[SciPy-Dev] Updates to VODE and ZVODE solvers in single step mode

[Benny Malengier]

2015-03-02 9:59 GMT+01:00 Paul Nation <nonhermitian at gmail.com>:

> The zvode docs say that mode 5 returns the exact time answer and not an
> interpolated result.
>
> Paul
>

Yes, I did not say mode 5 was not like that. I noted that the other mode
also give you a good value at the wanted output time, only interpolated. In
practise this would not be very different.

Changing RHS as you have is a valid use of stop time. Just being able to
stop on stop time is quite limiting however, more complicated solver have
rootfinding, and can stop on every root found (stoptime is just root of
t-stoptime).

As to ZVODE, as far as I'm aware, nobody developed this further? One should
take real and imaginary and convert to a CVODE problem I believe, but I
never did complex problems. I do see http://netlib.sandia.gov/ode/zvode.f
mentions such an approach:

or a complex stiff ODE system in which f is not analytic,
ZVODE is likely to have convergence
failures, and for this problem one should instead use DVODE on the
equivalent real system (in the real and imaginary parts of y).

I don't mind somebody adding extra capabilities to VODE/ZVODE in scipy, if
you do a nice PR it probably would be accepted if there is no influence on
old code.
A somewhat better approach in my view would be to deprecate it and convert
to code which still sees releases. The API would be more complex though ...
That has been discussed before though with no movement, people seem hapy to
use ode.integrate for simple things, and then use other bindings when the
problem outgrows VODE.

Note that next release of the Sundials suite should be in the coming
months. Over the years, one can assume bugs in VODE/ZVODE have been fixed
in CVODE only.

Benny



>
>
> On Mar 2, 2015, at 17:43, Benny Malengier <benny.malengier at gmail.com>
> wrote:
>
>
>
> 2015-03-02 6:49 GMT+01:00 Paul Nation <nonhermitian at gmail.com>:
>
>> When using the single-step mode in either the VODE or ZVODE ode solver,
>> the default mode (2) called in:
>>
>>     def step(self, *args):
>>         itask = self.call_args[2]
>>         self.call_args[2] = 2 # Step mode is here
>>         r = self.run(*args)
>>         self.call_args[2] = itask
>>         return r
>>
>> results in taking a single step that (typically) goes beyond the output
>> time requested in the solver.  When doing, for example, monte carlo
>> algorithms, this leads to a big performance hit because one must take a
>> step back, reset the solver  and then use the normal mode to go to the
>> requested stop time.  Instead, these solvers support a mode (5) that will
>> never step beyond the end time.  The modified step function is in that case:
>>
>
> You do obtain the output at the requested time though, it is only an
> interpolated value of the actually computed solutions.
> So, the only reason you should do above is if something is happening at a
> certain time and you want to change data or so. You mention monte carlo,
> but I don't see how that is related to such a usecase in general. I suppose
> in your application probably yes, but in general MC does not need this
>
> The docs say only to use endtime if you have changing RHS or Jacobian, and
> to otherwise not try to outsmart the solver, as the solver needs extra work
> in case you set the endtime.
>
> Note that (Z)VODE was replaced by CVODE by the authors of VODE, which has
> many improvements and several python bindings, all of which expose setting
> a stop time. In my view, VODE is only present in scipy as a first attempt
> solver, to be replaced by more modern solvers for heavy lifting.
>
> Benny
>
>
>>
>> def step(self, *args):
>>         itask = self.call_args[2]
>>         self.rwork[0] = args[4]    #Set to stop time
>>         self.call_args[2] = 5       #Set single step mode to stop at
>> requested time.
>>         r = self.run(*args)
>>         self.call_args[2] = itask
>>         return r
>>
>> Currently in order to implement this, one needs to create their own ODE
>> integrator subclass of VODE or ZVODE, overload the step function, then
>> create an ode instance and then finally add the custom integrator using
>> ode._integrator.  I think supporting both options natively would be a nice
>> thing to have in SciPy.
>>
>> In addition, often it is not necessary to do a full reset of the ode
>> solver using ode.reset().  Often times one just needs to change the RHS
>> vector (and possibly the time) and set the flag for the solver to start
>> anew (ode._integrator.call_args[3] = 1).  This to results in a large
>> performance benefit for things like monte carlo solving. Right now I need
>> to call
>>
>> ode._y = new_vec
>> ode._integrator.call_args[3] = 1
>>
>> when I want to accomplish this.  Adding support for a “fast reset” might
>> also be a good thing to have in SciPy.
>>
>> All of the code to accomplish such things are already being used in the
>> QuTiP monte carlo solver(
>> https://github.com/qutip/qutip/blob/master/qutip/mcsolve.py) and would
>> therefore be fairly painless to add to SciPy.
>>
>> Best regards,
>>
>> Paul
>>
>>
>>
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>>
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