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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[]}}}
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