pyemma.thermo.WHAM¶

class pyemma.thermo.WHAM(bias_energies_full, maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', stride=1)¶

Weighted Histogram Analysis Method.

__init__(bias_energies_full, maxiter=10000, maxerr=1e-15, save_convergence_info=0, dt_traj='1 step', stride=1)¶

Weighted Histogram 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.
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 loglikelihood; 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*’
stride (int, optional, default=1) – not used

Example

>>> from pyemma.thermo import WHAM
>>> import numpy as np
>>> B = np.array([[0, 0],[0.5, 1.0]])
>>> wham = WHAM(B)
>>> 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])]
>>> wham = wham.estimate((ttrajs, dtrajs))
>>> wham.log_likelihood() 
-6.6...
>>> wham.state_counts 
array([[7, 3],
       [5, 5]])
>>> wham.stationary_distribution 
array([ 0.5...,  0.4...])
>>> wham.meval('stationary_distribution') 
[array([ 0.5...,  0.4...]), array([ 0.6...,  0.3...])]

References

[1]	Ferrenberg, A.M. and Swensen, R.H. 1988. New Monte Carlo Technique for Studying Phase Transitions. Phys. Rev. Lett. 23, 2635–2638

[2]	Kumar, S. et al 1992. The Weighted Histogram Analysis Method for Free-Energy Calculations on Biomolecules. I. The Method. J. Comp. Chem. 13, 1011–1021

Methods

__init__(bias_energies_full[, maxiter, ...]) Weighted Histogram 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) Estimates parameters - for compatibility with sklearn.

get_model_params([deep]) Get parameters for this model.

get_params([deep]) Get parameters for this estimator.

log_likelihood()

meval(f, *args, **kw) Evaluates the given function call for all models

register_progress_callback(call_back[, stage]) Registers the progress reporter.

set_model_params([models, f_therm, pi, f, label])

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.
`f`	The free energies (in units of kT) on the configuration states.
`f_full_state`
`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
`model_active_set`
`msm_active_set`
`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`
`show_progress`	whether to show the progress of heavy calculations on this object.
`stationary_distribution`	The stationary distribution on the configuration states.
`stationary_distribution_full_state`
`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.

ttrajs : list 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.
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.

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)¶

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

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.

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

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.

register_progress_callback(call_back, stage=0)¶

Registers the progress reporter.

Parameters:	call_back (function) – This function will be called with the following arguments: stage (int) instance of pyemma.utils.progressbar.ProgressBar optional args and named keywords (kw), for future changes stage* (int, optional, default=0) – The stage you want the given call back function to be fired.

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

show_progress¶: whether to show the progress of heavy calculations on this object.

stationary_distribution¶: The stationary distribution on the configuration states.

unbiased_state¶: Index of the unbiased thermodynamic state.

update_model_params(**params)¶: Update given model parameter if they are set to specific values