integral should take into account binwidths about fhist.jl HOT 4 CLOSED

mostly i figure if the histogram knows its widths i shouldn't have to type it

if useful you might crossreference other histograms in the julia ecosystem:
https://github.com/mitmath/18338/blob/master/JuliaNotebooks/0.0%20Histogramming.ipynb
see the word normalize used in different ways

from fhist.jl.

we model after this function:
https://root.cern.ch/doc/master/classTH1.html#aaf053a4b487c46b9e20c0bf534b34012

if option "width" is specified, the integral is the sum of the bin contents multiplied by the bin width in x.

maybe the answer is to specifically fix normalize? or we could add a ; width=false to integral() function and use that in normalize

from fhist.jl.

we actually use StatsBase under the hood haha, but yeah, HEP is weird.

There's not enough bandwidth in the community rn but one day I wish we could have a separate histogram package and StatsBase use that one, and we can sort out different "properties" of histograms by using the type system (where now there's like isdensity https://github.com/JuliaStats/StatsBase.jl/blob/39d0433f5044f8cafaa902cf31b3f83979585657/src/hist.jl#L190 field ad-hoc)

from fhist.jl.

ROOT's behavior when having variable bin width:

In [10]: ROOT.TH1D("test", "test", 3, array.array("d", [0, 1, 2, 4]))
Out[10]: <cppyy.gbl.TH1D object at 0x5de8700>

In [11]: t.Fill(0.5, 0.5)
Out[11]: 1

In [12]: t.Fill(0.5, 0.5)
Out[12]: 1

In [14]: t
Out[14]: <cppyy.gbl.TH1D object at 0x605e730>

In [15]: t.Integral()
Out[15]: 1.0

In [16]: t.Fill(2.5, 0.5)
Out[16]: 3

In [17]: t.Integral()
Out[17]: 1.5

In [18]: t.Integral("width")
Out[18]: 2.0

as for different "normalize()", see discussion: https://root-forum.cern.ch/t/different-ways-of-normalizing-histograms/15582

Method 4

In [28]: t.Scale(1. / t.Integral())

In [29]: t.GetBinContent(3)
Out[29]: 0.3333333333333333

Method 6

# re-make t
In [30]: t = ROOT.TH1D("test", "test", 3, array.array("d", [0, 1, 2, 4]))
TROOT::Append:0: RuntimeWarning: Replacing existing TH1: test (Potential memory leak).

In [31]: t.Fill(0.5, 0.5)
Out[31]: 1

In [32]: t.Fill(0.5, 0.5)
Out[32]: 1

In [33]: t.Fill(2.5, 0.5)
Out[33]: 3

In [34]: t.Scale(1. / t.Integral("width"))

In [35]: t.GetBinContent(3)
Out[35]: 0.25

In [36]: t.Integral()
Out[36]: 0.75

In [37]: t.Integral("width")
Out[37]: 1.0

from fhist.jl.