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RE: How to speed up this calculation?

• To: mathgroup at smc.vnet.net
• Subject: [mg37235] RE: [mg37200] How to speed up this calculation?
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 18 Oct 2002 05:16:49 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Cheng Liu [mailto:cliu at lanl.gov]
To: mathgroup at smc.vnet.net
>Sent: Wednesday, October 16, 2002 8:26 PM
>To: mathgroup at smc.vnet.net
>Subject: [mg37235] [mg37200] How to speed up this calculation?
>
>
>Dear group,
>
>         I have the following question regarding a lengthy calculation 
>using Mathematica:
>
>For given w points in x direction and h points in y direction, I can 
>construct all the points using
>
>         h=10; w=8;
>         points=Flatten[Transpose[Outer[List,Range[w],Range[h]]],1]
>
>Next, I need to find all the possible pairs of point including points 
>themselves, i.e., pair AA.  I can use
>
>         pairs=Outer[List,points,points,1]
>
>Then, I have to clear those pairs that repeat themselves, 
>i.e., pair AB and 
>pair BA.  Also, when w and h are of the order of 1000s, the 
>computation 
>takes a very long time.  Is there a better way of doing the 
>second part of 
>the computation?  Thanks in advance.
>
>Sincerely
>
>Cheng
>
>
>====================================================
>Cheng Liu, Ph.D.
>MST-8, Structure/Property Relations
>Materials Science and Technology Division
>Los Alamos National Laboratory
>Los Alamos, New Mexico 87545
>
>Phone: 505-665-6892 (office), 505-667-9950 (lab)
>Fax:   505-667-8021
>email: cliu at lanl.gov
>====================================================
>
>

Cheng,

you didn't tell about a specific order of your resulting pairs, so you not
need Transpose in your first line:

points = Flatten[Outer[List, Range[w], Range[h]], 1]


Now build the pairs (for sake of clarity , let me call the points
points = {p1, p2, p3, p4, p5}, of course you don't do that):

Flatten[
 With[{l = Length[points]}, 
  Array[If[#1>#2, Unevaluated[Sequence[]], points[[{#1, #2}]]]&, {l, l}]],
 1]
{{p1, p1}, {p1, p2}, {p1, p3}, {p1, p4}, {p1, p5}, 
 {p2, p2}, {p2, p3}, {p2, p4}, {p2, p5}, 
 {p3, p3}, {p3, p4}, {p3, p5}, 
 {p4, p4}, {p4, p5}, 
 {p5, p5}}


Alternatively you might do

pairs = Outer[List, points, points, 1]

Flatten[MapIndexed[Drop[#1, First[#2] - 1] &, pairs], 1]
{{p1, p1}, {p1, p2}, {p1, p3}, {p1, p4}, {p1, p5},
 {p2, p2}, {p2, p3}, {p2, p4}, {p2, p5},
 {p3, p3}, {p3, p4}, {p3, p5},
 {p4, p4}, {p4, p5},
 {p5, p5}}

...try out which is faster.

--
Hartmut Wolf