def setUp(self): self.k = 4 p = np.zeros(10) q = np.zeros(10) p[0:-1] = 0.5 q[1:] = 0.5 p[4] = 0.01 q[6] = 0.1 self.bdc = BirthDeathChain(q, p) self.mu = self.bdc.stationary_distribution() self.T = self.bdc.transition_matrix_sparse() """Test matrix-vector product against spectral decomposition""" R, D, L = rdl_decomposition(self.T, k=self.k) self.L = L self.R = R self.ts = timescales(self.T, k=self.k) self.times = np.array([1, 5, 10, 20, 100]) ev = np.diagonal(D) self.ev_t = ev[np.newaxis, :]**self.times[:, np.newaxis] """Observable""" obs1 = np.zeros(10) obs1[0] = 1 obs1[1] = 1 self.obs = obs1 """Initial distribution""" w0 = np.zeros(10) w0[0:4] = 0.25 self.p0 = w0
def setUp(self): self.k = 4 p = np.zeros(10) q = np.zeros(10) p[0:-1] = 0.5 q[1:] = 0.5 p[4] = 0.01 q[6] = 0.1 self.bdc = BirthDeathChain(q, p) self.mu = self.bdc.stationary_distribution() self.T = self.bdc.transition_matrix_sparse() R, D, L = rdl_decomposition(self.T, k=self.k) self.L = L self.R = R self.ts = timescales(self.T, k=self.k) self.times = np.array([1, 5, 10, 20, 100]) ev = np.diagonal(D) self.ev_t = ev[np.newaxis, :]**self.times[:, np.newaxis] obs1 = np.zeros(10) obs1[0] = 1 obs1[1] = 1 obs2 = np.zeros(10) obs2[8] = 1 obs2[9] = 1 self.obs1 = obs1 self.obs2 = obs2 self.one_vec = np.ones(10)
def setUp(self): self.k = 4 p = np.zeros(10) q = np.zeros(10) p[0:-1] = 0.5 q[1:] = 0.5 p[4] = 0.01 q[6] = 0.1 self.bdc = BirthDeathChain(q, p) self.mu = self.bdc.stationary_distribution() self.T = self.bdc.transition_matrix_sparse() R, D, L = rdl_decomposition(self.T, k=self.k) self.L = L self.R = R self.ts = timescales(self.T, k=self.k) self.times = np.array([1, 5, 10, 20]) ev = np.diagonal(D) self.ev_t = ev[np.newaxis, :]**self.times[:, np.newaxis] self.tau = 7.5 """Observables""" obs1 = np.zeros(10) obs1[0] = 1 obs1[1] = 1 obs2 = np.zeros(10) obs2[8] = 1 obs2[9] = 1 self.obs1 = obs1 self.obs2 = obs2 """Initial vector for relaxation""" w0 = np.zeros(10) w0[0:4] = 0.25 self.p0 = w0
def test_rdl_decomposition_rev(self): P = self.bdc.transition_matrix_sparse() mu = self.bdc.stationary_distribution() """Non-reversible""" """k=None""" with self.assertRaises(ValueError): Rn, Dn, Ln = rdl_decomposition(P, reversible=True) """norm='standard'""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, reversible=True, norm='standard') Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Standard l2-normalization of right eigenvectors except dominant one""" Yn = np.dot(Rn.T, Rn) assert_allclose(np.diag(Yn)[1:], 1.0) """ncv is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, reversible=True, norm='standard', ncv=self.ncv) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Standard l2-normalization of right eigenvectors except dominant one""" Yn = np.dot(Rn.T, Rn) assert_allclose(np.diag(Yn)[1:], 1.0) """norm='reversible'""" Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='reversible', k=self.k) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn) Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='reversible', k=self.k, ncv=self.ncv) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn) """mu is not None""" """norm='standard'""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, reversible=True, norm='standard', mu=mu) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Standard l2-normalization of right eigenvectors except dominant one""" Yn = np.dot(Rn.T, Rn) assert_allclose(np.diag(Yn)[1:], 1.0) """ncv is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, reversible=True, norm='standard', ncv=self.ncv, mu=mu) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Standard l2-normalization of right eigenvectors except dominant one""" Yn = np.dot(Rn.T, Rn) assert_allclose(np.diag(Yn)[1:], 1.0) """norm='reversible'""" Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='reversible', k=self.k, mu=mu) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn) Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='reversible', k=self.k, ncv=self.ncv, mu=mu) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn)
def test_rdl_decomposition(self): P = self.bdc.transition_matrix_sparse() mu = self.bdc.stationary_distribution() """Non-reversible""" """k=None""" with self.assertRaises(ValueError): Rn, Dn, Ln = rdl_decomposition(P) """k is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """k is not None, ncv is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, ncv=self.ncv) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversible""" """k=None""" with self.assertRaises(ValueError): Rn, Dn, Ln = rdl_decomposition(P, norm='reversible') """k is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, norm='reversible') Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn) """k is not None ncv is not None""" Rn, Dn, Ln = rdl_decomposition(P, k=self.k, norm='reversible', ncv=self.ncv) Xn = np.dot(Ln, Rn) """Right-eigenvectors""" assert_allclose(P.dot(Rn), np.dot(Rn, Dn)) """Left-eigenvectors""" assert_allclose(P.transpose().dot(Ln.transpose()).transpose(), np.dot(Dn, Ln)) """Orthonormality""" assert_allclose(Xn, np.eye(self.k)) """Probability vector""" assert_allclose(np.sum(Ln[0, :]), 1.0) """Reversibility""" assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn)