Using the Max function in the cost functional

Can you give a small example? The Max function should work in UFL expressions.

Hi Ahmad,

I came across this issue a few times as well. You can build your own max function in ufl with the conditional kewywork:

def max(x, y):
  x = triangle.x[0]
  ufl.conditional(gt(x, y), x, y)

Hope this helps.

Simon

Hi Simon
I just copied your given piece of code and added it to mine , but I still get something like " NameError: global name 'ufl' is not defined.

here is the code I'm using
it is mainly a combination of the examples mentioned in the documentation

from dolfin import *
from dolfin_adjoint import *

# Setup
n = 40
mesh = UnitCircleMesh(n)
V = FunctionSpace(mesh, "CG", 1)

u = Function(V,name="State")
m = Function(V, name="Control")
v = TestFunction(V)

# Run the forward model once to create the simulation record
F = (inner(grad(u), grad(v)) - m*v)*dx
bc = DirichletBC(V, 0.0, "on_boundary")
solve(F == 0, u,bc)

#######################
def max(x, y):
  x = triangle.x[0]
  ufl.conditional(gt(x, y), x, y)
#######################

# The functional of interest is the normed difference between desired
# and simulated temperature profile
x = triangle.x
u_desired = (1-x[0]*x[0]-x[1]*x[1])*x[0]#exp(-1/(1-x[0]*x[0])-1/(1-x[1]*x[1]))
J = Functional(( 0.5*inner(u-u_desired, u-u_desired)+0.1*0.5*inner(m,m)+1/(2*9)*inner(max(0,9*(u-1)),max(0,9*(u-1))) )*dx)

# Run the optimisation
reduced_functional = ReducedFunctional(J, InitialConditionParameter(m, value=m))
# Make sure you have scipy >= 0.11 installed
m_opt = minimize(reduced_functional, method = "L-BFGS-B",
                 tol=2e-08, bounds = (-0.2, 0.2), options = {"disp": True})

###############################################
# desire solution
proj_udes = project(u_desired,V)
plot(u_desired, mesh, interactive=True, title="Desired")
# Actual solution
solve(F == 0, u,bc)
plot(u, interactive=True, title="Actual")
# L1 error
proj_error = project(u-u_desired,V)
plot(proj_error, interactive=True, title="L1-Error")
# Optimal forcing
plot(m_opt, interactive=True, title="Control")

Try adding

import ulf

on the top of your program.

2013/8/1 ahmad ali <email address hidden>:
> Question #233315 on dolfin-adjoint changed:
> https://answers.launchpad.net/dolfin-adjoint/+question/233315
>
> Status: Answered => Open
>
> ahmad ali is still having a problem:
> Hi Simon
> I just copied your given piece of code and added it to mine , but I still get something like " NameError: global name 'ufl' is not defined.
>
>
> here is the code I'm using
> it is mainly a combination of the examples mentioned in the documentation
>
>
> from dolfin import *
> from dolfin_adjoint import *
>
> # Setup
> n = 40
> mesh = UnitCircleMesh(n)
> V = FunctionSpace(mesh, "CG", 1)
>
>
> u = Function(V,name="State")
> m = Function(V, name="Control")
> v = TestFunction(V)
>
> # Run the forward model once to create the simulation record
> F = (inner(grad(u), grad(v)) - m*v)*dx
> bc = DirichletBC(V, 0.0, "on_boundary")
> solve(F == 0, u,bc)
>
> #######################
> def max(x, y):
> x = triangle.x[0]
> ufl.conditional(gt(x, y), x, y)
> #######################
>
> # The functional of interest is the normed difference between desired
> # and simulated temperature profile
> x = triangle.x
> u_desired = (1-x[0]*x[0]-x[1]*x[1])*x[0]#exp(-1/(1-x[0]*x[0])-1/(1-x[1]*x[1]))
> J = Functional(( 0.5*inner(u-u_desired, u-u_desired)+0.1*0.5*inner(m,m)+1/(2*9)*inner(max(0,9*(u-1)),max(0,9*(u-1))) )*dx)
>
> # Run the optimisation
> reduced_functional = ReducedFunctional(J, InitialConditionParameter(m, value=m))
> # Make sure you have scipy >= 0.11 installed
> m_opt = minimize(reduced_functional, method = "L-BFGS-B",
> tol=2e-08, bounds = (-0.2, 0.2), options = {"disp": True})
>
>
> ###############################################
> # desire solution
> proj_udes = project(u_desired,V)
> plot(u_desired, mesh, interactive=True, title="Desired")
> # Actual solution
> solve(F == 0, u,bc)
> plot(u, interactive=True, title="Actual")
> # L1 error
> proj_error = project(u-u_desired,V)
> plot(proj_error, interactive=True, title="L1-Error")
> # Optimal forcing
> plot(m_opt, interactive=True, title="Control")
>
> --
> You received this question notification because you are a member of
> libadjoint developers, which is an answer contact for dolfin-adjoint.

--
Simon Wolfgang Funke

Postdoctoral Research Associate
Imperial College London
Applied Modelling and Computation Group
<email address hidden>

I did as you said , but i got a message ending with

File "/usr/lib/python2.7/dist-packages/ufl/log.py", line 154, in error
    raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Invalid type conversion: <type 'NoneType'> can not be converted to any UFL type.
The representation of the object is:
None

Thanks James Maddison, that solved my question.