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MathGroup Archive 2005

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Re: Re: Time needed for calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62477] Re: [mg62453] Re: Time needed for calculation
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Fri, 25 Nov 2005 02:25:36 -0500 (EST)
  • References: <dm1b2d$ie0$1@smc.vnet.net> <200511241133.GAA29338@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Peter Pein wrote:

>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.
>  
>
But I have found instances where the notebook becomes corrupted. 
Especially when the code involves graphics

Pratik

>Rumors were afloat, some companies use their computers 24 hours/day ;-)
>
>Regards,
>   Peter
>
>  
>


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