dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Wed, Jun 15, 2011 at 09:19:32AM +0100, Garth N. Wells wrote:
>
>
> On 14/06/11 20:53, Anders Logg wrote:
> > On Tue, Jun 14, 2011 at 09:03:31PM +0200, Marie E. Rognes wrote:
> >> On 06/14/2011 08:35 PM, Garth N. Wells wrote:
> >>>
> >>>
> >>> On 14/06/11 19:24, Anders Logg wrote:
> >>>> On Tue, Jun 14, 2011 at 10:19:20AM -0700, Johan Hake wrote:
> >>>>> On Tuesday June 14 2011 03:33:59 Anders Logg wrote:
> >>>>>> On Tue, Jun 14, 2011 at 09:25:17AM +0100, Garth N. Wells wrote:
> >>>>>>> On 14/06/11 08:53, Anders Logg wrote:
> >>>>>>>> 14 jun 2011 kl. 09:18 skrev "Garth N. Wells"<gnw20@xxxxxxxxx>:
> >>>>>>>>> On 14/06/11 08:03, Marie E. Rognes wrote:
> >>>>>>>>>> On 06/13/2011 11:16 PM, Anders Logg wrote:
> >>>>>>>>>>>>> But while we are heading in that direction, how about
> >>>>>>>>>>>>> abolishing the *Problem class(es) altogether, and just use
> >>>>>>>>>>>>> LinearVariationalSolver and
> >>>>>>>>>>>>> NonlinearVariationalSolver/NewtonSolver taking as input (a,
> >>>>>>>>>>>>> L,
> >>>>>>>>>>>>
> >>>>>>>>>>>> bc)
> >>>>>>>>>>>>
> >>>>>>>>>>>>> and (F, dF, bcs), respectively.
> >>>>>>>>>>>
> >>>>>>>>>>> This will be in line with an old blueprint. We noted some time
> >>>>>>>>>>> ago that problems/solvers are designed differently for linear
> >>>>>>>>>>> systems Ax = b than for variational problems a(u, v) = L(v).
> >>>>>>>>>>> For linear systems, we have solvers while for variational
> >>>>>>>>>>> problems we have both problem and solver classes.
> >>>>>>>>>>>
> >>>>>>>>>>>>> I mean, the main difference lies in how to solve the
> >>>>>>>>>>>>> problems, right?
> >>>>>>>>>>>
> >>>>>>>>>>> It looks like the only property a VariationalProblem has in
> >>>>>>>>>>> addition to (forms, bc) + solver parameters is the parameter
> >>>>>>>>>>> symmetric=true/false.
> >>>>>>>>>>>
> >>>>>>>>>>> If we go this route, we could mimic the design of the linear
> >>>>>>>>>>> algebra solvers and provide two different options, one that
> >>>>>>>>>>> offers more control, solver = KrylovSolver() + solver.solve(),
> >>>>>>>>>>> and one quick option that just calls solve:
> >>>>>>>>>>>
> >>>>>>>>>>> 1. complex option
> >>>>>>>>>>>
> >>>>>>>>>>> solver = LinearVariationalSolver() # which arguments to
> >>>>>>>>>>> constructor? solver.parameters["foo"] = ... u = solver.solve()
> >>>>>>>>>
> >>>>>>>>> I favour this option, but I think that the name
> >>>>>>>>> 'LinearVariationalSolver' is misleading since it's not a
> >>>>>>>>> 'variational solver', but solves variational problems, nor should
> >>>>>>>>> it be confused with a LinearSolver that solves Ax = f.
> >>>>>>>>> LinearVariationalProblem is a better name. For total control, we
> >>>>>>>>> could have a LinearVariationalProblem constructor that accepts a
> >>>>>>>>> GenericLinearSolver as an argument (as the NewtonSolver does).
> >>>>>>>>>
> >>>>>>>>>> For the eigensolvers, all arguments go in the call to solve.
> >>>>>>>>>>
> >>>>>>>>>>> 2. simple option
> >>>>>>>>>>>
> >>>>>>>>>>> u = solve(a, L, bc)
> >>>>>>>>>
> >>>>>>>>> I think that saving one line of code and making the code less
> >>>>>>>>> explicit isn't worthwhile. I can foresee users trying to solve
> >>>>>>>>> nonlinear problems with this.
> >>>>>>>>
> >>>>>>>> With the syntax suggested below it would be easy to check for errors.
> >>>>>>>>
> >>>>>>>>>> Just for linears?
> >>>>>>>>>>
> >>>>>>>>>>> 3. very tempting option (simple to implement in both C++ and
> >>>>>>>>>>> Python)
> >>>>>>>>>>>
> >>>>>>>>>>> u = solve(a == L, bc)    # linear u = solve(F == 0, J, bc) #
> >>>>>>>>>>> nonlinear
> >>>>>>>>>
> >>>>>>>>> I don't like this on the same grounds that I don't like the
> >>>>>>>>> present design. Also, I don't follow the above syntax
> >>>>>>>>
> >>>>>>>> I'm not surprised you don't like it. But don't understand why. It's
> >>>>>>>> very clear which is linear and which is nonlinear. And it would be
> >>>>>>>> easy to check for errors. And it would just be a thin layer on top of
> >>>>>>>> the very explicit linear/nonlinear solver classes. And it would
> >>>>>>>> follow the exact same design as for la with solver classes plus a
> >>>>>>>> quick access solve function.
> >>>>>>>
> >>>>>>> Is not clear to me - possibly because, as I wrote above, I don't
> >>>>>>> understand the syntax. What does the '==' mean?
> >>>>>>
> >>>>>> Here's how I see it:
> >>>>>>
> >>>>>> 1. Linear problems
> >>>>>>
> >>>>>>   solve(a == L, bc)
> >>>>>>
> >>>>>>   solve the linear variational problem a = L subject to bc
> >>>>>>
> >>>>>> 2. Nonlinear problems
> >>>>>>
> >>>>>>   solve(F == 0, bc)
> >>>>>>
> >>>>>>   solve the nonlinear variational problem F = 0 subject to bc
> >>>>>>
> >>>>>> It would be easy to in the first case check that the first operand (a)
> >>>>>> is a bilinear form and the second (L) is a linear form.
> >>>>>>
> >>>>>> And it would be easy to check in the second case that the first
> >>>>>> operand (F) is a linear form and the second is an integer that must be
> >>>>>> zero.
> >>>>>>
> >>>>>> In both cases one can print an informative error message and catch any
> >>>>>> pitfalls.
> >>>>>>
> >>>>>> The nonlinear case would in C++ accept an additional argument J for
> >>>>>> the Jacobian (and in Python an optional additional argument):
> >>>>>>
> >>>>>>   solve(F == 0, J, bc);
> >>>>>>
> >>>>>> The comparison operator == would for a == L return an object of class
> >>>>>> LinearVariationalProblem and in the second case
> >>>>>> NonlinearVariationalProblem. These two would just be simple classes
> >>>>>> holding shared pointers to the forms. Then we can overload solve() to
> >>>>>> take either of the two and pass the call on to either
> >>>>>> LinearVariationalSolver or NonlinearVariationalSolver.
> >>>>>>
> >>>>>> I'm starting to think this would be an ideal solution. It's compact,
> >>>>>> fairly intuitive, and it's possible to catch errors.
> >>>>>>
> >>>>>> The only problem I see is overloading operator== in Python if that
> >>>>>> has implications for UFL that Martin objects to... :-)
> >>>>>
> >>>>> Wow, you really like magical syntaxes ;)
> >>>>
> >>>> Yes, a pretty syntax has been a priority for me ever since we
> >>>> started. I think it is worth a lot.
> >>>>
> >>>
> >>> Magic and pretty are not the same thing.
> >
> > That's true, but some magic is usually required to make pretty.
> >
> > Being able to write dot(grad(u), grad(v))*dx is also a bit magic.
> > The step from there to solve(a == L) is short.
> >
> >>>>> The problem with this syntax is that who on earth would expect a
> >>>>> VariationalProblem to be the result of an == operator...
> >>>>
> >>>> I don't think that's an issue. Figuring out how to solve variational
> >>>> problems is not something one picks up by reading the Programmer's
> >>>> Reference. It's something that will be stated on the first page of any
> >>>> FEniCS tutorial or user manual.
> >>>>
> >>>> I think the solve(a == L) is the one missing piece to make the form
> >>>> language complete. We have all the nice syntax for expressing forms in
> >>>> a declarative way, but then it ends with
> >>>>
> >>>> problem = VariationalProblem(a, L)
> >>>> problem.solve()
> >>>>
> >>>> which I think looks ugly. It's not as extreme as this example taken
> >>> >from cppunit, but it follows the same "create object, call method on
> >>>> object" paradigm which I think is ugly:
> >>>>
> >>>>   TestResult result;
> >>>>   TestResultCollector collected_results;
> >>>>   result.addListener(&collected_results);
> >>>>   TestRunner runner;
> >>>>   runner.addTest(CppUnit::TestFactoryRegistry::getRegistry().makeTest());
> >>>>   runner.run(result);
> >>>>   CompilerOutputter outputter(&collected_results, std::cerr);
> >>>>   outputter.write ();
> >>>>
> >>>>> I see the distinction between FEniCS developers who have programming versus
> >>>>> math in mind when designing the api ;)
> >>>>
> >>>> It's always been one of the top priorities in our work on FEniCS to
> >>>> build an API with the highest possible level of mathematical
> >>>> expressiveness to the API. That sometimes leads to challenges, like
> >>>> needing to develop a special form language, form compilers, JIT
> >>>> compilation, the Expression class etc, but that's the sort of thing
> >>>> we're pretty good at and one of the main selling points of FEniCS.
> >>>>
> >>>
> >>> This is an exaggeration to me. The code
> >>>
> >>>   problem = [Linear]VariationalProblem(a, L)
> >>>   u = problem.solve()
> >>>
> >>> is compact and explicit. It's a stretch to call it ugly.
> >
> > Yes, of course it's a stretch. It's not very ugly, but enough to
> > bother me.
> >
> >>>>> Also __eq__ is already used in ufl.Form to compare two forms.
> >>>>
> >>>> I think it would be worth replacing the use of form0 == form1 by
> >>>> repr(form0) == repr(form1) in UFL to be able to use __eq__ for this:
> >>>>
> >>>> class Equation:
> >>>>   def __init__(self, lhs, rhs):
> >>>>       self.lhs = lhs
> >>>>       self.rhs = rhs
> >>>>
> >>>> class Form:
> >>>>
> >>>>   def __eq__(self, other):
> >>>>       return Equation(self, other)
> >>>>
> >>>> I understand there are other priorities, and others don't care as much
> >>>> as I do about how fancy we can make the DOLFIN Python and C++ interface,
> >>>> but I think this would make a nice final touch to the interface.
> >>>>
> >>>
> >>> I don't see value in it. In fact the opposite - it introduces complexity
> >>> and a degree of ambiguity.
> >
> > Complexity yes (but not much, it would require say around 50-100
> > additional lines of code that I will gladly contribute), but I don't
> > think it's ambiguous. We could perform very rigorous and helpful
> > checks on the input arguments.
> >
> >> Evidently, we all see things differently. I fully support Anders in
> >> that mathematical expressiveness is one of the key features of
> >> FEniCS, and I think that without pushing these types of boundaries
> >> with regard to the language, it will end up as yet another finite
> >> element library.
> >>
> >> Could we compromise on having the two versions, one explicit (based
> >> on LinearVariational[Problem|Solver] or something of the kind) and
> >> one terse (based on solve(x == y)) ?
> >
> > That's what I'm suggesting. The solve(x == y) would just rely on the
> > more "explicit" version and do
> >
> >   <lots of checks>
> >   LinearVariationalSolver solver(x, y, ...);
> >   solver.solve(u);
> >
> > So in essence what I'm asking for is please let me add that tiny layer
> > on top of what we already have + remove the Problem classes (replaced
> > by the Solver classes).
> >
>
> It seems that we (almost?) all agree to add to the C++ side:
>
>   LinearVariationalProblem
>
>   NonlinearVariationalProblem

Not yet, I'm still thinking this through. Martin is making a good
point that we need to differentiate between problems and solvers.
I'll comment more later when I've thought this through.

--
Anders


> I think that 'FooVariationalProblem' is probably a better name than
> 'FooVariationalSolver'. Could 'variational' (minimisation) and 'solver'
> imply some abstract linear algebra problem? Most accurate is probably
> 'FooVariationalProblemSolver', but it's a bit long.
>
> On the Python side, I don't mind others trying something fancy, but I'll
> reserve my judgement ;).
>
> Garth
>
>
>
>
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