Weighted average of irregular intervals

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Melissa
Melissa 2015-2-4
评论： Melissa 2015-2-10
Hello,
I have a 555x5 matrix
C = [Lat Lon Bm Lower Upper]
Bm represents biomass data. Lower and Upper represent the lower and upper boundaries of the depths (cm) from which the data was procured. The depths in C are irregularly spaced. I want to split up my data into two different weighted depths: one at 5cm, and one at 25 cm. For the 5cm, I want to contain all weighted datapoints in C between 0 and 15cm. For the 25cm, I want to contain all weighted datapoints in C between 15cm and 30cm
I'm looking to calculate the coefficient for each datapoint that correlates to the weight of the datapoint within depth intervals.
With the coefficient for each datapoint, I can calculate the weight of the measurement within the two separate intervals I need
EX:
-77.63 162.87 0.66 0 10 -> COEFF = 1.0 -> weighted bm = 0.66
-37.78 175.32 61.967 0 20 -> COEFF = 0.75 -> weighted bm = 46.47
The first line's coefficient is 1 because 100% of the measurement is contained within the interval of 0 and 15cm The second line's coefficient is 0.75 because only 75% of the measurement is contained within the interval of 0 and 15cm
This example only shows what I would like to have for my 5cm comparison, but I would also like to do the same for the 30cm comparison with the intervals between 15 and 30cm.
After I have those coefficients, I would like to get the weighted average by multiplying the coefficient with the biomass measurement, and then create two new matrixes that contains latitude, longitude, and biomass (555x3), one for the 5cm depth, and one for the 25cm depth.
But for the most part, I am having trouble trying to come up with a loop or code that will accomplish the coefficient calculation. The rest is pretty straightforward I feel.
I have attached the data so you can have a better idea of what I'm working with I have no idea how I should approach this, so any help would be greatly appreciated!
Thank you,
Melissa
  2 个评论
Geoff Hayes
Geoff Hayes 2015-2-4
Melissa - you didn't attach your data. Please make sure that you press the Attach File button once you have chosen the file.

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采纳的回答

Guillaume
Guillaume 2015-2-4
That is an interesting question. I will have to think of a way to make a cody problem out of it.
Here is how I would do it:
ranges = [0 15; 15 30; 30 45] %example data, col 1 is lower bound, col2 is upper bound
depths = [0 10; 0 15; 0 20; 5 10; 5 20; 20 30; 25 35; 5 40] %example data, lower/upper bounds
bm = [1 2 4 8 16 32 64 128]'; %example data
[dlow, rlow] = ndgrid(depths(:, 1), ranges(:, 1));
[dup, rup] = ndgrid(depths(:, 2), ranges(:, 2));
%we now have 2d matrices, where columns are ranges, rows are depths
inrange = (dlow < rup) & (dup > rlow);
coeffs = ((dup-dlow) - (dlow < rlow).*(rlow-dlow) - (dup>rup).*(dup-rup)) ./ (dup-dlow);
coeffs = coeffs .* inrange %calc when not in range is not valid
weightedbm = bsxfun(@times, bm, coeffs)

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