Module Ensembles

Generate a Bayesian ensemble of parameter sets consistent with the data in
the model. The sampling is done in terms of the bare parameters.

Inputs:
 (All not listed here are identical to those of ensemble_log_params.)
 recalc_func --- Function used to calculate the hessian matrix. It should
                 take only a parameters argument and return the matrix.
                 If this is None, default is to use m.GetJandJtJ.

Generate a Bayesian ensemble of parameter sets consistent with the data in
the model. The sampling is done in terms of the logarithm of the parameters.

Inputs:
 m -- Model to generate the ensemble for
 params -- Initial parameter KeyedList to start from 
 hess -- Hessian of the model
 steps -- Maximum number of Monte Carlo steps to attempt
 max_run_hours -- Maximum number of hours to run
 temperature -- Temperature of the ensemble
 step_scale -- Additional scale applied to each step taken. step_scale < 1
               results in steps shorter than those dictated by the quadratic
               approximation and may be useful if acceptance is low.
 sing_val_cutoff -- Truncate the quadratic approximation at eigenvalues
                    smaller than this fraction of the largest.
 seeds -- A tuple of two integers to seed the random number generator
 recalc_hess_alg --- If True, the Monte-Carlo is done by recalculating the
                     hessian matrix every timestep. This signficantly
                     increases the computation requirements for each step,
                     but it may be worth it if it improves convergence.
 recalc_func --- Function used to calculate the hessian matrix. It should
                 take only a log parameters argument and return the matrix.
                 If this is None, default is to use 
                 m.GetJandJtJInLogParameteters
 save_hours --- If save_to is not None, the ensemble will be saved to
                   that file every 'save_hours' hours.
 save_to --- Filename to save ensemble to.
 skip_elems --- If non-zero, skip_elems are skipped between each included 
                step in the returned ensemble. For example, skip_elems=1
                will return every other member. Using this option can
                reduce memory consumption.

Outputs:
 ens, ens_fes, ratio
 ens -- List of KeyedList parameter sets in the ensemble
 ens_fes -- List of free energies for each parameter set
 ratio -- Fraction of attempted moves that were accepted

The sampling is done by Markov Chain Monte Carlo, with a Metropolis-Hasting
update scheme. The canidate-generating density is a gaussian centered on the
current point, with axes determined by the hessian. For a useful 
introduction see:
 Chib and Greenberg. "Understanding the Metropolis-Hastings Algorithm" 
 _The_American_Statistician_ 49(4), 327-335

Return the mean and standard deviation trajectory objects for the given 
input list of trajectories. (All must be evaluated at the same points.)

Return the Principle Component Analysis eigenvalues and eigenvectors (in 
 log parameters) of an ensemble. (This function takes the logs for you.)