|
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
(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
(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 2024-06-08.