def build_msm_from_counts(counts, lag_time, symmetrize, return_rev_counts=False, trim=True):
"""
Estimates the transition probability matrix from the counts matrix.
Parameters
----------
counts : matrix
the MSM counts matrix
lag_time :
the lag time to build the msm with, in frames
symmetrize : {'MLE', 'Transpose', None}
symmetrization scheme so that we have reversible counts
return_rev_counts : bool
whether or not to return the reversible counts or not
Returns
-------
t_matrix : matrix
the transition probability matrix
rev_counts : matrix
the estimate of the reversible counts
(only returned if `return_rev_counts` is True)
"""
symmetrize = str(symmetrize).lower()
symmetrization_error = ValueError("Invalid symmetrization scheme requested: %s. Exiting." % symmetrize)
if symmetrize not in ['mle', 'transpose', 'none']:
raise symmetrization_error
if trim:
counts, mapping = ergodic_trim(counts)
# Apply a symmetrization scheme
if symmetrize == 'mle':
rev_counts = mle_reversible_count_matrix(counts, prior=0.0)
elif symmetrize == 'transpose':
rev_counts = 0.5*(counts + counts.transpose())
elif symmetrize == 'none':
rev_counts = counts
else:
raise symmetrization_error
t_matrix = estimate_transition_matrix(rev_counts)
if symmetrize in ['mle', 'transpose']:
populations = np.array(rev_counts.sum(0)).flatten()
elif symmetrize == 'none':
vectors = msm_analysis.get_eigenvectors(t_matrix, 5)[1]
populations = vectors[:, 0]
else:
populations = None
if populations is not None:
populations /= populations.sum()
return counts, rev_counts, t_matrix, populations, mapping
def fit(self, sequences, y=None):
"""Estimate model parameters.
Parameters
----------
sequences : list
List of integer sequences, each of which is one-dimensional
y : unused parameter
Returns
-------
self
"""
if self.n_states is None:
self.n_states = np.max([np.max(x) for x in sequences]) + 1
from msmbuilder import MSMLib
MSMLib.logger.info = lambda *args: None
from msmbuilder.msm_analysis import get_eigenvectors
from msmbuilder.MSMLib import mle_reversible_count_matrix, estimate_transition_matrix, ergodic_trim
self.rawcounts_ = self._count_transitions(sequences)
if self.prior_counts > 0:
self.rawcounts_ = scipy.sparse.csr_matrix(self.rawcounts_.todense() + self.prior_counts)
# STEP (1): Ergodic trimming
if self.ergodic_trim:
self.rawcounts_, mapping = ergodic_trim(scipy.sparse.csr_matrix(self.rawcounts_))
self.mapping_ = {}
for i, j in enumerate(mapping):
if j != -1:
self.mapping_[i] = j
else:
self.mapping_ = dict((zip(np.arange(self.n_states), np.arange(self.n_states))))
# STEP (2): Reversible counts matrix
if self.reversible_type in ["mle", "MLE"]:
self.countsmat_ = mle_reversible_count_matrix(self.rawcounts_)
elif self.reversible_type in ["transpose", "Transpose"]:
self.countsmat_ = 0.5 * (self.rawcounts_ + self.rawcounts_.T)
elif self.reversible_type is None:
self.countsmat_ = self.rawcounts_
else:
raise RuntimeError()
# STEP (3): transition matrix
self.transmat_ = estimate_transition_matrix(self.countsmat_)
# STEP (3.5): Stationary eigenvector
if self.reversible_type in ["mle", "MLE", "transpose", "Transpose"]:
self.populations_ = np.array(self.countsmat_.sum(0)).flatten()
elif self.reversible_type is None:
vectors = get_eigenvectors(self.transmat_, 5)[1]
self.populations_ = vectors[:, 0]
else:
raise RuntimeError()
self.populations_ /= self.populations_.sum() # ensure normalization
return self
def plot_distribution(mixture_model, grid, t_matrix=None, eigen=1, n_contours=80):
"""Plot the mixture distribution."""
xx, yy = grid
mixture_samples = np.c_[xx.ravel(), yy.ravel()]
contour_data = mixture_model.score(mixture_samples)
contour_data = -contour_data.reshape(xx.shape)
if t_matrix is not None:
_, vecs = msma.get_eigenvectors(t_matrix, n_eigs=eigen)
sizes = vecs[:, -1] * 300
print vecs[:, -1]
colors = ['r' if s > 0 else 'b' for s in sizes]
sizes = np.abs(sizes)
else:
sizes = 300
colors = 'y'
# Plot means
means = mixture_model.means_
pp.scatter(means[:, 0], means[:, 1], c=colors, s=sizes)
pp.contour(xx, yy, contour_data, n_contours)
def __init__(self, T, num_macrostates, flux_cutoff=None):
"""Base class for PCCA and PCCA+.
Parameters
----------
T : csr sparse matrix
Transition matrix
num_macrostates : int
Desired number of macrostates
flux_cutoff : float, optional
Can be set to discard low-flux eigenvectors.
"""
self.T = T
self.num_macrostates = num_macrostates
self.eigenvalues, self.left_eigenvectors = msm_analysis.get_eigenvectors(
T, self.num_macrostates)
utils.normalize_left_eigenvectors(self.left_eigenvectors)
if flux_cutoff != None:
self.eigenvalues, self.left_eigenvectors = utils.trim_eigenvectors_by_flux(
self.eigenvalues, self.left_eigenvectors, flux_cutoff)
self.num_macrostates = len(self.eigenvalues)
self.populations = self.left_eigenvectors[:, 0]
self.num_microstates = len(self.populations)
# Construct properly normalized right eigenvectors
self.right_eigenvectors = utils.construct_right_eigenvectors(
self.left_eigenvectors, self.populations, self.num_macrostates)
def run(tProb, observable, init_pops=None, num_vecs=10, output='evec_amps.h5'):
if init_pops is None:
init_pops = np.ones(tProb.shape[0]).astype(float) / float(tProb.shape[0])
else:
init_pops = init_pops.astype(float)
init_pops /= init_pops.sum()
assert (observable.shape[0] == init_pops.shape[0])
assert (observable.shape[0] == tProb.shape[0])
try:
f = io.loadh('eigs%d.h5' % num_vecs)
vals = f['vals']
vecsL = f['vecs']
except:
vals, vecsL = msm_analysis.get_eigenvectors(tProb, num_vecs + 1, right=False)
io.saveh('eigs%d.h5' % num_vecs, vals=vals, vecs=vecsL)
equil = vecsL[:,0] / vecsL[:,0].sum()
dyn_vecsL = vecsL[:, 1:]
# normalize the left and right eigenvectors
dyn_vecsL /= np.sqrt(np.sum(dyn_vecsL * dyn_vecsL / np.reshape(equil, (-1, 1)), axis=0))
dyn_vecsR = dyn_vecsL / np.reshape(equil, (-1, 1))
amps = dyn_vecsL.T.dot(observable) * dyn_vecsR.T.dot(init_pops)
io.saveh(output, evals=vals[1:], amplitudes=amps)
logger.info("saved output to %s" % output)
def plot_distribution(mixture_model,
grid,
t_matrix=None,
eigen=1,
n_contours=80):
"""Plot the mixture distribution."""
xx, yy = grid
mixture_samples = np.c_[xx.ravel(), yy.ravel()]
contour_data = mixture_model.score(mixture_samples)
contour_data = -contour_data.reshape(xx.shape)
if t_matrix is not None:
_, vecs = msma.get_eigenvectors(t_matrix, n_eigs=eigen)
sizes = vecs[:, -1] * 300
print vecs[:, -1]
colors = ['r' if s > 0 else 'b' for s in sizes]
sizes = np.abs(sizes)
else:
sizes = 300
colors = 'y'
# Plot means
means = mixture_model.means_
pp.scatter(means[:, 0], means[:, 1], c=colors, s=sizes)
pp.contour(xx, yy, contour_data, n_contours)
def test_get_eigenvectors_left():
# just some random counts
N = 100
counts = np.random.randint(1, 10, size=(N,N))
transmat, pi = build_msm(scipy.sparse.csr_matrix(counts), 'MLE')[1:3]
values0, vectors0 = get_eigenvectors(transmat, 10)
values1, vectors1 = get_reversible_eigenvectors(transmat, 10)
values2, vectors2 = get_reversible_eigenvectors(transmat, 10, populations=pi)
# check that the eigenvalues are the same using the two methods
np.testing.assert_array_almost_equal(values0, values1)
# check that the eigenvectors returned by both methods are _actually_
# left eigenvectors of the transmat
def test_eigenpairs(values, vectors):
for value, vector in zip(values, vectors.T):
np.testing.assert_array_almost_equal(
(transmat.T.dot(vector) / vector).flatten(), np.ones(N)*value)
np.testing.assert_array_almost_equal(pi, vectors0[:, 0])
np.testing.assert_array_almost_equal(pi, vectors1[:, 0])
np.testing.assert_array_almost_equal(pi, vectors2[:, 0])
test_eigenpairs(values0, vectors0)
test_eigenpairs(values1, vectors1)
test_eigenpairs(values2, vectors2)
def __init__(self, T, num_macrostates, flux_cutoff=None):
"""Base class for PCCA and PCCA+.
Parameters
----------
T : csr sparse matrix
Transition matrix
num_macrostates : int
Desired number of macrostates
flux_cutoff : float, optional
Can be set to discard low-flux eigenvectors.
"""
self.T = T
self.num_macrostates = num_macrostates
self.eigenvalues, self.left_eigenvectors = msm_analysis.get_eigenvectors(T, self.num_macrostates)
utils.normalize_left_eigenvectors(self.left_eigenvectors)
if flux_cutoff != None:
self.eigenvalues, self.left_eigenvectors = utils.trim_eigenvectors_by_flux(
self.eigenvalues, self.left_eigenvectors, flux_cutoff)
self.num_macrostates = len(self.eigenvalues)
self.populations = self.left_eigenvectors[:, 0]
self.num_microstates = len(self.populations)
# Construct properly normalized right eigenvectors
self.right_eigenvectors = utils.construct_right_eigenvectors(
self.left_eigenvectors, self.populations, self.num_macrostates)
def build_msm(counts, symmetrize='MLE', ergodic_trimming=True):
"""
Estimates the transition probability matrix from the counts matrix.
Parameters
----------
counts : matrix
the MSM counts matrix
symmetrize : {'MLE', 'Transpose', None}
symmetrization scheme so that we have reversible counts
ergodic_trim : bool (optional)
whether or not to trim states to achieve an ergodic model
Returns
-------
rev_counts : matrix
the estimate of the reversible counts
t_matrix : matrix
the transition probability matrix
populations : ndarray, float
the equilibrium populations of each state
mapping : ndarray, int
a mapping from the passed counts matrix to the new counts and transition
matrices
"""
symmetrize = str(symmetrize).lower()
symmetrization_error = ValueError("Invalid symmetrization scheme requested: %s. Exiting." % symmetrize)
if symmetrize not in ['mle', 'transpose', 'none']:
raise symmetrization_error
if ergodic_trimming:
counts, mapping = ergodic_trim(counts)
else:
mapping = np.arange(counts.shape[0])
# Apply a symmetrization scheme
if symmetrize == 'mle':
rev_counts = mle_reversible_count_matrix(counts)
elif symmetrize == 'transpose':
rev_counts = 0.5 * (counts + counts.transpose())
elif symmetrize == 'none':
rev_counts = counts
else:
raise symmetrization_error
t_matrix = estimate_transition_matrix(rev_counts)
if symmetrize in ['mle', 'transpose']:
populations = np.array(rev_counts.sum(0)).flatten()
elif symmetrize == 'none':
vectors = msm_analysis.get_eigenvectors(t_matrix, 5)[1]
populations = vectors[:, 0]
else:
raise symmetrization_error
populations /= populations.sum() # ensure normalization
return rev_counts, t_matrix, populations, mapping
def calculate_all_to_all_mfpt(tprob, populations=None):
"""
Calculate the all-states by all-state matrix of mean first passage
times.
This uses the fundamental matrix formalism, and should be much faster
than GetMFPT for calculating many MFPTs.
Parameters
----------
tprob : matrix
transition probability matrix
populations : array_like, float
optional argument, the populations of each state. If not supplied,
it will be computed from scratch
Returns
-------
MFPT : array, float
MFPT in time units of LagTime, square array for MFPT from i -> j
See Also
--------
GetMFPT : function
for calculating a subset of the MFPTs, with functionality for including
a set of sinks
"""
msm_analysis.check_transition(tprob)
if scipy.sparse.issparse(tprob):
tprob = tprob.toarray()
logger.warning('calculate_all_to_all_mfpt does not support sparse linear algebra')
if populations is None:
eigens = msm_analysis.get_eigenvectors(tprob, 5)
if np.count_nonzero(np.imag(eigens[1][:,0])) != 0:
raise ValueError('First eigenvector has imaginary parts')
populations = np.real(eigens[1][:,0])
# ensure that tprob is a transition matrix
msm_analysis.check_transition(tprob)
num_states = len(populations)
if tprob.shape[0] != num_states:
raise ValueError("Shape of tprob and populations vector don't match")
eye = np.transpose( np.matrix(np.ones(num_states)) )
limiting_matrix = eye * populations
#z = scipy.linalg.inv(scipy.sparse.eye(num_states, num_states) - (tprob - limiting_matrix))
z = scipy.linalg.inv(np.eye(num_states) - (tprob - limiting_matrix))
# mfpt[i,j] = z[j,j] - z[i,j] / pi[j]
mfpt = -z
for j in range(num_states):
mfpt[:, j] += z[j, j]
mfpt[:, j] /= populations[j]
return mfpt
def GetRateMatrix(T,EigAns=None,FixNegativity=True):
NumStates=T.shape[0]
if EigAns==None:
EigAns = get_eigenvectors(T,NumStates)
Pi=EigAns[1][:,0]
print("Done Getting Eigenvectors")
"""
K=np.zeros((NumStates,NumStates),dtype=T.dtype)
for i in range(1,NumStates):
phi=EigAns[1][:,i]
psi=phi/Pi
alpha=np.dot(phi,psi)**.5
psi/=alpha
phi/=alpha
K-=np.log(EigAns[0][i])*np.outer(psi,phi)
"""
#To Check, compare the following transition matrix with the input:
#T2=scipy.linalg.matfuncs.expm(-K)
#T2-T
ev=EigAns[1]
p=ev[:,0]
for i in xrange(NumStates):
ev[:,i]/=np.dot(ev[:,i]/p,ev[:,i])**.5
#Ld=np.diag(-np.log(EigAns[0]))
#K=np.dot(np.dot(np.dot(np.diag(1./Pi),ev),Ld),ev.transpose())
#return(K)
print("Getting evT and deleting old ev.")
ev=np.real(ev).copy()
lam=EigAns[0]
lam=np.abs(lam)
#lam[where(lam<0)]=1/np.e #Anything with negative eigenvalues is set to have timescale 1 lagtime.
del EigAns
D=scipy.sparse.dia_matrix((1/p,0),(NumStates,NumStates))
K=D.dot(ev)
print("Done 1st mm")
L=scipy.sparse.dia_matrix((-np.log(lam),0),(NumStates,NumStates))
K=K.transpose()
K=L.dot(K)
print("Done 2nd mm")
K=K.transpose()
K=np.array(K,dtype=lam.dtype,order="C")
ev=ev.transpose()
ev=np.array(ev,dtype=lam.dtype,order="C")
K=np.dot(K,ev)
print("Done 3rd mm")
if FixNegativity==True:#This enforces "reasonable" constraints on the rate matrix, e.g. negative off diagonals and positive diagonals
RemoveRateDiagonal(K)
return(K)
def estimate_mle_populations(matrix):
if msmb_version == '2.8.2':
t_matrix = estimate_transition_matrix(matrix)
populations = get_eigenvectors(t_matrix, 1, **kwargs)[1][:, 0]
return populations
elif msmb_version == '3.2.0':
obj = MarkovStateModel()
populations = obj._fit_mle(matrix)[1]
return populations
def GetRateMatrix(T, EigAns=None, FixNegativity=True):
NumStates = T.shape[0]
if EigAns == None:
EigAns = get_eigenvectors(T, NumStates)
Pi = EigAns[1][:, 0]
print("Done Getting Eigenvectors")
"""
K=np.zeros((NumStates,NumStates),dtype=T.dtype)
for i in range(1,NumStates):
phi=EigAns[1][:,i]
psi=phi/Pi
alpha=np.dot(phi,psi)**.5
psi/=alpha
phi/=alpha
K-=np.log(EigAns[0][i])*np.outer(psi,phi)
"""
#To Check, compare the following transition matrix with the input:
#T2=scipy.linalg.matfuncs.expm(-K)
#T2-T
ev = EigAns[1]
p = ev[:, 0]
for i in xrange(NumStates):
ev[:, i] /= np.dot(ev[:, i] / p, ev[:, i])**.5
#Ld=np.diag(-np.log(EigAns[0]))
#K=np.dot(np.dot(np.dot(np.diag(1./Pi),ev),Ld),ev.transpose())
#return(K)
print("Getting evT and deleting old ev.")
ev = np.real(ev).copy()
lam = EigAns[0]
lam = np.abs(lam)
#lam[where(lam<0)]=1/np.e #Anything with negative eigenvalues is set to have timescale 1 lagtime.
del EigAns
D = scipy.sparse.dia_matrix((1 / p, 0), (NumStates, NumStates))
K = D.dot(ev)
print("Done 1st mm")
L = scipy.sparse.dia_matrix((-np.log(lam), 0), (NumStates, NumStates))
K = K.transpose()
K = L.dot(K)
print("Done 2nd mm")
K = K.transpose()
K = np.array(K, dtype=lam.dtype, order="C")
ev = ev.transpose()
ev = np.array(ev, dtype=lam.dtype, order="C")
K = np.dot(K, ev)
print("Done 3rd mm")
if FixNegativity == True: #This enforces "reasonable" constraints on the rate matrix, e.g. negative off diagonals and positive diagonals
RemoveRateDiagonal(K)
return (K)
def kl_equilib(gold_eq, comp_tmatrix):
"""Return the KL divergence of comp_tmatrix from gold_tmatrix."""
comp_vals, comp_vecs = msma.get_eigenvectors(comp_tmatrix, n_eigs=1)
# Sanity check
if np.abs(comp_vals[0] - 1.0) > EPS:
print "Warning, comp eigenvalue is {}".format(comp_vals[0])
# Do KL
comp_eq = comp_vecs[0]
kl = np.sum(np.log(gold_eq / comp_eq) * gold_eq)
return kl
def kl_equilib(gold_eq, comp_tmatrix):
"""Return the KL divergence of comp_tmatrix from gold_tmatrix."""
comp_vals, comp_vecs = msma.get_eigenvectors(comp_tmatrix, n_eigs=1)
# Sanity check
if np.abs(comp_vals[0] - 1.0) > EPS:
print "Warning, comp eigenvalue is {}".format(comp_vals[0])
# Do KL
comp_eq = comp_vecs[0]
kl = np.sum(np.log(gold_eq / comp_eq) * gold_eq)
return kl
def get_implied_timescales(t_matrix, n_timescales=4, lag_time=1):
"""Get implied timescales from a transition matrix."""
try:
vals, vecs = msma.get_eigenvectors(t_matrix, n_eigs=n_timescales + 1)
implied_timescales = -lag_time / np.log(vals[1:])
implied_timescales_pad = np.pad(
implied_timescales, (0, n_timescales - len(implied_timescales)),
mode='constant')
return implied_timescales_pad
except Exception:
print "+++ Error getting implied timescales +++"
return np.zeros(n_timescales)
def get_implied_timescales(t_matrix, n_timescales=4, lag_time=1):
"""Get implied timescales from a transition matrix."""
try:
vals, vecs = msma.get_eigenvectors(t_matrix, n_eigs=n_timescales + 1)
implied_timescales = -lag_time / np.log(vals[1:])
implied_timescales_pad = np.pad(implied_timescales,
(0, n_timescales - len(implied_timescales)),
mode='constant')
return implied_timescales_pad
except Exception:
print "+++ Error getting implied timescales +++"
return np.zeros(n_timescales)
def main(dir, coarse , lag, type):
data=dict()
rmsd=numpy.loadtxt('%s/Coarsed_r10_gen/Coarsed%s_r10_Gens.rmsd.dat' % (dir, coarse), usecols=(2,))
#data['rmsd']=numpy.loadtxt('%s/Coarsed_r10_gen/Coarsed%s_r10_Gens.selfrmsd.dat' % (dir, coarse))
data['rmsd']=numpy.loadtxt('%s/Coarsed_r10_gen/Coarsed%s_r10_Gens.rmsd.dat' % (dir, coarse), usecols=(2,))
com=numpy.loadtxt('%s/Coarsed_r10_gen/Coarsed%s_r10_Gens.vmd_com.dat' % (dir, coarse), usecols=(1,))
com=[i/com[0] for i in com]
data['com']=com[1:]
modeldir='%s/msml%s_coarse_r10_d%s/' % (dir, lag, coarse)
pops=numpy.loadtxt('%s/Populations.dat' % modeldir)
map=numpy.loadtxt('%s/Mapping.dat' % modeldir)
map_rmsd=[]
map_com=[]
for x in range(0, len(data['rmsd'])):
if map[x]!=-1:
map_com.append(data['com'][x])
map_rmsd.append(data['rmsd'][x])
map_com=numpy.array(map_com)
map_rmsd=numpy.array(map_rmsd)
T=mmread('%s/tProb.mtx' % modeldir)
eigs_m=msm_analysis.get_eigenvectors(T, 10)
order=numpy.argsort(map_rmsd)
ordercom=numpy.argsort(map_com)
cm=pylab.cm.get_cmap('RdYlBu_r') #blue will be negative components, red positive
print numpy.shape(eigs_m[1][:,1])
for i in range(1,4):
if i==0:
print numpy.where(eigs_m[1][:,i]==max(eigs_m[1][:,i]))
else:
print numpy.where(eigs_m[1][:,i]==min(eigs_m[1][:,i]))
pylab.scatter(map_com[ordercom], map_rmsd[ordercom], c=eigs_m[1][ordercom,i], cmap=cm, s=1000*abs(eigs_m[1][ordercom,i]), alpha=0.5)
print map_com[ordercom][numpy.argmax(eigs_m[1][ordercom,i])]
print eigs_m[1][ordercom,i][1]
# pylab.scatter(map_rmsd[order], statehelix[order]*100., c=eigs_m[1][:,i], cmap=cm, s=50, alpha=0.7)
pylab.subplots_adjust(left = 0.1, right = 1.02, bottom = 0.10, top = 0.85, wspace = 0, hspace = 0)
CB=pylab.colorbar()
l,b,w,h=pylab.gca().get_position().bounds
ll, bb, ww, hh=CB.ax.get_position().bounds
CB.ax.set_position([ll, b+0.1*h, ww, h*0.8])
ylabel=pylab.ylabel('p53 RMSD to Bound Conformation ($\AA$)')
xlabel=pylab.xlabel(r'p53 to S100B($\beta$$\beta$) CoM Separation ($\AA$)')
pylab.ylim(0, max(map_rmsd))
#pylab.title('Folding and Binding \n Colored by Magnitudes of Slowest Eigenvector Components')
pylab.savefig('%s/2deigs%i_com_prmsd.pdf' %(modeldir, i),dpi=300)
pylab.show()
def test_eigenvector_norm():
N = 100
counts = np.random.randint(1, 10, size=(N,N))
transmat, pi = build_msm(scipy.sparse.csr_matrix(counts), 'MLE')[1:3]
left_values0, left_vectors0 = get_eigenvectors(transmat, 10, right=False, normalized=True)
right_values0, right_vectors0 = get_eigenvectors(transmat, 10, right=True, normalized=True)
left_values1, left_vectors1 = get_reversible_eigenvectors(transmat, 10, right=False, normalized=True)
right_values1, right_vectors1 = get_reversible_eigenvectors(transmat, 10, right=True, normalized=True)
np.testing.assert_array_almost_equal(left_values0, right_values0)
np.testing.assert_array_almost_equal(left_values1, right_values1)
test_left_vectors1 = left_vectors1 * np.sign(left_vectors0[0].reshape((1,-1))) * np.sign(left_vectors1[0].reshape((1,-1)))
test_right_vectors1 = right_vectors1 * np.sign(right_vectors0[0].reshape((1,-1))) * np.sign(right_vectors1[0].reshape((1,-1)))
np.testing.assert_array_almost_equal(left_vectors0, test_left_vectors1)
np.testing.assert_array_almost_equal(right_vectors0, test_right_vectors1)
Id = np.eye(10)
np.testing.assert_array_almost_equal(np.abs(left_vectors0.T.dot(right_vectors0)), Id)
np.testing.assert_array_almost_equal(np.abs(left_vectors1.T.dot(right_vectors1)), Id)
def analyze_msm(t_matrix, centroids, desc, neigen=4, show=False):
"""Analyze a particular msm.
Right now, it does this by printing eigenvalues and optionally plotting
eigenvectors.
"""
val, vec = msma.get_eigenvectors(t_matrix, neigen)
oolambda = -1.0 / np.log(val[1:])
print("\n%s" % desc)
print("Eigenvalues:\t%s" % val.__str__())
print("1/lambda:\t%s" % oolambda.__str__())
if show: plot_eigens(centroids, vec, val, desc)
return oolambda
def analyze_msm(t_matrix, centroids, desc, neigen=4, show=False):
"""Analyze a particular msm.
Right now, it does this by printing eigenvalues and optionally plotting
eigenvectors.
"""
val, vec = msma.get_eigenvectors(t_matrix, neigen)
oolambda = -1.0 / np.log(val[1:])
print("\n%s" % desc)
print("Eigenvalues:\t%s" % val.__str__())
print("1/lambda:\t%s" % oolambda.__str__())
if show: plot_eigens(centroids, vec, val, desc)
return oolambda
def step(self):
mapping, tprob = self.tprob()
# if we can guarentee that the counts matrix is reversible, we can
# do this faster without the eigensolver, but I don't want to do that yet.
vectors = msm_analysis.get_eigenvectors(tprob, min(5, tprob.shape[0]))[1]
populations = vectors[:, 0]
# this chooses the point from the multinomial, but its now indexed
# in the mapped (integer) space
chosen = np.where(np.random.multinomial(1, populations) == 1)[0][0]
# back out the chosen item as a tuple, such that mapping[k] == chosen
k = next(k for k,v in mapping.iteritems() if v == chosen)
self.walker.set_point(k)
def step(self):
mapping, tprob = self.tprob()
# if we can guarentee that the counts matrix is reversible, we can
# do this faster without the eigensolver, but I don't want to do that yet.
vectors = msm_analysis.get_eigenvectors(tprob, min(5,
tprob.shape[0]))[1]
populations = vectors[:, 0]
# this chooses the point from the multinomial, but its now indexed
# in the mapped (integer) space
chosen = np.where(np.random.multinomial(1, populations) == 1)[0][0]
# back out the chosen item as a tuple, such that mapping[k] == chosen
k = next(k for k, v in mapping.iteritems() if v == chosen)
self.walker.set_point(k)
def get_eigenvalues( count_matrix ):
bad_states = np.array(np.where( count_matrix.sum(axis=1) == 0 )[0]).flatten()
i_ary = count_matrix.nonzero()[0]
j_ary = count_matrix.nonzero()[1]
i_ary = np.concatenate( (i_ary, bad_states) )
j_ary = np.concatenate( (j_ary, bad_states) )
new_data = np.concatenate( (count_matrix.data, np.ones(len(bad_states))) )
print i_ary.shape, count_matrix.data.shape, new_data.shape, len(bad_states)
count_matrix = scipy.sparse.csr_matrix( (new_data, (i_ary, j_ary)) )
#count_matrix = count_matrix.tolil()
#count_matrix[(bad_states, bad_states)] = 1
#count_matrix = count_matrix.tocsr()
print count_matrix.data.shape, count_matrix.nonzero()[0].shape
#NZ = np.array(count_matrix.nonzero()).T
#keep_ind = []
#for i in xrange(len(NZ)):
# if NZ[i][0] in bad_states or NZ[i][1] in bad_states:
# pass
# else:
# keep_ind.append(i)
#keep_ind = np.array(keep_ind)
#N = NZ.max()+1
#count_matrix = scipy.sparse.csr_matrix( (np.array(count_matrix.data)[keep_ind], NZ[keep_ind].T), shape=(N,N), copy=True )
try:
t_matrix = MSMLib.build_msm(count_matrix, symmetrize=args.symmetrize)[1]
except:
return None
vals = msm_analysis.get_eigenvectors(t_matrix, args.num_vals, epsilon=1)[0]
vals.sort()
return vals[::-1]
def set_coordinate_as_eigvector2(self, lag_time=1, symmetrize='transpose'):
"""
Set the reaction coordinate to be the second eigenvector of the MSM generated
by counts, the provided lag_time, and the provided symmetrization method.
Parameters
----------
lag_time : int
The MSM lag time to use (in units of frames) in the estimation
of the MSM transition probability matrix from the `counts` matrix.
symmetrize : str {'mle', 'transpose', 'none'}
Which symmetrization method to employ in the estimation of the
MSM transition probability matrix from the `counts` matrix.
"""
t_matrix = MSMLib.build_msm_from_counts(self.counts, lag_time, symmetrize)
v, w = get_eigenvectors(t_matrix, 5)
self.reaction_coordinate_values = w[:, 1].flatten()
return
def set_coordinate_as_eigvector2(self, lag_time=1, symmetrize='transpose'):
"""
Set the reaction coordinate to be the second eigenvector of the MSM generated
by counts, the provided lag_time, and the provided symmetrization method.
Parameters
----------
lag_time : int
The MSM lag time to use (in units of frames) in the estimation
of the MSM transition probability matrix from the `counts` matrix.
symmetrize : str {'mle', 'transpose', 'none'}
Which symmetrization method to employ in the estimation of the
MSM transition probability matrix from the `counts` matrix.
"""
t_matrix = MSMLib.build_msm_from_counts(self.counts, lag_time, symmetrize)
v, w = get_eigenvectors(t_matrix, 5)
self.reaction_coordinate_values = w[:,1].flatten()
return
def get_implied_timescales(self, i, num_vals=2):
# Get the model
model_sql = self.all_models[i]
model = get_model_from_sql(model_sql)
transition_mat = model.transition_matrix
lag_time = model.lag_time
print('\n\n')
print(i)
if not msma.is_transition_matrix(transition_mat):
print ("%d is not a transition matrix!" % i)
eigenvals, _ = msma.get_eigenvectors(transition_mat, num_vals + 1, epsilon=1.0)
eigenvals = eigenvals[1:]
oo_lambda = [-1.0 / np.log(ev) for ev in eigenvals]
print(oo_lambda)
return oo_lambda
#!/usr/bin/env python
from msmbuilder import io
from msmbuilder import msm_analysis
from scipy.io import mmread
from argparse import ArgumentParser
import os
parser = ArgumentParser()
parser.add_argument('-t', dest='tProb', help='transition matrix', default='./tProb.mtx')
parser.add_argument('-o', dest='output', help='output filename', default='./eigs.h5')
parser.add_argument('-n', dest='num_vecs', help='number of eigenvectors to find.', default=500, type=int)
args = parser.parse_args()
if os.path.exists(args.output):
raise Exception("path (%s) exists!" % args.output)
tProb = mmread(args.tProb)
eigs = msm_analysis.get_eigenvectors(tProb, args.num_vecs)
io.saveh(args.output, vals=eigs[0], vecs=eigs[1])
def kl_equilib_setup(gold_tmatrix):
"""Save gold equilibrium population."""
gold_vals, gold_vecs = msma.get_eigenvectors(gold_tmatrix, n_eigs=1)
assert np.abs(gold_vals[0] - 1.0) < EPS, 'Gold eigenval is {}'.format(gold_vals[0])
return gold_vecs[0]
def GetEigenvectors_Right(*args, **kwargs):
warnings.warn(
'GetEigenvectors_Right is deprecated use get_eigenvectors() with the keyword Right=True'
)
kwargs['right'] = True
return msm_analysis.get_eigenvectors(*args, **kwargs)
def build_msm(counts, symmetrize='MLE', ergodic_trimming=True):
"""
Estimates the transition probability matrix from the counts matrix.
Parameters
----------
counts : scipy.sparse.csr_matrix
the MSM counts matrix
symmetrize : {'MLE', 'Transpose', None}
symmetrization scheme so that we have reversible counts
ergodic_trim : bool (optional)
whether or not to trim states to achieve an ergodic model
Returns
-------
rev_counts : matrix
the estimate of the reversible counts
t_matrix : matrix
the transition probability matrix
populations : ndarray, float
the equilibrium populations of each state
mapping : ndarray, int
a mapping from the passed counts matrix to the new counts and transition
matrices
"""
symmetrize = str(symmetrize).lower()
symmetrization_error = ValueError("Invalid symmetrization scheme "
"requested: %s. Exiting." % symmetrize)
if symmetrize not in ['mle', 'transpose', 'none']:
raise symmetrization_error
if ergodic_trimming:
counts, mapping = ergodic_trim(counts)
else:
mapping = np.arange(counts.shape[0])
# Apply a symmetrization scheme
if symmetrize == 'mle':
if not ergodic_trimming:
raise ValueError("MLE symmetrization requires ergodic trimming.")
rev_counts = mle_reversible_count_matrix(counts)
elif symmetrize == 'transpose':
rev_counts = 0.5 * (counts + counts.transpose())
elif symmetrize == 'none':
rev_counts = counts
else:
raise symmetrization_error
t_matrix = estimate_transition_matrix(rev_counts)
if symmetrize in ['mle', 'transpose']:
populations = np.array(rev_counts.sum(0)).flatten()
elif symmetrize == 'none':
vectors = msm_analysis.get_eigenvectors(t_matrix, 5)[1]
populations = vectors[:, 0]
else:
raise symmetrization_error
populations /= populations.sum() # ensure normalization
return rev_counts, t_matrix, populations, mapping
def kl_equilib_setup(gold_tmatrix):
"""Save gold equilibrium population."""
gold_vals, gold_vecs = msma.get_eigenvectors(gold_tmatrix, n_eigs=1)
assert np.abs(gold_vals[0] - 1.0) < EPS, 'Gold eigenval is {}'.format(
gold_vals[0])
return gold_vecs[0]
def build_msm_from_counts(counts,
lag_time,
symmetrize,
return_rev_counts=False,
trim=True):
"""
Estimates the transition probability matrix from the counts matrix.
Parameters
----------
counts : matrix
the MSM counts matrix
lag_time :
the lag time to build the msm with, in frames
symmetrize : {'MLE', 'Transpose', None}
symmetrization scheme so that we have reversible counts
return_rev_counts : bool
whether or not to return the reversible counts or not
Returns
-------
t_matrix : matrix
the transition probability matrix
rev_counts : matrix
the estimate of the reversible counts
(only returned if `return_rev_counts` is True)
"""
symmetrize = str(symmetrize).lower()
symmetrization_error = ValueError(
"Invalid symmetrization scheme requested: %s. Exiting." % symmetrize)
if symmetrize not in ['mle', 'transpose', 'none']:
raise symmetrization_error
if trim:
counts, mapping = ergodic_trim(counts)
# Apply a symmetrization scheme
if symmetrize == 'mle':
rev_counts = mle_reversible_count_matrix(counts, prior=0.0)
elif symmetrize == 'transpose':
rev_counts = 0.5 * (counts + counts.transpose())
elif symmetrize == 'none':
rev_counts = counts
else:
raise symmetrization_error
t_matrix = estimate_transition_matrix(rev_counts)
if symmetrize in ['mle', 'transpose']:
populations = np.array(rev_counts.sum(0)).flatten()
elif symmetrize == 'none':
vectors = msm_analysis.get_eigenvectors(t_matrix, 5)[1]
populations = vectors[:, 0]
else:
populations = None
if populations is not None:
populations /= populations.sum()
return counts, rev_counts, t_matrix, populations, mapping
# try to find eigenvectors in a file
file_list = glob.glob("eigs*.h5")
try:
fn = file_list[0]
f = io.loadh(fn)
vals = f['vals']
vecs = f['vecs']
vals = vals[:num_vecs + 1]
vecs = vecs[:, :num_vecs + 1]
except:
vals, vecs = msm_analysis.get_eigenvectors( T, num_vecs+1 )
#vals, vecs = eigs( T, k = num_vecs + 1 )
vecs=vecs.real
pi = vecs[:,0] / vecs[:,0].sum()
vecs /= np.sum( np.square( vecs ) / pi.reshape( (-1,1) ), axis=0 )
ord_param_ind = ord_param.argsort()
state_lines = np.array([ np.where( ord_param[ ord_param_ind ] == i )[0][0] for i in np.unique( ord_param ) ])[1:]
for i in range( num_vecs ):
figure()
eval = vals[i+1]
def GetEigenvectors_Right(*args, **kwargs):
warnings.warn('GetEigenvectors_Right is deprecated use get_eigenvectors() with the keyword Right=True')
kwargs['right'] = True
return msm_analysis.get_eigenvectors(*args, **kwargs)
def calculate_fluxes(sources, sinks, tprob, populations=None, committors=None):
"""
Compute the transition path theory flux matrix.
Parameters
----------
sources : array_like, int
The set of unfolded/reactant states.
sinks : array_like, int
The set of folded/product states.
tprob : mm_matrix
The transition matrix.
Returns
------
fluxes : mm_matrix
The flux matrix
Optional Parameters
-------------------
populations : nd_array, float
The equilibrium populations, if not provided is re-calculated
committors : nd_array, float
The committors associated with `sources`, `sinks`, and `tprob`.
If not provided, is calculated from scratch. If provided, `sources`
and `sinks` are ignored.
References
----------
.. [1] Metzner, P., Schutte, C. & Vanden-Eijnden, E. Transition path theory
for Markov jump processes. Multiscale Model. Simul. 7, 1192–1219
(2009).
.. [2] Berezhkovskii, A., Hummer, G. & Szabo, A. Reactive flux and folding
pathways in network models of coarse-grained protein dynamics. J.
Chem. Phys. 130, 205102 (2009).
"""
sources, sinks = _check_sources_sinks(sources, sinks)
msm_analysis.check_transition(tprob)
if scipy.sparse.issparse(tprob):
dense = False
else:
dense = True
# check if we got the populations
if populations is None:
eigens = msm_analysis.get_eigenvectors(tprob, 1)
if np.count_nonzero(np.imag(eigens[1][:, 0])) != 0:
raise ValueError('First eigenvector has imaginary components')
populations = np.real(eigens[1][:, 0])
# check if we got the committors
if committors is None:
committors = calculate_committors(sources, sinks, tprob)
# perform the flux computation
Indx, Indy = tprob.nonzero()
n = tprob.shape[0]
if dense:
X = np.zeros((n, n))
Y = np.zeros((n, n))
X[(np.arange(n), np.arange(n))] = populations * (1.0 - committors)
Y[(np.arange(n), np.arange(n))] = committors
else:
X = scipy.sparse.lil_matrix((n, n))
Y = scipy.sparse.lil_matrix((n, n))
X.setdiag(populations * (1.0 - committors))
Y.setdiag(committors)
if dense:
fluxes = np.dot(np.dot(X, tprob), Y)
fluxes[(np.arange(n), np.arange(n))] = np.zeros(n)
else:
fluxes = (X.tocsr().dot(tprob.tocsr())).dot(Y.tocsr())
# This should be the same as below, but it's a bit messy...
#fluxes = np.dot(np.dot(X.tocsr(), tprob.tocsr()), Y.tocsr())
fluxes = fluxes.tolil()
fluxes.setdiag(np.zeros(n))
return fluxes
def pcca_plus(T, N, flux_cutoff=None, do_minimization=True, objective_function="crisp_metastability"):
"""Perform PCCA+ lumping
Parameters
----------
T : csr sparse matrix
Transition matrix
M : int
desired (maximum) number of macrostates
flux_cutoff : float, optional
If desired, discard eigenvectors with flux below this value.
do_minimization : bool, optional
If False, skip the optimization of the transformation matrix.
In general, minimization is recommended.
objective_function: {'crisp_metastablility', 'metastability', 'metastability'}
Possible objective functions. See objective for details.
Returns
-------
A : ndarray
The transformation matrix.
chi : ndarray
The membership matrix
vr : ndarray
The right eigenvectors.
microstate_mapping : ndarray
Mapping from microstates to macrostates.
Notes
-----
PCCA+ is used to construct a "lumped" state decomposition. First,
The eigenvalues and eigenvectors are computed for a transition matrix.
An optimization problem is then used to estimate a mapping from
microstates to macrostates.
For each microstate i, microstate_mapping[i] is chosen as the
macrostate with the largest membership (chi) value.
The membership matrix chi is given by chi = dot(vr,A).
Finally, the transformation matrix A is the output of a constrained
optimization problem.
References
----------
.. [1] Deuflhard P, et al. "Identification of almost invariant
aggregates in reversible nearly uncoupled markov chains,"
Linear Algebra Appl., vol 315 pp 39-59, 2000.
.. [2] Deuflhard P, Weber, M., "Robust perron cluster analysis in
conformation dynamics,"
Linear Algebra Appl., vol 398 pp 161-184 2005.
.. [3] Kube S, Weber M. "A coarse graining method for the
identification of transition rates between molecular conformations,"
J. Chem. Phys., vol 126 pp 24103-024113, 2007.
See Also
--------
PCCA
"""
lam, vl = msm_analysis.get_eigenvectors(T, N)
normalize_left_eigenvectors(vl)
if flux_cutoff != None:
lam, vl = trim_eigenvectors_by_flux(lam, vl, flux_cutoff)
N = len(lam)
pi = vl[:, 0]
vr = vl.copy()
for i in range(N):
vr[:, i] /= pi
vr[:, i] *= np.sign(vr[0, i])
vr[:, i] /= np.sqrt(dot(vr[:, i] * pi, vr[:, i]))
A, chi, microstate_mapping = opt_soft(vr, N, pi, lam, T, do_minimization=do_minimization, objective_function=objective_function)
return A, chi, vr, microstate_mapping
def PCCA(T, num_macro, tolerance=1E-5, flux_cutoff=None):
"""Create a lumped model using the PCCA algorithm.
1. Iterate over the eigenvectors, starting with the slowest.
2. Calculate the spread of that eigenvector within each existing macrostate.
3. Pick the macrostate with the largest eigenvector spread.
4. Split the macrostate based on the sign of the eigenvector.
Parameters
----------
T : csr sparse matrix
A transition matrix
num_macro : int
The desired number of states.
tolerance : float, optional
Specifies the numerical cutoff to use when splitting states based on sign.
flux_cutoff : float, optional
If enabled, discard eigenvectors with flux below this value.
Returns
-------
microstate_mapping : ndarray
mapping from the Microstate indices to the Macrostate indices
Notes
-----
To construct a Macrostate MSM, you then need to map your Assignment data to
the new states (e.g. MSMLib.apply_mapping_to_assignments).
References
----------
.. [1] Deuflhard P, et al. "Identification of almost invariant
aggregates in reversible nearly uncoupled markov chains,"
Linear Algebra Appl., vol 315 pp 39-59, 2000.
"""
n = T.shape[0]
lam, vl = msm_analysis.get_eigenvectors(T, num_macro)
normalize_left_eigenvectors(vl)
if flux_cutoff is not None:
lam, vl = trim_eigenvectors_by_flux(lam, vl, flux_cutoff)
num_macro = len(lam)
pi = vl[:, 0]
vr = vl.copy()
for i in range(num_macro):
vr[:, i] /= pi
vr[:, i] *= np.sign(vr[0, i])
vr[:, i] /= np.sqrt(dot(vr[:, i] * pi, vr[:, i]))
#Remove the stationary eigenvalue and eigenvector.
lam = lam[1:]
vr = vr[:, 1:]
microstate_mapping = np.zeros(n, 'int')
#Function to calculate the spread of a single eigenvector.
spread = lambda x: x.max() - x.min()
"""
1. Iterate over the eigenvectors, starting with the slowest.
2. Calculate the spread of that eigenvector within each existing macrostate.
3. Pick the macrostate with the largest eigenvector spread.
4. Split the macrostate based on the sign of the eigenvector.
"""
for i in range(num_macro - 1): # Thus, if we want 2 states, we split once.
v = vr[:, i]
AllSpreads = np.array(
[spread(v[microstate_mapping == k]) for k in range(i + 1)])
StateToBeSplit = np.argmax(AllSpreads)
microstate_mapping[(microstate_mapping == StateToBeSplit)
& (v >= tolerance)] = i + 1
return (microstate_mapping)
def PCCA(T, num_macro, tolerance=1E-5, flux_cutoff=None):
"""Create a lumped model using the PCCA algorithm.
1. Iterate over the eigenvectors, starting with the slowest.
2. Calculate the spread of that eigenvector within each existing macrostate.
3. Pick the macrostate with the largest eigenvector spread.
4. Split the macrostate based on the sign of the eigenvector.
Parameters
----------
T : csr sparse matrix
A transition matrix
num_macro : int
The desired number of states.
tolerance : float, optional
Specifies the numerical cutoff to use when splitting states based on sign.
flux_cutoff : float, optional
If enabled, discard eigenvectors with flux below this value.
Returns
-------
microstate_mapping : ndarray
mapping from the Microstate indices to the Macrostate indices
Notes
-----
To construct a Macrostate MSM, you then need to map your Assignment data to
the new states (e.g. MSMLib.apply_mapping_to_assignments).
References
----------
.. [1] Deuflhard P, et al. "Identification of almost invariant
aggregates in reversible nearly uncoupled markov chains,"
Linear Algebra Appl., vol 315 pp 39-59, 2000.
"""
n = T.shape[0]
lam, vl = msm_analysis.get_eigenvectors(T, num_macro)
normalize_left_eigenvectors(vl)
if flux_cutoff is not None:
lam, vl = trim_eigenvectors_by_flux(lam, vl, flux_cutoff)
num_macro = len(lam)
pi = vl[:, 0]
vr = vl.copy()
for i in range(num_macro):
vr[:, i] /= pi
vr[:, i] *= np.sign(vr[0, i])
vr[:, i] /= np.sqrt(dot(vr[:, i] * pi, vr[:, i]))
#Remove the stationary eigenvalue and eigenvector.
lam = lam[1:]
vr = vr[:, 1:]
microstate_mapping = np.zeros(n, 'int')
#Function to calculate the spread of a single eigenvector.
spread = lambda x: x.max() - x.min()
"""
1. Iterate over the eigenvectors, starting with the slowest.
2. Calculate the spread of that eigenvector within each existing macrostate.
3. Pick the macrostate with the largest eigenvector spread.
4. Split the macrostate based on the sign of the eigenvector.
"""
for i in range(num_macro - 1): # Thus, if we want 2 states, we split once.
v = vr[:, i]
AllSpreads = np.array([spread(v[microstate_mapping == k]) for k in range(i + 1)])
StateToBeSplit = np.argmax(AllSpreads)
microstate_mapping[(microstate_mapping == StateToBeSplit) & (v >= tolerance)] = i + 1
return(microstate_mapping)
from matplotlib.pyplot import *
from scipy.io import mmread
import os, sys, re
matplotlib.rcParams['font.size']=22
#import warnings
#warnings.filterwarnings("ignore",category=DeprecationWarning)
if os.path.exists( options.writeFN +'%d.npy'%options.num_vals ):
print "Found %s, and using these values rather than recalculating them." % ( options.writeFN+'%d.npy'%options.num_vals )
Vals = np.load( options.writeFN+'%d.npy'%options.num_vals )
else:
T = mmread( options.T_FN )
Vals,Vecs = msm_analysis.get_eigenvectors( T, options.num_vals+1 )
Vals = Vals.real[1:]
np.save( options.writeFN + '%d.npy' % options.num_vals, Vals )
print "Saved values"
Vals = Vals[np.where(Vals > 0)]
figure()
subplot(132)
Taus = - options.lag / options.divisor / np.log( Vals )
hlines( Taus, 0, 1, color=options.color)
if options.y_lim == None:
ylim([10**int(np.log10(Taus.min())),10**int(np.log10(Taus.max())+1)])
else:
def main(modeldir, gensfile, write=False):
if not os.path.exists('%s/eig-states/' % modeldir):
os.mkdir('%s/eig-states/' % modeldir)
ohandle=open('%s/eig-states/eiginfo.txt' % modeldir, 'w')
project=Project.load_from('%s/ProjectInfo.yaml' % modeldir.split('Data')[0])
ass=io.loadh('%s/Assignments.Fixed.h5' % modeldir)
gens=Trajectory.load_from_lhdf(gensfile)
T=mmread('%s/tProb.mtx' % modeldir)
data=dict()
data['rmsd']=numpy.loadtxt('%s.rmsd.dat' % gensfile.split('.lh5')[0])
com=numpy.loadtxt('%s.vmd_com.dat' % gensfile.split('.lh5')[0], usecols=(1,))
data['com']=com[1:]
pops=numpy.loadtxt('%s/Populations.dat' % modeldir)
map=numpy.loadtxt('%s/Mapping.dat' % modeldir)
map_rmsd=[]
map_com=[]
for x in range(0, len(data['rmsd'])):
if map[x]!=-1:
map_com.append(data['com'][x])
map_rmsd.append(data['rmsd'][x])
map_com=numpy.array(map_com)
map_rmsd=numpy.array(map_rmsd)
T=mmread('%s/tProb.mtx' % modeldir)
eigs_m=msm_analysis.get_eigenvectors(T, 10)
cm=pylab.cm.get_cmap('RdYlBu_r') #blue will be negative components, red positive
print numpy.shape(eigs_m[1][:,1])
for i in range(0,1):
order=numpy.argsort(eigs_m[1][:,i])
if i==0:
maxes=[]
gen_maxes=[]
values=[]
ohandle.write('eig%s maxes\n' % i)
ohandle.write('state\tgenstate\tmagnitude\trmsd\tcom\n')
for n in order[::-1][:5]:
gen_maxes.append(numpy.where(map==n)[0])
maxes.append(n)
values.append(eigs_m[1][n,i])
ohandle.write('%s\t%s\t%s\t%s\t%s\n' % (n, numpy.where(map==n)[0], eigs_m[1][n,i], map_rmsd[n], map_com[n]))
print "maxes at ", maxes, values
maxes=numpy.array(maxes)
if write==True:
get_structure(modeldir, i, gen_maxes, maxes, gens, project, ass, type='max')
else:
maxes=[]
gen_maxes=[]
values=[]
ohandle.write('eig%s maxes\n' % i)
for n in order[::-1][:5]:
gen_maxes.append(numpy.where(map==n)[0])
maxes.append(n)
values.append(eigs_m[1][n,i])
ohandle.write('%s\t%s\t%s\t%s\t%s\n' % (n, numpy.where(map==n)[0], eigs_m[1][n,i], map_rmsd[n], map_com[n]))
print "maxes at ", maxes, values
order=numpy.argsort(eigs_m[1][:,i])
mins=[]
gen_mins=[]
values=[]
ohandle.write('eig%s mins\n' % i)
for n in order[:5]:
gen_mins.append(numpy.where(map==n)[0])
mins.append(n)
values.append(eigs_m[1][n,i])
ohandle.write('%s\t%s\t%s\t%s\t%s\n' % (n, numpy.where(map==n)[0], eigs_m[1][n,i], map_rmsd[n], map_com[n]))
print "mins at ", mins, values
if write==True:
get_structure(modeldir, i, gen_maxes, maxes, gens, project, ass, type='max')
get_structure(modeldir, i, gen_mins, mins, gens, project, ass, type='min')
pylab.scatter(map_com[order], map_rmsd[order], c=eigs_m[1][order,i], cmap=cm, s=1000*abs(eigs_m[1][order,i]), alpha=0.5)
print map_com[order][numpy.argmax(eigs_m[1][order,i])]
print eigs_m[1][order,i][1]
CB=pylab.colorbar()
l,b,w,h=pylab.gca().get_position().bounds
ll, bb, ww, hh=CB.ax.get_position().bounds
CB.ax.set_position([ll, b+0.1*h, ww, h*0.8])
CB.set_label('Eig%s Magnitudes' % i)
ylabel=pylab.ylabel('Ligand RMSD to Xtal ($\AA$)')
xlabel=pylab.xlabel(r'P Active Site - L COM Distance ($\AA$)')
pylab.legend(loc=8, frameon=False)
pylab.savefig('%s/2deigs%i_com_prmsd.png' %(modeldir, i),dpi=300)
def calculate_all_to_all_mfpt(tprob, populations=None):
"""
Calculate the all-states by all-state matrix of mean first passage
times.
This uses the fundamental matrix formalism, and should be much faster
than GetMFPT for calculating many MFPTs.
Parameters
----------
tprob : matrix
transition probability matrix
populations : array_like, float
optional argument, the populations of each state. If not supplied,
it will be computed from scratch
Returns
-------
MFPT : array, float
MFPT in time units of LagTime, square array for MFPT from i -> j
See Also
--------
GetMFPT : function
for calculating a subset of the MFPTs, with functionality for including
a set of sinks
References
----------
.. [1] Metzner, P., Schutte, C. & Vanden-Eijnden, E. Transition path theory
for Markov jump processes. Multiscale Model. Simul. 7, 1192–1219
(2009).
.. [2] Berezhkovskii, A., Hummer, G. & Szabo, A. Reactive flux and folding
pathways in network models of coarse-grained protein dynamics. J.
Chem. Phys. 130, 205102 (2009).
"""
msm_analysis.check_transition(tprob)
if scipy.sparse.issparse(tprob):
tprob = tprob.toarray()
logger.warning('calculate_all_to_all_mfpt does not support sparse linear algebra')
if populations is None:
eigens = msm_analysis.get_eigenvectors(tprob, 1)
if np.count_nonzero(np.imag(eigens[1][:, 0])) != 0:
raise ValueError('First eigenvector has imaginary parts')
populations = np.real(eigens[1][:, 0])
# ensure that tprob is a transition matrix
msm_analysis.check_transition(tprob)
num_states = len(populations)
if tprob.shape[0] != num_states:
raise ValueError("Shape of tprob and populations vector don't match")
eye = np.transpose(np.matrix(np.ones(num_states)))
limiting_matrix = eye * populations
#z = scipy.linalg.inv(scipy.sparse.eye(num_states, num_states) - (tprob - limiting_matrix))
z = scipy.linalg.inv(np.eye(num_states) - (tprob - limiting_matrix))
# mfpt[i,j] = z[j,j] - z[i,j] / pi[j]
mfpt = -z
for j in range(num_states):
mfpt[:, j] += z[j, j]
mfpt[:, j] /= populations[j]
return mfpt
from scipy.io import *
from msmbuilder import Trajectory
import numpy
import pylab
from msmbuilder import msm_analysis
T=mmread('./l6/tProb.mtx')
map=numpy.loadtxt('./l6/Mapping.dat')
com_dist=numpy.loadtxt('Gens_com_dist.dat', usecols=(1,))
prmsd=numpy.loadtxt('Gens_p53_rmsd.dat', usecols=(1,))
frames=numpy.where(map!=-1)[0]
stateprmsd=prmsd[frames]
statecom=com_dist[frames]
eigs_m=msm_analysis.get_eigenvectors(T, 10)
#import pdb
#pdb.set_trace()
order=numpy.argsort(stateprmsd)
ordercom=numpy.argsort(statecom)
cm=pylab.cm.get_cmap('RdYlBu_r') #blue will be negative components, red positive
print numpy.shape(eigs_m[1][:,1])
print len(stateprmsd)
print len(frames)
for i in range(0,4):
#pylab.scatter(statermsd[order], statehelix[order]*100., c=eigs_m[1][:,i], cmap=cm, s=1000*abs(eigs_m[1][:,i]), alpha=0.7)
pylab.scatter(statecom[ordercom], stateprmsd[ordercom]*10., c=eigs_m[1][ordercom,i], cmap=cm, s=1000*abs(eigs_m[1][ordercom,i]), alpha=0.5)
def pcca_plus(T,
N,
flux_cutoff=None,
do_minimization=True,
objective_function="crisp_metastability"):
"""Perform PCCA+ lumping
Parameters
----------
T : csr sparse matrix
Transition matrix
M : int
desired (maximum) number of macrostates
flux_cutoff : float, optional
If desired, discard eigenvectors with flux below this value.
do_minimization : bool, optional
If False, skip the optimization of the transformation matrix.
In general, minimization is recommended.
objective_function: {'crisp_metastablility', 'metastability', 'metastability'}
Possible objective functions. See objective for details.
Returns
-------
A : ndarray
The transformation matrix.
chi : ndarray
The membership matrix
vr : ndarray
The right eigenvectors.
microstate_mapping : ndarray
Mapping from microstates to macrostates.
Notes
-----
PCCA+ is used to construct a "lumped" state decomposition. First,
The eigenvalues and eigenvectors are computed for a transition matrix.
An optimization problem is then used to estimate a mapping from
microstates to macrostates.
For each microstate i, microstate_mapping[i] is chosen as the
macrostate with the largest membership (chi) value.
The membership matrix chi is given by chi = dot(vr,A).
Finally, the transformation matrix A is the output of a constrained
optimization problem.
References
----------
.. [1] Deuflhard P, et al. "Identification of almost invariant
aggregates in reversible nearly uncoupled markov chains,"
Linear Algebra Appl., vol 315 pp 39-59, 2000.
.. [2] Deuflhard P, Weber, M., "Robust perron cluster analysis in
conformation dynamics,"
Linear Algebra Appl., vol 398 pp 161-184 2005.
.. [3] Kube S, Weber M. "A coarse graining method for the
identification of transition rates between molecular conformations,"
J. Chem. Phys., vol 126 pp 24103-024113, 2007.
See Also
--------
PCCA
"""
lam, vl = msm_analysis.get_eigenvectors(T, N)
normalize_left_eigenvectors(vl)
if flux_cutoff != None:
lam, vl = trim_eigenvectors_by_flux(lam, vl, flux_cutoff)
N = len(lam)
pi = vl[:, 0]
vr = vl.copy()
for i in range(N):
vr[:, i] /= pi
vr[:, i] *= np.sign(vr[0, i])
vr[:, i] /= np.sqrt(dot(vr[:, i] * pi, vr[:, i]))
A, chi, microstate_mapping = opt_soft(
vr,
N,
pi,
lam,
T,
do_minimization=do_minimization,
objective_function=objective_function)
return A, chi, vr, microstate_mapping
def calculate_fluxes(sources, sinks, tprob, populations=None, committors=None):
"""
Compute the transition path theory flux matrix.
Parameters
----------
sources : array_like, int
The set of unfolded/reactant states.
sinks : array_like, int
The set of folded/product states.
tprob : mm_matrix
The transition matrix.
Returns
------
fluxes : mm_matrix
The flux matrix
Optional Parameters
-------------------
populations : nd_array, float
The equilibrium populations, if not provided is re-calculated
committors : nd_array, float
The committors associated with `sources`, `sinks`, and `tprob`.
If not provided, is calculated from scratch. If provided, `sources`
and `sinks` are ignored.
"""
sources, sinks = _check_sources_sinks(sources, sinks)
msm_analysis.check_transition(tprob)
if scipy.sparse.issparse(tprob):
dense = False
else:
dense = True
# check if we got the populations
if populations is None:
eigens = msm_analysis.get_eigenvectors(tprob, 5)
if np.count_nonzero(np.imag(eigens[1][:,0])) != 0:
raise ValueError('First eigenvector has imaginary components')
populations = np.real(eigens[1][:,0])
# check if we got the committors
if committors is None:
committors = calculate_committors(sources, sinks, tprob)
# perform the flux computation
Indx, Indy = tprob.nonzero()
n = tprob.shape[0]
if dense:
X = np.zeros((n, n))
Y = np.zeros((n, n))
X[(np.arange(n), np.arange(n))] = populations * (1.0 - committors)
Y[(np.arange(n), np.arange(n))] = committors
else:
X = scipy.sparse.lil_matrix((n,n))
Y = scipy.sparse.lil_matrix((n,n))
X.setdiag( populations * (1.0 - committors))
Y.setdiag(committors)
if dense:
fluxes = np.dot(np.dot(X, tprob), Y)
fluxes[(np.arange(n), np.arange(n))] = np.zeros(n)
else:
fluxes = np.dot(np.dot(X.tocsr(), tprob.tocsr()), Y.tocsr())
fluxes = fluxes.tolil()
fluxes.setdiag(np.zeros(n))
return fluxes
