Re: Slow odepkg

[Richard Crozier]

 On 16/08/2011 20:19, Jordi Gutiérrez Hermoso wrote:
> On 16 August 2011 07:24, Richard Crozier <address@hidden> wrote:
>> Under the hood, simulink uses the Matlab ode solver functions such as ode45,
>> ode23, ode15s etc. All simulink really does is provide a pretty interface
>> and some handy built-in blocks (such as SimPowerSystems).
>>
>> Octave has equivalents to these ode functions (in an octave-forge package at
>> least) so you can get the same functionality without being locked into
>> simulink if you are willing to invest the time in learning to use these.
>> They are significantly slower implementations in Octave though.
> I like optimising stuff. What's slow? The ode-pkg functions? All of
> them? Do you have some clues on where to speed things up? Some
> benchmarks?
>
> - Jordi G. H.
>

This is based on the benchmarks provided in the odepkg documentation
shown below:

matlab solvers
-----------------------------------------------------------------------------------------
 Solver  RelTol  AbsTol   Init   Mescd    Scd  Steps  Accept  FEval  JEval  
LUdec    Time
-----------------------------------------------------------------------------------------
 ode113  1e-007  1e-007  1e-009   7.57   5.37  24317   21442  45760             
   11.697
  ode23  1e-007  1e-007  1e-009   7.23   5.03  13876   13862  41629             
    2.634
  ode45  1e-007  1e-007  1e-009   7.91   5.70  11017   10412  66103             
    2.994
 ode15s  1e-007  1e-007  1e-009   7.15   4.95    290     273    534      8     
59   0.070
 ode23s  1e-007  1e-007  1e-009   6.24   4.03    702     702   2107    702    
702   0.161
 ode23t  1e-007  1e-007  1e-009   6.00   3.79    892     886   1103      5     
72   0.180
ode23tb  1e-007  1e-007  1e-009   5.85   3.65    735     731   2011      5     
66   0.230
-----------------------------------------------------------------------------------------

odepkg solvers
-----------------------------------------------------------------------------------------
 Solver  RelTol  AbsTol   Init   Mescd    Scd  Steps  Accept  FEval  JEval  
LUdec    Time
-----------------------------------------------------------------------------------------
  ode23   1e-07   1e-07   1e-09   7.86   5.44  17112   13369  51333             
  138.071
  ode45   1e-07   1e-07   1e-09   8.05   5.63   9397    9393  56376             
   92.065
  ode54   1e-07   1e-07   1e-09   8.25   5.83   9300    7758  65093             
   84.319
  ode78   1e-07   1e-07   1e-09   8.54   6.12   7290    6615  94757             
   97.746
  ode2r   1e-07   1e-07   1e-09   7.69   5.27     50      50    849     50     
59   0.624
  ode5r   1e-07   1e-07   1e-09   7.55   5.13     71      71    671     71     
81   0.447
  oders   1e-07   1e-07   1e-09   7.08   4.66    138     138    828    138    
138   0.661
  odesx   1e-07   1e-07   1e-09   6.56   4.13     30      26   1808     26    
205   1.057
 odebda   1e-07   1e-07   1e-09   6.53   4.11    401     400    582     42     
42   0.378
-----------------------------------------------------------------------------------------

Although these are for a non-stiff problem, and I don't see immediately
any comparisons for a stiff problem. There is a test suite of problems I
think provided with odepkg.

I'm afraid I wouldn't know where to start on improving these, I
understand the rough principle of their operation, but I'm really just a
user in this case, and doubt I could improve on the original author's
code. It's also possible, indeed I think likely, that the bottleneck is
not the solvers themselves but the speed of computation for the function
defining the ode since the odepkg functions actually take fewer steps to
solve the problem in these examples. The new profiler might tell us the
answer to this.

Richard


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