plot-diagonal-distribution.md

The plot_diagonal_distribution executable

Synopsis

Synopsis: plot_diagonal_distribution \
   [ -sgn | -abs ] [ -eta-bound <eta-bound> ] \
      <distribution> { <distribution> }

Plots a diagonal distribution.

The plot is output to file in Latex format. It will be given an appropriate name and written to the plots directory. If this directory does not exist, it will be created. If the plot already exists, an error will be reported.

Mandatory command line arguments

Arguments <distribution> where

• <distribution> is the path to the distribution

Optional command line arguments

Flags specifying the plot appearance (defaults to -sgn):

• -sgn draw a plot in the signed logarithm of the argument
• -abs draw a plot in the absolute value of the logarithm of the argument

Flag specifying the bound $B_\eta$ (defaults to $B_\eta$ used to generate the distribution):

• -eta-bound <eta-bound> sets $B_\eta$ to <eta-bound>

  The bound $B_\eta$ controls how many peak indices $\eta$ are included when collapsing the distribution in $(\alpha_r, \eta)$ to a distribution in $\alpha_r$ prior to plotting: More specifically, the peaks with peak indices $\eta \in [-B_\eta, B_\eta] \cap \mathbb Z$ are included.

  If the bound $B_\eta$ is specified, it must be less than or equal to the corresponding bound specified when generating the diagonal distribution or an error will be signalled.

Compiling the plot

To compile the source for the plot, you may use pdflatex as exemplified below:

$ ./plot_diagonal_distribution distributions/diagonal-distribution-det-dim-2048-m-2048-sigma-10-s-30.txt
Importing the distribution from "distributions/diagonal-distribution-det-dim-2048-m-2048-sigma-10-s-30.txt"...
Writing the plot to "plots/plot-diagonal-distribution-m-2048-sigma-10-s-30.tex"...
Done.
$ cd plots
$ pdflatex plot-diagonal-distribution-m-2048-sigma-10-s-30.tex

(..)

You may of course also use other versions of Latex such as xelatex. Note that the Latex source requires Tikz.

Interpreting the plot

The plot generated is in the signed logarithm of the argument $\alpha_r$:

Note that diagonal distributions store only a partial two-dimensional distribution in $(\alpha_r, \eta)$ computed using the expression for $f_\eta(\theta_r)$ given in [E19p]. The full distribution is computed on the fly by executables that sample the diagonal distribution.