def test_Ikpw_Jkpw_identities(): """Test the relations given in Wiktorsson2001 equation (2.1)""" dW = deltaW(N, m, h).reshape((N, m, 1)) A, I = Ikpw(dW, h) assert (A.shape == (N, m, m) and I.shape == (N, m, m)) Im = broadcast_to(np.eye(m), (N, m, m)) assert (np.allclose(I + _t(I), _dot(dW, _t(dW)) - h * Im)) assert (np.allclose(A, -_t(A))) assert (np.allclose(2.0 * (I - A), _dot(dW, _t(dW)) - h * Im)) # and tests for Stratonovich case A, J = Jkpw(dW, h) assert (A.shape == (N, m, m) and J.shape == (N, m, m)) assert (np.allclose(J + _t(J), _dot(dW, _t(dW)))) assert (np.allclose(2.0 * (J - A), _dot(dW, _t(dW))))
def test_Ikpw_Jkpw_identities(): """Test the relations given in Wiktorsson2001 equation (2.1)""" dW = deltaW(N, m, h).reshape((N, m, 1)) A, I = Ikpw(dW, h) assert(A.shape == (N, m, m) and I.shape == (N, m, m)) Im = broadcast_to(np.eye(m), (N, m, m)) assert(np.allclose(I + _t(I), _dot(dW, _t(dW)) - h*Im)) assert(np.allclose(A, -_t(A))) assert(np.allclose(2.0*(I - A), _dot(dW, _t(dW)) - h*Im)) # and tests for Stratonovich case A, J = Jkpw(dW, h) assert(A.shape == (N, m, m) and J.shape == (N, m, m)) assert(np.allclose(J + _t(J), _dot(dW, _t(dW)))) assert(np.allclose(2.0*(J - A), _dot(dW, _t(dW))))
def test_P(): """Test permutation matrix _P(m)""" Pm0 = _P(m) X = np.random.normal(0.0, 1.0, (N, m, 1)) Y = np.random.normal(0.0, 1.0, (N, m, 1)) assert (Pm0.shape == (m**2, m**2)) assert (np.allclose(Pm0, Pm0.T)) # symmetric assert (np.allclose(np.dot(Pm0, Pm0), np.eye(m**2))) # is its own inverse Pm = broadcast_to(Pm0, (N, m**2, m**2)) for n in range(0, N): assert (np.allclose(np.dot(Pm0, np.kron(X[n, :, 0], Y[n, :, 0])), np.kron(Y[n, :, 0], X[n, :, 0]))) # next line is equivalent to the previous 3 lines: assert (np.allclose(_dot(Pm, _kp(X, Y)), _kp(Y, X)))
def test_P(): """Test permutation matrix _P(m)""" Pm0 = _P(m) X = np.random.normal(0.0, 1.0, (N, m, 1)) Y = np.random.normal(0.0, 1.0, (N, m, 1)) assert(Pm0.shape == (m**2, m**2)) assert(np.allclose(Pm0, Pm0.T)) # symmetric assert(np.allclose(np.dot(Pm0, Pm0), np.eye(m**2))) # is its own inverse Pm = broadcast_to(Pm0, (N, m**2, m**2)) for n in range(0, N): assert(np.allclose(np.dot(Pm0, np.kron(X[n,:,0], Y[n,:,0])), np.kron(Y[n,:,0], X[n,:,0]))) # next line is equivalent to the previous 3 lines: assert(np.allclose(_dot(Pm, _kp(X, Y)), _kp(Y, X)))
def test_Iwik_Jwik_identities(): dW = deltaW(N, m, h).reshape((N, m, 1)) Atilde, I = Iwik(dW, h) M = m * (m - 1) // 2 assert (Atilde.shape == (N, M, 1) and I.shape == (N, m, m)) Im = broadcast_to(np.eye(m), (N, m, m)) assert (np.allclose(I + _t(I), _dot(dW, _t(dW)) - h * Im)) # can get A from Atilde: (Wiktorsson2001 equation between (4.3) and (4.4)) Ims = broadcast_to(np.eye(m * m), (N, m * m, m * m)) Pm = broadcast_to(_P(m), (N, m * m, m * m)) Km = broadcast_to(_K(m), (N, M, m * m)) A = _unvec(_dot(_dot((Ims - Pm), _t(Km)), Atilde)) # now can test this A against the identities of Wiktorsson eqn (2.1) assert (np.allclose(A, -_t(A))) assert (np.allclose(2.0 * (I - A), _dot(dW, _t(dW)) - h * Im)) # and tests for Stratonovich case Atilde, J = Jwik(dW, h) assert (Atilde.shape == (N, M, 1) and J.shape == (N, m, m)) assert (np.allclose(J + _t(J), _dot(dW, _t(dW)))) A = _unvec(_dot(_dot((Ims - Pm), _t(Km)), Atilde)) assert (np.allclose(2.0 * (J - A), _dot(dW, _t(dW))))
def test_Iwik_Jwik_identities(): dW = deltaW(N, m, h).reshape((N, m, 1)) Atilde, I = Iwik(dW, h) M = m*(m-1)/2 assert(Atilde.shape == (N, M, 1) and I.shape == (N, m, m)) Im = broadcast_to(np.eye(m), (N, m, m)) assert(np.allclose(I + _t(I), _dot(dW, _t(dW)) - h*Im)) # can get A from Atilde: (Wiktorsson2001 equation between (4.3) and (4.4)) Ims = broadcast_to(np.eye(m*m), (N, m*m, m*m)) Pm = broadcast_to(_P(m), (N, m*m, m*m)) Km = broadcast_to(_K(m), (N, M, m*m)) A = _unvec(_dot(_dot((Ims - Pm), _t(Km)), Atilde)) # now can test this A against the identities of Wiktorsson eqn (2.1) assert(np.allclose(A, -_t(A))) assert(np.allclose(2.0*(I - A), _dot(dW, _t(dW)) - h*Im)) # and tests for Stratonovich case Atilde, J = Jwik(dW, h) assert(Atilde.shape == (N, M, 1) and J.shape == (N, m, m)) assert(np.allclose(J + _t(J), _dot(dW, _t(dW)))) A = _unvec(_dot(_dot((Ims - Pm), _t(Km)), Atilde)) assert(np.allclose(2.0*(J - A), _dot(dW, _t(dW))))