Average value of range of vector elements

I have a huge amount of data with time stamps concerning temperature and displacement of a bridge deck.

I want to look at hourly intervals and have therefore assigned all the time stamps to their corresponding hour starting from a specific point in time, namely 1/1-2013 00:00.

To clarify:

• from 1/1-2013 00:00 to 1/1-2013 00:59 => hour number 0
• from 1/1-2013 01:00 to 1/1-2013 01:59 => hour number 1
• ...
• from 1/1-2013 07:00 to 1/1-2013 07:59 => hour number 7

This means that my data vectors now look like this:

if true  (this is the only way I could find to make the following in vector form)         
end
Time[h]        Temperature[deg C]        Displacement[cm]
0                 5.45                       0.133
0                 5.57                       0.136
0                 5.68                       0.140
1                 6.02                       0.145          
1                 6.24                       0.147
2                 6.56                       0.149
2                 6.78                       0.152
2                 6.76                       0.152
2                 6.80                       0.153
...                ....                       .....

Since I want to plot the relationship between temperature and displacement with hourly time steps, I would like to compute the mean value of every hour. This should go into a new vector containing only the hourly averaged time stamps.

My problem is that every hour has a different amount of data points, e.g. hour 0 has three, hour 1 has two and hour 2 has four. How do I go about this without making loops? I imagine that a vectorized method would save a lot of running time compared to loops.

The result I want should look something like the following:

if true  (this is the only way I could find to make the following in vector form)         
end
Time[h]        Temperature[deg C]        Displacement[cm]
0                 5.57                       0.136
1                 6.13                       0.146          
2                 6.73                       0.152
...                ....                       .....

I hope that I made the problem clear, otherwise I would be happy to elaborate.

Thanks in advance.

Tim

[Jan]

Your tables are nice. For suggesting a solution, it would be helpful, if you explain in which format your data are available. Is this a struct, cell array, 3 different vectors?

[Tim Skov Jacobsen]

Thanks! I have the data in excel, but have imported them into 3 different vectors in Matlab.

Answer 1

[Jan]

This is a perfect job for accumarray:

avgTemperature = accumarray(Time + 1, Temperature, [], @mean);

Unfortunately I have severe problems to understand the documentation of this command. Because I do not have access to Matlab currently, I can only guess, if the shown method is working.

[EDITED] Although accumarray allows a very compact solution, here a simple FOR loop:

Time1   = Time + 1;    % No zeros as indices
n       = length(Time1);
maxTime = max(Time1);
accum   = zeros(1, maxTime);
len     = zeros(1, maxTime);
for k = 1:n
  index = Time1(k);
  accum(index) = accum(index) + Temperature(k);
  len(index)   = len(index)   + 1;
end
result = accum ./ len;

(Not tested, typos might exist)

[Tim Skov Jacobsen]

I have also looked at "accumarray", but also found it hard to understand exactly what is does. I will have a look again since I now have confirmation that it is indeed relevant to this case.

[Tim Skov Jacobsen]

This kind of loop was also what I had in mind, but since I have three different displacements, three different temperatures and traffic data I thought it would be too time consuming to use for loops. I think I will try to do it though. Thanks!

[Tim Skov Jacobsen]

I managed to found a way to do it using accumarray. If anyone is interested a very similar problem is stated with examples of the solution in this link:

http://blogs.mathworks.com/loren/2008/02/20/under-appreciated-accumarray/

Thank you for your help!

[Jan]

@Tim: Please post your code here.

[Andrei Bobrov]

   z = [0                 5.45                       0.133
   0                 5.57                       0.136
   0                 5.68                       0.140
   1                 6.02                       0.145
   1                 6.24                       0.147
   2                 6.56                       0.149
   2                 6.78                       0.152
   2                 6.76                       0.152
   2                 6.80                       0.153]

   [ii jj] = ndgrid(z(:,1)+1,1:size(z,2)-1)
   z23 = z(:,2:end)
   out = [unique(z(:,1)),accumarray([ii(:),jj(:)],z23(:),[],@mean)

[Tim Skov Jacobsen]

The best and simplest way I found to compute the average of all data points within each time step is the following:

Vector description:

• d - displacement vector
• h - vector of hour numbers (see original post for clarification)

   datasum = accumarray(h,d); % sum of all data point within each time step
   indices = ones(size(h));   % indices for summing data point count
   datacount = accumarray(h,indices); % count of data points within each   time step
   mean = datasum./datacount; % average data value within each time step

The trick here is really the accumarray function, which is a kind of a conditional summation of vector components. What made me understand this function correctly was this article: http://blogs.mathworks.com/loren/2008/02/20/under-appreciated-accumarray/

Answer 2

[Image Analyst]

I remember this was answered before, maybe a year ago or so. I don't remember anything to search about it. On the other hand, this is fairly easy with the Image Processing Toolbox. The time is your "labels" and you just call regionprops() on each column to get the values of each label (time). Then sum up and divide by the number in each label. Do you have the Image Processing Toolbox?

[Tim Skov Jacobsen]

I tried to search but did not find anything that relevant. I only have a Matlab license from the university. I have never tried the Image Processing Toolbox, does it come with the standard Matlab or is it a separate program?

[Image Analyst]

Type "ver" on the command line to see what toolboxes are installed. Code using regionprops would go something like (untested):

measurements = regionprops(times, temperatures, 'Area', 'EulerNumber');
meanTempValues = [measurements.Area] ./ [measurements.EulerNumber];

The times and temperatures are assumed to already be extracted into 1D row or column vectors:

times = array2D(:,1);
temperatures = array2D(:, 2);
displacements = array2D(:, 3);

so do that first if you need to. Similarly, call regionprops() again to get the mean displacements over the hours.

measurements = regionprops(times, displacements, 'Area', 'EulerNumber');
meanDispValues = [measurements.Area] ./ [measurements.EulerNumber];

[Tim Skov Jacobsen]

Since I am not familiar with this toolbox I think I will go with the accumarray approach as described above. Thank you very much for your input though.