Editing Interval package
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
<div style="float: right; margin: 0 3em">[[File:Octave-interval.png|center]]</div>The GNU Octave interval package for real-valued interval arithmetic. | |||
[[File:Interval-sombrero.png|280px|thumb|right|Plotting the interval enclosure of a function]] | |||
[[File:Interval-sombrero.png|280px|thumb| | |||
== Distribution == | == Distribution == | ||
* [http://octave.sourceforge.net/interval/index.html Latest version at Octave Forge] | |||
** <code>pkg install -forge interval</code> | |||
** [http://octave.sourceforge.net/interval/overview.html function reference] | |||
** [http://octave.sourceforge.net/interval/package_doc/index.html package documentation] (user manual) | |||
'''Third-party''' | |||
* [https://tracker.debian.org/pkg/octave-interval Debian GNU/Linux], [https://launchpad.net/ubuntu/+source/octave-interval Launchpad Ubuntu] | * [https://tracker.debian.org/pkg/octave-interval Debian GNU/Linux], [https://launchpad.net/ubuntu/+source/octave-interval Launchpad Ubuntu] | ||
* [https://aur.archlinux.org/packages/octave-interval/ archlinux user repository] | * [https://aur.archlinux.org/packages/octave-interval/ archlinux user repository] | ||
* Included in [https://ftp.gnu.org/gnu/octave/windows/ official Windows installer] and installed automatically with Octave (since version 4.0.1) | * Included in [https://ftp.gnu.org/gnu/octave/windows/ official Windows installer] and installed automatically with Octave (since version 4.0.1) | ||
* [https:// | * [https://trac.macports.org/browser/trunk/dports/math/octave-interval MacPorts] for Mac OS X | ||
* [ | * [http://www.freshports.org/math/octave-forge-interval/ FreshPorts] for FreeBSD | ||
* [https://cygwin.com/cgi-bin2/package-grep.cgi?grep=octave-interval Cygwin] for Windows | * [https://cygwin.com/cgi-bin2/package-grep.cgi?grep=octave-interval Cygwin] for Windows | ||
* [https://build.opensuse.org/package/show/science/octave-forge-interval openSUSE build service] | * [https://build.opensuse.org/package/show/science/octave-forge-interval openSUSE build service] | ||
Line 39: | Line 19: | ||
== Development status == | == Development status == | ||
* Completeness | * Completeness | ||
** All required functions from | ** All required functions from IEEE Std 1788-2015, IEEE standard for interval arithmetic, are implemented. The standard was approved on June 11, 2015. It will remain active for ten years. | ||
** In addition there are functions for interval matrix arithmetic, plotting and solvers. | |||
** In addition there are functions for interval matrix arithmetic | |||
* Quality | * Quality | ||
** | ** Includes tests for all functions, many tests for basic functions | ||
** No known bugs. The package is quite new and still has a small user base, so there might be hidden bugs. Also some advanced functions will always need more testing. | |||
** | |||
* Portability | * Portability | ||
** Runs in GNU Octave ≥ 3.8.2 | ** Runs in GNU Octave ≥ 3.8.2 | ||
** Known to run under GNU/Linux, Microsoft Windows, macOS, and FreeBSD | ** Known to run under GNU/Linux, Microsoft Windows, macOS, and FreeBSD | ||
* Possible TODOs | |||
** To be considered in the future: Algorithms can be migrated from the C-XSC Toolbox (C++ code) from [http://www2.math.uni-wuppertal.de/wrswt/xsc/cxsc_new.html] (nlinsys.cpp and cpzero.cpp), however these would need gradient arithmetic and complex arithmetic. | |||
* To be considered in the future: Algorithms can be migrated from the C-XSC Toolbox (C++ code) from [http://www2.math.uni-wuppertal.de/wrswt/xsc/cxsc_new.html] (nlinsys.cpp and cpzero.cpp), however these would need gradient arithmetic and complex arithmetic. | ** Interval version of <code>interp1</code> | ||
* Interval version of <code>interp1</code> | ** Extend <code>subsasgn</code> to allow direct manipulation of inf and sup (and dec) properties. | ||
* Extend <code>subsasgn</code> to allow direct manipulation of inf and sup (and dec) properties. | |||
>> A = infsup ("[2, 4]"); | >> A = infsup ("[2, 4]"); | ||
>> A.inf = infsup ("[1, 3]") | >> A.inf = infsup ("[1, 3]") | ||
Line 67: | Line 41: | ||
>> A.inf.inf = 42 # should produce error? | >> A.inf.inf = 42 # should produce error? | ||
>> A.inf.sup = 42 # should produce error? | >> A.inf.sup = 42 # should produce error? | ||
* Tight Enclosure of Matrix Multiplication with Level 3 BLAS [http://kam.mff.cuni.cz/conferences/swim2015/abstracts/ozaki.pdf] [http://kam.mff.cuni.cz/conferences/swim2015/slides/ozaki.pdf] | :* Tight Enclosure of Matrix Multiplication with Level 3 BLAS [http://kam.mff.cuni.cz/conferences/swim2015/abstracts/ozaki.pdf] [http://kam.mff.cuni.cz/conferences/swim2015/slides/ozaki.pdf] | ||
* Verified Convex Hull for Inexact Data [http://kam.mff.cuni.cz/conferences/swim2015/abstracts/ohta.pdf] [http://kam.mff.cuni.cz/conferences/swim2015/slides/ohta.pdf] | :* Verified Convex Hull for Inexact Data [http://kam.mff.cuni.cz/conferences/swim2015/abstracts/ohta.pdf] [http://kam.mff.cuni.cz/conferences/swim2015/slides/ohta.pdf] | ||
* Implement user-controllable output from the interval standard (e. g. via printf functions): | :* Implement user-controllable output from the interval standard (e. g. via printf functions): | ||
a) It should be possible to specify the preferred overall field width (the length of s). | a) It should be possible to specify the preferred overall field width (the length of s). | ||
b) It should be possible to specify how Empty, Entire and NaI are output, | b) It should be possible to specify how Empty, Entire and NaI are output, | ||
Line 81: | Line 55: | ||
== Compatibility == | == Compatibility == | ||
The interval package's main goal is to be compliant with IEEE Std 1788-2015, so it is compatible with other standard-conforming implementations (on the set of operations described by the standard document). | The interval package's main goal is to be compliant with IEEE Std 1788-2015, so it is compatible with other standard-conforming implementations (on the set of operations described by the standard document). | ||
=== Octave Forge simp package === | === Octave Forge simp package === | ||
Line 102: | Line 72: | ||
* Basic operations can be found in both packages, but the availability of special functions depends | * Basic operations can be found in both packages, but the availability of special functions depends | ||
{{Code|In GNU Octave the interval package can also be run alongside INTLAB.|<syntaxhighlight lang="octave"> | |||
# INTLAB intervals | |||
A1 = infsup (2, 3); | |||
{{Code| | B1 = hull (-4, A1); | ||
pkg load interval | C1 = midrad (0, 2); | ||
# Interval package intervals | |||
pkg load interval | |||
A2 = infsup (2, 3); | |||
B2 = hull (-4, A2); | |||
A1 + B1 * C1 | C2 = midrad (0, 2); | ||
pkg unload interval | |||
# Computation with INTLAB | |||
A1 + B1 * C1 | |||
# Computation without INTLAB | |||
A2 + B2 * C2 | |||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
==== Known differences ==== | ==== Known differences ==== | ||
Line 163: | Line 127: | ||
| isintval (x) | | isintval (x) | ||
|} | |} | ||
== Similar software == | |||
For C++ there is an interval library [https://github.com/nehmeier/libieeep1788/ libieeep1788] by Marco Nehmeier (member of IEEE P1788). It aims to be standard compliant with IEEE Std 1788-2015 and is designed in a modular way, supporting several interval data types and different flavors of interval arithmetic [http://www.youtube.com/watch?v=GOa9aWAZO_Q]. The GNU Octave interval package shares several unit tests with libieeep1788. | |||
For Julia there is an evolving interval library [https://github.com/dpsanders/ValidatedNumerics.jl ValidatedNumerics.jl] by Luis Benet and David P. Sanders. It is planned to become conforming to IEEE Std 1788-2015 (or to the basic standard 1788.1) in the future. | |||
== Developer Information == | == Developer Information == | ||
Line 178: | Line 148: | ||
'''Build dependencies''' | '''Build dependencies''' | ||
<code>apt-get install libmpfr-dev autoconf automake inkscape zopfli</code> | <code>apt-get install libmpfr-dev autoconf automake git python3-ply python3-yaml inkscape zopfli</code> | ||
* Octave | |||
* Mercurial | |||
* Texinfo | |||
* MPFR | |||
* Octave package: doctest | |||
** Purpose: Verification of the examples in the manual and in the function documentation | |||
** Installation: Use <code>pkg install -forge doctest</code> inside Octave | |||
* Octave package: generate_html | |||
** Purpose: Generate HTML documenation for publication on Octave Forge (only needed for release) | |||
** Installation: Use <code>pkg install -forge generate_html</code> inside Octave | |||
* Autoconf & Automake | |||
** Purpose: Preparation of bundled crlibm library for a release | |||
* ITF1788 | |||
** Purpose: Compilation of unit-test | |||
** Installation: The git repository is automatically cloned by the Makefile | |||
* Inkscape | |||
** Purpose: Generate / convert images for the manual | |||
* Zopfli | |||
** Purpose: Optimize the size of the compressed release tarball | |||
=== Architecture === | === Architecture === | ||
Line 199: | Line 189: | ||
| | `- ... – further functions on decorated intervals | | | `- ... – further functions on decorated intervals | ||
| `- ... – a few global functions that don't operate on intervals | | `- ... – a few global functions that don't operate on intervals | ||
+- src/ | |||
| | +- mpfr_function_d.cc – computes various arithmetic functions correctly rounded (using MPFR) | |||
| | `- ... – other oct-file sources | |||
`- test/ – interval arithmetic unit tests | |||
=== Best practices === | === Best practices === | ||
Line 208: | Line 199: | ||
* Methods with more than 1 parameter must convert non-interval parameters to intervals using the class constructor. This allows the user to mix non-interval parameters with interval parameters and the function treats any inputs as intervals. Invalid values will be handled by the class constructors. | * Methods with more than 1 parameter must convert non-interval parameters to intervals using the class constructor. This allows the user to mix non-interval parameters with interval parameters and the function treats any inputs as intervals. Invalid values will be handled by the class constructors. | ||
if (not (isa (x, "infsup"))) | if (not (isa (x, "infsup"))) | ||
x = infsup (x); | |||
endif | endif | ||
if (not (isa (y, "infsup"))) | if (not (isa (y, "infsup"))) | ||
y = infsup (y); | |||
endif | endif | ||
if (not (isa (x, "infsupdec"))) | if (not (isa (x, "infsupdec"))) | ||
x = infsupdec (x); | |||
endif | endif | ||
if (not (isa (y, "infsupdec"))) | if (not (isa (y, "infsupdec"))) | ||
y = infsupdec (y); | |||
endif | endif | ||
Line 224: | Line 215: | ||
Octave functions may be used as long as they don't introduce arithmetic errors. For example, the ceil function can be used safely since it is exact on binary64 numbers. | Octave functions may be used as long as they don't introduce arithmetic errors. For example, the ceil function can be used safely since it is exact on binary64 numbers. | ||
function x = ceil (x) | function x = ceil (x) | ||
... parameter checking ... | |||
x.inf = ceil (x.inf); | |||
x.sup = ceil (x.sup); | |||
endfunction | endfunction | ||
If Octave functions would introduce arithmetic/rounding errors, there are interfaces to MPFR (<code>mpfr_function_d</code>) and crlibm (<code>crlibm_function</code>), which can produce guaranteed boundaries. | If Octave functions would introduce arithmetic/rounding errors, there are interfaces to MPFR (<code>mpfr_function_d</code>) and crlibm (<code>crlibm_function</code>), which can produce guaranteed boundaries. | ||
==== Vectorization & Indexing ==== | ==== Vectorization & Indexing ==== | ||
All functions should be implemented using vectorization and indexing. This is very important for performance on large data. For example, consider the plus function. It computes lower and upper boundaries of the result (x.inf, y.inf, x.sup, y.sup may be vectors or matrices) and then uses an indexing expression to adjust values where empty intervals would have produces problematic values. | All functions should be implemented using vectorization and indexing. This is very important for performance on large data. For example, consider the plus function. It computes lower and upper boundaries of the result (x.inf, y.inf, x.sup, y.sup may be vectors or matrices) and then uses an indexing expression to adjust values where empty intervals would have produces problematic values. | ||
function x = plus (x, y) | function x = plus (x, y) | ||
... parameter checking ... | |||
l = mpfr_function_d ('plus', -inf, x.inf, y.inf); | |||
u = mpfr_function_d ('plus', +inf, x.sup, y.sup); | |||
emptyresult = isempty (x) | isempty (y); | |||
l(emptyresult) = inf; | |||
u(emptyresult) = -inf; | |||
… | |||
endfunction | endfunction | ||
== VERSOFT == | == VERSOFT == | ||
The [http://uivtx.cs.cas.cz/~rohn/matlab/ VERSOFT] software package (by Jiří Rohn) has been released under a free software license (Expat license) and algorithms may be migrated into the interval package. | The [http://uivtx.cs.cas.cz/~rohn/matlab/ VERSOFT] software package (by Jiří Rohn) has been released under a free software license (Expat license) and algorithms may be migrated into the interval package. | ||
The following table is no longer up-to-date, it describes the situation before p-coded files have been disclosed. So, some functions are no longer trapped. | |||
{| | {| | ||
Line 264: | Line 258: | ||
|verdet | |verdet | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| depends on <code> | | depends on p-coded <code>ol</code> | ||
|- | |- | ||
|verdistsing | |verdistsing | ||
Line 271: | Line 265: | ||
|- | |- | ||
|verfullcolrank | |verfullcolrank | ||
|style="color:red"| | |style="color:red"| encrypted | ||
| | | implemented in p-coded <code>zd</code> | ||
|- | |- | ||
|vernorm2 | |vernorm2 | ||
Line 313: | Line 307: | ||
|- | |- | ||
|vereig | |vereig | ||
|style="color:red"| | |style="color:red"| encrypted | ||
| | | implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|<s>vereigback</s> | |<s>vereigback</s> | ||
Line 322: | Line 316: | ||
|verspectrad | |verspectrad | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| main part implemented in <code> | | main part implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|colspan="3"|Real (or complex) data only: Matrices: Decompositions | |colspan="3"|Real (or complex) data only: Matrices: Decompositions | ||
Line 336: | Line 330: | ||
|verspectdec | |verspectdec | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| main part implemented in <code> | | main part implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|verthinsvd | |verthinsvd | ||
|style="color:red"| | |style="color:red"| encrypted | ||
| implemented in <code> | | implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|colspan="3"|Real (or complex) data only: Matrix functions | |colspan="3"|Real (or complex) data only: Matrix functions | ||
Line 346: | Line 340: | ||
|vermatfun | |vermatfun | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| main part implemented in <code> | | main part implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|colspan="3"|Real data only: Linear systems (rectangular) | |colspan="3"|Real data only: Linear systems (rectangular) | ||
Line 365: | Line 359: | ||
|- | |- | ||
|verlcpall | |verlcpall | ||
|style="color: | |style="color:red"| trapped | ||
| depends on <code>verabsvaleqnall</code> | | depends on <code style="color:red">verabsvaleqnall</code> | ||
|- | |- | ||
|<s>verlinprog</s> | |<s>verlinprog</s> | ||
Line 373: | Line 367: | ||
|- | |- | ||
|verlinprogg | |verlinprogg | ||
|style="color:red"| | |style="color:red"| encrypted | ||
| | | implemented in p-coded <code>at</code> | ||
|- | |- | ||
|verquadprog | |verquadprog | ||
Line 384: | Line 378: | ||
|verroots | |verroots | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| main part implemented in <code> | | main part implemented in p-coded <code>ol</code> | ||
|- | |- | ||
|colspan="3"|Interval (or real) data: Matrices | |colspan="3"|Interval (or real) data: Matrices | ||
Line 393: | Line 387: | ||
|- | |- | ||
|verinverse | |verinverse | ||
|style="color: | |style="color:red"| trapped | ||
| depends on <code style="color: | | depends on <code style="color:red">verintervalhull</code> | ||
|- | |- | ||
|<s>verinvnonneg</s> | |<s>verinvnonneg</s> | ||
Line 405: | Line 399: | ||
|verregsing | |verregsing | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| dependency <code>verifylss</code> is implemented as <code>mldivide</code>; depends on <code>isspd</code> (by Rump, to be checked) and <code>verintervalhull</code>; see also [http://uivtx.cs.cas.cz/~rohn/publist/singreg.pdf] | | dependency <code>verifylss</code> is implemented as <code>mldivide</code>; depends on <code>isspd</code> (by Rump, to be checked) and <code style="color:red">verintervalhull</code>; see also [http://uivtx.cs.cas.cz/~rohn/publist/singreg.pdf] | ||
|- | |- | ||
|colspan="3"|Interval (or real) data: Matrices: Eigenvalues and singular values | |colspan="3"|Interval (or real) data: Matrices: Eigenvalues and singular values | ||
Line 411: | Line 405: | ||
|vereigsym | |vereigsym | ||
|style="color:red"| trapped | |style="color:red"| trapped | ||
| main part implemented in <code> | | main part implemented in p-coded <code>ol</code>, depends on <code style="color:red">verspectrad</code> | ||
|- | |- | ||
|vereigval | |vereigval | ||
Line 441: | Line 435: | ||
|- | |- | ||
|verenclinthull | |verenclinthull | ||
|style="color: | |style="color:red"| trapped | ||
| | | main part implemented in p-coded <code>ea</code> | ||
|- | |- | ||
|verhullparam | |verhullparam | ||
|style="color: | |style="color:red"| encrypted | ||
| | | implemented in p-coded <code>jz</code> | ||
|- | |- | ||
|verhullpatt | |verhullpatt | ||
|style="color: | |style="color:red"| trapped | ||
| | | main part implemented in p-coded <code>jz</code> | ||
|- | |- | ||
|verintervalhull | |verintervalhull | ||
|style="color: | |style="color:red"| encrypted | ||
| | | implemented in p-coded <code>intervalhull</code> (find algorithm in [http://uivtx.cs.cas.cz/~rohn/publist/intervalhull.pdf]) | ||
|- | |- | ||
|colspan="3"|Interval (or real) data: Linear systems (rectangular) | |colspan="3"|Interval (or real) data: Linear systems (rectangular) | ||
Line 480: | Line 474: | ||
|- | |- | ||
| verabsvaleqn | | verabsvaleqn | ||
|style="color: | |style="color:red"| trapped | ||
| | | main part implemented in p-coded <code>ek</code> (find algorithm in [http://uivtx.cs.cas.cz/~rohn/publist/signaccalg.pdf], improved version in [http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnreport.pdf]) | ||
|- | |- | ||
| verabsvaleqnall | | verabsvaleqnall | ||
|style="color: | |style="color:red"| trapped | ||
| depends on <code>verabsvaleqn</code>, see also [http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnall.pdf] | | depends on <code style="color:red">verabsvaleqn</code>, see also [http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnall.pdf] | ||
|- | |- | ||
| verbasintnpprob | | verbasintnpprob | ||
Line 494: | Line 488: | ||
[[Category:Octave Forge]] | [[Category:Octave-Forge]] |