 1.0,
|
||||||
|
});
|
||||||
|
|
||||||
|
// Compute descent direction
|
||||||
|
let dir = dbg!(optimizer.objective_gradient(x0, xlist_true[1], 0.0000001, 0..2));
|
||||||
|
|
||||||
|
// Check that this direction leads to smaller error
|
||||||
|
let s: Vect<f64, 3> = optimizer.model.get_settings().clone().into();
|
||||||
|
let y = optimizer.model.f(x0);
|
||||||
|
*optimizer.model.get_settings_mut() = (s - dir).into(); // Apply direction
|
||||||
|
let y_new = optimizer.model.f(x0);
|
||||||
|
assert!((y - xlist_true[1]).norm() >= (y_new - xlist_true[1]).norm());
|
||||||
|
}
|
||||||
|
}
|
||||||
41
examples/old/solver.rs
Normal file
41
examples/old/solver.rs
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
use crate::{model::*, opti::*, utils::*};
|
||||||
|
|
||||||
|
use nalgebra::{base::*, ComplexField};
|
||||||
|
|
||||||
|
pub trait Solver<T, S: Settings, M: Model<T, S, D>, const D: usize> {
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D>;
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct ExplicitEulerSolver<T: Copy + ComplexField<RealField = T>> {
|
||||||
|
pub dt: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Copy + ComplexField<RealField = T>, S: Settings, M: Model<T, S, D>, const D: usize>
|
||||||
|
Solver<T, S, M, D> for ExplicitEulerSolver<T>
|
||||||
|
{
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
model.f(x) * self.dt + x
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct ImplicitEulerSolver<T: Clone + ComplexField<RealField = T>> {
|
||||||
|
pub dt: T,
|
||||||
|
pub tol: T,
|
||||||
|
pub niters: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<
|
||||||
|
T: Copy + ComplexField<RealField = T> + PartialOrd,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D>,
|
||||||
|
const D: usize,
|
||||||
|
> Solver<T, S, M, D> for ImplicitEulerSolver<T>
|
||||||
|
where
|
||||||
|
Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
|
||||||
|
{
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
newton(model, x, self.dt, self.tol, self.niters)
|
||||||
|
}
|
||||||
|
}
|
||||||
94
examples/old/space.rs
Normal file
94
examples/old/space.rs
Normal file
|
|
@ -0,0 +1,94 @@
|
||||||
|
use crate::{
|
||||||
|
model::{Model, Settings},
|
||||||
|
solver::Solver,
|
||||||
|
utils::*,
|
||||||
|
};
|
||||||
|
|
||||||
|
use nalgebra::ComplexField;
|
||||||
|
use std::{collections::HashMap, marker::PhantomData};
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Point<T: Copy, const D: usize> {
|
||||||
|
pub pos: Vect<T, D>,
|
||||||
|
pub diffusion: Vect<T, D>,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct Source<T: Copy, const D: usize> {
|
||||||
|
pub amplitude: T,
|
||||||
|
pub fonction: fn(T) -> Vect<T, D>,
|
||||||
|
pub freq: T,
|
||||||
|
pub phase: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
pub struct Space<T: Copy, S: Settings, M: Model<T, S, D>, V: Solver<T, S, M, D>, const D: usize> {
|
||||||
|
pub model: M,
|
||||||
|
pub old_points: Vec<Point<T, D>>,
|
||||||
|
pub points: Vec<Point<T, D>>,
|
||||||
|
pub size: (usize, usize),
|
||||||
|
pub solver: V,
|
||||||
|
pub sources: HashMap<usize, Source<T, D>>,
|
||||||
|
pub time: T,
|
||||||
|
pub _p: PhantomData<S>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<
|
||||||
|
T: Copy + ComplexField<RealField = T>,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D>,
|
||||||
|
V: Solver<T, S, M, D>,
|
||||||
|
const D: usize,
|
||||||
|
> Space<T, S, M, V, D>
|
||||||
|
{
|
||||||
|
pub fn simulate(&mut self, delta_time: T) {
|
||||||
|
std::mem::swap(&mut self.old_points, &mut self.points);
|
||||||
|
for (i, (point, old_point)) in self
|
||||||
|
.points
|
||||||
|
.iter_mut()
|
||||||
|
.zip(self.old_points.iter())
|
||||||
|
.enumerate()
|
||||||
|
{
|
||||||
|
if let Some(source) = self.sources.get(&i) {
|
||||||
|
let t = self.time * source.freq + source.phase;
|
||||||
|
//Point{pos:t.sin()*source.amplitude, speed: t.cos()*source.amplitude}
|
||||||
|
point.pos = (source.fonction)(t) * source.amplitude;
|
||||||
|
} else {
|
||||||
|
*point = old_point.clone()
|
||||||
|
};
|
||||||
|
point.pos = self.solver.f(&self.model, point.pos);
|
||||||
|
}
|
||||||
|
|
||||||
|
let mut i = 0usize;
|
||||||
|
for y in 0..self.size.1 {
|
||||||
|
for x in 0..self.size.0 {
|
||||||
|
let old_point = self.old_points[i].clone();
|
||||||
|
let point = &mut self.points[i];
|
||||||
|
|
||||||
|
if y > 0 {
|
||||||
|
point.pos += (self.old_points[i - self.size.0].pos - old_point.pos)
|
||||||
|
.component_mul(&point.diffusion)
|
||||||
|
* delta_time;
|
||||||
|
}
|
||||||
|
if y < self.size.1 - 1 {
|
||||||
|
point.pos += (self.old_points[i + self.size.0].pos - old_point.pos)
|
||||||
|
.component_mul(&point.diffusion)
|
||||||
|
* delta_time;
|
||||||
|
}
|
||||||
|
if x > 0 {
|
||||||
|
point.pos += (self.old_points[i - 1].pos - old_point.pos)
|
||||||
|
.component_mul(&point.diffusion)
|
||||||
|
* delta_time;
|
||||||
|
}
|
||||||
|
if x < self.size.0 - 1 {
|
||||||
|
point.pos += (self.old_points[i + 1].pos - old_point.pos)
|
||||||
|
.component_mul(&point.diffusion)
|
||||||
|
* delta_time;
|
||||||
|
}
|
||||||
|
|
||||||
|
i += 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
self.time += delta_time;
|
||||||
|
}
|
||||||
|
}
|
||||||
16
examples/old/utils.rs
Normal file
16
examples/old/utils.rs
Normal file
|
|
@ -0,0 +1,16 @@
|
||||||
|
use nalgebra::base::*;
|
||||||
|
|
||||||
|
/// `<Type, Rows, Columns>`
|
||||||
|
pub type Mat<T, const R: usize, const C: usize> =
|
||||||
|
Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>;
|
||||||
|
pub type Vect<T, const R: usize> = Matrix<T, Const<R>, U1, ArrayStorage<T, R, 1>>;
|
||||||
|
|
||||||
|
pub fn max(l: &[f64]) -> f64 {
|
||||||
|
let mut m = l[0];
|
||||||
|
for &i in &l[1..] {
|
||||||
|
if i > m {
|
||||||
|
m = i;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
m
|
||||||
|
}
|
||||||
9
rustfmt.toml
Normal file
9
rustfmt.toml
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
hard_tabs = true
|
||||||
|
newline_style = "unix"
|
||||||
|
imports_granularity = "Crate"
|
||||||
|
|
||||||
|
unstable_features = true
|
||||||
|
format_code_in_doc_comments = true
|
||||||
|
format_macro_bodies = true
|
||||||
|
format_macro_matchers = true
|
||||||
|
format_strings = true
|
||||||
20
src/lib.rs
Normal file
20
src/lib.rs
Normal file
|
|
@ -0,0 +1,20 @@
|
||||||
|
pub mod model;
|
||||||
|
#[cfg(feature = "plot")]
|
||||||
|
pub mod plot;
|
||||||
|
pub mod solver;
|
||||||
|
mod util;
|
||||||
|
|
||||||
|
pub mod prelude {
|
||||||
|
#[cfg(feature = "plot")]
|
||||||
|
pub use crate::plot::{Plot, PlotBuilder, PlotBuilderError};
|
||||||
|
pub use crate::{
|
||||||
|
model::{Model, Settings},
|
||||||
|
solver::{
|
||||||
|
euler::{ExplicitEuler, ImplicitEuler},
|
||||||
|
Solver,
|
||||||
|
},
|
||||||
|
util::{Mat, Vect},
|
||||||
|
};
|
||||||
|
#[cfg(feature = "plot")]
|
||||||
|
pub use plotters::style::colors;
|
||||||
|
}
|
||||||
12
src/model.rs
Normal file
12
src/model.rs
Normal file
|
|
@ -0,0 +1,12 @@
|
||||||
|
use crate::util::*;
|
||||||
|
|
||||||
|
pub trait Settings {}
|
||||||
|
|
||||||
|
pub trait Model<T, S: Settings, const D: usize> {
|
||||||
|
/// Returns f(x)
|
||||||
|
fn f(&self, x: Vect<T, D>) -> Vect<T, D>;
|
||||||
|
/// Returns df(x)/dx
|
||||||
|
fn df(&self, x: Vect<T, D>) -> Mat<T, D, D>;
|
||||||
|
fn get_settings(&self) -> &S;
|
||||||
|
fn get_settings_mut(&mut self) -> &mut S;
|
||||||
|
}
|
||||||
107
src/plot.rs
Normal file
107
src/plot.rs
Normal file
|
|
@ -0,0 +1,107 @@
|
||||||
|
use std::cmp::Ordering;
|
||||||
|
|
||||||
|
use crate::util::*;
|
||||||
|
|
||||||
|
use nalgebra::Matrix;
|
||||||
|
use plotters::prelude::*;
|
||||||
|
|
||||||
|
#[derive(Clone, Debug, derive_builder::Builder)]
|
||||||
|
#[builder(setter(into), default)]
|
||||||
|
pub struct Plot {
|
||||||
|
dt: f64,
|
||||||
|
size: (u32, u32),
|
||||||
|
title: Option<String>,
|
||||||
|
x_label: Option<String>,
|
||||||
|
x_max: Option<f64>,
|
||||||
|
x_min: Option<f64>,
|
||||||
|
y_max: Option<f64>,
|
||||||
|
y_min: Option<f64>,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Default for Plot {
|
||||||
|
fn default() -> Self {
|
||||||
|
Self {
|
||||||
|
dt: 1.0,
|
||||||
|
size: (640, 480),
|
||||||
|
title: None,
|
||||||
|
x_label: None,
|
||||||
|
x_max: None,
|
||||||
|
x_min: None,
|
||||||
|
y_max: None,
|
||||||
|
y_min: None,
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Plot {
|
||||||
|
pub fn plot<const R: usize>(
|
||||||
|
&self,
|
||||||
|
path: impl AsRef<std::path::Path>,
|
||||||
|
data: &[Vect<f64, R>],
|
||||||
|
series: &[(&str, RGBColor); R],
|
||||||
|
) {
|
||||||
|
let root = BitMapBackend::new(path.as_ref(), self.size).into_drawing_area();
|
||||||
|
root.fill(&WHITE).unwrap();
|
||||||
|
let mut chart = ChartBuilder::on(&root);
|
||||||
|
if let Some(title) = &self.title {
|
||||||
|
chart.caption(
|
||||||
|
title,
|
||||||
|
FontDesc::new(FontFamily::SansSerif, 22.0, FontStyle::Normal),
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
let x_range =
|
||||||
|
self.x_min.unwrap_or(0.0)..self.x_max.unwrap_or_else(|| data.len() as f64 * self.dt);
|
||||||
|
let y_range = self
|
||||||
|
.y_min
|
||||||
|
.unwrap_or_else(|| find_extremum(data.iter().map(Matrix::min), Ordering::Less).unwrap())
|
||||||
|
..self.y_max.unwrap_or_else(|| {
|
||||||
|
find_extremum(data.iter().map(Matrix::max), Ordering::Greater).unwrap()
|
||||||
|
});
|
||||||
|
|
||||||
|
let mut chart = chart
|
||||||
|
.margin_right(12)
|
||||||
|
.y_label_area_size(30)
|
||||||
|
.x_label_area_size(30)
|
||||||
|
.build_cartesian_2d(x_range, y_range)
|
||||||
|
.unwrap();
|
||||||
|
|
||||||
|
let mut x_axis = chart.configure_mesh();
|
||||||
|
if let Some(x_label) = &self.x_label {
|
||||||
|
x_axis.x_desc(x_label);
|
||||||
|
}
|
||||||
|
x_axis.draw().unwrap();
|
||||||
|
|
||||||
|
for (i, (label, color)) in series.into_iter().enumerate() {
|
||||||
|
chart
|
||||||
|
.draw_series(LineSeries::new(
|
||||||
|
data.iter()
|
||||||
|
.enumerate()
|
||||||
|
.map(|(x, y)| (x as f64 * self.dt, y[i])),
|
||||||
|
color,
|
||||||
|
))
|
||||||
|
.unwrap()
|
||||||
|
.label(*label)
|
||||||
|
.legend(|(x, y)| PathElement::new(vec![(x, y), (x + 20, y)], color.clone()));
|
||||||
|
}
|
||||||
|
|
||||||
|
chart
|
||||||
|
.configure_series_labels()
|
||||||
|
.background_style(WHITE.mix(0.8))
|
||||||
|
.border_style(BLACK)
|
||||||
|
.draw()
|
||||||
|
.unwrap();
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn find_extremum<T: PartialOrd, I: IntoIterator<Item = T>>(iter: I, ord: Ordering) -> Option<T> {
|
||||||
|
let mut iter = iter.into_iter();
|
||||||
|
let extremum = iter.next()?;
|
||||||
|
Some(iter.fold(extremum, |extremum, i| {
|
||||||
|
if i.partial_cmp(&extremum) == Some(ord) {
|
||||||
|
i
|
||||||
|
} else {
|
||||||
|
extremum
|
||||||
|
}
|
||||||
|
}))
|
||||||
|
}
|
||||||
7
src/solver.rs
Normal file
7
src/solver.rs
Normal file
|
|
@ -0,0 +1,7 @@
|
||||||
|
pub mod euler;
|
||||||
|
|
||||||
|
use crate::{model::*, util::*};
|
||||||
|
|
||||||
|
pub trait Solver<T, S: Settings, M: Model<T, S, D>, const D: usize> {
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D>;
|
||||||
|
}
|
||||||
41
src/solver/euler.rs
Normal file
41
src/solver/euler.rs
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
use crate::{
|
||||||
|
model::{Model, Settings},
|
||||||
|
solver::Solver,
|
||||||
|
util::*,
|
||||||
|
};
|
||||||
|
|
||||||
|
use nalgebra::{base::*, ComplexField};
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct ExplicitEuler<T: Copy + ComplexField<RealField = T>> {
|
||||||
|
pub dt: T,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<T: Copy + ComplexField<RealField = T>, S: Settings, M: Model<T, S, D>, const D: usize>
|
||||||
|
Solver<T, S, M, D> for ExplicitEuler<T>
|
||||||
|
{
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
model.f(x) * self.dt + x
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Clone)]
|
||||||
|
pub struct ImplicitEuler<T: Clone + ComplexField<RealField = T>> {
|
||||||
|
pub dt: T,
|
||||||
|
pub tol: T,
|
||||||
|
pub niters: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<
|
||||||
|
T: Copy + ComplexField<RealField = T> + PartialOrd,
|
||||||
|
S: Settings,
|
||||||
|
M: Model<T, S, D>,
|
||||||
|
const D: usize,
|
||||||
|
> Solver<T, S, M, D> for ImplicitEuler<T>
|
||||||
|
where
|
||||||
|
Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
|
||||||
|
{
|
||||||
|
fn f(&self, model: &M, x: Vect<T, D>) -> Vect<T, D> {
|
||||||
|
newton(model, x, self.dt, self.tol, self.niters)
|
||||||
|
}
|
||||||
|
}
|
||||||
39
src/util.rs
Normal file
39
src/util.rs
Normal file
|
|
@ -0,0 +1,39 @@
|
||||||
|
use crate::model::{Model, Settings};
|
||||||
|
|
||||||
|
use nalgebra::{base::*, ComplexField};
|
||||||
|
|
||||||
|
/// Matrix `<Type, Rows, Columns>`
|
||||||
|
pub type Mat<T, const R: usize, const C: usize> =
|
||||||
|
Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>;
|
||||||
|
/// Vector `<Type, Dimension>` (column matrix)
|
||||||
|
pub type Vect<T, const R: usize> = Matrix<T, Const<R>, U1, ArrayStorage<T, R, 1>>;
|
||||||
|
|
||||||
|
pub fn newton<
|
||||||
|
T: Copy + Scalar + ComplexField<RealField = T> + PartialOrd,
|
||||||
|
S: Settings,
|
||||||
|
const D: usize,
|
||||||
|
>(
|
||||||
|
model: &impl Model<T, S, D>,
|
||||||
|
x0: Vect<T, D>,
|
||||||
|
dt: T,
|
||||||
|
tol: T,
|
||||||
|
niters: usize,
|
||||||
|
) -> Vect<T, D>
|
||||||
|
where
|
||||||
|
Const<D>: ToTypenum + DimMin<Const<D>, Output = Const<D>>,
|
||||||
|
{
|
||||||
|
let mut x = x0;
|
||||||
|
|
||||||
|
for _ in 0..niters {
|
||||||
|
if let Some(m) = (Mat::<T, D, D>::identity() - model.df(x) * dt).try_inverse() {
|
||||||
|
let dx = m * (x - x0 - model.f(x) * dt);
|
||||||
|
if dx.norm() < tol {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
x -= dx;
|
||||||
|
} else {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
x
|
||||||
|
}
|
||||||
Loading…
Reference in a new issue