The construction of the gradient is significantly different for the models , , , and . In Figure 15.1 the construction of the chi-squared gradient ∇χ2 for the global model is demonstrated. In this case
where ∇χ2i is the vector of partial derivatives of the chi-squared equation χ2i for the residue i. The length of this vector is
|∇χ2i = dim||(15.10)|
with each position of the vector j equal to where each θj is a parameter of the model.
The construction of the gradient ∇χ2 for the model is simply a subset of that of . This is demonstrated in Figure 15.1 by simply taking the component of the gradient ∇χ2i denoted by the symbol ∂ (the orange blocks) and summing these for all residues. This sum is given by (15.9) and
|∇χ2i = dim||(15.11)|
For the parameter set , which consists of the local τm parameter and the model-free parameters of a single residue, the gradient ∇χ2i for the residue i is simply the combination of the single orange block and single yellow block of the index i (Figure 15.1).
The model-free parameter set is even simpler. In Figure 15.1 the gradient ∇χ2i is simply the vector denoted by the single yellow block for the residue i.
The relax user manual (PDF), created 2019-06-14.