Function stats [was: Patch for new "stats" command]

[Ethan M. <merritt@u.washington.edu>]

 On Sunday 08 November 2009, Philipp K. Janert wrote:
> We'd like to hear feedback and suggestions. Is this
> useful? Are we missing anything?
 
Some first thoughts:
 
The behaviour for functions is not as obvious as for files of
data points.  For example:
 
 gnuplot> set xrange [0:10]
 gnuplot> stats '+' using 1:(sin($1))
 
 * FILE:
   Records:      100
 
 * COLUMNS:
   Mean:          5.0000              0.1792
   Minimum:       0.0000 [  1]       -0.9994 [ 48]
   Quartile:      2.5253 [ 26]       -0.3837 [ 36]
   Median:        5.0505 [ 51]        0.3082 [ 29]
   Quartile:      7.5758 [ 76]        0.8075 [ 85]
   Maximum:      10.0000 [100]        0.9997 [ 79]
 
 gnuplot> set samples 1000
 gnuplot> stats '+' using 1:(sin($1))
 
 * FILE:
   Records:      1000
 
 * COLUMNS:
   Mean:          5.0000               0.1835
   Minimum:       0.0000 [   1]       -1.0000 [ 472]
   Quartile:      2.5025 [ 251]       -0.3941 [ 983]
   Median:        5.0050 [ 501]        0.3149 [  33]
   Quartile:      7.5075 [ 751]        0.8113 [ 848]
   Maximum:      10.0000 [1000]        1.0000 [ 158]
 
I find several things disconcerting about this output, although
I know what the underlying causes are.
 
 - The min/max are artifacts of the sampling.
   They're not even symmetric even though sin(x) is a symmetric function
   You can reduce the problem by increasing the number of samples, but I
   think more drastic alternatives should be considered

   1) The 'stats' command could refuse to operate on functions
   2) The 'stats' command could temporarily bump up the sampling rate
      by 100x 
   3) The 'stats' command could do a systematic search in the area of
      the nominal extrema to determine more accurate values. 
      Even so, if the sampling is too coarse it may miss a true extremum 
      that lies elsewhere. 

 - The "mean" of a periodic function would normally be calculated over
   one period of the function rather than an arbitrary range.
   Yeah, I know, I gave an explicit xrange.  But still...
 
 - The quantities in [] are documented as "the" point at which the
   min/max/whatever occurs.  But there is no expectation for either data
   or functions that the minimum, for example, is only acheived only at a
   single point.   I don't think it makes any sense to give these values
   unless the data or function is monotonic.  And given sampling artifacts,
   it probably makes no sense to give them for function data at all.