human
Can you provide a the Python program you requested given the following:
3. Affine Decomposition
For this problem the affine decomposition is straightforward:
$$a(u,v;\boldsymbol{\mu})=\underbrace{1}{\Theta^{a}_0(\boldsymbol{\mu})}\underbrace{\int{\Omega}\nabla u \cdot \nabla v \ d\boldsymbol{x}}{a_0(u,v)},$$
$$c(u,v;\boldsymbol{\mu})=\underbrace{\mu_0}{\Theta^{c}0(\boldsymbol{\mu})}\underbrace{\int{\Omega}\frac{1}{\mu_1}\big(\exp{\mu_1u} - 1\big)v \ d\boldsymbol{x}}{c_0(u,v)},$$
$$f(v.
\boldsymbol{\mu}) = \underbrace{100}{\Theta^{f}0(\boldsymbol{\mu})} \underbrace{\int{\Omega}\sin(2\pi x_0)cos(2\pi x_1)v \ d\boldsymbol{x}}{f_0(v)}.$$
We will implement the numerical discretization of the problem in the class
class NonlinearElliptic(NonlinearEllipticProblem):
by specifying the coefficients $\Theta^{a}(\boldsymbol{\mu})$, $\Theta^{c}_(\boldsymbol{\mu})$ and $\Theta^{f}(\boldsymbol{\mu})$ in the method
def compute_theta(self, term):
and the bilinear forms $a_(u, v)$, $c(u, v)$ and linear forms $f_(v)$ in
def assemble_operator(self, term):
assistant
#Here is the Python program you requested.
@EIM("online")
@ExactParametrizedFunctions("offline")
class NonlinearElliptic(NonlinearEllipticProblem):

    # Default initialization of members
    def __init__(self, V, **kwargs):
        # Call the standard initialization
        NonlinearEllipticProblem.__init__(self, V, **kwargs)
        # ... and also store FEniCS data structures for assembly
        assert "subdomains" in kwargs
        assert "boundaries" in kwargs
        self.subdomains, self.boundaries = kwargs["subdomains"], kwargs["boundaries"]
        self.du = TrialFunction(V)
        self.u = self._solution
        self.v = TestFunction(V)
        self.dx = Measure("dx")(subdomain_data=self.subdomains)
        self.ds = Measure("ds")(subdomain_data=self.boundaries)
        # Store the forcing term expression
        self.f = Expression("sin(2*pi*x[0])*sin(2*pi*x[1])", element=self.V.ufl_element())
        # Customize nonlinear solver parameters
        self._nonlinear_solver_parameters.update({
            "linear_solver": "mumps",
            "maximum_iterations": 20,
            "report": True
        })

    # Return custom problem name
    def name(self):
        return "NonlinearEllipticEIM"

    # Return theta multiplicative terms of the affine expansion of the problem.
    @compute_theta_for_derivatives
    def compute_theta(self, term):
        mu = self.mu
        if term == "a":
            theta_a0 = 1.
            return (theta_a0,)
        elif term == "c":
            theta_c0 = mu[0]
            return (theta_c0,)
        elif term == "f":
            theta_f0 = 100.
            return (theta_f0,)
        elif term == "s":
            theta_s0 = 1.0
            return (theta_s0,)
        else:
            raise ValueError("Invalid term for compute_theta().")

    # Return forms resulting from the discretization of the affine expansion of the problem operators.
    def assemble_operator(self, term):
        v = self.v
        dx = self.dx
        if term == "a":
            du = self.du
            a0 = inner(grad(du), grad(v))...