Re: Bug #1503114

[Daniel J S. <dan...@ie...>]

Hans-Bernhard Br=F6ker wrote:
> Daniel J Sebald wrote:
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>> 2)  BUG 1503114        FIX: 1107709 plot [-1:1] x is plotted with
>> asymmetric y-axis
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> I'm still just as opposed to this fix as I was when I first commented o=
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> the bug report.  It's an attempt at fixing symptoms, and does so in the=
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> wrong place.
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>> I picked a bug in the list and fixed it. =20
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> Not really.  You just hid it in a spot where it's harder to trigger.

I'm still debating with myself if this is the case.

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> Floating-point rounding is tricky stuff.  It's completely inevitable=20
> that sometimes, results will surprise people.  All this patch does is=20
> move the surprise from a seemingly obvious place to a less obvious one.=
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>  An axis ending at 2.0000001 has no more business being artificially cu=
t=20
> down to 2.0 than one ending at 2.001.

I think it does in some cases, and depends on the range.  I'll illustrate=
 with two ranges determined by the data input.

1) [1.9999999 : 2.0000001]

2) [-2.0 : 2.0000001]

In the first case, yes definitely, the limits have no business being arti=
ficially shrunk.

However, in the second case I'm saying that cutting the upper limit inwar=
d to 2.0 rather than rounding outward to 2.5 is not egregious because its=
 effect is beyond the resolution of the plot.  That is the key point.  Th=
ere is enough slop in gnuplot's tic marks and line placement that 1e-6 is=
 irrelevant with respect to 0.5e0.  (Just take a look at some of gnuplot'=
s outputs for all.dem.  Some times pm3d surfaces slightly overlap a line,=
 sometimes not, the thickness of a line may be several orders of magnitud=
e than what would be discarded by rounding inward, etc.)

One might claim that it is possible to zoom in on plots and hence we shou=
ld retain [1.9999999 : 2.0000001].  But I think that isn't reliable.  Som=
e examples.  If I zoom into a plot using gv, really zoom in, the thing sl=
ows way down and may become unreliable because of arithmetic issues.  We =
also had a discussion once on X11 zooming.  I thought one could zoom by c=
hanging the scaling factor in the X11 window.  This worked, but I then ag=
reed with you that it is a fairly useless thing without a fresh, nicer re=
plot with scale readjustment.

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> The current behaviour may not be free from surprises, but at least it's
> correct: an autoscaled axis always contains all its inputs.

Define correct when we are talking that scale of things.  I think that is=
 the issue here.  Do we expand the scale outward, perhaps further comprom=
ising resolution?  Or feel free to toss out something that is beyond the =
resolution of any reasonable plotting device that can be viewed by the hu=
man eye?

In some sense related, I just put a patch on S.F. to illustrate some prob=
lems with the function integration demo in bivariat.dem.  There are some =
noticeable effects overlooked there, one of them being consideration for =
sample points not being exactly zero for a test x>=3D0.

Yes, dealing with machine precision may not be a joy, but it probably sho=
uld be done.

Dan