Earth Atmosphere - Revision history

Malhotra: infobox string

2023-11-30T09:30:51Z

infobox string

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 [[Category:SISO]]
 [[Category:Dense]]
 ==Description: Model of an Atmospheric Storm Track==

Mlinaric: Add categories, add Python code, edit math

2023-09-01T23:53:41Z

Add categories, add Python code, edit math

← Older revision		Revision as of 23:53, 1 September 2023
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	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
			[[Category:linear]]
			[[Category:time invariant]]
			[[Category:first differential order]]
	[[Category:SISO]]		[[Category:SISO]]
	[[Category:Dense]]		[[Category:Dense]]
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	This benchmark models the track of an [[wikipedia:Storm_track\|atmospheric storm track]].		This benchmark models the track of an [[wikipedia:Storm_track\|atmospheric storm track]].
	More details can be found in <ref name="farrell95"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.		More details can be found in <ref name="farrell95"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.


	==Origin==		==Origin==

	This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.		This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.


	==Data==		==Data==
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	The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [http://slicot.org/objects/software/shared/bench-data/eady.zip eady.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.		The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [http://slicot.org/objects/software/shared/bench-data/eady.zip eady.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.

			Here is [https://www.python.org Python] code for loading the matrices (<math>B</math> and <math>C</math> are stored as arrays of 8-bit unsigned integers):

			:<syntaxhighlight lang="python">
			import numpy as np
			from scipy.io import loadmat

			mat = loadmat('eady.mat')
			A = mat['A']
			B = mat['B'].astype(np.float64)
			C = mat['C'].astype(np.float64)
			</syntaxhighlight>

	==Dimensions==		==Dimensions==
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	:<math>		:<math>
	\begin{~~array}{rcl~~}		\begin{align}
	\dot{x}(t) &=~~& Ax~~(t) + Bu(t) \\		\dot{x}(t) &= A x(t) + B u(t) \\
	y(t) &=~~& Cx~~(t)		y(t) &= C x(t)
	\end{~~array~~}		\end{align}
	</math>		</math>

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	<math>B \in \mathbb{R}^{598 \times 1}</math>,		<math>B \in \mathbb{R}^{598 \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times 598}</math>.		<math>C \in \mathbb{R}^{1 \times 598}</math>.


	==Citation==		==Citation==
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	doi = {10.1175/1520-0469(1995)052<1642:SDOTMA>2.0.CO;2}		doi = {10.1175/1520-0469(1995)052<1642:SDOTMA>2.0.CO;2}
	}		}


	==References==		==References==

Lund: remove preliminary and stub warnings

2022-08-26T12:57:17Z

remove preliminary and stub warnings

← Older revision		Revision as of 12:57, 26 August 2022
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
	[[Category:SISO]]		[[Category:SISO]]
	[[Category:Dense]]		[[Category:Dense]]

	~~'''This is a stub. Please expand.'''~~

	==Description: Model of an Atmospheric Storm Track==		==Description: Model of an Atmospheric Storm Track==

Himpe: key fix

2018-08-08T10:30:09Z

key fix

← Older revision		Revision as of 10:30, 8 August 2018
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	* For the background on the benchmark:		* For the background on the benchmark:

	@ARTICLE{~~DraSB92~~,		@ARTICLE{FarI95,
	author = <nowiki>{B.F. Farrell and P.J. Ioannou}</nowiki>,		author = <nowiki>{B.F. Farrell and P.J. Ioannou}</nowiki>,
	title = {Stochastic Dynamics of the Midlatitude Atmospheric Jet},		title = {Stochastic Dynamics of the Midlatitude Atmospheric Jet},

Himpe: init earth atmosphere

2018-08-07T08:21:39Z

init earth atmosphere

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:SLICOT]]
[[Category:SISO]]
[[Category:Dense]]

'''This is a stub. Please expand.'''

==Description: Model of an Atmospheric Storm Track==

This benchmark models the track of an [[wikipedia:Storm_track|atmospheric storm track]].
More details can be found in <ref name="farrell95"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.

==Origin==

This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.

==Data==

The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [http://slicot.org/objects/software/shared/bench-data/eady.zip eady.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.

==Dimensions==

System structure:

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

System dimensions:

<math>A \in \mathbb{R}^{598 \times 598}</math>,
<math>B \in \mathbb{R}^{598 \times 1}</math>,
<math>C \in \mathbb{R}^{1 \times 598}</math>.

==Citation==

To cite this benchmark, use the following references:

* For the benchmark itself and its data:
::Niconet e.V., '''SLICOT - Subroutine Library in Systems and Control Theory''', http://www.slicot.org

@MANUAL{slicot_cdisc,
title = {{SLICOT} - Subroutine Library in Systems and Control Theory},
organization = {Niconet e.V.}
address = <nowiki>{\url{http://www.slicot.org}}</nowiki>,
key = {SLICOT}
}

* For the background on the benchmark:

@ARTICLE{DraSB92,
author = <nowiki>{B.F. Farrell and P.J. Ioannou}</nowiki>,
title = {Stochastic Dynamics of the Midlatitude Atmospheric Jet},
journal = {Journal of the Atmospheric Sciences},
volume = {52},
number = {10},
pages = {1642--1656},
year = {1995},
doi = {10.1175/1520-0469(1995)052<1642:SDOTMA>2.0.CO;2}
}

==References==

<references>

<ref name="farrell95"> B.F. Farrell, P.J. Ioannou. [https://doi.org/10.1175/1520-0469(1995)052%3C1642:SDOTMA%3E2.0.CO;2 Stochastic Dynamics of the Midlatitude Atmospheric Jet]. Journal of the Atmospheric Sciences, 52(10): 1642--1656, 1995.</ref>

<ref name="chahlaoui02"> Y. Chahlaoui, P. Van Dooren, [http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf A collection of Benchmark examples for model reduction of linear time invariant dynamical systems], Working Note 2002-2: 2002.</ref>

<ref name="chahlaoui05"> Y. Chahlaoui, P. Van Dooren, [https://doi.org/10.1007/3-540-27909-1_24 Benchmark Examples for Model Reduction of Linear Time-Invariant Dynamical Systems], Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 379--392, 2005.</ref>

</references>