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Re: Time needed for calculation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62453] Re: Time needed for calculation
*From*: Peter Pein <petsie at dordos.net>
*Date*: Thu, 24 Nov 2005 06:33:53 -0500 (EST)
*References*: <dm1b2d$ie0$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
JikaiRF at aol.com schrieb:
> Dear Sirs,
> I have some questions about how long a computer can calculate, without
> damages on hard wear.
> More specifically speaking, I intend to depict trajectories on (k, c) axis,
> which are derived from programming on Mathematica.
> My program is as follows:
>
> << Graphics`ImplicitPlot`
> L = 48;
>
> a = 0.1;
>
> A = 1;
>
> r = 0.1;
>
> t = 0.046296296296296294`;
>
> ImplicitPlot[A r L (1 - a)((1 -t) c k^a == (a+(1-a)(1- t)) L^2 (1-a)^2 (1- t
> )^3 k^(3a-1)
> +L(1-a) c (1- t) (-A(a+(1-a)(1- t))(2- t)-(1-a)(1- t)^2
> +A a(1- t)) k^(2a-1)
> +A c^2 (A(a+(1-a)(1- t))+(1-a)(1- t) -A a(1- t)) k^(a-1)
> +A^2 r c^2, {k, 0.8, 1.5}]
>
> This program seems to work well. However, I cannot obtain the curve which
> should be derived from the above program, though my computer continues to
> calculate more than fifteen minutes.
>
> I would like to know how long a computer can calculate without damages on
> hardware, and additionally how long it takes to obtain the required curve based
> on my computer.
> Especially, my computer is PowerBook G4 with 1.5 GHz processor.
>
> Sincerely,
> Fujio Takata.
>
>
Hello,
when you specify only one range in ImplicitPlot, Mathematica tries to
solve the equation before plotting. When you give the ranges of k _and_
c, then another Algorithm will be used. I'm afraid, Mathematica tries to
solve w.r.t. k. Otherwise the answer should come almost instantly.
In[1]:= L = 48; a = 1/10; A = 1; r = 1/10; t = 5/108;
eqn = FullSimplify[
A*r*L*(1 - a)*(1 - t)*c*k^a ==
(a + (1 - a)*(1 - t))*L^2*(1 - a)^2*(1 - t)^3*k^(3*a - 1) +
L*(1 - a)*c*(1 - t)*((-A)*(a + (1 - a)*(1 - t))*(2 - t) -
(1 - a)*(1 - t)^2 + A*a*(1 - t))*k^(2*a - 1) +
A*c^2*(A*(a + (1 - a)*(1 - t)) + (1 - a)*(1 - t) -
A*a*(1 - t))*k^(a - 1) + A^2*r*c^2,
k > 0]
Out[2]=
103*c*(16819*k^(1/10) + 648*k) ==
15*c^2*(1859 + 108*k^(9/10)) + 25132721*k^(1/5)
In[3]:=
First[Timing[ImplicitPlot[eqn, {k, 0.8, 1.2}, {c, 0, 50},
PlotPoints -> 300, ImageSize -> 500, AspectRatio ->
GoldenRatio - 1]]]
[plot omitted]
Out[3]= 0.234*Second
And don't be afraid; if you did not overclock your hardware,
long-lasting calculations will not do any harm to your machine.
Rumors were afloat, some companies use their computers 24 hours/day ;-)
Regards,
Peter
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