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Re: Tilting at Windmills?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62148] Re: [mg62106] Tilting at Windmills?
*From*: gardyloo <gardyloo at mail.wsu.edu>
*Date*: Sat, 12 Nov 2005 03:32:56 -0500 (EST)
*References*: <200511110752.CAA29692@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi, Matt,
I didn't look to see what large testLists you were working with, or
I'd never have attempted what I'll post here. But my timings aren't too
bad, for a really naive approach. I don't know how the memory usage
compares to yours, but the last line shows a memory usage of just under
3MB (I think).
Hope this helps!
Curtis
In[1]:=
parseList[list_?ListQ]:={{list[[#]], list[[#]]}, {list[[#]], list[[#+1]]}}&/@
Range[Length[list]-1]
In[2]:=
parseList[{a,b,c,d,e,f,g}]
Out[2]=
{{{a,a},{a,b}},{{b,b},{b,c}},{{c,c},{c,d}},{{d,d},{d,e}},{{e,e},{e,f}},{{f,
f},{f,g}}}
In[3]:=
testList=Range[200000];
In[4]:=
Timing[parseList[testList];]
Out[4]=
{0.232964` Second,Null}
In[5]:=
Take[parseList[testList], 10]
Out[5]=
{{{1,1},{1,2}},{{2,2},{2,3}},{{3,3},{3,4}},{{4,4},{4,5}},{{5,5},{5,6}},{{6,
6},{6,7}},{{7,7},{7,8}},{{8,8},{8,9}},{{9,9},{9,10}},{{10,10},{10,11}}}
In[6]:=
$Version
Out[6]=
"5.2 for Linux (June 20, 2005)"
In[7]:=
MemoryInUse[]
Out[7]=
2941472
Matt wrote:
>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,xn}
>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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