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_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_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_)