def test_Collocation_2():
# Full 2PBVP test problem
# This is calculating the 4th eigenvalue of Mathieu's Equation
# This problem contains an adjustable parameter.
def odefun(t, X, p, const):
return (X[1], -(p[0] - 2 * 5 * np.cos(2 * t)) * X[0])
def bcfun(t0, X0, q0, tf, Xf, qf, p, ndp, aux):
return (X0[1], Xf[1], X0[0] - 1)
algo = Collocation(odefun, None, bcfun)
solinit = Solution()
solinit.t = np.linspace(0, np.pi, 30)
solinit.y = np.vstack(
(np.cos(4 * solinit.t), -4 * np.sin(4 * solinit.t))).T
solinit.dynamical_parameters = np.array([15])
out = algo.solve(solinit)
assert abs(out.t[-1] - np.pi) < tol
assert abs(out.y[0][0] - 1) < tol
assert abs(out.y[0][1]) < tol
assert abs(out.y[-1][0] - 1) < tol
assert abs(out.y[-1][1]) < tol
assert abs(out.dynamical_parameters[0] - 17.09646175) < tol
def guess_mapper(sol):
n_c = len(constants_of_motion)
if n_c == 0:
return sol
sol_out = Solution()
sol_out.t = copy.copy(sol.t)
sol_out.y = np.array([[fn(*sol.y[0]) for fn in states_2_states_fn]])
sol_out.q = sol.q
if len(quads) > 0:
sol_out.q = -0.0 * np.array([np.ones((len(quads)))])
sol_out.dynamical_parameters = sol.dynamical_parameters
sol_out.dynamical_parameters[-n_c:] = np.array(
[fn(*sol.y[0]) for fn in states_2_constants_fn])
sol_out.nondynamical_parameters = sol.nondynamical_parameters
sol_out.aux = sol.aux
return sol_out
def test_Shooting_3():
# This problem contains a parameter, but it is not explicit in the BCs.
# Since time is buried in the ODEs, this tests if the BVP solver calculates
# sensitivities with respect to parameters.
def odefun(t, X, p, const):
return 1 * p[0]
def bcfun(t0, X0, q0, tf, Xf, qf, p, ndp, aux):
return (X0[0] - 0, Xf[0] - 2)
algo = Shooting(odefun, None, bcfun)
solinit = Solution()
solinit.t = np.linspace(0, 1, 2)
solinit.y = np.array([[0], [0]])
solinit.dynamical_parameters = np.array([1])
out = algo.solve(solinit)
assert abs(out.dynamical_parameters - 2) < tol