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{{OctaveForge
+
<div style="float: right; margin: 0 3em">[[File:Octave-interval.png|center]]</div>The GNU Octave interval package for real-valued interval arithmetic.
| name = interval
 
| logo = [[File:Interval.png|100px]]
 
| short description = Real-valued interval arithmetic.
 
| version = 3.2.0
 
| date = 2018-07-01
 
| author 1 name  = Oliver Heimlich
 
| author 1 email = <oheim@posteo.de>
 
| maintainer 1 name  = Oliver Heimlich
 
| maintainer 1 email = <oheim@posteo.de>
 
| license = GPL-3.0+
 
| group = Community package
 
| doc 1 = [https://octave.sourceforge.io/interval/overview.html Function reference]
 
| doc 2 = [https://octave.sourceforge.io/interval/package_doc/ User manual]
 
| download 1 = [https://octave.sourceforge.io/download.php?package=interval-3.2.0.tar.gz interval-3.2.0.tar.gz]
 
| repository 1 = https://octave.sourceforge.io/pkg-repository/interval/
 
| dependency 1 = octave &ge; 3.8.0
 
| dependency 2 = '''Runtime:''' mpfr (&ge; 3.1.0) [https://packages.debian.org/search?keywords=libmpfr4 libmpfr4 for Debian]
 
| dependency 3 = '''Build:''' mpfr (&ge; 3.1.0) [https://packages.debian.org/search?keywords=libmpfr-dev libmpfr-dev for Debian]
 
}}
 
  
The GNU Octave interval package for real-valued [https://en.wikipedia.org/wiki/Interval_arithmetic interval arithmetic].
+
[[File:Interval-sombrero.png|280px|thumb|right|Plotting the interval enclosure of a function]]  
* Intervals are closed, connected subsets of the real numbers. Intervals may be unbound (in either or both directions) or empty. In special cases <code>+inf</code> and <code>-inf</code> are used to denote boundaries of unbound intervals, but any member of the interval is a finite real number.
 
* Classical functions are extended to interval functions as follows: The result of function f evaluated on interval x is an interval '''enclosure of all possible values''' of f over x where the function is defined. Most interval arithmetic functions in this package manage to produce a very accurate such enclosure.
 
* The result of an interval arithmetic function is an interval in general. It might happen, that the mathematical range of a function consist of several intervals, but their union will be returned, e. g., 1 / [-1, 1] = [Entire].
 
 
 
[[File:Interval-sombrero.png|280px|thumb|left|Example: Plotting the interval enclosure of a function]]
 
<div style="clear:left"></div>
 
  
 
== 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://github.com/macports/macports-ports/tree/master/math/octave-interval/ MacPorts] for Mac OS X
+
* [https://trac.macports.org/browser/trunk/dports/math/octave-interval MacPorts] for Mac OS X
* [https://www.freshports.org/math/octave-forge-interval/ FreshPorts] for FreeBSD
+
* [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 [https://standards.ieee.org/findstds/standard/1788-2015.html IEEE Std 1788-2015], IEEE standard for interval arithmetic, are implemented. The standard was approved by IEEE-SA on June 11, 2015. It will remain active for ten years. The standard was approved by ANSI in 2016.
+
** 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.
** Also, the minimalistic standard [https://standards.ieee.org/findstds/standard/1788.1-2017.html IEEE Std 1788.1-2017], IEEE standard for interval arithmetic (simplified) is fully implemented. The standard was approved by IEEE-SA on December 6, 2017 (and published in January 2018).
+
** In addition there are functions for interval matrix arithmetic, plotting and solvers.
** In addition there are functions for interval matrix arithmetic, N-dimensional interval arrays, plotting, and solvers.
 
 
* Quality
 
* Quality
** Most arithmetic operations produce tight, correctly-rounded results. That is, the smallest possible interval with double-precision (binary64) endpoints, which encloses the exact result.
+
** Includes tests for all functions, many tests for basic functions
** Includes [https://github.com/oheim/ITF1788 large test suite] for arithmetic 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.
** For open bugs please refer to the [https://savannah.gnu.org/search/?words=forge+interval&type_of_search=bugs&only_group_id=1925&exact=1 bug tracker].
 
* Performance
 
** All elementary functions have been [https://octave.org/doc/interpreter/Vectorization-and-Faster-Code-Execution.html vectorized] and run fast on large input data.
 
** Arithmetic is performed with the [http://www.mpfr.org/ GNU MPFR] library internally. Where possible, the optimized [http://web.archive.org/web/20170128033523/http://lipforge.ens-lyon.fr/www/crlibm/ CRlibm] library is used.
 
 
* 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, Mac OS X and FreeBSD
 
+
* Possible TODOs
== Project ideas (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):
 
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,
 
    e.g., whether lower or upper case, and whether Entire becomes [Entire] or [-Inf, Inf].
 
c) For l and u, it should be possible to specify the field width,
 
    and the number of digits after the point or the number of significant digits.
 
    (partly this is already implemented by output_precision (...) / `format long` / `format short`)
 
d) It should be possible to output the bounds of an interval without punctuation,
 
    e.g., 1.234 2.345 instead of [1.234, 2.345]. For instance, this might be a
 
    convenient way to write intervals to a file for use by another application.
 
  
 
== 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). Other implementations, which are known to aim for standard conformance are:
+
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).
 
 
* [https://github.com/JuliaIntervals/IntervalArithmetic.jl IntervalArithmetic.jl package] (Julia)
 
* [https://github.com/jinterval/jinterval JInterval library] (Java)
 
* [https://github.com/nadezhin/libieeep1788 ieeep1788 library] (C++) created by Marco Nehmeier, later forked by Dmitry Nadezhin
 
  
 
=== Octave Forge simp package ===
 
=== Octave Forge simp package ===
Line 102: Line 62:
 
* 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">
<div style="display:flex; align-items: flex-start">
+
# INTLAB intervals
<div style="margin-right: 2em">
+
A1 = infsup (2, 3);
{{Code|Computation with this interval package|<syntaxhighlight lang="octave">
+
B1 = hull (-4, A1);
pkg load interval
+
C1 = midrad (0, 2);
A1 = infsup (2, 3);
+
# Interval package intervals
B1 = hull (-4, A2);
+
pkg load interval
C1 = midrad (0, 2);
+
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>
 
}}
 
}}
</div><div>
 
{{Code|Computation with INTLAB|<syntaxhighlight lang="octave">
 
startintlab
 
A2 = infsup (2, 3);
 
B2 = hull (-4, A2);
 
C2 = midrad (0, 2);
 
 
A2 + B2 * C2
 
</syntaxhighlight>
 
}}
 
</div>
 
</div>
 
  
 
==== Known differences ====
 
==== Known differences ====
Line 163: Line 117:
 
| 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 ==
 
=== Source Code Repository ===
 
=== Source Code Repository ===
 
https://sourceforge.net/p/octave/interval/ci/default/tree/
 
https://sourceforge.net/p/octave/interval/ci/default/tree/
 
=== Dependencies ===
 
apt-get install liboctave-dev mercurial make automake libmpfr-dev
 
  
 
=== Build ===
 
=== Build ===
Line 178: Line 135:
  
 
'''Build dependencies'''
 
'''Build dependencies'''
<code>apt-get install libmpfr-dev autoconf automake inkscape zopfli</code>
+
* Octave
 +
** Version 3.8.0 or greater
 +
** No need to compile from source, but you need development files e.g. package <code>liboctave-dev</code> in Debian.
 +
* Mercurial
 +
* Texinfo
 +
* MPFR
 +
** Version 3.1.0 or greater
 +
** No need to compile from source, but you need development files e.g. package <code>libmpfr-dev</code> in Debian.
 +
* 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
 +
* ITF1788
 +
** Purpose: Compilation of unit-test
 +
** Installation:
 +
**# Clone the git repository from https://github.com/oheim/ITF1788
 +
**# Install python 3 and the dependencies described by ITF1788's <code>setup.py</code> file
 +
**# Set up an environment variable ITF1788_HOME to point to your local git workspace, for example put the line <code>export IFT1788_HOME=/home/user/ITF1788</code> into your <code>.bashrc</code>.
 +
* LilyPond, Inkscape, Poppler
 +
** Purpose: Generate / convert images for the manual
 +
** Installation: Use your distribution's package manager (look for packages called <code>lilypond</code> <code>inkscape</code> <code>poppler-utils</code>)
  
 
=== Architecture ===
 
=== Architecture ===
Line 199: Line 178:
 
  |  |  `- ...                – 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/
+
  +- src/
    +- mpfr_function_d.cc     – computes various arithmetic functions correctly rounded (using MPFR)
+
|  |  +- mpfr_function_d.cc – computes various arithmetic functions correctly rounded (using MPFR)
    `- ...                     – other oct-file sources
+
|  |  `- ...                 – other oct-file sources
 +
`- test/                      – interval arithmetic unit tests
  
 
=== Best practices ===
 
=== Best practices ===
Line 208: Line 188:
 
* 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);
+
    x = infsup (x);
 
  endif
 
  endif
 
  if (not (isa (y, "infsup")))
 
  if (not (isa (y, "infsup")))
  y = infsup (y);
+
    y = infsup (y);
 
  endif
 
  endif
  
 
  if (not (isa (x, "infsupdec")))
 
  if (not (isa (x, "infsupdec")))
  x = infsupdec (x);
+
    x = infsupdec (x);
 
  endif
 
  endif
 
  if (not (isa (y, "infsupdec")))
 
  if (not (isa (y, "infsupdec")))
  y = infsupdec (y);
+
    y = infsupdec (y);
 
  endif
 
  endif
  
Line 224: Line 204:
 
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 ...
+
... parameter checking ...
  x.inf = ceil (x.inf);
+
x.inf = ceil (x.inf);
  x.sup = ceil (x.sup);
+
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 ...
+
... parameter checking ...
  l = mpfr_function_d ('plus', -inf, x.inf, y.inf);
+
l = mpfr_function_d ('plus', -inf, x.inf, y.inf);
  u = mpfr_function_d ('plus', +inf, x.sup, y.sup);
+
u = mpfr_function_d ('plus', +inf, x.sup, y.sup);
 
   
 
   
  emptyresult = isempty (x) | isempty (y);
+
emptyresult = isempty (x) | isempty (y);
  l(emptyresult) = inf;
+
l(emptyresult) = inf;
  u(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 247:
 
|verdet
 
|verdet
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| depends on <code>vereig</code>
+
| depends on p-coded <code>ol</code>
 
|-
 
|-
 
|verdistsing
 
|verdistsing
Line 271: Line 254:
 
|-
 
|-
 
|verfullcolrank
 
|verfullcolrank
|style="color:red"| trapped
+
|style="color:red"| encrypted
| depends on <code>verpinv</code>
+
| implemented in p-coded <code>zd</code>
 
|-
 
|-
 
|vernorm2
 
|vernorm2
Line 313: Line 296:
 
|-
 
|-
 
|vereig
 
|vereig
|style="color:red"| trapped
+
|style="color:red"| encrypted
| depends on proprietary <code>verifyeig</code> function from INTLAB, depends on complex interval arithmetic
+
| implemented in p-coded <code>ol</code>
 
|-
 
|-
 
|<s>vereigback</s>
 
|<s>vereigback</s>
Line 322: Line 305:
 
|verspectrad
 
|verspectrad
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| main part implemented in <code>vereig</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 319:
 
|verspectdec
 
|verspectdec
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| main part implemented in <code>vereig</code>
+
| main part implemented in p-coded <code>ol</code>
 
|-
 
|-
 
|verthinsvd
 
|verthinsvd
|style="color:red"| trapped
+
|style="color:red"| encrypted
| implemented in <code>vereig</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 329:
 
|vermatfun
 
|vermatfun
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| main part implemented in <code>vereig</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 348:
 
|-
 
|-
 
|verlcpall
 
|verlcpall
|style="color:green"| free
+
|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 356:
 
|-
 
|-
 
|verlinprogg
 
|verlinprogg
|style="color:red"| trapped
+
|style="color:red"| encrypted
| depends on <code>verfullcolrank</code>
+
| implemented in p-coded <code>at</code>
 
|-
 
|-
 
|verquadprog
 
|verquadprog
Line 384: Line 367:
 
|verroots
 
|verroots
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| main part implemented in <code>vereig</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 376:
 
|-
 
|-
 
|verinverse
 
|verinverse
|style="color:green"| free
+
|style="color:red"| trapped
| depends on <code style="color:green">verintervalhull</code>, to be migrated
+
| depends on <code style="color:red">verintervalhull</code>
 
|-
 
|-
 
|<s>verinvnonneg</s>
 
|<s>verinvnonneg</s>
Line 405: Line 388:
 
|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 394:
 
|vereigsym
 
|vereigsym
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| main part implemented in <code>vereig</code>, depends on <code style="color:red">verspectrad</code>
+
| main part implemented in p-coded <code>ol</code>, depends on <code style="color:red">verspectrad</code>
 
|-
 
|-
 
|vereigval
 
|vereigval
Line 441: Line 424:
 
|-
 
|-
 
|verenclinthull
 
|verenclinthull
|style="color:green"| free
+
|style="color:red"| trapped
| to be migrated
+
| main part implemented in p-coded <code>ea</code>
 
|-
 
|-
 
|verhullparam
 
|verhullparam
|style="color:green"| free
+
|style="color:red"| encrypted
| depends on <code>verintervalhull</code>, to be migrated
+
| implemented in p-coded <code>jz</code>
 
|-
 
|-
 
|verhullpatt
 
|verhullpatt
|style="color:green"| free
+
|style="color:red"| trapped
| depends on <code>verhullparam</code>, to be migrated
+
| main part implemented in p-coded <code>jz</code>
 
|-
 
|-
 
|verintervalhull
 
|verintervalhull
|style="color:green"| free
+
|style="color:red"| encrypted
| to be migrated
+
| 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 463:
 
|-
 
|-
 
| verabsvaleqn
 
| verabsvaleqn
|style="color:green"| free
+
|style="color:red"| trapped
| to be migrated
+
| 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:green"| free
+
|style="color:red"| trapped
| depends on <code>verabsvaleqn</code>, see also [http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnall.pdf], to be migrated
+
| depends on <code style="color:red">verabsvaleqn</code>, see also [http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnall.pdf]
 
|-
 
|-
 
| verbasintnpprob
 
| verbasintnpprob
Line 494: Line 477:
  
  
[[Category:Octave Forge]]
+
[[Category:Octave-Forge]]

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