HistogramFactory struggles with samples with various scales

[josephmure]

What happened?

When the first part of a sample has very low scale, and the second part a larger scale, issues happen with HistogramFactory::build.

1. When the sample size is small, build does not return.
2. When the sample size is large, it produces a std::bad_alloc error.

How to reproduce the issue?

import openturns as ot
sample = ot.Uniform(-1e-10, 1e-10).getSample(100) # use sample size 10 to get the no return problem
sample2 = ot.Uniform(-1, 1).getSample(5)
sample.add(sample2)
hf = ot.HistogramFactory()
hf.build(sample)

Version

master

Operating System

Linux

Installation media

from source

Additional Context

No response

[josephmure]

Tagging @vchabri who discovered the issue.

[jschueller]

in that case the bandwith computed with the default Freedman and Diaconis bandwith rule, and is small (~1e-10) wrt the range resulting in a huge binNumber (14482017289):

const UnsignedInteger binNumber = static_cast<UnsignedInteger>(ceil((max - min) / bandwidth + 0.5));

else the Scott rule yields something usable ~1e-1, (set useQuantile=False)

not sure what should do here to select Scott in these cases, but sounds important to get into 1.23