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 = deeptime.data.birth_death_chain(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 = deeptime.data.birth_death_chain(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 = deeptime.data.birth_death_chain(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)