Convection Reaction - Revision history

Malhotra: infobox string

2023-11-30T09:28:49Z

infobox string

@@ Line 6: / Line 6: @@
 [[Category:Sparse]]
 [[Category:SISO]]
 ==Description==

Mlinaric: Fix Python

2023-09-01T23:49:14Z

Fix Python

← Older revision		Revision as of 23:49, 1 September 2023
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	mat = loadmat('build.mat')		mat = loadmat('build.mat')
	A = mat['A'].astype(np.~~float_~~)		A = mat['A'].astype(np.float64)
	B = mat['B'].toarray()		B = mat['B'].toarray()
	C = mat['C'].toarray()		C = mat['C'].toarray()

Mlinaric: Add categories, edit SLICOT links, add Python code, edit math

2023-08-30T13:01:32Z

Add categories, edit SLICOT links, add Python code, edit math

← Older revision		Revision as of 13:01, 30 August 2023
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	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
			[[Category:linear]]
			[[Category:time invariant]]
			[[Category:first differential order]]
	[[Category:Sparse]]		[[Category:Sparse]]
	[[Category:SISO]]		[[Category:SISO]]
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	More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.		More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.


	==Origin==		==Origin==
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	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==~~		The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [https://www.slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [https://www.slicot.org/objects/software/shared/bench-data/pde.zip pde.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>A</math> is a sparse matrix of 16-bit integers and <math>B</math> and <math>C</math> are full matrices stored as sparse matrices):

	~~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/pde.zip pde.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.		:<syntaxhighlight lang="python">
			import numpy as np
			from scipy.io import loadmat

			mat = loadmat('build.mat')
			A = mat['A'].astype(np.float_)
			B = mat['B'].toarray()
			C = mat['C'].toarray()
			</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}^{84 \times 1}</math>,		<math>B \in \mathbb{R}^{84 \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times 84}</math>.		<math>C \in \mathbb{R}^{1 \times 84}</math>.


	==Citation==		==Citation==

Lund: remove preliminary and stub warnings

2022-08-26T08:24:48Z

remove preliminary and stub warnings

← Older revision		Revision as of 08:24, 26 August 2022
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
	[[Category:Sparse]]		[[Category:Sparse]]
	[[Category:SISO]]		[[Category:SISO]]

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

	==Description==		==Description==

Lund: Lund moved page Partial Differential Equation to Convection Reaction: name change

2022-08-26T08:21:23Z

Lund moved page Partial Differential Equation to Convection Reaction: name change

← Older revision	Revision as of 08:21, 26 August 2022
(No difference)

Himpe: update description.

2021-12-02T10:18:41Z

update description.

← Older revision		Revision as of 10:18, 2 December 2021
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	</math>		</math>

	with Dirichlet boundary conditions.		with Dirichlet boundary conditions and discretized with centered difference approximation.

	The output vector equals the input vector <math>C = B^T</math>		The input vector <math>B</math> is composed of random elements and the output vector equals the input vector <math>C = B^T</math>.

	More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.		More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.

Himpe: Add equation and fix link.

2021-12-02T10:13:01Z

Add equation and fix link.

← Older revision		Revision as of 10:13, 2 December 2021
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	==Description==		==Description==

	This benchmark models a chemical reaction by a [[wikipedia:Convection-diffusion_equation\|convection]]-[[wikipedia:Reaction-diffusion\|reaction]] partial differential equation.		This benchmark models a chemical reaction by a [[wikipedia:Convection-diffusion_equation\|convection]]-[[wikipedia:Reaction-diffusion\|reaction]] partial differential equation on the unit square,
			given by:

			:<math>
			\frac{\partial x}{\partial t} = \frac{\partial^2 x}{\partial y^2} + \frac{\partial^2 x}{\partial z^2} + 20 \frac{\partial x}{\partial z} - 180 x + f(y,z) x(t),
			</math>

			with Dirichlet boundary conditions.

			The output vector equals the input vector <math>C = B^T</math>

	More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.		More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.

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	<ref name="saad88"> Y. Saad. <span class="plainlinks">[https://doi.org/10.1109/9.406 Projection and deflation method for partial pole assignment in linear state feedback]</span>, IEEE Transactions on Automatic Control, 33(3): 290--297, 1988.</ref>		<ref name="saad88"> Y. Saad. <span class="plainlinks">[https://doi.org/10.1109/9.406 Projection and deflation method for partial pole assignment in linear state feedback]</span>, IEEE Transactions on Automatic Control, 33(3): 290--297, 1988.</ref>

	<ref name="grimme97"> E.J. Grimme. <span class="plainlinks">[~~http~~://~~hdl~~.~~handle~~.~~net~~/~~2142~~/~~81180~~ Krylov Projection Methods for Model Reduction]</span>. PhD Thesis, University of Illinois at Urbana-Champaign, 1998.</ref>		<ref name="grimme97"> E.J. Grimme. <span class="plainlinks">[https://www.proquest.com/dissertations-theses/krylov-projection-methods-model-reduction/docview/304361372/se-2?accountid=14597 Krylov Projection Methods for Model Reduction]</span>. PhD Thesis, University of Illinois at Urbana-Champaign, 1998.</ref>

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

Himpe: Himpe moved page Partial Differentia Equation to Partial Differential Equation without leaving a redirect

2018-08-17T10:50:02Z

Himpe moved page Partial Differentia Equation to Partial Differential Equation without leaving a redirect

← Older revision	Revision as of 10:50, 17 August 2018
(No difference)

Himpe: init pde

2018-08-17T10:49:49Z

init pde

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:SLICOT]]
[[Category:Sparse]]
[[Category:SISO]]

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

==Description==

This benchmark models a chemical reaction by a [[wikipedia:Convection-diffusion_equation|convection]]-[[wikipedia:Reaction-diffusion|reaction]] partial differential equation.
More details can be found in <ref name="raschman80"/>, <ref name="saad88"/>, <ref name="grimme97"/> 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/pde.zip pde.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}^{84 \times 84}</math>,
<math>B \in \mathbb{R}^{84 \times 1}</math>,
<math>C \in \mathbb{R}^{1 \times 84}</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_pde,
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{Saa88,
author = <nowiki>{Y. Saad}</nowiki>,
title = {Projection and deflation method for partial pole assignment in linear state feedback},
journal = {IEEE Transactions on Automatic Control},
volume = {33},
number = {3},
pages = {290--297},
year = {1988},
doi = {10.1109/9.406}
}

==References==

<references>

<ref name="raschman80"> P. Raschman, M. Kuhicek, M. Maros. Waves in distributed chemical systems: Experiments and computations. In: New Approaches to Nonlinear Problems in Dynamics - Proceedings of the Asilomar Conference Ground: 271--288, SIAM, 1980.</ref>

<ref name="saad88"> Y. Saad. [https://doi.org/10.1109/9.406 Projection and deflation method for partial pole assignment in linear state feedback], IEEE Transactions on Automatic Control, 33(3): 290--297, 1988.</ref>

<ref name="grimme97"> E.J. Grimme. [http://hdl.handle.net/2142/81180 Krylov Projection Methods for Model Reduction]. PhD Thesis, University of Illinois at Urbana-Champaign, 1998.</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>