# pymbar

Python implementation of the multistate Bennett acceptance ratio (MBAR) method for estimating expectations and free energy differences from equilibrium samples from multiple probability densities. See our docs.

## Installation

The easiest way to install the `pymbar`

release is via conda:

```
conda install -c conda-forge pymbar
```

You can also install `pymbar`

from the Python package index using `pip`

:

```
pip install pymbar
```

The development version can be installed directly from github via `pip`

:

```
pip install git+https://github.com/choderalab/pymbar.git
```

## Usage

Basic usage involves importing `pymbar`

and constructing an `MBAR`

object from the reduced potential of simulation or experimental data.

Suppose we sample a 1D harmonic oscillator from a few thermodynamic states:

```
>>> from pymbar import testsystems
>>> [x_n, u_kn, N_k, s_n] = testsystems.HarmonicOscillatorsTestCase().sample()
```

We have the `nsamples`

sampled oscillator positions `x_n`

(with samples from all states concatenated), reduced potentials in the `(nstates,nsamples)`

matrix `u_kn`

, number of samples per state in the `nsamples`

array `N_k`

, and indices `s_n`

denoting which thermodynamic state each sample was drawn from.

To analyze this data, we first initialize the `MBAR`

object:

```
>>> mbar = MBAR(u_kn, N_k)
```

Estimating dimensionless free energy differences between the sampled thermodynamic states and their associated uncertainties (standard errors) simply requires a call to `getFreeEnergyDifferences()`

:

```
>>> results = mbar.getFreeEnergyDifferences(return_dict=True)
```

Here `results`

is a dictionary with keys `Deltaf_ij`

, `dDeltaf`

, and `Theta`

. `Deltaf_ij[i,j]`

is the matrix of dimensionless free energy differences `f_j - f_i`

, `dDeltaf_ij[i,j]`

is the matrix of standard errors in this matrices estimate, and `Theta`

is a covariance matrix that can be used to propagate error into quantities derived from the free energies. By default, `return_dict`

is `False`

and the return will be a tuple.

Expectations and associated uncertainties can easily be estimated for observables `A(x)`

for all states:

```
>>> A_kn = x_kn # use position of harmonic oscillator as observable
>>> results = mbar.computeExpectations(A_kn, return_dict=True)
```

where `results`

is a dictionary with keys `mu`

, `sigma`

, and `Theta`

, where `mu[i]`

is the array of the estimate for the average of the observable for in state i, `sigma[i]`

is the estimated standard deviation of the `mu`

estimates, and `Theta[i,j]`

is the covarinace matrix of the log weights.

See the docstring help for these individual methods for more information on exact usage; in Python or IPython, you can view the docstrings with `help()`

.

## Authors

- Kyle A. Beauchamp [email protected]
- John D. Chodera [email protected]
- Levi N. Naden [email protected]
- Michael R. Shirts [email protected]

## References

Please cite the original MBAR paper:

Shirts MR and Chodera JD. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys. 129:124105 (2008). DOI

Some timeseries algorithms can be found in the following reference:

Chodera JD, Swope WC, Pitera JW, Seok C, and Dill KA. Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations. J. Chem. Theor. Comput. 3(1):26-41 (2007). DOI

The automatic equilibration detection method provided in `pymbar.timeseries.detectEquilibration()`

is described here:

Chodera JD. A simple method for automated equilibration detection in molecular simulations. J. Chem. Theor. Comput. 12:1799, 2016. DOI

## License

`pymbar`

is free software and is licensed under the MIT license.

## Thanks

We would especially like to thank a large number of people for helping us identify issues and ways to improve `pymbar`

, including Tommy Knotts, David Mobley, Himanshu Paliwal, Zhiqiang Tan, Patrick Varilly, Todd Gingrich, Aaron Keys, Anna Schneider, Adrian Roitberg, Nick Schafer, Thomas Speck, Troy van Voorhis, Gupreet Singh, Jason Wagoner, Gabriel Rocklin, Yannick Spill, Ilya Chorny, Greg Bowman, Vincent Voelz, Peter Kasson, Dave Caplan, Sam Moors, Carl Rogers, Josua Adelman, Javier Palacios, David Chandler, Andrew Jewett, Stefano Martiniani, and Antonia Mey.

## Notes

`alchemical-analysis.py`

described in this publication has been relocated here.