def test_spy(self):
ocp, _, _ = integrator_control_problem()
ocp.solve()
ocp.spy()
import matplotlib.pylab as plt
self.assertEqual(plt.gca().title._text,
"Lagrange Hessian: 101x101,0nz")
def test_show_infeasibilities(self):
for method in [MultipleShooting(), DirectCollocation()]:
ocp, x, u = integrator_control_problem(stage_method=method, x0=0)
ocp.subject_to(ocp.at_t0(x) == 2)
with self.assertRaises(Exception):
sol = ocp.solve()
with StringIO() as buf, redirect_stdout(buf):
ocp.show_infeasibilities(1e-4)
out = buf.getvalue()
self.assertIn("ocp.subject_to(ocp.at_t0(x)==2)", out)
def test_all(self):
T = 1
M = 1
b = 1
t0 = 0
x0 = 0
for scheme in [MultipleShooting(N=40, M=1, intg='rk'),
DirectCollocation(N=40)]:
(ocp, x, u) = integrator_control_problem(T, b, x0, scheme, t0)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0],x0,places=6)
self.assertAlmostEqual(xs[-1],x0-b*T,places=6)
def test_initial(self):
for stage_method in [MultipleShooting(), DirectCollocation()]:
ocp, x, u = integrator_control_problem(x0=None,
stage_method=stage_method)
v = ocp.variable()
ocp.subject_to(ocp.at_t0(x) == v)
ocp.subject_to(0 == sin(v))
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], 0, places=6)
ocp.set_initial(v, 2 * pi)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], 2 * pi, places=6)
def test_grid_integrator(self):
N, T, u_max, x0 = 10, 10, 2, 1
tolerance = 1e-6
ocp, x, u = integrator_control_problem(T, u_max, x0, MultipleShooting(N=N,M=3,intg='rk'))
sol = ocp.solve()
ts, xs = sol.sample(x, grid='integrator')
ts, us = sol.sample(u, grid='integrator')
ts, uxs = sol.sample(u * x, grid='integrator')
t_exact = np.linspace(0, T, N * 3 + 1)
x_exact = np.linspace(1, x0 - 10 * u_max, N * 3 + 1)
u_exact = np.ones(N * 3 + 1) * (-u_max)
assert_allclose(ts, t_exact, atol=tolerance)
assert_allclose(xs, x_exact, atol=tolerance)
assert_allclose(us, u_exact, atol=tolerance)
assert_allclose(uxs, u_exact * x_exact, atol=tolerance)
tsa, tsb = sol.sample(ocp.t, grid='integrator')
assert_allclose(tsa, tsb, atol=tolerance)
def test_basic(self):
for T in [1, 3.2]:
for M in [1, 2]:
for u_max in [1, 2]:
for t0 in [0, 1]:
for x0 in [0, 1]:
for method in [
MultipleShooting(N=4, M=M, intg='rk'),
MultipleShooting(N=4, M=M, intg='cvodes'),
MultipleShooting(N=4, M=M, intg='idas'),
DirectCollocation(N=4, M=M)
]:
ocp, x, u = integrator_control_problem(
T, u_max, x0, method, t0)
sol = ocp.solve()
ts, xs = sol.sample(x, grid='control')
self.assertAlmostEqual(xs[0], x0, places=6)
self.assertAlmostEqual(xs[-1],
x0 - u_max * T,
places=6)
self.assertAlmostEqual(ts[0], t0)
self.assertAlmostEqual(ts[-1], t0 + T)