Manifold - Revision history

en>Quondum: replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function

2014-12-08T01:27:12Z

replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function

← Older revision		Revision as of 03:27, 8 December 2014
Line 1:		Line 1:
	~~Hi there! :) My name~~ is ~~Antoine, I'm a student studying Industrial~~ and ~~Labor Relations from Zurich, Switzerland~~.<br><br>my ~~webpage:~~ [http://~~www~~.~~golfidence.nl~~/~~userinfo~~.~~php?uid=49211 Fifa 15 Coin Generator~~]		Wilber Berryhill is what his wife loves to contact him and he completely enjoys this title. To perform lacross is one of the issues she loves most. Distributing manufacturing has been his occupation for some time. Her family lives in Ohio but her husband wants them to transfer.<br><br>my page; tarot card readings ([http://sharevideosonline.net/users/CCarslaw sharevideosonline.net])

en>BeaumontTaz: /* Circle */ Added internal link and changed wording on defining t

2014-02-28T04:37:06Z

Circle: Added internal link and changed wording on defining t

← Older revision		Revision as of 06:37, 28 February 2014
Line 1:		Line 1:
	~~{{Infobox Algorithm~~		Hi there! :) My name is Antoine, I'm a student studying Industrial and Labor Relations from Zurich, Switzerland.<br><br>my webpage: [http://www.golfidence.nl/userinfo.php?uid=49211 Fifa 15 Coin Generator]
	~~\|class=[[Sorting algorithm]]~~
	~~\|image=[[File~~:~~Batcher Odd-Even Mergesort for eight inputs.svg\|Visualization of the odd–even mergesort network with eight inputs]]~~
	~~\|caption=Visualization of the odd–even mergesort network with eight inputs~~
	~~\|data=[[Array data structure\|Array]]~~
	~~\|best-time= <math>O(\log^2(n))</math> parallel time~~
	~~\|average-time= <math>O(\log^2(n))</math> parallel time~~
	~~\|time=<math>O(\log^2(n~~)~~)</math> parallel time~~
	~~\|space=<math>O(n\log^2(n))</math> comparators~~
	~~\|optimal=No~~
	}}

	~~'''Batcher's odd–even mergesort'''~~ is ~~a generic construction devised by [[Ken Batcher]] for [[sorting network]]s of size O(''n'' (log ''n'')<sup>2</sup>) and depth O((log ''n'')<sup>2</sup>)~~, ~~where~~ ''n'' is the number of items to be sorted. Although it is not asymptotically optimal, [[Donald Knuth\|Knuth]] concluded in 1998, with respect to the [[Sorting_network#Optimal_sorting\|AKS network]] that "Batcher's method is much better, unless ''n'' exceeds the total memory capacity of all computers on earth!"<ref>[[Donald Knuth\|D.E. Knuth]]. ''[[The Art of Computer Programming]]'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219–247.</ref>

	It is popularized by the second ''[[GPU Gems]]'' book,<ref>http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter46.html</ref> as an easy way of doing reasonably efficient sorts on graphics-processing hardware.

	~~== Example code ==~~

	~~The following is an implementation of odd–even mergesort algorithm in [[Python (programming language)\|Python]]. The input is a list ''x'' of length a power of 2. The output is~~ a ~~list sorted in ascending order.~~
	~~<source lang="python">~~
	~~def oddeven_merge(lo, hi, r):~~
	~~step = r * 2~~
	~~if step < hi - lo:~~
	~~yield from oddeven_merge(lo, hi, step)~~
	~~yield from oddeven_merge(lo + r, hi, step)~~
	~~yield from [(i, i + r) for i in range(lo + r, hi - r, step)]~~
	~~else:~~
	~~yield (lo, lo + r)~~

	~~def oddeven_merge_sort_range(lo, hi):~~
	~~""" sort the part of x with indices between lo and hi.~~

	~~Note: endpoints (lo and hi) are included.~~
	~~"""~~
	~~if (hi - lo) >= 1:~~
	~~# if there is more than one element, split the input~~
	~~# down the middle and first sort the first~~ and ~~second~~
	~~# half, followed by merging them.~~
	~~mid = lo + ((hi - lo) // 2)~~
	~~yield from oddeven_merge_sort_range(lo, mid)~~
	~~yield~~ from ~~oddeven_merge_sort_range(mid + 1~~, ~~hi)~~
	~~yield from oddeven_merge(lo, hi, 1)~~

	~~def oddeven_merge_sort(length):~~
	~~""" "length" is the length of the list to be sorted~~.
	~~Returns a list of pairs of indices starting with 0 """~~
	~~yield from oddeven_merge_sort_range(0, length - 1)~~

	~~def compare_and_swap(x, a, b):~~
	~~if x[a] > x[b]:~~
	~~x[a], x[b] = x[b], x[a]~~
	<~~/source~~>
	<~~source lang="pycon">~~
	~~>>> data = [2, 4, 3, 5, 6, 1, 7, 8]~~
	~~>>> pairs_to_compare = list(oddeven_merge_sort(len(data)))~~
	>>> ~~pairs_to_compare~~
	~~[(0, 1), (2, 3), (0, 2), (1, 3), (1, 2), (4, 5), (6, 7), (4, 6), (5, 7), (5, 6), (0, 4), (2, 6), (2, 4), (1, 5), (3, 7), (3, 5), (1, 2), (3, 4), (5, 6)]~~
	~~>>> for i in pairs_to_compare~~: ~~compare_and_swap(data, *i)~~
	~~>>> data~~
	~~[1, 2, 3, 4, 5, 6, 7, 8]~~
	~~</source>~~

	~~==See also==~~
	* [[Bitonic sorter]]

	~~== References ==~~
	~~{{reflist}}~~

	~~==External links==~~
	*[http://www.~~iti.fh-flensburg~~.~~de/lang/algorithmen~~/~~sortieren/networks/oemen~~.~~htm Odd–even mergesort] at fh-flensburg.de~~

	~~{{sorting}}~~

	~~{{DEFAULTSORT:Batcher odd-even mergesort}}~~
	~~[[Category:Sorting algorithms]~~]


	~~{{algorithm-stub}}~~

en>Slawekb: Glued from" suggests that the Euclidean spaces are the glue, not the pieces. Glue together is the correct phrasal verb. Also compare google hits "glued together from" (millions) versus "glued from" (tens of thousands).

2014-01-03T12:26:02Z

Glued from" suggests that the Euclidean spaces are the glue, not the pieces. Glue together is the correct phrasal verb. Also compare google hits "glued together from" (millions) versus "glued from" (tens of thousands).

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+'''Batcher's odd–even mergesort''' is a generic construction devised by [[Ken Batcher]] for [[sorting network]]s of size O(''n''&nbsp;(log&nbsp;''n'')<sup>2</sup>) and depth O((log&nbsp;''n'')<sup>2</sup>), where ''n'' is the number of items to be sorted. Although it is not asymptotically optimal, [[Donald Knuth|Knuth]] concluded in 1998, with respect to the [[Sorting_network#Optimal_sorting|AKS network]] that "Batcher's method is much better, unless ''n'' exceeds the total memory capacity of all computers on earth!"<ref>[[Donald Knuth|D.E. Knuth]]. ''[[The Art of Computer Programming]]'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219&ndash;247.</ref>
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en>Quondum: Undid revision by The Anome – "near each point locally"? That's a tautology (rhetoric)

2012-08-24T09:45:12Z

Undid revision by The Anome – "near each point locally"? That's a tautology (rhetoric)

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