def test_spbvp_1():
# Full 2PBVP test problem
# This is the simplest BVP
def odefun(X, u, p, const):
return X[1], -abs(X[0])
def bcfun(X0, q0, u0, Xf, qf, uf, p, ndp, const):
return X0[0], Xf[0] + 2
algo = spbvp(odefun, None, bcfun)
solinit = Trajectory()
solinit.t = np.linspace(0, 4, 4)
solinit.y = np.array([[0, 1], [0, 1], [0, 1], [0, 1]])
solinit.const = np.array([])
out = algo.solve(solinit)['sol']
assert out.y[0][0] < tol
assert out.y[0][1] - 2.06641646 < tol
assert out.y[-1][0] + 2 < tol
assert out.y[-1][1] + 2.87588998 < tol
assert out.t[-1] - 4 < tol
assert abs(out.y[0][1] - solinit.y[0][1]) > tol
assert abs(out.y[-1][0] - solinit.y[-1][0]) - 2 < tol
def test_T14(const):
def odefun(X, u, p, const):
return 2 * X[1],\
2 * ((X[0] - const[0] * np.pi ** 2 * np.cos(np.pi * X[2]) - np.cos(np.pi * X[2])) / const[0]),\
2
def odejac(X, u, p, const):
df_dy = np.array(
[[0, 2, 0],
[
2 / const[0], 0,
(2 * (np.pi * np.sin(np.pi * X[2]) +
const[0] * np.pi**3 * np.sin(np.pi * X[2]))) / const[0]
], [0, 0, 0]])
df_dp = np.empty((3, 0))
return df_dy, df_dp
def bcfun(X0, q0, u0, Xf, qf, uf, p, ndp, const):
return X0[0], Xf[0], X0[2] + 1
algo = spbvp(odefun, None, bcfun)
algo.set_derivative_jacobian(odejac)
solinit = Trajectory()
solinit.t = np.linspace(0, 1, 2)
solinit.y = np.array([[0, 0, -1], [0, 0, 1]])
solinit.const = np.array([const])
sol = algo.solve(solinit)['sol']
e1 = np.cos(np.pi * sol.y[:, 2]) + np.exp(
-(1 + sol.y[:, 2]) / np.sqrt(sol.const[0])) + np.exp(
-(1 - sol.y[:, 2]) / np.sqrt(sol.const[0]))
e2 = np.exp((sol.y[:, 2] - 1) / np.sqrt(sol.const[0])) / np.sqrt(
sol.const[0]) - np.pi * np.sin(
np.pi * sol.y[:, 2]) - 1 / (np.sqrt(sol.const[0]) * np.exp(
(sol.y[:, 2] + 1) / np.sqrt(sol.const[0])))
assert all(e1 - sol.y[:, 0] < tol)
assert all(e2 - sol.y[:, 1] < tol)
def test_T18(const):
def odefun(X, u, p, const):
return X[1], (-X[1] / const[0]), 1
def odejac(X, u, p, const):
df_dy = np.array([[0, 1, 0], [0, -1 / const[0], 0], [0, 0, 0]])
df_dp = np.empty((3, 0))
return df_dy, df_dp
def bcfun(X0, q0, u0, Xf, qf, uf, p, ndp, const):
return X0[0] - 1, Xf[0] - np.exp(-1 / const[0]), X0[2]
algo = spbvp(odefun, None, bcfun)
algo.set_derivative_jacobian(odejac)
solinit = Trajectory()
solinit.t = np.linspace(0, 1, 2)
solinit.y = np.array([[0, 0, 0], [0, 0, 1]])
solinit.const = np.array([const])
sol = algo.solve(solinit)['sol']
e1 = np.exp(-sol.y[:, 2] / sol.const[0])
e2 = -1 / (sol.const[0] * np.exp(sol.y[:, 2] / sol.const[0]))
assert all(e1 - sol.y[:, 0] < tol)
assert all(e2 - sol.y[:, 1] < tol)
def test_R8(const):
def odefun(X, u, p, const):
return -X[0] / const[0]
def quadfun(X, u, p, const):
return X[0]
def bcfun(X0, q0, u0, Xf, qf, uf, p, ndp, const):
return q0[0] - 1, qf[0] - 2
algo = spbvp(odefun, quadfun, bcfun)
solinit = Trajectory()
solinit.t = np.linspace(0, 1, 2)
solinit.y = np.array([[1], [1]])
solinit.q = np.array([[0], [0]])
solinit.const = np.array([const])
sol = algo.solve(solinit)['sol']
e1 = (1.e0 - np.exp(
(sol.t - 1.e0) / sol.const)) / (1.e0 - np.exp(-1.e0 / sol.const))
e2 = np.exp((sol.t - 1) / sol.const) / (sol.const *
(1 / np.exp(1 / sol.const) - 1))
assert all(e1 - sol.q[:, 0] < tol)
assert all(e2 - sol.y[:, 0] < tol)