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From: mathfanda on 22 Jul 2010 05:44
Dear Mathematica friends,

the following program runs 4.7 times faster and uses 22.7 times less
memory
in Mathematica 5.2 than in Mathematica 7.0.
Fortunately, it gives the same result.

ClearAll["Global`*"];
c[1] = 2;
Table[
a = Sum[c[i] r^i,{i,1,n}] + O[r]^(n+1);
s = 4(1-1/(1+1/3+r-a*Cos[2t]))//Normal//TrigReduce;
Table [ b[2i]= Coefficient[s,Cos[2i*t]]/2,{i,n}];
b[0] = s-2*Sum[b[2i]*Cos[2i*t],{i,n}]//Simplify;
b[x_?OddQ]=0;
m=Table[If[i==j,b[0]-(n+1-i)^2,b[Abs[i-j]]],{i,2n+1},{j,2n+1}];
m=Simplify[m];
d=Det[m]+O[r]^(n+1)//Simplify//Normal;
c[n-1]=c[n-1]/.First[Solve[d==0,c[n-1]]];
,{n,3,5}];
Print[$Version];
Print["c[4]=",c[4]];
Print["time=",TimeUsed[]];
Print["memory=",MaxMemoryUsed[]/2^20.," MB"];

Here are the results:

5.2 for Linux x86 (64 bit) (June 20, 2005)
38475
c[4]=-(-----)
16384
time=0.98
memory=6.07137 MB

7.0 for Linux x86 (64-bit) (February 18, 2009)
38475
c[4]=-(-----)
16384
time=4.61
memory=136.313 MB

The conclusion might be: do not uninstall Mathematica 5.2 yet :-)
Or am I wrong?

Pavel



From: Bruno Campanini on 23 Jul 2010 07:11
"mathfanda" <KKratky(a)seznam.cz> wrote in message
news:i293uc$mck$1(a)smc.vnet.net...

> Dear Mathematica friends,
>
> the following program runs 4.7 times faster and uses 22.7 times less
> memory
> in Mathematica 5.2 than in Mathematica 7.0.
> Fortunately, it gives the same result.
[...]

My results:

7.0 for Microsoft Windows (64-bit) (November 11, 2008)
c[4]=-(38475/16384)
time=24.217
memory=142.09 MB

Winserver 2008 R2 64-bit, 4Gb RAM

Very bad indeed!

Bruno



From: juan flores on 24 Jul 2010 05:05
On a Mac,
--------
7.0 for Mac OS X x86 (64-bit) (November 11, 2008)
c[4]=-(38475/16384)
time=6.2792
memory=140.069 MB
--------

Results depend on how busy your computer is. The above results were
gotten on a fresh kernel running nothing else, but Mathematica.

Also, TimeUsed[] gives the total number of seconds of CPU time used so
far in the current Mathematica session.

So, results will vary if you run it twice or later on a non-fresh
kernel session.

Just some thoughts.

Juan


On Jul 23, 6:11 am, "Bruno Campanini" <bruno...(a)libero.it> wrote:
> "mathfanda" <KKra...(a)seznam.cz> wrote in message
>
> news:i293uc$mck$1(a)smc.vnet.net...
>
> > Dear Mathematica friends,
>
> > the following program runs 4.7 times faster and uses 22.7 times less
> > memory
> > in Mathematica 5.2 than in Mathematica 7.0.
> > Fortunately, it gives the same result.
>
> [...]
>
> My results:
>
> 7.0 for Microsoft Windows (64-bit) (November 11, 2008)
> c[4]=-(38475/16384)
> time=24.217
> memory=142.09 MB
>
> Winserver 2008 R2 64-bit, 4Gb RAM
>
> Very bad indeed!
>
> Bruno


From: David Skulsky on 24 Jul 2010 05:09
On Jul 22, 2:44 am, mathfanda <KKra...(a)seznam.cz> wrote:
> Dear Mathematica friends,
>
> the following program runs 4.7 times faster and uses 22.7 times less
> memory
> in Mathematica 5.2 than in Mathematica 7.0.
> Fortunately, it gives the same result.
>
> ClearAll["Global`*"];
> c[1] = 2;
> Table[
> a = Sum[c[i] r^i,{i,1,n}] + O[r]^(n+1);
> s = 4(1-1/(1+1/3+r-a*Cos[2t]))//Normal//TrigReduce;
> Table [ b[2i]= Coefficient[s,Cos[2i*t]]/2,{i,n}];
> b[0] = s-2*Sum[b[2i]*Cos[2i*t],{i,n}]//Simplify;
> b[x_?OddQ]=0;
> m=Table[If[i==j,b[0]-(n+1-i)^2,b[Abs[i-j]]],{i,2n+1},{j,2n+1}];
> m=Simplify[m];
> d=Det[m]+O[r]^(n+1)//Simplify//Normal;
> c[n-1]=c[n-1]/.First[Solve[d==0,c[n-1]]];
> ,{n,3,5}];
> Print[$Version];
> Print["c[4]=",c[4]];
> Print["time=",TimeUsed[]];
> Print["memory=",MaxMemoryUsed[]/2^20.," MB"];
>
> Here are the results:
>
> 5.2 for Linux x86 (64 bit) (June 20, 2005)
> 38475
> c[4]=-(-----)
> 16384
> time=0.98
> memory=6.07137 MB
>
> 7.0 for Linux x86 (64-bit) (February 18, 2009)
> 38475
> c[4]=-(-----)
> 16384
> time=4.61
> memory=136.313 MB
>
> The conclusion might be: do not uninstall Mathematica 5.2 yet :-)
> Or am I wrong?
>
> Pavel

TimeUsed[] doesn't seem like the right choice to evaluate speed (it's
the total number of seconds of CPU time used in the current session).
On my machine, the timing result increases every time I run your
example. Why not use AbsoluteTiming instead?

There may be a similar issue with how you're evaluating memory usage,
but I'm not sure.

David

From: Pavel Pokorny on 25 Jul 2010 01:57
A big surprise is that Mathematica 5.2 performs much better than Mathematica 7.0.
The difference becomes more important if you want to compute more
coefficients.
Pavel

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