Schuetz2 at 05:38, 17 June 2025

2025-06-17T05:38:05Z

← Older revision		Revision as of 05:38, 17 June 2025
Line 59:		Line 59:
	title = {Randomly Generated},		title = {Randomly Generated},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Randomly_Generated}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Randomly_Generated}</nowiki>,
	year = {2018}		year = {2018}
	}		}

Lund: remove preliminary warning

2022-08-26T13:04:48Z

remove preliminary warning

← Older revision		Revision as of 13:04, 26 August 2022
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:procedural]]		[[Category:procedural]]

Himpe: Init randomly generated

2018-11-21T12:17:28Z

Init randomly generated

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:procedural]]
[[Category:linear]]
[[Category:first differential order]]
[[Category:time invariant]]
[[Category:SISO]]

==Description==

This '''randomly generated''' state-space system is a procedural SISO test system for model reduction of linear time-invariant systems from <ref name="willcox02"/>.
All matrices are generated from a uniformly random distribution: the system matrix is a diagonal matrix with elements in <math>[-1,0]</math>, where as the input and output vectors are drawn from <math>[0,1]</math>.
The generated systems are stable and minimal, due to structure of <math>N</math> disconnected subsystems.



==Data==

The following Matlab code assembles the above described <math>A</math>, <math>B</math> and <math>C</math> matrix for a given state-space dimension <math>N</math> and optionally a seed <math>S</math> for the random number generator.

<div class="thumbinner" style="width:540px;text-align:left;">
<source lang="matlab">
function [A,B,C] = rnd(N,S)

if(nargin>1 && not(isempty(S))), rand('seed',S); end;

A = spdiags(-rand(N,1),0,N,N);
B = rand(N,1);
C = rand(1,N);
end
</source>
</div>

==Dimensions==

System structure:
:<math>
\begin{align}
\dot{x}(t) &= Ax(t) + Bu(t) \\
y(t) &= Cx(t)
\end{align}
</math>

System dimensions:

<math>A \in \mathbb{R}^{N \times N}</math>,
<math>B \in \mathbb{R}^{N \times 1}</math>,
<math>C \in \mathbb{R}^{1 \times N}</math>.

==Citation==

To cite this benchmark, use the following references:

* For the benchmark itself and its data:
::The MORwiki Community, '''Randomy Generated'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Randomly_Generated

@MISC{morwiki_rnd,
author = <nowiki>{{The MORwiki Community}}</nowiki>,
title = {Randomly Generated},
howpublished = {{MORwiki} -- Model Order Reduction Wiki},
url = <nowiki>{http://modelreduction.org/index.php/Randomly_Generated}</nowiki>,
year = {2018}
}

* For the background on the benchmark:

@ARTICLE{morWilP02,
author = <nowiki>{K. Willcox and J. Peraire}</nowiki>,
title = {Balanced Model Reduction via the Proper Orthogonal Decomposition},
journal = {AIAA Journal},
volume = {40},
number = {11},
pages = {2323--2330},
year = {2002},
doi = {10.2514/2.1570}
}

==Reference==

<references>

<ref name="willcox02">K. Willcox and J. Peraire. "<span class="plainlinks">[https://doi.org/10.2514/2.1570 Balanced Model Reduction via the Proper Orthogonal Decomposition]</span>", AIAA Journal, 40(11): 2323--2330, 2002.</ref>

</references>

==Contact==

''[[User:Himpe|Christian Himpe]]''

Randomly Generated - Revision history

Schuetz2 at 05:38, 17 June 2025

Lund: remove preliminary warning

Himpe: Init randomly generated