Scaling

Structure factor scaling corrects for experimental effects and bulk solvent.

Overview

The Scaler class handles:

Overall scale factor
Anisotropic scaling (6-parameter tensor)
Bulk solvent correction

Basic Usage

from torchref import Scaler

scaler = Scaler(model, reflection_data, verbose=1)

scaler.initialize()

scaler.refine_lbfgs() # refine scaling parameters

# Apply scaling to calculated structure factors
F_calc_scaled = scaler(F_calc)

Bin wise scaling

Data is binned by resolution shells and overall scale factors for each resolution bin are calculated. This is enabled by default with 20 bins.

scaler = Scaler(model, reflection_data, verbose=1,nbins=1) # sets nbins to 1, so now its just an overall scale factor
scaler.calc_initial_scale()

Bulk Solvent Model

TorchRef uses the flat bulk solvent model:

\[F_{calc}^{total} = k \cdot F_{calc}^{model} + k_s \exp(-B_s s^2 / 4) \cdot F_{calc}^{solvent}\]

where:

\(k\) is the overall scale factor
\(k_s\) is the solvent scale
\(B_s\) is the solvent B-factor
\(s = 1/d\) is the reciprocal resolution

Anisotropic Scaling

Anisotropic scaling corrects directional effects on the scattering of a crystal (mainly crystal shape).

The anisotropic scale factor is given by:

\[k_{aniso}(\mathbf{h}) = \exp\left( -\mathbf{h}^T \mathbf{U} \mathbf{h} \right)\]

This scaling is enabled by calling the initialize method in Scaler.