Gaussian fit for Python

Question

I m trying to fit a Gaussian for my data  which is already a rough gaussian   I ve already taken the advice of those here and tried curve fit and leastsq but I think that I m missing something more fundamental  in that I have no idea how to use the command    Here s a look at the script I have so far   import pylab as plb import matplotlib pyplot as plt    Read in data -- first 2 rows are header in this example   data   plb loadtxt  part 2 csv   skiprows 2  delimiter       x   data   2  y   data   3  mean   sum x y  sigma   sum y  x - mean   2   def gauss function x  a  x0  sigma       return a np exp - x-x0   2  2 sigma  2   popt  pcov   curve fit gauss function  x  y  p0    1  mean  sigma   plt plot x  gauss function x   popt   label  fit      plot data  plt plot x  y  b      Add some axis labels  plt legend   plt title  Fig  3 - Fit for Time Constant   plt xlabel  Time  s    plt ylabel  Voltage  V    plt show     What I get from this is a gaussian-ish shape which is my original data  and a straight horizontal line     Also  I d like to plot my graph using points  instead of having them connected   Any input is appreciated

User · Answer

After losing hours trying to find my error, the problem is your formula:

sigma = sum(y*(x-mean)**2)/n

This previous formula is wrong, the correct formula is the square root of this!;

sqrt(sum(y*(x-mean)**2)/n)

Hope this helps

User · Answer

Here is corrected code     import pylab as plb import matplotlib pyplot as plt from scipy optimize import curve fit from scipy import asarray as ar exp  x   ar range 10   y   ar  0 1 2 3 4 5 4 3 2 1    n   len x                            the number of data mean   sum x y  n                    note this correction sigma   sum y  x-mean   2  n         note this correction  def gaus x a x0 sigma       return a exp - x-x0   2  2 sigma  2    popt pcov   curve fit gaus x y p0  1 mean sigma    plt plot x y  b    label  data   plt plot x gaus x  popt   ro   label  fit   plt legend   plt title  Fig  3 - Fit for Time Constant   plt xlabel  Time  s    plt ylabel  Voltage  V    plt show     result

User · Answer

There is another way of performing the fit  which is by using the  lmfit  package   It basically uses the cuve fit but is much better in fitting and offers complex fitting as well  Detailed step by step instructions are given in the below link  http   cars9 uchicago edu software python lmfit model html model best fit

User · Answer

Explanation  You need good starting values such that the curve fit function converges at  good  values  I can not really say why your fit did not converge  even though the definition of your mean is strange - check below  but I will give you a strategy that works for non-normalized Gaussian-functions like your one   Example  The estimated parameters should be close to the final values  use the weighted arithmetic mean - divide by the sum of all values    import matplotlib pyplot as plt from scipy optimize import curve fit import numpy as np  x   np arange 10  y   np array  0  1  2  3  4  5  4  3  2  1      weighted arithmetic mean  corrected - check the section below  mean   sum x   y    sum y  sigma   np sqrt sum y    x - mean   2    sum y    def Gauss x  a  x0  sigma       return a   np exp - x - x0   2    2   sigma  2    popt pcov   curve fit Gauss  x  y  p0  max y   mean  sigma    plt plot x  y   b     label  data   plt plot x  Gauss x   popt    r-   label  fit   plt legend   plt title  Fig  3 - Fit for Time Constant   plt xlabel  Time  s    plt ylabel  Voltage  V    plt show     I personally prefer using numpy   Comment on the definition of the mean  including Developer s answer   Since the reviewers did not like my edit on  Developer s code  I will explain for what case I would suggest an improved code  The mean of developer does not correspond to one of the normal definitions of the mean    Your definition returns    gt  gt  gt  sum x   y  125   Developer s definition returns    gt  gt  gt  sum x   y    len x  12 5  for Python 3 x   The weighted arithmetic mean    gt  gt  gt  sum x   y    sum y  5 0   Similarly you can compare the definitions of standard deviation  sigma   Compare with the figure of the resulting fit     Comment for Python 2 x users  In Python 2 x you should additionally use the new division to not run into weird results or convert the the numbers before the division explicitly   from   future   import division   or e g   sum x   y    1    sum y

User · Answer

You get a horizontal straight line because it did not converge   Better convergence is attained if the first parameter of the fitting  p0  is put as max y   5 in the example  instead of 1

User · Answer

Actually  you do not need to do a first guess  Simply doing import matplotlib pyplot as plt   from scipy optimize import curve fit from scipy import asarray as ar exp  x   ar range 10   y   ar  0 1 2 3 4 5 4 3 2 1    n   len x                            the number of data mean   sum x y  n                    note this correction sigma   sum y  x-mean   2  n         note this correction  def gaus x a x0 sigma       return a exp - x-x0   2  2 sigma  2    popt pcov   curve fit gaus x y   popt pcov   curve fit gaus x y p0  1 mean sigma    plt plot x y  b    label  data   plt plot x gaus x  popt   ro   label  fit   plt legend   plt title  Fig  3 - Fit for Time Constant   plt xlabel  Time  s    plt ylabel  Voltage  V    plt show    works fine  This is simpler because making a guess is not trivial  I had more complex data and did not manage to do a proper first guess  but simply removing the first guess worked fine    P S   use numpy exp   better  says a warning of scipy

User · Answer

sigma   sum y  x - mean   2    should be   sigma   np sqrt sum y  x - mean   2

[python] Gaussian fit for Python

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