Re:Re: Vectorization

• To: mathgroup at smc.vnet.net
• Subject: [mg60820] Re:[mg60653] Re: Vectorization
• From: "Marcelo Mayall" <mmayall at bol.com.br>
• Date: Thu, 29 Sep 2005 05:42:00 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Maxim Rytin,

Although it is not very intuitive, using N[I] instead of I really reduces significantly the computational cost:

In[1]:=
Sin[Table[I Random[],{300000}]]//Timing//First
Sin[Table[N[I] Random[],{300000}]]//Timing//First

Out[1]=
0.766 Second

Out[2]=
0.297 Second

Curious however, that with complex numbers there is almost no difference (in terms of computational cost) among using Table[Sin [...],...] or Sin[Table [...],...].
Will it be due to some limitation of the processor?

In[3]:=
Table[Sin[N[I] Random[]],{300000}]//Timing//First
Sin[Table[N[I] Random[],{300000}]]//Timing//First

Out[3]=
0.328 Second

Out[4]=
0.313 Second

In[5]:=
Table[Sin[Random[]],{1000000}]//Timing//First
Sin[Table[Random[],{1000000}]]//Timing//First

Out[5]=
0.344 Second

Out[6]=
0.203 Second

Thanks,

Marcelo Mayall

---------- Início da mensagem original -----------
De: "Maxim" ab_def at prontomail.com
Para: mathgroup at smc.vnet.net
Data: Fri, 23 Sep 2005 04:19:58 -0400 (EDT)
Assunto: [mg60653] Re: Vectorization
> On Thu, 22 Sep 2005 06:38:28 +0000 (UTC), Marcelo Mayall
> wrote:
>
> > It's possible to initialize a vector starting from an elementary
> > functions:
> >
> > In[1]:=
> > Table[Sin[Random[]],{10000000}]//Timing//First
> >
> > Out[1]=
> > 3.203 Second
> >
> > The same problem can be done a bit more efficiently if the elementary
> > function is applied to the numerical vector:
> >
> > In[2]:=
> > Sin[Table[Random[],{10000000}]]//Timing//First
> >
> > Out[2]=
> > 1.969 Second
> >
> > But why the tendency is opposed when the numbers are complex ? Is this a
> > bug ?
> >
> > In[3]:=
> > Table[Sin[I Random[]],{1000000}]//Timing//First
> > Sin[Table[I Random[],{1000000}]]//Timing//First
> >
> > Out[3]=
> > 2.484 Second
> >
> > Out[4]=
> > 2.656 Second
> >
> >
> > Thanks,
> >
> > Marcelo Mayall
> >
>
> There was a discussion of a similar problem in sci.math.symbolic recently:
> Table[1.*I*Random[], {10^6}] doesn't generate a packed array, and neither
> does Table[Complex[0., 1.]*Random[], {10^6}]. You need to use Table[(0.
> + 1.*I)*Random[], {10^6}] or Table[N[I]*Random[], {10^6}] instead, which
> is not very obvious, as Complex[0., 1.], (0. + 1.*I) and N[I] evaluate to
> the same thing.
>
> What's more, Table[N[Complex[0, 1]]*Random[], {10^6}] doesn't produce a
> packed array either. Apparently some symbolic preprocessing is taking
> place, and the preprocessor is very picky.
>
> Maxim Rytin
> m.r at inbox.ru
>
>

```

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