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MathGroup Archive 2005

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Re: Tilting at Windmills?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62138] Re: [mg62106] Tilting at Windmills?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 12 Nov 2005 03:32:28 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

createListOfListsForCobwebTypePlot[data_]:=
    Partition[Drop[Drop[Flatten[
            Table[#,{4}]&/@data],3],-3],2];

data=ToExpression[Table["x"<>ToString[k],{k,5}]]

{x1,x2,x3,x4,x5}

createListOfListsForCobwebTypePlot[data]

{{x1, x2}, {x2, x2}, {x2, x3}, {x3, x3}, {x3, x4}, {x4, x4}, {x4, x5}}

data=Range[200000];

createListOfListsForCobwebTypePlot[data]//Timing//First

0.447221 Second


Bob Hanlon

> 
> From: "Matt" <anonmous69 at netscape.net>
To: mathgroup at smc.vnet.net
> Date: 2005/11/11 Fri AM 02:52:32 EST
> Subject: [mg62138] [mg62106] Tilting at Windmills?
> 
> Hello,
>   Where there's a chance of success, I tend to agonize over details of
> implementation.  Memory usage is one such area.  Here is a statement of
> a problem I was trying to solve in Mathematica:
> 
>  Given a list of the following form:{x1,x2,x3,...,xn-1,xn} I want to
> develop an algorithm that will iterate over the input list to produce
> output of the following
> form:
{x1,x2,x2,x2,x2,x3,x3,x3,x3,x4,x4,x4,x4,x5,...,xn-2,xn-1,xn-1,xn-1,xn-1,x
n}
> which will then need to be partitioned to end up in the following form:
> {{x1,x2},{x2,x2},{x2,x3},{x3,x3},{x3,x4},{x4,x4},{x4,x5},...,{xn-2,xn-1},
{xn-1,xn-1},{xn-1,xn}}
> which means that if I had a flattened list of length'n' as input, then
> the new flattened list would have a length of 4*(n-2)+2
> 
> Here is my first solution to this problem, along with a test harness
> for validation:
> 
> Clear[createListOfListsForCobwebTypePlot,testRun];
> createListOfListsForCobwebTypePlot[x:(_List?((Length[#]>0&&Depth[#]\
[Equal]2)&)),debugOn:(_?(#\[Element]Booleans&)):False]:=Module[{tempList=
{},lengthOfInList,retLength,ret},If[debugOn\[Equal]True,
>         lengthOfInList=Length[x];
>         Print["Length of input list: ",lengthOfInList]
>         ];
>       (tempList={tempList,#,#,#,#})&/@x;
>       If[debugOn\[Equal]True,
>         Print["Out list before flattening: ",tempList]
>         ];
>       ret=Delete[Flatten[tempList],{{1},{2},{3},{-3},{-2},{-1}}];
>       If[debugOn\[Equal]True,
>         retLength=Length[ret];
>         Print["Length of out list: ",retLength];
>         Print["Out list length equal to 4(n-2) +
> 2?\n",retLength\[Equal]4 (lengthOfInList-2)+2]
>         ];
>       Partition[ret,2]
>       ];
> testRun[debugOn:(_?(#\[Element]Booleans&)):False]:=Module
[{testList},testList=Range[20];
>       Print[createListOfListsForCobwebTypePlot[testList,debugOn]];];
> testRun[True]
> 
> Although it seems to work just fine, I'm not satisfied with it because
> of this line:
> (tempList={tempList,#,#,#,#})&/@x;
> 
> It seems very bad to me to keep creating a new list of objects as more
> elements are added, i.e. in C or C++ I would allocate the appropriate
> amount of memory up front, and then fill the 'slots'.  One list, one
> memory allocation.  So, I thought to myself about how I might
> 'allocate' or 'reserve' memory up front in Mathematica.  What I figured to 
do,
> was to generate a table object with enough elements (with dummy values)
> up front and then use the object[[n]]=newValue paradigm to replace the
> dummy value with a real value.  That way, there's only one list
> allocated up front.  Because my input list was going to contain
> elements all with a head of Integer, I decided to create the dummy
> table with Integer elements.  If my experiment proved fruitful, I would
> have modified it to contend with other atomic types as appropriate.
> Here is what my modified and 'streamlined' function along with its
> accompanying test harness is:
> 
> Clear[createListOfListsForCobwebTypePlotAlt,testRun];
> createListOfListsForCobwebTypePlotAlt[x:(_List?((Length[#]>0&&Depth[#]
==2)&)),debugOn:(_?(#\[Element]Booleans&)):False]:=Module[{tempList=
{},lengthOfInList,allocLength,allocList,index=1,retLength,ret},
>       lengthOfInList=Length[x];
>       allocLength=4 lengthOfInList;
>       allocList=Table[11,{allocLength}];
>       If[debugOn\[Equal]True,
>         Print["Length of input list: ",lengthOfInList];
>         Print["Length of allocList: ",allocLength]
>         ];
> 
> Fold[(allocList[[#1]]=#2;allocList[[#1+1]]=#2;allocList[[#1+2]]=#2;allocList
[[#1+3]]=#2;#1+4)&,index,x];
>       ret=Delete[allocList,{{1},{2},{3},{-3},{-2},{-1}}];
>       If[debugOn\[Equal]True,
>         retLength=Length[ret];
>         Print["Length of out list: ",retLength];
>         Print["Out list length equal to 4(n-2) +
> 2?\n",retLength\[Equal]4 (lengthOfInList-2)+2];
>         ];
>       Partition[ret,2]
>       ];
> testRun[debugOn:(_?(#\[Element]Booleans&)):False]:=Module
[{testList},testList=Range[20];
>       Print[createListOfListsForCobwebTypePlotAlt[testList,debugOn]];];
> testRun[True]
> 
> This produces identical results as the previous solution.  Now, for the
> test:
> 
> testList=Range[200000];
> Timing[Do[createListOfListsForCobwebTypePlot[testList], {1}]][[1]]
> Timing[Do[createListOfListsForCobwebTypePlotAlt[testList], {1}]][[1]]
> 
> With results of
> 1.078 Second
> 2.109 Second
> 
> much to my chagrin.  You may be wondering why I'm doing this.  The
> reason is that I want to learn and establish proper Mathematica discipline 
with
> primitive operations such as this, so that I don't have to break bad
> habits later.  I have a feeling the answer is going to be something
> along the lines of:  "There's not much you can do about it, and in fact
> there really is no memory allocation schemes that you can take
> advantage of in Mathematica."  If that's the case, I'm fine with that.  I just
> want to be sure is all.
> 
> Thanks,
> 
> Matt
> 
> 


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