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[docs] improve docs for estimator matrix output (#353)
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* Fix #347 
* update docs to explain why estimator output is in form of a matrix and what one can do with the data
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xiki-tempula authored May 15, 2024
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Expand Up @@ -34,7 +34,13 @@ The :meth:`~alchemlyb.estimators.MBAR.fit` method is used to perform the free en
>>> mbar_vdw = MBAR().fit(u_nk_vdw)

The sum of the endpoint free energy differences will be the free energy of solvation for benzene in water.
The free energy differences (in units of :math:`k_B T`) between each :math:`\lambda` window can be accessed via the ``delta_f_`` attribute::
The free energy differences (in units of :math:`k_B T`) between each :math:`\lambda` window can be accessed via the ``delta_f_`` attribute.

The elements of the resulting matrix ``delta_f_`` represent the free energy differences between different lambda windows. Specifically, ``delta_f_[i, j]`` represents the free energy difference between lambda window ``j`` and lambda window ``i``. This matrix can be utilized to obtain the desired free energy differences for various states.

For instance, to obtain the free energy difference between the lambda values of 0 and 1, you can directly access ``delta_f_.loc[0.00, 1.00]``.

Additionally, the errors on these differences are accessible via the ``d_delta_f_`` attribute.

>>> mbar_coul.delta_f_
0.00 0.25 0.50 0.75 1.00
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