pyemma.thermo.MEMM¶

class pyemma.thermo.MEMM(models, f_therm, pi=None, f=None, label='ground state')¶

Coupled set of Markov state models at multiple thermodynamic states

Parameters:

models (list of Model objects) – List of Model objects, e.g. StationaryModel or MSM objects, at the different thermodynamic states. This list may include the ground state, such that self.pi = self.models[0].pi holds. An example for that is data obtained from parallel tempering or replica-exchange, where the lowest simulated temperature is usually identical to the thermodynamic ground state. However, the list does not have to include the thermodynamic ground state. For example, when obtaining data from umbrella sampling, models might be the list of stationary models for n umbrellas (biased ensembles), while the thermodynamic ground state is the unbiased ensemble. In that case, self.pi would be different from any self.models[i].pi
f_therm (ndarray(k)) – free energies at the different thermodynamic states
pi (ndarray(n), default=None) – Stationary distribution of the thermodynamic ground state. If not already normalized, pi will be scaled to fulfill \(\sum_i \pi_i = 1\). If None, models[0].pi will be used
f (ndarray(n)) – Discrete-state free energies of the thermodynamic ground state.
label (str, default='ground state') – Human-readable description for the thermodynamic ground state or reference state of this multiensemble. May contain a temperature description, such as ‘300 K’ or a description of bias energy such as ‘unbiased’.

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

Parameters:

models (list of model objects) – List of model objects, e.g. StationaryModel or :class:`ThermoMSM <pyemma.thermo.models.memm.ThermoMSM> objects, at the different thermodynamic states. This list may include the ground state, such that self.pi = self.models[*].pi holds, where * denotes the ground state. An example for that is data obtained from parallel tempering or replica-exchange, where the lowest simulated temperature is usually identical to the thermodynamic ground state. However, the list does not have to include the thermodynamic ground state. For example, when obtaining data from umbrella sampling, models might be the list of stationary models for n umbrellas (biased ensembles), while the thermodynamic ground state is the unbiased ensemble. In that case, self.pi would be different from any self.models[i].pi.
f_therm (numpy.ndarray(k)) – Free energies of the different thermodynamic states.
pi (numpy.ndarray(n), default=None) – Stationary distribution of the thermodynamic ground state. If not already normalized, pi will be scaled to fulfill \(\sum_i \pi_i = 1\). If None, models[0].pi will be used.
f (numpy.ndarray(n)) – Discrete-state free energies of the thermodynamic ground state.
label (str, optional, default='ground state') – Human-readable description for the thermodynamic ground state or reference state of this multiensemble. May contain a temperature description, such as ‘300 K’ or a description of bias energy such as ‘unbiased’.

Methods

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

param models:	List of model objects, e.g.

expectation(a) Equilibrium expectation value of a given observable.

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

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

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

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.
`model_active_set`
`msm`	MSM of the unbiased thermodynamic state; only present when unbiased data available.
`msm_active_set`
`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`
`unbiased_state`	Index of the unbiased thermodynamic state.

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

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.

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

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

meval(f, *args, **kw)¶: Evaluates the given function call for all models Returns the results of the calls in a list

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

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.

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