Re: Logit scale? Was Re: New patch supporting nonlinear axes

[Ethan A M. <sf...@us...>]

On Friday, 01 April, 2016 14:50:12 Nicolas Brouard wrote:
> 
> > 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".
[snip]
> 
> 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?

I think that would be

   logit(p) = log(p/(1-p))
   logistic(a) = 1. / (1. + exp(-a))

   set nonlinear y via logistic(y) inverse logit(y)

   plot [.001:.999] logit(x) title "should be a straight line"

I don't use either the logit or probit conventions in my own work so I
may have the desired forward/reverse settings backwards.

Can you suggest a nice data-driven demo using logit scale?
Or point me to a published graph that uses it?

If the ascii art from "set term dumb" survives, the output of the above
commands is shown here:

  4 +---+---+----+---+---+---+---+----+---+-----   
  3 +                                      ***+   
  2 +  logit(x) *******                  ***  +   
    |                                  **     |   
    |                                **       |   
  1 +                              **         +   
    |                           ***           |   
    |                         ***             |   
    |                       ***               |   
    |                     ***                 |   
  0 +                   ***                   +   
    |                 ***                     |   
    |               ***                       |   
    |             ***                         |   
    |           ***                           |   
 -1 +         **                              +   
    |       **                                |   
    |     **                                  |   
 -2 +  ***                                    +   
 -3 +***                                      +   
 -4 +---+---+----+---+---+---+---+----+---+-----   
    0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  1   


	Ethan