Re: Re: Tilting at Windmills?

• To: mathgroup at smc.vnet.net
• Subject: [mg62137] Re: Re: [mg62106] Tilting at Windmills?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 12 Nov 2005 03:32:17 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```The second method provides a slight improvement in efficiency

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

createListOfListsForCobwebTypePlot2[data_]:=
Partition[Rest[Most[Flatten[
Table[#,{2}]&/@data]]],2,1];

data=Range[200000];

createListOfListsForCobwebTypePlot[data]//Timing//First

0.480638 Second

createListOfListsForCobwebTypePlot2[data]//Timing//First

0.430115 Second

createListOfListsForCobwebTypePlot[data]==
createListOfListsForCobwebTypePlot2[data]

True

Bob Hanlon

>
> From: Bob Hanlon <hanlonr at cox.net>
To: mathgroup at smc.vnet.net
> Date: 2005/11/11 Fri AM 11:49:05 EST
> To: "Matt" <anonmous69 at netscape.net>, <mathgroup at smc.vnet.net>
> Subject: [mg62137] Re: [mg62106] Tilting at Windmills?
>
> 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: [mg62137] [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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