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MathGroup Archive 2006

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List programming, speed improvement

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65801] List programming, speed improvement
  • From: Dr Reinhard Simonovits <Reinhard.Simonovits at uni-graz.at>
  • Date: Mon, 17 Apr 2006 02:28:57 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

soon I have to give a Mathematica presentation.

There I would like to demonstrate various programming techniques.


One of the problems is: Given a list of pairs of any reals, convert 
it to Graphics primitives in the following way: (* I just choose 1,2,3,4,5,6 *)

{ {1.,2.}, {3.,4.}, {5.,6.} } -> {Line[{{1., 0}, {1., 2.}}], 
Line[{{3., 0}, {3., 4.}}], Line[{{5., 0}, {5., 6.}}]}

I have 3 solutions following pattern matching, pure functions, only 
List commands.



1) Can anyone show me a quicker solutions, including Compile? It must 
run under Mathematica 4.0, the participants must work with it for 
other problems.

2) But I could also demonstrate a solution under Mathematica 5.2, 
just to show the version improvements.

So actually I need a 4.0 and 5.2 version. I think only List commands 
better programmed must be a hit.


data = Table[{Random[Real, {1, 10}], Random[Integer, {1, 10}]}, {100000}];

Here are my solutions:

solution1 = data /. a : {_, _} :> Line[{{a[[1]], 0}, a }]; // Timing
{0.469 Second, Null}

solution2 = Line[{ {#1, 0}, {#1, #2}}] & @@@ data; // Timing
{0.344 Second, Null}


solution3 = ( {xcoord, ycoord} = Transpose[ data];
         Line /@ Partition[
             Transpose[{Transpose[ {xcoord, xcoord}] // Flatten,
                 Transpose[{  Table[0, {Length@xcoord}], ycoord}] //
                   Flatten} ], 2]);
   // Timing
{0.531 Second, Null}

solution1 == solution2 == solution3
True

In solution3  {{1, 2}, {3, 4}, {5, 6}} -> {{1, 0}, {1, 2}, {3, 0}, 
{3, 4}, {5, 0}, {5, 6}}  was created first.


-Reinhard
-- 
********************************************
              Dr. Reinhard Simonovits
Handelsakademie  |  Karl Franzens University
Math Department  |  Inst. for Mathematics
Grazbachgasse 71 |  Heinrichstrasse 36
               A-8010 Graz, Austria

Email: Reinhard.Simonovits at uni-graz.at
*********************************************


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