Anomalous histogram for small argument

Running the following code from the command line with c = 1e-15 or greater leads to a normal histogram

c = 1e-15; figure; histogram(c * rand(100,1))

Running the following code with c = 1e-16 or less leads to an incorrect histogram

c = 1e-16; figure; histogram(c * rand(100,1))

The problem appears also in apps when the histogram function is invoked.

Is this a bug?

Gordon

Answer 1

[Bruno Luong]

Yes it is a BUG. I chase back and in the file

C:\Program Files\MATLAB\R2019a\toolbox\matlab\datafun\+matlab\+internal\+math\binpicker.m

line #20 (R2019a)

there is a test

if xrange > max(sqrt(eps(xscale)), realmin(class(xscale)))

To me the correct test should be (without sqrt)

    if xrange > max(eps(xscale), realmin(class(xscale)))

Now if I change this line and rerun the code

        c = 1e-16; figure; histogram(c * rand(100,1))

it produces correct plot

More seriously, the function binpicker is called by HISTCOUNT. So HISTCOUNT is also buggy. Not only plotting but calculation might be wrong.

[Gordon Edwards]

Thanks for your reply.and I believe that you have spotted the error in function binpicker.Since eps(x) ~ 1e-16*x, and in my case xscale and xrange are nearly equal, the condition that

xrange > sqrt(eps(xscale))

leads to xrange >~ 1e-16 which is what I find.

Answer 2

[Jackson Burns]

Here's a similar question asked a few years ago which was never really solved either. This comment may be your best approach, but I would reccomend just bringing the values to unity with something like this:

c = 1E-16;
figure
mydata = c * rand(100,1);
histogram(mydata./max(mydata))

You could then modify the xticklabels to match whatever the original values were.