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

 ∇χ2 = ∇χ2i, (15.9)

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 2020-08-26.