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Re: Memory problem using NDSolve in For Loop

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83363] Re: Memory problem using NDSolve in For Loop
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Sun, 18 Nov 2007 04:51:12 -0500 (EST)
  • References: <fhmhrn$atl$1@smc.vnet.net>

DBK wrote:
> I am running a number of simulations (sim) with different initial
> conditions (ic). The code I have written runs fine until I increase
> the number of simulations. In my "For" loop below, I thought that
> previous solutions (sol[sim]) were being cleared but this obviously is
> not happening. How do I clear sol and reduce my memory usage? Sorry if
> this is pretty basic stuff.
> 
> For[sim = 1, sim < 2500, sim = sim + 1,
>   sol[sim] =
>    NDSolve[{equations, a[0] == 10, b[0] == .45, c[0] == .30,
>      d[0] == .40, e[0] == ic[[sim, 1]], f[0] == ic[[sim, 2]]}, {a, b,
>      c, d, e, f}, {t, 0, time}, MaxSteps -> Infinity,
>     WorkingPrecision -> 5, MaxStepSize -> 0.10];
>   AppendTo[outlist, {ic[[sim, 1]], ic[[sim, 2]], e[time] /. sol[sim],
>     f[time] /. sol[sim]}]];
> 

Never use For[] for simple looping in Mathematica.  Use Do[] instead. 
Instead of

For[sim = 1, sim < 2500, sim = sim + 1,
   ...]

use

Do[ ... , {sim, 1, 2499}]

or simply

Do[ ... , {sim, 2499}]

Whenever you need to collect the results into a list, use Table[] 
instead of Do[].

This is a direct transformation of your program:

Table[
  With[{sol =
     NDSolve[{equations, a[0] == 10, b[0] == .45, c[0] == .30,
       d[0] == .40, e[0] == ic[[sim, 1]], f[0] == ic[[sim, 2]]}, {a, b,
        c, d, e, f}, {t, 0, time}, MaxSteps -> Infinity,
      WorkingPrecision -> 5, MaxStepSize -> 0.10]},
   {ic[[sim, 1]], ic[[sim, 2]], e[time] /. sol, f[time] /. sol}],
  {sim, 2500}]

With[] is used to create local constants ('sol' in this case), but it 
not strictly necessary here since you could just use
{ic[[sim, 1]], ic[[sim, 2]], e[time], f[time]} /. NDsolve[...]
instead of

sol = NDSolve[ ... ]
{ic[[sim, 1]], ic[[sim, 2]], e[time] /. sol, f[time] /. sol}

It can probably be made even more compact, but I cannot tell without 
knowing the exact structure of 'ic'.  You could try something like the 
following (untested):

({#1, #2, e[time], f[time]} /.
     NDSolve[{equations, a[0] == 10, b[0] == .45, c[0] == .30,
       d[0] == .40, e[0] == #1, f[0] == #2}, {a, b, c, d, e, f}, {t, 0,
        time}, MaxSteps -> Infinity, WorkingPrecision -> 5,
      MaxStepSize -> 0.10]) & @@@ ic

Szabolcs


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