| Author |
Comment/Response |
Fprum Moderator
|
 11/05/07 12:19pm
I got a lot of help from Peter Pein in understanding what the issues were in your example. It looks like a couple of things are going on.
First V6 counts into different bins than V5. Here is an example of the different behaviors:
---6.0----
In[28]:= BinCounts[{100}, {98, 102, 1}]
Out[28]= {0,0,1,0}
----5.2----
In[2]:=
<<Statistics`
In[3]:=
BinCounts[{100},{98,102,1}]
Out[3]=
{0,1,0,0}
I think that this is documenting in V6.0 as "In BinCounts[data, {{b1,
b2, ...}}], elements are counted in bin i when their values satisfy
b_i <= x < b_i+1."
... although it does not explicitly say that things are different from
V5.
Looks like this is a machine arithmetic issue in the end, I have this from
one of our developers from a discussion of whether the problem was that the trailing 1 shows up in:
In[1]:= Ceiling[98.65051300731969, .2] // InputForm
Out[1]//InputForm= 98.80000000000001
---
0.2 is not exactly representable in binary.
It has a recurring expansion:
In[1]:= RealDigits[1/5, 2]
Out[1]= {{{1, 1, 0, 0}}, -2}
What we obtain in the Ceiling computation is 494 * 0.2
Now 0.2 is rounded up from:
In[1]:= RealDigits[1/5, 2, 54]
Out[1]= {{1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,
> 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
1, 1,
> 0, 0, 1, 1, 0, 0, 1, 1}, -2}
The last 1 causes rounding up and we get:
In[1]:= FromDigits[ {{1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0}, -2}, 2]
3602879701896397
Out[1]= -----------------
18014398509481984
In[2]:= % > 1/5
Out[2]= True
so it is very slightly larger.
Here are the results of floating point numbers just above and below 0.2:
In[1]:= 494 Interval[0.2]
Out[1]= Interval[{98.8, 98.8}]
In[2]:= InputForm[%]
Out[2]//InputForm= Interval[{98.79999999999998, 98.80000000000004}]
So we can expect a number between these bounds, but not necessarily 98.8
in decimal.
Based on this, the position of the middle 1 in the BinCounts example is
an artifact of machine arithmetic and consistent with the docs, and the
user can use an exact step of 1/5 to avoid this.
---------
So, this works:
In[28]:= BinCounts[{101.13528790591918`,100,98.85051300731969`},{98.8,101,1/5}]
Out[28]=
{1,0,0,0,0,0,1,0,0,0,0,1}
Tom Zeller
URL: , |
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