[firedrake] Problem with Jacobian

[Stephan Kramer]

On 05/11/15 10:08, Lawrence Mitchell wrote:
>
>> On 5 Nov 2015, at 09:49, Buesing, Henrik <HBuesing at eonerc.rwth-aachen.de> wrote:
>>
>> Dear all,
>>
>> I’m having a variable Sw, which I calculate pointwise in a routine calc_Sw (see attachment). This variable depends on my primary unknown h: Sw = (h-hn)/(hw-hn) (hn,hw known values).
>>
>> But now it seems like automatic differentiation for this routine does not work. I’m getting zero entries for the Jacobian, whereas d(Sw)/dh = 1.0 should hold.
>
> Yes, this is because the AD doesn't know about the relationship between Sw and dh.  UFL has a facility for this, but I notice we don't expose it in firedrake (however, it is straightforward to do):
>
>
> We want
>
> derivative(F, u)
>
> But F contains a coefficient, S, whose derivative wrt u is 1.0 (however, they are not symbolically related in a way UFL understands).  So we build a mapping from this coefficient to its derivative wrt u:
>
> coefficient_derivatives = {S: 1.0}
>
> and then pass this additional information to the derivative call.
>
> derivative(F, u, coefficient_derivatives=coefficient_derivatives)
>
> Firedrake uses the UFL derivative function, but does not expose this extra argument in the interface.  It is straightforward to alter the definition in firedrake/ufl_expr.py to take this extra argument and pass it through.  If this works for you, do you want to propose a patch that adds this functionality?
>
> Cheers,
>
> Lawrence
>

Are you sure the problem isn't that he needs bounds for his solve? 
AFAICS dS/dh=0 for h<hw or h>hn. Otherwise shouldn't rewriting this with 
conditionals have worked? Henrik, I presume you are looking for a 
solution hw<h<hn ?

Cheers
Stephan