def test_02(self): t = np.array([0.0, 1.0, 1.0, 3.0]) u = np.array([0.0, 0.0, 1.0, 1.0]) # Simple integrator: x'(t) = u(t) system = ([1.0],[1.0,0.0]) tout, y, x = lsim2(system, u, t, X0=[1.0]) expected_x = np.maximum(1.0, tout) assert_almost_equal(x[:,0], expected_x)
def test_03(self): t = np.array([0.0, 1.0, 1.0, 1.1, 1.1, 2.0]) u = np.array([0.0, 0.0, 1.0, 1.0, 0.0, 0.0]) # Simple integrator: x'(t) = u(t) system = ([1.0],[1.0, 0.0]) tout, y, x = lsim2(system, u, t, hmax=0.01) expected_x = np.array([0.0, 0.0, 0.0, 0.1, 0.1, 0.1]) assert_almost_equal(x[:,0], expected_x)
def test_03(self): t = np.array([0.0, 1.0, 1.0, 1.1, 1.1, 2.0]) u = np.array([0.0, 0.0, 1.0, 1.0, 0.0, 0.0]) # Simple integrator: x'(t) = u(t) system = ([1.0], [1.0, 0.0]) tout, y, x = lsim2(system, u, t, hmax=0.01) expected_x = np.array([0.0, 0.0, 0.0, 0.1, 0.1, 0.1]) assert_almost_equal(x[:, 0], expected_x)
def test_02(self): t = np.array([0.0, 1.0, 1.0, 3.0]) u = np.array([0.0, 0.0, 1.0, 1.0]) # Simple integrator: x'(t) = u(t) system = ([1.0], [1.0, 0.0]) tout, y, x = lsim2(system, u, t, X0=[1.0]) expected_x = np.maximum(1.0, tout) assert_almost_equal(x[:, 0], expected_x)
def test_06(self): """Test use of the default values of the arguments `T` and `U`.""" # Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = 0. # With initial conditions x(0)=1.0 and x'(t)=0.0, the exact solution # is (1-t)*exp(-t). system = ([1.0], [1.0, 2.0, 1.0]) tout, y, x = lsim2(system, X0=[1.0, 0.0]) expected_x = (1.0 - tout) * np.exp(-tout) assert_almost_equal(x[:,0], expected_x)
def test_01(self): t = np.linspace(0,10,1001) u = np.zeros_like(t) # First order system: x'(t) + x(t) = u(t), x(0) = 1. # Exact solution is x(t) = exp(-t). system = ([1.0],[1.0,1.0]) tout, y, x = lsim2(system, u, t, X0=[1.0]) expected_x = np.exp(-tout) assert_almost_equal(x[:,0], expected_x)
def test_06(self): """Test use of the default values of the arguments `T` and `U`.""" # Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = 0. # With initial conditions x(0)=1.0 and x'(t)=0.0, the exact solution # is (1-t)*exp(-t). system = ([1.0], [1.0, 2.0, 1.0]) tout, y, x = lsim2(system, X0=[1.0, 0.0]) expected_x = (1.0 - tout) * np.exp(-tout) assert_almost_equal(x[:, 0], expected_x)
def test_01(self): t = np.linspace(0, 10, 1001) u = np.zeros_like(t) # First order system: x'(t) + x(t) = u(t), x(0) = 1. # Exact solution is x(t) = exp(-t). system = ([1.0], [1.0, 1.0]) tout, y, x = lsim2(system, u, t, X0=[1.0]) expected_x = np.exp(-tout) assert_almost_equal(x[:, 0], expected_x)
def test_04(self): t = np.linspace(0, 10, 1001) u = np.zeros_like(t) # Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = 0. # With initial conditions x(0)=1.0 and x'(t)=0.0, the exact solution # is (1-t)*exp(-t). system = ([1.0], [1.0, 2.0, 1.0]) tout, y, x = lsim2(system, u, t, X0=[1.0, 0.0]) expected_x = (1.0 - tout) * np.exp(-tout) assert_almost_equal(x[:,0], expected_x)
def test_04(self): t = np.linspace(0, 10, 1001) u = np.zeros_like(t) # Second order system with a repeated root: x''(t) + 2*x(t) + x(t) = 0. # With initial conditions x(0)=1.0 and x'(t)=0.0, the exact solution # is (1-t)*exp(-t). system = ([1.0], [1.0, 2.0, 1.0]) tout, y, x = lsim2(system, u, t, X0=[1.0, 0.0]) expected_x = (1.0 - tout) * np.exp(-tout) assert_almost_equal(x[:, 0], expected_x)
def test_07(self): """Test the simulation of a MIMO system""" # Basic MIMO system. Two inputs, two outputs. Output same as input. A = np.zeros((1, 1)) B = np.zeros((1, 2)) C = np.zeros((2, 1)) D = np.eye(2) t = np.arange(3) u0 = np.arange(3) u1 = 2 * u0 u = np.vstack((u0, u1)).T tout, y, x = lsim2((A, B, C, D), T=t, U=u) expected_y = u expected_x = np.zeros((3, 1)) assert_almost_equal(y, expected_y) assert_almost_equal(x, expected_x)
def test_05(self): # This test triggers a "BadCoefficients" warning from scipy.signal.filter_design, # but the test passes. I think the warning is related to the incomplete handling # of multi-input systems in scipy.signal. # A system with two state variables, two inputs, and one output. A = np.array([[-1.0, 0.0], [0.0, -2.0]]) B = np.array([[1.0, 0.0], [0.0, 1.0]]) C = np.array([1.0, 0.0]) D = np.zeros((1,2)) t = np.linspace(0, 10.0, 101) tout, y, x = lsim2((A,B,C,D), T=t, X0=[1.0, 1.0]) expected_y = np.exp(-tout) expected_x0 = np.exp(-tout) expected_x1 = np.exp(-2.0*tout) assert_almost_equal(y, expected_y) assert_almost_equal(x[:,0], expected_x0) assert_almost_equal(x[:,1], expected_x1)
def test_05(self): # This test triggers a "BadCoefficients" warning from scipy.signal.filter_design, # but the test passes. I think the warning is related to the incomplete handling # of multi-input systems in scipy.signal. # A system with two state variables, two inputs, and one output. A = np.array([[-1.0, 0.0], [0.0, -2.0]]) B = np.array([[1.0, 0.0], [0.0, 1.0]]) C = np.array([1.0, 0.0]) D = np.zeros((1, 2)) t = np.linspace(0, 10.0, 101) tout, y, x = lsim2((A, B, C, D), T=t, X0=[1.0, 1.0]) expected_y = np.exp(-tout) expected_x0 = np.exp(-tout) expected_x1 = np.exp(-2.0 * tout) assert_almost_equal(y, expected_y) assert_almost_equal(x[:, 0], expected_x0) assert_almost_equal(x[:, 1], expected_x1)