pyemma.thermo.estimate_multi_temperature

pyemma.thermo.estimate_multi_temperature(energy_trajs, temp_trajs, dtrajs, energy_unit='kcal/mol', temp_unit='K', reference_temperature=None, maxiter=10000, maxerr=1e-15, save_convergence_info=0, estimator='wham', lag=1, dt_traj='1 step', init=None, init_maxiter=10000, init_maxerr=1e-08, **kwargs)

This function acts as a wrapper for tram(), dtram(), mbar, and wham() and handles the calculation of bias energies (bias) and thermodynamic state trajectories (ttrajs) when the data comes from multi-temperature simulations.

Parameters

• energy_trajs (list of N arrays, each of shape (T_i,)) – List of arrays, each having T_i rows, one for each time step, containing the potential energies time series in units of kT, kcal/mol or kJ/mol.

• temp_trajs (list of N int arrays, each of shape (T_i,)) – List of arrays, each having T_i rows, one for each time step, containing the heat bath temperature time series (at which temperatures the frames were created) in units of K or C. Alternatively, these trajectories may contain kT values instead of temperatures.

• dtrajs (list of N int arrays, each of shape (T_i,)) – The integers are indexes in 0,…,n-1 enumerating the n discrete states or the bins the trajectory is in at any time.

• energy_unit (str, optional, default='kcal/mol') – The physical unit used for energies. Current options: kcal/mol, kJ/mol, kT.

• temp_unit (str, optional, default='K') – The physical unit used for the temperature. Current options: K, C, kT

• reference_temperature (float or None, optional, default=None) – Reference temperature against which the bias energies are computed. If not given, the lowest temperature or kT value is used. If given, this parameter must have the same unit as the temp_trajs.

• 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 loglikelihood; 0 means no storage.

• estimator (str, optional, default='wham') –

  Specify one of the available estimators

  ’wham’: use WHAM

  ’mbar’: use MBAR

  ’dtram’: use the discrete version of TRAM

  ’tram’: use TRAM

• lag (int or list of int, optional, default=1) – Integer lag time at which transitions are counted. Providing a list of lag times will trigger one estimation per lag time.

• 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 the 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 (only with dtram)

  ’mbar’: perform a short MBAR estimate to initialize the free energies (only with tram)

• 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.

• **kwargs (dict, optional) – You can use this to pass estimator-specific named parameters to the chosen estimator, which are not already coverd by estimate_multi_temperature().

Returns

The requested estimator/model object, i.e., WHAM, MBAR, DTRAM or TRAM. If multiple lag times are given, a list of objects is returned (one MEMM per lag time).

Return type

A MultiThermModel or MEMM object or list thereof

Example

We look at 1D simulations at two different kT values 1.0 and 2.0, already clustered data, and we use TRAM for the estimation:

>>> from pyemma.thermo import estimate_multi_temperature as estimate_mt
>>> import numpy as np
>>> energy_trajs = [np.array([1.6, 1.4, 1.0, 1.0, 1.2, 1.0, 1.0]), np.array([0.8, 0.7, 0.5, 0.6, 0.7, 0.8, 0.7])]
>>> temp_trajs = [np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]), np.array([2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0])]
>>> dtrajs = [np.array([0, 1, 2, 2, 2, 2, 2]), np.array([0, 1, 2, 2, 1, 0, 1])]
>>> tram = estimate_mt(energy_trajs, temp_trajs, dtrajs, energy_unit='kT', temp_unit='kT', estimator='tram', lag=1)
>>> tram.f 
array([ 2.90...,  1.72...,  0.26...])

Note that alhough we only used one temperature per trajectory, estimate_multi_temperature() can handle temperature changes as well.

See MultiThermModel or MEMM for a full documentation.

class pyemma.thermo.models.multi_therm.MultiThermModel(*args, **kwargs)

Coupled set of stationary models at multiple thermodynamic states

Methods

expectation(a)	Equilibrium expectation value of a given observable.
get_model_params([deep])	Get parameters for this model.
load(file_name[, model_name])	Loads a previously saved PyEMMA object from disk.
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.
update_model_params(**params)	Update given model parameter if they are set to specific values

Attributes

meval(f, *args, **kw)

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

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’.

property unbiased_state

Index of the unbiased thermodynamic state.

class pyemma.thermo.models.memm.MEMM(*args, **kwargs)

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’.

Methods

expectation(a)	Equilibrium expectation value of a given observable.
get_model_params([deep])	Get parameters for this model.
load(file_name[, model_name])	Loads a previously saved PyEMMA object from disk.
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.
update_model_params(**params)	Update given model parameter if they are set to specific values

Attributes

property msm

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