# Aquire random sampling of plot values

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Baily Thomas on 22 Jul 2020
Commented: Sindar on 27 Jul 2020
Hello,
I have two plots. These two plots follow the same trend but are slighly variable. The X axis denotes time for this graph. I would like to determine the minimum amount of time (number of points along the x axis) in which the %difference between the two plots is below a certain value. I would like this to be repeatable along any point along the graphs.
My thoughts are to randomly select a certain amount of points along the x axis (number of points selected determines the amount of time that is being tested (ex: 100 points = 1 second) and then check the percent difference. Then repeat that process until statistically the %difference is accturate for the plot.
Does anyone have any idea of how to randomly sample points on two graphs along the x axis, determine the percent differnce for those two points, and then average all of that together to determine the total % differnce?
I apologize if the wording is confusion and appreciate any input! thanks!

Sindar on 22 Jul 2020
Assuming your two datasets share x values and are not absurdly massive, this direct method is probably faster
% generate some sample data
x = 1:100;
y1 = rand(1,100);
y2 = rand(1,100);
% set a threshold of 5%
p_thresh = 0.05;
% calculate the percent difference between sets for each point
y_pdiff = y1./y2-1;
% calculate the cumulative mean
y_pdiff_mean = movmean(y_pdiff, [length(y_pdiff)-1 0]);
% find the first time the cumulative mean is less than your threshold
idx = find(y_pdiff_mean<p_thresh,1,'first');
% find the x-location corresponding to this point
x_thresh = x(idx);

Sindar on 22 Jul 2020
If the plots do not share x points, check out interp1
Baily Thomas on 22 Jul 2020
The two graphs at first have an offset to each other. After determining the average differnce between the two graphs I make a correction to the offset to somewhat lay the two graphs overtop one another.
Once I have the graphs atop one another, there is still error between the two. This is where I want to find what is the smallest number of X points I can take in order to have an acceptable % difference.
One way of doing this would be to just cut out a section, check the % difference, and then increase or reduce the size of that section until i get below the desired % difference threashold. Then I would have to test to make sure that the size of the section rings true no matter what section I take.
The other way I was hoping to do is take a random sampling of X points, determine the average % difference (Betwen the two graphs) at each point, and then deterine how many points do I have to sample to repeatably stay below the % difference threashold.
To awnser you questions, I have used the fillgaps function so that each graph has a corresponding y point for each x point that may be selected.
Thank you for your assistance Sindar and hope that this helps in narrowing down my matlab delima.
Sindar on 27 Jul 2020
I'm a bit confused. Why would a larger section necessarily have a lower % difference?
(I assumed you had two signals that eventually converged)