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<== Date ==> <== Thread ==>
Subject: Re: The select record MEDIAN calculation
From: Andrew Johnson <[email protected]>
To: Dennis Armstrong <[email protected]>
Cc: EPICS Tech-Talk <[email protected]>
Date: Tue, 08 Apr 2008 12:40:27 -0500
Hi Dennis,

I can explain your results; the main issue is how many inputs the record is actually using.

Dennis Armstrong wrote: 

Quote "In probability theory and statistics, a median is described as
the number separating the higher half of a sample, a population, or a
probability distribution, from the lower half. The median of a finite
list of numbers can be found by arranging all the observations from
lowest value to highest value and picking the middle one. If there is an
even number of observations, the median is not unique, so one often
takes the mean of the two middle values." unquote

When I use an even number of input values the output is wrong as it
fails to produce the average value of the two middle input values.

Please note the last sentence of your Wikipedia definition includes the words "one often" â that doesn't mean one has to. I didn't write it, but I think the select record's decision of what to do when there are an even number of samples is reasonable. IMHO the median of a set should always be a member of that set, whereas if you take the mean of the middle two items that's only the case if the two are the same. We can add another select method to average the middle two if someone needs it though.

When I use an odd number of input values this is sometimes wrong as it
fails to sometimes select the middle input values.

I think this may be because the record uses NaN field values to exclude inputs from the calculation, but it only ever sets the fields to NaN when the record is initialized. If your 12th field contained anything other than a NaN when you were only setting 11 input values, the record was still using the 12th.

So is anybody using the select record in this mode? and what results do
you get?

Here's what I get when I test the latest CVS version (the median calculation has not changed since R3.14.9 although other parts that don't affect these results have changed slightly). Each column below is a new experiment with one additional input â the NaN values are not used in the median calculation. SELN tells you which item it's selected as the median value after sorting, and VAL is that median value.

sel.A     nan  1    1    1    1    1    1    1    1    1    1    1    1
sel.B     nan  nan  2    2    2    2    2    2    2    2    2    2    2
sel.C     nan  nan  nan  3    3    3    3    3    3    3    3    3    3
sel.D     nan  nan  nan  nan  4    4    4    4    4    4    4    4    4
sel.E     nan  nan  nan  nan  nan  5    5    5    5    5    5    5    5
sel.F     nan  nan  nan  nan  nan  nan  6    6    6    6    6    6    6
sel.G     nan  nan  nan  nan  nan  nan  nan  7    7    7    7    7    7
sel.H     nan  nan  nan  nan  nan  nan  nan  nan  8    8    8    8    8
sel.I     nan  nan  nan  nan  nan  nan  nan  nan  nan  9    9    9    9
sel.J     nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  10   10   10
sel.K     nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  11   11
sel.L     nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  12
sel.SELN  0    0    1    1    2    2    3    3    4    4    5    5    6
sel.VAL   0    1    2    2    3    3    4    4    5    5    6    6    7

Notes:
* When there are an even number of inputs it always picks the higher of the middle two values.
* The first column's result is wrong, when there are no inputs at all the result should be a NaN. I'll fix that for R3.14.10.
* SELN would probably be more useful if it gave you the number of inputs it's using rather than half that number, truncated. This behaviour was new in R3.14.9, so unless anyone objects I'll probably change it for R3.14.10.

HTH,

- Andrew
--
When a distinguished but elderly scientist states that something is
possible, he is almost certainly right.  When he states that something
is impossible, he is very probably wrong.  -- Arthur C. Clarke
References:
The select record MEDIAN calculation Dennis Armstrong
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