dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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).

--
Anders