title: Take errors on data into account when using lmfit
body: <p>I am trying to fit a curve to some data (the model would be 3 Gaussians plus background). The data is at the bottom of this post (not sure how to attach it), and the columns are (x, y, err_y), with err_y being the square root of y. Here is my code:</p>
  
  <pre><code>import numpy as np
  from matplotlib import pyplot as plt
  from lmfit.models import GaussianModel, LinearModel
  
  data = np.loadtxt("data.txt")
  x = data[:,0]
  y = data[:,1]
  err = data[:,2]
  
  background = LinearModel(prefix='line1_')
  pars = background.guess(y,x=x)
  
  peak1 = GaussianModel(prefix='g1_')
  pars.update(peak1.make_params())
  
  pars['g1_center'].set(9200, min=9000, max=10000)
  pars['g1_sigma'].set(300, min=100, max=700)
  
  peak2 = GaussianModel(prefix='g2_')
  pars.update(peak2.make_params())
  
  pars['g2_center'].set(10500, min=10000, max=11000)
  pars['g2_sigma'].set(300, min=100, max=700)
  
  peak3 = GaussianModel(prefix='g3_')
  pars.update(peak3.make_params())
  
  pars['g3_center'].set(13000, min=12000, max=14000)
  pars['g3_sigma'].set(300, min=100, max=700)
  
  model =  peak1 + peak2 + peak3 + background
  weight = 1/err**2/np.sum(1/err**2)
  
  out = model.fit(y, pars, x=x)#, weights = weight)
  
  print(out.fit_report(min_correl=0.1))
  
  plt.errorbar(x,y,err, fmt="b.")
  plt.plot(x, out.best_fit, 'r-')
  plt.show()
  </code></pre>
  
  <p>If for the fit I use this: <code>out = model.fit(y, pars, x=x)</code>, so without using the errors on the y, I get these values for the parameters (I post just mu and sigma here):</p>
  
  <pre><code>mu_1 =  9359.791209085675  +/-  5.509374978209427
  sigma_1 =  348.86904194695535  +/-  6.18259118657156
  mu_2 =  10522.11131671362  +/-  3.288369260611981
  sigma_2 =  243.53890651538205  +/-  3.43678656935972
  mu_3 =  13098.71965433265  +/-  4.737992827401577
  sigma_3 =  324.0256260123612  +/-  5.054936854719746
  </code></pre>
  
  <p>and this is the fit itself:</p>
  
  <p><a href="https://i.stack.imgur.com/vFaW7.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/vFaW7.png" alt="enter image description here"></a></p>
  
  <p>If I want to take into account the errors: <code>out = model.fit(y, pars, x=x, weights = weight)</code> (the weight are the inverse of the squares of the errors, as the formula for the least-square fit is sum{1/sigma^2*(y_data-y_pred)^2}, right?) I get these numbers:</p>
  
  <pre><code>mu_1 =  9979.839872555114  +/-  12.208145818989209
  sigma_1 =  296.96756984463025  +/-  30.943773101487675
  mu_2 =  10000.004017862604  +/-  14.082237906871443
  sigma_2 =  424.30653650290424  +/-  22.751836748822086
  mu_3 =  13103.00302126283  +/-  10.795125319448884
  sigma_3 =  328.0535307828716  +/-  8.157121458823843
  </code></pre>
  
  <p>and this fit:</p>
  
  <p><a href="https://i.stack.imgur.com/Ixt2u.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Ixt2u.png" alt="enter image description here"></a></p>
  
  <p>Not only the fit looks bad, but the printed parameters are not even what the figure shows (the center of the first peak is for sure smaller than 9980). Can someone tell me what is going on? Am I using the weights parameter the way it is supposed to be used? Why does the fit looks so bad now? Why are the printed parameters wrong? And how can I fix it? Thank you!</p>
  
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