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MathGroup Archive 2002

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RE: Re: Newbie Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32776] RE: [mg32728] Re: [mg32686] Newbie Question
  • From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
  • Date: Sat, 9 Feb 2002 05:11:50 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: Sseziwa Mukasa [mailto:mukasa at jeol.com]
To: mathgroup at smc.vnet.net
> Sent: Thursday, February 07, 2002 11:10 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg32776] [mg32728] Re: [mg32686] Newbie Question
> 
> 
> "Brunsman, Kenneth J" wrote:
> 
> >
> > I can parse out the column I need using Take [data [[All, 
> Column #]]] --- no
> > big deal.  So far, so good.
> >
> 
> I'm not sure what you're using Take for, data[[All,Column #]] 
> should be
> sufficient.
> 
> >
> > Now here's the problem --- How do I get % Differences 
> between any of 10,000
> > items in that list?  I need to take % Differences between 
> adjacent pairs,
> > i.e. n and n-1, as well as items n and n-m where m can 
> range from 1 to
> > 10,000.
> >
> 
> Do you want all the differences n-m (m = 1..n-1) at once or just for a
> particular m?  For an individual m I got good results with
> 
> f[x_,m_Integer]:=Block[{a=Drop[x,m]},(a-Drop[x,-m])/a]
> 
> On a PowerMac with an 800MHz G4 processor it takes 0.02 
> seconds to evaluate
> f[x,1] where x is a list of length 10000.  
> Table[f[x,i],{i,Length[x]-1}] will
> of course give you all the differences for m = 1..n-1.
> 
> >
> > Further, I need to make sure that this code runs fast 
> because I'm about to
> > run this on a data set of 10^8 data points (financial times 
> series).  I
> > could do this standing on my head in Fortran, but I'm bound 
> and determined
> > to learn Mathematica if it takes the rest of my unnatural life.
> >
> 
> The key difference between Fortran programming and 
> Mathematica in my opinion is
> that writing explicit loops in Mathematica is generally 
> inefficient, so is
> indexing elements of lists and arrays.  Take advantage of the 
> fact that many
> operators will automatically apply themselves to every 
> element in a list.  Also
> avoid making copies as much as possible by using lambda 
> functions and mapping.
> Finally, variables are best used to eliminate common 
> subexpressions as in the
> Block statement in the function above.
> 
> Incidentally though, keeping a list of 10^8 elements in 
> memory is probably not
> a good idea, the list should probably be broken up and 
> processed in smaller
> pieces to avoid spending all your time swapping memory to disk.
> 
> > This is my first time attempting list processing and all 
> I'm doing is
> 
> > screwing up royally.
> >
> 
> Functional programming and pattern matching are not generally 
> practiced outside
> of academic programming exercises and they are a very 
> different paradigm from
> traditional imperative programming (object oriented techniques being a
> different kettle of fish entirely).  Practice makes perfect 
> of course.  There
> are many excellent books that not only teach efficient 
> programming style in
> Mathematica but generally do so while applying to techniques 
> to domain specific
> problems.  I don't do any financial series analysis myself 
> but a quick search
> on Amazon.com for "mathematica finance" turns up 6 titles on 
> using Mathematica
> for economic and financial modeling.
> 
> Regards,
> 
> Sseziwa Mukasa
> 
> 
Sseziwa,

this is the right way to deal with the problem, I think. Here 
just a little modification of this idea, and an other one following
a suggestion from Andrzej Kozlowski:

 
In[1]:= ll = Table[Random[Real, {0, 100}], {300}];

your suggestion:

In[2]:=
f[x_, m_Integer] := Block[{a = Drop[x, m]}, (a - Drop[x, -m])/a]
In[3]:=
r1 = Table[f[ll, i], {i, Length[ll] - 1}];

my variant:

In[4]:=
r2 = (#1 - #2)/#1 & @@@ 
      Drop[NestList[{Drop[First[#], 1], Drop[Last[#], -1]} &, {ll, ll}, 
          Length[ll] - 1], 1];

In[5]:= r1 == r2
Out[5]= True

The idea was: dropping the first or last element of a list
is faster than dropping half of it.

Another idea (trying to use efficient list operations):

In[6]:=
g[x_, y_] := (y - x)/y; g[_] := Sequence[];
In[7]:=
r3 = Drop[ListCorrelate[ll, ll, {1, 1}, {}, g, List], 1];

In[8]:= r3 == r2
Out[8]= True

Timing however excludes this variant; compare the other two:

 
In[9]:= ll = Table[Random[Real, {0, 100}], {4000}];

In[16]:=
(r = Table[f[ll, i], {i, Length[ll] - 1}]); // Timing
Out[16]=
{20.57 Second, Null}
In[17]:= Remove[r];
 
In[18]:=
(r = (#1 - #2)/#1 & @@@ 
          NestList[{Drop[First[#], 1], Drop[Last[#], -1]} &, 
                   {Drop[ll, 1], Drop[ll, -1]}, 
                    Length[ll] - 2]); // Timing
Out[18]=
{13.359 Second, Null}
In[19]:= Remove[r];

Your variant however is more economic with memory, and I was 
not able to run the test with a list of 10000. (400 MHz P II 
Notebook, 192 MB real memory). I estimate that 10000 will take 
about 3 minutes. This would mean 10^8 data will at least take 
several days, perhaps too much to make any predictions.

Anyways I agree with you that this is not the right task for 
Mathematica, producing a vaste of numbers of little information 
content. From which you finally will have to read off something, 
what? how?

--
Hartmut



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