obj.fcn: The objective function for UWHAM

In UWHAM: Unbinned Weighted Histogram Analysis Method (UWHAM)

The objective function for UWHAM

Description

This function computes the objective function, its gradient and its hessian matrix for UWHAM.

Usage

obj.fcn(ze, logQ, size, base)

Arguments

ze	A vector of log-normalizing constants (or free energies) for the sampled thermodynamic states.
logQ	The matrix of log of unnormalized density ratios for the sampled thermodynamic states over the baseline.
size	A vector giving the individual sample sizes for the sampled thermodynamic states.
base	The baseline index.

Details

The objective function is convex as discussed in Tan et al. (2012). See also Gill et al. (1998) for related results on biased sampling models.

Value

value	The value of the objective function.
gradient	The gradient of the objective function.
hessian	The hessian matrix of objective function.

References

Gill, R., Vardi, Y., and Wellner, J. (1998) "Large sample theory of empirical distributions in biased sampling models," Annals of Statistics, 16, 1069–1112.

Tan, Z., Gallicchio, E., Lapelosa, M., and Levy, R.M. (2012) "Theory of binless multi-state free energy estimation with applications to protein-ligand binding," Journal of Chemical Physics, 136, 144102.

UWHAM documentation built on May 20, 2022, 5:05 p.m.