Why does Jpattern option not improve execution time of ODE solver?

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Francisco de Castro
Francisco de Castro 2018-10-26
编辑： Torsten 2018-10-26
I have a system of ~100 ODEs. They represent interactions between species in an ecosystem. Each species interacts only with a small set of other species, so the matrix of interactions is relatively empty (~65% zeros). I'm trying to improve the speed of integration by using the option 'JPattern' in odeset, as:
options= odeset('JPattern',sparse(A))
where A is a 0 and 1 square matrix in which Aij= 1 means variables i and j interact. However, including 'JPattern' in the options actually increases execution time by a factor of 2: from 4.8 sec. to 9.7 sec. in average. It happens with at least several ODE solvers. Shouldn't the execution time reduce at least somewhat? Does the matrix A need to have some level of 'sparsiness' to improve the speed? Any ideas what am I doing wrong here?
Thanks
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Francisco de Castro
Francisco de Castro 2018-10-26
Yes, of course, I realize 65% is not sparse. However, why should including it as JPattern increase integration time? Shouldn't at least left it unafected? In the near future, I plan to use larger systems, which are more sparse (to > 90% zeros). Will be the JPattern option useless/detrimental in that case too?
Torsten
Torsten 2018-10-26
编辑：Torsten 2018-10-26
This has to be tested for each case separately. No general rule can be given.
Try a really sparse example, e.g. the discretized heat equation in one dimension.

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