Grid Shifting
After the values of the score function have been calculated, gmak
allows one to update the origin of the grid based on those values,
effectively displacing the search-space boundaries in the parameter
space. This is provided as a way to automatically explore nearby
parameter values whenever the results suggest that this is likely to
improve the optimal-parameter estimate. The main assumption is that,
within the limitations of the statistical uncertainties, one should be
able to roughly determine whether there is a significant chance that
the optimal parameter does not lie, in fact, within the lastly
considered search-space boundaries. The process will be referred to as
grid shifting.
The default grid-shifting strategy used in gmak is rather simple
and intuitive. It starts by ranking the grid cells from best to worst
score. After that, the center-of-geometry (CG) of the
\(n_{\text{cut}} \times N_{1} \times N_{2} \times \cdots \times
N_{D}\) best ones is calculated, where \(n_{\text{cut}}\) is a
parameter defined in the input file and
\(N_{1}, N_{2}, \cdots ,N_{D}\) are the dimensions of the
main variation. The positions
considered in this calculation are the tuple indexes of the points. If the location
\(\mathbf{x}_{\text{CG}}^{(k)} =
(x_{\text{CG},i}^{(k)})_{i=1\cdots D}\) of the CG lies within some
pre-defined (in the input file) margins
\((\delta_{i})_{i=1\cdots D}\), \((\Delta_{i})_{i=1\cdots
D}\), i.e.
or the number of grid shifts, \(k - 1\), reaches a maximum value
(also defined in the input file), then the
grid is not shifted. This signals the end of the run for gmak.
Otherwise, the grid is shifted (see Variation Shifting and The Parameter-search Grid) so that
the cell closest to the CG is the center of the new grid, and the
counter \(k\) is incremented.
For flexibility, one can create customized grid-shifting procedures and use them by means of the customization API.
Note
The indexes defining the sampled grid points are not altered during grid shifting. This means that the parameter values are shifted together with the grid.
Note
Grid-shifting iterations are indepedent from each other. The data and output files of each iteration are kept in disk, but are not accessed by the program during other iterations. This includes simulation files, property estimates, etc.