def _compute_eigendecomposition(self, neig):
""" Conducts the eigenvalue decomposition and stores k eigenvalues, left and right eigenvectors """
from msmtools.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 update(self, Tij, Pi=None):
r""" Updates the transition matrix and recomputes all derived quantities """
# EMMA imports
from msmtools import analysis as msmana
# save a copy of the transition matrix
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(
self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[
0] == self._nstates, 'Given transition matrix has unexpected number of states '
# initial / stationary distribution
if (Pi is not None):
assert np.all(
Pi >= 0
), 'Given initial distribution contains negative elements.'
Pi = np.array(Pi) / np.sum(
Pi) # ensure normalization and make a copy
if (self._stationary):
pT = msmana.stationary_distribution(self._Tij)
if Pi is None: # stationary and no stationary distribution fixed, so computing it from trans. mat.
self._Pi = pT
else: # stationary but stationary distribution is fixed, so the transition matrix must be consistent
assert np.allclose(Pi, pT), 'Stationary HMM requested, but given distribution is not the ' \
'stationary distribution of the given transition matrix.'
self._Pi = Pi
else:
if Pi is None: # no initial distribution given, so use stationary distribution anyway
self._Pi = msmana.stationary_distribution(self._Tij)
else:
self._Pi = Pi
# reversible
if self._reversible:
assert msmana.is_reversible(
Tij
), 'Reversible HMM requested, but given transition matrix is not reversible.'
# try to do eigendecomposition by default, because it's very cheap for hidden transition matrices
from scipy.linalg import LinAlgError
try:
if self._reversible:
self._R, self._D, self._L = msmana.rdl_decomposition(
self._Tij, norm='reversible')
# 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 = msmana.rdl_decomposition(
self._Tij, norm='standard')
self._eigenvalues = np.diag(self._D)
self._spectral_decomp_available = True
except LinAlgError:
logger().warn('Eigendecomposition failed for transition matrix\n' +
str(self._Tij) +
'\nspectral properties will not be available')
self._spectral_decomp_available = False
def test_rdl_decomposition(self):
P = self.bdc.transition_matrix()
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')
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 update(self, Tij, Pi=None):
r""" Updates the transition matrix and recomputes all derived quantities """
# EMMA imports
from msmtools import analysis as msmana
# save a copy of the transition matrix
self._Tij = np.array(Tij)
assert msmana.is_transition_matrix(self._Tij), 'Given transition matrix is not a stochastic matrix'
assert self._Tij.shape[0] == self._nstates, 'Given transition matrix has unexpected number of states '
# initial / stationary distribution
if (Pi is not None):
assert np.all(Pi >= 0), 'Given initial distribution contains negative elements.'
Pi = np.array(Pi) / np.sum(Pi) # ensure normalization and make a copy
if (self._stationary):
pT = msmana.stationary_distribution(self._Tij)
if Pi is None: # stationary and no stationary distribution fixed, so computing it from trans. mat.
self._Pi = pT
else: # stationary but stationary distribution is fixed, so the transition matrix must be consistent
assert np.allclose(Pi, pT), 'Stationary HMM requested, but given distribution is not the ' \
'stationary distribution of the given transition matrix.'
self._Pi = Pi
else:
if Pi is None: # no initial distribution given, so use stationary distribution anyway
self._Pi = msmana.stationary_distribution(self._Tij)
else:
self._Pi = Pi
# reversible
if self._reversible:
assert msmana.is_reversible(Tij), 'Reversible HMM requested, but given transition matrix is not reversible.'
# try to do eigendecomposition by default, because it's very cheap for hidden transition matrices
from scipy.linalg import LinAlgError
try:
if self._reversible:
self._R, self._D, self._L = msmana.rdl_decomposition(self._Tij, norm='reversible')
# 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 = msmana.rdl_decomposition(self._Tij, norm='standard')
self._eigenvalues = np.diag(self._D)
self._spectral_decomp_available = True
except LinAlgError:
logger().warn('Eigendecomposition failed for transition matrix\n'+str(self._Tij)+
'\nspectral properties will not be available')
self._spectral_decomp_available = False
def _compute_eigendecomposition(self, neig):
""" Conducts the eigenvalue decomposition and stores k eigenvalues, left and right eigenvectors """
from msmtools.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)
self._eigenvalues = np.diag(self._D)
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 rdl_decomposition(P, reversible=True):
# TODO: this treatment is probably not meaningful for weakly connected matrices.
import msmtools.estimation as msmest
import msmtools.analysis as msmana
# output matrices
n = np.shape(P)[0]
if reversible:
dtype = np.float64
norm = 'reversible'
else:
dtype = complex
norm = 'standard'
R = np.zeros((n, n), dtype=dtype)
D = np.zeros((n, n), dtype=dtype)
L = np.zeros((n, n), dtype=dtype)
# treat each strongly connected set separately
S = msmest.connected_sets(P)
for s in S:
indices = np.ix_(s, s)
if len(s) > 1:
right_eigvec, eigval_diag, left_eigvec = msmana.rdl_decomposition(
P[s, :][:, s], norm=norm)
# write to full
R[indices] = right_eigvec
D[indices] = eigval_diag
L[indices] = left_eigvec
else: # just one element. Write 1's
R[indices] = 1
D[indices] = 1
L[indices] = 1
# done
return R, D, L
def rdl_decomposition(P, reversible=True):
# TODO: this treatment is probably not meaningful for weakly connected matrices.
import msmtools.estimation as msmest
import msmtools.analysis as msmana
# output matrices
n = np.shape(P)[0]
if reversible:
dtype = np.float64
else:
dtype = complex
R = np.zeros((n, n), dtype=dtype)
D = np.zeros((n, n), dtype=dtype)
L = np.zeros((n, n), dtype=dtype)
# treat each strongly connected set separately
S = msmest.connected_sets(P)
for s in S:
I = np.ix_(s, s)
if len(s) > 1:
if reversible:
r, d, l = msmana.rdl_decomposition(P[s, :][:, s],
norm='reversible')
# everything must be real-valued - this should rather be handled by msmtools
R[I] = r.real
D[I] = d.real
L[I] = l.real
else:
r, d, l = msmana.rdl_decomposition(P[s, :][:, s],
norm='standard')
# write to full
R[I] = r
D[I] = d
L[I] = l
else: # just one element. Write 1's
R[I] = 1
D[I] = 1
L[I] = 1
# done
return R, D, L
def rdl_decomposition(P, reversible=True):
# TODO: this treatment is probably not meaningful for weakly connected matrices.
import msmtools.estimation as msmest
import msmtools.analysis as msmana
# output matrices
n = np.shape(P)[0]
if reversible:
dtype = np.float64
else:
dtype = complex
R = np.zeros((n, n), dtype=dtype)
D = np.zeros((n, n), dtype=dtype)
L = np.zeros((n, n), dtype=dtype)
# treat each strongly connected set separately
S = msmest.connected_sets(P)
for s in S:
I = np.ix_(s, s)
if len(s) > 1:
if reversible:
r, d, l = msmana.rdl_decomposition(P[s, :][:, s], norm='reversible')
# everything must be real-valued - this should rather be handled by msmtools
R[I] = r.real
D[I] = d.real
L[I] = l.real
else:
r, d, l = msmana.rdl_decomposition(P[s, :][:, s], norm='standard')
# write to full
R[I] = r
D[I] = d
L[I] = l
else: # just one element. Write 1's
R[I] = 1
D[I] = 1
L[I] = 1
# done
return R, D, L
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)
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)
def main(nEigenvectors,
nRuns,
m,
outputFolder,
plotEigenvectors,
plotGMRQ,
plotPMF,
clusters,
lagtimes,
native,
save_plots,
showPlots,
filtered,
destFolder,
resname,
plotTransitions=True):
minPos = get_min_Pos(native, resname)
if save_plots and outputFolder is None:
outputFolder = "plots_MSM"
eigenPlots = os.path.join(outputFolder, "eigenvector_plots")
GMRQPlots = os.path.join(outputFolder, "GMRQ_plots")
PMFPlots = os.path.join(outputFolder, "PMF_plots")
TransitionPlots = os.path.join(outputFolder, "transitions")
if save_plots and not os.path.exists(outputFolder):
os.makedirs(outputFolder)
if filtered is not None:
filter_str = "_filtered"
else:
filter_str = ""
if plotEigenvectors and save_plots and not os.path.exists(eigenPlots):
os.makedirs(eigenPlots)
if plotGMRQ and save_plots and not os.path.exists(GMRQPlots):
os.makedirs(GMRQPlots)
if plotPMF and save_plots and not os.path.exists(PMFPlots):
os.makedirs(PMFPlots)
if plotTransitions and save_plots and not os.path.exists(TransitionPlots):
os.makedirs(TransitionPlots)
minPos = np.array(minPos)
GMRQValues = {}
print("Running from " + destFolder)
if plotGMRQ:
GMRQValues = []
if not os.path.exists(os.path.join(destFolder, "eigenvectors")):
os.makedirs(os.path.join(destFolder, "eigenvectors"))
for i in range(nRuns):
titleVar = "%s, run %d" % (destFolder, i)
if plotGMRQ or plotEigenvectors:
msm_object = utilities.readClusteringObject(
os.path.join(destFolder, "MSM_object_%d.pkl" % i))
if plotGMRQ:
GMRQValues.append(np.sum(msm_object.eigenvalues()[:m]))
if plotEigenvectors or plotPMF:
clusters = np.loadtxt(
os.path.join(destFolder, "clusterCenters_%d.dat" % i))
distance = np.linalg.norm(clusters - minPos, axis=1)
volume = np.loadtxt(
os.path.join(destFolder, "volumeOfClusters_%d.dat" % i))
print("Total volume for system %s , run %d" % (destFolder, i),
volume.sum())
if filtered is not None:
volume = volume[filtered]
clusters = clusters[filtered]
distance = distance[filtered]
if plotEigenvectors:
if clusters.size != msm_object.stationary_distribution.size:
mat = computeDeltaG.reestimate_transition_matrix(
msm_object.count_matrix_full)
else:
mat = msm_object.transition_matrix
_, _, L = rdl_decomposition(mat)
figures = []
axes = []
for _ in range((nEigenvectors - 1) // 4 + 1):
f, axarr = plt.subplots(2, 2, figsize=(12, 12))
f.suptitle(titleVar)
figures.append(f)
axes.append(axarr)
for j, row in enumerate(L[:nEigenvectors]):
pdb_filename = os.path.join(destFolder, "eigenvectors",
"eigen_%d_run_%d.pdb" % (j + 1, i))
if j:
atomnames = utilities.getAtomNames(
utilities.sign(row, tol=1e-3))
utilities.write_PDB_clusters(clusters,
use_beta=False,
elements=atomnames,
title=pdb_filename)
else:
utilities.write_PDB_clusters(np.vstack(
(clusters.T, row)).T,
use_beta=True,
elements=None,
title=pdb_filename)
if filtered is not None:
row = row[filtered]
np.savetxt(
os.path.join(
destFolder, "eigenvectors",
"eigen_%d_run_%d%s.dat" % (j + 1, i, filter_str)), row)
axes[j // 4][(j // 2) % 2, j % 2].scatter(distance, row)
axes[j // 4][(j // 2) % 2,
j % 2].set_xlabel("Distance to minimum")
axes[j // 4][(j // 2) % 2,
j % 2].set_ylabel("Eigenvector %d" % (j + 1))
if save_plots:
for j, fg in enumerate(figures):
fg.savefig(
os.path.join(
eigenPlots, "eigenvector_%d_run_%d%s.png" %
(j + 1, i, filter_str)))
plt.figure()
plt.scatter(distance, L[0])
plt.xlabel("Distance to minimum")
plt.ylabel("Eigenvector 1")
plt.savefig(
os.path.join(
eigenPlots,
"eigenvector_1_alone_run_%d%s.png" % (i, filter_str)))
if plotPMF:
data = np.loadtxt(os.path.join(destFolder, "pmf_xyzg_%d.dat" % i))
g = data[:, -1]
if filtered is not None:
g = g[filtered]
print("Clusters with less than 2 PMF:")
print(" ".join(map(str, np.where(g < 2)[0])))
print("")
plt.figure()
plt.title("%s" % (destFolder))
plt.scatter(distance, g)
plt.xlabel("Distance to minima")
plt.ylabel("PMF")
if save_plots:
plt.savefig(
os.path.join(PMFPlots,
"pmf_run_%d%s.png" % (i, filter_str)))
if plotGMRQ:
for t in GMRQValues:
plt.figure()
plt.title("%s" % (destFolder))
plt.xlabel("Number of states")
plt.ylabel("GMRQ")
plt.boxplot(GMRQValues)
if save_plots:
plt.savefig(os.path.join(GMRQPlots, "GMRQ.png" % t))
if plotTransitions:
sasas = []
for file in glob.glob("*/repor*"):
sasas.extend(
pd.read_csv(file, sep=' ',
engine='python')["sasaLig"].values)
sasas = np.array(sasas)
plt.figure()
plt.title("%s" % (destFolder))
plt.xlabel("SASA")
plt.ylabel("Transition Counts")
plt.hist(sasas, 50, alpha=0.75)
if save_plots:
plt.savefig(os.path.join(TransitionPlots, "transition_hist.png"))
if showPlots and (plotEigenvectors or plotGMRQ or plotPMF):
plt.show()
def main(nEigenvectors, nRuns, m, outputFolder, plotEigenvectors, plotGMRQ,
plotPMF, clusters, lagtimes, minPos, save_plots, showPlots, filtered,
destFolder, sasa_col, path_to_report):
if save_plots and outputFolder is None:
outputFolder = "plots_MSM"
if outputFolder is not None:
eigenPlots = os.path.join(outputFolder, "eigenvector_plots")
GMRQPlots = os.path.join(outputFolder, "GMRQ_plots")
PMFPlots = os.path.join(outputFolder, "PMF_plots")
if save_plots and not os.path.exists(outputFolder):
os.makedirs(outputFolder)
if filtered is not None:
filter_str = "_filtered"
else:
filter_str = ""
if plotEigenvectors and save_plots and not os.path.exists(eigenPlots):
os.makedirs(eigenPlots)
if plotGMRQ and save_plots and not os.path.exists(GMRQPlots):
os.makedirs(GMRQPlots)
if plotPMF and save_plots and not os.path.exists(PMFPlots):
os.makedirs(PMFPlots)
minPos = np.array(minPos)
GMRQValues = {}
print("Running from", destFolder)
if plotGMRQ:
GMRQValues = []
if not os.path.exists(os.path.join(destFolder, "eigenvectors")):
os.makedirs(os.path.join(destFolder, "eigenvectors"))
for i in range(nRuns):
if sasa_col is not None:
representatives_files = os.path.join(
destFolder,
"representative_structures/representative_structures_%d.dat" %
i)
sasa = getSASAvalues(representatives_files, sasa_col,
path_to_report)
titleVar = "%s, run %d" % (destFolder, i)
if plotGMRQ or plotEigenvectors:
msm_object = utilities.readClusteringObject(
os.path.join(destFolder, "MSM_object_%d.pkl" % i))
if plotGMRQ:
GMRQValues.append(np.sum(msm_object.eigenvalues()[:m]))
if plotEigenvectors or plotPMF:
clusters = np.loadtxt(
os.path.join(destFolder, "clusterCenters_%d.dat" % i))
distance = np.linalg.norm(clusters - minPos, axis=1)
volume = np.loadtxt(
os.path.join(destFolder, "volumeOfClusters_%d.dat" % i))
print("Total volume for system %s , run %d" % (destFolder, i),
volume.sum())
if filtered is not None:
volume = volume[filtered]
clusters = clusters[filtered]
distance = distance[filtered]
if sasa_col is not None:
sasa = sasa[filtered]
if plotEigenvectors:
if clusters.size != msm_object.stationary_distribution.size:
mat = computeDeltaG.reestimate_transition_matrix(
msm_object.count_matrix_full)
else:
mat = msm_object.transition_matrix
_, _, L = rdl_decomposition(mat)
figures = []
axes = []
for _ in range((nEigenvectors - 1) // 4 + 1):
f, axarr = plt.subplots(2, 2, figsize=(12, 12))
f.suptitle(titleVar)
figures.append(f)
axes.append(axarr)
for j, row in enumerate(L[:nEigenvectors]):
pdb_filename = os.path.join(destFolder, "eigenvectors",
"eigen_%d_run_%d.pdb" % (j + 1, i))
if j:
atomnames = utilities.getAtomNames(
utilities.sign(row, tol=1e-3))
utilities.write_PDB_clusters(clusters,
use_beta=False,
elements=atomnames,
title=pdb_filename)
else:
utilities.write_PDB_clusters(np.vstack(
(clusters.T, row)).T,
use_beta=True,
elements=None,
title=pdb_filename)
if filtered is not None:
row = row[filtered]
np.savetxt(
os.path.join(
destFolder, "eigenvectors",
"eigen_%d_run_%d%s.dat" % (j + 1, i, filter_str)), row)
axes[j // 4][(j // 2) % 2, j % 2].scatter(distance, row)
axes[j // 4][(j // 2) % 2,
j % 2].set_xlabel("Distance to minimum")
axes[j // 4][(j // 2) % 2,
j % 2].set_ylabel("Eigenvector %d" % (j + 1))
Q = msm_object.count_matrix_full.diagonal(
) / msm_object.count_matrix_full.sum()
plt.figure()
plt.scatter(distance, Q)
plt.xlabel("Distance to minimum")
plt.ylabel("Metastability")
if save_plots:
plt.savefig(
os.path.join(eigenPlots,
"Q_run_%d%s.png" % (i, filter_str)))
if save_plots:
for j, fg in enumerate(figures):
fg.savefig(
os.path.join(
eigenPlots, "eigenvector_%d_run_%d%s.png" %
(j + 1, i, filter_str)))
plt.figure()
plt.scatter(distance, L[0])
plt.xlabel("Distance to minimum")
plt.ylabel("Eigenvector 1")
plt.savefig(
os.path.join(
eigenPlots,
"eigenvector_1_alone_run_%d%s.png" % (i, filter_str)))
if plotPMF:
data = np.loadtxt(os.path.join(destFolder, "pmf_xyzg_%d.dat" % i))
g = data[:, -1]
annotations = ["Cluster %d" % i for i in range(g.size)]
if filtered is not None:
g = g[filtered]
annotations = np.array(annotations)[filtered].tolist()
print("Clusters with less than 2 PMF:")
print(" ".join(map(str, np.where(g < 2)[0])))
print("")
fig_pmf, axarr = plt.subplots(2, 2, figsize=(12, 12))
fig_pmf.suptitle(titleVar)
sc1 = axarr[1, 0].scatter(distance, g)
sc2 = axarr[0, 1].scatter(distance, volume)
sc3 = axarr[0, 0].scatter(g, volume)
axes = [axarr[0, 1], axarr[1, 0], axarr[0, 0]]
scs = [sc2, sc1, sc3]
if sasa_col is not None:
axarr[1, 1].scatter(sasa, g)
axarr[1, 0].set_xlabel("Distance to minima")
axarr[1, 0].set_ylabel("PMF")
axarr[0, 1].set_xlabel("Distance to minima")
axarr[0, 1].set_ylabel("Volume")
axarr[0, 0].set_xlabel("PMF")
axarr[0, 0].set_ylabel("Volume")
annot1 = axarr[1, 0].annotate("",
xy=(0, 0),
xytext=(20, 20),
textcoords="offset points",
bbox=dict(boxstyle="round", fc="w"),
arrowprops=dict(arrowstyle="->"))
annot1.set_visible(False)
annot2 = axarr[0, 1].annotate("",
xy=(0, 0),
xytext=(20, 20),
textcoords="offset points",
bbox=dict(boxstyle="round", fc="w"),
arrowprops=dict(arrowstyle="->"))
annot2.set_visible(False)
annot3 = axarr[0, 0].annotate("",
xy=(0, 0),
xytext=(20, 20),
textcoords="offset points",
bbox=dict(boxstyle="round", fc="w"),
arrowprops=dict(arrowstyle="->"))
annot3.set_visible(False)
annot_list = [annot2, annot1, annot3]
if sasa_col is not None:
axarr[1, 1].set_xlabel("SASA")
axarr[1, 1].set_ylabel("PMF")
if save_plots:
fig_pmf.savefig(
os.path.join(PMFPlots,
"pmf_run_%d%s.png" % (i, filter_str)))
if plotGMRQ:
for t in GMRQValues:
plt.figure()
plt.title("%s" % (destFolder))
plt.xlabel("Number of states")
plt.ylabel("GMRQ")
plt.boxplot(GMRQValues)
if save_plots:
plt.savefig(os.path.join(GMRQPlots, "GMRQ.png" % t))
if showPlots and (plotEigenvectors or plotGMRQ or plotPMF):
if plotPMFs:
def update_annot(ind, sc, annot):
"""Update the information box of the selected point"""
pos = sc.get_offsets()[ind["ind"][0]]
annot.xy = pos
annot.set_text(annotations[int(ind["ind"][0])])
# annot.get_bbox_patch().set_facecolor(cmap(norm( z_values[ind["ind"][0]])))
def hover(event):
"""Action to perform when hovering the mouse on a point"""
# vis = any([annot.get_visible() for annot in annot_list])
for i, ax_comp in enumerate(axes):
vis = annot_list[i].get_visible()
if event.inaxes == ax_comp:
for j in range(len(axes)):
if j != i:
annot_list[j].set_visible(False)
cont, ind = scs[i].contains(event)
if cont:
update_annot(ind, scs[i], annot_list[i])
annot_list[i].set_visible(True)
fig_pmf.canvas.draw_idle()
else:
if vis:
annot_list[i].set_visible(False)
fig_pmf.canvas.draw_idle()
fig_pmf.canvas.mpl_connect("motion_notify_event", hover)
plt.show()