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{{OctaveForge
 
| 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].
 
The GNU Octave interval package for real-valued [https://en.wikipedia.org/wiki/Interval_arithmetic interval arithmetic].
* 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]]
+
[[File:Interval-sombrero.png|280px|thumb|right|Plotting the interval enclosure of a function]]  
<div style="clear:left"></div>
 
  
 
== Distribution ==
 
== Distribution ==
 +
* [https://octave.sourceforge.io/interval/ Latest version at Octave Forge]
 +
** <code>pkg install -forge interval</code>
 +
** [https://octave.sourceforge.io/interval/overview.html function reference]
 +
** [https://octave.sourceforge.io/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]
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* 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
  
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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 ====
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== 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.
  
 
{|
 
{|
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|verdet
 
|verdet
 
|style="color:red"| trapped
 
|style="color:red"| trapped
| depends on <code>vereig</code>
+
| depends on p-coded <code>ol</code>
 
|-
 
|-
 
|verdistsing
 
|verdistsing
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|-
 
|-
 
|verfullcolrank
 
|verfullcolrank
|style="color:red"| trapped
+
|style="color:red"| encrypted
| depends on <code>verpinv</code>
+
| implemented in p-coded <code>zd</code>
 
|-
 
|-
 
|vernorm2
 
|vernorm2
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|-
 
|-
 
|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>
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|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
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|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
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|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)  
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|-
 
|-
 
|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>
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|-
 
|-
 
|verlinprogg
 
|verlinprogg
|style="color:red"| trapped
+
|style="color:red"| encrypted
| depends on <code>verfullcolrank</code>
+
| implemented in p-coded <code>at</code>
 
|-
 
|-
 
|verquadprog
 
|verquadprog
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|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
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|-
 
|-
 
|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>
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|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
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|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
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|-
 
|-
 
|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)
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|-
 
|-
 
| 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
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[[Category:Octave Forge]]
+
[[Category:Octave-Forge]]

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