How can I find the average of Y values for a given X?

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Juan Fiscina 2016-8-11

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评论： Juan Fiscina 2016-8-11

Ok, so I have 2 vectors: V for Velocity and F for Force. For each Velocity value, there are several values of Force, for which I want to find the average. It might be worth noting that the Velocity vector is not ordered or a line, but a sinusoidal. What I mean by this is that the velocity oscillates from X to -X several cycles, so there are multiple velocity=x values.

The commands that I need are quite specific: I basically need a function/loop/whatever that will get the velocity value 1, then see how many values of force apply for it, then calculate the average of those force values. Next it gets the velocity value of 2 and average all the force values for v=2, etc.

Thanks in advance and please let me know if you require further detail! :)

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Answer 1

Azzi Abdelmalek 2016-8-11

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编辑：Azzi Abdelmalek 2016-8-11

在 MATLAB Online 中打开

Look at this example

M=randi(10,100,2)  % First column is velocity varying from 1 to 10, the second is Force
[V,jj,kk]=unique(M(:,1))  % Unique values of V
mean_F=accumarray(kk,(1:numel(kk))',[],@(x) mean(M(x,2)))  % mean of F
out=[V,mean_F]

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Azzi Abdelmalek 2016-8-11

在 MATLAB Online 中打开

Look at this small example

M=[1 10;1 20;1 30;2 50;  2  70]
M =
     1    10
     1    20
     1    30
     2    50
     2    70
[V,jj,kk]=unique(M(:,1))  % Unique values of V
V =
   1
   2
jj =
   1
   4
kk =
   1
   1
   1
   2
   2
mean_F=accumarray(kk,(1:numel(kk))',[],@(x) mean(M(x,2)))  % mean of F
mean_F =
    20
    60

you need to read the documentation of accumarray

Juan Fiscina 2016-8-11

Ok I got it working, many thanks! :)

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Answer 2

Peter Perkins 2016-8-11

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在 MATLAB Online 中打开

Two other possibilities that are very simple, using Azzi's example:

1) If you have R2013b or later,

>> M = randi(10,100,2);  % First column is velocity varying from 1 to 10, the second is Force
>> t = array2table(M,'VariableNames',{'Velocity' 'Force'});
>> varfun(@mean,t,'GroupingVariable','Velocity')
ans = 
    Velocity    GroupCount    mean_Force
    ________    __________    __________
     1          11            5.5455    
     2          11            3.8182    
     3           9            4.7778    
     4           4                 4    
     5           9            4.6667    
     6          13            5.7692    
     7          12              4.25    
     8           6               6.5    
     9          14            4.5714    
    10          11            6.2727

2) If you are using R2016a or later,

>> g = findgroups(M(:,1));
>> splitapply(@mean,M(:,2),g)
ans =
       5.5455
       3.8182
       4.7778
            4
       4.6667
       5.7692
         4.25
          6.5
       4.5714
       6.2727

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Answer 3

John D'Errico 2016-8-11

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Too late for you to accept or not, but as an alternative for others who might chance upon this question, is my consolidator tool, as found on the file exchange.

http://www.mathworks.com/matlabcentral/fileexchange/8354-consolidator

It solves exactly the question that you ask, returning a single set of x values that are now all unique, with the average y at that value x. Or in your case, it will reduce the F vector, by averaging, looking for replicates at each V in the vector.

Note there is a serious issue you will need to recognize, IF your vector V is in the form of floating point numbers. So if the vector V here is composed of only nice simple integers, then the accumarray trick works well. If not, then you need some sort of a tolerance. In that case, consolidator allows you to collect those points that are near each other.

Finally, you might decide to use a binning technique. In that case, you might pick bins, such that ever point that lies in exactly one of a set of intervals. So you might use break points like this

Vbreaks = linspace(min(V),max(V),20);

then you would use a tool to determine which bin every value of V falls in. The function histc (now replaced by histcounts) does this. At then end, accumarray would again be a good tool to take the averages within each set of bins. (Be careful though, as if any bin had no points that fell into it, this scheme would yield zero for that bin as the average.)

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Juan Fiscina 2016-8-11

Thanks for the reply.

My velocity vector was indeed an array of floating points logged from the test, but I went around it by rounding the numbers [round(x)] to less decimals, hence making what you are calling bins if I am not mistaken.

So instead of having this: 11.7919 11.7859 11.7790 11.7705 11.7599 11.7464 11.7296 11.7089

I end up with: 11.8000 11.8000 11.8000 11.8000 11.8000 11.7000 11.7000 11.7000 11.7000

I need to try your approach anyway, for the result I got from the previous answers needs to be filtered:

I am not sure why the average does not look like the actual filtered data, which is the result I was expecting! :S

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