def test_rdl_decomposition(self):
P = self.bdc.transition_matrix
assert is_reversible(P)
mu = self.bdc.stationary_distribution
"""Non-reversible"""
"""k=None"""
Rn, Dn, Ln = rdl_decomposition(P)
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), np.dot(Dn, Ln))
"""Orthonormality"""
assert_allclose(Xn, np.eye(self.dim))
"""Probability vector"""
assert_allclose(np.sum(Ln[0, :]), 1.0)
"""k is not None"""
Rn, Dn, Ln = rdl_decomposition(P, k=self.k)
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), 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"""
Rn, Dn, Ln = rdl_decomposition(P, norm='reversible')
assert Dn.dtype in (np.float32, np.float64)
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), np.dot(Dn, Ln))
"""Orthonormality"""
assert_allclose(Xn, np.eye(self.dim))
"""Probability vector"""
assert_allclose(np.sum(Ln[0, :]), 1.0)
"""Reversibility"""
assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn)
"""k is not None"""
Rn, Dn, Ln = rdl_decomposition(P, norm='reversible', k=self.k)
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), 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 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 = 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 = 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 test_relaxation(fingerprints_data):
T = fingerprints_data.transition_matrix
R, D, L = rdl_decomposition(T, k=4 if fingerprints_data.sparse else None)
times = np.array([1, 5, 10, 20, 100])
ev = np.diagonal(D)
ev_t = ev[np.newaxis, :]**times[:, np.newaxis]
obs = np.zeros(10)
obs[0] = 1
obs[1] = 1
p0 = np.zeros(10)
p0[:4] = 0.25
if not fingerprints_data.sparse:
"""k=None"""
relax_amp = np.dot(p0, R) * np.dot(L, obs)
relax = np.dot(ev_t, relax_amp)
relaxn = relaxation(T, p0, obs, times=times)
assert_allclose(relaxn, relax)
"""k=4"""
k = 4
relax_amp = np.dot(p0, R[:, 0:k]) * np.dot(L[0:k, :], obs)
relax = np.dot(ev_t[:, 0:k], relax_amp)
relaxn = relaxation(T, p0, obs, k=k, times=times)
assert_allclose(relaxn, relax)
def test_rdl_decomposition(scenario, ncv_values, norm, statdist, reversible):
k, bdc = scenario
dim = bdc.q.shape[0]
P = bdc.transition_matrix
mu = bdc.stationary_distribution
with assert_raises(ValueError) if bdc.sparse and k is None else nullcontext():
Rn, Dn, Ln = rdl_decomposition(P, reversible=reversible, norm=norm,
ncv=ncv_values, k=k, mu=mu if statdist else None)
Xn = Ln @ Rn
"""Right-eigenvectors"""
assert_allclose(P @ Rn, Rn @ Dn)
"""Left-eigenvectors"""
assert_allclose(Ln @ P, Dn @ Ln)
"""Orthonormality"""
assert_allclose(Xn, np.eye(dim if k is None else k))
"""Probability vector"""
assert_allclose(np.sum(Ln[0, :]), 1.0)
if norm == 'standard' and reversible:
"""Standard l2-normalization of right eigenvectors except dominant one"""
Yn = Rn.T @ Rn
assert_allclose(np.diag(Yn)[1:], 1.0)
if norm == 'reversible':
"""Reversibility"""
assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn)
def test_fingerprint_correlation(fingerprints_data, observables):
obs1, obs2 = observables
T = fingerprints_data.transition_matrix
ts = timescales(T, k=4 if fingerprints_data.sparse else None)
R, D, L = rdl_decomposition(T, k=4 if fingerprints_data.sparse else None)
mu = fingerprints_data.stationary_distribution
tau = 7.5
if not fingerprints_data.sparse:
"""k=None, tau=1"""
acorr_amp = np.dot(mu * obs1, R) * np.dot(L, obs1)
tsn, acorr_ampn = fingerprint_correlation(T, obs1)
assert_allclose(tsn, ts)
assert_allclose(acorr_ampn, acorr_amp)
"""k=None, tau=7.5"""
tau = tau
tsn, acorr_ampn = fingerprint_correlation(T, obs1, tau=tau)
assert_allclose(tsn, tau * ts)
assert_allclose(acorr_ampn, acorr_amp)
"""k=4, tau=1"""
k = 4
acorr_amp = np.dot(mu * obs1, R[:, 0:k]) * np.dot(L[0:k, :], obs1)
tsn, acorr_ampn = fingerprint_correlation(T, obs1, k=k)
assert_allclose(tsn, ts[0:k])
assert_allclose(acorr_ampn, acorr_amp)
"""k=4, tau=7.5"""
tau = tau
tsn, acorr_ampn = fingerprint_correlation(T, obs1, k=k, tau=tau)
assert_allclose(tsn, tau * ts[0:k])
assert_allclose(acorr_ampn, acorr_amp)
"""Cross-correlation"""
if not fingerprints_data.sparse:
"""k=None, tau=1"""
corr_amp = np.dot(mu * obs1, R) * np.dot(L, obs2)
tsn, corr_ampn = fingerprint_correlation(T, obs1, obs2=obs2)
assert_allclose(tsn, ts)
assert_allclose(corr_ampn, corr_amp)
"""k=None, tau=7.5"""
tau = tau
tsn, corr_ampn = fingerprint_correlation(T, obs1, obs2=obs2, tau=tau)
assert_allclose(tsn, tau * ts)
assert_allclose(corr_ampn, corr_amp)
"""k=4, tau=1"""
corr_amp = np.dot(mu * obs1, R[:, 0:k]) * np.dot(L[0:k, :], obs2)
tsn, corr_ampn = fingerprint_correlation(T, obs1, obs2=obs2, k=k)
assert_allclose(tsn, ts[0:k])
assert_allclose(corr_ampn, corr_amp)
"""k=4, tau=7.5"""
tsn, corr_ampn = fingerprint_correlation(T, obs1, obs2=obs2, k=k, tau=tau)
assert_allclose(tsn, tau * ts[0:k])
assert_allclose(corr_ampn, corr_amp)
def _compute_eigendecomposition(self, neig):
""" Conducts the eigenvalue decomposition and stores k eigenvalues, left and right eigenvectors """
self._p_id = _hash_numpy_array(self.transition_matrix)
from deeptime.markov.tools.analysis import rdl_decomposition
if self.reversible:
self._R, self._D, self._L = rdl_decomposition(self.transition_matrix, norm='reversible',
k=neig, ncv=self.ncv)
# everything must be real-valued
self._R = self._R.real
self._D = self._D.real
self._L = self._L.real
else:
self._R, self._D, self._L = rdl_decomposition(self.transition_matrix, k=neig, norm='standard', ncv=self.ncv)
# if the imaginary parts are zero, discard them.
if _np.all(self._R.imag == 0):
self._R = _np.real(self._R)
if _np.all(self._D.imag == 0):
self._D = _np.real(self._D)
if _np.all(self._L.imag == 0):
self._L = _np.real(self._L)
self._eigenvalues = _np.diag(self._D)
def test_fingerprint_relaxation(fingerprints_data, observables):
obs1, obs2 = observables
T = fingerprints_data.transition_matrix
ts = timescales(T, k=4 if fingerprints_data.sparse else None)
R, D, L = rdl_decomposition(T, k=4 if fingerprints_data.sparse else None)
"""Initial vector for relaxation"""
p0 = np.zeros(10)
p0[0:4] = 0.25
if not fingerprints_data.sparse:
"""k=None"""
relax_amp = np.dot(p0, R) * np.dot(L, obs1)
tsn, relax_ampn = fingerprint_relaxation(T, p0, obs1)
assert_allclose(tsn, ts)
assert_allclose(relax_ampn, relax_amp)
"""k=4"""
k = 4
relax_amp = np.dot(p0, R[:, 0:k]) * np.dot(L[0:k, :], obs1)
tsn, relax_ampn = fingerprint_relaxation(T, p0, obs1, k=k)
assert_allclose(tsn, ts[0:k])
assert_allclose(relax_ampn, relax_amp)
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 = 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_correlation(fingerprints_data, observables):
obs1, obs2 = observables
T = fingerprints_data.transition_matrix
R, D, L = rdl_decomposition(T, k=4 if fingerprints_data.sparse else None)
mu = fingerprints_data.stationary_distribution
times = np.array([1, 5, 10, 20, 100])
ev = np.diagonal(D)
ev_t = ev[np.newaxis, :]**times[:, np.newaxis]
if not fingerprints_data.sparse:
"""k=None"""
acorr_amp = np.dot(mu * obs1, R) * np.dot(L, obs1)
acorr = np.dot(ev_t, acorr_amp)
acorrn = correlation(T, obs1, times=times)
assert_allclose(acorrn, acorr)
"""k=4"""
k = 4
acorr_amp = np.dot(mu * obs1, R[:, 0:k]) * np.dot(L[0:k, :], obs1)
acorr = np.dot(ev_t[:, 0:k], acorr_amp)
acorrn = correlation(T, obs1, times=times, k=k)
assert_allclose(acorrn, acorr)
"""Cross-correlation"""
if not fingerprints_data.sparse:
"""k=None"""
corr_amp = np.dot(mu * obs1, R) * np.dot(L, obs2)
corr = np.dot(ev_t, corr_amp)
corrn = correlation(T, obs1, obs2=obs2, times=times)
assert_allclose(corrn, corr)
"""k=4"""
k = k
corr_amp = np.dot(mu * obs1, R[:, 0:k]) * np.dot(L[0:k, :], obs2)
corr = np.dot(ev_t[:, 0:k], corr_amp)
corrn = correlation(T, obs1, obs2=obs2, times=times, k=k)
assert_allclose(corrn, corr)
def __init__(self, complete: bool = True):
self.complete = complete
data = np.load(os.path.join(os.path.dirname(os.path.realpath(__file__)), 'resources', 'TestData_OOM_MSM.npz'))
if complete:
self.dtrajs = [data['arr_%d' % k] for k in range(1000)]
else:
excluded = [
21, 25, 30, 40, 66, 72, 74, 91, 116, 158, 171, 175, 201, 239, 246, 280, 300, 301, 310, 318,
322, 323, 339, 352, 365, 368, 407, 412, 444, 475, 486, 494, 510, 529, 560, 617, 623, 637,
676, 689, 728, 731, 778, 780, 811, 828, 838, 845, 851, 859, 868, 874, 895, 933, 935, 938,
958, 961, 968, 974, 984, 990, 999
]
self.dtrajs = [data['arr_%d' % k] for k in np.setdiff1d(np.arange(1000), excluded)]
# Number of states:
self.N = 5
# Lag time:
self.tau = 5
self.dtrajs_lag = [traj[:-self.tau] for traj in self.dtrajs]
# Rank:
if complete:
self.rank = 3
else:
self.rank = 2
# Build models:
self.msmrev = OOMReweightedMSM(lagtime=self.tau, rank_mode='bootstrap_trajs').fit(self.dtrajs)
self.msmrev_sparse = OOMReweightedMSM(lagtime=self.tau, sparse=True, rank_mode='bootstrap_trajs') \
.fit(self.dtrajs)
self.msm = OOMReweightedMSM(lagtime=self.tau, reversible=False, rank_mode='bootstrap_trajs').fit(self.dtrajs)
self.msm_sparse = OOMReweightedMSM(lagtime=self.tau, reversible=False, sparse=True,
rank_mode='bootstrap_trajs').fit(self.dtrajs)
self.estimators = [self.msmrev, self.msm, self.msmrev_sparse, self.msm_sparse]
self.msms = [est.fetch_model() for est in self.estimators]
# Reference count matrices at lag time tau and 2*tau:
if complete:
self.C2t = data['C2t']
else:
self.C2t = data['C2t_s']
self.Ct = np.sum(self.C2t, axis=1)
if complete:
self.Ct_active = self.Ct
self.C2t_active = self.C2t
self.active_faction = 1.
else:
lcc = msmest.largest_connected_set(self.Ct)
self.Ct_active = msmest.largest_connected_submatrix(self.Ct, lcc=lcc)
self.C2t_active = self.C2t[:4, :4, :4]
self.active_fraction = np.sum(self.Ct_active) / np.sum(self.Ct)
# Compute OOM-components:
self.Xi, self.omega, self.sigma, self.l = oom_transformations(self.Ct_active, self.C2t_active, self.rank)
# Compute corrected transition matrix:
Tt_rev = compute_transition_matrix(self.Xi, self.omega, self.sigma, reversible=True)
Tt = compute_transition_matrix(self.Xi, self.omega, self.sigma, reversible=False)
# Build reference models:
self.rmsmrev = MarkovStateModel(Tt_rev)
self.rmsm = MarkovStateModel(Tt)
# Active count fraction:
self.hist = count_states(self.dtrajs)
self.active_hist = self.hist[:-1] if not complete else self.hist
self.active_count_frac = float(np.sum(self.active_hist)) / np.sum(self.hist) if not complete else 1.
self.active_state_frac = 0.8 if not complete else 1.
# Commitor and MFPT:
a = np.array([0, 1])
b = np.array([4]) if complete else np.array([3])
self.comm_forward = self.rmsm.committor_forward(a, b)
self.comm_forward_rev = self.rmsmrev.committor_forward(a, b)
self.comm_backward = self.rmsm.committor_backward(a, b)
self.comm_backward_rev = self.rmsmrev.committor_backward(a, b)
self.mfpt = self.tau * self.rmsm.mfpt(a, b)
self.mfpt_rev = self.tau * self.rmsmrev.mfpt(a, b)
# PCCA:
pcca = self.rmsmrev.pcca(3 if complete else 2)
self.pcca_ass = pcca.assignments
self.pcca_dist = pcca.metastable_distributions
self.pcca_mem = pcca.memberships
self.pcca_sets = pcca.sets
# Experimental quantities:
a = np.array([1, 2, 3, 4, 5])
b = np.array([1, -1, 0, -2, 4])
p0 = np.array([0.5, 0.2, 0.2, 0.1, 0.0])
if not complete:
a = a[:-1]
b = b[:-1]
p0 = p0[:-1]
pi = self.rmsm.stationary_distribution
pi_rev = self.rmsmrev.stationary_distribution
_, _, L_rev = ma.rdl_decomposition(Tt_rev)
self.exp = np.dot(self.rmsm.stationary_distribution, a)
self.exp_rev = np.dot(self.rmsmrev.stationary_distribution, a)
self.corr_rev = np.zeros(10)
self.rel = np.zeros(10)
self.rel_rev = np.zeros(10)
for k in range(10):
Ck_rev = np.dot(np.diag(pi_rev), np.linalg.matrix_power(Tt_rev, k))
self.corr_rev[k] = np.dot(a.T, np.dot(Ck_rev, b))
self.rel[k] = np.dot(p0.T, np.dot(np.linalg.matrix_power(Tt, k), a))
self.rel_rev[k] = np.dot(p0.T, np.dot(np.linalg.matrix_power(Tt_rev, k), a))
self.fing_cor = np.dot(a.T, L_rev.T) * np.dot(b.T, L_rev.T)
self.fing_rel = np.dot(a.T, L_rev.T) * np.dot((p0 / pi_rev).T, L_rev.T)
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)
def test_rdl_decomposition_rev(self):
P = self.bdc.transition_matrix
mu = self.bdc.stationary_distribution
"""norm='standard'"""
"""k=None"""
Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='standard')
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), np.dot(Dn, Ln))
"""Orthonormality"""
assert_allclose(Xn, np.eye(self.dim))
"""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)
"""k is not None"""
Rn, Dn, Ln = rdl_decomposition(P,
k=self.k,
reversible=True,
norm='standard')
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), 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'"""
"""k=None"""
Rn, Dn, Ln = rdl_decomposition(P, reversible=True, norm='reversible')
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), np.dot(Dn, Ln))
"""Orthonormality"""
assert_allclose(Xn, np.eye(self.dim))
"""Probability vector"""
assert_allclose(np.sum(Ln[0, :]), 1.0)
"""Reversibility"""
assert_allclose(Ln.transpose(), mu[:, np.newaxis] * Rn)
"""k is not None"""
Rn, Dn, Ln = rdl_decomposition(P,
reversible=True,
norm='reversible',
k=self.k)
Xn = np.dot(Ln, Rn)
"""Right-eigenvectors"""
assert_allclose(np.dot(P, Rn), np.dot(Rn, Dn))
"""Left-eigenvectors"""
assert_allclose(np.dot(Ln, P), 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)
