Talk:Tridiagonal matrix algorithm - Revision history

Cewbot: Maintain {{WPBS}}: 1 WikiProject template. Remove 1 deprecated parameter: field.

2024-03-09T05:45:51Z

Maintain {{WPBS}}: 1 WikiProject template. Remove 1 deprecated parameter: field.

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	{{WikiProject Mathematics\|priority=Low ~~\|field=applied~~}}		{{WikiProject Mathematics\|priority=Low }}
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	Tridiagonal matrix algorithm l'exemple de trensport de la chaleure dans un bare		Tridiagonal matrix algorithm l'exemple de trensport de la chaleure dans un bare

Qwerfjkl (bot): Implementing WP:PIQA (Task 26)

2024-01-26T17:34:03Z

Implementing WP:PIQA (Task 26)

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	{{~~Maths rating \|class=C~~ \|priority=Low \|field=applied}}		{{WikiProject Mathematics\|priority=Low \|field=applied}}
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	Tridiagonal matrix algorithm l'exemple de trensport de la chaleure dans un bare		Tridiagonal matrix algorithm l'exemple de trensport de la chaleure dans un bare

MalnadachBot: Fixed Lint errors. (Task 12)

2023-02-03T18:46:14Z

Fixed Lint errors. (Task 12)

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	:I've removed Hu-Gallash. Probably a hoax. <span style="">[[User:Salih\|<~~font~~ style="color:#e90;">Salih</~~font~~>]] [[User talk:Salih\|(<~~font~~ style="color:#08c;">talk</~~font~~>)]]</span> 13:04, 28 July 2009 (UTC)		:I've removed Hu-Gallash. Probably a hoax. <span style="">[[User:Salih\|<span style="color:#e90;">Salih</span>]] [[User talk:Salih\|(<span style="color:#08c;">talk</span>)]]</span> 13:04, 28 July 2009 (UTC)

	== correct me if I'm wrong... ==		== correct me if I'm wrong... ==

D.Lazard: /* "specific matrices" */ rp

2022-09-16T09:01:46Z

"specific matrices": rp

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	Surely the only matrices that tridiagonal matrix algorithm deals with is tridiagonal matrices, thus should be "tridiagonal matrices"? Or does it make better sense that such short description be written as "[...] specific matrices" for the sake of consistency of genericy? [[User:Qwertyxp2000\|'''Q'''wertyxp2000]] ([[User talk:Qwertyxp2000\|talk]] \| [[Special:Contributions/Qwertyxp2000\|contribs]]) 02:43, 16 September 2022 (UTC)		Surely the only matrices that tridiagonal matrix algorithm deals with is tridiagonal matrices, thus should be "tridiagonal matrices"? Or does it make better sense that such short description be written as "[...] specific matrices" for the sake of consistency of genericy? [[User:Qwertyxp2000\|'''Q'''wertyxp2000]] ([[User talk:Qwertyxp2000\|talk]] \| [[Special:Contributions/Qwertyxp2000\|contribs]]) 02:43, 16 September 2022 (UTC)
			:[[WP:SDDUPLICATE]] says "avoid duplicating information that is already in the title". I have chosen this formulation for clarifying that this is not a general algorithm that uses tridiagonal matrices, but rather an algorithm that applies only to tridiagonal matrices. Also, "specific" is shorter than "tridiagonal", in view of [[WP:SD40]]. Maybe, a better formulation can be found ... [[User:D.Lazard\|D.Lazard]] ([[User talk:D.Lazard\|talk]]) 09:01, 16 September 2022 (UTC)

Qwertyxp2000: /* "specific matrices" */ new section

2022-09-16T02:43:55Z

"specific matrices": new section

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	- Comment: I don't think the C++ code works, unless the array 'a' is length n instead of n-1 (this would make the a[0] entry off the matrix). <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/2001:388:1034:1D01:7921:DF12:5039:2149\|2001:388:1034:1D01:7921:DF12:5039:2149]] ([[User talk:2001:388:1034:1D01:7921:DF12:5039:2149\|talk]]) 23:30, 6 June 2014 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->		- Comment: I don't think the C++ code works, unless the array 'a' is length n instead of n-1 (this would make the a[0] entry off the matrix). <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/2001:388:1034:1D01:7921:DF12:5039:2149\|2001:388:1034:1D01:7921:DF12:5039:2149]] ([[User talk:2001:388:1034:1D01:7921:DF12:5039:2149\|talk]]) 23:30, 6 June 2014 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

			== "specific matrices" ==

			Surely the only matrices that tridiagonal matrix algorithm deals with is tridiagonal matrices, thus should be "tridiagonal matrices"? Or does it make better sense that such short description be written as "[...] specific matrices" for the sake of consistency of genericy? [[User:Qwertyxp2000\|'''Q'''wertyxp2000]] ([[User talk:Qwertyxp2000\|talk]] \| [[Special:Contributions/Qwertyxp2000\|contribs]]) 02:43, 16 September 2022 (UTC)

Qwerfjkl (bot): Replaced deprecated tags with (via WP:JWB)

2022-05-07T20:40:14Z

Replaced deprecated <source> tags with <syntaxhighlight> (via WP:JWB)

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	Note that the index <math>i</math> here is [[Array data type\|one based]], in other words <math>i = 1, 2, \dots, n</math> where <math>n</math> is the number of unknowns.		Note that the index <math>i</math> here is [[Array data type\|one based]], in other words <math>i = 1, 2, \dots, n</math> where <math>n</math> is the number of unknowns.

	<~~source~~ lang="Matlab">		<syntaxhighlight lang="Matlab">
	function x = TDMAsolver(a,b,c,d)		function x = TDMAsolver(a,b,c,d)
	n = length(b);		n = length(b);
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	x(i) = d(i) - c(i) * x(i + 1);		x(i) = d(i) - c(i) * x(i + 1);
	end		end
			</syntaxhighlight>
	</source>

	Maybe someone could fix it, or correct the first code so it makes one iteration.		Maybe someone could fix it, or correct the first code so it makes one iteration.

179.87.13.132: /* Complicated derivation */

2016-10-01T22:40:15Z

Complicated derivation

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	:Agreed. But actually it's not exactly the same algorithm, though the mathematical result is equivalent. In the usual one, only bi and di are updated in the forward step, here only ci and di are updated. I also have a ref (Rotella & Borne, see next section) stating this variant is from Cholesky, but I shall double-check this. [[User:Arbautjc\|Arbautjc]] ([[User talk:Arbautjc\|talk]]) 22:06, 23 August 2013 (UTC)		:Agreed. But actually it's not exactly the same algorithm, though the mathematical result is equivalent. In the usual one, only bi and di are updated in the forward step, here only ci and di are updated. I also have a ref (Rotella & Borne, see next section) stating this variant is from Cholesky, but I shall double-check this. [[User:Arbautjc\|Arbautjc]] ([[User talk:Arbautjc\|talk]]) 22:06, 23 August 2013 (UTC)

	It's not just you - it is RIDICULOUSLY complicated as written out - All you need is ~~one~~ row ~~operation~~ to reduce the matrix to Upper Hessenberg ~~Form~~, modify the d vector and you're all set for back substitution. Here's the VBA snippet that I use virtually every day!		It's not just you - it is RIDICULOUSLY complicated as written out - All you need are N row operations to reduce the matrix to Upper Hessenberg form, followed by the same operation to modify the d-vector and you're all set for back substitution. Here's the VBA snippet that I use virtually every day!

	Sub TDMA(N%, A#(), B#(), C#(), D#(), X#())		Sub TDMA(N%, A#(), B#(), C#(), D#(), X#())
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	Next i		Next i
	End Sub		End Sub
			[[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132\|talk]]) 22:40, 1 October 2016 (UTC)
	[[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132\|talk]]) 22:38, 1 October 2016 (UTC)		[[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132\|talk]]) 22:38, 1 October 2016 (UTC)
	<!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132#top\|talk]]) 16:39, 1 October 2016 (UTC)</small> <!--Autosigned by SineBot-->		<!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132#top\|talk]]) 16:39, 1 October 2016 (UTC)</small> <!--Autosigned by SineBot-->

179.87.13.132: /* Complicated derivation */

2016-10-01T22:38:14Z

Complicated derivation

← Previous revision		Revision as of 22:38, 1 October 2016
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	X(i) = (DP(i) - C(i) * X(i + 1)) / BP(i)		X(i) = (DP(i) - C(i) * X(i + 1)) / BP(i)
	Next i		Next i
			End Sub
⚫	~~End Sub~~ <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132#top\|talk]]) 16:39, 1 October 2016 (UTC)</small> <!--Autosigned by SineBot-->
			[[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132\|talk]]) 22:38, 1 October 2016 (UTC)
		⚫	<!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132#top\|talk]]) 16:39, 1 October 2016 (UTC)</small> <!--Autosigned by SineBot-->

	== An important limitation ==		== An important limitation ==

SineBot: Signing comment by 179.87.13.132 - "/* Complicated derivation */"

2016-10-01T16:39:30Z

Signing comment by 179.87.13.132 - "Complicated derivation: "

← Previous revision		Revision as of 16:39, 1 October 2016
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	X(i) = (DP(i) - C(i) * X(i + 1)) / BP(i)		X(i) = (DP(i) - C(i) * X(i + 1)) / BP(i)
	Next i		Next i
			End Sub <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/179.87.13.132\|179.87.13.132]] ([[User talk:179.87.13.132#top\|talk]]) 16:39, 1 October 2016 (UTC)</small> <!--Autosigned by SineBot-->
	End Sub

	== An important limitation ==		== An important limitation ==

179.87.13.132: /* Complicated derivation */

2016-10-01T16:39:08Z

Complicated derivation

@@ Line 82: / Line 82: @@
 Is it only me, or are there others out there too who find the presentation of the derivation unnecessarily complicated? Anyone who knows the standard Gauss elimination can straight away derive the necessary recursive equations. Provided that we are trying to upper triangularize the matrix, I think it would be more helpful to present the row operations using notation such as <math>R_i \leftarrow R_i - (a_i/b'_{i-1}) \times R_i</math>, where <math>b'_i = b_i - \frac{a_i c_{i-1}}{b'_{i-1}}</math>. Perhaps someone can clean it up. ([[User:Manoguru|Manoguru]] ([[User talk:Manoguru|talk]]) 16:18, 27 January 2012 (UTC))
 :Agreed. But actually it's not exactly the same algorithm, though the mathematical result is equivalent. In the usual one, only bi and di are updated in the forward step, here only ci and di are updated. I also have a ref (Rotella & Borne, see next section) stating this variant is from Cholesky, but I shall double-check this. [[User:Arbautjc|Arbautjc]] ([[User talk:Arbautjc|talk]]) 22:06, 23 August 2013 (UTC)
 == An important limitation ==