On 21/06/11 08:58, Anders Logg wrote:
> Thanks for looking into this. So it looks like this will work out
> fine. So are there any objections to changing the VariationalProblem
> (which depends on the order of arguments) to the more explicit
>
> LinearVariationalSolver
> NonlinearVariationalSolver
>
> *solver* classes (instead of problem classes so that it's consistent
> with the way we treat la),
What about also having
LinearVariationalProblem
NonlinearVariationalProblem
as more-or-less containers for defining the problem. Something that
these may be useful for is writing and reading restart files (especially
in parallel),
// Create problem
LinearVariationProblem problem(......);
// Write check point
problem.checkpoint("restart_file.hdf5");
or
File f("restart_file.hdf5");
f << problem;
We could then have a common
VariationalSolver variation_solver(problem, linear_solver, . . . );
interface.
Garth
> and adding on top of this the free function
> solve() as a shortcut:
>
> solve(a == L, ...)
> solve(F == 0, ...)
>
> If not, I can get started on implementing this.
>
> --
> Anders
>
>
> On Tue, Jun 21, 2011 at 09:36:18AM +0200, Martin Sandve Alnæs wrote:
>> On 15 June 2011 13:06, Anders Logg <l...@simula.no> wrote:
>>> Would this work? What it does is to define a simple Equation class
>>> that holds a pair of forms (lhs, rhs) but can still be used for
>>> comparisons.
>>
>> Short story:
>> I'm pretty sure this will work out fine, except that the
>> Equation.__eq__ function must be dropped or changed
>> as explained below.
>>
>>
>> The details:
>>
>>> class Equation:
>>>
>>> def __init__(self, lhs, rhs):
>>> self.lhs = lhs
>>> self.rhs = rhs
>>
>>
>> Allowing the syntax (a == L) == True has severe pitfalls,
>> and I see no use for it. It breaks the Python model.
>> In general, <expression> == True is not good python code,
>> as many boolean expressions are allowed to return non-bool
>> objects. That's why this works out in the first place, so we
>> should respect that :)
>>
>> Anyway, we only need bool(a == L) to say "if a == L" and use
>> a and L in dicts and sets. So this would have to change:
>>
>> (class Equation)
>>> def __eq__(self, other):
>>> if isinstance(other, bool):
>>> return self.__nonzero__() == other
>>> else:
>>> return repr(self) == repr(other)
>>
>> It can eventually be replaced with this:
>>
>> def __eq__(self, other):
>> return isinstance(other, Equation) and\
>> bool(self.lhs == other.lhs) and\
>> bool(self.rhs == other.rhs)
>>
>>
>> As a generic implementation pattern, this should rather
>> use comparison functions from lhs and rhs:
>>
>>> def __nonzero__(self):
>>> return repr(self.lhs) == repr(self.rhs)
>> def __nonzero__(self):
>> return self.lhs.eval_equals(self.rhs) # or another name, maybe
>> __cmp__ == 0
>>
>> But for this particular case, it's probably ok since lhs and rhs are always
>> Form objects, and repr is used in that single __eq__ implementation today.
>>
>> Note that I have only evaluated this for Form/Equation, my conclusion
>> that I guess this is ok does not extend to any other part of the universe...
>> E.g., if we were to use this trick for Expr as well, it could have severe
>> performance penalties, so that's not something to do in a hurry.
>>
>> Martin
>>
>>
>>> class Form:
>>>
>>> def __init__(self, a):
>>> self.a = a
>>>
>>> def __eq__(self, other):
>>> return Equation(self, other)
>>>
>>> def __repr__(self):
>>> return str(self.a)
>>>
>>> f1 = Form(1)
>>> f2 = Form(2)
>>> f3 = Form(1)
>>>
>>> eq = f1 == f2
>>> print eq == False
>>> print eq == True
>>>
>>> if f1 == f2:
>>> print "f1 == f2 is True"
>>>
>>> if f1 == f3:
>>> print "f1 == f3 is True"
>>>
>>>
>>>
>>> On Tue, Jun 14, 2011 at 10:01:47PM +0200, Martin Sandve Alnæs wrote:
>>>> I agree it is pretty in a way, but here comes the showstopper... Sorry! ;)
>>>>
>>>> There can be no ufl.Form.__eq__ implementation
>>>> that does not conform to the Python conventions
>>>> of actually comparing objects and returning
>>>> True or False, because that will break usage
>>>> of Form objects in built in Python data structures.
>>>>
>>>> Martin
>>>>
>>>> On 14 June 2011 21:53, Anders Logg <l...@simula.no> 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"<gn...@cam.ac.uk>:
>>>>>>>>>>>>> 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).
>>>>>
>>>>>
>>>>> _______________________________________________
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>>>
>
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