human
Write me a code to 3 given the following:
3. Affine decomposition
In order to obtain an affine decomposition, we proceed as in the previous tutorial and recast the problem on a fixed, parameter independent, reference domain $\Omega$. As reference domain which choose the one characterized by $\mu_0 = 1$ which we generate through the generate_mesh notebook provided in the data folder.
As in the previous tutorial, we pull back the problem to the reference domain $\Omega$."
Please write code following the instructions in jupyter notebook style.
assistant
#Here is code to 3.

@SCM()
@PullBackFormsToReferenceDomain()
@ShapeParametrization(
    ("x[0]", "x[1]"),  # subdomain 1
    ("mu[0]*(x[0] - 1) + 1", "x[1]"),  # subdomain 2
)
class Graetz(EllipticCoerciveProblem):

    # Default initialization of members
    @generate_function_space_for_stability_factor
    def __init__(self, V, **kwargs):
        # Call the standard initialization
        EllipticCoerciveProblem.__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.u = TrialFunction(V)
        self.v = TestFunction(V)
        self.dx = Measure("dx")(subdomain_data=subdomains)
        self.ds = Measure("ds")(subdomain_data=boundaries)
        # Store the velocity expression
        self.vel = Expression("x[1]*(1-x[1])", element=self.V.ufl_element())
        # Customize eigen solver parameters
        self._eigen_solver_parameters.update({
            "bounding_box_minimum": {
                "problem_type": "gen_hermitian", "spectral_transform": "shift-and-invert",
                "spectral_shift": 1.e-5, "linear_solver": "mumps"
            },
            "bounding_box_maximum": {
                "problem_type": "gen_hermitian", "spectral_transform": "shift-and-invert",
                "spectral_shift": 1.e5, "linear_solver": "mumps"
            },
            "stability_factor": {
                "problem_type": "gen_hermitian", "spectral_transform": "shift-and-invert",
                "spectral_shift": 1.e-5, "linear_solver": "mumps"
            }
        })

    # Return custom problem name
    def name(self):
        return "Graetz2"

    # Return theta multiplicative terms of the affine expansion of the problem.
    @compute_theta_for_stability_factor
    def compute_theta(self, term):
        mu = self.mu
        if term == "a":
            theta_a0 = mu[1]
            theta_a1 = 1.0
            return...