Optimizing polynomial compression parameters¶

Polycomp implements a number of tools to simplify the choice of the parameters for polynomial compression. The parameters are $N_\mathrm{chunk}$ , the number of samples per chunk, and $\deg p(x) + 1$ , the number of coefficients in the interpolating polynomial. Polycomp’s strategy to optimize these parameters is to test a number of configuration and pick the one with the best compression ratio $C_r$ .

Two algorithms are implemented:

A naive algorithm that scans rectangular regions of the parameter space $N_\mathrm{chunk} \times (\deg p(x) + 1)$ ;
A simplex-downhill algorithm that hunts for local minima in the parameter space.

Scanning rectangular regions of the parameter space¶

To find the best values for $N_\mathrm{chunk}$ and $(\deg p(x) + 1)$ within a rectangular region of the parameter plane, the user can specify the values to be checked using the usual parameters num_of_coefficients and samples_per_chunk. Instead of specifying only one value, a set of values can be specified using the following syntax:

Ranges can be specified using the syntax NN-MM or NN:MM;
Intervals can be specified using the syntax NN:D:MM, where D is the interval;
Multiple values and ranges can be concatenated, using commas (,) as separators.

Optimizing polynomial compression parameters¶

Scanning rectangular regions of the parameter space¶

Simplex-downhill strategy¶