pyemma.thermo.DTRAM

class pyemma.thermo.DTRAM(bias_energies_full, lag, count_mode='sliding', connectivity='reversible_pathways', maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', init=None, init_maxiter=10000, init_maxerr=1e-08)

Discrete Transition(-based) Reweighting Analysis Method.

__init__(bias_energies_full, lag, count_mode='sliding', connectivity='reversible_pathways', maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', init=None, init_maxiter=10000, init_maxerr=1e-08)

Discrete Transition(-based) Reweighting Analysis Method

Parameters

  • bias_energies_full (numpy.ndarray(shape=(num_therm_states, num_conf_states)) object) – bias_energies_full[j, i] is the bias energy in units of kT for each discrete state i at thermodynamic state j.

  • 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='reversible_pathways') –

    One of ‘reversible_pathways’, ‘summed_count_matrix’ or None. 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.

    • ’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!

    • None : assume that everything is connected. For debugging.

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

  • maxiter (int, optional, default=10000) – The maximum number of self-consistent iterations before the estimator exits unsuccessfully.

  • maxerr (float, optional, default=1.0E-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*’

  • 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
    ’wham’: perform a short WHAM estimate to initialize the free energies

  • init_maxiter (int, optional, default=10000) – The maximum number of self-consistent iterations during the initialization.

  • init_maxerr (float, optional, default=1.0E-8) – Convergence criterion for the initialization.

Example

>>> from pyemma.thermo import DTRAM
>>> import numpy as np
>>> B = np.array([[0, 0],[0.5, 1.0]])
>>> dtram = DTRAM(B, 1)
>>> ttrajs = [np.array([0,0,0,0,0,0,0,0,0,0]),np.array([1,1,1,1,1,1,1,1,1,1])]
>>> dtrajs = [np.array([0,0,0,0,1,1,1,0,0,0]),np.array([0,1,0,1,0,1,1,0,0,1])]
>>> dtram = dtram.estimate((ttrajs, dtrajs))
>>> dtram.log_likelihood() # doctest: +ELLIPSIS
-9.805...
>>> dtram.count_matrices # doctest: +SKIP
array([[[5, 1],
        [1, 2]],
[[1, 4],

[3, 1]]], dtype=int32)

>>> dtram.stationary_distribution # doctest: +ELLIPSIS
array([ 0.38...,  0.61...])
>>> dtram.meval('stationary_distribution') # doctest: +ELLIPSIS
[array([ 0.38...,  0.61...]), array([ 0.50...,  0.49...])]

References

1

Wu, H. et al 2014 Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states J. Chem. Phys. 141, 214106

Methods

__init__(bias_energies_full, lag[, …])

Discrete Transition(-based) Reweighting Analysis Method

estimate(trajs)

param X

Simulation trajectories. ttrajs contain the indices of the thermodynamic state and

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()

meval(f, *args, **kw)

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

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(trajs)
Parameters

X (tuple of (ttrajs, dtrajs)) –

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

ttrajslist of numpy.ndarray(X_i, dtype=int)

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

dtrajslist 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.

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

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.

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