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 > > >

**References**:**Re: Time needed for calculation***From:*Peter Pein <petsie@dordos.net>