Figuring out the most fitting prefix for a vector dataset

Hello fellow Matlab users,

I'd like to ask for your advice concerning a numerical topic. So I mainly use Matlab for simulation purposes (electrical circuits). My simulations return vectors containing state variables and power / energy quantities. I'm trying to fully automate a report generation with Matlab code but I'm facing a small problem. I'd like to determine the best prefix for a data set. So for example I get a vector with 1000 values. My initial idea was to get the exponents through a mathematical trick floor(10log10(vect)) and then calculate the mean of the vector containing the exponents, which would give me the mean exponent. From the exponent I can determine the nearest prefix (milli, micro...) . My problem is that some simulations return values with an accuracy of 10e-80 which totally falsifies the mean. So do you guys have any idea on how to basically get the mean exponent of a vector dataset ?

I appreciate all your thoughts and answers

[Adam Danz]

What about mode() instead of mean()? Median is better than mean, too.

[Bakr Al Beattie]

Yes I tried that we well. But for example when a quantity has the value 10-6 for the first 5 seconds and is then zero for the last 10 seconds I'd still want to get the exponent -6.

[Ameer Hamza]

What about ignoring the zeros and use the median value as suggested by Adam

median(nonzeros(x))

[Bakr Al Beattie]

My values are near zero not exactly zero. I'd probably have to filter out numbers under a certain limit e.g. anything smaller than 1e-24. Because I get values like 10e-80 instead of zeros

[Adam Danz]

So, try it out, then.

median(x(abs(x)>1e20)) % play around with the threshold value.

If that doesn't work, plot the vector of values and show us the results. Something like this would be useful

figure()
subplot(2,1,1)
plot(y,'o-')
subplot(2,1,2)
histogram(y)

[Bakr Al Beattie]

Sorry for the late replay but I have been a but busy this past week. So I tried your suggestions and still get the same problem. E.g.

So this is a histogram for one dataset. The corresponding plots:

Specifically, the histogram corresponds to the orange graph in the subplot(3,1,1). But the same problem is still existent in all plots. As can be seen, there is a long period where the data can be zero. Even when I filter out every exponent above abs(10^24), my prefix is still falsified.

Edit: here is the code I use:

function Exp = getExponent(Var)
   vecWithExp  = abs(floor(log10(abs(Var))));
   vecWithExp  = vecWithExp(~isinf(vecWithExp));
   vecWithExp  = vecWithExp(abs(vecWithExp) < 24);
   meanExp     = median(vecWithExp);
   vecWithSign = floor(log10(Var));
   sign        = round(mean(vecWithSign(~isinf(vecWithSign))));
     if isempty(meanExp)
      Exp = 0;
   else
      Exp = sgn(sign)*round(meanExp);
     end
end

Answer 1

[Adam Danz]

There are no axis labels on the histogram so I'm not sure what it represents. If it represents a distribution of y-values for the orange line in the first subplot, I'd expect a giant bar at x=0 but I don't see that.

I don't undersant what the problem is with taking the median of values greater than some very small number.

m = median(vector(abs(vector)>0.001));

You can play around with the threshold value. If you zoom into the axes using ylim([-.001,.001]) you can see whether all of the undesired data fall into those limits.

[Bakr Al Beattie]

Sorry about the labels. So if you look at my code, you can see that I calculate the exponents and save them in a vector (vecWithExp). The histogram represents the distrubution of the exponents histogram(vecWithExp). The results were obtained using median(vecWithExp(abs(vecWithExp)<24)), which basically filters out all exponents that may falsify the outcome. Please note that I am trying to find a method that works in general cases. In this case my numbers are small. In other simulations these numbers might be large depending on the quantity that I am observing. Additionally, I want to avoid manipulating the threshold everytime I start a simulation and integrate the prefix setting function as a part of the framework, so that it becomes fully automatic. Is there maybe an alternative method? In my histogram, large numbers (6,7,8...) are probably the numbers nearing zero.