human
I am working on the file "Ipopt.ipynb".
The first task is:
Next step:
Rewrite (or extend) the OCP to use interior-point solver in place of the specific SOCP structured solver
Can you write Python code for it?
 Give me a the Python code you requested?
assistant
#Here is the Python code you requested.

from scipy.interpolate import interp1d

class TestClass(OCP):
    """ A very basic vanderpol oscillator for testing OCP solver """

    def __init__(self, mu, x0, xf, tf):
        self.mu = mu
        self.x0 = x0
        self.xf = xf
        self.tf = tf

    def dyn(self, x):
        # returns f,g evaluated at x (vectorized)
        return np.array([x[1],-x[0] + self.mu*(1-x[0]**2)*x[1]]), np.vstack((np.zeros_like(x[0]),np.ones_like(x[0]))).squeeze()

    def dynamics(self, x, t, u):  # integrable function
        f, g = self.dyn(x)
        return f + g*u

    def jac(self, x, *args):
        x1, x2 = x
        shape = [x.shape[0]]
        shape.extend(x.shape)
        A = np.zeros(shape)

        B = np.vstack((np.zeros_like(x1),np.ones_like(x1))).squeeze()

        A[0,1,:] = np.ones_like(x[0])
        A[1,0,:] = -np.ones_like(x[0]) - 2*self.mu*x1*x2
        A[1,1,:] = self.mu*(1-x[0]**2)

        return np.moveaxis(A, -1, 0), np.moveaxis(B, -1, 0)

    def lagrange(self, t, x, u, xr, ur, *args):
        return (np.array(u)+ur)**2
#         return np.array([ self.solver.model.sqrt(ui**2) for ui in (u+ur) ])

    def mayer(self, *args, **kwargs):
        return 0

    def constraints(self, t, x, u, x_ref, u_ref):
        """ Implements all constraints, including:
            boundary conditions
            control constraints
            trust regions
        """
        for xi, x0i in zip(x[0], x_ref[0]):
            self.solver.Equation(xi==0)
            
        for xi, xfi in zip(x[-1], x_ref[-1]):
            self.solver.Equation(xfi+xi==0)

        trust_region = 4
        umax = 3

        for ti, (xi, xr) in enumerate(zip(x, x_ref)):
#             self.solver.Equation( sum((xi - xr)**2) < trust_region**2 )
            self.solver.Equation((u[ti]+u_ref[ti])**2 <= umax**2)
        return 

    def plot(self, T, U, X, J, ti, tcvx):
        for i, xux in enumerate(zip(T, U, X)):

            t, u, xc = xux

            # plt.figure(1)
            # plt.plot(x[0], x[1], label=str(i))
            #...