Logit scale? Was Re: New patch supporting nonlinear axes

[Nicolas B. <br...@in...>]

> Le 1 avr. 2016 à 05:35, sfeam <sf...@us...> a écrit :
> 
> I have placed a patchset on SourceForge that introduces a general mechanism
> for defining nonlinear axes in a plot.
> 
>    https://sourceforge.net/p/gnuplot/patches/728/
> 
> Demos here:
> 
>    http://skuld.bmsc.washington.edu/~merritt/gnuplot/#nonlinear
> 
> It uses the linked-axis mechanism of forward and reverse mappings introduced
> in the "set link {axis} via f(x) inverse g(x)" command with the major 
> difference that it links a non-linear visible axis with a hidden axis that is
> always linear.
> 
> One motivation is to eventually replace the current implementation of
> logscale axes with something that is both more general and less expensive.
> The effect of the existing command
> 	set logscale x
> can be achieved by the new command
> 	set nonlinear x via log10(x) inverse 10**x
> 
> A major advantage over the existing logscale implementation is that
> coordinates are not transformed on input.  The current logscale 
> code stores the log of the true coordinate, which then requires that
> every single reference to that coordinate throughout the core gnuplot
> code is mediated by macros AXIS_DO_LOG, AXIS_UNDO_LOG, AXIS_LOG_VALUE,
> etc.  Every time the coordinate is needed we check whether it was
> stored as the log, unlog it if so, do whatever it was we wanted, 
> then reapply the log for comparison with other stored values. 
> By contrast the new nonlinear axis code simply stores the original 
> coordinate value.  The nonlinear mapping (log in this case) is only
> needed when we map it to a position on the output terminal canvas.
> 
> The log()/exp() transform is an example of a nonlinear axis mapping,
> but the new code is happy to accept other transforms as well.
> This defines a probability plot axis:
> 	set nonlinear x via norm(x) inverse invnorm(x)
> See demo "probably_tux.dem".
> 
> Another non-obvious example is creation of a "broken axis" plot.
> This is a recurring feature request.  In this case the hidden linear
> axis spanning the full range [min:max] is mapped onto a visible axis
> that shows only the first part and the last part of the range (see demo).
> 
> Notes:
> 
>   The "set nonlinear x" command itself is sufficient to create a 
>   log-scaled x axis.  For backwards compatibility with the existing
>   behaviour, there is a second command "set xtics log" that reuses the
>   old tic-placement code. 
> 
>   This version of the patch set only reserves space for hidden axes
>   shadowing the x and y axes.  Extending it to handle the other visible
>   axes (x2 y2 z cb) should be trivial.
> 
>   The pieces are already in place to construct log-scaled or broken
>   axis plots, as shown by the demos.  Once any bugs are shaken out, 
>   I envision wrapping these in simple commands for easier use.  
> 
>   For example, the command "set log" will continue to do what is has
>   always done but will use the new code rather than all those 
>   LOG/DE_LOG macros underneath.
> 
>   The manual definition of mappings and axis markings for a broken axis
>   can be automated by introducing some new command analogous to the way
>   "set multiplot layout ..." automates manipulation of the scale and 
>   offset parameters.
> 
> 

Hi, 
I haven’t looked at the patch yet but my dream was to have a logit scale implemented in Gnuplot.
Some years (decade?) ago, I gave up because of the y-axis notation which of course should be implemented as for the log scale (.001 0.01 0.99 .999 etc).
Would your patch do this?

Nicolas
--
Nicolas Brouard
Institut national d'études démographiques
133 Boulevard Davout 75020 Paris
mél: br...@in...