def test_uncertainties_backward():
n = 4
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False).fit(seqs)
sigma_ts = model.uncertainty_timescales()
sigma_lambda = model.uncertainty_eigenvalues()
sigma_pi = model.uncertainty_pi()
sigma_K = model.uncertainty_K()
yield lambda: np.testing.assert_array_almost_equal(
sigma_ts, [9.13698928, 0.12415533, 0.11713719])
yield lambda: np.testing.assert_array_almost_equal(sigma_lambda, [
1.76569687e-19, 7.14216858e-05, 3.31210649e-04, 3.55556718e-04
])
yield lambda: np.testing.assert_array_almost_equal(
sigma_pi, [0.00741467, 0.00647945, 0.00626743, 0.00777847])
yield lambda: np.testing.assert_array_almost_equal(sigma_K, [
[3.39252419e-04, 3.39246173e-04, 0.00000000e+00, 1.62090239e-06],
[3.52062861e-04, 3.73305510e-04, 1.24093936e-04, 0.00000000e+00],
[0.00000000e+00, 1.04708186e-04, 3.45098923e-04, 3.28820213e-04],
[1.25455972e-06, 0.00000000e+00, 2.90118599e-04, 2.90122944e-04]
])
yield lambda: np.testing.assert_array_almost_equal(model.ratemat_, [
[-2.54439564e-02, 2.54431791e-02, 0.00000000e+00, 7.77248586e-07],
[2.64044208e-02, -2.97630373e-02, 3.35861646e-03, 0.00000000e+00],
[0.00000000e+00, 2.83988103e-03, -3.01998380e-02, 2.73599570e-02],
[6.01581838e-07, 0.00000000e+00, 2.41326592e-02, -2.41332608e-02]
])
def test_uncertainties_backward():
n = 4
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False).fit(seqs)
sigma_ts = model.uncertainty_timescales()
sigma_lambda = model.uncertainty_eigenvalues()
sigma_pi = model.uncertainty_pi()
sigma_K = model.uncertainty_K()
yield lambda: np.testing.assert_array_almost_equal(
sigma_ts, [9.508936, 0.124428, 0.117638])
yield lambda: np.testing.assert_array_almost_equal(sigma_lambda, [
1.76569687e-19, 7.14216858e-05, 3.31210649e-04, 3.55556718e-04
])
yield lambda: np.testing.assert_array_almost_equal(
sigma_pi, [0.007496, 0.006564, 0.006348, 0.007863])
yield lambda: np.testing.assert_array_almost_equal(sigma_K, [[
0.000339, 0.000339, 0., 0.
], [0.000352, 0.000372, 0.000122, 0.], [0., 0.000103, 0.000344, 0.000329
], [0., 0., 0.00029, 0.00029]])
yield lambda: np.testing.assert_array_almost_equal(model.ratemat_, [[
-0.0254, 0.0254, 0., 0.
], [0.02636, -0.029629, 0.003269, 0.], [0., 0.002764, -0.030085, 0.027321
], [0., 0., 0.024098, -0.024098]])
def test_uncertainties_backward():
n = 4
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False).fit(seqs)
sigma_ts = model.uncertainty_timescales()
sigma_lambda = model.uncertainty_eigenvalues()
sigma_pi = model.uncertainty_pi()
sigma_K = model.uncertainty_K()
yield lambda: np.testing.assert_array_almost_equal(
sigma_ts, [9.13698928, 0.12415533, 0.11713719])
yield lambda: np.testing.assert_array_almost_equal(
sigma_lambda, [1.76569687e-19, 7.14216858e-05, 3.31210649e-04, 3.55556718e-04])
yield lambda: np.testing.assert_array_almost_equal(
sigma_pi, [0.00741467, 0.00647945, 0.00626743, 0.00777847])
yield lambda: np.testing.assert_array_almost_equal(
sigma_K,
[[ 3.39252419e-04, 3.39246173e-04, 0.00000000e+00, 1.62090239e-06],
[ 3.52062861e-04, 3.73305510e-04, 1.24093936e-04, 0.00000000e+00],
[ 0.00000000e+00, 1.04708186e-04, 3.45098923e-04, 3.28820213e-04],
[ 1.25455972e-06, 0.00000000e+00, 2.90118599e-04, 2.90122944e-04]])
yield lambda: np.testing.assert_array_almost_equal(
model.ratemat_,
[[ -2.54439564e-02, 2.54431791e-02, 0.00000000e+00, 7.77248586e-07],
[ 2.64044208e-02,-2.97630373e-02, 3.35861646e-03, 0.00000000e+00],
[ 0.00000000e+00, 2.83988103e-03, -3.01998380e-02, 2.73599570e-02],
[ 6.01581838e-07, 0.00000000e+00, 2.41326592e-02, -2.41332608e-02]])
def test_uncertainties_backward():
n = 4
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False).fit(seqs)
sigma_ts = model.uncertainty_timescales()
sigma_lambda = model.uncertainty_eigenvalues()
sigma_pi = model.uncertainty_pi()
sigma_K = model.uncertainty_K()
yield lambda: np.testing.assert_array_almost_equal(
sigma_ts, [9.508936, 0.124428, 0.117638])
yield lambda: np.testing.assert_array_almost_equal(
sigma_lambda,
[1.76569687e-19, 7.14216858e-05, 3.31210649e-04, 3.55556718e-04])
yield lambda: np.testing.assert_array_almost_equal(
sigma_pi, [0.007496, 0.006564, 0.006348, 0.007863])
yield lambda: np.testing.assert_array_almost_equal(
sigma_K,
[[0.000339, 0.000339, 0., 0.],
[0.000352, 0.000372, 0.000122, 0.],
[0., 0.000103, 0.000344, 0.000329],
[0., 0., 0.00029, 0.00029]])
yield lambda: np.testing.assert_array_almost_equal(
model.ratemat_,
[[-0.0254, 0.0254, 0., 0.],
[0.02636, -0.029629, 0.003269, 0.],
[0., 0.002764, -0.030085, 0.027321],
[0., 0., 0.024098, -0.024098]])
def test_0():
# Verify that the partial derivatives of the ith eigenvalue of the
# transition matrix with respect to the entries of the transition matrix
# is given by the outer product of the left and right eigenvectors
# corresponding to that eigenvalue.
# \frac{\partial \lambda_k}{\partial T_{ij}} = U_{i,k} V_{j,k}
X = load_doublewell(random_state=0)['trajectories']
Y = NDGrid(n_bins_per_feature=10).fit_transform(X)
model = MarkovStateModel(verbose=False).fit(Y)
n = model.n_states_
u, lv, rv = _solve_msm_eigensystem(model.transmat_, n)
# first, compute forward difference numerical derivatives
h = 1e-7
dLambda_dP_numeric = np.zeros((n, n, n))
# dLambda_dP_numeric[eigenvalue_index, i, j]
for i in range(n):
for j in range(n):
# perturb the (i,j) entry of transmat
H = np.zeros((n, n))
H[i, j] = h
u_perturbed = sorted(np.real(eigvals(model.transmat_ + H)), reverse=True)
# compute the forward different approx. derivative of each
# of the eigenvalues
for k in range(n):
# sort the eigenvalues of the perturbed matrix in descending
# order, to be consistent w/ _solve_msm_eigensystem
dLambda_dP_numeric[k, i, j] = (u_perturbed[k] - u[k]) / h
for k in range(n):
analytic = np.outer(lv[:, k], rv[:, k])
np.testing.assert_almost_equal(dLambda_dP_numeric[k], analytic, decimal=5)
def test_doublewell():
trjs = load_doublewell(random_state=0)['trajectories']
for n_states in [10, 50]:
clusterer = NDGrid(n_bins_per_feature=n_states)
assignments = clusterer.fit_transform(trjs)
for sliding_window in [True, False]:
model = ContinuousTimeMSM(lag_time=100, sliding_window=sliding_window)
model.fit(assignments)
assert model.optimizer_state_.success
def test_optimize_1():
n = 100
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(use_sparse=True, verbose=True).fit(seqs)
y, x, n = model.loglikelihoods_.T
x = x-x[0]
cross = np.min(np.where(n==n[-1])[0])
def test_doublewell():
trjs = load_doublewell(random_state=0)['trajectories']
for n_states in [10, 50]:
clusterer = NDGrid(n_bins_per_feature=n_states)
assignments = clusterer.fit_transform(trjs)
for sliding_window in [True, False]:
model = ContinuousTimeMSM(lag_time=100,
sliding_window=sliding_window)
model.fit(assignments)
assert model.optimizer_state_.success
def test_pipeline():
from msmbuilder.example_datasets import load_doublewell
from msmbuilder.cluster import NDGrid
from sklearn.pipeline import Pipeline
ds = load_doublewell(random_state=0)
p = Pipeline([('ndgrid', NDGrid(n_bins_per_feature=100)),
('msm', MarkovStateModel(lag_time=100))])
p.fit(ds.trajectories)
p.named_steps['msm'].summarize()
def test_1():
X = load_doublewell(random_state=0)['trajectories']
for i in range(3):
Y = NDGrid(n_bins_per_feature=10).fit_transform([X[i]])
model1 = MarkovStateModel(verbose=False).fit(Y)
model2 = ContinuousTimeMSM().fit(Y)
print('MSM uncertainty timescales:')
print(model1.uncertainty_timescales())
print('ContinuousTimeMSM uncertainty timescales:')
print(model2.uncertainty_timescales())
print()
def test_doublewell():
X = load_doublewell(random_state=0)['trajectories']
for i in range(3):
Y = NDGrid(n_bins_per_feature=10).fit_transform([X[i]])
model1 = MarkovStateModel(verbose=False).fit(Y)
model2 = ContinuousTimeMSM().fit(Y)
print('MSM uncertainty timescales:')
print(model1.uncertainty_timescales())
print('ContinuousTimeMSM uncertainty timescales:')
print(model2.uncertainty_timescales())
print()
def test_hessian():
grid = NDGrid(n_bins_per_feature=10, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
seqs = [seqs[i] for i in range(10)]
lag_time = 10
model = ContinuousTimeMSM(verbose=True, lag_time=lag_time)
model.fit(seqs)
msm = MarkovStateModel(verbose=False, lag_time=lag_time)
print(model.summarize())
print('MSM timescales\n', msm.fit(seqs).timescales_)
print('Uncertainty K\n', model.uncertainty_K())
print('Uncertainty pi\n', model.uncertainty_pi())
def test_hessian_3():
grid = NDGrid(n_bins_per_feature=4, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
seqs = [seqs[i] for i in range(10)]
lag_time = 10
model = ContinuousTimeMSM(verbose=False, lag_time=lag_time)
model.fit(seqs)
msm = MarkovStateModel(verbose=False, lag_time=lag_time)
print(model.summarize())
# print('MSM timescales\n', msm.fit(seqs).timescales_)
print('Uncertainty K\n', model.uncertainty_K())
print('Uncertainty eigs\n', model.uncertainty_eigenvalues())
def test_14():
from msmbuilder.example_datasets import load_doublewell
from msmbuilder.cluster import NDGrid
from sklearn.pipeline import Pipeline
ds = load_doublewell(random_state=0)
p = Pipeline([
('ndgrid', NDGrid(n_bins_per_feature=100)),
('msm', MarkovStateModel(lag_time=100))
])
p.fit(ds.trajectories)
p.named_steps['msm'].summarize()
def test_hessian_1():
n = 5
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(use_sparse=False).fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C, n)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C, n)[1])
hessian2 = Hfun(theta)
# not sure what the cutoff here should be (see plot_test_hessian)
assert np.linalg.norm(hessian1-hessian2) < 1
def test_fit_2():
grid = NDGrid(n_bins_per_feature=5, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=True, lag_time=10)
model.fit(seqs)
t1 = np.sort(model.timescales_)
t2 = -1/np.sort(np.log(np.linalg.eigvals(model.transmat_))[1:])
model = MarkovStateModel(verbose=False, lag_time=10)
model.fit(seqs)
t3 = np.sort(model.timescales_)
np.testing.assert_array_almost_equal(t1, t2)
# timescales should be similar to MSM (withing 50%)
assert abs(t1[-1] - t3[-1]) / t1[-1] < 0.50
def test_fit_2():
grid = NDGrid(n_bins_per_feature=5, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False, lag_time=10)
model.fit(seqs)
t1 = np.sort(model.timescales_)
t2 = -1 / np.sort(np.log(np.linalg.eigvals(model.transmat_))[1:])
model = MarkovStateModel(verbose=False, lag_time=10)
model.fit(seqs)
t3 = np.sort(model.timescales_)
np.testing.assert_array_almost_equal(t1, t2)
# timescales should be similar to MSM (withing 50%)
assert abs(t1[-1] - t3[-1]) / t1[-1] < 0.50
def test_5():
trjs = load_doublewell(random_state=0)['trajectories']
clusterer = NDGrid(n_bins_per_feature=5)
mle_msm = MarkovStateModel(lag_time=100, verbose=False)
b_msm = BayesianMarkovStateModel(
lag_time=100, n_samples=1000, n_chains=8, n_steps=1000,
random_state=0)
states = clusterer.fit_transform(trjs)
b_msm.fit(states)
mle_msm.fit(states)
# this is a pretty silly test. it checks that the mean transition
# matrix is not so dissimilar from the MLE transition matrix.
# This shouldn't necessarily be the case anyways -- the likelihood is
# not "symmetric". And the cutoff chosen is just heuristic.
assert np.linalg.norm(b_msm.all_transmats_.mean(axis=0) - mle_msm.transmat_) < 1e-2
def _plot_test_hessian():
# plot the difference between the numerical hessian and the analytic
# approximate hessian (opens Matplotlib window)
n = 5
grid = NDGrid(n_bins_per_feature=n, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(use_sparse=False).fit(seqs)
theta = model.theta_
C = model.countsmat_
hessian1 = _ratematrix.hessian(theta, C, n)
Hfun = nd.Jacobian(lambda x: _ratematrix.loglikelihood(x, C, n)[1])
hessian2 = Hfun(theta)
import matplotlib.pyplot as pp
pp.scatter(hessian1.flat, hessian2.flat, marker='x')
pp.plot(pp.xlim(), pp.xlim(), 'k')
print('Plotting...', file=sys.stderr)
pp.show()
def test_5():
trjs = load_doublewell(random_state=0)['trajectories']
clusterer = NDGrid(n_bins_per_feature=5)
mle_msm = MarkovStateModel(lag_time=100, verbose=False)
b_msm = BayesianMarkovStateModel(lag_time=100,
n_samples=1000,
n_chains=8,
n_steps=1000,
random_state=0)
states = clusterer.fit_transform(trjs)
b_msm.fit(states)
mle_msm.fit(states)
# this is a pretty silly test. it checks that the mean transition
# matrix is not so dissimilar from the MLE transition matrix.
# This shouldn't necessarily be the case anyways -- the likelihood is
# not "symmetric". And the cutoff chosen is just heuristic.
assert np.linalg.norm(
b_msm.all_transmats_.mean(axis=0) - mle_msm.transmat_) < 1e-2
def test_0():
# Verify that the partial derivatives of the ith eigenvalue of the
# transition matrix with respect to the entries of the transition matrix
# is given by the outer product of the left and right eigenvectors
# corresponding to that eigenvalue.
# \frac{\partial \lambda_k}{\partial T_{ij}} = U_{i,k} V_{j,k}
X = load_doublewell(random_state=0)['trajectories']
Y = NDGrid(n_bins_per_feature=10).fit_transform(X)
model = MarkovStateModel(verbose=False).fit(Y)
n = model.n_states_
u, lv, rv = _solve_msm_eigensystem(model.transmat_, n)
# first, compute forward difference numerical derivatives
h = 1e-7
dLambda_dP_numeric = np.zeros((n, n, n))
# dLambda_dP_numeric[eigenvalue_index, i, j]
for i in range(n):
for j in range(n):
# perturb the (i,j) entry of transmat
H = np.zeros((n, n))
H[i, j] = h
u_perturbed = sorted(np.real(eigvals(model.transmat_ + H)),
reverse=True)
# compute the forward different approx. derivative of each
# of the eigenvalues
for k in range(n):
# sort the eigenvalues of the perturbed matrix in descending
# order, to be consistent w/ _solve_msm_eigensystem
dLambda_dP_numeric[k, i, j] = (u_perturbed[k] - u[k]) / h
for k in range(n):
analytic = np.outer(lv[:, k], rv[:, k])
np.testing.assert_almost_equal(dLambda_dP_numeric[k],
analytic,
decimal=5)
def test_score_1():
grid = NDGrid(n_bins_per_feature=5, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = ContinuousTimeMSM(verbose=False, lag_time=10, n_timescales=3).fit(seqs)
np.testing.assert_approx_equal(model.score(seqs), model.score_)
#!/usr/bin/env python
"""
Bayesian Estimation of MSMs
< http://msmbuilder.org/latest/examples/bayesian-msm.html>
"""
import numpy as np
from matplotlib import pyplot as plt
plt.style.use("ggplot")
from mdtraj.utils import timing
from msmbuilder.example_datasets import load_doublewell
from msmbuilder.cluster import NDGrid
from msmbuilder.msm import BayesianMarkovStateModel, MarkovStateModel
trjs = load_doublewell(random_state=0)['trajectories']
plt.hist(np.concatenate(trjs), bins=50, log=True)
plt.ylabel('Frequency')
plt.show()
def test_score_1():
grid = NDGrid(n_bins_per_feature=5, min=-np.pi, max=np.pi)
seqs = grid.fit_transform(load_doublewell(random_state=0)['trajectories'])
model = (ContinuousTimeMSM(verbose=False, lag_time=10,
n_timescales=3).fit(seqs))
np.testing.assert_approx_equal(model.score(seqs), model.score_)
