# Generating a Random Potential **URL:** \ **Category:** variational formulation\ **Created:** [November 8, 2019, 12:45am UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856 "2019-11-08T00:45:02Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![abelthayil](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@abelthayil](https://fenicsproject.discourse.group/u/abelthayil)\ **Post date:** [November 8, 2019, 12:45am UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/1 "2019-11-08T00:45:02Z")
I’m trying to solve the following equation (-\nabla ^2+ V)u = 1 , where V is a random potential. This random potential takes different random values uniformly, say from 0 to N on different nodes. I can solve the problem when I have a simple expression for V = x^2 + y^2 as follows ``` mesh = UnitSquareMesh(8,8) V = FunctionSpace(mesh, 'P', 1) # Define boundary condition u_D = Expression('0', degree=0) def boundary(x, on_boundary): return on_boundary bc = DirichletBC(V, u_D, boundary) potential = Expression('x[0]*x[0] + x[1]*x[1]', element = V.ufl_element()) # Define variational problem u = TrialFunction(V) v = TestFunction(V) f = Constant(1.0) a = dot(grad(u), grad(v))*dx a = (inner(grad(u), grad(v)) \ + potential*u*v)*dx L = f*v*dx # Compute solution u = Function(V) solve(a == L, u, bc) ``` How should I go about creating a subclass for Expression that can implement a random potential on my mesh? ---
**Author:** ![causem](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@causem](https://fenicsproject.discourse.group/u/causem)\ **Post date:** [November 8, 2019, 10:20am UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/2 "2019-11-08T10:20:09Z")
Hi @abelthayil, you might have a look at the Cahn-Hilliard demo ([https://fenicsproject.org/docs/dolfin/1.6.0/python/demo/documented/cahn-hilliard/python/documentation.html](https://fenicsproject.org/docs/dolfin/1.6.0/python/demo/documented/cahn-hilliard/python/documentation.html)). There the initial condition is implemented by a subclass of Expression with random values. ---
**Author:** ![abelthayil](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@abelthayil](https://fenicsproject.discourse.group/u/abelthayil)\ **Post date:** [November 8, 2019, 3:32pm UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/3 "2019-11-08T15:32:20Z")
Thank you for your reply. When I try to implement a sub class inspired by the example shared above as follows: ``` # Class representing the random potential class RandomPotential(Expression): def __init__ (self): random.seed(2) def eval(self, values, x): values[0] = random.randint(5) def value_shape(self): return (0,) ``` I get the following error when I call `potential = RandomPotential()` `RecursionError: maximum recursion depth exceeded in comparison` ---
**Author:** ![causem](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@causem](https://fenicsproject.discourse.group/u/causem)\ **Post date:** [November 8, 2019, 5:07pm UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/4 "2019-11-08T17:07:55Z")
Hi @abelthayil, I can not reproduce your error, but the line values[0] = random.randint(5) seems suspicious to me. I think you need to give two arguments to random.randint(a, b)… And shouldn’t the function value\_shape return (1,)? ---
**Author:** ![abelthayil](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@abelthayil](https://fenicsproject.discourse.group/u/abelthayil)\ **Post date:** [November 10, 2019, 9:57am UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/5 "2019-11-10T09:57:27Z")
Hello @causem, Sorry, the error wasn’t coming from `potential = RandomPotential()` but instead when I try to evaluate ``` a = (inner(grad(u), grad(v)) \ + potential*u*v)*dx ``` Here is the complete error statement: ``` RecursionError Traceback (most recent call last) in 8 f = Constant(1.0) 9 a = (inner(grad(u), grad(v)) \ ---> 10 + potential*u*v)*dx 11 # L = f*v*dx 12 ~/anaconda3/envs/fenicsproject/lib/python3.7/site-packages/ufl/exproperators.py in _mul(self, o) 191 return NotImplemented 192 o = as_ufl(o) --> 193 return _mult(self, o) 194 195 ~/anaconda3/envs/fenicsproject/lib/python3.7/site-packages/ufl/exproperators.py in _mult(a, b) 122 # - matrix-matrix (A*B, M*grad(u)) => A . B 123 # - matrix-vector (A*v) => A . v --> 124 s1, s2 = a.ufl_shape, b.ufl_shape 125 r1, r2 = len(s1), len(s2) 126 ~/anaconda3/envs/fenicsproject/lib/python3.7/site-packages/ufl/coefficient.py in ufl_shape(self) 71 def ufl_shape(self): 72 "Return the associated UFL shape." ---> 73 return self._ufl_shape 74 75 def ufl_function_space(self): ~/anaconda3/envs/fenicsproject/lib/python3.7/site-packages/dolfin/function/expression.py in __getattr__ (self, name) 430 return self._parameters 431 else: --> 432 return self._parameters[name] 433 434 def __setattr__ (self, name, value): ... last 1 frames repeated, from the frame below ... ~/anaconda3/envs/fenicsproject/lib/python3.7/site-packages/dolfin/function/expression.py in __getattr__ (self, name) 430 return self._parameters 431 else: --> 432 return self._parameters[name] 433 434 def __setattr__ (self, name, value): RecursionError: maximum recursion depth exceeded in comparison ``` To address your concerns, `randint` defaults a to 0 if there is only one argument. I’ve tried with shape (1,) and the error persists so I doubt that’s the issue. Thanks again! ---
**Author:** ![causem](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@causem](https://fenicsproject.discourse.group/u/causem)\ **Post date:** [November 10, 2019, 1:12pm UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/6 "2019-11-10T13:12:29Z")
Hi @abelthayil, I think there has been a change in the way of defining custom Expressions, the Parent class now is UserExpression (instead of Expression). So the RandomPotential would then be: ``` class RandomPotential(UserExpression): def __init__ (self, **kwargs): random.seed(2 + MPI.rank(MPI.comm_world) ) super(). __init__ (**kwargs) def eval(self, values, x): values[0] = random.randint(0,5) def value_shape(self): return () ``` Sorry for pointing you to the outdated example! ---
**Author:** ![abelthayil](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@abelthayil](https://fenicsproject.discourse.group/u/abelthayil)\ **Post date:** [November 10, 2019, 5:56pm UTC](https://fenicsproject.discourse.group/t/generating-a-random-potential/1856/7 "2019-11-10T17:56:12Z")
Thank you, this seems to work now!