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TimeConstrained and returning a partial answer

• To: mathgroup at smc.vnet.net
• Subject: [mg88200] TimeConstrained and returning a partial answer
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 28 Apr 2008 04:38:30 -0400 (EDT)
• Organization: University of Bergen

The following came up on sci.math.symbolic:

Among the examples on the doc page of TimeConstrained there is one where 
a partial (less precise) answer is returned even if the calculation 
cannot be finished within the time constraint.

I was wondering if there is a way to create user-defined functions with 
this behaviour.  I found two relevant functions in the docs: 
AbortProtect and CheckAbort.

Here's a small test program:

AbortProtect@CheckAbort[
   x = 0;
   Do[Pause[.1]; x++, {100}];
   x,
   x]

This program will return an answer even if the calculation is aborted 
with Alt+.  (or the menu item Evaluation -> Abort evaluation).

Now let us try to use it with TimeConstrained:

TimeConstrained[
   AbortProtect@CheckAbort[
     x = 0;
     Do[Pause[.1]; x++, {100}];
     x,
     x],
   1
   ] // AbsoluteTiming

Unfortunately this always runs for 10 full seconds, and then returns 
$Aborted (i.e. the worst possible thing happens: the calculation is not 
stopped after 1 sec, but no answer is returned.)

** Question:  How can this program be modified so that TimeConstrained 
will be able to stop it after 1 sec, and it will still return an answer?


Note:  I experimented a little with the example from the docs, and I 
cannot reproduce the result that is presented there.  If the calculation 
cannot be finished within the time constraint, $Aborted is returned:


In[1]:= Timing[NDSolve[{Derivative[2][x][t] + x[t] == 0, x[0] == 1,
        Derivative[1][x][0] == 0}, x, {t, 0, 50000*Pi},
      MaxSteps -> Infinity]]

Out[1]= {5.578, {{x -> InterpolatingFunction[]}}}

In[2]:= AbsoluteTiming[TimeConstrained[
      NDSolve[{Derivative[2][x][t] + x[t] == 0, x[0] == 1,
          Derivative[1][x][0] == 0}, x, {t, 0, 50000*Pi},
        MaxSteps -> Infinity], 5]]

Out[2]= {5.0625`8.155910029718697, $Aborted}

In[3]:= AbsoluteTiming[TimeConstrained[
      NDSolve[{Derivative[2][x][t] + x[t] == 0, x[0] == 1,
          Derivative[1][x][0] == 0}, x, {t, 0, 50000*Pi},
        MaxSteps -> Infinity], 6]]

Out[3]= {5.984375`8.228563793480708, {{x -> InterpolatingFunction[]}}}