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MathGroup Archive 1996

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Re:programming competition Correction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5031] Re:[mg4904] programming competition Correction
  • From: espen.haslund at fys.uio.no (Espen Haslund)
  • Date: Sat, 19 Oct 1996 16:40:34 -0400
  • Organization: Universitet i Oslo
  • Sender: owner-wri-mathgroup at wolfram.com

In article <53a6b6$oa6 at dragonfly.wolfram.com>, hay at haystack.demon.co.uk says...
>
>Please change line 6 in the code that I gave from
>        If[n<2, {#1},
>to      If[n<1, {#1},
>
>giving
>
>linearInterpolate2[ li_List, m_ ] :=
>   Block[{},
>      Append[
>         Join@@Partition[ li, 2,1,
>            (  n=Floor[Sqrt[(#2-#1).(#2-#1)//N]/m];
>               If[n<1,
>               {#1},
>                    Table[#1 + k #2, {k,0,n}]&[#1,(#2-#1)/(n+1)],
>                
>               ]
>            )&
>          ],
>          Last[li]
>      ]
>   ];
>
>(the error crept in because of changing from Ceiling to Floor)
>
>I time it (and check it!) against the fastest code in  Xah Lee's  
>posting "[mg4900] Re: programming competition",  due to  
>espen.haslund at fys.uio.no (Espen Haslund):
>
....
>Allan Hayes
>hay at haystack.demon.co.uk
>URL:haystack.demon.co.uk
>
>
>
Hi Allan;

I have made some improvements on my function, and it now runs
as fast as yours on the random data, and a bit faster 
in some other cases.

Note: I think you should have a "n" in your Block (i.e. Block[{n}, )
      also note that changing from Ceiling to Floor make a small
      difference in special cases (i.e. when the distance 
      between points is exactly equal to maxLength)


linearInterpolateEH3[ li_List, maxLength_ ]:=
Module[{p1, d, n},
 Append[Join @@ Table[
  d = N[li[[i+1]] - (p1 = li[[i]])];
   n = Ceiling[Sqrt[#.#]&[d]/maxLength];
    If[n > 1,
       Table[p1 + d*j,{j,0,1-.5/n,1./n}]
    ,  
       {p1}
    ],
     {i,Length[li]-1}], Last[li] ]
]


li = Table[{Random[], Random[]},{1000}]; 

tim1 = Map[First, {
Timing[linearInterpolateEH3[li, .1] ],
Timing[linearInterpolate2[li, .1] ]}];


li = Table[{i,i},{i,100}]; 

tim2 = Map[First, {
Timing[linearInterpolateEH3[li, 0.02] ], 
Timing[linearInterpolate2[li, 0.02] ]}];

li = Table[{i,i},{i,3000}]; 

tim3 = Map[First, {
Timing[linearInterpolateEH3[li, 2] ], 
Timing[linearInterpolate2[li, 2] ]}];



res = {{"linearInterpolateEH3", "linearInterpolate2"},
tim1, tim2, tim3} //TableForm


(*
Out[2]//TableForm= linearInterpolateEH3   linearInterpolate2

                   15.16 Second           15.77 Second

                   12.3 Second            18.18 Second

                   12.58 Second           14.06 Second
*)


-Espen



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