pyemma.thermo.TRAM

class pyemma.thermo.TRAM(lag, count_mode='sliding', connectivity='post_hoc_RE', nstates_full=None, equilibrium=None, maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', nn=None, connectivity_factor=1.0, direct_space=False, N_dtram_accelerations=0, callback=None, init='mbar', init_maxiter=5000, init_maxerr=1e-08, overcounting_factor=1.0)

Transition(-based) Reweighting Analysis Method.

__init__(lag, count_mode='sliding', connectivity='post_hoc_RE', nstates_full=None, equilibrium=None, maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', nn=None, connectivity_factor=1.0, direct_space=False, N_dtram_accelerations=0, callback=None, init='mbar', init_maxiter=5000, init_maxerr=1e-08, overcounting_factor=1.0)

Transition(-based) Reweighting Analysis Method

Parameters:

• lag (int) – Integer lag time at which transitions are counted.
• count_mode (str, optional, default='sliding') –

  mode to obtain count matrices from discrete trajectories. Should be one of: * ‘sliding’ : A trajectory of length T will have \(T-\tau\) counts at time indexes

  \[(0 \rightarrow \tau), (1 \rightarrow \tau+1), ..., (T-\tau-1 \rightarrow T-1)\]

  • ’sample’ : A trajectory of length T will have \(T/\tau\) counts at time indexes

    \[(0 \rightarrow \tau), (\tau \rightarrow 2 \tau), ..., ((T/\tau-1) \tau \rightarrow T)\]

  Currently only ‘sliding’ is supported.

• connectivity (str, optional, default='post_hoc_RE') –

  One of ‘post_hoc_RE’, ‘BAR_variance’, ‘reversible_pathways’ or ‘summed_count_matrix’. Defines what should be considered a connected set in the joint (product) space of conformations and thermodynamic ensembles. * ‘reversible_pathways’ : requires that every state in the connected set

  can be reached by following a pathway of reversible transitions. A reversible transition between two Markov states (within the same thermodynamic state k) is a pair of Markov states that belong to the same strongly connected component of the count matrix (from thermodynamic state k). A pathway of reversible transitions is a list of reversible transitions [(i_1, i_2), (i_2, i_3),…, (i_(N-2), i_(N-1)), (i_(N-1), i_N)]. The thermodynamic state where the reversible transitions happen, is ignored in constructing the reversible pathways. This is equivalent to assuming that two ensembles overlap at some Markov state whenever there exist frames from both ensembles in that Markov state.

  • ’post_hoc_RE’ : similar to ‘reversible_pathways’ but with a more strict requirement for the overlap between thermodynamic states. It is required that every state in the connected set can be reached by following a pathway of reversible transitions or jumping between overlapping thermodynamic states while staying in the same Markov state. A reversible transition between two Markov states (within the same thermodynamic state k) is a pair of Markov states that belong to the same strongly connected component of the count matrix (from thermodynamic state k). Two thermodynamic states k and l are defined to overlap at Markov state n if a replica exchange simulation [2]_ restricted to state n would show at least one transition from k to l or one transition from from l to k. The expected number of replica exchanges is estimated from the simulation data. The minimal number required of replica exchanges per Markov state can be increased by decreasing connectivity_factor.
  • ’BAR_variance’ : like ‘post_hoc_RE’ but with a different condition to define the thermodynamic overlap based on the variance of the BAR estimator [3]_. Two thermodynamic states k and l are defined to overlap at Markov state n if the variance of the free energy difference Delta f_{kl} computed with BAR (and restricted to conformations form Markov state n) is less or equal than one. The minimally required variance can be controlled with connectivity_factor.
  • ’summed_count_matrix’ : all thermodynamic states are assumed to overlap. The connected set is then computed by summing the count matrices over all thermodynamic states and taking it’s largest strongly connected set. Not recommended!

  For more details see pyemma.thermo.extensions.cset.compute_csets_TRAM().

• nstates_full (int, optional, default=None) – Number of cluster centers, i.e., the size of the full set of states.
• equilibrium (list of booleans, optional) – For every trajectory triple (ttraj[i], dtraj[i], btraj[i]), indicates whether to assume global equilibrium. If true, the triple is not used for computing kinetic quantities (but only thermodynamic quantities). By default, no trajectory is assumed to be in global equilibrium. This is the TRAMMBAR extension.
• maxiter (int, optional, default=10000) – The maximum number of self-consistent iterations before the estimator exits unsuccessfully.
• maxerr (float, optional, default=1E-15) – Convergence criterion based on the maximal free energy change in a self-consistent iteration step.
• save_convergence_info (int, optional, default=0) – Every save_convergence_info iteration steps, store the actual increment and the actual log-likelihood; 0 means no storage.
• dt_traj (str, optional, default='1 step') –

  Description of the physical time corresponding to the lag. May be used by analysis algorithms such as plotting tools to pretty-print the axes. By default ‘1 step’, i.e. there is no physical time unit. Specify by a number, whitespace and unit. Permitted units are (* is an arbitrary string):

  ’fs’, ‘femtosecond*’

  ’ps’, ‘picosecond*’

  ’ns’, ‘nanosecond*’

  ’us’, ‘microsecond*’

  ’ms’, ‘millisecond*’

  ’s’, ‘second*’
• connectivity_factor (float, optional, default=1.0) – Only needed if connectivity=’post_hoc_RE’ or ‘BAR_variance’. Values greater than 1.0 weaken the connectivity conditions. For ‘post_hoc_RE’ this multiplies the number of hypothetically observed transitions. For ‘BAR_variance’ this scales the threshold for the minimal allowed variance of free energy differences.
• direct_space (bool, optional, default=False) – Whether to perform the self-consistent iteration with Boltzmann factors (direct space) or free energies (log-space). When analyzing data from multi-temperature simulations, direct-space is not recommended.
• N_dtram_accelerations (int, optional, default=0) – Convergence of TRAM can be speeded up by interleaving the updates in the self-consistent iteration with a dTRAM-like update step. N_dtram_accelerations says how many times the dTRAM-like update step should be applied in every iteration of the TRAM equations. Currently this is only effective if direct_space=True.
• init (str, optional, default=None) –

  Use a specific initialization for self-consistent iteration:

  None: use a hard-coded guess for free energies and Lagrangian multipliers

  ’mbar’: perform a short MBAR estimate to initialize the free energies
• init_maxiter (int, optional, default=5000) – The maximum number of self-consistent iterations during the initialization.
• init_maxerr (float, optional, default=1.0E-8) – Convergence criterion for the initialization.
• overcounting_factor (double, default = 1.0) – Only needed if equilibrium contains True (TRAMMBAR). Sets the relative statistical weight of equilibrium and non-equilibrium frames. An overcounting_factor of value n means that every non-equilibrium frame is counted n times. Values larger than 1 increase the relative weight of the non-equilibrium data. Values less than 1 increase the relative weight of the equilibrium data.

References

[1]	Wu, H. et al 2016 Multiensemble Markov models of molecular thermodynamics and kinetics Proc. Natl. Acad. Sci. USA 113 E3221–E3230

Methods

__init__(lag[, count_mode, connectivity, …])	Transition(-based) Reweighting Analysis Method
estimate(X, **params)	param X:Simulation trajectories. ttrajs contain the indices of the thermodynamic state, dtrajs
expectation(a)	Equilibrium expectation value of a given observable.
fit(X[, y])	Estimates parameters - for compatibility with sklearn.
get_model_params([deep])	Get parameters for this model.
get_params([deep])	Get parameters for this estimator.
load(file_name[, model_name])	Loads a previously saved PyEMMA object from disk.
log_likelihood()	Returns the value of the log-likelihood of the converged TRAM estimate.
mbar_pointwise_free_energies([therm_state])
meval(f, *args, **kw)	Evaluates the given function call for all models Returns the results of the calls in a list
pointwise_free_energies([therm_state])	Computes the pointwise free energies \(-\log(\mu^k(x))\) for all points x.
save(file_name[, model_name, overwrite, …])	saves the current state of this object to given file and name.
set_model_params([models, f_therm, pi, f, label])	Call to set all basic model parameters.
set_params(**params)	Set the parameters of this estimator.
update_model_params(**params)	Update given model parameter if they are set to specific values

Attributes

active_set	The active set of states on which all computations and estimations will be done.
dt_traj
f	The free energies (in units of kT) on the configuration states.
f_full_state
force_constants	The individual force matrices labelled accordingly to ttrajs.
free_energies	The free energies (in units of kT) on the configuration states.
free_energies_full_state
label	Human-readable description for the thermodynamic state of this model.
logger	The logger for this class instance
model	The model estimated by this Estimator
msm	MSM of the unbiased thermodynamic state; only present when unbiased data available.
name	The name of this instance
nstates	Number of active states on which all computations and estimations are done.
nstates_full	Size of the full set of states.
pi	The stationary distribution on the configuration states.
pi_full_state
stationary_distribution	The stationary distribution on the configuration states.
stationary_distribution_full_state
temperatures	The individual temperatures labelled accordingly to ttrajs.
umbrella_centers	The individual umbrella centers labelled accordingly to ttrajs.
unbiased_state	Index of the unbiased thermodynamic state.

active_set

The active set of states on which all computations and estimations will be done.

estimate(X, **params)

Parameters:X (tuple of (ttrajs, dtrajs, btrajs)) –

Simulation trajectories. ttrajs contain the indices of the thermodynamic state, dtrajs contains the indices of the configurational states and btrajs contain the biases.

ttrajs : list of numpy.ndarray(X_i, dtype=int)

Every element is a trajectory (time series). ttrajs[i][t] is the index of the thermodynamic state visited in trajectory i at time step t.

dtrajs : list of numpy.ndarray(X_i, dtype=int)

dtrajs[i][t] is the index of the configurational state (Markov state) visited in trajectory i at time step t.

btrajs : list of numpy.ndarray((X_i, T), dtype=numpy.float64)

For every simulation frame seen in trajectory i and time step t, btrajs[i][t,k] is the bias energy of that frame evaluated in the k’th thermodynamic state (i.e. at the k’th Umbrella/Hamiltonian/temperature).

expectation(a)

Equilibrium expectation value of a given observable.

Parameters:a ((M,) ndarray) – Observable vector Returns:val – Equilibrium expectation value of the given observable Return type:float

Notes

The equilibrium expectation value of an observable a is defined as follows

\[\mathbb{E}_{\mu}[a] = \sum_i \mu_i a_i\]

\(\mu=(\mu_i)\) is the stationary vector of the transition matrix \(T\).

f

The free energies (in units of kT) on the configuration states.

fit(X, y=None)

Estimates parameters - for compatibility with sklearn.

Parameters:X (object) – A reference to the data from which the model will be estimated Returns:estimator – The estimator (self) with estimated model. Return type:object

force_constants

The individual force matrices labelled accordingly to ttrajs. (only set, when estimated from umbrella data).

free_energies

The free energies (in units of kT) on the configuration states.

get_model_params(deep=True)

Get parameters for this model.

Parameters:deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators. Returns:params – Parameter names mapped to their values. Return type:mapping of string to any

get_params(deep=True)

Get parameters for this estimator.

Parameters:deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators. Returns:params – Parameter names mapped to their values. Return type:mapping of string to any

label

Human-readable description for the thermodynamic state of this model.

classmethod load(file_name, model_name='default')

Loads a previously saved PyEMMA object from disk.

Parameters:

• file_name (str or file like object (has to provide read method)) – The file like object tried to be read for a serialized object.
• model_name (str, default='default') – if multiple models are contained in the file, these can be accessed by their name. Use pyemma.list_models() to get a representation of all stored models.

Returns:

obj

Return type:

the de-serialized object

log_likelihood()

Returns the value of the log-likelihood of the converged TRAM estimate.

logger

The logger for this class instance

meval(f, *args, **kw)

Evaluates the given function call for all models Returns the results of the calls in a list

model

The model estimated by this Estimator

msm

MSM of the unbiased thermodynamic state; only present when unbiased data available.

name

The name of this instance

nstates

Number of active states on which all computations and estimations are done.

nstates_full

Size of the full set of states.

pi

The stationary distribution on the configuration states.

pointwise_free_energies(therm_state=None)

Computes the pointwise free energies \(-\log(\mu^k(x))\) for all points x.

\(\mu^k(x)\) is the optimal estimate of the Boltzmann distribution of the k’th ensemble defined on the set of all samples.

Parameters:therm_state (int or None, default=None) – Selects the thermodynamic state k for which to compute the pointwise free energies. None selects the “unbiased” state which is defined by having zero bias energy. Returns:mu_k – list of the same layout as dtrajs (or ttrajs). mu_k[i][t] contains the pointwise free energy of the frame seen in trajectory i and time step t. Frames that are not in the connected sets get assiged an infinite pointwise free energy. Return type:list of numpy.ndarray(X_i, dtype=numpy.float64)

save(file_name, model_name='default', overwrite=False, save_streaming_chain=False)

saves the current state of this object to given file and name.

Parameters:

• file_name (str) – path to desired output file
• model_name (str, default='default') – creates a group named ‘model_name’ in the given file, which will contain all of the data. If the name already exists, and overwrite is False (default) will raise a RuntimeError.
• overwrite (bool, default=False) – Should overwrite existing model names?
• save_streaming_chain (boolean, default=False) – if True, the data_producer(s) of this object will also be saved in the given file.

Examples

>>> import pyemma, numpy as np
>>> from pyemma.util.contexts import named_temporary_file
>>> m = pyemma.msm.MSM(P=np.array([[0.1, 0.9], [0.9, 0.1]]))

>>> with named_temporary_file() as file: # doctest: +SKIP
...    m.save(file, 'simple') # doctest: +SKIP
...    inst_restored = pyemma.load(file, 'simple') # doctest: +SKIP
>>> np.testing.assert_equal(m.P, inst_restored.P) # doctest: +SKIP

set_model_params(models=None, f_therm=None, pi=None, f=None, label='ground state')

Call to set all basic model parameters.

Parameters:

• pi (ndarray(n)) – Stationary distribution. If not already normalized, pi will be scaled to fulfill \(\sum_i \pi_i = 1\). The free energies f will then be computed from pi via \(f_i = - \log(\pi_i)\).
• f (ndarray(n)) – Discrete-state free energies. If normalized_f = True, a constant will be added to normalize the stationary distribution. Otherwise f is left as given. Then, pi will be computed from f via \(\pi_i = \exp(-f_i)\) and, if necessary, scaled to fulfill \(\sum_i \pi_i = 1\). If both (pi and f) are given, f takes precedence over pi.
• normalize_energy (bool, default=True) – If parametrized by free energy f, normalize them such that \(\sum_i \pi_i = 1\), which is achieved by \(\log \sum_i \exp(-f_i) = 0\).
• label (str, default=None) – Human-readable description for the thermodynamic state of this model. May contain a temperature description, such as ‘300 K’ or a description of bias energy such as ‘unbiased’ or ‘Umbrella 1’.

set_params(**params)

Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object. :returns: :rtype: self

stationary_distribution

The stationary distribution on the configuration states.

temperatures

The individual temperatures labelled accordingly to ttrajs. (only set, when estimated from multi-temperature data).

umbrella_centers

The individual umbrella centers labelled accordingly to ttrajs. (only set, when estimated from umbrella data).

unbiased_state

Index of the unbiased thermodynamic state.

update_model_params(**params)

Update given model parameter if they are set to specific values