How to generate vector with non-linear spacing?
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Ryan
on 14 Aug 2024 at 12:01
Commented: Ryan
on 14 Aug 2024 at 12:59
Hello,
I am attempting to generate an array with non-linear spacing between the elements but struggling to figure out a way to impliment this. I need an array x of points spaced from a real, negative value a to a real, positive value b. Ideally the spacing should follow a Gaussian distribution such that many points are clustered about x=0 in the vicinity of some finite width d. Conversely the spacing should be large at the boundaries. More generally it doesn't have to be Gaussian but some guidance on a scheme where I can specify a length d<<|b-a| across which many points should be distributed would be really appreciated.
I tried to work out an algorithm of sorts from pen and paper but it didn't really work and resulted in something that did not appear to be immediately solveable.
Thanks
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Accepted Answer
John D'Errico
on 14 Aug 2024 at 12:50
Edited: John D'Errico
on 14 Aug 2024 at 12:52
It sounds like you want a deterministic, non-random set of points. You can use the inverse gaiussian CDF to do what you want.
a = -2.5;
b = 3;
N = 40;
x = norminv(linspace(normcdf(a),normcdf(b),N));
xline(x,'r')
So most dense at zero, and a density that drops off away from there. I chose limits that are not centered around zero, but had they been centered, the set would be perfectly symmetric.
Of course, you can adjust the speed of fall off, by use of a different variance on the implicit Gaussian.
More Answers (2)
Aquatris
on 14 Aug 2024 at 12:40
A = 1;
B = 5;
std = .9; % need to play with this to get desired shape within desired range,
% if too high, it does not become a normal distribution
% if too low, it does not cover the whole A-B range
mean = 3;
step1Result = mean + std * randn(1e3,1); % create random data with mean and std
step2Result = min(max(step1Result,A),B); % make sure they end up in A-B range
hist(step2Result)
ylabel('# of occurence')
xlabel('Data Value')
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