Full width at half maximum of random data in Fortran

Question

I have a set of a Gaussian randomly generated data. The way i obtain this data is of no importance, but its trough a particle code with diffusion.

I know that there are functions in python that can do this, however i cannot afford to write this data in a file at each time step, and then analyse it after because i need it for a diagnostic. Therefore i need to calculate it in the code.

My code is written in Fortran 95.

An example of the data i need to find the full width at half maximum is this (full data is down bellow)

However as you can see, it is a bit to noisy.

By hand i calculated this length to be 0.00235 (Because this is the starting data i know this length to be 0.0023548200450309495, so it is really close). However i had to estimate a maximum (33.6) with my cursor and then find the length with my cursor.

Is there a way to do it with code in Fortran? It can also be the algorithm to use if you don't know Fortran (i can translate it to Fortran by my self)

Do not hesitate to ask any question.

Edit: I forgot to mention that i already do the calculation of Sigma trough:

Sigma = Sum( (x - Av(x))**2 )/N

the thing is that this gives me an answer, but because of some physical properties, at least at the start of a simulation it does not give me the right value, it works for latter time steps but not at the start.

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Answer 1

Assuming a Gaussian distribution you can compute the FWHM using the mean value and standard deviation.

An example implementation

program main
  implicit none
  integer           :: n
  real              :: mu, sigma, FWHM
  real, allocatable :: x(:)

  ! read data from file. here we just set some values as an easy example
  x = [-2, 0, 5, -10, 3]

  ! estimator for mean value
  n  = size(x)
  mu = sum(x) / n

  ! estimator for standard deviation (biased estimator -> divide by (n-1) )
  sigma = sqrt(sum((x-mu)**2)/(n-1))

  ! full-width half maximum is simple scaling of standard deviation
  ! for Gaussian distribution
  FWHM = 2*sqrt(2*log(2.0)) * sigma
end program