Problems with histogram examples code in manual

--=-=-=
Content-Type: text/plain; format=flowed; charset=WINDOWS-1252
Content-Transfer-Encoding: quoted-printable


Dear gnuplot developers,

I have found two problems with some example code in the "plot data=20
smooth frequency" section of the manual (page 95 in v5.2, page 90=20
for v5.0), designed to give equal-width intervals and rectangles=20
whose heights equal each interval frequency:

  binwidth =3D <something> # set width of x values in each bin
  bin(val) =3D binwidth * floor(val/binwidth)
  plot "datafile" using (bin(column(1))):(1.0) smooth frequency

One problem is minor, one is major.

The minor problem is: the histogram bins are centred 0.5*binwidth=20
to the left of where they should be. The definition of "bin()"=20
above replaces each data value with the left endpoint of the=20
interval it lands in, but then centres each interval at that=20
point. To fix the problem, simply replace the definition with

   bin(val) =3D binwidth * (floor(val/binwidth) + 0.5)

and then each data point is replaced by the midpoint of the=20
interval it lands in.

The major problem is: if there are any "empty bins", this code=20
(potentially) generates an incorrect histogram. If any midpoint in=20
the range of the data is not represented in bin(column(1)), this=20
code causes the "smooth frequency" procedure to do the wrong=20
thing. Rather than produce an empty interval at that position, it=20
makes the intervals either side wider (with endpoints halfway=20
between those midpoints that are represented. Worse, the heights=20
of those wider intervals are not adjusted appropriately, so that=20
area no longer reflects frequency in those intervals.

I have attached a script and a PDF that it generates to illustrate=20
the problem with a simple example (I have v5.0 on fedora 28) which=20
does show clearly that using "floor()" with "smooth frequency" in=20
this way is problematic. Interestingly, the (experimental) "bins"=20
procedure, documented in the v5.2 manual but not available on my=20
v5.0, ostensibly does the right thing.=20

It may be that you are waiting for "bins" to be no longer=20
"experimental" before making this change, I guess that would make=20
sense. Apologies if this has already been flagged, but I couldn't=20
see it mentioned on the bug tracker page.

Cheers,

Michael

--=-=-=
Content-Type: text/plain; format=flowed; charset=WINDOWS-1252
Content-Transfer-Encoding: quoted-printable


--=20

Michael Stewart
School of Mathematics and Statistics
The University of Sydney

sydney.edu.au/science/maths/ut/people?who=3DM_Stewart

CRICOS 00026A
This email plus any attachments to it are confidential. Any=20
unauthorised
use is strictly prohibited. If you receive this email in error,=20
please
delete it and any attachments.

--=-=-=
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

------------------------------------------------------------------------------
Check out the vibrant tech community on one of the world's most
engaging tech sites, Slashdot.org! http://sdm.link/slashdot
--=-=-=
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

_______________________________________________
gnuplot-bugs mailing list
[email protected]
Membership management via: https://lists.sourceforge.net/lists/listinfo/gnuplot-bugs

--=-=-=--